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UBC Theses and Dissertations

A hybrid modeling approach to simulating past-century understory solar irradiation in Alberta, Canada Erickson, Adam Michael 2017

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© Adam Michael Erickson, 2017  A HYBRID MODELING APPROACH TO SIMULATING PAST-CENTURY UNDERSTORY SOLAR IRRADIATION IN ALBERTA, CANADA  by  Adam Michael Erickson  B.A., University of Puget Sound, 2004 M.C.R.P., University of Oregon, 2011  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 2017   ii  Abstract   In western Canada, the effects of warming and increasing human activity may alter the structure, composition, and function of forests, producing quantitatively and qualitatively different understory light conditions. While difficult to measure directly, process-based models may facilitate inference of historical forest states. Yet, existing models are limited in the dynamics they represent. A promising new approach in hybrid modeling, first demonstrated here, is the fusion of machine learning and process-based models to simulate pattern-based processes. The objective of this dissertation was to simulate the effects of past-century climate and fire conditions on understory global solar irradiation trajectories across a 25.2 million ha landscape in Alberta, Canada. The LANDIS-II forest landscape model was applied to simulate past-century changes to competition, fire, and regeneration. Simulated tree species and age maps were classified into landcover types. A regression model of canopy light transmission as a function of landcover and site index showed good fit with field observations (R2 = 0.94) and was applied to a classification of LANDIS-II outputs. Canopy light transmission was multiplied by mean annual bare-earth global solar irradiation to produce understory light maps. Empirical and semi-mechanistic fire models were also applied. A variant of stochastic gradient descent was applied for parameter optimization, improving fire model performance (!"	= 0.96; Δ!"= +0.14). Simulations showed a mild decline in forested area across the 1923-2012 period, attributable to a velocity of warming three times faster than migration. Migration was primarily controlled by fire and secondarily by regeneration. Simulated understory light levels declined across the period due to reduced mortality rates, preceding a likely long-term increase in light attributable to reduced regeneration rates. The key innovations of this work are as follows: characterization of human-iii  dominated fire regimes in western Alberta (Chapter 4); advancement of the TACA-GEM regeneration model (Chapter 5); development of an algorithm for fire model parameter optimization (Chapter 6); development of new LiDAR models of canopy light transmission (Chapter 7); demonstration of a new hybrid modeling approach to simulating pattern-based processes, applied to understory light (Chapter 8); demonstration of long-term climatic regulation of understory solar irradiation through forest regeneration (Chapter 8).  iv  Lay Summary  This work seeks to understand the effects of warming and increased human activity on forests in western Alberta over the past century. The research relies on an advanced class of models known as hybrid models, which combine different model architectures together in a single model. Hybrid models are used for two reasons: (1) to enable large-scale simulations; (2) to model pattern-based processes poorly represented by physical models. Historical data on climate, fire, species traits, and forest cover were used for parameterization. An analysis of historical fires showed that humans now cause most fires and have shifted the fire regime toward more frequent and smaller fires. Model results suggest that the rate of forest recovery may be outpaced by disturbance. Model results also suggest that reduced mortality may decrease understory light in the short-term while inhibiting species from tracking warming. This has the potential to produce broad forest change over time. v  Preface  This dissertation contains elements of six scientific papers of which I am the lead author, presented in five chapters, as Chapter 3 contains content from two papers. The initial project was proposed by Dr. Nicholas Coops, in collaboration with Gordon Stenhouse of Foothills Research Institute. In Chapters 4 and 5, Dr. Craig Nitschke of University of Melbourne designed the Tree and Climate Assessment Germination and Establishment Model (TACA-GEM) and provided tree species parameters. Dr. Steven Cumming assisted in interpreting TACA-GEM model results. Dr. Robert Scheller of Portland State University led development of the LANDIS-II model. Drs. Andreas Hamann and Laura Gray of University of Alberta provided modeled tree species distributions. Drs. Sally Aitken, Robert Guy, and Scott Nielsen provided valuable manuscript edits and feedback along the way. Foothills Research Institute provided airborne LiDAR data on behalf of Hinton Wood Products. I located parameterization data, conducted the simulations, built statistical models, performed analyses, and led authorship of the manuscripts. In Chapter 3, I detail novel fire regime changes under Anthropocene conditions in Alberta in comparison with national trends. In Chapter 4, I develop new soil and daily weather parameterization methods for TACA-GEM applicable across Canada. In Chapter 5, I develop a new method for efficient parameter optimization with forest fire models, solving a longstanding modeling challenge. I also develop LANDIS-II parameterization methods for Alberta, Canada. The simulation results shed light on a recently observed, but poorly understood, decline in forested area for some regions of the western U.S. and Canada. In Chapter 6, I develop two new airborne LiDAR metrics of canopy light transmission. This work is the first, to my knowledge, to quantify the effects of common fisheye lens geometry models on the estimation of canopy light transmission using vi  LiDAR data. I also develop a 2-D vertically layered variant of the spike-free canopy height model algorithm of Khosravipour, Skidmore, and Isenburg (2016). In Chapter 7, I develop a method of combining empirical regression models of canopy light transmission with LANDIS-II simulation outputs. This work is also the first, to my knowledge, to combine machine learning with a dynamic vegetation model.  