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The use of remote sensing to characterize forest structure and improve the modeling of snow processes… Varhola, Andrés 2013

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The use of remote sensing to characterize forest structure and  improve the modeling of snow processes in extensively disturbed watersheds  by  Andr?s Varhola  For. Eng., Universidad Austral de Chile, 2001     A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF  DOCTOR OF PHILOSOPHY   in   The Faculty of Graduate and Postdoctoral Studies  (Forestry)       THE UNIVERSITY OF BRITISH COLUMBIA  (Vancouver)     August 2013    ? Andr?s Varhola, 2013 Abstract   The lodgepole pine (Pinus contorta) forests of British Columbia have been recently af-fected by mountain pine beetle (MPB) (Dendroctonus ponderosae), constituting one of the most destructive insect outbreaks in North America.  In such a snow-dominated envi-ronment, a receding forest cover is associated with increases in snow accumulation dur-ing winter, enhancements of snowmelt rates and suppression of spring transpiration.  These changes can elevate flooding risk and thus threaten society.  However, the un-precedented extent of the disturbance and particular nature of the beetles? severe but gradual effect on the forests? integrity have challenged scientists aiming to quantify the real ecological impacts.  Even though hydrologic models remain as the only tool cur-rently available to evaluate the effects of MPB on hydrologic dynamics, they are im-paired in their present form for relying on coarse and oversimplified characterizations of forest structure.  Remote sensing technologies such as Airborne Laser Scanning (ALS), which provides detailed three-dimensional representations of canopy structure, offer a remarkable alternative to fill this knowledge gap.  The main objective of this thesis is to determine how hydrologic modeling can be improved by remote sensing through a better characterization of forest structure.  Given the variety and complexity of hydrologic mod-els, the same research question is applied independently to the simplest forms of plot-level univariate empirical models and complex physically-based simulators operating at the watershed level.  It was found that remotely-sensed forest metrics are better predictors of snow accumulation and ablation at the plot level than traditional ground-based vari-ables, and that the accurate estimation of maximum snow accumulation and snow abla-ii  tion with ultrasonic range devices significantly increases the quality of simple empirical models.  It was also shown that a novel method, which minimizes the geometrical differ-ences between ALS and traditional ground instruments? data, was fundamental to obtain accurate plot-level estimates of forest structure metrics identified as primary drivers of snow processes.  Wall-to-wall watershed-level coverage of hydrologically-relevant forest variables was successfully achieved by integrating ALS and Landsat metrics.  The meth-ods developed will result in better inputs for hydrologic models with the potential to im-prove the quality of snow process and streamflow predictions.    iii  Preface  This research was originally proposed by Markus Weiler and Nicholas Coops, and fully broadened and executed by Andr?s Varhola (including field work, data analysis, manu-script writing, artwork preparation, paper submission and discussion with academic refe-rees).  This thesis consists of six scientific publications where Andr?s Varhola is the lead author; co-authors and peer reviewers provided methodological guidance, suggestions and editorial comments.  These publications and their corresponding sections are:  Varhola A., Coops N.C., Weiler M., Moore R.D.  2010.  Forest canopy effects on snow accumulation and ablation: An integrative review of empirical results. Journal of Hydrology 392: 219?233 (Section 1.2; Section 3.2).  Varhola A., Coops N.C., Bater C.W., Teti P., Boon S., Weiler M.  2010.  The influence of ground- and lidar-derived forest structure metrics on snow accumulation and ab-lation in disturbed forests.  Canadian Journal of Forest Research 40(4): 812?821 (Section 3.3).  Varhola A., Wawerla J., Weiler M., Coops N.C., Bewley D., Alila Y.  2010.  A new low-cost, stand-alone sensor system for snow monitoring.  Journal of Atmospheric and Oceanic Technology 27(12): 1973?1978 (Section 3.4).  Varhola A., Frazer G.W., Teti P., Coops N.C.  2012.  Estimation of forest structure met-rics relevant to hydrologic modelling using coordinate transformation of airborne laser scanning data.  Hydrology and Earth System Sciences 16: 3749?3766 (Section 4.3)  Varhola A., Coops N.C.  2013.  Estimation of watershed-level distributed forest structure metrics relevant to hydrologic modeling using LiDAR and Landsat.  Journal of Hy-drology 487: 70?86 (Section 4.4)  Varhola A., Coops N.C., Alila Y., Weiler M.  2013.  Exploration of remotely-sensed for-est structure and ultrasonic range sensor metrics to improve empirical snow models. Hydrological Processes, DOI: 10.1002/hyp.9952 (Section 3.5).  iv  Table of contents  Abstract .............................................................................................................................. ii?Preface ............................................................................................................................... iv?Table of contents ............................................................................................................... v?List of tables .................................................................................................................... viii?List of figures .................................................................................................................... ix?Glossary of acronyms ..................................................................................................... xii?Acknowledgements ........................................................................................................ xiii?Dedication ....................................................................................................................... xvi?1? Introduction ................................................................................................................ 1?1.1? General background, objectives and chapter overview ........................................ 1?1.2? The complex processes and drivers of snow accumulation and ablation ........... 10?1.2.1? Snowfall magnitude and inter-annual variations ............................................................... 11?1.2.2? Elevation ........................................................................................................................... 13?1.2.3? Aspect ................................................................................................................................ 15?1.2.4? Slope .................................................................................................................................. 17?1.2.5? Clearcut size ...................................................................................................................... 18?1.2.6? Wind .................................................................................................................................. 20?1.2.7? Specific weather conditions ............................................................................................... 21?1.2.8? Canopy geometry and tree spatial distribution .................................................................. 22?1.2.9? Measurement errors ........................................................................................................... 24?1.3? Mountain pine beetle and its effects on water resources .................................... 27?2? Study area and available data ................................................................................. 30?2.1? Study area ........................................................................................................... 30?2.2? Airborne laser scanning and high-resolution aerial photography ..................... 32?2.3? Landsat ............................................................................................................... 33?2.4? Hemispherical photography ............................................................................... 33?2.5? Weather stations ................................................................................................. 34?v  2.6? Ultrasonic snow depth sensors ........................................................................... 34?2.7? Ground plot overview: forest inventories and snow surveys .............................. 35?3? Empirical snow-vegetation models ......................................................................... 37?3.1? Introduction and chapter overview ..................................................................... 37?3.2? Meta-analysis of historical data to derive a simple empirical snow model ....... 40?3.2.1? Introduction ....................................................................................................................... 40?3.2.2? Empirical data review and compilation ............................................................................. 40?3.2.3? Data standardizing ............................................................................................................. 43?3.2.4? Statistical analysis ............................................................................................................. 44?3.2.5? Results ............................................................................................................................... 47?3.2.6? Discussion ......................................................................................................................... 55?3.2.7? Conclusions ....................................................................................................................... 57?3.3? The influence of ground- and LiDAR-derived forest structure metrics on snow accumulation and ablation in disturbed forests ................................................. 59?3.3.1? Introduction ....................................................................................................................... 59?3.3.2? Methods ............................................................................................................................. 60?3.3.3? Results ............................................................................................................................... 65?3.3.4? Discussion ......................................................................................................................... 72?3.3.5? Conclusions ....................................................................................................................... 76?3.4? Validation of prototype ultrasonic snow depth sensors for snow monitoring .... 77?3.4.1? Introduction ....................................................................................................................... 77?3.4.2? Sensor design and specifications ....................................................................................... 79?3.4.3? Field testing of LOCUS-2 ................................................................................................. 80?3.4.4? Results ............................................................................................................................... 83?3.4.5? Examples and applications ................................................................................................ 85?3.4.6? Discussion and conclusions ............................................................................................... 87?3.5? Exploration of remotely-sensed forest structure and ultrasonic snow depth sensor metrics to improve empirical snow models ............................................. 89?3.5.1? Introduction ....................................................................................................................... 89?3.5.2? Methods ............................................................................................................................. 90?3.5.3? Results ............................................................................................................................... 98?3.5.4? Discussion ....................................................................................................................... 105?3.5.5? Conclusions ..................................................................................................................... 115?4? Physically-based hydrologic models ..................................................................... 117?4.1? Introduction and chapter overview ................................................................... 117?4.2? Overview of the forest structure metrics used in physically-based hydrologic models ............................................................................................................... 122?vi  4.2.1? Leaf area index (LAI) ...................................................................................................... 122?4.2.2? Sky-view factor (SVF) ..................................................................................................... 125?4.2.3? Forest cover (FC) ............................................................................................................ 126?4.2.4? Forest height (H) ............................................................................................................. 127?4.3? Estimation of forest structure metrics relevant to hydrologic modeling using coordinate transformation of airborne laser scanning data ............................ 127?4.3.1? Introduction ..................................................................................................................... 127?4.3.2? Methods ........................................................................................................................... 131?4.3.3? Results ............................................................................................................................. 146?4.3.4? Discussion ....................................................................................................................... 154?4.3.5? Conclusions ..................................................................................................................... 163?4.4? Estimation of watershed-level distributed forest structure metrics relevant to hydrologic modeling using Landsat and LiDAR .............................................. 165?4.4.1? Introduction ..................................................................................................................... 165?4.4.2? Methods ........................................................................................................................... 167?4.4.3? Results ............................................................................................................................. 179?4.4.4? Discussion ....................................................................................................................... 194?4.4.5? Conclusions ..................................................................................................................... 200?5? General conclusions ............................................................................................... 202?Bibliography .................................................................................................................. 212?   vii  List of tables  Table 3.2.1.  List of studies used for empirical data relating forest cover to snow accumulation and melting. ....................................................................................................................................................................... 42?Table 3.2.2.  Description of variables used in modeling. .............................................................................. 46?Table 3.2.3.  Correlation coefficients (r) between independent variables and snow accumulation and ablation. ......................................................................................................................................................... 48?Table 3.2.4.  Results of simple linear regression. ......................................................................................... 51?Table 3.3.1.  General plot information. ......................................................................................................... 61?Table 3.3.2.  List of variables subject to correlation analysis with snow accumulation and ablation. .......... 64?Table 3.3.3.  Ground-based plot information (from data collected during summer 2007). ........................... 66?Table 3.3.4.  Snow survey results in spring 2008. ........................................................................................ 67?Table 3.3.5.  LiDAR-derived forest structure metrics. .................................................................................. 70?Table 3.3.6.  List of forest structure variables with significant (p < 0.05) correlations with absolute peak SWE and maximum ablation rate. .................................................................................................................. 71?Table 3.5.1.  Number of ground plots according to stand type and elevation above sea level. ..................... 91?Table 3.5.2.  Number of ground plots according to available forest and snow data sources. ....................... 91?Table 3.5.3.  Variable data sources, symbols and description. ...................................................................... 96?Table 4.3.1.  Stand locations and physical characteristics as of 2008. ........................................................ 133?Table 4.3.2.  ALS simple metric summary for each major plot. ................................................................. 133?Table 4.3.3.  Hemispherical photo parameter calibration. .......................................................................... 140?Table 4.3.4.  Variable acronyms and description. ....................................................................................... 142?Table 4.3.5.  Correlation matrix showing the coefficient of correlation (r) between variables used in multiple regression (gap fraction only, for simplicity); non-significant (p > 0.05) values shown in italic grey. ............................................................................................................................................................. 149?Table 4.3.6.  Multiple linear regression results (refer to Table 4.3.4 for RMSE and RMSES units). .......... 153?Table 4.4.1.  Landsat pixel distribution according to stand height and age (from VRI data)...................... 169?Table 4.4.2.  Independent ground plots for model validation. .................................................................... 170?Table 4.4.3.  Variable symbols and description. ......................................................................................... 173?Table 4.4.4.  Correlation matrix of ALS metrics and Landsat indices a b .................................................... 180?Table 4.4.5.  Modeling results (operational models in bold). ..................................................................... 183?Table 4.4.6.  Observed and predicted variable ranges in modeling dataset pixels (as predicted by operational models, Table 4.4.5). ................................................................................................................ 184?Table 4.4.7.  Ranges of predicted variables and percentage of pixels with values valid for forested environments according to land use at Baker Creek. ................................................................................... 185?Table 4.4.8.  Percentage of forested pixels classified as non-forest (error type I) and non-forested pixels classified as forests (error type II) as determined by ranges valid for forested vegetation obtained from operational models applied to all pixels in Baker Creek, regardless of land use (Table 4.4.7). .................. 185?Table 4.4.9.  Prediction errors and r2 for ground validation plots. .............................................................. 193?viii  List of figures  Figure 1.1.1.  Interconnections between data sources and thesis chapters and sections (shown in blue) (see glossary of acronyms for definitions). ........................................................................................................... 10?Figure 1.2.1.  Relationship between storm size and the ratio of fresh snow accumulated under the forest and at a nearby open site (adapted from McNay et al., 1988) ....................................................................... 13?Figure 1.2.2.  Snow depth as a function of elevation in Little Slocan Valley, British Columbia (adapted from D?Eon, 2004). ....................................................................................................................................... 14?Figure 1.2.3.  Effect of aspect on peak SWE and melting in coniferous forests with 35, 65 and 90% of forest cover in Central Sierra Snow laboratory, California (adapted from Anderson et al., 1958). .............. 16?Figure 1.2.4.  Effect of aspect on snow depth according to elevation ranges in Little Slocan Valley, British Columbia (adapted from D?Eon, 2004). ........................................................................................................ 17?Figure 1.2.5.  Effect of slope (%) on peak SWE and melting in coniferous forests with 35, 65 and 90% of forest cover (adapted from Anderson et al., 1958). ....................................................................................... 18?Figure 1.2.6.  Influence of clearcut size (in number of tree heights of adjacent forests, H) on snow accumulation in James River, Alberta (adapted from Golding & Swanson, 1986). ...................................... 19?Figure 2.1.1.  Study area within British Columbia; black transects indicate ALS data collection. .............. 30?Figure 2.1.2.  Mean monthly temperature and precipitation data for the Quesnel station, representative of the study area (ID 1096630, elevation 545 m) (adapted from Environment Canada, 2013). ........................ 31?Figure 3.2.1.  Distribution of relevant studies according to location (left) and decade (right).  BC = British Columbia (Canada); MT = Montana (USA); CA = California (USA); CO = Colorado (USA); other Canadian provinces include Saskatchewan, Ontario and Yukon, while other USA states include Wyoming, Oregon, Minnesota and Vermont. ................................................................................................................. 43?Figure 3.2.2.  Compilation of results showing change in snow accumulation (top) and ablation (bottom) according to change in forest cover. .............................................................................................................. 49?Figure 3.2.3.  Correlations between snow accumulation and representative geographic and climatic variables. ........................................................................................................................................................ 49?Figure 3.2.4.  Correlations between snow ablation and representative geographic and climatic variables. . 50?Figure 3.2.5.  Simple linear models relating changes in forest structure to changes in snow accumulation (left) and ablation (right) (Equations 3.2.2 and 3.2.3 were fitted using the data in the figures). ................... 51?Figure 3.2.6.  Observed vs. predicted snow accumulation (left) and ablation (right) for simple linear models. .......................................................................................................................................................... 52?Figure 3.2.7.  Comparison of simple linear models (Pomeroy et al., 2002; Kuz?min, 1960) predicting effects of forest structure on snow accumulation. ......................................................................................... 54?Figure 3.3.1.  Basal area per plot according to MPB attack stage (healthy, red, grey and other species not affected by MPB).  See Table 3.2.1 and Methods section for description of plots. ....................................... 66?Figure 3.3.2.  Absolute peak SWE and maximum ablation rate in forested plots relative to nearby clearcuts (which would represent 100%).  See Table 3.2.1 and Methods section for description of plots. .................. 68?Figure 3.3.3.  Snow water equivalent in Baker Creek (left) and Vanderhoof (right) plots. .......................... 69?Figure 3.3.4.  Scatterplots of forest structure variables with the highest correlations with absolute peak SWE [a) and b)] and maximum ablation rate [c) and d)] (all correlations with p < 0.01). ............................. 71?Figure 3.4.1.  Top row: side, top and bottom of the LOCUS-2.  Bottom row: examples of LOCUS-2 sensors installed in the field; sensors in forested sites (left) were oriented N-S to minimize the entry of ix  direct sunlight in the PVC cover, while sensors in open areas (center) were fully covered.  Some sensors were installed without a protective cover (right). .......................................................................................... 81?Figure 3.4.2.  Comparison of snow depth (top) and mean daily air temperature (bottom) between data obtained from one LOCUS-2 sensor and two nearby weather stations. ........................................................ 85?Figure 3.4.3.  Examples of the use of LOCUS-2 sensors in applied research: snow depth measurements in two study areas according to relative canopy conditions (top); and detection of the effect of temperature on snow ablation (bottom). ................................................................................................................................. 86?Figure 3.5.1.  Representative examples of three stands with LiDAR point clouds (left), hemispherical images derived from coordinate-transformed LiDAR returns (centre) and calibrated with their optical ground-based counterparts (right).................................................................................................................. 93?Figure 3.5.2.  Maximum (upper dashes), mean (diamonds) and minimum (lower dashes) r2 values between snow accumulation and ablation metrics and various forest structure metrics from ALS (a), hemispherical images (b) and Landsat spectral indices (c).  Snow accumulation definitions:  ?SWEA = absolute SWEmax; ?SWEB = SWE right before a period of sustained ablation.  Snow ablation definitions:  ?SARC = snow ablation from absolute SWEmax to snow disappearance; ?SARD = snow ablation from peak right before ablation to snow disappearance; ?SARE = mid-period 10-day ablation.  Snow indicators taken from manual snow surveys and LOCUS sensors are indicated in black and grey, respectively. ........................................ 99?Figure 3.5.3.  Relationships between absolute standardized SWEmax (?SWEA) and its best forest structure predictor (a), and between standardized snow ablation for the entire ablation period (?SARC) and its best forest structure predictor (b); both snow indicators were obtained from LOCUS sensor data.  Outlier plot codes are presented. ..................................................................................................................................... 102?Figure 3.5.4.  Three representative forested stands where snow was measured by manual snow surveys (top) and LOCUS-derived SWE (bottom). ................................................................................................... 104?Figure 4.3.1.  Effect of projected ALS return size on the relationship between observed and predicted gap fractions.  The projected circle size of synthetic image examples (a, b, c) and corresponding relationships (d, e, f) is expressed as the fraction between the diameter of each ALS return and the diameter of the image:  0.0137 (a, d), 0.0176 (b, e), and 0.0215 (c, f). ............................................................................................. 134?Figure 4.3.2.  Example of the projection of an ALS spherical return into a 2-D focal plane (a), and azimuthal radial distortion correction at representative zenith angles (b). .................................................. 137?Figure 4.3.3.  Representative examples of ALS point clouds (left), ALS synthetic hemispherical images (center) and real optical hemispherical photographs (HP) (right) for each stand; azimuths (?) are shown on the hemispherical illustrations. .................................................................................................................... 148?Figure 4.3.4.  Relationship between ALS-derived (LGF?) and HP-derived gap fraction (FGF?) (a, b, c) and between predicted and observed values of gap fraction obtained from simple (d, e, f) and multiple (g, h, i) linear regression models across three representative zenith AOV (30?, top; 60?, center; and 90?, bottom); legends in sub-figures a and i apply to all. .................................................................................................. 150?Figure 4.3.5.  Relationship between gap fraction predicted from multiple linear regression (Equation 4.3.4) (YM(?)) and model residuals (FGF? - YM(?)) for three representative zenith AOV. ........................................ 153?Figure 4.3.6.  Comparison between the relationship of plot-level average gap fractions obtained from optical HP and a) vertical gap fraction estimated from untransformed ALS, and b) gap fractions from calibrated synthetic hemispherical images. ................................................................................................. 154?Figure 4.4.1.  Example of modeling data experimental design showing VRI stands (red boundaries) with their centroids consisting of four contiguous Landsat pixels (top, left) and 36 ALS sampling points per pixel (yellow dots); the ALS transect boundary (blue) is shown over the Landsat image (top) and with high-resolution aerial photography (bottom).  The total number of VRI stands was 88, equivalent to 352 individual Landsat pixels. ............................................................................................................................ 169?x  Figure 4.4.2.  High-resolution aerial photographs (top), optical ground-based hemispherical example pictures (middle), and ALS-derived synthetic hemispherical example pictures (bottom) of five representative validation ground plots. ........................................................................................................ 171?Figure 4.4.3.  Predicted vs. observed values of structural metrics relevant to hydrologic modeling as obtained from Landsat spectral indices at the individual pixel level (a-d) (n = 352), aggregation of two pixels (e-h) (n = 176) and c) aggregation of four pixels (i-l) (n = 88).  Continuous central black line is a 45? reference; inner dotted lines are regression confidence bands; and outer segmented lines are prediction confidence bands (all with ? = 0.05). .......................................................................................................... 186?Figure 4.4.4.  Modeling residual root mean square error (RMSE) percentiles for FC0.5, H99, LAI5 and SVF. ..................................................................................................................................................................... 187?Figure 4.4.5.  Means (points), standard deviations (boxes) and minimum ? maximum ranges (bars) of predictor spectral indices (left) and corresponding predicted structural metrics (right) of validation plots (Table 4.4.2) grouped by MPB foliage status (x-axis). ................................................................................ 189?Figure 4.4.6.  Maps of distributed FC0.5 (a), H99 (b), LAI5 (c), and SVF (d), for Baker Creek, 2008 (white = cloud; black = cloud shadow; blue = water bodies; purple = wetlands; brown = bare soil / recent clearcuts; green scale = vegetation with minimum and maximum values indicated for each variable; FC0.5 and SVF are fractions, H99 is in m and LAI5 in m2/m2.). ............................................................................................. 191?Figure 4.4.7.  Histograms of variables in Baker Creek (FC0.5, H99, LAI5, SVF) distributed continuously by this study?s methodology (a-d) (color scales match Figure 4.4.6) and discretely by traditional approaches (e-h). ............................................................................................................................................................ 192?   xi  Glossary of acronyms  Acronym* Description ALS Airborne Laser Scanning AOV Angle of view AVHRR Advanced Very High Resolution Radiometer AWS Automatic weather station CRHM Cold Regions Hydrologic Model DBH Diameter at breast height DEM Digital elevation model DHP Digital Hemispherical Photography software DHSVM Distributed Hydrological Soil Vegetation Model EVI Enhanced vegetation index FC Forest cover FMI Foliar moisture index FW Full waveform (LiDAR) GF Gap fraction GIS Geographic Information System GLA Gap Light Analyzer GPS Global positioning system H Height HP Hemispherical photography LAI Leaf area index LAI-2000 LI-COR? LAI-2000 Plant Canopy Analyzer LiDAR Light Detection and Ranging LOCUS Low-Cost Ultrasonic Sensor MODIS Moderate-Resolution Imaging Spectroradiometer MPB Mountain pine beetle NDVI Normalized difference vegetation index NIR Near infrared PAI Plant area index PVC Polyvinyl chloride  RMSE Root mean square error SAR Snow ablation rate SSE Sum of squares of the error SUF Spectral unmixing fraction SVF Sky-view factor SWE Snow water equivalent TCI Tasseled-cap index TLS Terrestrial Laser Scanning TM Thematic Mapper (Landsat) USGS United States Geological Survey VI Vegetation index VRI Vegetation Resources Inventory  * Numeric variables are indicated in italic; only variable acronyms repeated consis-tently throughout the thesis are included in this table, whereas each section has their own variable specifications, which might vary slightly between sections.  xii  Acknowledgements  This research would have not been possible without the constant support of my supervi-sor, Nicholas Coops, who created a working environment that most professionals could only dream of and whose unique combination of efficiency, generosity and sharp sense of humor set the bar too high.  My co-supervisor, Markus Weiler, was fundamental for my acceptance at UBC and to him my family and I will always owe the pleasure of living in one of the most beautiful cities in the world.  Thanks to my committee members, Dan Moore and Mark Johnson, who provided essential and unconditional guidance throughout these years.  I cannot express my gratitude enough to Younes Alila, a splendid counsellor and now close friend who open-handedly shared his knowledge and time as if he were a part of my committee, and granted me the great opportunity to teach his Hydrology course while temporarily away.  Dan Bewley provided crucial help during field work, but mostly snowmobile-riding fun, soccer talks, and remarkable mentorship in topics of Hy-drology.  Thanks to Jens Wawerla from the Simon Fraser University, we could success-fully develop our prototype ultrasonic snow depth sensors.  This thesis substantially de-pended on data and logistics contributions from Pat Teti, a colleague and dear friend from the British Columbia Ministry of Forests.  Christopher Bater was an outstanding field as-sistant who smilingly coped with the most extreme weather conditions (-35?C) while in-stalling my snow sensors.  Gordon Frazer appeared during a crucial moment of my doc-torate program to contribute with excellent and influential ideas.  Dennis & Roxanne Gordon warmly hosted me in their house as if I was part of their family while doing fieldwork.  Thanks to all my friends from the Integrated Remote Sensing Studio (IRSS) at xiii  UBC for unconditionally helping me with technical questions but mostly for their su-preme friendships and a load of good memories.  A very special acknowledgement is de-served by Jennifer Ragu? for generously proofreading this thesis in depth even though snow processes and their drivers, whether remotely-sensed or not, rank very poorly among her topics of interest.  Thanks to my thesis examiners Anne Nolin, Hans Schreier and Marwan Hassan for their thoughtful suggestions.  My wife Alejandra has been my inspiration, example and cheerful support in all aspects of life, PhD endeavors being among the most challenging.  Not a single word of this the-sis was written without thinking of her.  My parents Yvonne and Roberto, and my aunt Adriena, who lovingly viewed my academic education as her life mission, are the divine original architects of all my achievements ?thus silent co-authors of this work.  My brothers and in-laws have always brought me the joy that gives a meaning to life (Esteban, Alex, Pablo, Ana Cris, Laurita, Bel?n, Jacobito, Ruthy, Xime, Thomas, Jacobo and Ruth).  Emilia, Alegr?a, Karla, Ana Sara, Victoria, Anah?, Lucas and all the beautiful children yet to come, are and will always be my primary motivation to work hard.  Many people made important contributions to this research in the form of academic ad-vice, field work assistance, email exchanges, administrative matters, manuscript proof-reading, data providing or enlightening conversations during conferences or in the hall-ways (in no particular order):  Valerie LeMay, Thomas Hilker, Georg Jost, Russell Qualls, Mike Wulder, Russell Smith, Sally Taylor, Colin Ferster, Rory Tooke, Doug Bol-ton, Greg Rickbeil, Sam Coggins, Jessica Lundquist, John Pomeroy, Dan Naidu, Gayle xiv  Kosh, Heather Akai, Debbie McPherson, David Aquino, Jerry Maedel, Marissa Relova, Jerry Whalley, Rita Winkler, Harry Verwoerd, Steve Burges, Kaity Castellani, Sarah Boon, Robert D?Eon, Esko Kuusisto, David Tait, William Veatch, Jenna Forsyth, Yeganeh Asadian, Mike Meitner, Matthew Sturms, Nick Goodwin, Vartan Vartanian, Anna Yuill, Craig Murray, Nils Ilchmann, Sylvain Leblanc and Holly Maness.  Thanks to all the editors and referees of my published articles.  Thanks to all my students during these golden years of teaching assistantships and lecturing.  I am deeply grateful to my former mentors at Liceo Internacional, Universidad Austral de Chile and Aglomerados Cotopaxi:  Nelly Hinojosa, Diego Carri?n, Milena Montoya, Samuel Arriagada, Renato Grez, Antonio Lara, Claudio Donoso, Fernando Droppelmann, V?ctor Gerding, Antonio Hadad, Fernando Montenegro, Xavier Su?rez and Federico Arteta.    This research was mainly funded by a PGSD3 scholarship to Andr?s Varhola and a Dis-covery Grant to Nicholas Coops, both from the Natural Sciences and Engineering Re-search Council (NSERC), a UBC Four Year Fellowship to Andr?s Varhola and a grant from the provincial Forest Sciences Program (FSP) to Markus Weiler and Nicholas Coops.  Very special thanks to all the donors of independent merit-based funds I have been a proud recipient of:  Adrian Weber Memorial Scholarship in Forest Ecology, Don-ald S. McPhee Fellowship, Canadian Water Resources Association Memorial Award, St. John?s College Reginald and Annie Van Fellowship, Killam Graduate Teaching Assistant Award, and Mary and David Macaree Fellowship.  Thanks to all my friends.  I would be nobody without you.  xv  xvi  Dedication          To Alejandra,  the most beautiful human being I have ever seen. I love you     1 Introduction  1.1 General background, objectives and chapter overview  The structural and physiological attributes of forests exert a profound influence on the multi-scale components of the hydrologic cycle.  While these relationships have been studied for centuries (Dingman, 2002), the non-exact and stochastic nature of Hydrology as well as complexities associated with understanding the erratic trails of water through the heterogene-ous landscape continue to encourage new research and the revision of current scientific knowledge.  Generally it is accepted that, at the small catchment level, water that is evapo-rated from canopies as rain or snow is intercepted and water transpired via root uptake from the soil together constitute losses that result in reduced streamflow in forested areas when compared to open counterparts (Connaughton, 1935; Haupt, 1951; Eisenbies et al., 2007).  Additionally, water evaporation rates from the ground tend to be slower under forest cano-pies due to shading and the consequent reduction of driving energy.  The disturbance or re-moval of substantial portions of forested vegetation in a watershed will therefore likely in-crease the average periodic water yield (Chang, 2006) and exacerbate flood regimes (Kura? et al., 2012; Green & Alila, 2012), among other effects.  In larger basins of regional or conti-nental dimensions, where water delivered by ocean evaporation is distant, a major share of precipitation has been found to be supplied by the forests themselves (van der Ent et al., 2012; Ellison et al., 2012), which transfer water to the atmosphere that would otherwise be captured by the decelerated pathways of underground hydraulics.  Increases in water yield by forest removal in small watersheds might therefore be offset by a reduction in the supply of 1  this recycled water if the deforested area is large enough, although these thresholds have not been established yet (Ellison et al., 2012).   Although the processes described above are applicable in general, different hydroclimate re-gimes and specific situations often exhibit their own particularities.  Snow accumulation and melt play a particularly important role in the hydrology of montane snow-dominated regions, where water supply is highly dependent on spring melting from forested areas (Uunila et al., 2006).  In western North America, for example, 75% of the total water input in streams comes from snowmelt (Service, 2004).  Unlike rain-dominated regimes, where runoff dy-namics are mostly modulated by individual storms, the quantity and rate of water input into streams during spring in snow-dominated regions is mainly driven by the amount of energy available to melt the solid precipitation accumulated throughout winter.  When there is abun-dance of both snow and energy, severe flooding events might occur if soil infiltration rates are exceeded by basin-wide melt rates (Bewley et al., 2010; Green & Alila, 2012).  Evi-dently, the role of forests in influencing these processes can be of major importance.  As forest cover increases, snow accumulation on the ground is generally reduced because part of the snowfall intercepted in the canopies is returned to the atmosphere by sublimation (Essery et al., 2003).  Although the magnitude of these combined phenomena varies accord-ing to specific conditions, studies indicate that up to 60% of annual snowfall can be inter-cepted in dense coniferous forest canopies of temperate and boreal regions, where 60 to 80% of this amount may be sublimated (Hedstrom & Pomeroy, 1998; Pomeroy et al., 1998; Storck et al., 2002).  As a result, snow accumulated on the ground of forested areas can be 2  substantially lower compared to nearby open sites (D?Eon, 2004; Winkler et al., 2005; Jost et al., 2007).  The primary driver of snow ablation ?which includes melt, sublimation and drift? is the net energy available.  Its balance can be calculated by measuring the shortwave radiation incoming from the sun and the portion that is reflected by the snow surface, the dif-ference between longwave radiation arriving to the snow from external sources and emitted by the snow itself, sensible heat transfers at the snow surface ? atmosphere interface, and la-tent heat gains or losses as water condensates or evaporates, respectively, in the snowpack (Brooks et al., 2003; Boon, 2007).  Forest cover is critical in this energy balance because even though canopy elements can increase the input of longwave radiation to the snow (Sicart et al., 2004) and decrease its albedo through debris contribution (Hardy et al., 2000; Melloh et al., 2001), they also attenuate incoming shortwave radiation and thus generally lead to net losses in the total energy budget available for melting (Meagher, 1938; D?Eon, 2004; Essery et al., 2008).  Additionally, forest cover shelters snow on the ground and hence reduces the eroding-sublimating effect of wind (Gary, 1975) while impairing sensible and latent heat exchanges (Dingman, 2002).  Empirical studies in North America have shown that, due to these factors, snowmelt rates in forests can be up to 70% slower than in open ar-eas (e.g. Hendrick et al., 1971; Boon, 2007; Teti, 2008).  The removal or disturbance of for-ested stands will therefore likely lead to increases in snow accumulation and faster ablation rates, with enhanced snowmelt discharges constituting potential sources of severe flooding (Brooks et al., 2003).  Flat catchments with little topographic variation, where all the snow melts simultaneously, are more vulnerable to these changes (Hendrick et al., 1971; Bewley et al., 2010).  Although flooding generally gets most of the attention through its destructive-ness, alterations in snow accumulation and ablation dynamics can also impact wildlife, 3  streamflow regimes including low flows, fisheries? productivity, irrigation planning, hydro-power production and forest fire occurrence (Service, 2004; Mote et al., 2005; Rood et al., 2008).  Understanding the complex interactions between forests and snow processes has continu-ously challenged scientists, principally due to difficulties in measuring areal snow water equivalent (SWE) distribution and the several stochastic factors that affect snow accumula-tion and ablation.  This has motivated the establishment of several modeling approaches, with two principal objectives: 1) improve our understanding of the drivers of hydrologic processes and 2) enable hydrometeorological forecasting.  Methods to develop these models vary from simple local-scale empirical comparisons between forested and non-forested areas (Pomeroy et al., 2002; Winkler et al., 2005; Woods et al., 2006; Boon, 2009) to the descrip-tion and compilation of detailed process-based equations aiming to account for governing physical phenomena (e.g. Wigmosta et al., 1994; Tarboton & Luce, 1996; Pomeroy et al., 2007).  The latter are, in principle, applicable to a wide range of conditions but require input data that are not often readily available in operational contexts.  Empirical models, on the other hand, have been derived from a wide range of studies to provide first-order estimates of the effects of forest cover changes on snow processes (e.g. Kuz?min, 1960; Woods et al., 2006; Varhola et al., 2010b).  