Versions of Chapters 3 and 5 are in review. Versions of Chapters 6 and 7, as well as an expanded version of Chapter 3, are in preparation for submission. A version of Chapter 4 is published in the following, re-printed here with the consent of the publisher:  • Erickson, A., Nitschke, C., Coops, N., Cumming, S., Stenhouse, G. (2015) Past-century decline in forest regeneration potential across a latitudinal and elevational gradient in Canada. Ecological Modelling. 313, 94-102.  vii  Table of Contents  Abstract .......................................................................................................................................... ii	Lay Summary ............................................................................................................................... iv	Preface .............................................................................................................................................v	Table of Contents ........................................................................................................................ vii	List of Tables ............................................................................................................................... xii	List of Figures ............................................................................................................................. xiii	List of Symbols ........................................................................................................................... xvi	List of Abbreviations ................................................................................................................. xix	Acknowledgements .................................................................................................................. xxiii	Dedication ................................................................................................................................. xxiv	Chapter 1: Introduction ................................................................................................................1	1.1	 Global Change and Forest Ecosystems ........................................................................... 1	1.2	 Global Change in Forests of Canada .............................................................................. 2	1.3	 Global Change in Boreal and Montane Forests of Alberta ............................................. 4	1.4	 Understory Plants and Canopy Light Transmission ....................................................... 7	1.5	 Dynamically Simulating Understory Solar Irradiation ................................................... 8	1.5.1	 Hybrid Models of Forest Ecosystems ................................................................... 10	1.5.2	 Airborne Laser Scanning Models of Canopy Light Transmission ....................... 14	1.6	 Research Overview ....................................................................................................... 16	Chapter 2: Model Data and Descriptions ..................................................................................20	2.1	 Introduction ................................................................................................................... 20	viii  2.2	 Fire History Data ........................................................................................................... 20	2.3	 Tree Regeneration Model ............................................................................................. 21	2.3.1	 Model Description ................................................................................................ 22	2.3.2	 Data Requirements ................................................................................................ 25	2.3.3	 Daily Weather ....................................................................................................... 25	2.3.4	 Soil Textural Classes ............................................................................................. 26	2.3.5	 Species Biophysical Attributes ............................................................................. 28	2.4	 LANDIS-II Forest Landscape Model ........................................................................... 34	2.4.1	 Model Description ................................................................................................ 34	2.4.2	 Data Requirements ................................................................................................ 38	2.4.3	 Model Core ........................................................................................................... 41	2.4.4	 Base Fire ............................................................................................................... 44	2.4.5	 Dynamic Fuels and Fire System ........................................................................... 44	2.5	 Airborne Laser Scanning Data ...................................................................................... 46	Chapter 3: Past-century Fire Regimes of Western Alberta, Canada .....................................48	3.1	 Introduction ................................................................................................................... 48	3.2	 Methods......................................................................................................................... 52	3.3	 Results ........................................................................................................................... 55	3.4	 Discussion ..................................................................................................................... 70	3.5	 Limitations .................................................................................................................... 81	Chapter 4: Tree Species Regeneration Modeling .....................................................................83	4.1	 Introduction ................................................................................................................... 83	4.2	 Methods......................................................................................................................... 85	ix  4.3	 Results ........................................................................................................................... 87	4.4	 Discussion ..................................................................................................................... 94	4.5	 Limitations .................................................................................................................... 96	Chapter 5: Forest Landscape Modeling ....................................................................................99	5.1	 Introduction ................................................................................................................... 99	5.2	 Methods....................................................................................................................... 101	5.2.1	 Historical Fire Regimes ...................................................................................... 104	5.2.2	 Model Scenarios .................................................................................................. 104	5.3	 Results ......................................................................................................................... 107	5.4	 Discussion ................................................................................................................... 119	5.5	 Limitations .................................................................................................................. 123	Chapter 6: Airborne Laser Scanning Models of Canopy Light Transmission ....................125	6.1	 Introduction ................................................................................................................. 125	6.2	 Methods....................................................................................................................... 133	6.2.1	 Pre-processing ..................................................................................................... 133	6.2.2	 Spike-free Canopy Height Model Algorithm ..................................................... 134	6.2.3	 Hemispherical Voronoi Gap Fraction ................................................................. 136	6.2.4	 Point-density Normalized Gap Fraction ............................................................. 139	6.2.5	 Comparison with Other ALS LiDAR Metrics .................................................... 142	6.3	 Results ......................................................................................................................... 146	6.3.1	 ALS Estimates of ACC and Po ........................................................................... 146	6.3.2	 Point-density Normalized Canopy Gap Fraction ................................................ 156	6.3.3	 Spike-free Canopy Height Model ....................................................................... 157	x  6.3.4	 Tree and Crown Metrics ..................................................................................... 158	6.4	 Discussion ................................................................................................................... 162	6.5	 Limitations .................................................................................................................. 164	Chapter 7: Simulation of Understory Global Solar Irradiation ............................................166	7.1	 Introduction ................................................................................................................. 166	7.2	 Methods....................................................................................................................... 168	7.2.1	 Data ..................................................................................................................... 168	7.2.2	 Linear and Machine Learning Regression Models of Po .................................... 170	7.2.3	 Landcover Classification of LANDIS-II Species-age Cohorts ........................... 171	7.2.4	 Bare-earth Global Solar Irradiation Model ......................................................... 172	7.3	 Results ......................................................................................................................... 173	7.3.1	 Simulation of Po and Iu with Model Fusion ........................................................ 177	7.4	 Discussion ................................................................................................................... 181	7.5	 Limitations .................................................................................................................. 184	Chapter 8: Conclusion ...............................................................................................................186	8.1	 Limitations .................................................................................................................. 193	8.2	 Research Contributions ............................................................................................... 196	8.3	 Areas of Future Research ............................................................................................ 199	References ...................................................................................................................................207	Appendix A: Statistical Analysis of Historical Fire Regimes .................................................272	Appendix B: ALS Models of ACC and VCC ..........................................................................277	Appendix C: Random Forest Algorithm .................................................................................282	Appendix D: ABMI Landcover 2010 Classification Scheme and Algorithm .......................284	xi  Appendix E: Bare-earth Global Solar Irradiation Algorithm ...............................................286	Appendix F: Validation of TACA-GEM with Permanent Sample Plot Data ......................290	 xii  List of Tables  Table 2.1 Soil texture and latitudinal parameters used with TACA-GEM version 4.4 ................ 28	Table 2.2 Source of tree species parameters used in the TACA model ........................................ 29	Table 2.3 TACA-EM parameters used in the LANDIS-II simulations ........................................ 30	Table 2.4 Tree species biophysical parameters used in TACA-GEM .......................................... 32	Table 2.5 Sources of life history attribute species parameters used in LANDIS-II ..................... 42	Table 2.6 Tree species life history attributes used in LANDIS-II simulations ............................. 43	Table 3.1 Fire regime statistics by period for the western Alberta study area .............................. 57	Table 3.2 Fire regime change by season ....................................................................................... 61	Table 3.3 Fire seasonality ............................................................................................................. 61	Table 5.1 Simulation scenario codes based on model configuration and period ........................ 106	Table 5.2 Simulated and observed fire time-series statistics ...................................................... 