However, they do not explicitly account for physical processes, which vary in both space and time, and cannot therefore be relied upon to generate accurate predictions at different sites or periods.  The ultimate goal of snow models, regardless of type or complexity, is to estimate the maximum amount of SWE accumulated on the ground prior to spring melt and the rate of subsequent ablation ?indicators that are fundamental to predict 4  runoff generation and streamflow input in snow-dominated watersheds (Luce et al., 1998; Liston, 1999; Jost et al., 2009).  The simplest empirical models will provide plot-level peak SWE and coarse average snow ablation rates (SAR) representing the entire snowpack deple-tion phase, while the most advanced physically-based models can derive SWE at sub-daily intervals in pre-defined individual spatial units covering an entire watershed if appropriate meteorological data are available.  However, all models are currently still subject to impor-tant limitations even if high-quality data are used, especially when simulating snow processes under forest canopies (Rutter et al., 2009).   Since there is no technology currently capable of directly measuring SWE at scales and spatiotemporal resolutions useful for practical man-agement applications, our persistent reliance on models justifies constant efforts to improve them.  With regards to snow modeling in forested environments, the most obvious constraint is our inability to accurately characterize the complex and heterogeneous architecture of for-est canopies in wide areas, even in small watersheds.  While studies have identified measur-able forest structure metrics with strong physical links to processes such as snow interception (Pomeroy et al., 1998) or radiation attenuation (Bartelink, 1998; Ellis et al., 2011) at the small plot level, challenges remain when attempting to extrapolate these metrics to obtain wall-to-wall watershed coverage.  This has generally resulted in a poor characterization of vegetation in the majority of hydrologic modeling exercises, which are mostly restrained to evaluate the gross effects of clear-cutting on the water dynamics of relatively small water-sheds (e.g. VanShaar et al., 2002; Schnorbus & Alila, 2004; Kura? et al., 2012).  The recent massive infestation of mountain pine beetle (MPB) in the snow-dominated region of central British Columbia has reinforced the need for more accurate hydrological modeling 5  approaches, precisely spotlighting the limitations of the current ones.  The large areas im-pacted and the changes in forest structure as MPB infestation defoliated and killed forested watersheds during a decade could not be adequately evaluated with conventional modeling to establish hydrologic impacts with reasonable certainty (Boon, 2009; Bewley et al., 2010).  Advantageously, modern remote sensing technologies offer solutions that are yet to be ap-plied broadly for operational and research purposes in Hydrology ?both at the plot and land-scape scales.  Considering the particular issue of a poor characterization of forest structure in hydrologic modeling, Light Detection and Ranging (LiDAR) has emerged as the most prom-ising alternative as it is capable of providing three-dimensional, spatially explicit representa-tions of canopy structure over large, continuous areas.  LiDAR sensors actively emit laser pulses and record the distance between sensor and target, providing point cloud-type illustra-tions of the scanned objects (Lefsky et al., 2002).  LiDAR systems are generally classified as either Terrestrial Laser Scanning (TLS) or Airborne Laser Scanning1 (ALS) according to supporting platform, or as discrete or full-waveform according to the type of digitisation fil-ter (Lim et al., 2003).  Discrete ALS sensors mounted on helicopters or airplanes at low fly-ing altitudes (500?1000 m) are currently the most widely used LiDAR systems in forestry (Lee et al., 2009) due to their extensive spatial coverage and sampling densities of one to several laser returns per square meter (Wulder et al., 2008).  If the cost of acquiring LiDAR over large areas remains high, freely-available satellite imagery such as Landsat Thematic Mapper (TM) can complement LiDAR in the task of characterizing vegetation over the land-scape.  In synthesis, two principal ways remote sensing can help hydrologic modeling are:  1) by more accurately quantifying forest structure with novel detailed variables that summarize                                                  1 Although ALS is a type of LiDAR acquisition, in this thesis the terms ALS and LiDAR are mostly used inter-changeably (note that only ALS was collected for this research). 6  the dimensional complexity of canopy elements and 2) by enabling a wall-to-wall, spatially explicit characterization of these metrics applicable to entire watersheds.    The main objective of this thesis is to establish approaches through which remote sensing ?primarily ALS? can be specifically used to improve the characterization of forest structure as required to enhance hydrologic snow modeling.  Given the variety of hydrologic models, the same research question is applied independently to the simplest forms of plot-level em-pirical models as well as complex physically-based simulators operating at the watershed level.  No previous study was found in the published literature directly correlating novel ALS-derived forest structure metrics to snow accumulation and ablation, so the development of such simple models is a logical initial step.  Similarly, the use of remote sensing to consis-tently and systematically obtain all the forest structure metrics that are commonly required by physically-based models has not been attempted in a pixel-by-pixel approach.  From this general objective, four specific research questions are formulated:  1) How are novel ALS-derived forest structure metrics correlated to indicators of snow ac-cumulation and ablation? 2) What are the benefits of using remote sensing, in combination with ultrasonic snow depth sensors, to directly predict plot-level snow accumulation and ablation with simple mod-els? 3) How can ALS be used to estimate the plot-level forest structure metrics currently used by physically-based hydrologic models? 7  4) How can ALS-derived forest structure metrics relevant to hydrologic modeling be ex-trapolated to the watershed-level with the support of other remote sensing tools?  Questions 1) and 2) are addressed by Chapter 3, while questions 3) and 4) are the focus of Chapter 4.  Section 1.2 is an introductory literature review which identifies and describes the most im-portant factors that influence snow accumulation and ablation ?a background necessary to better understand the sources of variation of snow processes.  Since this research takes place in the MPB-infested areas of British Columbia, Section 1.3 focuses on explaining the nature of the infestation and, particularly, the effects of that insect on forest structure.  Section 2 is a detailed description of the study area and the data constituting the basis of this thesis.  These overlapping sources include remotely-sensed indicators of forest structure and spectral properties, ground-based optical and traditional forest variables, snow measurements from both manual surveys and prototype ultrasonic snow depth sensors, and meteorological information from a network of weather stations.  Chapter 3 explores the positive effects of a progressive, step-by-step input of improved met-rics in simple empirical snow models.  These enhanced metrics include remotely-sensed for-est structure variables and snow indicators measured by ultrasonic devices.  Section 3.2 starts with a metadata analysis of historic snow-forest records published in the literature, and estab-lishes the methodology to standardize data from different sources to produce baseline models 8  predicting peak SWE and SAR from forest metrics obtained from field measurements.  Sec-tion 3.3 is a study that directly demonstrates how ALS-derived forest structure metrics are better correlated to peak SWE and SAR than ground-based forest metrics.  Section 3.4 intro-duces a prototype ultrasonic snow depth sensor designed to accurately capture peak SWE and snow disappearance, with the purpose of improving the methodology to estimate the re-sponse variables of simple empirical models.  In Section 3.5, the relationships between all the remotely-sensed forest metrics available in the study area and improved indicators of snow accumulation and melt as measured by ultrasonic snow depth sensors are explored.  Chapter 4 focuses on the application of remote sensing to improve physically-based, spatially distributed models.  Firstly, the main forest structure variables required by current popular models are identified and described in Section 4.2.  Section 4.3 shows a novel methodology to estimate these variables from ALS data at the plot level, while Section 4.4 develops an ap-proach to extrapolate these metrics, originally available only within ALS coverage, to the wider landscape by analyzing their relationships with Landsat-derived spectral indices.  The end products of this chapter are detailed pixel-by-pixel distributions of the four forest struc-ture modulators of snow processes.  Chapter 5 synthesizes the general conclusions of the previous chapters and sub-sections, fo-cusing on their links with the four research questions listed above and how they were an-swered.  It also provides a discussion about persisting issues and limitations of snow model-ing and recommendations for the future.  9  The interconnections between the key chapters and sections of this thesis, as well as both snow and forest structure data sources, are shown in Figure 1.1.1.  GroundALSLandsatManual surveysUltrasonic sensors (3.4)Simple base models (3.2)ALS ? snow relationships (3.3)Multiple remote sensing ? enhanced snow indicators (3.5)ALS plot level metrics (4.3)Watershed level metrics (4.4)Snow data Empirical models(Chapter 3)Forest structure data Physically-based models(Chapter 4)HP Figure 1.1.1.  Interconnections between data sources and thesis chapters and sections (shown in blue) (see glossary of acronyms for definitions).   1.2 The complex processes and drivers of snow accumulation and ablation   To develop a better understanding of the interaction between forest structure and snow ac-cumulation and ablation, it is necessary to identify the factors that explain the spatial and temporal distribution patterns of snow.  This knowledge helps to establish appropriate ex-perimental designs when developing snow models, understand potential causes of scatter and explain outliers.  This section has been published in (Varhola et al., 2010b).  10  Snow accumulation is most often represented by the peak SWE (mm) on the ground before the snow starts to melt, while SAR (mm/day) is usually computed as the peak SWE divided by the number of days of the ablation period (from date of peak SWE to date of snow disap-pearance).  Several factors can influence the interactions between peak SWE, SAR and forest cover, and errors in measuring these three variables can also add substantial variability to ob-servations within statistical models.  As the effects of forest cover on snow accumulation and ablation have been subject of substantial research over the last century, this section summa-rizes the published literature about the factors that affect snow processes.  It also compiles, adapts and reanalyzes some of the authors? results into comprehensive figures.  1.2.1 Snowfall magnitude and inter-annual variations  Since tree branches cannot intercept an unlimited amount of snow, the influence of forest cover decreases in importance as total snowfall increases beyond a certain threshold (Boon, 2009).  Similar to what occurs with rain (Brooks et al., 2003), a higher proportion of snow precipitation can be intercepted by tree canopies and sublimated to the atmosphere if the events are small.  Snowfall magnitude varies significantly from year to year in many loca-tions (Wilm & Dunford, 1948; Anderson, 1956), thus suggesting that relative and absolute snow accumulation under the same forested site will be different if measured consecutively during a long period of time.  Connaughton (1935) studied snow accumulation and melting in five plots in Idaho in re-sponse to the recommendation of cutting forests in order to increase water supplies.  The 11  study revealed the strong influence of snowfall magnitude on forest-snow interactions:  in a light snowfall year (1931), forested sites accumulated 27.5% less snow than open areas, while in the following average year that figure dropped to 4.3%.  Winkler & Moore (2006) studied the relationship between forest stand properties and snow accumulation at two sites in the Interior Plateau region of British Columbia, Canada, for a three year period (1995?1997).  They found that inter-annual variability in peak SWE was significant at both sites and explained 28% to 42% of the total variance.  Additionally, the greatest interannual variations were found at the forested sites and not in the clearcuts, suggesting that the interaction be-tween the effects of total snowfall and canopy cover is not linear.  Boon (2009) found similar differences in snow accumulation in forests relative to clearcuts in a two-year study at Fraser Lake, British Columbia.  In the same province, Jost et al. (2007) showed that the influence of forest cover, relative to aspect and elevation, changes according to snowfall magnitude.  The influence of individual snowfall events on snow interception was studied by McNay et al. (1988) in Douglas-fir (Pseudotsuga menziesii) and western hemlock (Tsuga heterophylla) forests on Vancouver Island, British Columbia.  Regression analysis was used to relate forest cover and storm size to predict the amount of fresh snow under the canopy.  The authors found a non-linear relationship between storm size and snow depth for events smaller than 15 cm and a linear trend for larger events.  Figure 1.2.1 summarizes the data of McNay et al. (1988) to show the overall relationship between storm size and the ratio of fresh snow accu-mulated under the forest and open areas for the storm events.  A slight but significant [Pear-son correlation coefficient (r) = 0.37; probability (p) = 0.008] positive correlation was found between storm size and the proportion of snow that accumulates under the forest as snowfall 12  events become larger, although the lower frequency of large events is a limitation in the analysis.    Figure 1.2.1.  Relationship between storm size and the ratio of fresh snow accumulated un-der the forest and at a nearby open site (adapted from McNay et al., 1988)   1.2.2 Elevation  Elevation also has an influence on the magnitude of snowfall events and snow processes (Anderson & West, 1965).  In the Nelson Forest Region (British Columbia), snow accumula-tion in paired forested and clearcut sites along an elevation gradient was found to increase at a rate of 11 to 15 mm of SWE per 100 m increase in elevation for forested sites, and 21 to 27 mm for open sites (Toews & Gluns, 1986).  D?Eon (2004) measured snow accumulation in 27 transects (455 plots) in open and forested areas ranging in elevation from 500 to 1,500 m.  The absolute values of snow depth showed a significant correlation with elevation (r2 = 0.40; p < 0.001) (Figure 1.2.2).  However, the relation between canopy cover and snow depth proved to be significant only in low elevation sites, which the author attributed to greater snow accumulation in the higher sites and a corresponding decrease in the importance of 13  canopy influence.  Elevation also provided the best correlation and regression coefficients with snow depth in a study of snow distribution in forested and deforested landscapes in New Brunswick (Daugharty & Dickison, 1982).    Figure 1.2.2.  Snow depth as a function of elevation in Little Slocan Valley, British Colum-bia (adapted from D?Eon, 2004).  Lower temperatures at higher elevations are also expected to have an influence on snow melting rates.  Hendrick et al. (1971) studied the influences of elevation, slope-aspect and forest cover types on snowmelt in the Sleepers River Watershed (Vermont).  The 111 km2 watershed (200 to 800 m in elevation) was stratified into 96 environments that represented the combinations of the three variables of study.  The significant influence of elevation on snowmelt led the authors to conclude that mountainous watersheds with high variability in elevation are at a lower risk of spring snowmelt flooding due to differentiated onset and rates of melting along the gradient.  Similar conclusions are reported by Alila et al. (2007a), while rare exceptions to this generalization are explained by Lundquist et al. (2004).   14  1.2.3 Aspect  The effect of aspect on snow accumulation and melting is principally a function of exposure to solar radiation, with more snow expected to accumulate on northerly aspects (in the north-ern hemisphere) due to reduced melting and sublimation rates during the accumulation phase (Golding & Swanson, 1986).  Predominant local wind directions may also influence the ef-fect of aspect on accumulation and melting.  Berndt (1965) conducted an experiment in lodgepole pine stands and clearcuts in Wyoming to determine changes in peak snow accumulation due to aspect and clearcut size.  The results indicated that the combination of both variables had a significant influence on snow accumu-lation, with east aspects showing greater responses to clearcutting and south aspects subject to a larger influence of clearcut sizes than the others.  Murray & Buttle (2003) analyzed the effect of north- and south-facing slopes on snow accumulation and melt in the Turkey Lakes Watershed (Ontario) by comparing a hardwood maple stand and a nearby open site in 2000 and 2001.  As expected, melt rates were significantly higher in south-facing sites with the forested south-facing stands showing an even higher rate than the north-facing clearcut.  It was concluded that aspect had a stronger influence on melting than forest cover.  Comparable results were reported by other studies (Haupt, 1951; Anderson & West, 1965; Hendrick et al., 1971; Rowland & Moore, 1992; D?Eon, 2004; Jost et al., 2007).  In California, a network of snow sampling points ranging in elevation from 1,800 to 2,400 m was established to compare coniferous forests and clearcuts having different slopes and as-15  pects (Anderson et al., 1958a).  The effect of aspect on April 22 SWE and June 1 melting rates is shown in Figure 1.2.3.  Forests with 35% cover showed larger peak SWE in north as-pect sites, a tendency that is weaker in 65% cover forests and unclear in 90% cover forests.  Snow melting occurred faster in south and west aspect sites across the three different forest cover values.  In all cases, forests with 90% cover tended to show less snow accumulation and lower melting rates.  In British Columbia, D?Eon (2004) showed that southern aspects (180?) generally presented decreased amounts of snow accumulation relative to northern as-pects in different elevation ranges (Figure 1.2.4).    Figure 1.2.3.  Effect of aspect on peak SWE and melting in coniferous forests with 35, 65 and 90% of forest cover in Central Sierra Snow laboratory, California (adapted from Anderson et al., 1958).    16    Figure 1.2.4.  Effect of aspect on snow depth according to elevation ranges in Little Slocan Valley, British Columbia (adapted from D?Eon, 2004).  1.2.4 Slope  The overall impact of increasing slope is to reduce snow accumulation due to snow moving downhill, exposure to wind and higher temperatures in sunnier aspects during the accumula-tion period (Golding & Swanson, 1986).  Slope is expected to influence snow melting in combination with aspect (e.g. a south-facing steeper slope exposes the snow to solar radiation at lower incidence angles in the northern hemisphere).  In Wyoming, Berndt (1965) compared snow accumulation in three clearcuts on south-facing aspects covering a range of slopes.  Results indicated that a plot with 18% slope accumulated 17  20% to 30% less snow than those sites with gentler slopes (5% and 6%).  Figure 1.2.5 sum-marizes a similar comparison undertaken in California (Anderson et al., 1958a), where a clear trend in the impact of slope on snow accumulation was not evident; however, 30% slopes had a higher melt rate than 15% slopes and more variability existed on gentler rather than steeper slopes.    Figure 1.2.5.  Effect of slope (%) on peak SWE and melting in coniferous forests with 35, 65 and 90% of forest cover (adapted from Anderson et al., 1958).  1.2.5 Clearcut size  When comparing snow accumulation and melting between forested sites and nearby clear-cuts, the size of the latter plays an important role.  Small clearcut openings are often still sheltered by surrounding forests, while larger clearcuts are exposed to wind erosion that re-duces overall snow accumulation (Pomeroy et al., 2002).  Intermediate-sized clearcuts are therefore expected to accumulate the largest amounts of snow.  With respect to snow melting, shade from adjacent trees in smaller clearcuts has been shown to retard melting by decreasing 18  the daily incoming shortwave radiation and reducing the differences in melting rates in the adjacent forest.      Figure 1.2.6.  Influence of clearcut size (in number of tree heights of adjacent forests, H) on snow accumulation in James River, Alberta (adapted from Golding & Swanson, 1986).  In James River and the Marmot Creek Experimental Watershed (Alberta), Golding & Swanson (1986) expressed the clearcut diameter in terms of number of tree heights of sur-rounding forests (H).  The results of average peak SWE measured from 1973 to 1976 in James River indicated that at most of the locations, snow accumulation was higher in clear-cuts of 2 and 3 H diameter (Figure 1.2.6).   Peak SWE increased significantly from forests (0 H) to clearcuts of 0.25, 0.5, 0.75 and 1 H, suggesting that snow interception of the adjacent forest maintains an important role below that threshold.  In Colorado, Troendle & Leaf (1980) found maximum snow accumulation in 5 H clearcuts, while in Saskatchewan Pomeroy et al. (1997) found no differences in snow accumulation between a large (km scale) and small (100 m) clearcut, which was attributed to lower local wind speeds than in other areas.  Berndt (1965) also found minor differences in snow accumulation and melting in 2, 4 and 8 ha clearcut blocks in Wyoming.  However, all three clearcut sizes showed up to 40% 19  more snow accumulation and snow disappearance 10 days earlier than the surrounding lodgepole pine stands, indicating that the combination of clearcut size and aspect was more influential on snowpacks than their individual impacts.  In the Central Sierra Nevada (California), Anderson & West (1965) sampled 163 snow courses to determine the effect of terrain and year-to-year snowfall variation on snow accu-mulation and melting.  The effect of snowfall magnitudes interacted closely with clearcut size, as accumulation was higher on a 4 H than in a 1 H clearcut in the year of heaviest snow-fall, and differences were reduced by more than 60% in the following two dry years.  They also observed that larger clearcuts accumulated more snow in higher than in lower elevations.  1.2.6 Wind  Just as aspect and slope interact to produce combined effects on snow accumulation and melting, so do clearcut size and wind speed (Woods et al., 2006).  As suggested by Pomeroy et al. (1997), wind is the main factor affecting snow redistribution since it can reduce snow accumulation in clearcuts by erosion and enhanced sublimation, and increase SAR during the melting period.  This effect was examined in detail by Gary (1975), who hypothesized that the greater amount of snow in openings is explained by the lack of interception as well as snow movement from the forest to the clearing?s leeward edge.  This implies that total quan-tities of snow in the system as a whole may not always be affected by changing proportions of forests and openings.  This hypothesis is supported by the results of Troendle & King (1987), which showed that the overall average peak snow accumulation in a catchment in 20  Colorado did not change after harvesting.  Wind is one of the drivers of these important re-distribution processes.  Measurements of snow accumulation and wind speed before and after a clearcutting treatment in a lodgepole pine stand in Wyoming indicated that accumulation was consistently larger in the geometrical center of a 1 H ? 5 H clearing, where the wind speed declines and releases the snow transported from upwind canopy flow (Gary, 1975).  Woods et al. (2006) studied the effect of thinning on snow accumulation in lodgepole pine stands at the Tenderfoot Creek Experimental Forest (Montana).  Thinning increased wind speed and solar radiation, producing sublimation that offset the effect of the interception re-duction.  As a result, the treatment had no net effect on peak SWE.    In coastal British Co-lumbia, McNay et al. (1988) performed linear regression analysis to study the relationship between snow interception and several descriptors of forest structure and snowfall event size.  Explicitly acknowledging the confounding effects of wind as a snow redistributor, the au-thors measured interception immediately after each storm.  In central Ontario, accumulation differences on a ridge crest and a south-facing slope in a clearcut were the result of the redis-tributing effects of northerly winter winds (Murray & Buttle, 2003).  1.2.7 Specific weather conditions  As energy is the primary driver of snow melting, this process is particularly susceptible to local and short-term variations of weather systems.  Murray & Buttle (2003) measured snow melting duration in forested sites during two consecutive years and found that the ablation period took 27 days longer than a clearcut in 2000 and only 4 days longer in 2001.    21  Lundquist et al. (2004) observed that while generally snow melting started at lower eleva-tions in two catchments at Sierra Nevada, California, streams showed a synchronous rise on March 29, 2002.  This was a result of simultaneous snow melting in 70% of the sites due to an unusual 12?C temperature increase in 5 days, providing enough energy to overwhelm the effects of elevation (1,500 ? 3,400 m), aspect and forest cover.  A follow-up article (Lundquist & Flint, 2006) explained how weather conditions, hypothetically ideal to initiate synchronous melting in mountainous environments, can be offset by shading if they take place too early in spring, when solar angles are lower.  1.2.8 Canopy geometry and tree spatial distribution  In the Fraser Experimental Forest (Colorado), an aspen stand with 65% forest cover showed greater snow accumulation than an open area and a lodgepole pine stand with 75% cover (Dunford & Niederhof, 1944).  Pomeroy et al. (2002) compared snow accumulation in sev-eral forest types and found that a mature jack pine with 82% forest cover and a black spruce stand with 95% forest cover consistently showed the same percentage of reduction in peak SWE in comparison with the clearcut control during several years of measurement.  These studies concluded that forest cover per se is not a physical attribute that can explain all ob-served differences in snow accumulation.  In the case of the aspen stand studied by Dunford & Niederhof (1944), the higher accumulation was attributed to a leafless canopy that reduced snow interception, yet provided enough shelter and shade to prevent sublimation and erosion by wind.  The nearby pine plot with similar canopy cover was a more efficient snow inter-ceptor due to the differences in canopy structure and geometry.  Correspondingly, Pomeroy 22  et al. (2002) found that the amount of accumulated snow was similar despite the 13% differ-ence in forest cover between the black spruce and jack pine stands.  Several properties in the forest canopies can explain these factors.  Branch flexibility was proposed by Schmidt et al. (1988) and Lundberg & Halldin (2001) as influential on snow interception.  In an experiment to better understand interception processes in trees, Pfister & Schneebeli (1999) utilised boards to simulate branches of different sizes, shapes and inclination, concluding that all of these properties systematically influenced snow accumulation.  Despite their importance, metrics describing these attributes in real trees are difficult to measure (Parveaud et al., 2008) and therefore are seldom used in models of snow interception.  Tree distribution also has an influence on snow accumulation.  Even-spaced stands are ex-pected to show less variability in snow accumulation, which will normally decrease as the forest becomes denser.  A less predictable trend might exist in stands with clustered trees that resemble a combination of dense homogeneous stands and adjacent small openings.  In both cases, there is evidence showing that spatial variability in snow processes will be higher when forest cover approaches zero.  Regarding snow melting, stands with reduced forest cover (either due to a small number of trees or small tree size) can increase melting rates be-cause the canopies are unable to provide significant shading to the surface and will addition-ally increase the longwave radiation component of the energy balance (Swanson & Stevenson, 1971).  Studies conducted in New Mexico by Veatch et al. (2009) showed a strong control of forest edges on snow depth, where the absence of interception and the shad-ing of nearby trees favoured more snow accumulation than the interior of the forest.  This process is also influenced by the orientation of the edge interacting with local distribution 23  patterns, as Golding & Swanson (1986) and Veatch et al. (2009) found larger snow accumu-lation on northern edges.  1.2.9 Measurement errors  Measurements and calculation of peak SWE, snow melt rates and forest cover are subject to errors that can add significant bias to developed models.  They are explained below.  Peak SWE.  This variable is defined as the maximum snow water equivalent accumulated at a specific site prior to melting.  Since snowfall varies from year to year, it is impractical for field crews to determine exactly the date on which peak SWE occurs.  This has led to the standardization of April 1 as the date for comparisons in North America.  If SWE is captured in paired sites, often the peak occurs at different dates at each site (e.g. Skidmore et al., 1994), raising questions about how the comparison should be done (using real peaks from different dates or comparing two SWE measurements taken at one specific moment).  Addi-tionally, manual snow surveys are usually performed with aluminum snow tubes that extract samples from the ground to be weighed.  This procedure could lead to a bias of up to 12% (Peterson & Brown, 1975; Goodison et al., 1981) due to snow compression when taking the sample, scale calibration, scale reading, retention of the snow core in the sampler (Winkler et al., 2005) and subjective measurement of debris and soil depth in the bottom of the pit.  Pos-sibly the most important source of error when measuring SWE is landscape heterogeneity, as large sample sizes are often needed to account for the effects of terrain variation.  The opti-mal sampling schemes for the estimation of SWE under variable landscape conditions were 24  studied by Watson et al. (2006), who concluded that up to 54 cores are needed to obtain a representative mean at small scales (<100 m) by reducing the effects of vegetation and radia-tion on snowpack.  Additional considerations about snow survey sampling are given by Peterson & Brown (1975), Spittlehouse & Winkler (1996) and Watson et al. (2006).  SAR.  Since snowmelt is estimated from peak SWE, it is subject to the same errors plus addi-tional biases derived by dividing peak SWE by the ablation period to obtain snowmelt rates.  First, the precision with which the date of snow disappearance is determined is limited by the frequency of site visits (Jost et al., 2007).  Some studies record this date while others calcu-late melting rates between two consecutive snow surveys that do not necessarily account for the entire melting period.  Snow disappearance is also subject to variability within a plot, as it does not occur in all the area simultaneously.  Second, additional snowfall occurring during the melting period and mid-winter melting is often ignored in the calculations (Smith, 2011).  Third, SWE samples taken in melting, denser snow are subject to larger measurement errors, especially when the snowpack layer is thin and liquid water is present on the surface.  Boon (2009) measured melting rates both by dividing peak SWE by the melting period and with the use of an energy balance model.  The latter provided melt rates up to three times larger than the former, thus revealing the errors and uncertainty inherent in the estimations with both methods.    Forest cover.  The term ?forest cover? is often used in many studies without formal defini-tion; however, there are differences in the specific concepts and measurement methods.  For-est cover is usually understood as a percentage where 0% corresponds to an open field and 25  100% to a dense forest where there are no gaps between the touching canopies.  However, the lack of consistency in precisely defining forest cover is evident when listing all the termi-nology used in the literature:  canopy cover (Moore & McCaughey, 1998; Pomeroy et al., 2002), forest density (Anderson et al., 1958a), forest shade (Anderson, 1956; Anderson et al., 1958b), percent canopy density (Hardy & Hansen-Bristow, 1990), canopy closure (Patch, 1981), crown closure (Winkler & Roach, 2005), crown completeness (Bunnell & Vales, 1990), and crown coverage (Kittredge, 1953).  Other variables such as leaf area index (LAI) have been used by some studies as an indicator of forest cover and can be transformed to percentage by simple equations (Pomeroy et al., 2002).  Only a few authors have defined what they consider a measure of forest cover [e.g. ?the proportion of the sky obstructed by tree foliage from a point on the ground? (D?Eon, 2004)] and provide details about how they measured this variable (e.g. Ingebo, 1955; Moore & McCaughey, 1998; Pomeroy et al., 2002).  Further evidence showing that the procedure by which forest cover is measured can have critical effects on statistical analyses is provided by Moore & McCaughey (1998), who used two different instruments (spherical densitometer and a 30? photocanopyometer) for this purpose and discarded the first due to low accuracy and poor regression with SWE.  Bunnell & Vales (1990) reviewed the use and measurement of forest cover in studies of snow-canopy interactions.  Novel remote sensing-based forest structure metrics potentially applicable to snow process modeling are explored in Section 3.3 of this thesis (Varhola et al., 2010a).     26  1.3 Mountain pine beetle and its effects on water resources  Lodgepole pine forests of British Columbia have been affected for more than a decade by a widespread infestation of MPB that is considered the largest ever recorded in North America (Kurz et al., 2008), involving a cumulative area of more than 180,000 km2 (British Columbia Ministry of Forests Lands and Natural Resource Operations, 2013).  As the data for this the-sis were acquired within the MPB-infested interior plateau of British Columbia, it is essential to understand how MPB affects the structural and physiological characteristics of forests and how those changes can potentially impact hydrologic responses in this area.  Following initial beetle attack, individual trees undergo gradual defoliation (3 ? 5 years), branch loss (10 ? 15 years) and blow-down (5 ? 15 years) (Mitchell & Preisler, 1998).  Dur-ing the green-attack phase, trees show signs of MPB on the bark but retain green or yellowish foliage.  This is followed by the red-attack stage, where the needles turn reddish brown in the canopy.  The final stage, grey-attack, occurs once the needles fall to the ground.  Canopy fad-ing during this defoliation process is highly variable between individual trees and climatic conditions, resulting in overlapping attack stages in the same stand and among regions (Wulder et al., 2006).  The outbreak in British Columbia added structural complexity to the landscape by initially affecting mature stands, followed by medium-aged forests ?an infes-tation pattern that, at the time this research took place, resulted in a mosaic of mature grey-attack, medium-aged red-attack, unattacked small-diameter stands, and salvage logging cle-arcuts.    27  Previous studies show that considerable hydrologic impacts are likely to occur under these conditions.  During the late 1970s, a MPB outbreak in Jack Creek, Montana, led to 35% pine mortality and resulted in a 15% increase in annual water yield in the watershed, 10% increase in low flows and early snow melt.  Examples from Colorado, Montana and Wyoming provide comparable results:  increased annual water yield by 11 - 28%, increased monthly low flows by 10 - 32%, increased monthly high flows by 14 - 52%, and evidence of increased instanta-neous peak flows (Uunila et al., 2006).    In British Columbia, studies have found evidence of an increase in snow accumulation and ablation rates at the site level in stands with severe pine mortality caused by MPB (Teti, 2008; Boon, 2009; Winkler et al., 2010).  Higher peak SWE in beetle-attacked stands is mainly related to a reduction of the snow interception capacity of defoliated canopies (Winkler et al., 2012), while enhanced melt is the result of increases in the radiative energy that reaches the snow surface due to less sunlight blockage and longwave radiation inputs from fallen needles (Boon, 2009; Pugh & Small, 2011; Winkler et al., 2012).  However, it is still difficult to generalize the quantitative effects of MPB on snow accumulation and abla-tion because stand-level experiments have been subject to inter-annual variations in meteor-ology and snow patterns, and were based on paired-plot comparisons rather than long-term observations in permanent plots as defoliation and tree fall progressed (Boon, 2007, 2009, 2011; Varhola et al., 2010a; Winkler et al., 2012).  Due to the same difficulties associated with short-term records, potential changes in water yield, magnitude and frequency of peak flows in large watersheds (> 100 km2) affected by the insect remain uncertain (Bewley et al., 2010; Pugh & Gordon, 2012).  Extensive insect infestations can affect other elements of hy-28  drologic responses, such as evapotranspiration (Maness et al., 2012) or water quality (Clow et al., 2011).  However, this thesis is focused on snow accumulation and ablation and is hence limited to the analysis of forest structure because potential changes in evapotranspira-tion caused by MPB tree mortality in the study area are more closely related to out-of-scope stand-level physiological aspects.     29  2 Study area and available data  This chapter describes the data acquired and applied throughout the thesis, except for Section 3.2 which is based on information retrieved from the literature.  Specific procedures regard-ing how the data described below were used and processed are explained in each section.  2.1 Study area  Figure 2.1.1.  Study area within British Columbia; black transects indicate ALS data collec-tion.  This research took place in central British Columbia, Canada, near the cities of Quesnel and Vanderhoof (Figure 2.1.1).  Most of the data was specifically acquired at two sites within this wider area, namely: the Baker Creek watershed, west of Quesnel, and a small area 40 km south of Fraser Lake.  For a decade, this region has been affected by an outbreak of MPB that significantly changed the landscape by defoliating and killing large continuous forests of lodgepole pine, the dominant species, which are commonly accompanied by white spruce 30  (Picea glauca) individuals or small stands.     -15-10-505101520253001020304050607080Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov DecTemperature (?C)Precipitation (mm)Snowfall (mm)Rainfall (mm)Daily mean temperature (?C)Daily maximum temperature (?C)Daily minimum temperature (?C)Figure 2.1.2.  Mean monthly temperature and precipitation data for the Quesnel station, rep-resentative of the study area (ID 1096630, elevation 545 m) (adapted from Environment Canada, 2013).  The interior plateau of British Columbia is characterized by cold, dry winters with snow cover for up to seven months every year; snow melt constitutes a main source of water during spring and is also associated with annual peak streamflow (Bewley et al., 2010).  The climate is similar in Baker Creek and Fraser Lake, with mean temperatures ranging from around ?9?C in January to 17?C in July and annual precipitation averaging 540 mm, 28% of which falls as snow (Environment Canada, 2013).  Temperature and precipitation monthly means averaged from daily values for the 1971 ? 2000 period are presented in Figure 2.1.2.  Baker Creek?s topography, representative of the region, is relatively flat, with elevations ranging between 480 ? 1530 m but mostly consisting of a large internal plateau.  Since the physical processes that govern snow accumulation and ablation are highly sensitive to changes in for-est cover, the impacts of forest disturbance on hydrologic regimes has recently been under 31  intensive research in British Columbia (Uunila et al., 2006; Teti, 2008, 2009; Boon, 2009; Coops et al., 2009; Varhola et al., 2010a; Bewley et al., 2010).  2.2 Airborne laser scanning and high-resolution aerial photography  ALS data were acquired during sunny and clear conditions on February 19, 2008 by Terra Remote Sensing (Sidney, British Columbia) using the TRSI Mark II discrete return sensor mounted on a Bell 206 Jet Ranger helicopter platform flying at a height of ~800 m above ground level.  This LiDAR sensor has a wavelength of 1,064 nm and was configured with a pulse repetition frequency of 50 kHz, maximum off-nadir scan angle of 15 degrees, and a fixed beam divergence angle of 0.5 mrad.  Ground and non-ground returns were separated by the vendor using Terrascan v 4.006 (Terrasolid, Helsinki, Finland).  A 200 km ? 400 m ALS transect was acquired over the ground plots in four separate sections, as shown in Figure 2.1.1, with a resulting average foot-print size of 0.35 m and an average effective density of 4.8 returns/m2.  High-resolution (15 cm) aerial photography was taken simultaneously with the ALS surveys.  ALS ground and non-ground returns were separated with the filtering algorithm by Kraus and Pfeifer (1998) used in FUSION? software (McGaughey, 2010), and ground points were rasterized into a 5 m digital elevation model (DEM) from which plot elevations and canopy metrics were later obtained.  The DEM?s spatial resolution was detailed enough to capture the terrain details in this flat study area.  32  2.3 Landsat  A Landsat 5 TM scene of the study area from August 4, 2008 (sun elevation and azimuth were 50.4? and 147.7? respectively) was acquired from the United States Geological Survey (USGS). This summer image, chosen to avoid snow reflectance, had the lowest cloud cover (5%), highest quality close to ALS acquisition, and was ortho-rectified by USGS (error ~4.3 m).  At-surface reflectance atmospheric correction was undertaken based upon the COST model (Chavez, 1996), which estimated the effects of absorption by atmospheric gases and Rayleigh scattering and removed systematic atmospheric haze.  2.4 Hemispherical photography  Hemispherical photography (HP) is a technique commonly used to characterize forest struc-ture.  It consists of a digital photographic camera with an upward-looking fisheye lens that captures an image covering a semi-sphere.  For this thesis, optical hemispherical photographs were taken inside sample ground plots in specific points of a squared grid or cross, depending on plot design (Section 2.7).  The images were captured by Teti (2008), Bewley et al. (2010) and specifically for this thesis in the summer of 2008.  In all cases, images were acquired with a Nikon Coolpix 4500 digital camera with a Nikkor FC-E8 auxiliary fisheye lens (view angle = 183?) mounted 110 cm above the ground as specified by Teti (2008).  Although it is recommended to capture HP during overcast skies in order to favour maximum contrast with the canopy elements (Frazer et al., 2001), these ideal conditions are rarely present in central British Columbia.  To prevent sunlight from directly hitting the lens, a small shading paddle 33  was used which was later eliminated from the images by careful retouching.  Although the sampling points were registered by a Global Positioning System (GPS) with differential cor-rection, the exact location of the optical camera when acquiring the HP still contained some error and thus the maximum estimated deviation between each sampling point and the actual corresponding camera position was approximately 1.5 m.  2.5 Weather stations  Seven automatic weather stations (AWS) were installed in Baker Creek in June, 2007, as ex-plained in detail by Bewley et al. (2010).  Using multiple sensors, these AWS were able to record rainfall, snow depth, air temperature, relative humidity, wind speed, incoming short-wave and longwave radiation at hourly intervals.  2.6 Ultrasonic snow depth sensors  Part of this thesis consisted in the development and assembly of prototype ultrasonic range sensors with the objective of accurately measuring continuous changes in snow depth in mul-tiple sites at a low cost.  Section 3.4 is specifically dedicated to describe these devices in de-tail and validate their measurements, while Section 3.5 explains how their data were used.  The installation and decommission procedures are explained in Section 3.4.3.   34  2.7 Ground plot overview: forest inventories and snow surveys  Ground plots are an essential component of this research.  They provide forest structure data to calibrate and validate remotely-sensed metrics, a detailed description of stand-level attrib-utes such as MPB-infestation status, and constitute the fundamental unit of snow measure-ments.  This thesis takes advantage of plots pre-established in the study area by Teti (2008) and Bewley et al. (2010) and additional plots installed for this research to broaden the exist-ing information (Varhola et al., 2010a).  This section describes the generalities about the in-stallation and measurements common to all plots.  However, since different sections use dif-ferent combinations of plots given their specific purposes, the corresponding relevant infor-mation is detailed in each methodological section as needed.  The plots installed by Teti (2008) and Bewley et al. (2010) during the summer of 2007 corre-spond to permanent 2,500 m2 squares (50 ? 50 m) where 36 individual stakes separated 10 m between them in a grid were used as sampling points for snow surveys and hemispherical photos (Section 2.4).  Additional plots installed by Varhola et al. (2010a) (Section 3.3) one year later were 50 ? 