110	Table 6.1 Understory light metrics calculated in this study ........................................................ 132	Table 6.2 Additional VCC metrics ............................................................................................. 144	Table 6.3 Comparison of top three univariate ALS models (VCCfci; VCCfr; VCCir) with Ppdn .. 155	Table 6.4 Comparison of height-to-crown-area model results ................................................... 159	Table 7.1 Multiple linear regression model ................................................................................ 174	Table D.1 ABMI Landcover 2010 classification scheme ........................................................... 284	Table F.1 Linear models of total understory regeneration change by height class ..................... 298	 xiii  List of Figures  Figure 1.1 Study area in western Alberta, Canada .......................................................................... 4	Figure 2.1 TACA-GEM model diagram (Erickson et al., 2015) .................................................. 24	Figure 2.2 Alberta study area overlaid on NASA SRTM version 2 ............................................. 27	Figure 3.1 Mean annual trends for fires in the Alberta study area, 1919 to 2012 ........................ 56	Figure 3.2 Fire adjacency to roads by cause overlaid on SRTM 90 m elevation data .................. 59	Figure 3.3 Decadal area burned by fire source for the Alberta study area ................................... 60	Figure 3.4 2-D kernel density estimation for fire frequency by ordinal date and year ................. 62	Figure 3.5 Mean annual trends for fires Canada-wide, 1919 to 2012 ........................................... 63	Figure 3.6 Fire regime change-point segmentation using the binary segmentation algorithm ..... 65	Figure 3.7 Fire regime patterns nationwide and Alberta study area changes in seasonality ........ 66	Figure 3.8 Monthly and daily patterns of fire frequency, mean fire size, and total area burned .. 69	Figure 3.9 Fire statistics by reported detection source Canada-wide ........................................... 75	Figure 4.1 TACA-GEM parameterization scheme for Canada .................................................... 86	Figure 4.2 Modeled mean change in species regeneration across regions for the full period ...... 88	Figure 4.3 Mean change in species regeneration probability, 1923-1952 to 1983-2012 period .. 89	Figure 4.4 Regeneration probability boxplots .............................................................................. 93	Figure 5.1 Model parameterization, fusion, and optimization of TACA-EM and LANDIS-II .. 103	Figure 5.2 Historical fire statistics by region and time period .................................................... 108	Figure 5.3 Simulated annual fire regimes by period and scenario .............................................. 111	Figure 5.4 Simulated annual total forested area (sum of 1 ha pixels) by year and scenario ....... 113	Figure 5.5 Simulated annual individual and ensemble model results for scenarios and species 114	xiv  Figure 5.6 Simulated annual incremental change in species abundance by scenario ................. 117	Figure 5.7 Mean annual simulated forest change ....................................................................... 118	Figure 6.1 Univariate linear model angular canopy closure (ACC) model R2 by metric ........... 149	Figure 6.2 Change to univariate linear ACC model R2 by metric due to filtering disturbances . 150	Figure 6.3 Example LiDAR plot process colored by point height ............................................. 152	Figure 6.4 Example LiDAR plot demonstrating each of the hemispherical lens geometries ..... 153	Figure 6.5 Metrics based on Monsi & Saeki (1953) and the Beer-Lambert Law ....................... 156	Figure 6.6 ALS canopy height models for an example site, 1 m resolution ............................... 157	Figure 6.7 Empirical height-to-crown-area linear models .......................................................... 160	Figure 6.8 Individual tree crown detection for an example ALS plot ........................................ 161	Figure 7.1 Predictor variable maps for the study area ................................................................ 170	Figure 7.2 Random Forest variable importance used for initial feature selection ...................... 175	Figure 7.3 Random Forest model out-of-bag MSE by the number of trees parameter .............. 176	Figure 7.4 Modeling of mean landscape full-spectrum understory solar irradiation (Iu) .......... 178	Figure 7.5 Mean understory solar irradiation (Iu) across all simulation years by scenario ........ 180	Figure 7.6 Change in understory solar irradiation (Iu) by simulation year and scenario ........... 181	Figure A.1 Model fit for log-transformed fire sizes Canada-wide ............................................. 273	Figure A.2 Anderson-Darling Weibull parameter estimation for fire sizes Canada-wide ......... 274	Figure A.3 Mixed Gaussian model probability density of log-transformed fire size, Alberta ... 275	Figure A.4 Fire size distribution ................................................................................................. 276	Figure B.1 Pearson’s correlation coefficient (r) for convex spherical densiometer measurements and hemispherical Voronoi gap fraction (Phv) ............................................................................ 277	Figure B.2 Pearson’s correlation coefficient (r) for ground measurements and ALS metrics ... 279 xv  Figure B.4 VCCfci model fit for all 950 ground ACC measurement plots .................................. 279	Figure B.5 Models of Ppdn and ground ACC measurements ...................................................... 280	Figure B.6 Individual tree segmentation using three-dimensional α-shapes .............................. 281	Figure F.1 Changes in regeneration and observation frequency over time in SDS plot data ..... 292	Figure F.2 Box plots of mean tree age and height for all age classes ......................................... 293	Figure F.3 Regeneration changes in the PSP data by year ......................................................... 295	Figure F.4 Plots for understory and overstory angular canopy closure (ACC) class, mean site tree age, and mean tree height by year for PSP data .......................................................................... 297	Figure F.5 Correlations between height classes, total regeneration, and year (r) ....................... 299	Figure F.6 Changes to regeneration by height class in the PSP data .......................................... 300	Figure F.7 Frequency of height class 1 regeneration by tree height and age .............................. 301	 xvi  List of Symbols  ASector(i,j) AHemisphere A2 ACChv ACCpdn Creturns(i,j) C-7 CHMfpf CL cx, cy D DFirstReturns DDcanopy DDcrown VCCaci VCCbl VCCcv VCCfci VCCfr VCCir Area of hemisphere sector i,j Area of hemisphere Anderson-Darling statistic Hemispherical Voronoi angular canopy closure Point-density normalized angular canopy closure Point set within polar and azimuthal sector i,j FBP System Ponderosa pine and Douglas fir fuel class Fast-pit-free canopy height model Clay-Loam soil textural class Principal distances along the x,y plane Hartigan’s dip test Point density of first returns on the x,y plane Distance and direction to nearest canopy pixel Distance and direction to nearest detected crown pixel Above-height cover index Beer’s Law-modified intensity-return ratio Cartesian Voronoi vertical canopy cover First-echo cover index Canopy-to-total-first-return ratio Intensity-return ratio xvii  VCCp VCCr VCCsci F G '( ITCmw ITCwat K-L K-S L Le M-1/M-2 nFirstReturns(i,j) p50 φ Po Phv Ppdn r R r * θ Canopy-to-total-pixel ratio Canopy-to-total-return ratio Solberg’s cover index F-test statistic Leaf angle distribution; Basal area Understory solar irradiation Variable-radius moving window individual tree crown detection Watershed segmentation individual tree crown detection Kullback-Leibler divergence Kolmogorov-Smirnov statistic Leaf area index Effective leaf area index FBP System Boreal Mixedwood fuels classes Number of first returns in hemisphere sector i,j Leaf water potential at 50% loss of hydraulic conductivity Azimuth angle Canopy gap fraction Hemispherical Voronoi gap fraction Point-density normalized gap fraction Radial distance; Pearson’s correlation coefficient Radius of a sphere or hemisphere Radial projection function xviii   R2  ρ SiCL t T θ W Wt x’H, y’H x’i, x’j Xw i x’, Δy’ returns i returns j )  app Coefficient of determination Spearman’s rank correlation coefficient Silt-Clay-Loam soil textural class t-test statistic Canopy light transmission Zenith or polar angle Wilks-Shapiro test statistic Weight matrix Principal point coordinates for point x,y Image sensor coordinates for point i,j Three-dimensional point coordinates Barycentric coordinate i Camera distortion model Zenith angle point subset Azimuth angle point subset Cramér-Von Mises statistic Apparent clumping index xix  List of Abbreviations  ACC AGL AIC ALS ALTM ANOVA ASPRS ASWC BEHAVE BIC BRDF CESM1 CHM ClimateNA CNN COSEWIC COTS ED EM EMD Angular canopy closure Above ground level Akaike information criterion Airborne LASER scanning Airborne LASER terrain mapper Analysis of variance American Society of Photogrammetry and Remote Sensing Available soil water capacity Fire behavior prediction and fuel modeling system Bayesian information criterion Bidirectional reflectance distribution function Community earth system model, version one Canopy height model Climate North America Convolutional neural network Committee on the Status of Endangered Wildlife in Canada Consumer-off-the-shelf Ecosystem demography model Expectation-maximization algorithm Earth mover’s distance (Wasserstein metric) xx  ENVI-IDL Envisat-MERIS fAPAR FARSITE FBP System FIRETEC FMC FORÊT FPGA FRP FWI GAN GCI GDD GHCN-D GIS GPGPU GPS-INS HESFIRE HIGRAD ITC JABOWA Environment for visualizing images – interactive data language Environment satellite – medium resolution imaging spectrometer Fraction of absorbed photosynthetically active radiation Fire area simulator Fire behavior prediction system Transport model for prediction of wildfire behavior Foliar moisture content Forests of eastern Tennessee model Field-programmable gated array Fire rotation period Fire weather index Generative adversarial network Grassland curing index Growing degree days Global historical climatology network – daily Geographic information system General purpose graphics processing unit Global positioning system – inertial navigation system Human-earth system fire model High resolution model for strong gradient applications Individual tree crown Janak, Botkin, and Wallace model xxi  LAI LANDIS-II LANDSIM LAS LASER LAStools LFDB LiDAR LMG LSTM MCMC MFRI MODIS MODIS HS NASA NDVI NFDB NIRV NOAA NSR PAR PMVD Leaf area index Landscape disturbance and succession model version two Landscape simulator LASER file format Light amplification by stimulated emission of radiation LAS file processing tools by Martin Isenburg Large fire database Light detection and ranging Lindemann, Merenda and Gold statistic Long short-term memory Markov-chain Monte Carlo simulation Mean fire return interval Moderate resolution imaging spectroradiometer MODIS hotspot product National Aeronautical and Space Agency Normalized Difference Vegetation Index National fire database Near-infrared reflectance of vegetation National Oceanic and Atmospheric Administration Natural subregions of Alberta Photosynthetically active radiation Proportion marginal variance decomposition xxii  PnET PPFD R RADAR RMSE RNN rOpenSci SAR SIF NSDB-SLC SORTIE-PPA SRTM TACA-EM TACA-GEM TIN TLP TLS USGS VCC WRF-Fire ZELIG ZELIG++ Photosynthetic evapotranspiration model Photosynthetic photon flux density The R programming language Radio detection and ranging Root-mean-square error Recurrent neural network R Open Science Foundation Synthetic aperture RADAR Solar-induced fluorescence National soil database – Soil landscapes of Canada SORTIE perfect plasticity approximation Shuttle RADAR topography mission Tree and climate assessment – Establishment model Tree and climate assessment – Germination and establishment model Triangulated irregular network Turgor loss point Terrestrial LASER scanning United States Geological Survey Vertical canopy cover Weather research and forecasting – fire model ZELIG stand simulator model ZELIG stand simulator model, C++ version  xxiii  Acknowledgements  This research was generously funded through Foothills Research Institute’s Grizzly Bear Program and an NSERC grant to Dr. Nicholas Coops. Foothills Research Institute provided the collection performed by Aerial Imaging.  I would like to thank Dr. Nicholas Coops for his generous support over the past three years. I also thank my committee members, Drs. Sally Aitken, Robert Guy, and Scott Nielsen, for their informative questions, support, and counsel. I am very grateful to Drs. Craig Nitschke of University of Melbourne and Patrick Waeber of ETH Zürich for providing guidance on TACA-GEM. I am also grateful to Drs. Robert Scheller of North Carolina State University and Matthew Duveneck of Harvard University for their guidance on LANDIS-II.  