50 m crosses aligned according to cardinal points with sampling points separated 5 m in each axis, also to indicate the locations for snow survey and hemispherical image collection.  The entire network of plots was designed to represent the wide variety of forest stand types of the study area, and ALS transects overlapped with most of this network (Section 2.2).   The specific plot locations and characteristics are provided in each section.  Table 3.5.1 shows the distribution of all of the available plots according to elevation above 35  sea level and forest stand characteristics, while Table 3.5.2 indicates the number of plots with different sources of information.  Two sets of data were collected at each plot:  traditional forest inventory metrics and periodic snow surveys.  Inventory surveys were conducted between the summers of 2007 and 2008 in each of two or four circular sub-plots with an area of 100, 200, 400 or 800 m2 (depending on pre-assessed variability and estimated stem density aiming to capture between 20 and 50 trees per plot).  Diameter at breast height (DBH) was measured in all trees with a diameter greater than 4 cm; species and defoliation condition (green, red, grey; see Section 1.3) were recorded.  Within each circular sub-plot, height was measured in a sub-sample of up to 20 trees that adequately represented the overall DBH frequency distribution.  Calculated pa-rameters included stems per hectare by species and condition (n/ha), mean DBH (cm), basal area (m2/ha), mean tree height (m) and basal area-weighted mean height (m) (referred to as Lorey?s height).  Finally, the percentages of basal area subject to MPB green, red and grey attacks (Section 1.3) were estimated for each plot.  In all plots, field campaigns were conducted to measure snow depth in each set of sampling points to adequately represent its average spatial distribution.  Snow depths were transformed to SWE by averaging a subset of density measurements collected with a standard snow tube (Varhola et al., 2010a; Bewley et al., 2010) or sample pits (Teti, 2008).  In most of the plots, surveys aimed to capture SWEmax close to April 1 and estimate SWE at least one time during the ablation period in the springs of 2008 and 2009.  Details about snow measurements are provided by Teti (2008), Bewley et al. (2010) and Varhola et al. (2010a) (Section 3.3).36  3 Empirical snow-vegetation models  3.1 Introduction and chapter overview  Simple snow models have been developed to facilitate the estimation of two basic snow indi-cators:  peak SWE (SWEmax) prior to the onset of spring melt ?representing total snow ac-cumulation? and SAR from the time of peak SWE occurrence to snow disappearance.  Gen-erally, empirical models predict SWEmax or SAR in forested sites as a function of observed snow measurements in a nearby open site and forest structure metrics (e.g. Kuz?min, 1960; Pomeroy et al., 2002; Winkler & Roach, 2005; Winkler & Moore, 2006).  They operate at the plot level and are designed for three main objectives:  identify the most important drivers of snow processes, predict SWEmax or SAR locally if their variation is substantially explained by statistically-significant predictors, and/or assist in the development of more sophisticated physical models.  The predictive power of empirical models and their applicability to larger areas can be im-proved by revising and incorporating new predictors, by measuring both response and predic-tor variables more accurately, and by expanding the spatio-temporal reach of datasets and experimental designs.  Using an open/forest paired-plot approach, Winkler (2001), Winkler & Roach (2005) and Winkler & Moore (2006) showed that the variability of relative differ-ences in SWEmax and SAR in forested plots of south-central British Columbia can be ex-plained by ground-based metrics, with r2 ranging from 0.3 (Winkler & Moore, 2006) to up to 0.96 in exceptional cases (Winkler & Roach, 2005).  However, it was suggested that the 37  physical drivers of snow processes might be more consistently correlated to variables better representing crown size and distribution, such as leaf area or gap fraction, which were not obtained by these studies.    Remote sensing technologies such as ALS can provide new forest structural metrics that might be better linked to the physical processes that govern snow dynamics, but the use of this technology to directly improve snow?vegetation models is in its very early stages (e.g.  Varhola et al. (2010a), Section 3.3).  Besides ALS, other sources of forest metrics can be used to develop empirical snow models. These include HP (e.g. Rich, 1990) ?widely used to parameterize physically-based hydrologic models? and satellite-derived spectral indices (e.g. Wang et al., 2010).  The relationships between the latter and snow indicators have not been widely explored but may be useful for practical purposes, given that spectral indices are easy to acquire worldwide (e.g. by Landsat TM).  The study by Winkler (2001) obtained SWEmax and SAR from traditional manual snow sur-veys.  As novel forest structure metrics better related physically to snow processes have the potential to improve empirical snow models, so do more accurate estimates of snow indica-tors.  Estimating SWEmax and SAR solely from discrete manual snow surveys introduces sev-eral sources of error summarized in Section 1.2.9, which are primarily related to difficulties in capturing the exact moments of SWEmax and snow disappearance since site visits are gen-erally infrequent.  Continuous ?daily or sub-daily? measurements of snow depth or SWE through an entire snow season are achievable with the use of lysimeters, snow pillows or ul-38  trasonic range sensors, but their high costs and issues associated with deployment and power-ing in forested sites have limited their more widespread use.  To overcome this constraint, Section 3.4 (Varhola et al., 2010c) describes the development the Low-Cost Ultrasonic Sensor (LOCUS) and successfully tested 48 units in research sites close to Quesnel and Fraser Lake (Section 2.1).  These sensors are stand-alone, battery-powered and inexpensive, making them ideal to monitor snow dynamics in a wide range of sub-canopy conditions.  Ultrasonic range sensors can provide continuous and accurate meas-urements of snow depth by recording the distance from the sensor to the snow and subtract-ing it from height above bare ground.  SWE can then be derived from snow depth by interpo-lating measurements of snow density or applying time-based algorithms (e.g. Verseghy, 1991).  This chapter consists of a number of studies aiming to develop and improve simple empirical snow models by progressively incorporating remotely-sensed variables.  Section 3.2 collects historic data from the published literature reporting measurements of peak SWE and/or SAR in plots where forest structure was numerically evaluated.  The section also introduces the methodology required to standardize data from multiple sources, which is required in the subsequent sections.  Section 3.3 directly correlates ALS-derived novel metrics with snow indicators and compares the quality of these relationships with those based on traditional in-ventory metrics collected in a small sample of plots.  Section 3.4 introduces the ultrasonic snow depth sensors developed for this thesis to improve the accuracy of peak SWE and SAR ?the independent variables in empirical models? estimation.  Section 3.5 broadens and in-39  tegrates the previous analyses by utilizing all of the plots and snow data to examine the corre-lations between a suite of standardized snow indicators and all of the forest metrics available in the plots (structural and spectral, remotely-sensed and ground-based).  Such a comprehen-sive analysis about the use of novel remote sensing metrics in simple empirical snow models has not been found in the published literature.  3.2 Meta-analysis of historical data to derive a simple empirical snow model  3.2.1 Introduction  The main objective of this section is to use meta-analyzed published data to generate empiri-cal models that could be used to predict the effects of forest cover change on snow processes, along with an estimate of the uncertainty associated with the prediction.  Such a model could become a valid operational tool for generating first-order estimates of forest-snow interac-tions, particularly over large areas with sparse weather data, where the application of proc-ess-based models may involve significant uncertainty.  This section has been published in Varhola et al. (2010b).  3.2.2 Empirical data review and compilation  Empirical studies have traditionally evaluated the effects of canopy cover on snow accumula-tion and melting using a paired-plot approach.  Open areas adjacent to the studied forest stands are the most common reference controls (e.g. Hendrick et al., 1971; Winkler & Roach, 40  2005), while fully stocked stands (with forest cover approaching 100%) are usually the base-line for the evaluation of the effects of thinning or harvesting (e.g. Wilm & Dunford, 1948; Woods et al., 2006).  Some studies include measurements of forest cover or describe forest structure in some way (basal area, volume, number of trees, etc.), while others only provide snow measurements for forests and controls without quantifying forest cover (Connaughton, 1935; Meagher, 1938; Haupt, 1951; Brechtel, 1970, 1979; Swanson & Stevenson, 1971; Brechtel & Balazas, 1976; Brechtel & Scheele, 1981; Schwarz, 1982; Troendle et al., 1988; Felix et al., 1988).  Many of these experiments have been designed to isolate the effects of one or several of the sources of variation mentioned above; however, their results have not been integrated and standardized to explore the possibilities of developing a global model suitable not only for making usefully accurate predictions but also quantifying the uncertain-ties in the predictions.  As a first step, previously published results were reviewed to select studies appropriate for inclusion in the meta-analysis.  Only studies sharing reasonably compatible methodological procedures and experimental designs were considered prior to building a central database, although it is certain that such an integration involving several decades of research inevitably introduces an unknown additional magnitude of error to any analysis.  To ensure supplemen-tary consistency for the statistical modeling, only datasets explicitly presenting numerical indicators of forest cover, snow accumulation and/or ablation in nearby locations were con-sidered.    Thus, a total of 33 publications complied with these requirements and were sum-marized for this analysis (Table 3.2.1, Figure 3.2.1).  They included 65 different individual locations in Canada (26), the United States (24), Finland (12), Switzerland (2) and Germany 41  (2).  All the studies except 3 were fully based on conifer species, 13 of which were related to lodgepole pine.  Table 3.2.1.  List of studies used for empirical data relating forest cover to snow accumula-tion and melting. Source Area Site(s) Species Control descriptionAnderson & Gleason (1960) California Swain Mountain Experimental Forest, Onion Creek Red fir, white fir Fully stocked stand Anderson et al. (1958a) California Central Sierra Snow Laboratory Various conifers Fully stocked stand Anderson et al. (1976) California Central Sierra Snow Laboratory Red fir Fully stocked stand Berndt (1965) Wyoming Big Horn Mountains Lodgepole pine Fully stocked stand Berris & Harr (1987) Oregon Andrews Experimental Forest Douglas fir, western hem-lock Open area Bewley et al. (2010) British Columbia Baker Creek Lodgepole pine Open area Boon (2007) British Columbia Nechako Plateau, Vanderhoof Lodgepole pine Open area Boon (2009) British Columbia Fraser Lake Lodgepole pine Open area Davis et al. (1997) Saskatchewan BOREAS Southern Study Area Black spruce Open area D?Eon (2004) British Columbia Little Slocan Valley Lodgepole pine Open area Dunford & Niederhof (1944) Colorado Fraser Experimental Forest Aspen Open area Goodell (1952) Colorado Fraser Experimental Forest Lodgepole pine Fully stocked stand Hardy & Hansen-Bristow (1990) Montana Hyalite Creek Watershed Subalpine fir Open area Hendrick et al. (1971) Vermont Sleepers River Watershed Various species Open area Kittredge (1953) California Stanislaus National Forest Red fir Open area Kuusisto (1980) Finland Various Pine Open area Mayer et al. (1997) Germany Forstbezirk Schluchsee Spruce Open area McCaughey & Farnes (2001) Montana Tenderfoot Creek Experimental Forest Lodgepole pine Open area McCaughey et al. (1995) Montana Tenderfoot Creek Experimental Forest Lodgepole pine Open area Moore & McCaughey (1998) Montana Tenderfoot Creek Experimental Forest Various conifers Fully stocked stand Murray & Buttle (2003) Ontario Turkey Lakes Watershed Hardwood species Open area Pomeroy et al. (1998) Saskatchewan Waskesiu Lake, Prince Albert National Park Black spruce Assumed clearcut Pomeroy et al. (2002) Saskatchewan, Yukon Prince Albert Model Forest, Wolf Creek Research Basin Jack pine Open area Skidmore et al. (1994) Montana Gallatin National Forest Lodgepole pine Open area St?hli et al. (2000) Switzerland Erlenh?he, Br?ch Norway spruce, silver fir Open area Teti (2008) British Columbia Baker Creek, Fraser Lake, Mayson Lake, Rosita, Taseko, Moffat Lodgepole pine Open area Troendle & King (1987) Colorado Deadhorse Creek Subalpine forest Fully stocked stand Weitzman & Bay (1959) Minnesota Northern Minnesota Aspen Fully stocked stand Wilm & Dunford (1948) Colorado Fraser Experimental Forest Englemann spruce Fully stocked stand Winkler & Moore (2006); Winkler (2001) British Columbia Upper Penticton Creek Lodgepole pine Open area Winkler & Roach (2005) British Columbia Upper Penticton Creek Lodgepole pine Open area Winkler et al. (2005) British Columbia Mayson lake Lodgepole pine Open area Woods et al. (2006) Montana Tenderfoot Creek Experimental Forest Lodgepole pine Fully stocked stand   For each study, the following additional parameters were compiled:  year(s) of experiment, forest species, elevation above sea level (m), latitude and longitude, forest structure variable 42  used in the analysis and type of reference control (either open sites or fully stocked stands).  Information on the average climate was based on the following variables:  historic mean temperature (?C), historic winter mean temperature (?C) (average of December-March mean temperatures), historic March-April mean temperature (average of March and April mean temperatures) (?C), historic total annual precipitation (mm), historic winter precipitation (mm) and historic March-April precipitation (mm).  The data, as well as elevation for each site, were extracted from the WorldClim database (http://www.worldclim.org), a global 1 km-resolution geographic raster dataset providing climatic data representative of 1950 ? 2000 (Hijmans et al., 2005).    Figure 3.2.1.  Distribution of relevant studies according to location (left) and decade (right).  BC = British Columbia (Canada); MT = Montana (USA); CA = California (USA); CO = Colorado (USA); other Canadian provinces in-clude Saskatchewan, Ontario and Yukon, while other USA states include Wyoming, Oregon, Minnesota and Vermont.  3.2.3 Data standardizing  In order to ensure consistent comparisons of the snow accumulation and melting, observa-tions were normalised to a percentage relative to a reference site.  This normalisation isolates the influence of inter-annual and inter-location variability in snowfall magnitude.  The fol-lowing equation was applied for this purpose: 43   x Ry 1R?? ?? = ?? ?? ? 00                   3.2.1  where ?y is the change in the variable of interest (%), x is the value of the variable in a spe-cific site, and R is the value of the same variable in a nearby reference site.  Since this refer-ence (R) represents either an open area or a fully stocked stand, ?y can be negative or posi-tive as snow accumulation and ablation are usually higher in open areas than in forests.  Each value for ?y was paired with the corresponding value of change in forest cover.  These changes were assigned negative values of forest cover in studies using fully stocked stands as references, and positive values in studies using open areas.   Overall, the 33 studies provided 234 observations reporting snow accumulation and forest cover, and 110 observations for snow ablation.  3.2.4 Statistical analysis  First, simple correlation matrices were examined to assess the relationship between the rela-tive snow accumulation and ablation with forest cover and the other site variables.  Pearson correlation coefficients (r) and significance levels (p) were used to determine the strength of the correlations.  44  Second, simple linear regression was used to relate the forest cover variable to the snow ac-cumulation and ablation observations.  The purpose of fitting simple linear models from the data is to provide an empirically-based tool to estimate relative changes in snow accumula-tion and ablation derived from changes in forest cover.  These empirical models are useful for establishing a general relationship between the variables, and are readily applicable given that only a gross average change in snow accumulation or ablation is required (e.g. for multi-site and/or multi-temporal studies in which it can be assumed that sources of variation other than forest cover compensate each other when modeling snow processes).  The models are not applicable to make accurate predictions under specific conditions.  Two assumptions were made prior to fitting the models:  that the relationship between forest cover and snow accumulation and ablation is linear (i.e. a reduction of forest cover from 70% to 50% has the same effect as a reduction from 50% to 30%), and that the use of fully stocked stands as a reference (i.e. reduction in forest cover) provides the same ?but mirror-imaged? results as using open areas as references (i.e. increase in forest cover).  The null hypothesis of linear regression, stating that there is no relationship between the variables, was tested with F tests and rejected when p < ? (? = 0.05).  Since a 0% change in forest cover should result in a 0% change in either snow accumulation or melting, the regression models did not include an intercept.    Multiple linear regression was then applied to include the geographic and climatic variables described in Table 3.2.2.  Variables were added in a stepwise procedure, where all possible combinations for each step were generated automatically.  Models that showed the best im-45  provements in coefficient of determination (R2) compared to the simple linear model were subject to further analysis: t-tests were performed in order to reject or accept the null hy-pothesis stating that each variable is not significant given the presence of other variables (with ? = 0.05).  Non-significant variables and those showing variance inflation factors larger than 30 were dropped, one at a time, and the analysis was redone with the remaining vari-ables until all complied with these requirements.    Table 3.2.2.  Description of variables used in modeling. Code Units Description AC % Change in snow accumulation AB % Change in snow ablation FC % Change in forest cover ELEV m Elevation above sea level LAT ? Latitude MTEMP ?C Mean temperature WTEMP ?C Winter temperature (Dec, Jan, Feb, Mar) ATEMP ?C Ablation temperature (Mar, Apr) PP mm Total annual precipitation WPP mm Winter precipitation (Dec, Jan, Feb, Mar) APP mm Ablation precipitation (Mar, Apr)   Validation of the models was performed by the method described by Kutner et al. (2005), which involves running the regression with all but one record for n times, where n is the number of observations.  The similarity between the sum of squares of the error (SSE) from this procedure and the SSE for the model using all data reveals a good performance of the model with independent observations.  Both simple and multiple linear models were subject to analysis of residuals.  Shapiro-Wilk, Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling tests were applied to test for deviations from normality of the residuals.  In these tests, the null hypothesis assumes that the residuals are normally distributed and is re-jected when p < ?.  White?s test (White, 1980) was applied to test for deviations from homo-46  geneity of error variances (null hypothesis states homogeneity and is rejected when p < ?, where ? was set to 0.05 for all tests).  Finally, these multivariate models were examined to confirm that the fitted coefficients were consistent with physical processes (e.g. checking if an increase in temperature would result in a higher change in melting).  3.2.5 Results  3.2.5.1 Correlations  The correlation matrix between site variables and snow accumulation and ablation is pre-sented in Table 3.2.3.  For both changes in snow accumulation and melting, forest cover is the most highly correlated variable, providing the strongest and most significant correlations.  Elevation was the second best potential predictor of snow accumulation, with a positive cor-relation supporting the assumption that the differences become smaller in forested and non-forested sites at higher sites.  Elevation also had a significant positive correlation with changes in snow ablation, showing that at higher altitudes the differences between melting in the forests and clearcuts become smaller.  The correlation between latitude and snow accu-mulation suggests that at higher latitudes the absolute differences in snow accumulation in forests and open sites increase, possibly due to higher incidence of sublimation.   These dif-ferences also become larger for snow ablation as latitude increases, indicating that ablation is more synchronous in lower latitudes.  This is likely due to an increased predominance of sen-sible heat fluxes as a driver of snow melt as latitude decreases.  Of all the extracted tempera-ture indicators, only winter mean temperature was significantly correlated to snow accumula-47  tion: absolute differences between forests and open sites are reduced in warmer locations.  The same occurs with SAR.  March-April precipitation was significantly correlated to both snow accumulation and melting.  Table 3.2.3.  Correlation coefficients (r) between independent variables and snow accumula-tion and ablation. Variable Snow accumulation (n = 234) Snow ablation (n = 110) Forest cover -0.76*** -0.85*** Elevation 0.42*** 0.53*** Latitude -0.37*** -0.65*** Mean temperature 0.10 0.10 Winter mean temperature 0.22** 0.24* March-April mean temperature 0.01 -0.18 Total annual precipitation 0.05 0.19* Winter precipitation 0.11 0.34*** March-April precipitation 0.20** 0.44***  * p < 0.05; ** p < 0.01; *** p <0.001   Figure 3.2.2 presents the relation between change in forest cover and change in snow accu-mulation and ablation.  Despite the scatter, there is a clear trend for both snow accumulation and ablation to decrease as forest cover increases.  The studies show maximum absolute changes in snow accumulation and ablation of up to 75% and 110% respectively.  Figure 3.2.2 also highlights that the majority of studies used clearcuts as a reference (positive change in forest cover).  Figure 3.2.3 shows the correlation trends between snow accumulation and elevation, latitude and representative variables of temperature and precipitation.  The same information is pre-sented for snow ablation in Figure 3.2.4.  48    Figure 3.2.2.  Compilation of results showing change in snow accumulation (top) and abla-tion (bottom) according to change in forest cover.      Figure 3.2.3.  Correlations between snow accumulation and representative geographic and climatic variables. 49    Figure 3.2.4.  Correlations between snow ablation and representative geographic and cli-matic variables.  3.2.5.2 Simple regression  The two simple linear models fitted from the data described in Sections 3.2.2 and 3.2.3 are:  AC = b?FC          3.2.2  AB = b?FC          3.2.3  where AC = predicted change in snow accumulation (%), AB = predicted change in snow ab-lation (%), b = fitted regression slope and FC = change in forest cover (%).  The results of 50  the simple linear regression, including the value for parameter b, are shown in Table 3.2.4, while the fitted equations are illustrated with the data on Figure 3.2.5.    Table 3.2.4.  Results of simple linear regression. Equation Analysis of variance Parameter estimates n F p > F r2 Adjusted r2 b b 95% upper limit b 95% lower limit SE t p > t 3.2.2 234 539.4 < 0.0001 0.698 0.697 ?0.396 ?0.361 ?0.431 0.017 -23.23 < 0.0001 3.2.3 110 352.5 < 0.0001 0.717 0.714 ?0.536 ?0.472 ?0.599 0.032 -16.60 < 0.0001      Figure 3.2.5.  Simple linear models relating changes in forest structure to changes in snow accumulation (left) and ablation (right) (Equations 3.2.2 and 3.2.3 were fitted using the data in the figures).   51  For both models, normality tests for residuals did not indicate significant deviations from normality, with p ranging from 0.15 to 0.28 for all four tests in the case of Equation 3.2.2, and from 0.07 to 0.15 for Equation 3.2.3 (p < 0.05 was required to discard normal distribu-tion of the residuals).  Homogeneity of variance was also confirmed for the residuals of Equation 3.2.2 and 3.2.3, with p = 0.26 and 0.24, respectively.  Predicted vs. observed values are shown in Figure 3.2.6.  Validation of the models was successful, with SSE from the leave-one-out procedure (Kutner et al., 2005) differing from the SSE including all data by only 0.7% for Equation 3.2.2 and 2% for Equation 3.2.3.   Figure 3.2.6.  Observed vs. predicted snow accumulation (left) and ablation (right) for sim-ple linear models.  Other studies have also fitted simple models relating snow accumulation with forest cover.  Two models presented by Pomeroy et al. (2002) and one by Kuz?min (1960) were adapted to be expressed in the same form as Equations 3.2.2 and 3.2.3.  The models by Pomeroy et al. (2002), originally using LAI as independent variable, were transformed to use forest cover instead of LAI with the equation provided by the same author:  52  Cc = 0.29?ln(LAI) + 0.55              3.2.4  where Cc = forest cover (%) and LAI = leaf area index.  The resulting equations were:  FC 0.55AC 1 0.144 0.2230.29?= ? ? +  (Pomeroy et al., 2002)           3.2.5  FC 0.55AC 1 0.125 0.2370.29?= ? ? +  (Pomeroy et al., 2002)         3.2.6  AC = 1 ? 0.37*FC (Kuz?min, 1960)                    3.2.7  In order to assess the similarity of the developed model (Equation 3.2.2) with those by Kuz?min (1960) and Pomeroy et al. (2002), the equations were plotted together in Figure 3.2.7.  The four linear models linking forest cover to snow accumulation are similar, showing a maximum difference of 10% in snow accumulation prediction when change in forest cover equals 100 or ?100%.  Equation 3.2.5, in particular, shows higher differences than the other snow accumulation equations as forest cover approaches these values.  The differences be-tween the models are mainly due to the use of different datasets to derive their parameters, especially in the case of the Kuz?min equation, developed in Russia (Pomeroy et al., 2002).    53   Figure 3.2.7.  Comparison of simple linear models (Pomeroy et al., 2002; Kuz?min, 1960) predicting effects of forest structure on snow accumulation.  3.2.5.3 Multiple regression  The poor correlations between snow accumulation and melting with variables other than change in forest cover (Table 3.2.3) prevented the development of multi-variable models.  In general, the inclusion of geographic and historic climatic variables did not significantly im-prove the regression coefficients.  R2 values only increased marginally (by up to 0.03) when more variables were added to the simple linear model based on forest cover changes.  The resulting multivariate models that complied with the assumptions of regression did not show logical physical meaning and were difficult to interpret, suggesting that neither the data, nor the model structure, were appropriate for the purpose of obtaining valid snow accumulation and melting models of intermediate complexity from the variables analyzed.  Testing empiri-cal models with different structures is not in the scope of this research because it would also require an improvement in the original dataset.  54  3.2.6 Discussion  The results of this review confirm that the relationship between snow accumulation and melt-ing with forest cover is strong and significant but complex and highly variable.  The confi-dence limits shown in Figure 3.2.5 indicate that despite the dispersion of the data, the sample size was large enough to locate the regression lines with certainty, and therefore the general inferences made with regard to the relationship between forest cover and snow accumulation and ablation have a solid basis.  However, the prediction limits indicate that observed per-centage changes can differ from predicted values by up to 30% to 40% at a 95% confidence level. Therefore, caution is required when analyzing individual records.  Of particular con-cern is that several show behaviour opposite to the general trend.  For example, stands with up to a 70% increase in forest cover still led to an increase in snow accumulation.  A similar case is observed for snow ablation, thus demonstrating that snow interception, sublimation and energy balance could often be governed by variables other than forest cover, or possibly that measurement errors can obscure the effect.  Since the majority of the studies of the data-set took place in the cold, dry areas of the interior of North America, where interception and sublimation dominate, data dispersion is not attributable to significantly different geoclimatic conditions.  A combination of the many factors discussed in Section 1.2 is a better explana-tion for the variability observed in Figure 3.2.2.  Given that most of the studies do not pro-vide specific information about those factors, it is not possible to isolate their influence in a statistical model.  55  The development of the two simple regression models for the estimation of changes in snow accumulation and melt with changes in forest cover over such a wide range of sites confirms the strong universal relationship between these factors. To apply these models at new sites requires the absolute value of snow accumulation in a reference site (either a fully stocked stand or an open area) to be known as well as an expression of forest cover.  The simple lin-ear snow accumulation model (Equation 3.2.2) was consistent with similar models found in the literature, suggesting that no significant improvements can be achieved by this approach.  Equation 3.2.2 has a conceptual advantage when compared to the simple models presented by Kuz?min (1960) and Pomeroy et al. (2002) because it intercepts the origin (i.e. 0% change in forest cover = 0% change in snow accumulation).  However, all these simple models are not capable of accurately predicting snow accumulation and ablation under specific condi-tions, and are only useful to obtain general average estimations.  The inclusion of general geographic and historic climatic parameters failed to provide greater predictive power.  One of the reasons for the relatively poor relation between snow processes and these variables is the repetition of values within the same location.  Several studies pro-vided multi-temporal results of snow accumulation and/or melting that had to be linked with unique values of elevation, latitude, temperature and precipitation.  If studies had provided detailed climatic information for the actual years of the experiments, it may have been possi-ble to generate a more accurate model, given the known dependence of forest-snow interac-tions on the characteristics of snow storms and weather conditions during melt periods.  Fu-ture empirical studies should therefore provide detailed information such as accurate coordi-nates, elevation, aspect, slope and reference clearcut size.  Ideally, detailed measurements of 56  temperature and precipitation during the monitoring periods should also be recorded.  This review shows again how important metadata are in order to use collected information for later analysis.  Furthermore, inclusion of such information would allow the data to be used in modeling studies.  Evidence shows that the interaction of the many factors adding variability to the snow proc-esses ?snowfall, interception, sublimation, accumulation, redistribution and melting? is too complex to be modeled, even by physically-based equations.  In fact, Rutter et al. (2009) evaluated 33 snowpack models of a wide range of complexity and purpose in forests and open sites of five locations of the Northern Hemisphere during two winter seasons.  They concluded that there is no universal best model that fits all the locations, and no consistency was found regarding general models? behaviour in open and forested sites.  Despite intensive measurements, many other studies have failed to fully explain the origin of the energy that leads to rates of snow evaporation that are significantly larger than expected.  This lack of closure of the energy balance shows how complex snow processes can be (Lundberg & Halldin, 2001).  It is not a surprise, then, that the simple historic empirical information com-piled in this review was only useful for fitting simple general linear models.  3.2.7 Conclusions  The main contribution of this section is the compilation of data from studies extending back to the 1930s and standardizing the results so that they could be subjected to meta-analysis.  This exercise provided two simple models able to predict changes in snow accumulation and 57  melting associated with changes in forest cover.  While the fitted relations were significant and the sample size was large enough to define the average trend with reasonable precision, there was substantial scatter, so that the models would not provide accurate predictions for particular cases.  Unfortunately, most studies did not deliver enough information so that other variables could be incorporated in the models.  Geographic and historic climatic variables were compiled from available data sources for all the sites, but their inclusion did not im-prove the fit of the models.  Further research exploring the relationship between forest cover and snow processes should aim to develop new experimental designs that measure as many sources of variability as pos-sible.  There is still a need for models of intermediate complexity that can be easily applica-ble to other areas by using simple additional variables such as elevation, latitude, aspect, slope, clearcut size and temperature.  These variables do not require special techniques or equipment to be measured, and yet no model was found in the literature that incorporates them to predict snow accumulation and melting.  An ideal situation for a multivariate ap-proach to be successful would require:  a) that the locations of all the studies be accurate enough so that microclimate factors could be retrieved; b) that current meteorological condi-tions (temperature, precipitation, radiation, etc.) at the moments during which the experi-ments took place were available rather than historic averages; c) that the authors of the stud-ies described in more detail the experimental sites and specific methodologies, especially to obtain topographic conditions such as aspect and slope which, despite being easy to measure, are rarely provided.  If this information would have been collected by all the studies, result-58  ing empirical models of intermediate complexity might be in a better position to compete with physically-based models.  Given that stream discharge is of ultimate interest to water resources management because it affects water availability, properties of drought and flooding events, stability of wildlife habi-tats, hydropower production, fisheries, and others, it is important for snow accumulation and ablation to be properly linked to the magnitude-frequency of low / peak flows at the water-shed level.  For this purpose, long-term time series of snow accumulation and ablation must be recorded so that their temporal (and not only spatial) variability can be assessed and com-prehensive frequency analyses can be conducted.    Empirical studies might continue to be important in the future for new research at larger scales and basins, where detailed parameterization of processes is unlikely to be successful given our current knowledge.  Authors in Hydrology and other disciplines are encouraged to provide as much information as possible in their experimental designs and publications to ensure better integration and meta-analysis in the future.   3.3 The influence of ground- and LiDAR-derived forest structure metrics on snow accumulation and ablation in disturbed forests  3.3.1 Introduction  This section investigates the relationship between ALS-derived metrics of forest structure and indicators of snow interception and ablation across a range of forest plots with varying 59  MPB infestation levels.  Given that it was concluded in Section 3.2 that differences in the procedures to measure forest structure among researchers may have introduced substantial sources of variations into the relationships between forest metrics and snow indicators, how much of that scatter would decrease if forest structure had been systematically estimated from ALS?   Analyzing vegetation?snow links at the plot level with this technology will pro-vide useful data for further evaluation of the impacts of forest structure changes on snow hy-drology at the watershed level.  This work was published in Varhola et al. (2010a).  3.3.2 Methods  3.3.2.1 Study area and field inventory measurements  A total of 11 plots (Table 3.3.1) were established in the Quesnel and Fraser Lake areas (Sec-tion 2.1) as explained in Section 2.7.  Two of the plots (CC1 and CC5) were located in recent clearcuts to serve as reference sites for snow accumulation and ablation in the absence of for-est cover.  Two plots were in stands under 15 years old (YR2, YR3) and one plot was in a 70 year old stand with a very high stem density (YR5).  The two young stands and the over-dense stand consisted of almost pure pine with DBH of 8 cm or less.  As such, they had vir-tually no MPB attack due the observed beetle?s preference for larger trees (the 25% grey in YR5 was inferred to be due to competition and snow damage).  One plot (RD1) corresponded to a medium-sized stand with slightly more than 50% of the basal area undergoing a red-attack stage.  The remaining five plots were located in stands predominantly affected by a grey-attack stage.  One of these (GY5) represented a medium-sized dense stand while the rest 60  (GY3, GY4, GY9 and GY10) were considered mature (see Table 3.3.3 for more plot details).  The number and distribution of the plots in the stand conditions described above was the best possible outcome given some cost and technical limitations.  Even though they were labelled based on their predominant MPB infestation stage to facilitate their identification, it is impor-tant to note that they represented a range of levels of infestation and complex forest structure conditions.  Table 3.3.1.  General plot information. Code1 Original code2 Reference clearcut Latitude Longitude Elevation (m) CC1 BCC - 52.637 -122.992 1,224 CC5 VCC - 53.722 -124.916 882 YR2 BRC1 CC1 52.670 -123.017 1,231 YR3 - CC1 52.691 -123.023 1,240 YR5 VYN CC5 53.718 -124.953 900 RD1 BRC2 CC1 52.672 -123.017 1,229 GY3 BOD3 CC1 52.638 -122.993 1,222 GY4 BOD1 CC1 52.676 -123.016 1,218 GY5 - CC1 52.696 -123.023 1,241 GY9 VOD2 CC5 53.718 -124.955 836 GY10 VOD1 CC5 53.720 -124.949 902  1 YR = small DBH; RD = stand with predominant red attack; GY = stand with predominant grey attack; CC = clearcut. 2 From previous studies (Teti, 2008; Boon, 2009).   Inventory metrics obtained for each plot, as explained in Section 2.7, included mean DBH, basal area, mean height, and Lorey?s height, and basal-area MPB infestation percentages in-volving green, red and grey categories (see Section 1.3).   3.3.2.2 Snow surveys  Six snow surveys were conducted as explained in Section 2.7 between late February and early May, 2008, in nine of the eleven plots, while two plots established later in the study to 61  strengthen the database (YR3 and GY5) were subject to four surveys from estimated peak accumulation at early April until early May.  The dates of the surveys were similar in all stands, varying only by one or two days.  Snow surveys provided plot-level averages of snow depth, snow density and SWE (see Section 2.7 for estimation procedures).  Two indicators of SWE accumulation were derived for each plot:  absolute peak SWE (maxi-mum SWE recorded among all surveys), and the SWE measured in early April. Absolute peak SWE is defined as the highest SWE measured among all the surveys in each plot, but it should be noted that due to the discrete nature of manual snow surveys, this does not necessarily correspond to the real absolute peak SWE.    SAR were calculated with the following equation:   P)SWESWE(SAR fi?=                                                             3.3.1   where SAR is in mm/day, SWEi is the initial SWE (mm), SWEf is the final SWE and P is the number of days between the measurement of SWEi and SWEf.  In this section, three ablation rate indicators were calculated by using absolute peak SWE, early April SWE and mid-April SWE as starting points (SWEi).  The last snow surveys in early May were used to obtain SWEf in all cases.  The ablation rate calculated between the last two consecutive surveys was as-sumed to be the maximum ablation rate because during this period the temperatures are likely higher and the melting curves are expected to be steeper than in the previous cooler periods.  62  3.3.2.3 ALS processing  Based on results reported by Bater & Coops (2009), a 1 m spatial resolution DEM was gen-erated by applying a natural neighbour interpolation algorithm to the ALS ground returns (Sibson, 1981; Sambridge et al., 1995).  The heights of vegetation returns above the snow (ground was covered by an average of 50 cm at the time) were computed by subtracting the DEM heights from the vegetation return heights.  A number of plot-level variables extracted from the LiDAR vegetation data were selected based on previous research demonstrating strong correlations with vertical structure and cover (e.g. Magnussen & Boudewyn, 1998; Gobakken & N?sset, 2005; Andersen et al., 2005) on the assumption that these variables would also be well correlated to the observed snow processes.  As a result, height percentiles (30, 60 and 90%) mean height, height stan-dard deviation; and Weibull ? and ? parameters [where ? provides a vertical scaling and po-sitioning factor for movement of the height distribution, and ? provides the capacity to in-crease or decrease the breadth of the distribution (Bailey & Dell, 1973; Xu & Harrington, 1998)] were calculated from the LiDAR returns within the same plot areas covered by the snow surveys (2,500 m2).  Finally, forest cover was also estimated at the plot level based on ratios between returns above 0.5 and 2 m from the surface and the total number of returns.  Because changes in survey configuration such as an increase in flying altitude may affect the number and distribution of multiple returns (Morsdorf et al., 2008; N?sset, 2009), only first echoes were used to estimate cover.  63  3.3.2.4 Statistical analysis  All the variables derived from ground assessment, LiDAR data and snow surveys are sum-marized in Table 3.3.2.    Table 3.3.2.  List of variables subject to correlation analysis with snow accumulation and ablation. Source Variable Units Ground Stem density n/ha Mean DBH cm Basal area m2/ha Mean height m Lorey?s height m Percentage of pine % Basal area of healthy trees m2/ha Basal area of red trees m2/ha Basal area of grey trees m2/ha Percentage of healthy trees (basal area weighed) % Percentage of red trees (basal area weighed) % Percentage of grey trees (basal area weighed) % Percentage of infested (red + grey) trees % Percentage of infested (red + grey) trees (basal area weighed) % LiDAR Mean height m Height standard deviation m Forest cover (> 0.5 m) % Forest cover (> 2 m) % Height 30% percentile m Height 60% percentile m Height 90% percentile m Weibull ? parameter - Weibull ? parameter - Snow surveys Absolute peak SWE mm Early April SWE mm Absolute peak ? early May ablation rate mm/day Early April ? early May ablation rate mm/day Maximum snow ablation (mid April ? early May) mm/day    The purpose of the statistical analysis was to determine which snow accumulation and abla-tion indicators showed the strongest correlations with forest structure metrics (derived from both LiDAR and ground data).  Thus, absolute peak SWE, early April SWE and the three ab-lation indicators described above were correlated to a total of 23 ground and LiDAR-derived 64  forest variables.  A matrix of Pearson correlation coefficients (r) and significance levels (p < 0.05 considered significant) was used to determine the strength of these relationships.  Due to the relatively small sample size of this study, this correlation analysis was considered an ex-ploratory rather than a conclusive tool.  3.3.3 Results  A standard forest inventory description of the plots is shown in Table 3.3.3, as well as the degree of MPB infestation expressed as the proportion of basal area affected by different at-tack levels (Figure 3.3.1).  The information of Table 3.3.3 reveals the high variability and complexity of the different stands represented by the plots, with densities that range from 550 to more than 7,000 stems/ha, mean DBH from 4 to 25 cm and a MPB infestation status that includes healthy young regeneration stands, mature plots with as little as 5% of the trees un-affected by the insect, and many intermediate conditions.    The uneven patterns of MPB infestation are evident as no stands, except for plot YR2 with 100% of healthy trees, show different combinations of trees in the three infestation catego-ries.  For example, a considerable proportion of trees have survived MPB attacks in stands like RD1 (48%), GY5 (27%) and GY10 (22%): evidence that the presence of the insect does not always lead to complete mortality of the stands.     65  Table 3.3.3.  Ground-based plot information (from data collected during summer 2007). Plot Inventory information Defoliation status* Trees (n/ha) Mean DBH (cm) Basal area (m2/ha) Mean height (m) Pine (%) GN (%) RD (%) GY (%) YR2 1,312 5.4 3.1 3.9 95 100 0 0 YR3 2,867 4.0 3.3 5.1 100 98 2 0 YR5 7,648 8.0 34.0 9.7 100 75 0 25 RD1 1,025 13.5 15.0 10.1 98 48 52 0 GY3 550 25.5 28.7 17.3 69 8 15 77 GY4 1,800 18.5 55.4 18.2 76 4 19 77 GY5 4,633 10.7 44.9 11.0 100 27 7 66 GY9 1,687 21.6 55.6 13.2 83 5 5 90 GY10 1,387 18.0 19.0 9.0 73 22 0 78  * GN = healthy; RD = red attack; GY = grey attack.  MPB distribution in % of total plot basal area including other species.      Figure 3.3.1.  