I thank Dr. Brian Sturtevant and Brian Miranda of the USDA Forest Service, Cordy Tymstra, Ralph Wright, and Bob Mazurik at Government of Alberta, and, Drs. Brad Hawkes and Marc-Andre Parisien at Natural Resources Canada, for providing guidance on the application of forest fire models. I also thank Dr. Steven Cumming of Laval University for his valuable insights on model design. Finally, I thank Drs. George Church of Harvard University, Timothy Lu of MIT, Steven Strauss of Oregon State University, and Harris Wang of Princeton for their conversations on extending process-based vegetation models into the era of next-generation sequencing, precise gene editing, and synthetic ecology. Most of all, I thank my family for giving me the opportunity to pursue a dream. xxiv  Dedication  This work is dedicated to the memory of my friend, collaborator, and a source of inspiration, Dr. Thomas Hilker. This work is also dedicated to all who have endured hardship to advance our scientific understanding of the world, as the path to discovery is often a rocky road. I am most inspired by the work of Alan Turing, who pioneered new fields long before their time. Turing’s last works provide a glimpse into today’s deepening union of computing, biology, and artificial intelligence. I also dedicate this work to the memory of John von Neumann and Stanislaw Ulam, whose cellular automata and Monte Carlo methods developed at Los Alamos are the basis of forest landscape and classical fire models. Furthermore, I am inspired by the pioneering transdisciplinary research of C.S. Holling, Daniel Botkin, Richard Rothermel, Masami Monsi, Toshiro Saeki, Greg Asner, John Gamon, my supervisor, Nicholas Coops, and many others that brought a first-principles approach to ecology. Mathematicians prove concepts, engineers build them, and ecologists use them to reduce a forest of complexity. 1 Chapter 1: Introduction  1.1 Global Change and Forest Ecosystems Forests are essential to biodiversity and provide many ecosystem services for the world’s growing population (Costanza et al., 1997, 2006; Rockström et al., 2009). Given the persistence of Anthropocene trends, the future of the world’s forests remains uncertain (Magnani et al., 2007; Bonan, 2008; Houghton et al., 2012; Worrall et al., 2013). Despite recent policy-related gains in regions such as China (Viña et al., 2016), the global land area occupied by forests is at a historic low, with a net loss of ~7 to 11 million km2 of forestland over the past 300 years (Ramankutty & Foley, 1999; Foley et al., 2005; World Resources Institute, 2014).  Larger losses are estimated over greater timescales, in connection with agricultural land clearing (Ruddiman, 2003). The global rate of deforestation is likely increasing, with only Asia and North America experiencing recent net gains in forestland (Rudel et al., 2005; Lindquist et al., 2012). Meanwhile, the rate of forest loss surged in Canada and Russia for the 2011-2013 period, primarily attributable to forest fires, accounting for 34% of global forest loss (World Resources Institute, 2014). Many existing forests are managed forests, which lack the structural and functional attributes of primary forests (Nepstad et al., 1999; Chazdon, 2008). Large trees have declined in frequency (Lindenmayer et al., 2014), notable for their carbon storage (Luyssaert et al., 2008; Stephenson et al., 2014) and habitat provisions (Franklin et al., 1981; Hansen et al., 1991).   2 Despite evidence of a recent increase in forest net primary production (Cao & Woodward, 1998; Bonan, 2008; Keenan et al., 2014), a long-term decline is evidenced by net annual deforestation rates ranging from 5.2 million hectares (Food and Agrigulture Organization of the United Nations, 2010) to 13.5 million hectares (Lindquist et al., 2012). Globally, forest carbon emissions are estimated to outweigh carbon sequestration five-to-one (Potter, 1999; Mason Earles et al., 2012). An increased rate of soil respiration at high latitudes, attributable to enhanced microbial activity under warming, may further amplify carbon emissions beyond the predictions of existing models (Karhu et al., 2014).  Warming directly impacts the cryosphere, with reduced surface albedo due to snowmelt providing an additional warming feedback (Perovich et al., 2007; Lee et al., 2011). Snowpack reductions also stress freshwater and estuarine ecosystems while increasing the incidence of drought and wildfire (Knowles, 2002; Westerling et al., 2006; Abatzoglou & Williams, 2016). Higher rates of global tree mortality have been attributed to drought under existing levels of warming (Allen et al., 2010; Anderegg et al., 2013). Global forest fire activity has similarly increased, due to higher fuel severity under warming (Abatzoglou & Williams, 2016). Critically, climatic changes to germination and establishment may prevent some forests from regenerating following disturbance (Nitschke & Innes, 2008; Worrall et al., 2013).  1.2 Global Change in Forests of Canada Canada is home to 9% of the world’s forests, 93% of which are publicly owned (Gillis et al., 2005). Due to the relative intactness of its forests, despite accelerated fire-induced forest loss in the 2011-2013 period (World Resources Institute, 2014), scientific inquiry in Canada focuses  3 less on land-use conversion and more on structural and functional aspects (Chen et al., 2003). Canada experienced nominal deforestation over the past three centuries, losing ~5% of its forests to land-use conversion (Ramankutty & Foley, 1999). Yet, a low rate of land-use conversion obscures the extent of human influence. Over 67% of Canada’s forestland is managed (Power & Gillis, 2006; Canadian Forest Service, 2013b), including forestland managed for any type of use (e.g., conservation, economic, or recreation) per Section of the Good Practice Guidance for Land-use and Land-use Change in Forestry (Intergovernmental Panel on Climate Change, 2003). Less than 0.3% of Canada’s 347 million ha of forestland is harvested annually, while 7% was disturbed by fire or insects in 2014 (Natural Resources Canada, 2016). Similar to other regions, Canada’s forests are further impacted by indirect anthropogenic effects, such as warming, hydrological cycle change, CO2 fertilization, and nitrogen deposition, which may also alter the evolutionary trajectory of these forests.  