Basal area per plot according to MPB attack stage (healthy, red, grey and other spe-cies not affected by MPB).  See Table 3.2.1 and Methods section for description of plots.  The snow accumulation and ablation rate indicators are shown in Table 3.3.4.  Snow accu-mulation and ablation were comparable in magnitudes among the two study areas, allowing the use of a single dataset to analyse absolute values.  Although early April surveys are con-sidered a standard in North America to evaluate snow accumulation, absolute peak SWE only occurred in that period in three of the eleven plots and took place earlier in the remainder.  The standard deviation of snow accumulation within plots showed a substantial spatial vari-66  ability of snow accumulation patterns, with coefficients of variation ranging from 10 to 28% in absolute peak SWE and from 10 to 46% in early April SWE.  Table 3.3.4.  Snow survey results in spring 2008. Area Plot Peak SWE (mm)* Mean ablation rates (mm/day) Absolute Early April Absolute peak ? early May Early April ? early MayMid April ? early May Baker Creek CC1 179 (36) 156 (25) 6.7 3.3 6.7 YR2 147 (37) 126 (59) 2.3 3.5 5.1 YR3 168 (47) 168 (47) 4.2 4.2 5.7 RD1 137 (25) 135 (30) 2.6 3.6 4.8 GY3 129 (23) 125 (36) 2.0 3.5 4.6 GY4 136 (22) 122 (23) 2.2 2.7 4.6 GY5 148 (19) 134 (17) 5.5 2.7 5.5 Vanderhoof CC5 172 (17) 158 (16) 2.9 4.8 5.7 YR5 133 (24) 123 (28) 2.2 3.6 4.3 GY9 150 (24) 150 (24) 4.4 4.4 4.9 GY10 149 (39) 149 (39) 4.4 4.4 4.7  * Standard deviation in parentheses.    As expected, the clearcuts were subject to greater peak SWE and ablation rates than the sur-rounding forested sites.  Figure 3.3.2 shows the percentage of absolute peak SWE in all the forested sites relative to their nearby clearcuts in descending order of relative snow accumu-lation.  After doing this comparison, forested plots showed reductions of snow accumulation ranging from 7 to 27% and reductions in ablation rates from 15 to 31%, which indicate the strong influence of forest cover in these processes.  The plot ranking of declining snow ac-cumulation was almost identical to that of snow ablation, evidence of tight links between both processes.     Changes in mean SWE estimated from the sequential snow surveys for some representative plots are shown in Figure 3.3.3.  In the Vanderhoof area, there was a smaller difference in 67  snow ablation during the melting period between the clearcut and the forested stands, while in Baker Creek the ablation curve of the clearcut was generally steeper than the other plots.  In Baker Creek as well as Vanderhoof, peak SWE was observed in different dates from early March to early April among the plots.  In Baker Creek, only the clearcut?s peak occurred in mid-April, just before maximum ablation, while forested sites showed the highest snow ac-cumulation earlier.  In Vanderhoof, the clearcut (CC5) and the dense stand (YR5) showed maximum peak in the early March survey, while it occurred in early April in the two grey stands.     Figure 3.3.2.  Absolute peak SWE and maximum ablation rate in forested plots relative to nearby clearcuts (which would represent 100%).  See Table 3.2.1 and Methods section for description of plots.   Plot level LiDAR variables are summarized in Table 3.3.5.  The differences between forest cover calculated using returns above 0.5 and 2 m were relatively small in most cases except for the two young regeneration plots (YR2 and YR3), where using returns above 2 m signifi-cantly reduces the indicator of forest cover.  This is logical considering the mean heights of 3.9 and 5.1 m respectively in these plots (Table 3.3.3).  The structural complexity of the plots, well captured by LiDAR-derived height standard deviations, is evident from resulting 68  coefficients of variations in the order of 20 to 60%.  A first comparison between the forest cover derived from LiDAR and ground-based variables expected to be highly correlated to forest cover (such as stem density or basal area), revealed a rather weak relationship between the two and points out that forest cover in this research is more likely driven by insect distur-bance.  For example, the 4,633 stems/ha of plot GY5 ?one of the highest densities in the dataset? were associated with one of the lowest values of forest cover.  YR5, on the other hand, which had the highest proportion of healthy trees among the mid-sized stands and more than 7,600 stems/ha, did show one of the highest values of forest cover.  These comparisons suggest that defoliation plays an important role in this forest structural attribute.    Figure 3.3.3.  Snow water equivalent in Baker Creek (left) and Vanderhoof (right) plots.  Overall, the average r2 of all ground-based variables and absolute peak SWE was 0.25, a value that is doubled to 0.51 with the use of LiDAR variables.  A comparable improvement occurs in the correlations with maximum snow ablation, showing an increase of average r2 from 0.20 (all ground-based variables) to 0.44 (LiDAR variables).  The selection of both ground-based and LiDAR variables with significant correlations with absolute peak SWE and 69  maximum ablation rate is shown in Table 3.3.6.  The other indicators of snow accumulation and ablation did not prove to be mostly explained by forest structure variables and were hence excluded from further analyses.  Absolute peak SWE and maximum ablation rate were most highly correlated with the LIDAR attributes, while only three of the fourteen ground-based variables showed the same potential.  Particularly strong were the correlations between forest cover (> 2 m) and both absolute peak SWE and maximum ablation rate.  Notably, all r values in Table 3.3.6 are negative and thus reveal, as expected, that an increase in both verti-cal (height) and horizontal (DBH, basal area, cover) stand attributes is associated with de-creases in snow accumulation and ablation.  Correlations between the forest structure vari-ables and absolute peak SWE were in general stronger than those with maximum ablation rate.   Figure 3.3.4 illustrates the relationship of the two variables with the highest correlation with absolute peak SWE and maximum ablation rate.  Forest cover was most highly corre-lated with both absolute peak SWE and maximum ablation rate, followed by 90% height per-centile and height standard deviation, respectively.     Table 3.3.5.  LiDAR-derived forest structure metrics. Area Plot Height stan-dard devia-tion (m) Forest cover > 0.5 m (m) Forest cover > 2 m (m) Height 60% percentile (m) Height 90% percentile (m) Baker Creek CC1 0.0 0.0 0.0 0.0 0.0 YR2 0.6 19.1 2.8 1.7 2.6 YR3 0.4 24.5 1.4 1.5 2.0 RD1 1.8 29.8 28.4 6.1 8.0 GY3 6.0 17.5 15.9 15.6 19.9 GY4 6.8 20.9 19.0 17.0 21.4 GY5 2.3 12.4 12.2 12.8 15.0 Vanderhoof CC5 0.0 0.0 0.0 0.0 0.0 YR5 3.0 29.6 21.7 8.5 10.3 GY9 4.6 14.1 12.0 14.6 17.0 GY10 4.9 20.7 15.8 9.4 14.6  70  Table 3.3.6.  List of forest structure variables with significant (p < 0.05) correlations with absolute peak SWE and maximum ablation rate. Source Variable Absolute peak SWE Max. ablation rate r r2 p r r2 p Ground inven-tories Mean DBH -0.78 0.61 0.01 -0.68 0.46 0.02 Mean height -0.78 0.60 0.01 -0.68 0.46 0.02 Percentage of pine -0.66 0.44 0.03 -0.62 0.39 0.04 LiDAR Mean height -0.73 0.53 0.01 -0.63 0.40 0.04 Height standard deviation -0.72 0.52 0.01 -0.72 0.51 0.01 Forest cover (> 0.5 m) -0.71 0.50 0.02 -0.74 0.54 0.01 Forest cover (> 2 m) -0.84 0.70 0.00 -0.77 0.59 0.01 Height 60% percentile -0.74 0.54 0.01 -0.65 0.43 0.03 Height 90% percentile -0.75 0.57 0.01 -0.68 0.47 0.02       Figure 3.3.4.  Scatterplots of forest structure variables with the highest correlations with ab-solute peak SWE [a) and b)] and maximum ablation rate [c) and d)] (all correlations with p < 0.01).     71  3.3.4 Discussion  The results presented in this section show the high variability in stand physical characteris-tics, MPB infestation patterns and snow accumulation and ablation processes between plots.  Forest structure variability is evident in the wide ranges of both ground and LiDAR-derived metrics between stands.  Figures 3.3.2 and 3.3.3 indicate that the clearcut plots accumulated more snow than the forested sites, which is consistent with other studies (Murray & Buttle, 2003; Winkler et al., 2005; Jost et al., 2007).  Plot YR5 for example, located in an old (70 years) small DBH and height stand (~8 cm and ~10 m, respectively), had the densest forest cover and the smallest peak SWE and ablation rate, showing the strong effects of snow inter-ception and the reduction of incoming shortwave radiation on the surface during the snow melting period.  The main evidence showing the variability of snow data is the occurrence of peak SWE on different dates at nearby sites.  For example, the clearcut in the Baker Creek area had its peak SWE on April 18, more than one month later than a nearby grey stand, 300 m away.  The op-posite occurred in the Vanderhoof sites, where a clearcut and the densest stand showed the peak SWE at the same time during the early March survey, while two grey stands had their highest snow accumulation one month later (Figure 3.3.4).  There are several snow redistri-bution processes that may account for this variability.  For example, year to year variations in snowfall magnitude impact the proportion of intercepted snow; since tree branches cannot intercept an unlimited amount of snow, the influence of forest cover becomes negligible when total snowfall exceeds a certain threshold (Boon, 2009).  Other sources of variation, as 72  explained in Section 1.2, include: aspect (higher temperatures in warm aspects) (Murray & Buttle, 2003; D?Eon, 2004); the size of the clearcut which is used as a reference for compari-son (higher ablation in larger clearcuts where snow is eroded by wind, offsetting the gains due to lack of interception) (Golding & Swanson, 1986; Pomeroy et al., 2002); and specific canopy interception properties, particular to different species (Lundberg & Halldin, 2001) (see Section 1.2).  However, these factors do not fully explain the occurrence of peak SWE on different dates at nearby sites since all the plots in each study area were located at the same elevation, and were consistently located on relatively flat terrain (ruling out the effects of aspect).  In some cases, the difference between SWE in a particular site was very small be-tween surveys, suggesting that sampling errors could play a role in capturing the precise value and moment of peak occurrence.  The relationships between snow processes and LiDAR-derived forest cover are particularly strong.  Despite the sample size, the capacity of LiDAR technology to characterize forest structure is evident as all LiDAR-derived variables showed significant correlations with ab-solute peak SWE, and only two did not produce similar results with maximum snow ablation.  The contrasting results obtained with ground-based variables, with only a few showing sig-nificant correlations, constitute further evidence of LiDAR?s enhanced ability to capture for-est structural attributes in detail.  These are promising results especially due to the increasing popularity of LiDAR data for operational purposes in recent years (Wulder et al., 2008).  Li-DAR-derived forest cover, calculated as the ratio of the number of vegetation first returns to the total number of returns, is a function of the arrangement and density of canopy elements, which are in turn related to interception and ablation.  Just as dense canopies intercept large 73  amounts of snow, they also reflect a larger number of LiDAR pulses and shade the underly-ing ground surface from both solar and laser-emitted radiation.  Consequently, it was ex-pected that forest cover would show the best correlations with snow processes as it was ob-served in this section.  The results suggest that forest cover > 2 m is a potentially better pre-dictor of snow accumulation and ablation than forest cover > 0.5 m and the other variables (indicating that this portion of the canopies may have a stronger influence on snow and radia-tion interception).  However, the relative similarity in r2 among the different variables em-phasizes that precaution is needed when selecting a particular variable for operational use.  For example, it remains unclear if the height 90% percentile is in fact a better predictor of snow processes than the height 60% percentile, a question that could potentially be answered by further studies and might depend on specific forest conditions and research objectives.  The relationships between LiDAR-derived forest structure metrics and snow processes need to be quantified in different hydroclimate regimes such as rain-snow transition zones.  The fact that the forest structure variables which explained most of the variation in peak SWE were the same as those significantly correlated to maximum ablation rate suggests that these hydrological processes are driven by the same principles.  These results confirm the findings of previous studies showing that changes in forest cover have a similar effect on both snow accumulation and melting (Anderson & Gleason, 1960; Hardy et al., 1998; McCaughey & Farnes, 2001).  In this section, the correlations between forest structure and snow accumula-tion were better than those with snow ablation, indicating that more sources of variation in-fluence the latter, and that further research analyzing ablation processes should take this into consideration.   74   The correlations between ground-derived MPB infestation indices and snow accumulation and melting were not significant.  Possible explanations for this poor correlation include the relatively small dataset in the analysis and the presence of young regeneration plots with low values of forest cover and null MPB infestation (more closely resembling a clearcut), which become outliers in the expected trend.  However, as LiDAR-derived forest cover was signifi-cantly correlated to peak SWE and maximum snow ablation, predicting changes in these processes due to MPB infestation is best represented in terms of changes in forest cover (i.e. defoliation).  The slopes of the equations presented in Figure 3.3.4 are therefore potentially useful to forest managers for quantifying the effects of forest cover on snow accumulation and ablation.  The main limitation of this research is the small sample size of 11 plots, which makes it diffi-cult to extrapolate results to larger areas and draw definitive conclusions.  However, the good correlations obtained between LiDAR variables and snow accumulation and ablation show promise for further research.  These results confirm that forest structure is strongly linked to snow processes, but additional work is required to directly link LiDAR-derived metrics to the timing and magnitude of seasonal stream discharge.  Another limitation involves the use of discrete manual snow surveys to estimate snow indicators.  Continuous measurements of snow from ultrasonic snow depth devices are likely to substantially increase the accuracy of peak SWE and SAR estimation.   75  3.3.5 Conclusions  This section has shown that LiDAR-derived forest structure metrics were better predictors of peak SWE and maximum ablation rates than conventional ground-based metrics, showing significant correlations in most of the cases.  This was an expected result because LiDAR is unrivaled at accurately characterizing the 3-dimensional complexity of continuous forested areas.  LiDAR-derived forest cover was the variable with the best performance for modeling changes in these hydrologic processes: an expected result since forest cover is a good repre-sentation of the canopy attributes that explain interception.  Linear correlation analysis is, however, only a preliminary tool for understanding the interactions of forest structure and snow processes as significant portions of the variance of these relationships remain unex-plained.  Future research based on more powerful statistical procedures is needed to confirm which LiDAR-derived variables could be incorporated to improve the performance of more complex snow models.  If these models account for sources of variation other than forest structure, such as topography and meteorological input, promising outcomes can be expected.  Peak SWE showed slightly better correlations with forest structure variables than snow abla-tion, but the fact that both snow processes were significantly correlated with the same vari-ables is evidence that they are both influenced by the same canopy attributes, which are accu-rately characterized by LiDAR.  Increasing forest cover reduces snow accumulation due to interception and sublimation, and it also reduces SAR by intercepting incoming radiation.    76  The results presented in this section can be used to infer possible changes in snow accumula-tion and melting following changes in forest cover.  This is important for forest resource managers because they can predict potential responses of these snow processes to a wide range of practices such as thinning, harvesting, salvage logging or planting.  The changes in cover associated with defoliation caused by the MPB in British Columbia can be incorpo-rated in models to predict the hydrologic response of affected catchments at a broader scale.  Further research should focus on improving the accuracy of snow indicator estimations with the use of more advanced instrumentation such as ultrasonic snow depth sensors.  3.4 Validation of prototype ultrasonic snow depth sensors for snow monitoring   3.4.1 Introduction  Researchers in all disciplines are often challenged by the need to automate and improve measurements while facing budgetary constraints.  Hydrologic studies have commonly relied on manual surveys for measuring snow, but their high costs lead to the use of discrete, infre-quent records that ignore snowfall and ablation between field campaigns and lead to a bias in the estimates of accumulation/depletion rates.  This has persisted despite the efforts to auto-mate snow measurements in the United States (Brazenec, 2005; Ryan et al., 2008) and Can-ada (Goodison et al., 1984; Brown et al., 2000), and was recognized as a major limitation for snow model development in the previous section of this thesis.  77  Snow ultrasonic sensors able to continuously measure snow depth have been developed in earlier decades (Caillet et al., 1979; Gubler, 1981) and applied for hydrological monitoring (Pomeroy & Essery, 1999; Naftz, 2002), avalanche prediction (Lehning et al., 1999) and model fitting / validation (Flerchinger et al., 1996; Hardy et al., 1998; Essery et al., 1999; Strack et al., 2004).  High prices have limited their more widespread use, but the need to fur-ther promote ultrasonic applications for hydrology is repeatedly mentioned in the literature (Bergman, 1989; Brazenec, 2005; Ryan et al., 2008).  This section, published in Varhola et al. (2010c), presents and describes the development of a prototype Low-Cost Ultrasonic Sensor (LOCUS-X) designed and built for this research in order to better capture the continuous sub-daily changes in snowpack that will lead to a more accurate estimation of plot-level peak SWE and SAR.  Being significantly more economical than other devices2, this sensor represents a promising alternative to substantially increase the sample size of locations to monitor snow dynamics and other complementary hydromete-orological variables.  The section presents technical information about this low-cost sensor, establishes a methodology to process its raw data, and validates its quality by comparing snow depth and temperature records with manual measurements and weather station data.                                                       2 The basic LOCUS model costs ~US$180 including materials and labour for 100 initial units, while the US$600 Judd Communications and the US$1,000 Campbell Scientific SR-50 tested by Ryan et al. (2008) do not include data loggers and power sources. 78  3.4.2 Sensor design and specifications  LOCUS-X is a ready-to-deploy battery-powered standalone sensor system with a built-in data logger, where X represents the number of complementary hydrometeorological variables measured by the different hardware models.  This section is focused on the simplest version (LOCUS-2) that records range and air temperature.   Its watertight 5.5?16.6?8.5 cm plastic enclosure (Figure 3.4.1) weighs 245 g (520 g including batteries) and holds a 3V lithium-ion battery to power the real time clock and four C-cell 1.5 V alkaline batteries to perform at least 1,500 measurements (30 samples per measurement).  Recordings are triggered at freely programmable time intervals to obtain a required number of sample readings whose average is flagged as corrupt should the sample variance exceed a user-defined threshold.  The com-ponents are rated to at least -40?C.  Range is measured with an LV-MaxSonar? EZ1 High Performance Sonar Range Finder, which records the distance to the closest object in the signal path by measuring the round-trip time of an emitted acoustic signal.  The beam cone angle is 36? and the maximum range is 6.45 m (2.5 cm resolution).  Snow depth is obtained by measuring the distance between the sensor and the top snow layer, given a known mounting height above the ground.  Besides range and air temperature, LOCUS-X is designed to readily connect supplementary sensors to measure relative humidity, snow temperature (eight depth levels), and luminosity.  A transistor-transistor logic level counter input allows interfacing with additional compo-nents (e.g. off-the-shelf tipping bucket rain gauge) while other digital sensors can be con-79  nected through an expansion port based on the common inter-integrated circuit bus.  In all versions, a three-axis accelerometer records the sensors? pitch and roll angles to facilitate the correction of distance readings in case of tilting by external factors or to identify the moment of complete downfall and retrieve valid portions of the dataset.  3.4.3 Field testing of LOCUS-2  3.4.3.1 Sensor installation and decommission  A total of 48 LOCUS-2 sensors were installed in December 2008 near Quesnel and Fraser Lake (British Columbia), mostly on forested sites of varying canopy conditions and a few nearby open areas.  The units were mounted at a minimum height of 150 cm above the ground based on previous observations of peak snow depth in the area, and were pro-grammed for 3-hourly recording.  The mounting hardware consisted of a polyvinyl chloride (PVC) pedestal supported by a metal rebar hammered into the ground and guy wires tied to trees or logs.  Ventilated PVC shelters were added to most of the sensors to avoid heating by direct sunlight and consequent biases in temperature measurements, while some were in-stalled unprotected to test their impermeability and resistance to direct weather exposure   A standard probe was used to manually measure snow depth within the sensors? field of view immediately after installation, at estimated peak snow accumulation and during the ablation period.  It was not possible to perform these three measurements for all sensors, but a total of 83 records provided a solid database for comparison.  Additionally, two nearby (~12 km) 80  AWS equipped with Campbell Scientific SR-50 ultrasonic snow depth devices and Vaisala HMP45C temperature sensors (Bewley et al., 2010) provided accurate hourly data for com-parison.  Due to the high spatial variability of snow distribution, the relationship between LOCUS-2 and AWS snow depth data were only intended to confirm general consistency of the basin-wide changes throughout the season (i.e. shape of the curves) rather than the accu-racy of the measurements.  The sensors were decommissioned in May 2009.   Figure 3.4.1.  Top row: side, top and bottom of the LOCUS-2.  Bottom row: examples of LOCUS-2 sensors installed in the field; sensors in forested sites (left) were oriented N-S to minimize the entry of direct sunlight in the PVC cover, while sensors in open areas (center) were fully covered.  Some sensors were installed without a protective cover (right).  3.4.3.2 Data download and processing  Ultrasonic snow depth sensors are known to produce noisy datasets due to the irregular sur-face of snow (especially when fresh) (Brazenec, 2005; Ryan et al., 2008).  A simple algo-rithm was developed to process snow depth data by eliminating records showing more than 5 81  and 2 cm/h of snow accumulation and ablation, respectively (inspecting previous AWS re-cords provided these thresholds).  Biases in range readings due to changes in the sensors? in-clination were corrected by:  DA= DR?cos(?)?cos(?) + sin(?)?L ? sin(?i)?L     3.4.1  where DA = angle-corrected distance (cm), DR = raw distance (cm), ? = pitch angle (rad), ? = roll angle (rad), L = length of horizontal pipe holding the sensor and ?i = installation pitch (rad).  The data were then corrected by air temperature, known to affect the speed of sound (Osterhuber et al., 1994), using a standard formula (Huang & Young, 2009):  DT = DA?[(T + 273.15)/(Tc + 273.15)]0.5       3.4.2  where DT = temperature-corrected distance (cm), T = current temperature (?C) and Tc = cali-bration temperature (?C) (here, 20.7?C).  Ranges of unsheltered sensors were corrected with temperature data of the closest sheltered sensor.  Range was transformed to snow depth by subtracting it from the final distance provided by the sensors after snow disappearance, and 3-hourly records were then aggregated into daily averages.  Finally, the curves were adjusted to a position where the average difference be-tween sensor data and manual records was minimized.  This was done assuming that the final distance reading provided by the sensor after snow disappearance could have been biased by an irregular surface, and to evaluate the extent to which this offset the sensors? readings on bare ground. 82   3.4.3.3 Quality assessment  The quality of the range data was evaluated by calculating the residual snow depth measure-ment after snow disappearance (which ideally should equal zero), the root mean square error (RMSE) between sensor and manual snow depths and between sensor and AWS tempera-tures, and visual comparison of the sensors? and AWS? snow depth and temperature records.  3.4.4 Results  3.4.4.1 Instrument operation  The overall operation of the installed sensors was excellent, with only one device discarded due to corrupt data.  Both sheltered and unsheltered sensors lasted the entire winter with no damage and absence of condensation inside the enclosures.  The mounting system performed relatively well, especially in forested stands where the sensors could be tied to trees.  Slight tilting was the most common problem observed and attributed to the flexibility of the PVC pipes and the loss of tension in the guy wires, but even observed maximum pitch or roll an-gles close to 10? could be corrected by Equation 3.4.1.  Units deployed without PVC covers in clearcut areas successfully recorded valid snow depth data despite the presence of extreme weather and high wind speeds during the installation, common in the study areas.  Minimum temperatures as low as -35?C did not prevent the batteries from powering the sensors for five months until decommission. 83   3.4.4.2 Data quality  Correcting for changes in the mounting angle and temperature was critical, especially for mid-winter data when the differences between calibration and field temperatures were as high as 50?C and would have resulted in a distance error of up to 10 cm.  The final average distance to the ground after adjusting the snow depth curves to match man-ual records was 9.7 cm, with 87% of the sensors showing a value smaller than 15 cm.  Linear regression between the 83 paired manual and sensor snow depth records was highly signifi-cant for both unadjusted (r2 = 0.74, p < 0.001; RMSE = 12.3 cm) and adjusted curves (r2 = 0.93, p < 0.001; RMSE = 4.2 cm).  Visual comparisons of the LOCUS-2 and AWS snow depth curves (Figure 3.4.2, top) show agreement in the shape of the lines, correctly identifying new snowfall events, subsequent compaction, and the continuous snowpack decline during ablation.  Snow disappearance oc-curred later for the LOCUS-2 than for the AWS because the latter were located in open areas, where ablation is generally faster.  Visual comparison of graphed temperature data from the LOCUS-2 sensors and nearby AWS sensors was satisfactory (Figure 3.4.2, bottom).  The RMSE between AWS and LOCUS-2 temperatures was 2.6?C, a reasonable bias considering the distance and elevation differences 84  between the field sites and the AWS, and given that most of the LOCUS-2 units were located in subcanopy conditions rather than open areas as both AWS.   Figure 3.4.2.  Comparison of snow depth (top) and mean daily air temperature (bottom) be-tween data obtained from one LOCUS-2 sensor and two nearby weather stations.  3.4.5 Examples and applications  LOCUS-2 sensors can be used for diverse environmental research studies.  Examples of final curves obtained for different sensors are shown in Figure 3.4.3 (top), illustrating their utility to evaluate snow processes in different study areas and canopy conditions.  A detailed inter-85  pretation of these examples is beyond this section?s scope, but the figure shows the LOCUS-2 sensitivity to capturing subtle differences.   Figure 3.4.3.  Examples of the use of LOCUS-2 sensors in applied research: snow depth measurements in two study areas according to relative canopy conditions (top); and detection of the effect of temperature on snow ablation (bottom).  Variations in snow depth during the ablation period can be graphed with air temperature to establish links between these variables.  Figure 3.4.3 (bottom) shows how temperature peaks coincide with increases in the slope of snow ablation, while reductions of temperature retard changes in the snowpack.  The fact that minor variations in ablation rate concur with the temperature trends is evidence of the accuracy and precision of the LOCUS-2.   86   3.4.6 Discussion and conclusions  The LOCUS-2 sensors were successfully used in a winter-long field experiment in British Columbia.  Benefits of these devices included a robust hermetic enclosure, an integrated power supply particularly useful for sub-canopy measurements, low power consumption that allowed prolonged operation and a ready-to-use design with built-in data logger.  The LOCUS-2 data were found to consistently underestimate snow depth when compared to manual measurements, which is common for all ultrasonic snow depth sensors (Goodison et al., 1984; Metcalfe et al., 1987; Ryan et al., 2008) and is mainly attributed to the pulses penetrating the porous snow surface, the large beam angle and the temperature gradients be-tween the sensor and the ground.  Additional sources that can impact the sensors? perform-ance may include:  inclined snow surface, high wind speeds that attenuate ultrasound, vibra-tion of the sensors while recording, occurrence of intense snowfalls, snow blowing and ob-structing the ultrasound pulses, extremely low temperatures, and snow crystal size/type (Goodison et al., 1984; Brazenec, 2005; Ryan et al., 2008).  It is important to consider that not all the biases are attributable to the sensors, and can be as large as 10 cm in manual read-ings as well (Ryan et al., 2008).  The average underestimation of snow depth by the LOCUS-2 sensors, close to 10 cm, is higher than the 2 cm bias found by Brazenec (2005) and Ryan et al. (2008) with other ultra-sonic devices.  Even though this error is not negligible, it represents slightly more than 10% 87  of the total average maximum snow depth accumulated in the area that winter (80 cm).  Pos-sible explanations for this bias are that the PVC mountings favoured some vibration and tilt-ing, and the irregular surfaces after snow disappearance (with logs and branches) affected sensor measurements on bare ground increasing the difference between readings in their spe-cific measurement points.  It is recommended to install the sensors before the first season?s snowfall over clean, flat and regular ground surfaces, and on more rigid hardware.  Despite these issues, the LOCUS-2 can considerably reduce the amount of field work re-quired to obtain comprehensive snowpack and meteorological data.  Although ultrasonic sen-sors cannot substitute manual snow surveys if spatially-distributed SWE or depth are of inter-est, continuous snow depth records at one point in space constitute a useful complement that can accurately provide important information such as dates of peak accumulation and snow disappearance, and continuous accumulation and ablation rates.  Snow depth curves can be transformed to SWE by interpolating discrete measurements of snow density (Boon, 2009; Bewley et al., 2010), while extrapolation of point-level measurements to the wider plot is possible with the method by Neumann et al. (2006).  Further work with the LOCUS-2 will involve additional testing in a variety of environments (e.g. alpine, high latitudes, coastal) and the use of the ultrasonic sensor to measure water level or glacier dynamics.  This system would also be well suited to run in parallel with an automatic camera to monitor additional environmental variables and conditions such as rain-on-snow events and snow interception (Floyd & Weiler, 2008).  Technical improvements of 88  the LOCUS-X sensor system could include the incorporation of wireless technology to transmit data in real time.  This experience with the LOCUS-X system demonstrates that low cost units built from inex-pensive sensors and hardware available in the market offer a remarkable solution to compete with brand-name costly instruments.   3.5 Exploration of remotely-sensed forest structure and ultrasonic snow depth sensor metrics to improve empirical snow models    3.5.1 Introduction  The main objective of this section is to re-evaluate the development of simple snow models predicting peak SWE and SAR (Section 3.3) by broadening the dataset of forest structure met-rics to include additional sources, by considering two snow seasons and by improving the accuracy of snow indicator estimation.  This section takes advantage of the multiple forest metrics obtained at the plot level from ALS, HP and Landsat in Chapter 4 of this thesis, the standardized compilation of snow indicators published by others in Baker Creek (Teti, 2008; Bewley et al., 2010), and comprehensive peak SWE and SAR data measured by LOCUS sen-sors (Section 3.4).  As Section 3.3 illustrated that remotely-sensed forest metrics are poten-tially better predictors of snow indicators than traditional ground estimates, here it is shown how continuous measurements of plot-level SWE from ultrasonic sensors are essential to ac-curately capture SWEmax and SAR and further improve their correlations with vegetation structure.  This section has been published in Varhola et al. (2013). 89   The specific objectives of this section are:  1) Explore the relationships between snow indica-tors and a wide range of forest metrics (obtained from LiDAR, HP and Landsat) to identify the best potential predictors of SWEmax and SAR.  2) Test two definitions of SWEmax and three definitions of SAR to evaluate which are better related to forest metrics.  3) Quantify the benefit of using continuous ultrasonic sensor data as an addition to traditional surveys in or-der to estimate snow indicators with forest metrics.  4) Determine if temperature and relative humidity indicators have the potential to improve the predictive power of SWEmax and SAR.  3.5.2 Methods  3.5.2.1 Study area  The data used for this section belong to the Baker Creek watershed and the area located ap-proximately 40 km south of Fraser Lake, as shown in Section 2.1 and Figure 2.1.1.  The ele-vation range of plots is 900 ? 1,350 and 880 ? 910 m above sea level in the Baker Creek and Fraser Lake areas, respectively (Section 2.1).  3.5.2.2 Data acquisition  Ground plots.  As explained in Section 2.7, ground plots were established between 2007 and 2008 and further described by Bewley et al. (2010), Teti (2008) and Varhola et al. (2010a).  Most plots are 2,500 m2 squares distributed among the stand types present at the study area at 90  the moment of data collection, which represent varying combinations of size attributes (from young regeneration to mature), MPB defoliation status (from healthy to grey; see Coops et al. (2009) for definitions), and species (from spruce- to pine-dominated).  Table 3.5.1 shows the distribution of the 38 plots according to these stand characteristics and elevation ranges.   Table 3.5.1.  Number of ground plots according to stand type and elevation above sea level. Stand type Elevation range (m) 800-900 900-1,000 1,000-1,100 1,100-1,200 1,200-1,300 1,300-1,400 Total Clearcut 1 2 3 1 2 1 10 Young regenerating pine - 2 - - 2 - 4 Medium healthier pine - 2 - - 1 - 3 Medium red pine - 1 - 1 4 1 7 Mature grey pine 1 4 1 - 5 1 12 Mature healthy spruce - 1 1 - - - 2 Total 2 12 5 2 14 3 38   ALS, vegetation spectral indices and hemispherical photos were obtained as explained in Sections 2.2, 2.3 and 2.4, respectively.  ALS covered 23 of 38 ground plots, HP was avail-able in all 38 plots, while Landsat overlapped with 32 plots (excluding 4 plots in Fraser Lake).  Table 3.5.2.  Number of ground plots according to available forest and snow data sources. Forest data source Snow data source Manual surveys  Ultrasonic snow sensor Airborne Laser Scanning 23 23 Hemispherical photography 38 26 Landsat spectral indices 32 21   Manual snow surveys.  In all plots, field campaigns were conducted to obtain average snow depth, density and SWE (Section 2.7) in a sequence of surveys.   In most of the plots, surveys 91  aimed to capture SWEmax close to April 1 and estimate SWE at least one time during the abla-tion period in the springs of 2008 and 2009, while those including LOCUS data were only monitored during the 2009 spring.  Further details about snow measurements are provided by Teti (2008) and Bewley et al. (2010).  LOCUS data.  48 LOCUS sensors were distributed within 22 plots in Baker Creek and 4 plots in Fraser Lake as detailed in Section 3.4.3.  The sensors continuously captured 3-hourly records of snow depth, air temperature and relative humidity from installation (December, 2008) to decommission (May, 2009).  3.5.2.3 Data processing  Forest structure metrics.  A number of variables representing forest structure were derived from LiDAR data, HP and Landsat TM (Table 3.5.3).  Within each plot?s boundaries, the ra-tio between LiDAR returns over a specified height above the ground (representing the can-opy) and the total number of returns (including ground) is a good indicator of forest cover.  Following Section 3.3, forest cover above 0.5 and 2.0 m was calculated (Table 3.5.3).  An additional set of metrics was derived, as explained in detail in Section 4.3, from a grid of syn-thetic hemispherical images created at each plot by re-projecting LiDAR returns with a polar coordinate system and calibrated by paired optical counterparts with specialized software (Frazer et al., 1999).  These metrics include two versions of leaf area index (LAI4 and LAI5) (Welles & Norman, 1991; Stenberg et al., 1994) and five versions of gap fraction (GF).  GF is estimated from hemispherical images as the ratio of sky (white) to forest (black) pixels 92  (Figure 3.5.1) across concentric circles representing a specified angle of view (?) from the zenith (image center) towards the horizon, where ? varies in this thesis from 30 to 90? in 15? increments.  Teti (2003) and Moore & McCaughey (1998) suggested that snow indicators are better correlated to GF when ? = 30? than broader angles of view, which is subject to further exploration here.     Figure 3.5.1.  Representative examples of three stands with LiDAR point clouds (left), hemi-spherical images derived from coordinate-transformed LiDAR returns (centre) and calibrated with their optical ground-based counterparts (right).  Plot-level averages of LAI4, LAI5 and GF? were obtained from both LiDAR- and optical cam-era-derived hemispherical images, which are shown in Figure 3.5.1.  Preceding letters L and 93  F were used to distinguish between equal variables derived from LiDAR and HP, respec-tively (Table 3.5.3).  Finally, spectral indices retrieved from Landsat pixels overlapping with ground plots and identified as the best predictors of forest structure in Section 4.4 completed the forest metric database (Table 3.5.3).  These indices include the Enhanced Vegetation In-dex (EVI), a foliar moisture index (MI2), pixel brightness (BRI), greenness (GRE) and wet-ness (WET), and a forest spectral unmixing fraction (FOR).     Plot-level continuous SWE.  LOCUS devices provided 3-hourly records of snow depth rep-resenting a small area (a few cm2) captured by the sensors? field of view (Section 3.4).  These data were transformed to mean daily plot-level SWE by averaging 3-hourly records, linearly interpolating snow densities averaged for each plot in different sequential field surveys and by establishing regression equations between daily records pairing observed sensor snow depth and plot-level SWE from the surveys.  This procedure was optimum in providing con-tinuous SWE curves that almost perfectly fitted plot-level field observations (4% error), showing that LOCUS snow curve shapes were representative of site-specific snow dynamics.  Snow accumulation.  Both LOCUS- and manual survey-derived SWE (mm) measurements were used to estimate two different versions of peak SWE at each plot:  1) the absolute maximum SWE in the entire record regardless of the date of occurrence (SWEA), and 2) the highest value of SWE right before sustained ablation started (SWEB) (i.e. when significant increases in SWE due to additional snowfall no longer occurred) (Table 3.5.3).  In many cases these two definitions of SWEmax coincided, especially when estimated with discrete manual surveys. 94   Snow ablation.  Three measures of snow ablation (mm/day) were derived from the change in SWE in different time periods:  1) from absolute maximum peak SWE until snow disappear-ance (SARC); 2) from SWE before sustained ablation to snow disappearance (SARD), and 3) during 10 days centered within the sustained ablation period of each reference clearcut (SARE) (Table 3.5.3).  The purpose of including the third definition was to eliminate the ef-fect of a varying ablation period duration on SAR calculations.  Paired-plot standardization.  Absolute values of SWEmax and SAR are not suitable for a di-rect comparison with forest metrics because they do not isolate inter-site or inter-annual dif-ferences in snow indicators.  Winkler (2001) and Varhola et al. (2010b) (Section 3.2) use a paired-plot approach replicated in this section that consists of calculating the relative change of SWEmax and SAR at a specific forested plot when compared to a nearby clearcut (see Equa-tion 3.2.1).  Two approaches were conducted to pair the forested plots with one of the ten clearcuts: 1) simply considering the closest clearcut as the reference, and 2) using the small-est, sheltered clearcut in each study area as the sole reference for all plots in order to elimi-nate potential biases introduced by snow drift and sublimation in larger clearcuts exposed to wind.  These standardizations were applied to the two definitions of SWEmax and three defini-tions of SAR to produce the generic relative changes listed as ?SWE and ?SAR in Table 3.5.3.  As a result, all plots featured sets of records with these versions of ?SWE and ?SAR paired with available forest metrics (Table 3.5.1).   95  Table 3.5.3.  Variable data sources, symbols and description. Type / Source Symbol Variable (unit) Description ALS FC0.5 Forest cover above 0.5 m (ALS returns > 0.5 m) / (all ALS returns) FC2.0 Forest cover above 2 m (ALS returns > 2.0  m) / (all ALS returns) LLAI4 Leaf area index 0?60? (m2/ m2) See Stenberg et al. (1994) LLAI5 Leaf area index 0?75? (m2 /m2) See Welles & Norman (1991) LGF? Gap fraction where ? = 30, 45, 60, 75 and 90? (Sky pixels) / (Total pixels) for ? HP FLAI4 Leaf area index 0?60? (m2/ m2) See Stenberg et al. (1994) FLAI5 Leaf area index 0?75? (m2/ m2) See Welles & Norman (1991) FGF? Gap fraction where ? = 30, 45, 60, 75 and 90? (Sky pixels) / (Total pixels) for ? Landsat EVI Enhanced Vegetation Index Vegetation index (see Section 4.4) MI2 Foliar Moisture Index II Foliar moisture index (see Section 4.4) BRI Brightness Tasseled cap index (see Section 4.4) GRE Greenness Tasseled cap index (see Section 4.4) WET Wetness Tasseled cap index (see Section 4.4) FOR Forest spectral fraction Spectral unmixing forest fraction (see Section 4.4) Snow surveys / LOCUS sen-sors SWEA Peak SWE in record (mm) Absolute maximum SWE in record SWEB Peak SWE before sustained ablation [mm] Maximum SWE before sustained ablation ?SWEA Standardized SWEmax Standardized difference between SWEmax in forested plots and nearby clearcuts ?SWEB Standardized SWES Standardized difference between SWES in forested plots and nearby clearcuts SARC Snow ablation rate from SWEmax (mm/day) Change in SWE from SWEmax to snow disappearance SARD Snow ablation rate from SWES (mm/day) Change in SWE from SWES to snow disappearance SARE Mid-ablation rate (mm/day) Change in SWE during 10 days in the middle of the ablation period for reference clearcuts. ?SARC Standardized SARC Standardized difference between SARC in forested plots and nearby clearcuts ?SARD Standardized SARD Standardized difference between SARD in forested plots and nearby clearcuts ?SARE Standardized SARE Standardized difference between SARE in forested plots and nearby clearcuts LOCUS sen-sors Tx Mean temperature (?C) Temperature integrated for x = time period* MXTx Maximum temperature (?C) Temperature integrated for x = time period* MNTx Minimum temperature (?C) Temperature integrated for x = time period* RHx Mean relative humidity (%) Relative humidity for x = time period* MXRHx Maximum  relative humidity (%) Relative humidity for x = time period* MNRHx Minimum  relative humidity (%) Relative humidity for x = time period* Ex Mean vapor pressure (kPa) Vapor pressure for x = time period* MXEx Maximum  vapor pressure (kPa) Vapor pressure for x = time period* MNEx Minimum  vapor pressure (kPa) Vapor pressure integrated for x = time period*  * Means, maximums and minimums of meteorological variables were calculated for all months from January (x = 1) to April (x = 4) and for the first (x = 4a) and last (x = 4b) two weeks of April.   Correlation analysis.  Given that this section is based on the compilation of data from dif-ferent sources, groups of plots sharing common information were firstly isolated to represent distinct combinations of snow indicator definitions, forest metric sources (LiDAR, HP and Landsat), and snow data sources (manual surveys and LOCUS devices).  Within each group of plots, coefficients of correlation (r), coefficients of determination (r2) and significance 96  values (p) were generated between each forest metric and the different indicators of ?SWE and ?SAR.  For each definition of ?SWE and ?SAR, the range of r2 values and number of forest metrics with statistically significant correlations (p < 0.05) were reported separately for each forest (LiDAR, HP and Landsat) and snow (manual surveys and LOCUS) sources (Fig-ure 3.5.2).  From this analysis, the best definitions of ?SWE and ?SAR and their potentially best forest structure predictors were identified.  Linear regression and meteorological data.  Once the optimum definitions of ?SWE and ?SAR and the forest metrics best correlated to them were identified, simple linear regression models were developed.  To determine how much more variance could be explained by the available data, multiple linear regression models then incorporated additional forest metrics and meteorological variables.  Mean, maximum and minimum monthly air temperature (?C), relative humidity (%) (measured by LOCUS) and vapor pressure (kPa) (estimated from rela-tive humidity) were derived for sites where LOCUS data were available, from January to April (April data were also aggregated biweekly).  Each meteorological variable showing the highest correlation with the best indicator of ?SWE and ?SAR was added to its primary forest metric predictor to build multiple regression linear models.  Only the best representative of each type of variable (LiDAR, HP, temperature, relative humidity-vapor pressure) was added to the models to avoid co-linearity and minimize degrees of freedom.  Meteorological vari-ables from January to March were included in the ?SWE models, and April monthly and bi-weekly variables were added in ?SAR models.  Statistically not-significant model coeffi-cients were subsequently eliminated until all the remaining variables were significant (p < 0.05).  Model quality was assessed by multiple and adjusted r2, overall significance (p), 97  RMSE and residual normality based on the Anderson-Darling test (p > 0.05 required).  3.5.3 Results  3.5.3.1 Plot pairing approach  As explained above, all the data were processed based on two different approaches for pair-ing forested plots with nearby clearcuts.  When the single smallest clearcut was used as a ref-erence for all forested plots in Baker Creek, the quality of the relationships between forest metrics and snow indicators was consistently and substantially weaker than if the clearcut closest to each plot was set as a reference.  All of the following results are therefore exclu-sively related to a multiple-clearcut pairing approach.  3.5.3.2 Forest structure metrics  Figures 3.5.2a, 3.5.2b and 3.5.2c compare the range of correlations between LiDAR, HP and Landsat metrics, respectively, and the two definitions of ?SWE (A, B) and three definitions of ?SAR (C, D, E).  The figure also presents the fraction of statistically significant and total number of correlations assessed for all variables in each case.  98        Figure 3.5.2.  Maximum (upper dashes), mean (diamonds) and minimum (lower dashes) r2 values between snow accumulation and ablation metrics and various forest structure metrics from ALS (a), hemispherical images (b) and Landsat spectral indices (c).  Snow accumula-tion definitions:  ?SWEA = absolute SWEmax; ?SWEB = SWE right before a period of sustained ablation.  Snow ablation definitions:  ?SARC = snow ablation from absolute SWEmax to snow disappearance; ?SARD = snow ablation from peak right before ablation to snow disappear-ance; ?SARE = mid-period 10-day ablation.  Snow indicators taken from manual snow sur-veys and LOCUS sensors are indicated in black and grey, respectively.  99  In general, forest metrics from LiDAR, HP and Landsat did not explain major portions of the variability of ?SWE; r2 values reaching maxima slightly above 0.3 thus limit the possibility of developing models with predictive capacity.  The best snow accumulation relationships were represented by the correlations between LiDAR-derived forest cover above 0.5 m (FC0.5) and ?SWEA obtained from LOCUS data (r = ?0.58; r2 = 0.34; p = 0.007) (Figure 3.5.2a, A, grey), and pixel brightness (BRI) with ?SWEA estimated from snow surveys (r = 0.58; r2 = 0.34; p < 0.001) (Figure 3.5.2c, A, black).  Forest metrics directly proportional to vegetation biomass, such as FC and LAI, showed the expected negative correlations with ?SWE:  as forest cover increases, there is less snow accumulated in the ground (Figure 3.5.2a) due to higher canopy interception capacities (Pomeroy et al., 1998).  GF?, on the other hand, which is inversely proportional to vegetation biomass, consistently showed posi-tive correlations with ?SWE.  Notable differences in the quality of the correlations between ?SWE and GF for varying ? values were not detected.  BRI is negatively correlated to forest structure as clearcut pixels with a higher reflectance from bare ground or grass darken as for-ests grow (Section 4.4) (Varhola & Coops, 2013); therefore, the positive correlation between BRI and ?SWE was expected and consistent.  Forest metrics show larger numbers of statistically significant relationships and explain a higher proportion of the variability of snow ablation than snow accumulation, as shown by contrasting ?SWE variable groups in Figure 3.5.2 (A, B) with ?SAR (C, D, E).  ?SARC, cal-culated for the absolute SWEmax to snow disappearance period (Figure 3.5.2b) with LOCUS data, was best predicted by GF45 (r = 0.75; r2 = 0.57; p < 0.001) derived from optical HP, although r2 and p values shown by all other HP-derived metrics were similar.  An increasing 100  vegetation biomass consistently resulted in negative correlations between ?SAR and FC or LAI since ablation rates are relatively lower in dense forests than in clearcuts, due to the at-tenuation of incoming solar radiation (Pomeroy & Dion, 1996) and wind suppression driven by canopy elements (Marks et al., 1999).  Correspondingly, higher values of GF in this study area represent the opposite conditions which favor ablation rates that become similar to open areas as gaps between canopy elements are enlarged (Figure 3.5.3b).  Similar to ?SWE, vary-ing the angle of view to produce different GF? did not consistently enhance the relationships with ?SAR.  Forest metrics derived from HP are highly correlated to each other and therefore show less variability in r2 (Figure 3.5.2b) with snow indicators compared to LiDAR metrics (Figure 3.5.2a).  Landsat-derived spectral indices, on the other hand, are estimated by very different methods (Silleos et al., 2006) and therefore show the widest range of relationship quality with snow indicators (Figure 3.5.2c).  Overall, the best correlations between forest structure and snow indicators ??SAR in particular? were provided by metrics derived from HP.  Scatterplots representing the best overall potential predictors of ?SWE and ?SAR are illus-trated in Figure 3.5.3, where notable outliers have been identified for further discussion.  101    Figure 3.5.3.  Relationships between absolute standardized SWEmax (?SWEA) and its best forest structure predictor (a), and between standardized snow ablation for the entire ablation period (?SARC) and its best forest structure predictor (b); both snow indicators were obtained from LOCUS sensor data.  Outlier plot codes are presented.  3.5.3.3 Snow indicator definitions and data sources  In general, forest metrics were better predictors of SWEmax estimated as the absolute SWEmax on record than SWEmax prior to sustained ablation (Figure 3.5.2).  Twenty out of the 56 SWE-max records from manual snow surveys showed marked differences between these two defini-tions of peak SWE, averaging a deviation of 19 mm and 22 days between dates of detection.  In 2008, these differences were due to manual surveys capturing absolute SWEmax before the ablation period, as early as March 7.  In 2009, on the other hand, a substantial snowfall oc-curred in Baker Creek between April 12 and 15 which produced a second SWEmax very simi-102  lar to the one captured around April 4 in some plots.  Manual snow survey records often con-cealed the ablation taking place between these two SWE peaks, which was clearly detected by LOCUS devices as shown by the clearcut data on Figure 3.5.4.  This snowfall delayed the start of sustained ablation in 8 out of 26 LOCUS records by an average of 11 days in 2009.  The mean difference between absolute SWEmax and SWEmax prior to sustained ablation in these plots was 8 mm.  Overall, forested sites accumulated on average 20% less snow than their nearby clearcuts in 2008, and this difference was reduced to 8% in 2009.  The relationships between ?SARE (estimated for a 10-day mid-ablation period) and forest structure were notably inferior to those from the other two definitions of ?SAR (Figure 3.5.2).  Some LiDAR and Landsat-derived metrics can equally explain the variance of ?SAR based both on SWEA and SWEB.  In all these cases, maximum r2 values are close to 0.5.  Met-rics derived from HP are better predictors of ?SARC, with the maximum r2 reaching 0.58.  The r2 ranges for HP-derived metrics are the smallest, while spectral indices exhibit the greatest variability (Figure 3.5.2).  The most notable result of this section is related to the improvement introduced by continu-ous estimates of SWE from LOCUS devices when analyzing the relationships between forest structure and snow indicators.  The purpose of Figure 3.5.4 is to illustrate this by contrasting SWE data collected by both manual surveys (Figure 3.5.4a) and LOCUS devices (Figure 3.5.4b) on three representative plots:  a clearcut, a young regeneration pine stand and a ma-ture defoliated pine stand.  Continuous measurements of SWE are required to adequately cap-ture SWEmax and calculate SAR by identifying the days of snow disappearance across sites 103  (Section 3.4) (Varhola et al., 2010c).  Figure 3.5.4 shows how only one manual survey con-ducted during spring melt might produce biased estimates of SAR by not representing the en-tire ablation period.  Differences between defining snow indicators ?especially ?SAR? from manual surveys and LOCUS sensors are critical as shown by black and grey bars, re-spectively, on Figure 3.5.2.   While less than 15% of the variability of ?SAR estimated from manual snow surveys is explained by forest metrics, this value increases to around 50% when LOCUS-derived ?SAR indicators are used (Figure 3.5.2).  These differences are not so large for ?SWE.   Figure 3.5.4.  Three representative forested stands where snow was measured by manual snow surveys (top) and LOCUS-derived SWE (bottom).   104  3.5.3.4 Linear regression and meteorological variables  Table 3.2.4 shows the results of simple and multiple linear regression.  It was not possible to produce a valid simple linear regression model for ?SWEA (first two models in Table 3.2.4) since residual normality could not be established.  The first iteration of a multiple regression model incorporated LLAI5, MNT1 and MNRH1 as predictors and the resulting adjusted R2 in-creased to 0.48 compared to 0.27 of the simplest model; however, only MNRH1 was statisti-cally significant among the additional predictors.  A final model eliminating LLAI5 and MNT1 passed all the tests but only explained 43% of the total ?SWEA variance (Table 3.2.4).  Incor-porating MNE4b and MNT4b in a multiple regression model to predict ?SARC only marginally improved some model indicators; however, these variables were not statistically significant in the model and adjusted R2 was actually reduced by 2% when compared to a simple linear model based on FGF45 as the sole predictor, which passed all tests.   In general, the capability of these models to produce operational predictions is limited due to their relatively low ad-justed R2.  3.5.4 Discussion  3.5.4.1 Correlation and outliers  In general, r2 values obtained here to evaluate the relationships between snow indicators and forest structure were somewhat higher than those presented by Winkler & Moore (2006), but lower than Winkler (2001) and Section 3.3 of this thesis (Varhola et al., 2010a).  The rela-105  tionships shown in this section are negatively affected by a larger number of plots obtained from multiple sources (Teti, 2008; Varhola et al., 2010a; Bewley et al., 2010).  A larger sam-ple size is associated with a higher probability of capturing major outliers, and even small variations in the approaches to measure snow and vegetation by different field crews can in-troduce additional uncertainty.  While data for this section were collected from a total of 38 different ground plots, Winkler (2001), Winkler & Moore (2006) and Varhola et al. (2010a) (Section 3.3) based their results on 6, 9 and 11, respectively, which might not represent the full ranges of variation of both forest structure and snow metrics.  Another factor that could have affected these results is a particular pattern of snow distribution in 2009.  Bewley et al. (2010) found that a clear gradient of snow accumulation increasing from lower to higher ele-vation sites on 2008 was not detectable in 2009, the year that provided most of the records for this research, which was attributed to a cooler and windier snow accumulation phase dur-ing 2009 (when precipitation in Baker Creek was 23% higher than in 2008).  Higher wind speeds result in enhanced snow redistribution processes and increased sublimation in clear-cuts during the accumulation phase, while more snowfall can surpass the interception capac-ity of canopies (Pomeroy et al., 1998).  Thus, the relative differences between SWEmax of for-ested and open sites were smaller for 2009 (9%) compared to 2008 (20%).  All forested plots showed less snow accumulation than the clearcuts in 2008, while the opposite happened in some plots during 2009 ?enough to generate notable outliers.  Inter-annual fluctuations can therefore introduce additional variability to the relationships between snow indicators and forest metrics.  106  The outliers of Figure 3.5.3 are partly explained by these meteorological conditions.  Plot GY6, a mature defoliated pine stand (15.5 m tall; 1,425 stems/ha) paired with clearcut CC2, appears as an outlier for both ?SWEA and ?SARC (Figure 3.5.3a, 3.5.3b).  LOCUS data show that 2009 SWEmax and SAR at stand GY6 were 29% higher and 15% faster than its nearby clearcut, respectively, making this stand the only one with marked opposite trends in the dataset.  A higher snow accumulation in a forested stand in this area is explained by a loss of snow to wind drift and sublimation during the accumulation period in the nearby clearcut, which is likely the case for this pair of plots located on a hilltop.  A faster SAR in plot GY6 during the ablation period is probably the result of a higher contribution of longwave radia-tion from stem and canopy elements, but there is no evidence to explain why this was the only mature stand with such a condition.  The case of plot VOD1, another mature defoliated stand (9.0 m tall; 1,387 stems/ha), is similar to GY6 but showing only 8% more snow accu-mulation and an ablation rate marginally slower (1%) than its reference clearcut.  Higher wind speeds reducing SWEmax in the clearcut remain as the most probable explanation for this stand.  A healthy dense spruce plot (SP2) (9.0 m tall; 2,800 stems/ha) represents the third stand that appears as an outlier of both ?SWE and ?SAR (Figure 3.5.3), in this case showing relative differences in SWEmax and SAR larger than the general trend of the remainder plots (26% less SWEmax and 50% slower SAR), but highly consistent with what is expected in the study area.  Another spruce stand with the densest forest cover of all plots (SP1) (10.2 m tall; 6,700 stems/ha), however, presented only a small 7% reduction in SWEmax compared to its reference clearcut, which could have been affected by snow losses due to wind.  Its ?SAR of 0.37, on the other hand, was in good agreement with the general trend (Figure 3.5.3b).  Fi-nally, one of the young regeneration stands (YR3) (5.1 m tall; 2,870 stems/ha) appears to 107  have excessively retarded snow ablation given its large gap fraction (Figure 3.5.3b).  LOCUS data revealed that the mid-ablation snowfall that took place between April 12 and April 15, 2009, was more efficiently accumulated on the ground of this stand than its nearby larger counterparts, thus retarding the date of snow disappearance.  It is notable that these young regeneration and dense spruce stands, representing the extremes of the forest structure spec-trum in the area, were identified as outliers when aiming to predict snow indicators from structural metrics.  The suppression of these records from the dataset would have increased r2 of Figure 3.5.3a from a 0.33 to 0.62 and from 0.57 to 0.84 in Figure 3.5.3b.  3.5.4.2 Data sources and variable definitions  In general, LiDAR provided the variables that explained more variation of snow accumula-tion.  Since the interception of LiDAR pulses by canopy elements is analogous to the inter-ception of snowfall, it has been confirmed again, as in Section 3.3 (Varhola et al., 2010a), that LiDAR-derived forest cover is the structural metric best related to snow accumulation.  However, while in Section 3.3 it was found that FC2.0 was a substantially better predictor of SWEmax, in this section FC0.5 explained 7% more of its variation than FC2.0.  This suggests that it is useful to test several definitions of structural variables in different studies, and that further research is required to specifically analyze the physical relationship between the ver-tical distribution of LiDAR points and SWEmax.  LiDAR datasets with a higher return density are required for such a purpose.  108  HP-derived metrics were the best potential predictors of ?SAR.  One of the primary drivers of snowmelt in the study area is incoming shortwave radiation (Bewley et al., 2010).  The up-ward-looking hemispherical representation of vegetation structure as captured by HP (Figure 3.5.1) can incorporate the sun?s daily paths across canopy elements and is therefore highly related to radiative energy and snowmelt (Musselman et al., 2012), which was confirmed here.  While hemispherical metrics can also be derived from coordinate-transformed LiDAR data (Table 3.2.3) as shown in Section 4.3 (Varhola et al., 2012), these contain some calibra-tion errors that are absent from images directly captured by HP and will therefore introduce some additional variability to the correlations with ?SAR.  However, since HP acquisitions across the landscape require intensive fieldwork, LiDAR-derived GF or LAI are better suited to predict spatially-distributed ?SAR in the study area with an additional plot-level error of 13% if compared to HP.  Direct relationships between satellite-derived spectral indices and snow indicators have not been previously explored, perhaps because they are considered too empirical.  However, if strong links exist between spectral and structural properties of vegetation (see Section 4.4) (Varhola & Coops, 2013), predicting spatially-distributed snow indicators directly from spec-tral indices is highly desirable because it saves the costs of intense field surveys or LiDAR acquisitions, even if the errors are slightly higher (Figure 3.5.2).  It was shown here that the performance of some spectral indices in predicting snow accumulation and ablation was comparable to HP and LiDAR, opening a new line of research with important practical con-siderations.  109  In general, ?SWE and ?SAR were better predicted by forest metrics when absolute SWEmax was used in the calculations (?SWEA).  This is advantageous because identifying the absolute SWEmax in continuous snow curves is simpler than defining a period of sustained ablation, which was different from the ablation period based on absolute SWEmax as a starting point in some plots and not in others ?despite their geographical proximity.  Additionally, SWEA is a better representative of the total amount of water available at the watershed level prior to melt.  The results of this section indicate that:  1) continuous measurements are required to correctly identify periods of sustained snow ablation; and 2) clear definitions of SWEmax are required to explore the relationship between snow accumulation and forest structure.  Appropriate definitions of SAR might differ according to the purpose of a specific study.  While SAR was better predicted at the plot level by forest metrics derived from HP when considering the full ablation period ?lasting an average of 26 days in Baker Creek and Fra-ser Lake? catchment peak flows with flooding potential might be associated with a more specific time subset ?daily or even sub-daily? when there is maximum energy available for melt and the highest runoff contribution from the catchment area.  In any case, having con-tinuous records of SWE measurements and meteorological data from appropriate instrumen-tation such as LOCUS devices is fundamental for the development of different SAR defini-tions and the identification of particular conditions generating flooding.     110  3.5.4.3 Linear regression and meteorological variables  While statistically-valid models could be developed to predict ?SWEA and ?SARC, their pre-dictive power was limited by low r2.  The addition of minimum January relative humidity (MNRH1) through multiple regression improved the potential of forest structure to predict ?SWEA; however, it is difficult to explain the physical basis of this relationship in a simple empirical model.  Relative humidity plays a role in the amount of precipitation, vapor pres-sure gradients between snow surface and atmosphere that can enhance snow sublimation, and contribution of latent heat to a snowpack from water vapor condensation.  The influence of bulk winter meteorological conditions on snow accumulation via their effect on precipitation and snowpack development in the context of simple empirical models requires additional, focused research.  Since sensible heat fluxes are as important as shortwave radiation in driving snowmelt in this study area (Bewley et al. 2010), the poor performance of temperature indicators in snowmelt models was unexpected.  None of the temperature or vapor pressure indicators estimated was significantly correlated to ?SAR, a result also found in Section 3.2.  This is perhaps partly due to the relatively small variability of meteorological metrics, which showed a coefficient of variation of 20% that contrasts with 52% for forest metrics derived from HP and 104% for ?SAR.  More research is needed to identify additional forest, meteorological and physi-ographic indicators able to reduce the unexplained variance of ?SWE and ?SAR.   111  3.5.4.4 Limitations and strengths  Records representing two snow seasons, with snow being monitored by LOCUS sensors only in 2009, is a shortcoming that hindered the analyses.  A paired-plot approach based on refer-ence open areas and nearby forested plots is affected by the different conditions that charac-terize those open areas, which will show variable patterns of snow accumulation and ablation according to clearcut shape and area, patchiness, wind fetch and elevation.  While our plots were all located on a relatively flat plateau, other areas could also be affected by major dif-ferences in the energy available for melt across slope-aspect gradients.  Moreover, individual plots located within an open area might not adequately represent the actual SWEmax or SAR of the entire clearcut and hence may produce biased estimates that will replicate in the standard-ized forested plots, which can also be inaccurately quantifying stand-level characteristics.  Supporting this, Winkler (2001) concluded that snow processes are more predictable at the stand level (1 ha) than in traditional smaller plots (which, on the other hand, are easier to measure).  Finally, even though the effects of defoliation by MPB are detected in most of our plots by LiDAR, HP and Landsat, the nature of snow interception and radiation extinction is likely different in healthy stands with similar values of forest structure metrics.  The results of this research are therefore not applicable to healthy forests or other study areas.  Address-ing the limitations of this section and isolating some of the confounding effects identified can potentially improve the relationships between forest structure and snow indicators.  An advantage of this section is the use of a large number of experimental plots and a stan-dardization procedure to merge data from various sources.  A larger sample size is associated 112  with a higher likelihood of detecting outliers, which in turn help explain anomalous condi-tions that affect the relationship between forest structure and snow indicators, and will there-fore provide valuable information to improve future experimental designs.  Here, a pair of plots located on a hilltop considerably weakened the relationships (Figure 3.5.3) by showing less snow accumulation and slower ablation rates in the clearcut than in the forest.  Addition-ally, the development of a wide range of forest structure metrics and spectral indices fa-voured a comprehensive analysis of which variables are more suitable for the prediction of snow indicators.  This allows for an adequate selection of data sources for future studies by considering both practical and accuracy matters.  The most relevant advantage and contribu-tion of this research was demonstrating that continuous snow depth measurements of snow from LOCUS devices, transformed to plot-level SWE with simple interpolation of density samples, was fundamental to explain important portions of the variability of snow indicators.  Traditional snow surveys were not suitable in this case to establish any noteworthy relation-ship between snow indicators and forest metrics.  Finally, an original contribution of this sec-tion is the correlation analysis between spectral indices and snow indicators, the positive re-sults of which suggest that future research of those relationships is justified.  3.5.4.5 Future work  Future research to improve empirical snow-vegetation models should focus on addressing the limitations described above and designing consistent, long-term experiments that incorporate the best remote sensing technologies to measure both snow and forest properties at various spatial scales.  The end goal is to produce watershed-level, spatially-explicit maps of SWEmax 113  and SAR in both forested and open pixels so that the relative contribution of snowmelt from each pixel can be routed as runoff and streamflow.  The effect of accuracy in both pixel-level estimation and spatial distribution of snow indicators needs to be systematically evaluated to understand how it affects the sensitivity of streamflow simulations.  There seems to be more room for improvement in our techniques to estimate spatially-distributed SWE in areas larger than our small plots than there is to characterize forest structure.  While the latter is relatively static and successfully measured with current tools, monitoring snow dynamics in detail at the hectare or squared kilometer scale has long eluded scientists.  Radar satellites can be used to estimate SWE at these scales but require intensive data processing capabilities and cannot be used in forested conditions.  Sequential LiDAR acquisitions (e.g. Hopkinson et al., 2004, 2012) throughout the snow accumulation and ablation phases, on the other hand, can provide good estimates of snow depth and forest structure simultaneously, and are likely the best ap-proach to improve our understanding of how SWEmax is spatially distributed in both clearcuts and adjacent forests in multiple scales if complemented with ground-based SWE surveys and ultrasonic snow depth measurements.  Obtaining accurate estimates of watershed-level SWE distribution prior to spring melt is fundamental for the subsequent prediction of streamflow (Golding & Swanson, 1986).       114  3.5.5 Conclusions  This section aimed to explore the relationships between a wide array of forest structure met-rics ?obtained from LiDAR, optical hemispherical photography and spectral indices? and indicators of snow accumulation and ablation estimated from traditional field surveys and ultrasonic range sensors.  It was confirmed that LiDAR-derived forest cover was best corre-lated to absolute peak SWE among other forest structure metrics, although r2 values were not high enough to enable accurate predictions, even if additional variables were incorporated.  Vegetation variables derived from hemispherical images ranked the highest as predictors of snow ablation, with gap fraction integrated for a 45? angle of view from the zenith being slightly better than gap fractions for other angles.  Some spectral indices derived from Land-sat, despite being indirectly related to forest structure and snow indicators, explained compa-rable portions of the variation of ablation rate as LiDAR and HP-derived metrics.  This shows potential for further research since obtaining snow indicators directly from freely-available satellite imagery has important practical implications.  Absolute peak SWE was bet-ter correlated to forest metrics than peak SWE captured right before a period of sustained ab-lation, and ablation rates were better predicted by forest structure metrics when the full abla-tion period (from absolute peak SWE to snow disappearance) was considered, as opposed to the period of sustained ablation.  The main contribution of this study was demonstrating the importance of adequately capturing peak SWE and snow disappearance dates with continuous daily SWE averages estimated from inexpensive ultrasonic snow depth sensors (LOCUS) coupled with snow density data collected from surveys.  Previous snow-vegetation empirical 115  studies relied on manual, discrete snow surveys to obtain their results and would have bene-fited from the use of continuous estimates of SWE.  This research has not been able to show an improvement in the relationships between snow indicators and forest structure as compared to previous publications, mainly because data from several sources were used and involved only two years of snow monitoring.  However, the use of a wide range of plots helped to identify some outliers and explain additional sources of variation that could be isolated in future experimental designs.  Current approaches to predict snow accumulation and ablation at the watershed level, whether physically-based or empirical, all seem to be affected by large uncertainties and se-vere limitations.  The revision of empirical snow?vegetation models should continue in fu-ture research seeking for the development of simple methods to provide spatially-explicit predictions of snow accumulation and ablation.  Many previous studies have been based on small samples and/or have not used the full potential of remote sensing or modern tools to measure both snow and forest structure consistently in long-term experiments.   116  4 Physically-based hydrologic models  4.1 Introduction and chapter overview  One of the main challenges for distributed hydrologic modeling is the requirement of physi-cally-meaningful allocations of pixel- and watershed-level parameters; while some can be directly estimated, others often need to be fine-tuned to produce reasonable outcomes.  This introduces modeling errors and the risk of achieving the right results for the wrong reasons ?a concept known as equifinality (Beven, 2001).  In Hydrology, parameter uncertainties are partly a result of the stochastic nature of water dynamics and science not being able to char-acterize the complexities of catchment attributes such as soil properties, bedrock conditions, the spatial distribution of meteorological forcing inputs and biophysical conditions of vegeta-tion.  Particularly, modeling snow interception, radiation attenuation and other biophysical processes requires a detailed characterisation of vegetation structure.  While the capacity of forests to intercept snow is primarily affected by snow density, stand architecture and branch flexibility (Parviainen & Pomeroy, 2000), spatiotemporal patterns of light transmission through the canopies are created by the interaction between local solar paths, the anisotropy of diffuse sky brightness, cloud cover and the three-dimensional distribution of all canopy elements (i.e., foliage, branches, boles and gap space) (Hardy et al., 2004). Variations of these factors can create an unlimited array of micro-environments within a forest, each with a distinctive gap distribution that ultimately determines how much of the falling snow and in-coming radiation actually reaches the ground (Hardy et al., 2004; Essery et al., 2007). Char-acterising sub-canopy snow dynamics and radiation regimes within a specific spatial unit 117  thus requires quantification of this structural complexity into numerical parameters readily available as inputs for hydrologic models.  The four forest structure metrics that are almost invariably used in most popular distributed physically-based models are leaf area index (LAI), forest cover (FC), sky-view factor (SVF) and forest height (H) (Wigmosta et al., 1994; Tarboton & Luce, 1996; Storck et al., 2002; Pomeroy et al., 2007).  A fifth variable, gap fraction (GF), is only seldom used directly by models (e.g. Chen et al., 2005; Liston & Elder, 2006), but is also of importance because it is directly used to derive LAI and SVF (Section 4.3) (Varhola et al., 2012).   LAI (m2/m2) is mainly defined as the ratio of one-half (i.e. one-sided) of the total leaf area per unit of ground surface area (Watson, 1947; Chen et al., 1997).  Because this variable is difficult to measure directly in forested environments, researchers have commonly estimated it using optical methods such as hemispherical photography.  Even though this version of LAI does not ac-count for foliage clumping nor distinguish between leaves and woody elements, it has been consistently used as the main vegetation structure parameter in hydrologic models (Varhola et al., 2012).  LAI is the one of the primary drivers of radiation attenuation affecting snow-melt and also influences the estimation of canopy snow interception capacity and wind speed reduction (Pomeroy & Dion, 1996; Storck, 2000; Pomeroy et al., 2009; Ellis et al., 2010).  FC is the fraction of a two-dimensional horizontal spatial unit that is occupied by tree ele-ments and is commonly measured with ground surveys, high-resolution aerial photography or empirical relationships with other variables (Pomeroy et al., 2002; Varhola et al., 2010b).  In hydrologic models, FC modulates pixel-level solar radiation transmission, direct precipita-tion and intercepted snow load (Wigmosta et al., 1994; Ellis et al., 2010).  H usually refers to 118  the mean height of a sample or all trees within a spatial unit, where individual tree height is the distance from the ground to the highest point in each canopy.  Several equations and con-ditional statements involve H within hydrologic models, mainly related to wind speed reduc-tion, canopy resistance and snow redistribution (Pomeroy et al., 2007).  SVF is defined as the fraction of sky visible from a point near the forest floor (Sicart et al., 2004), essentially rep-resenting the portion of a hemispherical image occupied by sky pixels as calculated from a cosine-weighted 180? integration of angular gap fractions (Frazer et al., 1999).  SVF is spe-cifically used in hydrologic models to estimate the net longwave radiation of snowpack sur-face.  Finally, GF is the fraction of view that is unobstructed by canopy elements in any par-ticular angular direction (Welles & Cohen, 1996), equivalent to the probability of a light beam passing through the forest to reach a point near the ground (Danson et al., 2007).  Sec-tion 4.2 explains in detail the roles of these variables in hydrologic models.  Although technological advances are not expected to provide detailed estimates of many ba-sin-level parameters required for hydrologic models, especially those related to soil and bed-rock, the models are in constant need of revision in light of emerging remote sensing tools.  In fact, one of the aspects of hydrologic modeling that is now suitable for substantial im-provement by remote sensing is the characterization of vegetation structure as represented by the variables described above.  Fully-distributed models such as the Distributed Hydrological Soil Vegetation Model (DHSVM) (Wigmosta et al., 1994) currently input only a few vegeta-tion classes that are often poorly parameterized with sparse, averaged ground-based meas-urements (Bewley et al., 2010).  This limitation might not be critical in modeling experi-ments designed to evaluate the effects of clearcutting on streamflow (e.g. Kura? et al., 2012), 119  but will introduce large uncertainties where disturbances partially or gradually affect the structural and physiological integrity of vegetation ?such as the MPB-infested lodgepole pine forests of British Columbia.  Most of the studies evaluating the hydrologic effects of de-foliation and tree fall in MPB-affected forests have focused on snow processes at the plot scale (e.g. Boon, 2007, 2009; Teti, 2008; Jackson & Prowse, 2009), while authors conducting modeling exercises at the catchment level have explicitly acknowledged that improved fully-distributed forest structure metrics acquired from remote sensing are necessary to evaluate the effects of these disturbance types (Bewley et al., 2010).    Even though ALS emerges as an obvious resource to overcome these limitations, the applica-tion of this technology to directly improve hydrologic modeling has been explored mostly through the use of accurate high-resolution DEMs rather than vegetation structure metrics (Chen et al., 2005).  Contrasting with the body of literature focusing on LiDAR DEMs (e.g. Fang et al., 2010; Murphy et al., 2008; N?elz et al., 2006; Petroselli, 2012; Shengli et al., 2011; Shook & Pomeroy, 2011; Vetter et al., 2011), only a few studies have been published about using this tool to directly review the relationships between biophysical properties of vegetation and components of the water cycle, and mostly focusing on the plot scale (e.g. Hennon et al., 2010; Roth et al., 2012; Varhola et al., 2010a).    While stand-level studies are important to advance our understanding of the relationship be-tween forest structure and water dynamics, hydrologic modeling needs to be ultimately im-proved at the watershed level by applying physically-based, spatially-explicit approaches.  Some researchers have conducted distributed modeling experiments using vegetation remote 120  sensing inputs mainly based on coarse-resolution (> 1 km scale) LAI products derived from sensors such as the Moderate-Resolution Imaging Spectroradiometer (MODIS) (Liu et al., 2012) or the Advanced Very High Resolution Radiometer (AVHRR) (Andersen et al., 2002; Biftu & Gan, 2001; Droogers & Kite, 2002).  These sensors may be appropriate for very large basins but offer limited opportunities to analyze the finer-scale physical relationships between vegetation and hydrologic processes or to detect model sensitivity to fully-distributed variables (Liu et al., 2012).  Chen et al. (2005) modified DHSVM to allow the use of a suite of remote sensing inputs for evapotranspiration modeling, including a finer spatial resolution (30 m) Landsat-derived LAI which was spatially distributed in six categories within a ~200 km2 watershed.  However, besides acknowledging the influence of LAI spatial distribution on evapotranspiration, the study lacked direct comparisons between results from the original and modified version of DHSVM and did not consider other relevant forest struc-ture metrics.  New approaches should thus focus on developing methodologies to directly obtain all the variables needed as inputs to parameterize distributed hydrologic models across large areas and with the highest spatial resolution possible.    This chapter is divided into three sections.  Section 4.2 is an introductory background review-ing the forest structure metrics currently used by popular hydrologic models, and describing their specific roles within process-based equations relevant to snow processes.  Section 4.3 investigates the ability of ALS to provide versions of these metrics that are as similar as pos-sible to those commonly used by hydrologic models.  Since the ALS acquisition for this the-sis does not cover an entire watershed, the purpose of Section 4.4 is to show how forest struc-121  ture metrics obtained with ALS can be extrapolated through the landscape by means of novel and comprehensive models predicting these metrics from Landsat-derived spectral indices.     4.2 Overview of the forest structure metrics used in physically-based hydro-logic models   This section briefly reviews the definitions of the four main forest structure variables used by hydrologic models, and the physically-based process equations that describe their relation-ship to hydrologic processes.  The fully-distributed DHSVM (Wigmosta et al., 1994) and the semi-distributed Cold Regions Hydrologic Model (CRHM) (Pomeroy et al., 2007) are used as references because both models are involved in previous (Bewley et al., 2010) and future articles in the study area.  4.2.1 Leaf area index (LAI)  LAI is the most commonly ?and often unique? used variable to relate forest structure with hydrologic processes, and has been also widely applied in forestry and other environmental sciences.  The only method that directly measures LAI is based on destructive sampling that is not really applicable to forests, so many indirect alternatives have been developed: relationships between leaf area and other stand attributes, ground-based optical instruments, LiDAR, and satellites (e.g. Br?da, 2003; Darvishzadeh et al., 2008; Solberg et al., 2009; Jensen et al., 2011; Varhola et al., 2012).  The literature about LAI estimation in forests is so 122  vast and the numerical methods to integrate it from optical measurements so complex, that many of the resulting versions of the variable often detract from its original definition.  In studies parameterizing hydrologic models, LAI has been mostly obtained from hemispherical photography (e.g Essery et al., 2008; Bewley et al., 2010) or the LI-COR? LAI-2000 Plant Canopy Analyzer (LAI-2000) (e.g. Hedstrom & Pomeroy, 1998; Sicart et al., 2004), both providing a very similar simplistic LAI proxy that does not account for foliage clumping nor distinguishes leaves from woody boles and branches (Welles & Norman, 1991; Stenberg et al., 1994).  For this reason it is sometimes referred to as plant area index (PAI) (e.g. Bewley et al., 2010) or effective leaf area index (LAIe or LAI?) (e.g. Pomeroy et al. 2002), but very frequently just regarded as LAI (e.g. VanShaar et al., 2002).  This thesis does not account for controversies about the procedures to estimate LAI or its original physical definition (Ryu et al., 2010), but simply assumes it is the variable used in hydrologic models as obtained from hemispherical photography processed with specialized software [e.g. Gap Light Analyzer, GLA (Frazer et al., 1999)] or LAI-2000.  The interception capacity of forests is estimated for defined time steps as a function of LAI in CRHM (Ellis et al., 2010):  Is = Sp (0.27 + 46 ?s?1) LAI        4.2.1  where Is is the species-specific maximum intercepted snow load (kg/m2), Sp is the maximum snow load per unit area of branch, and ?s is snow density (kg/m3).  A similar approach is used by DHSVM to estimate interception based on a maximum interception capacity de-123  pendent on LAI (Storck, 2000; Bewley et al., 2010).  Some values of Sp have been published in the literature for different species (Jost et al., 2012).  LAI is also used in DHSVM and CRHM to estimate the attenuation of radiation passing through forest canopies based on a Beer?s law equation, modified by (Pomeroy & Dion, 1996) and later by (Pomeroy et al., 2009) to account for local solar angles (Ellis et al., 2010):  ?F = exp[?1.081 LAI ? cos(?) sin(?) ?1]      4.2.2  where ?F is the solar radiation transmission coefficient through the canopies (unitless) and ? is the solar angle above the horizon (radians).  ? is then used to calculate the total incoming radiation absorbed by snow at the pixel or plot level by adjusting for FC (Equation 4.2.7).  The canopy wind extinction coefficient (wext) (unitless), fundamental to estimate turbulent energy fluxes, is also calculated from LAI (Pomeroy et al., 2007):  wext = ? LAI (1 ? Zvent)        4.2.3  where ? is a parameter set to 1.15 by default in CRHM, and Zvent (unitless) is the ventilation wind speed height calculated as a ratio between the height at which wind speed is measured and canopy height.  124  Finally, LAI can be used to estimate FC and SVF if these are not available (Pomeroy et al., 2002, 2009):  SVF = 0.45 ? 0.29 ln(LAI)        4.2.4  FC = 0.29 ln(LAI) + 0.55        4.2.5  There are additional calculations done by CRHM with LAI, which are not shown here for brevity.  4.2.2 Sky-view factor (SVF)  SVF essentially represents the portion of a hemispherical image occupied by sky pixels and is similar to the gap fraction of the entire image as calculated from a cosine-weighted 180? in-tegration of angular gap fractions (Frazer et al., 1999).  In hydrologic models, SVF is specifi-cally used to estimate net longwave radiation of snowpack surface (L):  L = SVF L? + (1 ? SVF) ?f ? Tf4 ? ?s ? Ts4      4.2.6  where L? is the incoming longwave radiation from the sky (W/m2), ? is the thermal emissiv-ity, ? is the Stefan?Boltzmann constant (W/m2/K4), T is temperature (K) and the subscripts f and s respectively indicate forest or snow (Ellis et al., 2010).  This equation thus accounts for incoming longwave radiation from the atmosphere (first term), radiation emission from the forest?s structural elements (second term) and the radiation losses from the snow (third term).  125  SVF is traditionally measured from hemispherical photography or LAI-2000, estimated from LAI with Equation 4.2.4 or indirectly from radiation measurements (Sicart et al., 2004).  4.2.3 Forest cover (FC)  In hydrologic models, this variable is used to model pixel-level solar radiation transmission (?P) (unitless), direct precipitation (Pd) (mm), and intercepted snow load (I) when wind speeds are higher than 1 m/s:   ?P = ?F FC + (1 ? FC)         4.2.7  Pd = P (1 ? FC)         4.2.8  I = (Is ? SL) [1 ? exp(?FC Ps Is?1)]       4.2.9  where ?F has been defined for Equation 4.2.2, P is precipitation (mm), SL is the canopy snow load at a certain time step (mm), Ps is snow precipitation (mm) and Is has been defined in Equation 4.2.1.  FC is also used for evapotranspiration calculations under certain conditional statements, not shown for brevity.  FC is usually measured through ground surveys recording stem locations and crown dimensions, with high-resolution aerial photography where crowns can be delineated, through empirical relationships with other variables (Equation 4.2.5), or with ALS.  ALS is known to be very accurate at measuring FC because the ratio between canopy-intercepted and total number of near-vertical pulses is conceptually equivalent to a horizontal measure of forest cover (Wulder et al., 2008).  