The evolution of boreal forests, as a class of species interaction network (Proulx et al., 2005; Peralta, 2016), was shaped by climate and fire, and fire remains the most prominent disturbance type (Rowe & Scotter, 1973). Wildfires were historically climatic and indigenous in cause, with lightning strikes and controlled burning providing major sources of ignition (Wright & Bailey, 1982; Baker, 2012). Early European settlers viewed fire as destructive to timber resources and property, motivating a policy of fire suppression that may reshape vegetation communities (Bond et al., 2005; Thorpe & Daniels, 2012). While harvest patterns emulating natural disturbance regimes have undergone extensive research (Work et al., 2004), existing methods cannot replicate important physiological interactions with fire. The importance of these interactions is  4 evidenced by the initial evolution of pyrogenic traits in boreal genera such as Pinus beginning over 100 million years ago (He et al., 2012).  1.3 Global Change in Boreal and Montane Forests of Alberta This dissertation focuses on the Rocky Mountain foothills region of Alberta. To incorporate neighborhood effects, the 25.2-million-hectare western Alberta study area boundary of the Foothills Research Institute’s Grizzly Bear Program was utilized for Alberta (Figure 1.1).  Figure 1.1 Study area in western Alberta, Canada, overlaid on Canadian Forest Service boreal forest classes in NAD83 Lambert conformal conic coordinates with WGS84 graticules; Alaska displays the contiguity of boreal fires  5 The western Alberta study area is characterized by a strong elevational gradient and a related transition between montane Cordilleran forests in the southwest and boreal forests in the northeast, with the Great Plains (Canadian Prairies) beginning in the southeast (Natural Regions Committee, 2006). Mean elevations for biogeoclimatic regions range from 525 meters to 2,350 meters, while the latitudinal maxima range from 49° to 58° (Natural Regions Committee, 2006). Tree species diversity is lower here than in temperate and tropical zones, with only seventeen common species from six genera: Pinus, Picea, Populus, Betula, Larix, and Abies. About a third of species occur in the boreal, with approximately two-thirds in the foothills and montane regions. High-elevation areas (above 1,900 m) beyond the tree line are comprised of alpine meadows, exposed rock, snow, and glaciers (Natural Regions Committee, 2006).  Regional temperature and precipitation patterns reflect elevational and latitudinal gradients. While higher elevations and latitudes produce cooler temperatures, precipitation patterns are strongly influenced by local topography (Natural Regions Committee, 2006). Regions containing the shortest fire rotation periods, such as the boreal lowlands and plains, occur at lower elevations where precipitation is lowest and temperate extremes are highest, adjacent to more productive highlands (Natural Regions Committee, 2006). The foothills region is characterized by the most precipitation and the most productive forests, supporting an active timber industry.  The Cordilleran ice sheet covered the region during the Last Glacial Maximum, producing an abundance of well-drained upland soils. Parent materials are morainal and glacio-lacustrine in origin, with gray Luvisols and black Chernozems the most abundant soil types. Luvisols are more common in wetter regions, such as the boreal, while Chernozems are common in drier  6 regions. Soils in the eastern Albertan plains contain a relative abundance of sand and silt, attributable to aeolian deposition (Natural Regions Committee, 2006).  Many plants in the study area evolved competitive mechanisms not only to survive, but to thrive, following high-severity wildfires (Schwilk & Ackerly, 2001). While quaking aspen (Populus tremuloides Michaux) may act as a fuel break, resprouting vegetatively post-fire as a pioneer species (United States Forest Service, 2013), jack pine (Pinus banksiana Lambert) and lodgepole pine (Pinus contorta Douglas) are also pioneer species that rely on fire, but through cone serotiny (Burns & Honkala, 1990; Farrar, 1995b). In the absence of fire, these species may decline in abundance (Thorpe & Daniels, 2012).  The foothills region is characterized by relatively homogeneous stands of lodgepole pine, the result of large historical fires (Tande & Tande, 1979; Arno, 1980; Lotan & Perry, 1983; Critchfield, 1985). Lodgepole pine thrives on cool, dry sites and is estimated to have the widest range of environmental tolerances of any conifer in North America (Burns & Honkala, 1990). Alberta lodgepole pine are associated with glacial till, rather than alluvial soils or lacustrine deposits common in some parts of their range (Burns & Honkala, 1990). Other common tree species here include Engelmann spruce (Picea engelmannii Parry ex Engelmann), subalpine fir (Abies lasiocarpa (Hooker) Nuttall), and balsam fir (Abies balsamea (Linnaeus) Miller). Quaking aspen is the most abundant deciduous species (Nielsen et al., 2009).  Intensive extractive industrial activity has occurred in the foothills region in recent decades, as Alberta experienced population and economic growth (Nielsen et al., 2009). Over the past forty  7 years, forest harvest levels in Alberta increased four-fold (Canadian Forest Service, 2013a). Other regional extractive activities that affect forests include oil and gas exploration (e.g. seismic lines and well sites), and mining. The western Alberta study area is also home to iconic National Parks – Banff, Jasper, and Waterton Lakes – that comprise 23% of the 132,076 km2 brown bear core conservation area, within the study area (Nielsen 2009). These National Parks have attracted an unprecedented number of recreationists in recent years. In total, the number of people accessing Alberta’s forests is estimated to be at an all-time high (Bourbonnais et al., 2013; Fortin et al., 2016).  Effective fire suppression may alter forest composition. Due to fewer large fires in recent decades, Alberta’s lodgepole pine stands have transitioned toward a species composition of black spruce (Picea mariana Miller) and white spruce (Picea glauca (Moench) Voss) (Thorpe & Daniels, 2012). A diminished rate of burning may also reduce gross primary production for Pinus and Populus species through demographic change (Fahey & Knight, 1986; Magnani et al., 2007). Such strong demographic changes were recently shown for the region (Zhang et al., 2015), including reduced growth and recruitment rates.  