Despite this simple definition, for-126  est cover has not always been consistently described in hydrologic studies; Section 1.2.9 in-cluded a review of the terminology and some of the techniques applied to obtain FC by re-searchers in the context of hydrology.  4.2.4 Forest height (H)  The equations that involve H within hydrologic models are rarely reported in the articles de-scribing the models; however, this variable is very important for a number of processes, es-pecially related to wind speed reduction and, in CRHM, snow redistribution (Pomeroy et al., 2007).   4.3 Estimation of forest structure metrics relevant to hydrologic modeling us-ing coordinate transformation of airborne laser scanning data   4.3.1 Introduction  Reliable estimates of FC, LAI, SVF, H (and occasionally GF) are required to parameterize distributed hydrologic models.  ALS has already been successfully used to directly quantify FC (e.g. Ria?o et al., 2004; Wulder et al., 2008) and H (e.g. Popescu et al., 2002; Lim et al., 2003; Mora et al., 2013) based on simple canopy/ground return ratios and return elevation percentiles, respectively, with accuracies that likely surpass any known ground-based ap-proach.  The estimation of LAI, GF, and SVF from ALS, on the other hand, is subject to fur-127  ther improvements that should focus on narrowing the physical and geometrical resemblance between the point-cloud representations of canopies provided by ALS and the current meth-ods to estimate these variables in the field by hydrologists.  One instrument frequently used for this purpose is the LAI-2000, which can provide LAI and GF by simultaneously comparing incoming diffuse radiation above and below the canopy (Welles & Norman, 1991).  HP is another popular alternative that uses skyward-looking im-ages taken from beneath the forest to estimate various attributes of canopy structure and to model light penetration over periods of time (i.e., growing season).  Both the LAI-2000 and HP are based on a hemispherical projection geometry usually comprising a wide field of view (~ 180? for HP and 148? for LAI-2000), which is fundamental to provide multi-angular estimates of GF and, in HP, to account for local solar paths and the angular variation in dif-fuse sky brightness. Advantages of HP over the LAI-2000 are that HP does not require above-canopy measurements of diffuse sky radiation to compute GFs and it provides a per-manent image of the forest that can be processed with software tools to automatically obtain a variety of structural and site-specific radiation parameters [e.g. GLA by Frazer et al. (1999), or Hemiview by Rich et al. (1999)].  Although HP is not free of bias in the presence of heterogeneous lighting conditions and is subject to certain subjectivity when manually bi-narizing the images to separate canopy and sky pixels, it has been validated as a tool to accu-rately model radiation regimes beneath forest canopies, provided that a few basic local pa-rameters are known (Coops et al., 2004).  Hardy et al. (2004), for example, compared above- and below-canopy incoming global solar radiation measurements from pyranometers with radiation transmission estimates obtained from HP, and concluded that both agreed well 128  enough to be interchangeably used in snow models.  One disadvantage of HP, however, is that image acquisition and processing are time-consuming and, therefore, cannot be easily applied to vast, remote areas (Essery et al., 2007).  There is a significant body of literature investigating the application of ALS to predict tradi-tional stand attributes such as tree density, diameter, height, timber volume, biomass and for-est cover (e.g. N?sset, 2002; Lim et al., 2003; Lovell et al., 2003; Wulder et al., 2008), while only a few articles have directly compared ALS metrics with HP-derived stand parameters. Solberg et al. (2006), for example, parameterised models to estimate LAI from discrete ALS by fitting simple ALS return penetration ratios to LAI data obtained from HP and LAI-2000 measurements, with the aim of detecting and mapping defoliation caused by an insect out-break in Norway. They found a strong linear relationship between the log-transformed in-verse of vertical GF obtained from repeated ALS acquisitions and LAI estimated in the field.  To improve the relationship, follow-up studies reapplied similar methodologies varying im-age pre-processing procedures (Hanssen & Solberg, 2007) and testing different ranges of ALS plot radii, tree species and ALS return configurations (Solberg et al., 2009; Solberg, 2010). These and comparable articles published by Ria?o et al. (2004b), Morsdorf et al. (2006), Jensen et al. (2008, 2011) and Korhonen et al. (2011), all rely on regression-based estimates of LAI or GF using simple vertical ALS return ratios obtained from cylindrical plots as predictors. The studies recognise and conclude that the different perspectives and projection geometries associated with HP (upward-looking, angular) versus ALS (downward-looking, near-vertical) sensors make it difficult to establish an exact match between the two techniques. 129   The objective of this section is to develop a methodology to obtain HP-equivalent forest can-opy GF, LAI, SVF and solar radiation transmission metrics at any location within a discrete ALS cloud of points.  This novel approach transforms the Cartesian coordinates of the ALS return cloud into a polar coordinate system to produce synthetic, upward-looking hemi-spherical images suitable for processing with specialized software (GLA).  Metrics obtained from these images are then calibrated directly with real optical HP counterparts collected within a network of ground-reference sites.  This method has the following advantages com-pared to previous studies that have attempted to link ALS and HP metrics:  1) it is based on the same geometrical projection and therefore minimizes calibration errors; 2) it takes advan-tage of the entire functionality of GLA or Hemiview, including the calculation of forest structure parameters and a variety of light indices for user-defined requirements; 3) it is less restricted to any particular spatial resolution associated with ALS cylinder size (Zhao & Popescu, 2009); 4) it does not require direct radiation measurements for validation due to the proven ability of HP to predict radiation regimes (Hardy et al., 2004); 5) it is based on a paired one-on-one comparison of hemispherical images rather than plot averages, allowing a more detailed exploration of the ideal physical representation of canopies by ALS and the direct input of point-level forest structure metrics into hydrological models to analyze rele-vant processes at the finest possible scale (e.g. Pomeroy et al., 2007); and, finally, 6) it only requires raw ALS data and HP without relying on manual ground measurements, comple-mentary spectral remote sensing tools or sophisticated tree-reconstruction or stem mapping techniques (e.g. Roberts et al., 2005).    130  The analyses of this section are focused on obtaining the forest structure metrics that are cur-rently used by most hydrologic models at any point within an ALS return cloud.  The direct input of these remotely-sensed variables into the models is not tested because the main bene-fit of this methodology is the better characterization of canopy structure in space rather than the simulation of hydrologic processes at the point level, which can be achieved with tradi-tional optical HP.  The next section will take advantage of the opportunity to generate thou-sands of synthetic hemispherical images derived from ALS to assess the spatial distribution of forest structure metrics relevant to hydrologic modeling at the watershed level, and later fulfill the ultimate goal of allocating fully-distributed, spatially explicit versions of these met-rics to the models.  This section has been published in Varhola et al. (2012).  4.3.2 Methods  4.3.2.1 Study area  Seven forested plots established by Teti (2008) provided the model calibration data for this research, and are described in detail in Table 4.3.1.  The first four plots are located in the Baker Creek watershed, near Quesnel, while three are south of Fraser Lake (Section 2.1).  The plots are representative of the main stand types and their relative predominance in the area at the time of their installation, namely:  mature stands (height > 15 m) where most of the trees had been severely defoliated by MPB (BOD1, BOD3, VOD1 and VOD2); interme-diate (height ~10 m) stands affected by MPB but with their trees still holding dehydrated, red foliage (BRC2); and young healthy-looking stands (height ~3 m) (BRC1).  An additional plot 131  was located in a dense stand resulting from post-fire regeneration (VYN), with high stem densities and 25% mortality caused by within-stand competition and ice / snow-related breakage rather than MPB.  Eleven additional plots of a different size and configuration, which included additional stand types such as healthy spruce, were used to validate the methodology at the plot-level.   4.3.2.2 Data acquisition for modeling  ALS and HP were obtained as explained in Sections 2.2 and 2.4 respectively.  To estimate plot center elevations, a ground-level DEM with 5 m pixels (25 m2) was derived from ALS data, as explained in Section 2.2.  A selection of basic ALS metrics was obtained for each 50 ? 50 m plot to explore the overall variability of forest structure and data configuration (Table 4.3.2).  The total number of ALS returns per plot was separated into sub-canopy (below 0.5 m) and canopy (above 0.5 m) classes.  ALS return density was calculated by dividing the total number of laser returns by plot area (2,500 m2), while ALS metadata provided mean absolute scan angle directly.  Ver-tical GF was calculated for each plot as the ratio of sub-canopy returns (>0.5 m) to total ALS returns.  A mean canopy height proxy was the average height above ground of all canopy re-turns (different from mean tree height).  In all cases, no distinction was made between first and other return types.   132   Table 4.3.1.  Stand locations and physical characteristics as of 2008. General information Ground inventory metrics Foliage appearance (%) b Plot codes a Stand descrip-tion (age) Latitude (?) Longi-tude (?) Elevation (m) Stem density (n/ha) DBH (cm) Basal area (m2/ha) Mean height (m) Max. height (m) Green Red Grey BOD1 Mature heavily defoliated stand (216) 52.676 -123.016 1,218 1,800 18.5 55.4 18.2 28.9 0 19 77 BOD3 Mature defoli-ated stand (211) 52.638 -122.993 1,222 550 25.5 28.7 17.3 26.2 8 14 77 BRC1 Small healthy regeneration (10) 52.670 -123.017 1,231 1,312 5.4 1.1 3.9 5.6 100 0 0 BRC2 Medium red-attack stand (26) 52.672 -123.017 1,229 1,025 13.5 15.0 10.1 13.5 48 52 0 VOD1 Mature defoli-ated stand (135) 53.720 -124.949 902 1,387 18.0 19.0 9.0 17.3 22 0 78 VOD2 Mature heavily defoliated stand (135) 53.717 -124.955 836 1,687 21.6 55.6 13.2 20.8 5 5 90 VYN Dense natural post-fire stand (75) 53.719 -124.953 900 7,648 8.0 34.0 9.7 14.3 75 0 25  a Following codes by Teti (2008); first letter in code corresponds to the study area. b Defoliation percentage calculated as proportion of basal area falling into each health category, described in Section 1.3 and Section 2.7.   Table 4.3.2.  ALS simple metric summary for each major plot. Plot codes Stand description (age) Total ALS returns Ground ALS returns Canopy ALS returns Return density (n/m2) Mean absolute scan angle (?) a Vertical gap fraction Maximum return height (m) Mean can-opy return height (m) a BOD1 Mature heavily defoli-ated stand (216) 13,521 10,042 3,479 5.4 0.6 (118) 0.74 25.7 12.7 (55) BOD3 Mature defoliated stand (211) 21,209 16,070 5,139 8.5 7.7 (49) 0.76 23.8 12.3 (51) BRC1 Small healthy regen-eration (10) 18,273 15,275 2,998 7.3 5.0 (32) 0.84 4.2 1.3 (52) BRC2 Medium red-attack stand (26) 19,232 10,393 8,839 7.7 4.2 (48) 0.54 11.6 5.5 (53) VOD1 Mature defoliated stand (135) 17,095 12,899 4,196 6.8 13.7 (9) 0.75 20.5 7.0 (68) VOD2 Mature heavily defoli-ated stand (135) 17,014 13,611 3,403 6.8 3.9 (46) 0.80 20.4 11.9 (42) VYN Dense natural post-fire stand (75) 19,699 9,279 10,420 7.9 6.1 (27) 0.47 12.8 6.0 (46)  a Coefficients of variation (%) from individual returns in parentheses.     133  4.3.2.3 Synthetic ALS hemispherical image generation  ALS data were extracted for 75 m radius cylinders centered at each of the sampling points, a size  chosen to ensure that enough ALS returns were included closer to the horizon to mimic the infinite viewing distance of optical HP, yet small enough so that the entire cylinders fitted into the 400 m-wide data transect.  Only the three northernmost rows of plot VOD1 were ex-cluded as they were too close to the ALS boundary, thus reducing the sample to a total of 234 cylinders.  All the ALS returns (first, intermediate, last) were included in the cylinders to maximize density as proposed by Todd et al. (2003) and Lee et al. (2009).    Figure 4.3.1.  Effect of projected ALS return size on the relationship between observed and predicted gap fractions.  The projected circle size of synthetic image examples (a, b, c) and corresponding relationships (d, e, f) is expressed as the fraction between the diameter of each ALS return and the diameter of the image:  0.0137 (a, d), 0.0176 (b, e), and 0.0215 (c, f). 134  Each Cartesian (XYZ) reference position was set to 60 cm above the ALS DEM to account for the fact that ALS was collected during winter when ground returns recorded a snow layer averaging 50 cm of depth (Coops et al., 2009) rather than the bare soil where the HP camera was later positioned.  ALS returns at elevations below the camera?s maximum field of view were eliminated from the 75 m cylinders to increase data processing efficiency. The XYZ positions of all the remaining returns were transformed with simple trigonometry to polar coordinates composed of angles of azimuth (?) and zenith (?), and distance (m) with respect to each HP reference position.  Finally, angles of azimuth were flipped in an east ? west di-rection to reflect an upward-looking field of view as in HP.  The fine-scale representation of physical vegetation structure by individual ALS returns is not well understood, and several assumptions are therefore required to convert laser points into geometrically simplified, 3-D plant structures.  A sensitivity analysis was undertaken on a subsample of calibration plots to explore the impact of three main parameter settings re-lated to projected canopy element size and shape:  1) projecting returns with a fixed or vari-able size (inversely proportional to distance), or a combination of the two; 2) minimum ALS return circle size for fixed projections; and 3) ALS return sphere size for variable projections.  More details about these parameters and their implications are clarified below as the method-ology for generating the synthetic images is explained.  The optimal parameter settings were chosen by evaluating scatter plots and correlation coefficients of observed GFs in real versus synthetic images, while keeping the other parameters constant.  Figure 4.3.1 shows an exam-ple testing three different minimum fixed projected sizes.  135  Based on the results of the sensitivity analysis, each ALS return was represented as an opaque sphere with a 15 cm diameter centered on the original ALS XYZ return location.  These spheres were projected as black circles on a two-dimensional plane to create one syn-thetic hemispherical image for each sampling cylinder.  Calculating the diameter of each pro-jected ALS return first required the selection of an arbitrary radius to the circular images (r) and a theoretical focal length (f), both 10 cm.  The ratio between the projected (rp) and full-scale ALS return radii (rr) is then assumed equivalent to the ratio between the focal length (f) and the absolute distance between the return?s centroid and the camera position (d):  rp / rr = f / d.  This is illustrated in Figure 4.3.2a.  Optical distortions typical of hemispherical lenses were accounted for when generating the synthetic images.  When viewed from a distance d, a sphere subtends an angle equal to the arctangent of the ratio between the sphere?s diameter and d.  A sphere located along the opti-cal axis of a fisheye lens (i.e. at zenith = 0? in this case) appears as a circle when projected on the image and gradually flattens into an ellipse as the azimuthal diameter is stretched in pro-portion to the zenith angle (Figure 4.3.2b).  This can be illustrated by considering the polar coordinate representation of three points in the celestial hemisphere ?one at the zenith, one at the east horizon, and one at the north horizon.  In polar coordinates, the line connecting the zenith with one of the points on the horizon has a length equal to the image radius (r) whereas the line connecting the two points on the horizon has a length of ? ? r/2, even though the angular separation between all three points is 90?.  Thus, the apparent area of a feature in a hemispherical image increases from zenith to horizon according to Z/90?(?/2 ? 1), where Z (?) is the zenith angle of the feature (e.g. a sphere projected in the horizon (90?) 136  appears with its azimuthal radii ?/2 (57%) larger than a sphere at the zenith).  To simplify plotting synthetic images, circles were used to represent the modeled ALS returns with their areas increased to account for the stretching.  A subsample of images with and without this radial geometric correction was generated to quantify the effect of optical distortions on LAI in different stand types.   Figure 4.3.2.  Example of the projection of an ALS spherical return into a 2-D focal plane (a), and azimuthal radial distortion correction at representative zenith angles (b).    The radial location of ALS returns in the synthetic images followed the same equiangular projection produced by the optical lens system (FC-E8 fisheye converter) used to collect the 137  real HP images (Inoue et al., 2004), where the radial distance from the center of the image is directly proportional to the zenith angle (Rich et al., 1999).  A projection based solely on variable diameters resulted in unrealistic-looking images with distant returns appearing too small to be detected as dark pixels.  To avoid this, a minimum base constant return diameter (2.15 mm within a 20 cm diameter image, in this case; Figure 4.3.1) was assigned to all re-turns in the images so that only those returns close enough to the HP reference to exceed this diameter were projected at variable, larger sizes.  Finally, ALS returns closer than 75 cm to the reference were eliminated in accordance with the HP field procedures, which specified a minimum distance between foliage and camera lens for protection purposes and to eliminate the possibility of having a large proportion of the optical field of view obscured by a single foliage unit.  Each synthetic image was generated as a 750 ? 750 pixel bitmap image file (BMP).  All 234 files were automatically created in 5 minutes and 15 seconds using MATLAB? (1.3 seconds / image) on a 2.66 GHz, 4.0 GB RAM, 64-bit computer.  4.3.2.4 Data processing  HP analysis.  Both optical HP and ALS synthetic images were analyzed with GLA using the parameters listed on Table 4.3.3.  The binarization thresholds required for optical HP were provided by Teti (2008), while synthetic ALS photos were logically generated in black and white.  GLA processing was done manually for each of the 468 images (optical and syn-thetic) at a rate of around 17 seconds per file (excluding HP binarization).  Table 4.3.4 de-138  scribes the output variables obtained from the GLA analysis for each HP and synthetic image for the 234 sample locations.  All of the variables except LAI were numerically integrated across the following zenith angle of view (AOV) (?):  0-30, 0-45, 0-60, 0-75 and 0-90?.  Lower zenith angle limits were included here to allow later explorations of their relationships with hydrologic processes, based on previous findings.  Teti (2003), for example, concluded that a 0-30? zenith AOV was most effective at explaining differences in snow storage in the presence of different-sized gaps.  In addition, sky regions including the 0-45? and 0-60? ze-nith ranges contain most of the solar paths directly responsible for spring melt in the study area.  FLAI? and LLAI? (defined on Table 4.3.4) automatically integrate LAI for zenith angles of 60 and 75? (Welles & Norman, 1991; Stenberg et al., 1994).    In light of intensive discussions and debate about true LAI derivation for decades (Br?da, 2003), it must be highlighted that this thesis is only focused on the version of LAI that has been widely used in hydrologic models: that obtained from LAI-2000 or HP, commonly known as effective LAI (eLAI) or PAI (e.g. Pomeroy & Dion, 1996; Bewley et al., 2010).  It is not the goal of this research to correct for clumping, isolate foliage from stems or formu-late hypotheses about the angular distribution of leaves because more nuanced (or simply dif-ferent) versions of LAI would also require the reparameterization of existing hydrologic models.  In this respect, LAI obtained from optical HP is considered here as the ground-truth variable.    139  Table 4.3.3.  Hemispherical photo parameter calibration. Parameter Definition a / source of information Baker Creek Vanderhoof Latitude (?) Average of study area plots 52.664 N 53.719 N Longitude (?) Average of study area plots 123.011 W 124.952 W Elevation (m) Average of study area plots 1,230 903 Slope / aspect (?) Average of study area plots 0 / 0 0 / 0 Solar time step (min) Time interval for which the sun?s position is measured between sun-rise and sunset for the full length of the growing season.  GLA de-fault value used. 5 5 Growing season start / end These dates affect the range in the solar declination for the period of interest.  In this case, the growing season was approximated to the winter period due to our later interest in snow processes. October 1 / May 31 October 1 / May 31 Azimuth / zenith sky regions Discrete areas of the sky hemisphere separated by equal-interval divisions of azimuth and zenith. 16 / 18 16 / 18 Data source Method for deriving growing season above-canopy solar radiation data. Modeled Modeled Solar constant (W/m2) Total radiant flux of the sun on a perpendicular surface located out-side the Earth?s atmosphere at a mean distance of one astronomical unit.  GLA default value used. 1,367 1,367 Cloudiness index Site-specific measurement of cloudiness: fraction of extraterrestrial radiation that reaches the ground surface as total solar radiation.  Values for both sites calculated as an average fraction of daily GLA-modeled extraterrestrial radiation and radiation measured in a weather station located in the Baker Creek area (Bewley et al., 2010). 0.49 0.49 Spectral fraction Fraction of global solar radiation (0.25 to 25.0 ?m) incident on a horizontal surface at the ground that falls within a limited range of the electromagnetic spectrum.  Values set to 1.0 to include the entire spectrum. 1.0 1.0 Units Units of measure used to compute the incident radiant flux density data output. MJ/m2/d MJ/m2/d Beam fraction Ratio of direct to total spectral radiation incident on a horizontal surface at the ground over a specified period, which is a function of cloud cover for supra-daily periods.  Values calculated from cloudi-ness index as explained by Frazer et al. (1999). 0.44 0.44 Sky region brightness Method for describing the intensity of the solar disk and diffuse sky.  The selected Standard Overcast Sky (SOC) assumes that the zenith is three times as bright as the horizon. SOC SOC Clear sky transmission coefficient Factor that describes the regional clarity of the atmosphere with respect to the instantaneous transmission of direct (beam) radiation.  Value used recommended for the area by Frazer et al. (1999). 0.6 0.6  a All definitions taken from Frazer et al. (1999).   Standard ALS metrics.  The traditional ALS metrics (without coordinate transformation) listed at the bottom of Table 4.3.4 were calculated from variable-size cylinders whose diame-ter hypothetically intercepted the canopies at each zenith AOV (?) based on plot-level maxi-mum tree height (Table 4.3.1) (for ? = 90?, cylinder diameters calculated for ? = 75? were used).  From these point clouds, vertically projected gap fraction (LVGF), mean laser canopy height (LMH), return density (LD) and scan angles (LSA) were estimated for each of the field 140  plot locations (Table 4.3.2).  LVGF and LMH are important descriptors of stand structure, while LD and LSA are principally related to ALS sensor configuration and data acquisition conditions, all potentially important sources of variation as shown in Table 4.3.2.  More spe-cifically: ? LVGF represents a downward-looking ALS ground-to-canopy return penetration ratio known to be well correlated with upward-looking HP sky / canopy GFs (Solberg, 2010).  ? LMH is an indicator of stand height and provides substantial differentiation between stands. ? LD accounts for the varying ALS return density among plots (see Table 4.3.2) produced by changing flight altitude and speed (Bater et al., 2011; Goodwin et al., 2006), which can alter the probability of ALS returns being intercepted by the canopy.  Varying patterns of flight line overlap may also contribute to markedly different laser return densities throughout the spatial coverage, and must be explicitly accounted for when neighboring or intersecting datasets result in higher numbers of returns (ALS data used here were re-stricted to a single flight line and not subject to changes in density due to overlap).   ? LSA increases from the centre of the flight line (nadir) towards the swath edge and changes the probabilities of ALS hitting different canopy sections.  For example, if scan angles are too large, laser pulses are less likely to penetrate the canopy because of a higher probability of being intercepted, resulting in a different spatial representation of the forest (Korhonen et al., 2011).    141  Table 4.3.4.  Variable acronyms and description. Variable Units Code Definition a GLA output column # Modeling role Source Optical HP gap fraction - FGF? Fraction between # of sky and total # of pixels summed for angles <= ? 10 / 6 Dependent (YS or YM) Optical HP processed with GLA Optical HP total radiation transmittance MJ/m2/d FRT? Absolute amount of total (direct + diffuse) below-canopy radiation summed for angles <= ? 32 Optical HP sky-view factor % FSVF? Percentage of total sky area found in canopy gaps summed for angles <= ? 20 Optical HP leaf area index m2/m2 FLAI? Half of total effective leaf area per unit ground area integrated for angles <= ?. From appended output b ALS gap fraction - LGF? Same as FGF? 10 / 6 Main independ-ent (X1) Synthetic ALS hemispherical images proc-essed with GLA ALS total radiation transmit-tance MJ/m2/d LRT? Same as FRT? 32 ALS sky-view factor % LSVF? Same as FSVF? 20 ALS leaf area index m2/m2 LLAI? Same as FLAI? From appended output b ALS vertical gap fraction - LVGF Ratio of ground / total ALS returns - Supporting independent (X2, X3, X4, X5) ALS raw data in cylinders with radius matching ? ALS canopy return mean height m LMH Mean ALS return height above ground - ALS return density n/m2 LD ALS return spatial density (including ground returns) - ALS mean scan angle ? LSA Mean absolute ALS scan angle -  a All definitions of GLA-derived variables have been taken from Frazer et al. (1999), where they are described with more detail.   b FLAI? and LLAI? are obtained from the appended output of GLA, where LAI 4 ring corresponds to ? = 60? and LAI 5 ring corresponds to ? = 75?.  For additional information on LAI see Welles & Norman (1991) and Stenberg et al. (1994).   4.3.2.5 Regression modeling  GF, LAI, SVF and total direct and diffuse (global) radiation transmittance are GLA outputs directly applicable in hydrologic simulators (e.g. Wigmosta et al., 1994), and were therefore selected as the main response variables in this section (Table 4.3.4).  To simplify the regres-sion analyses, given the large number of variables and zenith AOV combinations, a specific modeling strategy was designed to ensure that all models:  1) shared a unique, stable struc-ture and 2) were applicable to the full range of sampling points, avoiding the need to pre-identify different forest populations or use indicator (dummy) variables.  A preliminary analysis showed no evidence suggesting the existence of non-linear relationships between the variables, so all models were maintained linear and variable transformations were not neces-142  sary.  Both simple and multiple linear regression analyses were applied to predict the four HP-derived metrics:   YS(?) = b0 + b 1X1(?)         4.3.1  YM(?) = ? 0 + ? 1X1(?) + ? 2X2 + ? 3X3 + ? 4X4 + ? 5X5     4.3.2  where ? is the maximum zenith AOV for metric aggregation (30, 45, 60, 75 and 90?); YS and YM can be either FGF?, FRT?, FSVF? or FLAI?; X1 is the ALS-derived counterpart of YS or YM (LGF?, LRT?, LSVF?, or LLAI?, respectively); X2 corresponds to LVGF, X3 is LMH; X4 is LD; and X5 is LSA.  Please refer to Table 4.3.4 for a comprehensive definition of these variables.  Correlations between the dependent variables and each of the independent variables were ex-amined through scatterplots, and a correlation matrix between all predictor variables (plus FGF?) was produced to ensure that variables with high inter-correlations were not added prior to fitting the models.  Eqs. 4.3.1 and 4.3.2 were fitted using ordinary least-squares regression for each zenith AOV (?) metric.  Also, in order to justify the need and benefit of performing ALS coordinate trans-formations, a simple linear model was fitted to predict HP gap fraction (FGF?) with the verti-cal ALS gap fraction (LVGF) only:  143  YS(?) = b0 + b 1X1         4.3.3  where YS(?) is the same as for Equation 4.3.1 and X1 corresponds to either simple LVGF or the transformation used by Solberg et al. (2006):  ln(LVGF-1).  Choosing the best common multiple regression model structure followed a manual backward stepwise approach for variable selection.  The intercept and all five predictor variables (Equation 4.3.2) were initially included in the regression to obtain a matrix of coefficient p values that included the entire response variable ? zenith AOV model combinations.  Model coefficients of the supporting predictor variables (X2 ? X5) that were significant less than twice in the matrix were removed until only those variables consistently showing statistical significance across all models were identified.  The equations were then validated using the tests described below.  Goodness of fit was evaluated based on the models? adjusted coefficients of determination (r2 and R2) and three versions of root mean square error: absolute (RMSE), leave-one-out cross-validation average derived by iteratively refitting the model with all but 1 of 9 randomly gen-erated data groups (RMSES), and normalized by the range of observed values to enable com-parisons between different variables (RMSEN).  All models were validated by observing the significance probability (p) of the regression coefficients and by performing Anderson-Darling and Shapiro-Wilk normality tests on the residuals, which confirmed the required normality if p > ? (in all tests, ? = 0.05).  Linearity and variance stability was assessed through visual inspection of predicted vs. observed and predicted vs. residual scatterplots.  95% prediction and confidence intervals were calculated and illustrated on the predicted vs. 144  observed figures.  For multiple regression, the confidence intervals were estimated with a quadratic function relating individual predicted values to their corresponding lower and up-per limits as generated by the statistical software (I = c0 + c1?P + c2?P2, where I = upper or lower interval limit, P = predicted value and c0, c1 and c2 are model coefficients).  Variance inflation factors were also estimated to check for multicollinearity (Field, 2005).  4.3.2.6 Plot level ground-truth model validation  Using the methodologies presented here, new and different grids of synthetic hemispherical images were generated in the same calibration plots and an additional set of 11 plots (other than those in Table 4.3.1) as part of Section 4.4 of this thesis.  The resulting average GFs were compared with those estimated from pre-existing optical HP available in these plots.  Although the number and distribution of synthetic and optical HP differed substantially within each plot, this comparison was very useful to validate the methodology with an inde-pendent dataset and justify the need for ALS coordinate transformation even if plot-level av-erages were required.  This was done by contrasting the relationship between optical HP-derived GFs and both a simple ratio of raw ALS ground / canopy returns (calculated as LVGH but for the extent of individual square plots) and GFs derived from synthetic hemi-spherical images.     145  4.3.3 Results  4.3.3.1 Preliminary sensitivity analysis  The sensitivity analysis applied to a sub-sample of images indicated that the projection of ALS spheres using inverse distance-weighted diameters generally had little effect for the ma-jority of synthetic images generated in mature stands, due to the large distances between the returns and the projection reference.  Increasing the theoretical diameter of the spheres be-yond 15 cm made returns close to the reference appear too big and subsequently blocked sig-nificant portions of the image, while substantially deteriorating the relationship between syn-thetic and optical estimates of GFs.  However, variable-diameter projections were still neces-sary to produce an adequate representation of canopy structure in the young regeneration stand, where 15 cm spheres appeared optimal in all cases.  On the other hand, varying the minimum size of projected returns is important for the calibration relationships because it affects the r2 via changes in the regression slope, but will not significantly influence RMSE due to a lack of discernible scatter reduction (Figure 4.3.1).  4.3.3.2 ALS-derived synthetic hemispherical photos  Figure 4.3.3 shows examples of ALS return clouds with corresponding synthetic and actual HP for six common stand structure types found in the study site.  In general, there is good visual agreement between the HP and synthetic images across the stands, although the return density (~ 5 returns/m2) of this ALS dataset makes identification of individual trees difficult.  146  In the taller stands (BOD1-C5, BOD3-C4), larger and continuous gaps in the forest canopy are apparent at smaller zenith angles of both the actual and synthetic images.  Denser and more homogeneous canopies (BRC2-C1, VYN-B4) show a more even distribution of canopy elements (i.e. ALS returns) across all the zenith angles.  Markedly different to the other stands is the young regeneration (BRC1-A3), where images are dominated by sky and shorter, clumped vegetation leads to interception of ALS returns much closer to the projec-tion reference.   4.3.3.3 Relationships between variables  The correlation matrix between GF as derived from the actual HP (FGF?) and estimated from the synthetic images (LGF?) for the five zenith AOV is shown in Table 4.3.5.  The relation-ship between the ALS and HP-derived GFs is significant at all zenith angles and becomes stronger as zenith AOV increases (r = 0.75 for ? = 30? and r = 0.93 for ? = 90?).  In addition, Table 4.3.5 summarizes correlations between the two angular GFs (FGF? and LGF?) and the ALS simple metrics (LVGF, LMH, LD, LSA), which are generally poor.  The best correlation occurs between mean LMH and LGF?, suggesting that taller stands have a smaller GF across all zenith angles.  The correlations between the predictor variables to be put into in the multiple regression model (Equation 4.3.2) are generally weak, so redundancy is not likely introduced.  147   Figure 4.3.3.  Representative examples of ALS point clouds (left), ALS synthetic hemi-spherical images (center) and real optical hemispherical photographs (HP) (right) for each stand; azimuths (?) are shown on the hemispherical illustrations. 148  Table 4.3.5.  Correlation matrix showing the coefficient of correlation (r) between variables used in multiple regression (gap fraction only, for simplicity); non-significant (p > 0.05) values shown in italic grey. Zenith FOV (?) Variable FGF? LGF? LVGF LMH LD LSA 30  FGF? -  LGF? 0.75 -  LVGF 0.56 0.42 -  LMH -0.41 -0.72 0.10 -  LD -0.37 -0.46 -0.57 0.30 -  LSA 0.11 0.01 -0.02 0.17 0.51 -  45 FGF? -  LGF? 0.85 -  LVGF 0.65 0.45 -  LMH -0.50 -0.77 0.09 -  LD -0.20 -0.25 -0.38 0.03 -  LSA 0.21 0.11 0.13 0.05 0.45 -  60  FGF? -  LGF? 0.89 -  LVGF 0.64 0.48 -  LMH -0.55 -0.77 0.10 -  LD 0.03 -0.06 -0.27 -0.22 -  LSA 0.24 0.15 0.24 0.01 0.42 -  75  FGF? -  LGF? 0.92 -  LVGF 0.62 0.47 -  LMH -0.56 -0.75 0.18 -  LD 0.07 0.00 -0.30 -0.32 -  LSA 0.20 0.13 0.34 0.07 0.17 -  90  FGF? -  LGF? 0.93 -  LVGF 0.63 0.50 -  LMH -0.56 -0.73 0.18 -  LD 0.08 0.01 -0.30 -0.32 -  LSA 0.20 0.13 0.34 0.07 0.17 -   Scatterplots between FGF? and LGF? are shown for all zenith AOV on Figure 4.3.4a?c.  Dif-ferences in structure across the stands result in distinct population clusters clearly visible in the figures, which prevent fitting a single model to the data.  The relationship between LGF? and FGF? shows that, with the current parameter setup, the synthetic images underestimate GF when compared to HP, with the exception of stand 149  BOD3.  The young regeneration stand (BRC1) also deviates from the LGF? ? FGF? general linear pattern and shows a considerably higher variability.   Figure 4.3.4.  Relationship between ALS-derived (LGF?) and HP-derived gap fraction (FGF?) (a, b, c) and between predicted and observed values of gap fraction obtained from simple (d, e, f) and multiple (g, h, i) linear regression models across three representative ze-nith AOV (30?, top; 60?, center; and 90?, bottom); legends in sub-figures a and i apply to all.  150  4.3.3.4 Simple linear regression  The simple regression model predicting FGF? from ALS untransformed data (Equation 4.3.3) was weak across all zenith AOV (r2 ranging from 0.31 to 0.41).  Adjusted r2 values increased (0.59 ? 0.87) and RMSE decreased when the ALS-transformed variable (LGF?) was used; however, nearly all the simple linear regression models failed residual normality tests.  This is illustrated in Figure 4.3.4d?f, where scatterplots of observed vs. predicted gap fractions indicate that a single regression line does not account for different populations of stand structures, particularly within the short regeneration stand (BRC1).  4.3.3.5 Multiple linear regression  After applying multiple regression to Equation 4.3.2 with all the predictor variables included, LMH proved to be non-significant for ? values of 30? and 45? in all cases and for FLAI60 and FLAI75, while LSA was consistently non-significant across all model specifications.  The in-tercept (?0) and LVGF were not significant in two cases only and were therefore maintained for a second run.  After eliminating LMH and LSA from the regression, all of the remaining parameters were statistically significant with no exception.  However, models for ? = 30? did not pass the two residual normality tests, and the FLAI60 model barely passed the Anderson-Darling test only.  As suggested by Kutner et al. (2005), transformations of the response variable YM were attempted to solve non-normality of residuals in these cases while maintain-ing the original modeling strategy.  None of the transformations tested (inverse, square, square-root, log) solved the problem for FGF30, FRT30, and FSVF30.  However, using the 151  square root of FLAI? (FLAI?0.5) allowed the models to pass the Anderson-Darling test without losing variable significance while improving R2 and RMSE.  Thus, the model that complied with all the conditions was:  YM(?) = ? 0 + ? 1?X1(?) + ? 2?X2 + ? 4?X4      4.3.4   Regression results for Equation 4.3.4 are provided in Table 4.3.6, which shows that model behaviour was very similar for all dependent variables.  Adjusted R2 improves as zenith AOV increases due to more pixel aggregation that reduces the probability of canopy returns being assigned to the wrong sky region.  RMSEN are very similar for FGF?, FSVF? and FRT? with the same ?, while the prediction accuracy of all models is validated by the consistent similarities between RMSE and RMSES (Kutner et al., 2005).  The fitted parameter estimates of ?0, ?1, ?2 and ?4 shown in Table 4.3.6 can be readily used to predict FGF, FSVF, FRT and FLAI at location within the current ALS data.  All models produced variance inflation factors ranging between 1.3 and 1.7, eliminating multicollinearity concerns (Myers, 1990).  Scatterplots of predicted vs. observed values of FGF? are shown in Figure 4.3.4g?i for ? = 30, 60 and 90?, respectively.  When comparing Figure 4.3.4d?f to Figure 4.3.4g?i, it is evi-dent that multiple linear regression was a successful tool to achieve more accurate predic-tions, especially by accounting for the distinct stand structure of the young regeneration stand (BRC1).  Figures 4.3.4d and 4.3.4g also show that outliers might be preventing model valida-tions for ? = 30?.  Scatterplots of predicted GFs and the model residuals appear visually satis-152  factory for all zenith AOV, with data points evenly distributed at both sides of the horizontal reference line of Figure 4.3.5.  Table 4.3.6.  Multiple linear regression results (refer to Table 4.3.4 for RMSE and RMSES units). Model variables a Zenith cut (?) Adjusted R2 RMSE RMSES RMSEN ?0 ?1 ?2 ?4 p Anderson-Darling p Shapiro-Wilk FGF? / LGF? 30 0.64 0.10 0.10 0.13 -0.15* 0.71** 0.39** 0.01* 0.00 0.00 45 0.82 0.07 0.07 0.10 -0.24** 0.68** 0.44** 0.00** 0.37 0.29 60 0.88 0.06 0.06 0.08 -0.34** 0.63** 0.42** 0.03** 0.16 0.17 75 0.91 0.05 0.05 0.07 -0.38** 0.57** 0.41** 0.03** 0.58 0.89 90 0.92 0.03 0.04 0.06 -0.26** 0.52** 0.28** 0.02** 0.53 0.74 FSVF? / LSVF? 30 0.64 1.28 1.28 0.13 -2.02 b 0.71** 5.18** 0.13* 0.00 0.00 45 0.82 2.00 2.03 0.10 -7.07** 0.68** 12.77** 0.39** 0.40 0.28 60 0.88 2.83 2.86 0.08 -17.2** 0.64** 21.37** 1.36** 0.15 0.19 75 0.91 3.54 3.58 0.07 -28.26** 0.58** 30.99** 2.40** 0.61 0.79 90 0.92 3.67 3.71 0.06 -27.32** 0.53** 30.52** 2.45** 0.60 0.71 FRT? / LRT? 30 0.65 0.15 0.15 0.13 -0.25* 0.73** 0.59** 0.02* 0.00 0.00 45 0.81 0.27 0.27 0.10 -0.82** 0.68** 1.60** 0.05** 0.51 0.67 60 0.86 0.39 0.39 0.08 -1.92** 0.62** 2.56** 0.17** 0.69 0.96 75 0.89 0.46 0.46 0.08 -3.02** 0.57** 3.55** 0.27** 0.08 0.07 90 0.89 0.47 0.47 0.08 -3.13** 0.55** 3.66** 0.29** 0.10 0.07 FLAI? / LLAI? 60 0.76 0.25 0.25 0.10 2.32** 0.61** -1.53** -0.09** 0.06 0.00 75 0.76 0.29 0.29 0.11 2.61** 0.59** -1.76** 0.11** 0.01 0.00 FLAI?0.5 / LLAI? 60 0.80 0.12 0.12 0.08 1.63** 0.33** -0.82** -0.04** 0.36 0.01 75 0.81 0.12 0.12 0.09 1.75** 0.30** -0.82** -0.06** 0.08 0.00  a Dependent (YM) / main independent (X1) variables; supporting variables X2 and X4 are common for all models. * Significant with 0.01 <= p < 0.05;  ** Significant with p < 0.01    Figure 4.3.5.  Relationship between gap fraction predicted from multiple linear regression (Equation 4.3.4) (YM(?)) and model residuals (FGF? - YM(?)) for three representative zenith AOV. 153  Figure 4.3.6b indicates that plot-level GF averages from optical HP are closely related to av-erages from new synthetic ALS images, both obtained for all the plots where ALS was avail-able in the study area.  The comparison between Figures 4.3.6a and 4.3.6b constitutes strong evidence to justify coordinate transformation to accurately predict GF.    Figure 4.3.6.  Comparison between the relationship of plot-level average gap fractions ob-tained from optical HP and a) vertical gap fraction estimated from untransformed ALS, and b) gap fractions from calibrated synthetic hemispherical images.   4.3.4 Discussion  The discussion regarding the methodology presented in this section is centered around the following questions: 1) how do synthetic hemispherical ALS images visually compare to their real HP counterparts and what are the main sources of error?; 2) how suitable is discrete ALS to represent the fine-scale canopy elements responsible for radiation transmission?; 3) how effective was the proposed modeling strategy aiming to predict HP-derived metrics from coordinate-transformed ALS?; 4) what are the perceived benefits of the methodology?; and 5) what lines of action are needed to improve and apply this approach in future research?  154   4.3.4.1 ALS synthetic hemispherical images  The results here presented indicate that coordinate transformation of ALS data produced syn-thetic HP images which were qualitatively and quantitatively similar to real optical HP.  The use of a 75 m diameter ALS cylinder was deemed appropriate for this dataset, given that enough spheres appeared in the synthetic images at higher zenith angles to reproduce the saturation that occurs in real HP under closed canopy conditions.  If needed, smaller cylin-ders could be tested for narrower ALS transects.  The effects of the radial distortion correc-tion were negligible in mature and medium stands, which showed a difference in resulting LAI of less than 1% due to the increased overlap and saturation that occurs at higher view angles and larger distances between returns and reference.  However, LAI was 20% higher in images with geometric correction in young regeneration stands due to the abundance of re-turns closer to the reference.  A visual inspection of the synthetic HP dataset showed that in-dividual trees were difficult to identify in most stands, and that ALS returns occasionally ap-peared where canopy elements were absent in HP.  There are three possible explanations for these differences: 1) density of the ALS point cloud was too low to capture basic crown-level structural details apparent in the optical HP; 2) HP was acquired six months after ALS and changes in stand structure (e.g. crown damage, tree fall, etc.) could have occurred in these stands affected by MPB, and 3) there were GPS positional errors in HP plot locations, cam-era orientation and image registration errors, as well as uncertain snowpack depths when ALS was collected.  155  4.3.4.2 Physical representation of canopy elements with ALS  Successful transformation of the ALS point cloud into realistic synthetic HP images depends on a number of factors.  First, the density of laser returns needs to be high enough to capture the basic geometry of individual tree crowns and branches.  Second, the size and shape of projected synthetic canopy elements (in this case spheres) must be closely related to some basic unit of light-intercepting foliage or branch structure found in real forests.  Third, the density and distribution of laser returns must be relatively uniform throughout the entire sur-vey area to avoid bias.    It was shown here that a minimum constant projected size was necessary for all returns to resemble HP; however, inverse-distance-weighted variable projections were still necessary for returns closer to the reference, particularly for the short regeneration stand.  ALS returns portrayed as opaque spheres represent a crude approximation of canopy structure as seen by a camera.  Real canopy elements are far more complex, but because it is impossible for dis-crete ALS returns to accurately characterize fine-scale details of plant canopies, some arbi-trariness is inevitable when assigning theoretical shapes and sizes to ALS returns.  It must be highlighted that this methodology was not designed to reproduce the scale of detail found in real HP images as is possible with higher density TLS (C?t? et al., 2009), but to capture the basic patterns of canopy structure responsible for light interception and penetration that may in turn influence snow accumulation and melt.  156  The detection of canopy elements by ALS and HP are both dependent on optical properties of the canopy; however, the former technique is based on reflectivity and the latter on opac-ity.  Another disparity between HP and ALS is that the downward, near-nadir view angle of ALS provides a biased vertical profile of forest canopies in which upper elements have a higher probability of being detected, leading to an underrepresentation of lower branches and stems (Hilker et al., 2010).  This may be compensated in synthetic ALS hemispherical pro-jections because image saturation increases towards the horizon mainly due to the corre-sponding exponential increase in the number of ALS returns, while in HP it is common to observe tree stems closer to the camera occluding the farther views as the main source of saturation.  This will have an effect on the amount of unexplained variance in the regression models, but the strength of model fits (adj. R2 = 0.8 to 0.92) for FGF, FSVF, FRT, and FLAI suggests that any bias in height distribution has little effect on the results.  While some of these shortcomings might be minimized by more sophisticated individual tree-reconstruction routines, volumetric rendering or ray-tracing methods, the corresponding uncertainties here are partly masked and absorbed by the calibration models.  In this research, several assumptions were made about the size and shape of a specific com-bination of predictors and parameter estimates were chosen so that the empirical relationship between canopy metrics derived from synthetic and real HP and their visual similarity was maximized.  This methodology, empirical in nature, is admittedly susceptible to interactions between parameters.  For instance, a larger minimum projected circle size (Figure 4.3.1) might be needed if ALS return density is lower, or the maximum sphere size could be re-duced if returns are too close to the reference.  The application of this methodology to a 157  wider combination of forest stands and ALS datasets is required to evaluate parameter stabil-ity and optimization.  4.3.4.3 Modeling strategy  Regression models using simple vertical gap fractions [LVGF or ln(LVGF-1)] to estimate HP metrics generally had low r2, high RMSEN and produced model residuals that failed normal-ity tests.  These results contrast with those of Solberg et al. (2006), Hanssen & Solberg (2007), Solberg et al. (2009) and others, in part because their statistical comparisons were based on the average of multiple photo plots rather than individual photo points, masking within-plot variability.  Simple linear regression directly estimating HP metrics from their ALS-derived counterparts (X1) was also unsuccessful because it failed to include other key explanatory variables (namely LVGF and LD) and describe the relationships among all stands in one single model, especially due to the deviations shown by BRC1 and BOD3 (Figure 4.3.4).  However, the need to perform coordinate transformations of ALS data to better pre-dict HP-derived metrics in individual sampling points was strongly justified (Figure 4.3.6).  Multiple linear regression was suitable to calibrate ALS metrics with HP by accounting for both forest structure and data configuration properties.  The models? R2 values above 0.80 and RMSEN below 10% across all zenith AOV higher than 45? suggest that confident predic-tions can be made throughout the entire ALS transect.  This idea is also supported by the wide structural diversity of stands included in the regression dataset and the successful vali-dation performed at plot-level averages in additional stands which represented even more di-158  verse conditions (Figure 4.3.6).  Better HP geographical registrations and simultaneous HP / ALS data collection plus a detailed outlier analysis are required to fully validate the models for ? = 30?.  A strong component of this section involved the use of a large network of individual ground-reference samples representing a heterogeneous collection of forest structure conditions that appropriately represented both within- and between-stand variability.  The latter was particu-larly important to understand the relationship between GF derived from ALS synthetic im-ages and HP across a broad range of GF estimates (e.g. 0.3 to 0.9 for ? = 60?, Figure 4.3.4h).  A more complete sample of stand structures would have included mature, non-defoliated pine stands; however, this stand type was absent from the study area at the time of data col-lection.  The accuracy of predicting HP metrics directly with ALS synthetic counterparts should be independent of stand health status in light of both ALS and HP being able to detect defoliation (Solberg et al., 2006).  The developed models (Equation 4.3.4, Table 4.3.6) proved suitable for our range of sampled forest structures and ALS data.  Consequently, they need to be tested and validated for dif-ferent stand types (species, densities, heights, health, etc.) and other ALS data acquisitions (e.g. return density, scan angle, footprint size, overlapping transects, return classes, etc.).  Of particular interest is the application of this method to full-waveform (FW) LiDAR data, which will be increasingly used in the future and provides a more detailed profile of canopy elements and additional radiometric information (Pirotti, 2011).  FW LiDAR also has the po-tential to assist in the improved estimation of the return dimensions by the analysis of target 159  backscatter cross sections (Wagner et al., 2006, 2008).  However, given that discrete ALS has been used extensively in many regions, this methodology is not likely to become obsolete in the near future.  Despite the supporting ALS vertical variables increasing the significance of the model if ap-plied to alternative datasets, new HP / ALS calibrations are required every time this approach is applied in a different area.  This includes reassessing variable significance and full model validation.  It is especially important to account for changes in ALS density caused by sys-tematic overlapping multiple transects, where duplicate sampling might not be properly cap-tured by LD alone.  A voxelization of the ALS point cloud might minimize the effect of vary-ing return densities, whereby each volume element (voxel) is coded as one if occupied by one or more ALS returns, or as zero if empty (C?t? et al., 2009).  4.3.4.4 Methodological advantages and applicability  There are a number of advantages associated with transforming ALS coordinates to generate hemispherical synthetic images.  First, geometrical discrepancies between ALS and HP are minimized, allowing a direct comparison of structural and radiation metrics at the individual point level.  Second, the methodology is simple because it is based on raw ALS point-cloud data and avoids the need for elaborate canopy models while minimizing the number and complexity of geometrical parameters.  Third, GLA or other specialized programs can be used to directly estimate GF, LAI, SVF and local transmission of direct, diffuse or total radia-tion through forest canopies.  The generation of synthetic hemispherical images from ALS 160  which are then readily available for processing with GLA was chosen because hemispherical photography has become one of the most popular methods to obtain GF and associated forest structure metrics, and its outcomes have been systematically used to parameterize hydrologic models (e.g. Woods et al., 2006; Ellis & Pomeroy, 2007; Ellis et al., 2011).  Alternative ap-proaches might produce versions of these metrics that can deviate substantially from those used to develop existing process-based equations, thus requiring their parameters to be re-vised.  Fourth, generating synthetic hemispherical images from ALS introduces unlimited flexibility in terms of sample size and experimental design layouts:  any number of images can be obtained at user-defined spacing options and sub-pixel specific locations.  Fifth, single calibration models for each variable proved to be applicable to a wide range of stand types.  Finally, variables directly applicable to hydrologic modeling can now be obtained at any point within ALS datasets ?significantly reducing fieldwork requirements while improving the parameterization of vegetation classes at the landscape-level.  The normal distribution of the calibration models? residuals suggests that the method is unlikely to produce systemati-cally biased estimates of forest structure variables, which will benefit fully-distributed hydro-logic modeling exercises.  4.3.4.5 Future work  Further research should focus on 1) improving the accuracy of the methodology by better geographical registration methods and coordinated data collection; 2) validating or reformu-lating the current models using different datasets and study areas (e.g. other species, moun-tainous topography) to evaluate parameter stability; 3) exploring the relationships between 161  structural variables obtained from synthetic ALS hemispherical images and satellite-derived spectral indices for watershed- or landscape-level extrapolations; 4) developing alternative methodologies to parameterize hydrologic models with metrics directly obtained from ALS and other remote sensing technologies; and 5) improving the functionality of HP processing algorithms to estimate radiation components at sub-daily time steps (e.g. Leach & Moore, 2010).  The latter represents a difficult challenge given the inaccuracies in camera orienta-tion, anisotropy of sky brightness and atmospheric attenuation, among others; however, if achieved, it would allow the direct input of radiation transmission into point-based process simulation of hydrologic models and better performances if above-canopy radiation is avail-able.  While GLA can directly estimate GF and radiation transmission, most hydrologic models have used LAI as the forest structure parameter input to calculate hourly or daily radiation components (e.g. Wigmosta et al., 1994; Pomeroy et al., 2007).  Nevertheless, the difficulties of accurately measuring true LAI in the field are well known, and optical methods only measure the effective plant area index unless corrections are made for foliage clumping and the surface area contributed by branches and boles (Br?da, 2003).  LAI-2000 or HP proc-essed with GLA are also impacted by this bias and yet remain a popular method to estimate LAI by integrating log-transformed gap fractions through cosine-weighted zenith rings (Welles & Norman, 1991), only to be used as an intermediate parameter to simulate radiation transmission and other processes in hydrologic models.  However, since radiation transmis-sion and all the light indices available from GLA are also directly obtained from the simple sky / canopy pixel ratio defined here as gap fraction (GF), this variable might constitute a 162  conceptually simpler and more parsimonious average forest structure parameter than LAI when modeling below-canopy radiation regimes.  Since producing alternative physically-based models requires detailed measurements of above- and sub-canopy shortwave and longwave radiation, precipitation interception and evaporation, snow accumulation and de-pletion, among others, new studies are required to re-parameterize hydrologic models to sub-stitute LAI with GF or other metrics directly obtained from remote sensing and quantify the resulting benefits or losses.  A new era of research in hydrologic modeling should use alter-native metrics derived from ALS, TLS and even satellite-derived spectral indices to develop entirely new process-based equations for multi-scale modeling of radiation transfer, precipi-tation interception, evapotranspiration and water routing, among others.  4.3.5 Conclusions  This section appears to be the first study that has attempted to re-project discrete ALS indi-vidual returns in a polar coordinate system to directly model forest structure and radiation regimes with currently available HP image processing tools.  The results suggest that repro-jection of the ALS point cloud is necessary if accurate HP-derived estimates of canopy gap fraction, LAI, SVF and solar radiation transmission are required at the point level.  It was not the goal of this research to provide prediction models with universal application across all forest types and ALS datasets, but to reveal the importance of coordinate transformation for the estimation of GF and other bulk-canopy metrics, and to demonstrate that these variables can be predicted from discrete ALS calibrated with HP.  The main research objective was fulfilled with the current approach as the models developed can operationally predict canopy 163  GF, LAI, SVF and light indices with reasonable accuracy in any location within this ALS dataset, regardless of forest type.  When evaluating the strategies to improve hydrologic models with remotely-sensed forest structure metrics, two alternatives arise:  1) redevelop process equations at the point level based on several years of detailed meteorological data collection to be directly linked with the 3-D capabilities of ALS or TLS to portray canopy structure, and 2) improve the charac-terization of forest structure at the landscape level so that spatially-explicit versions of the relevant variables can be directly put into existing fully-distributed hydrologic models.  While the two approaches need to be completed and this can be achieved in parallel, this the-sis focuses on the latter mainly because it has the potential to directly improve the modeling of snow and streamflow processes on a larger scale using the current tools available.  This section presents the first step towards obtaining the fully-distributed versions of the forest structure variables needed to parameterize current physically-based hydrologic models.  Fol-lowing the line of approach 2) mentioned above, the next stage consists of correlating these metrics ?now available at any location within the spatial extent of an ALS dataset? with satellite-derived spectral indices in order to obtain fully-distributed structural variables to re-place the bulk and discrete vegetation classes that are currently used.  The ultimate goal is to input these detailed, spatially-explicit and continuous versions of the variables into fully-distributed models to evaluate the changes in model efficiencies when estimating snow ac-cumulation and ablation as well as streamflow generation.  164  As ALS is becoming increasingly available worldwide, this section represents a major con-tribution to hydrologic studies by facilitating the estimation of forest structure metrics rele-vant to model parameterization through reduced fieldwork requirements and unlimited, spa-tially-explicit sampling designs.     4.4 Estimation of watershed-level distributed forest structure metrics relevant to hydrologic modeling using Landsat and LiDAR   4.4.1 Introduction  In the previous section, a methodology was developed to obtain LAI and SVF by transform-ing the Cartesian coordinates of ALS individual returns to a polar coordinate system.  While FC and H can be easily estimated from ALS without coordinate modifications, LAI and SVF have been traditionally retrieved from hemispherical photography because they are depend-ent on the angular distribution of gap fractions as viewed in all directions upward from a point beneath the canopy (Miller, 1967; Welles & Norman, 1991).  Even though other studies have estimated LAI from ALS without any specific geometrical projection (e.g. Morsdorf et al., 2006; Solberg et al., 2006), it was demonstrated in Section 4.3 that a higher accuracy was achievable if synthetic hemispherical images developed from ALS data were used to predict LAI at both the point and plot levels.  The technique also allows the generation of synthetic hemispherical images at any location within an ALS point cloud, which reduces the cost of acquiring optical hemispherical photographs and adds more flexibility to experimental de-165  signs.  Such an improvement in the methodologies to estimate LAI and SVF with ALS is con-sidered a contribution to hydrologic modeling; however, ALS is not necessarily available in any given area and acquisition-processing costs remain high.  The objective of this section is to develop a methodology to extrapolate ALS-derived LAI, SVF, FC and H to the wider landscape by correlating these metrics with a suite of Landsat spectral indices obtained from a large watershed in the MPB-infested region of British Co-lumbia.  Landsat data are free and provide an optimum spatial resolution for vegetation and snow studies because Landsat?s 30 m pixel size matches traditional ground plots and repre-sents a scale appropriate for the understanding of water and energy processes.  The result is a set of high spatial resolution (30 m) gridded predictions of the four variables, readily avail-able for input into fully-distributed hydrologic models.  Specific research questions are:  1) How are ALS-derived forest structure metrics correlated with a suite of Landsat-derived spectral indices?  2) Which model types are more appropriate for extrapolating structural metrics over the landscape, and what are their errors and biases?  3) Is there any discernible effect of MPB defoliation on spectral responses and the quality of the models?  Given the extension of these analyses, this section focuses on integrating ALS and Landsat to produce distributed maps of structural variables.  Future work should quantify the improvement of hydrologic model efficiencies when estimating SWE and streamflow if these spatially-explicit metrics are utilized instead of coarse vegetation classes.  This work is published in Varhola & Coops (2013).   166   4.4.2 Methods  4.4.2.1 Study area  This research was conducted in Baker Creek (Section 2.1, Figure 2.1.1), where the impact of MPB on Baker Creek over the past decade has been significant.  As detailed in Section 1.3, the defoliation stages caused by MPB on Pinus contorta can last several years and are essen-tially three (Mitchell & Preisler, 1998):  green attack (beetle present but no visible effect on foliage), red attack (foliage dehydration that turns all needles bright red) and grey attack (progressive needle and branch loss, followed by tree fall). Changes in spectral properties of tree crowns as the infestation progresses have been described in detail by Coops et al. (2009) and Wulder et al. (2006).  According to Bewley et al. (2010), the lodgepole pine forests oc-cupying 84% of Baker Creek in 2000 were essentially healthy.  By 2008, around 11% of the forested area was undergoing the red-attack phase while 55% had advanced to grey-attack, leaving only young pine regeneration and spruce stands to represent healthy forests in the watershed.  This landscape-level defoliation is expected to affect the spectral responses of vegetation, hence requiring attention in the analyses.  4.4.2.2 Experimental design and data acquisition  The experimental design is based on synthetic hemispherical images generated from ALS in Section 4.3, a 6-band Landsat TM scene (excluding the thermal band), high-resolution im-167  agery and ground plots.  ALS-derived metrics and spectral indices obtained from Landsat are correlated to extrapolate structural variables to the wider landscape, and validated with an independent dataset from ground plots supported by high-resolution aerial imagery.  ALS data and high resolution aerial photography were obtained as explained in Section 2.2.  To ensure that all the stand types present in the ALS transect were included in the modeling dataset, Vegetation Resource Inventory (VRI) polygons from the British Columbia Ministry of Forests were used to stratify the sampling of individual Landsat pixels.  Each cloud- and shadow-free centroid of all the VRI polygons within the ALS transect was extracted auto-matically with Geographic Information System (GIS) software.  The four Landsat pixels im-mediately contiguous to these centroids were selected to generate the modeling dataset (see examples on Figure 4.4.1) which totaled 88 stands and their corresponding 352 pixels, dis-tributed according to age and height as detailed on Table 4.4.1.  These four pixels per stand were included to explore the effect of pixel aggregation on the relationships between spectral indices and ALS metrics, and to facilitate the identification of resilient stand-level outliers.  In each pixel, a square grid of 36 sampling points spaced 5 m apart was generated as shown on Figure 4.4.1.  This spacing was chosen to account for spatial autocorrelation and to opti-mally capture the variability of metrics derived from hemispherical photography (Montes et al., 2008) within each pixel.  Thus, 12,672 points in total were used as reference points to ob-tain the ALS structural metrics as explained in depth below.  168     Figure 4.4.1.  Example of modeling data experimental design showing VRI stands (red boundaries) with their centroids consisting of four contiguous Landsat pixels (top, left) and 36 ALS sampling points per pixel (yellow dots); the ALS transect boundary (blue) is shown over the Landsat image (top) and with high-resolution aerial photography (bottom).  The total number of VRI stands was 88, equivalent to 352 individual Landsat pixels.   Table 4.4.1.  Landsat pixel distribution according to stand height and age (from VRI data). Stand height (m) Stand age (years) TOTAL 0 - 10 10 - 40 40 - 70 70 - 100 100 - 130 > 130 0 - 5 12 100 ? ? ? ? 112 5 - 10 ? 16 8 ? ? ? 24 10 - 15 ? ? ? 8 8 ? 16 15 - 20 ? ? ? 8 88 16 112 20 - 25 ? ? ? 4 32 48 84 > 25 ? ? ? ? ? 4 4 TOTAL 12 116 8 20 128 68 352  169  Fifteen existing ground plots from this and previous studies (Teti, 2008; Varhola et al., 2010a) within the ALS transect were selected for validation purposes and to illustrate the physical characteristics of representative stands in the study area (Table 4.4.2).  In these 50 ? 50 m plots, the same ALS metrics derived for the modeling dataset were generated using a similar grid of sampling points for comparison with the Landsat pixels.  The validation plots represent a wide variety of stand type combinations that range in height from small (~ 3 m regeneration) to mature (~ 25 m), from 20 to 100% dominance of lodgepole pine, from healthy to severely defoliated by MPB, and from very low to high stocking density (Table 4.4.2).  Figure 4.4.2 shows representative examples of high-resolution aerial photography, optical and synthetic hemispherical images for one plot of each stand category in Table 4.4.2.  Table 4.4.2.  Independent ground plots for model validation. General information Ground inventory metrics Pine foliage status  (%) a Plot codes Stand description Latitude (?) Longi-tude (?) Elevation (m) Stem density (n/ha1) DBH (cm) Basal area (m2 /ha1) Mean height (m) Max. height  (m) Green Red Grey BRC1 Healthy regeneration 52.670 -123.017 1,231 1,312 5.4 1.1 3.9 5.6 100 0 0 YR3 Healthy regeneration 52.690 -123.023 1,240 2,867 4.0 3.3 5.1 6.4 98 2 0 BRC2 Medium red 52.672 -123.017 1,229 1,025 13.5 15.0 10.1 13.5 48 52 0 RD2 Medium red 52.687 -123.018 1,231 1,200 12.3 15.8 11.1 16.5 13 83 1 RD3 Medium red 52.699 -123.024 1,247 3,300 10.5 33.1 10.3 15.4 20 70 1 BOD1 Mature grey 52.676 -123.016 1,218 1,800 18.5 55.4 18.2 28.9 0 19 77 BOD3 Mature grey 52.638 -122.993 1,222 550 25.5 28.7 17.3 26.2 8 14 77 GY2 Mature grey 52.632 -122.983 1,218 2,500 13.7 40.0 13.3 20.8 6 31 63 GY5 Mature grey 52.696 -123.023 1,241 4,633 10.7 44.9 11.0 18.2 27 7 66 GY6 Mature grey 52.771 -123.035 1,051 1,425 16.3 33.3 15.5 21.8 2 22 73 GY7 Mature grey 52.971 -123.082 988 3,150 10.7 37.4 10.5 22.0 38 0 62 GY8 Mature grey 53.055 -122.940 955 1,925 16.0 43.5 17.9 31.0 1 8 53 GN1 Mature healthier 52.971 -123.078 984 5,200 9.8 42.0 10.5 16.5 55 0 45 SP1 Healthy spruce 52.884 -123.060 1,013 6,700 8.7 45.5 10.2 19.0 11 0 16 SP2 Healthy spruce 53.055 -122.938 978 2,800 8.5 18.5 9.0 15.4 34 0 0  a Defoliation percentage calculated as proportion of basal area falling into each health category, as described in Section 3.3.2;  percentages apply to lodgepole pine only, so the sum of the three foliage categories indicates % of pine in the plot. 170   Figure 4.4.2.  High-resolution aerial photographs (top), optical ground-based hemispherical example pictures (middle), and ALS-derived synthetic hemispherical example pictures (bot-tom) of five representative validation ground plots.  4.4.2.3 Landsat indices  Landsat TM images are composed of six optical bands covering regions of the visible spec-trum and the near- and mid-infrared.  A significant body of literature investigating the use of these spectral bands to obtain indices related to vegetation conditions exists (e.g. Franklin, 2001b; Jensen, 2007; Williams, 1991), so only a short explanation is included here.  Wang et al. (2010) and Silleos et al. (2006) provide comprehensive reviews for a suite of spectral in-dices, several of which were calculated at each sampling pixel of the modeling dataset (Table 4.4.3).  Four types of indices were included to ensure maximum diversity and likelihood of obtaining good correlations with ALS metrics:  (1) vegetation indices (VI); (2) foliar mois-171  ture indices (FMI); (3) tasseled cap transformation indices (TCI); and (4) spectral unmixing fractions (SUF).  VI generally use the red (R) and the near infrared bands (NIR) to quantify the conditions and abundance of green vegetation.  As healthy vegetation tends to have lower R and higher NIR reflectances, the difference or ratio between these two bands is an indicator of foliage status (Jones & Vaughan, 2010).  In this section, eight slope-based normalized VIs were calculated at each pixel as listed in Table 4.4.3 and reviewed by Silleos et al. (2006) and Wang et al. (2010).  All are based only on the R and NIR bands except for the EVI, which incorporates the blue (B) band to account for atmospheric scattering, and the Green-Red Vegetation Index (GRVI) that uses the green (G) band instead of NIR.  FMI are similar to VI, but take advan-tage of the negative correlation between the shortwave infrared reflectance band (SWIR) and leaf water content (Toomey & Vierling, 2005).  Six FMI compiled by Wang et al. (2010) were included in this research (Table 4.4.3).  TCI, developed by Kauth & Thomas (1976), use linear combinations of bands to reduce multispectral information into parsimonious vari-ables related to scene physical characteristics that are easier to display and interpret (Kauth & Thomas, 1976; Franklin, 2001a).  Here, three TCI were calculated for each sampling pixel with ENVI software:  brightness (BRI), greenness (GRE) and wetness (WET).  Finally, spectral unmixing techniques were applied to the Landsat image to obtain the frac-tions of soil, grass and forest in each pixel.  SUF were included following Chen et al. (2004), who found that forest fractions were better correlated to LAI than other indices.  In this sec-tion, several pure pixels representing each endmember were manually selected from the 172  original image with the assistance of high-resolution aerial photography.    Table 4.4.3.  Variable symbols and description. Type / Source Symbol Variable (unit) Calculation Forest structure / untrans- formed ALS FC0.5 Forest cover above 0.5 m (ALS returns > 0.5 m) / (all ALS returns) FC2.0 Forest cover above 2 m (ALS returns > 2.0  m) / (all ALS returns) H75 75% height percentile (m) Maximum height of lowest 75% ALS returns H80 80% height percentile (m) Maximum height of lowest 80% ALS returns H90 90% height percentile (m) Maximum height of lowest 90% ALS returns H95 95% height percentile (m) Maximum height of lowest 95% ALS returns H99 99% height percentile (m) Maximum height of lowest 99% ALS returns Forest structure / coordinate-transformed ALS GF30 Gap fraction for ? = 30? (Sky pixels) / (Total pixels) for ? = 30? GF45 Gap fraction for ? = 45? (Sky pixels) / (Total pixels) for ? = 45? GF60 Gap fraction for ? = 60? (Sky pixels) / (Total pixels) for ? = 60? GF75 Gap fraction for ? = 75? (Sky pixels) / (Total pixels) for ? = 75? GF90 Gap fraction for ? = 90? (Sky pixels) / (Total pixels) for ? = 90? LAI4 Leaf area index 0?60? (m2 /m2) See Stenberg et al. (1994) LAI5 Leaf area index 0?75? (m2 /m2) See Welles & Norman (1991) SVF Sky-view factor ? (cosine-weighted gap fractions 0?90?); Section 4.3 Vegetation indices a / Landsat b NDVI Normalized Difference Vegetation Index (NIR ? R) / (NIR + R) SAVI Soil Adjusted Vegetation Index (NIR ? R) ? 1.5 / (NIR + R) TVI Transformed Vegetation Index [(NIR ? R) / (NIR + R)]0.5 + 0.5 CTVI Corrected Transformed Vegetation Index (NDVI + 0.5) ? abs(NDVI + 0.5)0.5 / abs(NDVI + 0.5)  TTVI Thiam?s Transformed Vegetation Index abs(NDVI + 0.5)0.5 NRVI Normalized Ratio Vegetation Index [(R / NIR) ? 1] / [(R / NIR) + 1] EVI Enhanced Vegetation Index 2.5 ? (NIR ? R) / (NIR + 6?R ? 7.5?B + 1) GRVI Green-Red Vegetation Index (G ? R) / (G + R) Foliar moisture indices a / Landsat b GVMI Global Vegetation Moisture Index [(NIR + 0.1) ? (SWIR + 0.02)] / [(NIR + 0.1) + (SWIR + 0.02)] MI1 Foliar Moisture Index I NIR / (R ? SWIR) MI2 Foliar Moisture Index II (NIR ? R) / [(NIR + R) ? SWIR] MI3 Foliar Moisture Index III 2.5 ? (NIR ? R) / [(NIR + 6?R ? 7.5?B + 1) ? SWIR] NDII Normalized Difference Infrared Index (NIR ? SWIR) / (NIR + SWIR) wNDII Wide-band Normalized Difference Infra-red Index (2?NIR ? SWIR) / (2?NIR + SWIR)  Tasseled-cap indices / Land-sat BRI Brightness See Huang et al. (2002) and Kauth & Thomas (1976) GRE Greenness See Huang et al. (2002) and Kauth & Thomas (1976) WET Wetness See Huang et al. (2002) and Kauth & Thomas (1976) Spectral un-mixing frac-tions / Landsat SOI Soil spectral fraction Fraction of soil endmember (Chen et al., 2004) GRA Grass spectral fraction Fraction of grass endmember (Chen et al., 2004) FOR Forest spectral fraction Fraction of forest endmember (Chen et al., 2004)  a Landsat spectral indices all calculated as shown by Chen et al. (2004), Silleos et al. (2006) and Wang et al. (2010).  b B = blue reflectance (Landsat TM band 1, 0.45 ? 0.52 ?m)   G = green reflectance (Landsat TM band 2, 0.52 ? 0.60 ?m)   R = red reflectance (Landsat TM band 3, 0.63 ? 0.69 ?m)   NIR = near infrared reflectance (Landsat TM band 4, 0.76 ? 0.90 ?m)   SWIR = shortwave infrared reflectance (Landsat TM band 5, 1.55 ? 1.75 ?m)  173  The final endmember pixels selected showed spectral responses very similar to those from Chen et al. (2004).  ENVI was used to estimate the SUF in the entire image, forcing their sum to a unit in each pixel.  This technique can sometimes produce negative values in one of the endmember fractions (Ngigi et al., 2009), which were only occasionally detected in the soil fraction of our data and mostly approaching zero.  4.4.2.4 ALS metrics  FC and H were extracted from ALS data covering the extent of each individual pixel as well as averaged from 25 m diameter cylinders centered at each of the 36 sampling points per pixel (following the procedures of Section 4.3), with almost identical results.  Two versions of FC were estimated according to the height above the ground separating canopy from non-canopy ALS returns (0.5 and 2 m) (Table 4.4.3).  Despite H referring to the mean tree height within a plot and ALS returns not necessarily capturing individualized tree tops, a number of methods have shown that ALS can predict H (Lim et al., 2003).  One of these approaches characterizes the cumulative distribution of ALS return heights to obtain height percentiles that are highly correlated to stand height.  Here, five H percentiles were calculated (75, 80, 90, 95 and 99%) which compared well (r2 ~ 0.85) to ground inventory mean height shown in Table 4.4.2.  As with FC, more than one H proxies were included to broaden the number of structural variables (Table 4.4.3) to be correlated with spectral indices.  Field observations close to the time of ALS collection indicated that the average snowpack depth among various plots was around 50 cm with a coefficient of variation of 26%, which was accounted for when calculating all ALS metrics as explained by in Section 4.3. 174   In each of the 12,672 sampling points, ALS synthetic hemispherical images were generated as specified in Section 4.3 and processed in a batch mode with Digital Hemispherical Pho-tography software (DHP) (Leblanc et al., 2005) to derive angular gap fractions in 5? intervals which were then integrated into LAI and SVF as shown by Frazer et al. (1999).  Two effec-tive LAI outputs were derived according to the number of zenith rings used.  LAI5 integrates five gap fraction rings from zenith to horizon (0 ? 75?) and was developed to match the field of view of the LAI-2000 optical instrument (Welles & Norman, 1991).  Stenberg et al. (1994) generated a four-ring version (LAI4) to neglect the fifth ring in cases where the sen-sor?s field of view would include areas outside small plots.  Additionally, gap fractions for different increasing zenith angles of view (?) were estimated as suggested by Varhola et al. (2012) since they are useful for some hydrologic models (Chen et al., 2005; Liston & Elder, 2006).  4.4.2.5 Model development  A correlation matrix based on the 352 sample pixels was generated to explore the relation-ships between forest structure metrics and spectral indices, help choose the best representa-tive of each forest structure variable with more than one proxy, reveal which spectral indices were the best predictors for each selected forest structure variable, and avoid redundancy from inter-correlated predictors in multiple regression models.  The correlation matrix and an exploratory regression analysis were thus used to generate the models to predict FC, H, LAI and SVF. 175   First, models with a single predictor ?the spectral index with the best correlation? were developed.  Depending on the observed type of relationship between the dependent and inde-pendent variables, ordinary least squares or non-linear least squares were applied to obtain model parameter values and goodness of fit measures.  Single-predictor models were gener-ated for the four structural variables from three different datasets: one containing all individ-ual pixels and two others grouping pixels as adjacent pairs or quartets (Figure 4.4.1).  This was done to explore the effects of pixel averaging on the quality of the models, and to sim-plify the identification of stand-level model outliers.  Second, ordinary least squares multiple regression models were developed from the individ-ual pixel dataset only following an iterative manual backward stepwise approach in which spectral indices showing the best correlations with the dependent variable were initially in-corporated.  Previously, a visual inspection of scatterplots between dependent and independ-ent variables was undertaken to identify the presence of non-linear relationships that would reduce modeling errors.  Predictors were eliminated from the models based on their signifi-cance (p < 0.05 required) and variance inflation factors (< 30 required to minimize co-linearity between predictors) (Field, 2005) until all remained statistically significant without adding redundancy.    Both single- and multiple-predictor models were evaluated based on adjusted coefficients of determination (R2), simple RMSE, RMSEN, and Anderson-Darling tests applied to confirm residual normality (? = 0.05).  Predicted vs. observed scatterplots of selected models includ-176  ing 95% prediction and confidence intervals, as well as predicted vs. residual scatterplots (not shown), assisted in a visual inspection of linearity, variance stability and outlier identifi-cation.  RMSE percentiles were plotted to evaluate model accuracies across cumulative pixel percentages.  Based on these measures, single- and multiple-predictor models were com-pared.  If a substantial improvement in adjusted R2 or a reduction in RMSE were not contrib-uted by multiple regression, models with a single predictor were preferred to produce distrib-uted maps of the four variables.  These operational models are identified in bold in Table 4.4.5.    The physical relationship between structural and spectral variables was analyzed for each op-erational model, and a careful outlier analysis was conducted with assistance of the high-resolution aerial images to characterize anomalous stands defined here as those outside the 95% prediction bands in the 4-pixel predicted vs. observed scatterplots.  Additionally, the individual gridded sampling points of validation plots (Table 4.4.2) were aggregated accord-ing to MPB status to explore if foliage condition produces identifiable signals to the spectral responses of the main model predictors and their corresponding structural variables.  4.4.2.6 Model applicability and watershed-level extrapolations  A key aspect of the models? validity focused on the ranges of the predicted structural vari-ables, which should fall within the natural variation of forested stands in the study area.  Ob-served and predicted ranges of all variables, along with the ranges of corresponding predic-tors, were retrieved to assess potential inconsistencies prior to extrapolation and to evaluate if 177  significant losses of variability resulted from regression.  Two approaches can be followed to use the models:  (1) apply them directly in all pixels re-gardless of cover type and discard those with values beyond valid ranges for the predicted variables, labeling them as non-forested, or (2) perform a previous independent classification of forested and non-forested pixels and apply the models to the former only.  Approach (1) is easier to apply but its accuracy must be firstly evaluated by quantifying the number of for-ested pixels erroneously producing out-of-range values for each predicted variable, defined here as error type I, and the number of non-forested pixels producing valid values, i.e. error type II.  In order to simultaneously assess approaches (1) and (2), operational models were applied to every Landsat pixel in Baker Creek and the resulting distributions of all predicted forest structure variables were extracted for each land cover class to quantify the percentage of pixels with values valid for forests.  For this purpose, the classification of Bewley et al. (2010) was used.  Based on our high-resolution aerial imagery, it was 95% accurate at differ-entiating forests from non-forests (water, wetlands, clearcuts, clouds and cloud shadows).  Maps showing a color-scaled distribution of each variable in forested pixels were generated, as well as their frequency distributions.  4.4.2.7 Validation  FC, H99, LAI5 and SVF values predicted by the models were extracted for pixels of ground plots (Table 4.4.2) where an additional set of ALS synthetic hemispherical images were available (Section 4.3).  The same variables were estimated from the ALS data within the 178  plots and their averages compared with the pixel-level predicted values to validate the mod-els and quantify the potential errors or biases.  4.4.3 Results  4.4.3.1 Relationships between spectral indices and structural metrics  Table 4.4.4 shows the correlation matrix between all variables belonging to each group of forest structure metrics (with untransformed and transformed coordinates) and spectral indi-ces (VI, FMI, TCI and SUF).  Two H percentiles are not shown in Table 4.4.4 as they have lower correlations with spectral indices, and only NDVI, EVI and GRVI (see Table 4.4.3) were included in the matrix to represent VIs because all others were fully correlated to NDVI.  All the correlations are in general agreement with logical physical interpretations.  Forest structure metrics indicative of biomass (FC, H and LAI) are always negatively correlated to those related to canopy openness (GF and SVF).  Except for the relationship between H and FC, correlations between ALS structural metrics are consistently strong.  The correlation co-efficients between spectral indices are more variable, although some general patterns can be distinguished.  FMI are highly correlated to each other and also show strong positive and negative r with wetness (WET) and soil fraction (SOI), respectively.  As expected, SOI is negatively correlated to all other spectral indices which essentially quantify vegetation.  The fraction of forest (FOR) counter-intuitively shows a negative correlation with EVI and NDVI, which are both predictors of healthy vegetation.  Grass, on the other hand, exhibits the typical spectral response of vegetation which translates into high correlations between grass fraction 179  (GRA) and NDVI and EVI (Table 4.4.4).  GRA and pixel greenness (GRE) can be considered equivalent and interchangeable given their r > 0.99.  Table 4.4.4.  Correlation matrix of ALS metrics and Landsat indices a b  Untransformed ALS metrics Coordinate-transformed ALS metrics Vegetation ind. Foliar moisture indices Tass. cap indices Unmix. fractions  FC0.5 FC2.0 H90 H95 H99 GF30 GF45 GF60 GF75 GF90 LAI4 LAI5 SVF NDVI EVI GRVI GVMI MI1 MI2 MI3 NDII BRI GRE WET SOI GRA FORFC0.5 --- 0.93 0.27 0.07 -0.11 -0.72 -0.70 -0.62 -0.58 -0.58 0.64 0.61 -0.59 0.19 0.00 0.12 0.64 0.62 0.67 0.56 0.55 -0.45 -0.02 0.67 -0.64 0.04 0.30FC2.0 0.93 --- 0.46 0.30 0.14 -0.84 -0.84 -0.78 -0.75 -0.76 0.77 0.75 -0.76 0.01 -0.21 0.15 0.49 0.52 0.61 0.40 0.37 -0.57 -0.23 0.55 -0.50 -0.18 0.47H90 0.27 0.46 --- 0.90 0.71 -0.81 -0.82 -0.84 -0.81 -0.78 0.79 0.79 -0.77 -0.49 -0.64 0.13 -0.18 -0.05 0.11 -0.27 -0.34 -0.61 -0.68 -0.08 0.12 -0.67 0.67H95 0.07 0.30 0.90 --- 0.92 -0.68 -0.71 -0.77 -0.78 -0.76 0.66 0.68 -0.76 -0.57 -0.73 0.18 -0.33 -0.16 0.00 -0.41 -0.50 -0.62 -0.79 -0.22 0.27 -0.79 0.73H99 -0.11 0.14 0.71 0.92 --- -0.50 -0.53 -0.63 -0.67 -0.68 0.49 0.53 -0.67 -0.60 -0.75 0.24 -0.42 -0.23 -0.07 -0.49 -0.58 -0.60 -0.82 -0.31 0.35 -0.84 0.73GF30 -0.72 -0.84 -0.81 -0.68 -0.50 --- 1.00 0.96 0.91 0.90 -0.96 -0.93 0.90 0.27 0.49 -0.16 -0.18 -0.27 -0.41 -0.07 -0.01 0.68 0.53 -0.27 0.22 0.50 -0.66GF45 -0.70 -0.84 -0.82 -0.71 -0.53 1.00 --- 0.98 0.94 0.92 -0.96 -0.94 0.92 0.30 0.52 -0.16 -0.15 -0.25 -0.41 -0.05 0.01 0.70 0.56 -0.25 0.20 0.53 -0.69GF60 -0.62 -0.78 -0.84 -0.77 -0.63 0.96 0.98 --- 0.99 0.97 -0.95 -0.96 0.97 0.39 0.62 -0.16 -0.06 -0.18 -0.35 0.05 0.12 0.74 0.66 -0.17 0.11 0.64 -0.75GF75 -0.58 -0.75 -0.81 -0.78 -0.67 0.91 0.94 0.99 --- 0.99 -0.90 -0.93 0.99 0.42 0.65 -0.19 -0.04 -0.16 -0.34 0.08 0.15 0.77 0.69 -0.15 0.09 0.67 -0.78GF90 -0.58 -0.76 -0.78 -0.76 -0.68 0.90 0.92 0.97 0.99 --- -0.88 -0.91 1.00 0.40 0.65 -0.21 -0.06 -0.18 -0.36 0.06 0.13 0.79 0.70 -0.18 0.11 0.67 -0.80LAI4 0.64 0.77 0.79 0.66 0.49 -0.96 -0.96 -0.95 -0.90 -0.88 --- 0.98 -0.88 -0.36 -0.55 0.11 0.11 0.18 0.35 -0.03 -0.06 -0.68 -0.58 0.21 -0.14 -0.55 0.68LAI5 0.61 0.75 0.79 0.68 0.53 -0.93 -0.94 -0.96 -0.93 -0.91 0.98 --- -0.91 -0.40 -0.60 0.13 0.08 0.16 0.34 -0.06 -0.10 -0.70 -0.62 0.19 -0.12 -0.60 0.71SVF -0.59 -0.76 -0.77 -0.76 -0.67 0.90 0.92 0.97 0.99 1.00 -0.88 -0.91 --- 0.40 0.64 -0.21 -0.07 -0.19 -0.37 0.05 0.12 0.79 0.69 -0.18 0.12 0.67 -0.80NDVI 0.19 0.01 -0.49 -0.57 -0.60 0.27 0.30 0.39 0.42 0.40 -0.36 -0.40 0.40 --- 0.91 0.32 0.61 0.63 0.41 0.81 0.76 0.37 0.84 0.47 -0.63 0.85 -0.59EVI 0.00 -0.21 -0.64 -0.73 -0.75 0.49 0.52 0.62 0.65 0.65 -0.55 -0.60 0.64 0.91 --- 0.05 0.43 0.36 0.11 0.63 0.64 0.69 0.98 0.27 -0.40 0.97 -0.85GRVI 0.12 0.15 0.13 0.18 0.24 -0.16 -0.16 -0.16 -0.19 -0.21 0.11 0.13 -0.21 0.32 0.05 --- 0.38 0.59 0.60 0.41 0.29 -0.45 -0.12 0.40 -0.44 -0.10 0.34GVMI 0.64 0.49 -0.18 -0.33 -0.42 -0.18 -0.15 -0.06 -0.04 -0.06 0.11 0.08 -0.07 0.61 0.43 0.38 --- 0.93 0.90 0.94 0.97 -0.27 0.38 0.98 -0.98 0.46 0.02MI1 0.62 0.52 -0.05 -0.16 -0.23 -0.27 -0.25 -0.18 -0.16 -0.18 0.18 0.16 -0.19 0.63 0.36 0.59 0.93 --- 0.96 0.94 0.87 -0.39 0.26 0.90 -0.94 0.33 0.14MI2 0.67 0.61 0.11 0.00 -0.07 -0.41 -0.41 -0.35 -0.34 -0.36 0.35 0.34 -0.37 0.41 0.11 0.60 0.90 0.96 --- 0.83 0.78 -0.60 0.02 0.91 -0.90 0.09 0.38MI3 0.56 0.40 -0.27 -0.41 -0.49 -0.07 -0.05 0.05 0.08 0.06 -0.03 -0.06 0.05 0.81 0.63 0.41 0.94 0.94 0.83 --- 0.97 -0.09 0.56 0.87 -0.93 0.62 -0.18NDII 0.55 0.37 -0.34 -0.50 -0.58 -0.01 0.01 0.12 0.15 0.13 -0.06 -0.10 0.12 0.76 0.64 0.29 0.97 0.87 0.78 0.97 --- -0.02 0.60 0.90 -0.93 0.66 -0.23BRI -0.45 -0.57 -0.61 -0.62 -0.60 0.68 0.70 0.74 0.77 0.79 -0.68 -0.70 0.79 0.37 0.69 -0.45 -0.27 -0.39 -0.60 -0.09 -0.02 --- 0.76 -0.42 0.34 0.71 -0.96GRE -0.02 -0.23 -0.68 -0.79 -0.82 0.53 0.56 0.66 0.69 0.70 -0.58 -0.62 0.69 0.84 0.98 -0.12 0.38 0.26 0.02 0.56 0.60 0.76 --- 0.23 -0.34 1.00 -0.91WET 0.67 0.55 -0.08 -0.22 -0.31 -0.27 -0.25 -0.17 -0.15 -0.18 0.21 0.19 -0.18 0.47 0.27 0.40 0.98 0.90 0.91 0.87 0.90 -0.42 0.23 --- -0.97 0.31 0.19SOI -0.64 -0.50 0.12 0.27 0.35 0.22 0.20 0.11 0.09 0.11 -0.14 -0.12 0.12 -0.63 -0.40 -0.44 -0.98 -0.94 -0.90 -0.93 -0.93 0.34 -0.34 -0.97 --- -0.41 -0.08GRA 0.04 -0.18 -0.67 -0.79 -0.84 0.50 0.53 0.64 0.67 0.67 -0.55 -0.60 0.67 0.85 0.97 -0.10 0.46 0.33 0.09 0.62 0.66 0.71 1.00 0.31 -0.41 --- -0.87FOR 0.30 0.47 0.67 0.73 0.73 -0.66 -0.69 -0.75 -0.78 -0.80 0.68 0.71 -0.80 -0.59 -0.85 0.34 0.02 0.14 0.38 -0.18 -0.23 -0.96 -0.91 0.19 -0.08 -0.87 ---  a Green ? blue color scale shows correlations from stronger positive to stronger negative; values shown in italic light grey are not significant (? > 0.05). b Refer to Table 4.4.3 for variable symbology and descriptions.   Even though the relationships between structural and spectral variables are weaker, each structural variable shows at least one or two strong correlations with spectral indices.  WET and FMI in general appear as good potential predictors of forest cover, with foliar moisture index II (MI2) standing out (r = 0.67) (Table 4.4.4).  A good correlation between WET and forest structure at the plot level was also found by Cohen & Spies (1992).  Height percentiles were highly correlated to EVI, pixel brightness (BRI), pixel greenness 180  (GRE), SOI and FOR, with H99 generally exhibiting the best r values.  The negative correla-tions that H and LAI have with EVI and GRE are also explained by the high influence of shadows in the spectral response of forests and the canopies covering understory grass (Chen et al., 2004).  GF calculated across all view angles (?) showed strong correlations with BRI (positive), GRE (positive) and FOR (negative), with absolute values of r always increasing as ? increases.  Although a larger ? involves a wider hemisphere and the potential influence of adjacent pix-els, GFs with a higher ? are likely less sensitive to variations in space and will therefore show a better correlation with any metric due to reduced scatter (Section 4.3) (Varhola et al., 2012).  The higher correlations that GF? show with spectral indices compared to those exhib-ited by vertical FC indicate that variables based on angular representations of the canopy across the sky hemisphere might be better capturing the multi-layered physical attributes that produce specific spectral responses.  The best potential predictors of LAI are BRI (negative correlation) and FOR (positive), al-though relationships with GRE and EVI are also strong (r < -0.60).  Higher values of BRI in-dicate less forest/shade, more soil or more grass, while higher values of EVI are associated to reduced forest cover (Table 4.4.4).  Finally, SVF, which is identical to GF90, is highly and positively correlated to BRI and negatively correlated to FOR.    181  4.4.3.2 Modeling results and applicability  Table 4.4.5 shows the models for predicting the four structural variables, classified according to the number of predictors and the number of pixels aggregated for each dataset.  Each of those models was selected based on maximizing adjusted R2, minimizing RMSE and through visual inspections of predicted vs. observed values and predicted vs. residuals.  LAI5 was chosen to represent LAI in modeling because it is most commonly obtained from LAI-2000 (Pomeroy & Dion, 1996; Sicart et al., 2004) or hemispherical photography (Bewley et al., 2010; Essery et al., 2008) to parameterize hydrologic models, and because its correlation co-efficients with spectral indices slightly exceeded those of LAI4 (Table 4.4.4).  The same ap-plied to FC0.5 and H99; lower height percentiles showed poorer modeling performance, tended to slightly underestimate mean stand height and involved more outliers. While opera-tional models for FC0.5, LAI5 and SVF were selected from the single-predictor list, H99 re-quired multiple regression to significantly improve R2 and RMSE (Table 4.4.5).  The rela-tionships between LAI and SVF and their corresponding predictors (BRI and FOR, respec-tively) were non-linear and an exponential transformation of the models proved optimal.  FC0.5 and LAI5 operational models did not pass the Anderson-Darling normality test for re-siduals due to a number of specific outliers present in the dataset.  The inclusion of spectral indices from the four different conceptual groups (Table 4.4.3) was justified as they all con-tributed at least one variable to the models.  Pixel aggregation did not represent a significant improvement in model performance, with a maximum increase of R2 of 0.05 (FC) and no detectable reduction of RMSE when using four 182  pixels instead of one (Table 4.4.5).  It is therefore more parsimonious to apply the models directly to individual pixels of a Landsat image to produce the highest spatial resolution (30 m) predictions without a notable decrease in accuracy.  All models, regardless of pixel ag-gregation and multiple predictor incorporation, showed reasonable R2 (0.57 ? 0.74) and RMSE (10 ? 18%) (Table 4.4.5).   Table 4.4.5.  Modeling results (operational models in bold). Predictors Pixels Model a Adjusted R2 RMSE b RMSEN p Ander-son-Darling Single 1 (n = 352) FC0.5 = ?0.1814 + 0.0913?MI2 0.57 0.09 0.13 <0.001 H99 = 37.16 ? 64.41?EVI 0.57 4.35 0.18 <0.001 LAI5 = 23.59?e-13.38?BRI 0.59 0.39 0.14 <0.001 SVF = 0.8426?e-1.62?FOR 0.66 0.07 0.11 0.28 2 (n = 176) FC0.5 = ?0.1831 + 0.0939?MI2 0.61 0.08 0.13 <0.001 H99 = 37.65 ? 65.74?EVI 0.58 4.28 0.18 0.001 LAI5 = 23.91?e-13.45?BRI 0.61 0.39 0.14 <0.01 SVF = 0.8438?e-1.62?FOR 0.66 0.07 0.11 0.52 4 (n = 88) FC0.5 = ?0.2013 + 0.0955?MI2 0.62 0.08 0.13 <0.001 H99 = 37.65 ? 65.74?EVI 0.59 4.19 0.18 0.54 LAI5 = 24.35?e-13.51?BRI 0.62 0.38 0.14 0.05 SVF = 0.8422?e-1.61?FOR 0.67 0.07 0.11 0.78 Multiple 1 (n = 352) FC0.5 = 0.327 + 0.032?MI2 ? 0.636?BRI + 3.040?WET 0.60 0.08 0.12 <0.001 H99 = 21.00 + 92.41?EVI ? 397.38?GRE 0.74 3.37 0.14 0.74 LAI5 = 1.65 +16.74?e-13.38?BRI ? 2.31? e-4.61?EVI ? 7.76?GRE 0.56 0.38 0.13 <0.001 SVF = 0.043 + 0.997?e-1.62?FOR ? 0.281?EVI 0.73 0.07 0.10 0.008  a All models have model and coefficient p values < 0.05; variance inflation is < 30 for multiple regression models.  Operational models used to produce maps (Figure 4.4.6), histograms (Figure 4.4.7), scatterplots (Figure 4) and error percentiles (Figure 5) are shown in bold.  b All RMSE units are fractions except for H99, in m.   The models operate within a range of values for each independent variable that will produce meaningful results, and are only applicable to pixels with forested vegetation ranging from short and sparse regeneration to mature, dense stands.  The range of observed and predicted values for each dependent and independent variable is shown on Table 4.4.6 to indicate pre-liminary model applicability to the study area.  Of all these predictions for the modeling data-set, only one of the 352 records at the pixel level showed an inconsistent result due to a high 183  value of GRE (H99 = ?0.25 m in stand 104, compared to its 4.7 m observed value).  A com-parison of observed vs. predicted ranges for all variables shows that models tend to slightly reduce the variances, which is expected from regression-based approaches (Alila et al., 2009).  Table 4.4.6.  Observed and predicted variable ranges in modeling dataset pixels (as predicted by operational models, Table 4.4.5). Variable a Observed b Predicted b Min Max Min Max FC0.5 0.01 0.70 0.06 0.62 MI2 2.61 8.73 - - H99 (m) 0.5 25.3 -0.3 24.0 EVI 0.19 0.60 - - GRE 0.05 0.19 - - LAI5 0.12 3.08 0.31 2.66 BRI 0.16 0.32 - - SVF 0.08 0.72 0.17 0.70 FOR 0.12 0.99 - -  a Dependent variable for each model in bold b Observed and predicted in the individual pixel dataset (n = 352)   The percentage of pixels belonging to each land use class in Baker Creek, the corresponding predicted ranges for each forest structure variable and the percentage of pixels valid for for-ested vegetation are shown in Table 4.4.7.  These percentages should be high for forests and low for non-forests to respectively minimize error types I and II and allow the direct use of approach (1) to apply the models (Section 4.4.2.6).  However, high percentages of valid pix-els are common in most non-forested pixels, especially for H99 and SVF, producing errors type II close to 10% at the watershed level (Table 4.4.8).  On the other hand, the percentage of valid pixels in the forest class is high for all variables, leading to a low incidence of error type I.  All variables predicted in the forest class show a negligible number of isolated pixels 184  with extremely low or high values, attributable mainly to classification errors in the borders between different classes (e.g. clouds classified as forests) and specific interactions between spectral index outlier values and model structure.  H99 appears as the variable with the largest error, with 6.2% of forested pixels showing invalid values and an overall 4.7% incidence of error type I ?almost double the other metrics.  Table 4.4.7.  Ranges of predicted variables and percentage of pixels with values valid for forested environments according to land use at Baker Creek. Type %  FC0.5 (0 ? 1)a  H99 (m) (0.1 ? 30)a  LAI5 (0.1 ? 3.5)a  SVF (0 ? 1)a  Min Max % Valid  Min Max % Valid  Min Max % Valid  Min Max % Valid    Cloud 5.8  -0.20 -0.03 0.0  -2.1 29.8 99.8  0.0 0.2 2.4  0.39 952.1 9.1    Shadow 1.8  0.30 3.76 16.1  18.9 26.3 100.0  4.7 9.5 0.0  0.07 0.13 100.0    Water 1.0  -0.17 6.37 22.3  -3.4 27.8 99.8  0.0 9.9 15.6  0.07 0.13 99.9    Wetland 7.3  -0.17 1.09 95.9  -17.0 26.3 91.2  0.0 4.7 98.6  0.08 1.42 98.8    Clearcut 7.0  -0.17 2.74 30.1  -4.5 26.2 99.0  0.0 1.8 99.6  0.09 1.66 93.9 Non-forest 22.8  -0.20 6.37 41.9  -17.01 29.8 96.8  0.0 9.91 63.2  0.07 952.1 74.6 Forest 77.2  -0.19 2.66 97.1  -14.8 27.7 93.8  0.0 4.8 99.0  0.07 2.41 98.3 TOTAL 100.0  ? ? 84.5  ? ? 94.5  ? ? 90.9  ? ? 92.9  a Range of each variable considered valid for forested environments in the study area.   Table 4.4.8.  Percentage of forested pixels classified as non-forest (error type I) and non-forested pixels classified as forests (error type II) as determined by ranges valid for forested vegetation obtained from operational models applied to all pixels in Baker Creek, regardless of land use (Table 4.4.7). Metric Error type I (%) Error type II (%)FC0.5 2.2 9.6 H99 4.7 8.9 LAI5 0.7 8.4 SVF 1.3 8.2   Predicted vs. observed values for each variable and pixel aggregation scheme are shown in Figure 4.4.3.  The relationships are good considering the challenges of relating structural to spectral properties and the numerous sources of variation involved, although outliers are not 185  uncommon (especially for FC, Figure 4.4.3a).  H99 appears to have distinct clusters of data (Figure 4.4.3b,f,j), but the residuals are normally distributed and the records must remain consolidated to preserve simplicity and consistency with the unified sampling methodology here proposed.     Figure 4.4.3.  Predicted vs. observed values of structural metrics relevant to hydrologic modeling as obtained from Landsat spectral indices at the individual pixel level (a-d) (n = 352), aggregation of two pixels (e-h) (n = 176) and c) aggregation of four pixels (i-l) (n = 88).  Continuous central black line is a 45? reference; inner dotted lines are regression confi-dence bands; and outer segmented lines are prediction confidence bands (all with ? = 0.05).   186  The outliers resulting from LAI5 (Figure 4.4.3c) were not adjustable by any model structure and indicate that an inevitable underestimation of LAI took place in some pixels.  SVF is the variable that shows the narrowest scatter (Figure 4.4.3d,h,l) and consequently the lower RMSE (Table 4.4.5).  RMSE percentiles (Figure 4.4.4) show that, despite the presence of outliers and scatter in the relationships, accurate predictions for all the variables can be achieved for the majority of pixels.  For instance, 80% of the pixels will have an error in FC of less than 0.1 (10%).  The steepness of the RMSE percentile curves increases only above the 80th percentile for all vari-ables (i.e. for 20% of the data).      Figure 4.4.4.  Modeling residual root mean square error (RMSE) percentiles for FC0.5, H99, LAI5 and SVF.   187  4.4.3.3 Outlier analysis  All of the outliers identified for each variable (Figure 4.4.3i-l) represent stands dominated by pine.  FC0.5 showed notable outliers at the single pixel level (Figure 4.4.3a) that mostly dis-appeared when averaging with 2 and 4 pixels (Figure 4.4.3e,f).  LAI5 also showed resilient outliers, all indicating underestimation; at the stand level, outliers of both H99 and SVF are barely outside the 95% prediction bands and indicate both under- and over-estimation.  All the outliers of FC0.5 (Figure 4.4.3i) belong to stands under some degree of red-attack.  In early stages, red stands will not show discernible differences in forest structure as measured by ALS, so FC0.5 outliers are most likely explained by spectral anomalies.  Since H99 is pre-dicted by two variables, low values of EVI and/or high values of GRE would produce under-estimation and vice versa; however, no extreme values of both predictors were found among H99 outliers.  LAI5 outliers all represent underestimation, most likely caused by high tree den-sities that could have excessively saturated synthetic images.  Finally, SVF is slightly under-estimated only in a few small regeneration stands, and slightly overestimated in the presence of red-attack trees.  This might be caused by an overestimation of SVF in the ALS synthetic images of young regeneration stands, or anomalies in the spectral reflectance that influences FOR in red stands.    The effect of defoliation on the spectral response of the main predictor indices (Table 4.4.5) is shown in Figure 4.4.5.  The figure must be interpreted with caution because sample size differs among defoliation categories and there is substantial variability in physical character-188  istics among stands.  Therefore, each foliage category does not necessarily produce a unique and differentiable spectral response.  Some inconsistencies are also apparent, such as red stands showing a higher MI2 index than the greener stand or regeneration (Figure 4.4.5a).  EVI (Figure 4.4.5c) and BRI (Figure 4.4.5e) are the highest for regeneration stands and de-crease progressively for red and grey plots as a result of a stronger influence of shadow in these taller stands and a higher proportion of herbaceous vegetation visible in regeneration pixels.  Mature healthy spruce stands, although generally shorter than grey stands (Table 4.4.2), show higher values of EVI if compared to grey stands (Figure 4.4.5c) due to the pre-dominance of green foliage, but maintain the lowest values of BRI (Figure 4.4.5e) that cor-rectly result in the highest predicted values of LAI5 among the different stand types (Figure 4.4.5f).  FOR (Figure 4.4.5g) exhibits the opposite pattern from BRI (Figure 4.4.5f), resulting in predictions of SVF (Figure 4.4.5h) that are expectedly the reverse of LAI5 estimations (Figure 4.4.5f).    Figure 4.4.5.  Means (points), standard deviations (boxes) and minimum ? maximum ranges (bars) of predictor spectral indices (left) and corresponding predicted structural metrics (right) of validation plots (Table 4.4.2) grouped by MPB foliage status (x-axis). 189   4.4.3.4 Maps and variable distributions  Figure 4.4.6 shows color-scaled maps with continuous distributions of FC0.5, H99, LAI5 and SVF as predicted by the models in the forested pixels of Baker Creek, with their correspond-ing frequency distributions on Figure 4.4.7a-d.  For comparison purposes, Figure 4.4.7e-h also includes histograms showing the discrete distributions of each variable as parameterized by Bewley et al. (2010) with a few vegetation classes covering the extent of Baker Creek.  It is apparent that the discrete values describe an incomplete snapshot of forest metrics distribu-tions across the watershed.  The continuous distributions of FC0.5 (Figure 4.4.7a) and LAI5 (Figure 4.4.7c) show two modes, the first of which (small for FC0.5) is likely representing the young regeneration stands that occupy around 10% of the catchment?s area.  Forty-six percent of the watershed is covered with mature, taller stands that were mostly healthy in 2000 and defoliated in 2008, which are represented by the major modes in all four variable distributions (Figure 4.4.7a-d).  190    Figure 4.4.6.  Maps of distributed FC0.5 (a), H99 (b), LAI5 (c), and SVF (d), for Baker Creek, 2008 (white = cloud; black = cloud shadow; blue = water bodies; purple = wetlands; brown = bare soil / recent clearcuts; green scale = vegetation with minimum and maximum values in-dicated for each variable; FC0.5 and SVF are fractions, H99 is in m and LAI5 in m2/m2.).  191    Figure 4.4.7.  Histograms of variables in Baker Creek (FC0.5, H99, LAI5, SVF) distributed continuously by this study?s methodology (a-d) (color scales match Figure 4.4.6) and dis-cretely by traditional approaches (e-h).    192  4.4.3.5 Validation  Values predicted by the operational models (Table 4.4.5) for each variable were retrieved at the independent validation ground plots (Table 4.4.2).  A comparison between predicted and observed values in these plots revealed a reasonable degree of accuracy (Table 4.4.9).  How-ever, two ground plots were located in red-attack stands that appeared as outliers in the ob-served vs. predicted validation scatterplots (not shown).  If these stands were removed from the validation dataset, R2 would have increased from 0.47 to 0.75 for FC0.5, from 0.72 to 0.77 for H99, from 0.63 to 0.68 for LAI5 and from 0.79 to 0.92 for SVF.    Table 4.4.9.  Prediction errors and r2 for ground validation plots. Modeling type Variable RMSE RMSEN r2 (predicted vs. observed) a Single predic-tor,  1 pixel FC0.5 0.13 0.30 0.47 H99 4.03 m 0.19 0.72 LAI5 0.35 0.17 0.63 SVF 0.05 0.14 0.79 Multiple predictor,  1 pixel FC0.5 0.12 0.28 0.59 H99 3.24 m 0.24 0.76 LAI5 0.34 0.16 0.58 SVF 0.06 0.17 0.72  a All correlations with p < 0.01   The relationship between predicted and H99 observed in the validation plots indicates a po-tential model bias that overestimates the height of small stands and underestimates the height of taller stands, both by approximately 5 m.  This is likely caused by the loss of variance re-sulting from regression.  Predicted vs. observed values from the modeling dataset (Figure 4.4.3b), where the bias is not evident, suggest that particular errors in the validation plots ac-centuated the over- and under-estimation of H99 in both extremes of this variable?s distribu-193  tion.  A similar but much smaller bias is observed for FC0.5, which results from estimation errors at individual pixels only ?biases disappear when red stands are eliminated.  SVF and LAI5 show a smaller bias that is related to model variance loss (Table 4.4.6).  In all cases, the smaller sample size involving validation plots can also play a role in model performance evaluations.  4.4.4 Discussion  4.4.4.1 Links between ALS structural variables and Landsat spectral indices  Inevitable challenges arise when correlating variables as different as spectral responses rep-resenting two-dimensional optical reflectances measured passively by satellite sensors, and detailed three-dimensional structural properties of vegetation captured actively by ALS.  Some authors argue that these relationships, while statistically significant, are empirical and often indirect.  For example, Franklin (2001a) discusses that satellite remote sensing has not succeeded at consistently estimating canopy height because its relationship with spectral in-dices is generally weak ?a statement contradicted by the results of this section as more than 70% height variability was explained by spectral indices (Table 4.4.5).  Similarly, LAI varies greatly across eco-regions and species and, as a result, spatial extrapolations via correlation with spectral indices must be done with caution.  This thesis also suggests that the spectral response is strongly influenced by the amount of shadow projected by the canopies, with taller trees tending to project larger shadows that can influence neighboring pixels.  These illumination conditions are likely the primary cause for indices such as EVI and NDVI having 194  a negative correlation with forest structure (Table 4.4.4).  Chen et al. (2004) found the same result and proposed that the impact of shadow reduces the explanatory power of the NIR and R bands to predict vegetation characteristics, but other factors may also play a role.  Bright-ness and greenness, which are positively correlated to NDVI and EVI (Table 4.4.4), decrease with age at the stand level in conifer species (McMillan & Goulden, 2008), while chlorophyll content varying at the needle level as trees mature (Zhang et al., 2008) will have an effect on stand-level estimates of spectral indices.    In this research, a single Landsat scene acquired as close as possible to the LiDAR data ac-quisition was used.  State of the art geometric and radiometric calibrations were applied to the dataset to minimize the effects of atmospheric conditions and sensor configuration.  It can be stated with confidence that the relationships derived for this research are robust and ap-propriate for the study area.  In addition, they are consistent with other published models re-lating forest structure metrics and spectra (e.g. Chen et al., 2004; Donoghue & Watt, 2006; Gill et al., 2009; Wolter et al., 2009).  Transferability to other areas and through time are im-portant considerations and will be the focus of ongoing research, once the accuracy of single scene estimates are validated here.   4.4.4.2 Model quality and applicability  The models developed to estimate FC, H, LAI and SVF across the landscape (Table 4.4.5) showed reasonable accuracy (Figure 4.4.3), which only marginally improved if multiple spectral predictors were incorporated.  While the models will inevitably produce outliers and 195  some did not pass tests of residual normality, the central question is whether these limitations will have a sensitive effect on the outcomes of hydrologic modeling.  The substantial en-hancement introduced by this methodology on the characterization of spatially-distributed variables, illustrated in Figure 4.4.7, suggests that large estimation errors in individual pixels might not have a pronounced effect on the overall frequency distributions of the four vari-ables.  High prediction errors for each variable are only to be found in 10 to 15% of the pix-els as shown by Figure 4.4.4.  Similarly, watershed-level spatial distributions of SWE or streamflow predictions might be subject to the cancelling effect of underestimation in some pixels and overestimation in others.    The outlier analysis revealed that our dataset contains two identifiable stand types that could lead to resilient biases if these occupied significant portions of a watershed.  First, high stocking density stands led to LAI underestimation in some cases due to a possible overesti-mation of LAI by ALS.  Second, stands with varying levels of MPB red-attack were com-monly listed as outliers.  However, distinct values among spectral bands and predictor indi-ces causing these anomalies were not identifiable in the dataset due to the high variability of stand characteristics, which represented a continuum of complex interactions between forest spectral and structural properties.  According to studies evaluating the spectral properties of stands affected by MPB in different stages (e.g. Franklin, 2003; Skakun et al., 2003), ex-periments designed for this purpose should isolate pixels entirely under the stage of interest in order to eliminate the scatter introduced by trees undergoing different foliage stages (Wulder et al., 2006).  Since the plots and pixels are heterogeneous, this section?s experimen-tal design is not optimal to evaluate the effects of foliage status on spectral responses.  Al-196  though inevitably affecting methodological simplicity, remedial measures to account for er-rors from both red and overstocked stands include fitting specific models for these cover types, which were not abundant in Baker Creek when data were collected.    Tables 4.4.7 and 4.4.8 indicate that if non-forested pixels occupy a significant portion of a watershed, its land cover types need to be previously classified in order to apply the models to forested pixels only [approach (2)].  An important number of non-forested pixels produced valid ranges for all variables, so they need to be discarded a-priori.  A consistent source of invalid H99 values affecting around 4% of the forested area was generated by some pixels classified as regeneration stands having a significant influence of grass that resulted in high values of greenness and consequently negative values of H99 (see Table 4.4.5).  Since no other consistent and identifiable source of error was detected for any other variable and the average incidence of error type I is around 2%, model application following approach (2) (Section 4.4.2.6) can be considered robust.  4.4.4.3 Implications for hydrologic modeling and the role of remote sensing  The role of remote sensing in hydrological modeling and the monitoring of water resources in general has been emphasized recently during the American Geophysical Union Chapman Conference on Remote Sensing of the Terrestrial Water Cycle (Kona, Hawaii, February 2012).  A new era of hydrologic modeling relies upon the technological improvements fre-quently offered by remotely sensing tools that can either better characterize vegetation, to-pography and soils, or provide estimates of specific components of the water cycle with 197  which models can be evaluated, calibrated or even parameterized if spatiotemporal resolu-tions are adequate (Wagner et al., 2009).  This research fits well with repeated calls from re-searchers to maximize the use of remote sensing tools in hydrologic studies, especially for larger catchments where, in fact, satellite-derived data might be the only alternative to prop-erly parameterize models (Schmugge et al., 2002; Wagner et al., 2009; Tang et al., 2009; Bewley et al., 2010; Burges, 2011; Nolin, 2011).    With its 40 year-long data collection record and global coverage, the Landsat archive remains the most promising source of information to extrapolate vegetation metrics in watersheds where systematic measurements of structural variables are available at any point in time since the early 1970s, either from ground-based methods or more recent LiDAR acquisitions.  As sample size becomes a limiting factor when correlating spectral indices with forest struc-ture metrics, any experimental design attempting to develop prediction models must have enough measurements of the latter adequately distributed to represent the entire extent of each pixel, and a sufficient number of pixels to facilitate statistical analyses.  In this section, a large sample size of 352 Landsat pixels with 12,672 gridded points to characterize forest structure with ALS constituted a dataset that allowed the development of prediction models applicable to individual or aggregated pixels across a continuous landscape.  Fortunately, hydrologists are nowadays being highly trained in GIS technologies and have been increasingly incorporating remote sensing data into their studies (e.g. Biftu & Gan, 2001; Andreadis & Lettenmaier, 2006; Immerzeel et al., 2009; Roy et al., 2010).  Hydrology journals, accordingly, are including remote sensing / GIS into their theme categories to clas-198  sify peer-reviewed articles not necessarily evaluating hydrological processes directly (e.g. Varhola et al., 2012).  These techniques can therefore be applied by hydrologic sciences re-searchers with a basic level of remote sensing knowledge.  4.4.4.4 Future work  Future research will incorporate spatially distributed versions of FC, H, LAI and SVF directly on watershed-level hydrologic models and compare the model efficiencies with those result-ing from parameterizations involving simplistic vegetation classes.  In snow-dominated envi-ronments, the objective is to evaluate the effects of using distributed variables on the spatial distribution of SWE and then on streamflow simulations.  More specifically, sensitivity exer-cises focused on streamflow regimes should progressively test:  1) the effect of inputting dis-tributed (Figure 4.4.7a-d) vs. discrete (Figure 4.4.7e-f) structural metrics; 2) the effect of changes in the frequency distributions of structural metrics (related to both location and shape parameters); and 3) the effect of altering the spatial allocation of pixel-level metric values but maintaining the properties of the watershed-level frequency distributions.    The results of these sensitivity analyses will determine if further efforts to refine the tech-niques to obtain forest structure metrics from remote sensing are necessary.  Improvements may come through the use of a-priori land cover classifications facilitating stratified model-ing for specific vegetation types, the application of different statistical techniques to develop multivariate models, and the addition of random sampling errors on predicted values to ac-count for regression-derived variability losses (Alila et al., 2009).   Reapplying these ap-199  proaches in other study areas and healthy forests would be of value.  Finally, models devel-oped within a particular Landsat scene can be directly applied to calibrated scenes from the same location but different acquisition dates to evaluate the method?s consistency and poten-tial to capture subtle changes of forest structure in watershed-level continuous frequency dis-tributions.  4.4.5 Conclusions  This appears to be the first study that has integrated three remote sensing components ?LiDAR, aerial photography and Landsat? to specifically derive the four vegetation metrics typically used in hydrologic models. This section is original because it: 1) used a large sam-ple size derived from thousands of ALS synthetic hemispherical images representing a wide variety of forest environments; 2) performed a comprehensive integration of ALS and Land-sat using a broad selection of metrics and spectral indices; and 3) developed models to di-rectly estimate FC, H and SVF in addition to LAI.   While the relationships between spectral indices and forest structure variables are subject to scatter, including a complete suite of indices allowed the development of statistically signifi-cant models able to predict FC, H, LAI and SVF with reasonable accuracy at the watershed level.  FC was strongly correlated to FMIs while the enhanced vegetation index, brightness, greenness, grass and forest spectral fractions were all good predictors of H, LAI and SVF.  The operational models developed are parsimonious, statistically significant and reasonably accurate. 200   It is unlikely that the models developed in this section can be directly applied to other areas. However, hydrologic modelers are encouraged to consider the proposed approach using re-mote sensing techniques to obtain local forest structure metrics and linking them to spectral indices through simple methods.  In light of remote sensing advances, hydrologic model de-velopers should allow fully-distributed models to accordingly accept spatially-explicit ver-sions of vegetation metrics as they currently do for DEMs.   Any approach would benefit greatly from LiDAR, which has consistently been shown to provide accurate proxies of forest structure in unparalleled spatial resolutions and levels of detail.      201  5 General conclusions  This research was motivated by the current limitations of hydrologic modeling at characteriz-ing vegetation structure in the context of the massive MPB infestation in lodgepole pine for-ests of British Columbia.  Modeling is the only methodology available to evaluate the hydro-logic effects of MPB because the areas affected are so large that empirical observations based on paired watershed approaches are not an option (Alila et al., 2007b).  Thus, scientists are still unable to realistically infer the effects of the insect outbreak on hydrological processes (Pugh & Small, 2011), with flooding ranking highest in the list of potentially destructive im-pacts (Boon, 2007; Bewley et al., 2010).  While directly solving this problem was not within the scope or reach of this thesis, it provides valuable methodological insights that will likely encourage the transformations required by hydrologic models to incorporate enhanced re-motely-sensed forest structure metrics into their algorithms.  The two issues that have con-strained the applicability of hydrologic models to relatively small watersheds and the evalua-tion of clearcutting rather than gradual disturbances such as MPB are:  1) our inability to ac-curately measure the structural complexity of vegetation at the plot level and, most impor-tantly, 2) the difficulties related to obtaining wall-to-wall, spatially-explicit coverage of these metrics.  This research shows that remote sensing ?represented by ALS and Landsat? has the potential to overcome these issues.  When incorporated appropriately into hydrologic modeling platforms, remote sensing has the potential to positively impact the accuracy of SWE spatio-temporal predictions and even streamflow regimes.  202  Chapter 3 of this thesis focused on the development and improvement of plot-level simple empirical models ?a topic directly related to a more accurate characterization of forest structure by remote sensing.  The best method to test this accuracy was through evaluating the quality of the correlations between remotely-sensed metrics and snow accumulation and ablation indicators, and by determining if statistically-valid models with predictive accuracy could be developed.  Also, the performance of such models needed to be compared with models using traditional ground-based metrics from inventories or hemispherical photogra-phy.    To set up a baseline, a meta-analysis was conducted to gather historic information on plots where forest structure and snow were measured (Section 3.2) (Varhola et al., 2010b).  Thirty three studies published in different regions from the 1930s to present day provided hundreds of data points from which simple models predicting peak SWE and SAR with a single, stan-dardized forest cover variable were developed.  These models were comparable to others in the literature (Kuz?min, 1960; Pomeroy et al., 2002) and their quality was reasonable, with predictors explaining around 70% of the total variance, but substantial scatter indicated that site-specific predictions should be made with caution.  This variability is expected in simple models given the several factors that affect snow processes (Section 1.2) and could not be incorporated in the study due to lack of original source data.  It was concluded that forest cover is the main variable affecting snow accumulation and ablation under the canopies when compared to nearby clearcuts.  However, the methods used to measure forest cover by the authors of the compiled studies were questionable as no details were provided, and additional scatter is understandably introduced if differences exist between these methods.  Therefore, it 203  is very likely that if all studies had used a single approach throughout these decades to con-sistently measure forest structure (see Section 1.2.9), better model performances would have been observed.  Evidence strongly suggesting that ALS is the best remote sensing technology to overcome these difficulties of forest structure assessment was provided by Section 3.3.  Based on a set of observations from one snow season, models predicting peak SWE and SAR from ALS-derived metrics were noticeably better than those from ground-based variables.  ALS is par-ticularly good at estimating forest cover because the thousands of pulses emitted by a LiDAR sensor to a forested ground plot represent an optimum sampling scheme where the ratio be-tween returns intercepted by the canopies and the total number of returns is conceptually ideal for such a purpose.  The interception of ALS pulses by canopy elements is analogous to the interception of snowfall ?which determines snow accumulation in the ground? and the interception of solar radiation ?a primary driver of snow ablation.  Thus, ALS-derived for-est cover emerged as the best potential predictor of both peak SWE (r2 = 0.70) and SAR (r2 = 0.59), surpassing other metrics obtained from ALS and ground measurements.  However, these models were developed from one snow season and eleven plots, so they are not appli-cable for actual predictions.  Thus, Section 3.3 positively answered the first research question formulated in this thesis:  How are novel ALS-derived forest structure metrics correlated to indicators of snow accumulation and ablation?   As the results and conclusions of Section 3.3 were based on a small sample size and snow indicators obtained from discrete manual snow surveys, which might not accurately capture 204  true peak SWE and SAR, a broader study of empirical models was conducted in Section 3.5.  The main purpose of this section was to show that if snow is continuously monitored by ad-vanced instrumentation such as ultrasonic snow depth sensors (Section 3.4), the improvement in accurately measuring the dependent variables of these empirical snow models ?peak SWE and SAR? would translate into overall model upgrading.  Also, a broader suite of forest met-rics was tested by incorporating hemispherical photography and Landsat as sources of infor-mation.  Unfortunately, anomalous meteorological conditions during one of the snow seasons (Bewley et al., 2010) apparently introduced noise to the data and created outliers that resulted in relationships between snow indicators and forest structure that were inferior (r2 up to 0.60) to those previously reported in Section 3.2 and 3.3.  However, it was demonstrated that the use of ultrasonic sensors to obtain indicators of snow accumulation and ablation was funda-mental for those relationships to be statistically significant, which could not be achieved by manual snow surveys.  Another important conclusion was that the correlations between some Landsat-derived spectral indices and snow indicators can be as good as those based on ALS metrics and HP.  Only future work will determine if Landsat can be directly used to estimate snow accumulation and ablation in forested watersheds by comparing the accuracy of such estimations with those obtained from ALS.  In synthesis, Section 3.5 partially answered the second research question of this thesis, related to the ability of remotely-sensed forest struc-ture metrics and ultrasonic snow depth sensors to produce simple models able to predict indi-cators of snow accumulation and ablation.  It was not possible, without arbitrarily discarding outliers in the dataset, to produce statistically-valid models with reasonable predictive capac-ity based on measurements made in the study area.  The addition of simple meteorological variables to these models was not successful as shown in both Section 3.2 and 3.5.  The sev-205  eral limitations that affect simple empirical snow models and the difficulties related to their development with short-term records encouraged the analysis of how remote sensing could improve hydrologic models in the opposite extreme of complexity.  The purpose of Chapter 4 was to propose a methodology that would most directly benefit fully-distributed physically-based hydrologic models by better characterizing vegetation with remote sensing.  The strategy involved the initial identification of the main forest structure metrics currently being used by the most popular hydrologic models, as well as a review of the methods used by hydrologists to measure them (Section 4.2).  It was found that LAI, FC, H and SVF are the metrics currently employed to parameterize most models and that the techniques to measure them in the field, although consistent among hydrologists (e.g. Hedstrom & Pomeroy, 1998; Lundberg et al., 2004; Musselman et al., 2012), showed room for improvement.  Section 4.3 was specifically designed to answer the third research question of this thesis:  How can ALS be used to estimate the plot-level forest structure metrics currently used by physically-based hydrologic models?  While methods to estimate FC and H from ALS had been already established by previous articles (e.g. Popescu et al., 2002; Holmgren et al., 2003; Ria?o et al., 2004a; Bater et al., 2011), the fact that LAI and SVF are derived from hemispherical projections suggested that the coordinate system of ALS returns could be transformed to better represent such geometrical properties.   Even though other studies had previously estimated LAI from traditional ALS metrics (e.g. Solberg et al., 2006; Morsdorf et al., 2006), Section 4.3 revealed that a re-projection of ALS returns in a polar coordinate sys-206  tem substantially increased the accuracy of LAI and SVF estimation from ALS.  Untrans-formed data explained 35% of the variation of GF (used to estimate LAI and SVF), while synthetic hemispherical images developed by this coordinate transformation resulted in 87% of that variance being explained.  For the first time, a methodology was presented to consis-tently elaborate synthetic hemispherical images within any location of an ALS point cloud, from where a number of forest structure and radiation transmission metrics can be obtained.  Thus, the third research question of this thesis was successfully addressed.  Since most watersheds lack ALS coverage and its acquisition costs remain high, Section 4.4 developed a methodology to extrapolate the metrics obtained at the plot level in Section 4.3.  Landsat data, which are now freely available, were chosen to obtain a wide range of spectral properties from which to select the best predictors of the four metrics relevant to hydrologic modeling, previously obtained from ALS.  This exercise was conducted in Baker Creek, where (Bewley et al., 2010) explicitly requested that future work incorporate remote sensing technologies to better represent the continuous distributions of structural variables across the watershed.  Satisfactory results were achieved and, for the first time in the published litera-ture (Varhola & Coops, 2013), high-resolution spatially-explicit versions of LAI, FC, H and SVF were estimated in a relatively large basin.  This represents a major contribution to hy-drologic modeling, and a successful answer to the fourth research question of this thesis:  How can ALS-derived forest structure metrics relevant to hydrologic modeling be extrapo-lated to the watershed-level with the support of other remote sensing tools?  207  In synthesis, these are the original contributions made by this thesis:  1) A comprehensive review and data compilation of snow processes from the 1930s to present day.  2) The first exploration of direct relationships between ALS-derived forest structure metrics and snow indicators.  3)  The development of a prototype ultrasonic snow depth device at a very low cost, which substantially improves the experimental designs of snow monitoring.  4) The first exploration of direct relationships between Landsat spectral indices and snow processes.  5) The first coordinate transformation of ALS data ?a simple method that allows a more accu-rate estimation of the hemispherical metrics that drive snow processes.  6) The first compre-hensive integration of ALS and Landsat to consistently extrapolate the four forest structure metrics required by most hydrologic models.  As the uncertainties related to the true effects of MPB on multi-scale hydrological processes remain high (Pugh & Gordon, 2012), it is important to discuss the applicability and limita-tions of both empirical and physically-based models enhanced with remote sensing as poten-tial contributors to reduce these uncertainties; in other words, how can the methodologies de-veloped in this thesis be used to move hydrologic science forward and what future work is needed to fill our knowledge gaps in this topic.  The ultimate goal is to infer the effects of a gradually-degrading forest structure on streamflow regimes, but understanding the spatial distribution and duration of the relative contributions of snowmelt to runoff and streamflow is an unavoidable initial step.  Both empirical and physically-based models have one com-mon property when it comes to simulating snow accumulation and ablation:  they are appli-cable and operate independently in each pixel (plot) constituting a grid that must cover the entire extent of a given watershed.   208   The universal empirical models developed in Section 3.2 (Equation 3.2.2 and 3.2.3) can be directly applied to each pixel of a watershed provided that the frequency distribution of forest cover is estimated with remote sensing as shown by Section 4.4 (e.g. Figure 4.4.6).  Addi-tionally, observations of SWE strategically collected in open areas constitute an inevitable requisite to serve as a reference for their nearby forested stands and to capture the variations driven by factors not accounted for by the models (e.g. elevation, slope-aspect, etc.).  This latter requirement is not easily accomplished with a network of manual snow surveys, but estimating observed SWE in open areas from other remote sensing tools such as Radar is pos-sible and a topic of current research (Clark et al., 2011; Nolin, 2011).  Snow cover retrieved during spring from satellites such as MODIS (Bewley et al., 2010; Akyurek et al., 2011) can also be very useful to determine the dates of snow disappearance and hence calculate SAR in open areas.  Once good estimates of peak SWE and SAR are available in key open areas of the watershed, the relative reductions of both variables in forested pixels can be estimated with Equations 3.2.2 and 3.2.3.  It is important to add random errors to these predictions so that the loss of variability caused by regression (Alila et al., 2009) is re-introduced to better represent reality.  Finally, forest cover can be arbitrarily modified on a pixel-by-pixel basis to reflect defoliation, branch loss and tree fall resulting from MPB in each stand type and corre-sponding changes in peak SWE and SAR recorded.  As these empirical models will only pro-vide bulk estimates of SAR involving the entire ablation period, their ability to infer flooding risk remains limited as such events generally occur during shorter time intervals.  209  Physically-based models overcome some of the weaknesses of empirical models, but are sub-ject to their own limitations.  They would not require direct measurements of SWE in open areas as those are derived from precipitation data in each pixel, and they can provide hourly estimates of SWE that result in sub-daily values of SAR.  However, they are very sensitive to the quality of forcing meteorological data and oversimplified interpolations of these data be-tween weather stations.  The applicability of the methods developed in Chapter 4 to improve physically-based models is firstly dependent upon changing their source codes so that rele-vant forest structure metrics can be input as a grid of pixels (e.g. Figure 4.4.6) with individual values rather than a handful of coarse vegetation classes (Bewley et al., 2010).  The gradual effects of MPB infestation on LAI, FC, H, and SVF must be then accurately monitored to run successive simulations based on the same meteorological input but a changing forest struc-ture.  A long-term record of streamflow simulations realistically reflecting the effects of dis-turbance and subsequent recovery of forests is, for now, the only means of evaluating the im-pacts of MPB on hydrologic processes.  A few questions remain that must guide these future steps and further work to improve hy-drologic modeling with an increasing participation of remote sensing tools.  First, the levels of accuracy at estimating forest structure metrics must be in accordance with the scale (i.e. basin size) at which predictions are required.  High-resolution (e.g. 30 ? 30 m) estimates of forest structure are appropriate for a watershed of the size of Baker Creek (~1,500 km2), but a different approach and model types will be required to evaluate the impacts of MPB on the Fraser River basin.  Regarding accuracy, also, the sensitivity of hydrologic models to errors in the estimation of forest structure metrics and their spatial distribution within a watershed 210  must be analyzed to avoid unnecessary efforts in characterizing forest structure.  For exam-ple, the methodologies presented in this thesis to measure forest structure are subject to addi-tive uncertainties from the different procedures and calibrations (e.g. obtaining ground-based hemispherical images, calibrating synthetic ALS images and extrapolating the resulting met-rics with Landsat).  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