1.4 Understory Plants and Canopy Light Transmission Photosynthetically active radiation is a key limiting factor of regeneration and productivity for understory plants (Monsi & Saeki, 2005). Models of understory plant distribution and abundance remain limited by uncertainties surrounding the understory light environment, a function of difficult-to-model succession and disturbance processes. Traditional statistical models and machine learning approaches are a modern application of the static Hutchinsonian niche,  8 performing well at coarse scales, but lacking dynamic processes needed to predict fine-scale patterns (Araújo & Peterson, 2012). Unlike climatic and edaphic variables that may hold for broad scales, light transmission is a function of leaf properties and forest gaps resulting from fine-scale mortality and regeneration patterns (Beaudet & Messier, 2002). Directly simulating salient processes of forest dynamics represents a promising approach to modeling the understory light environment.  1.5 Dynamically Simulating Understory Solar Irradiation	I hypothesized that past-century changes to fire disturbance and regeneration have had a significant effect on the long-term (50-year) trajectory of understory solar irradiation, ignoring changes to harvest levels. Accordingly, the purpose of this thesis was to quantify the effects of past-century changes in climate and fire regimes on understory solar irradiation in western Alberta, Canada, as a proxy for understory vegetation production potential. First, past-century changes to fire regimes were assessed. Next, climatic changes to tree regeneration potential were modeled. The results were used as inputs in forest landscape simulations to assess the effects of past-century changes to disturbance and regeneration on understory solar irradiation. The simulations were conducted across a 25.2 million ha forested landscape at 1 ha spatial resolution and annual temporal resolution across a fifty-year period. A hybrid modeling approach is provided with global change and biodiversity conservation applications.  Full-spectrum understory solar irradiation was dynamically simulated for four historical scenarios by combining process-based models of succession, disturbance, and regeneration with a regression model of canopy light transmission. The regression model utilizes site index values  9 and simulated changes to landcover to predict canopy light transmission. For forest site index, Canada Land Inventory values were used to capture the long-term productive capacity of sites. Site index differs from spectral photosynthesis metrics such as NDVI, SIF, and NIRV (Badgley et al., 2017), as it represents the integral rather than instantaneous photosynthetic capacity. Site index encapsulates centennial-scale variation in soils, climate, and drainage (Knight, 1967). Thus, I infer that site index exerts great influence on canopy light transmission. Resulting maps of canopy light transmission for each time-step were multiplied by bare-earth solar irradiation model outputs to predict mean annual stand-scale understory irradiation (* ha-1 yr-1). This allows representation of local understory light patterns produced by forest dynamics and local topographic conditions at the landscape scale. This work was conducted in seven components, each corresponding to a chapter:  • Chapter 2: Model design and parameterization data • Chapter 3: Analysis of fire regimes over the past century in Alberta and Canada • Chapter 4: Modeling tree species regeneration responses to past-century climate change • Chapter 5: Simulating forest ecosystems under past-century climate and fire conditions • Chapter 6: Models of canopy light transmission from convex spherical densiometer measurements and airborne laser scanning metrics • Chapter 7: Solar radiation modeling and fusion of linear and machine learning models of canopy light transmission • Chapter 8: Dynamic simulation of understory solar irradiation at the landscape scale over the past century   10 In the following section, I provide an overview of the hybrid modeling approach developed in this research.  1.5.1 Hybrid Models of Forest Ecosystems Forest ecosystems contain nonlinear dynamics from organismal to landscape scales that can be conceptualized as complex adaptive systems (Levin, 1998). The collective behavior of low-level individual agents produces high-level self-organization and emergence (Grimm et al., 2005; Levin, 2005). Due to their non-linear nature, simulating complex systems poses unique conceptual and computational challenges. Despite the advent of network-based models, under current computational and model design constraints, hybrid models that are both process-based and stochastic are perhaps best-suited to represent the ‘unavoidable criticality’ of biological systems (Bak et al., 1989; Mora & Bialek, 2011). This is due in part to the current immaturity of ecological network models, which typically lack multiple interaction types (Pilosof et al., 2017), species traits, agent-based interactions (Ings et al., 2009), and dispersal dynamics that may govern the formation of ecological networks (Thompson & Gonzalez, 2017). Nevertheless, the goal with both models is often the same: to locate a system state within the phase space, which may attract toward criticality (Mora & Bialek, 2011). By focusing on salient dynamics, hybrid models have a limited parameter space, reduced dimensionality, and a computationally efficient design, in comparison to physical individual-based models.  Forest landscape models blend the functionality of empirical growth-and-yield models with physical gap models in a hybrid model design (Bugmann, 2001; Kimmins et al., 2010). Based on the theory of forest dynamics (Shugart, 1984), stand-resolution and landscape-scale assumptions  11 are used to identify salient processes and reduce model complexity, enabling spatiotemporally explicit simulations across millions of interacting stands. Computational efficiency is achieved with two-dimensional cellular automata well suited to massively parallel high-performance computing systems, including general-purpose graphics processing units (GPGPUs) and heterogeneous CPU-GPU architectures.  An influx of remote sensing and ground network data combined with increased computational resources provide an opportunity to improve model parameterization, design, and implementation. While some recent modeling approaches are semi-empirical, relying on ground-satellite data assimilation to parameterize and constrain physical models (Quaife et al., 2008; Mandel et al., 2009), these models, as with current dynamic global vegetation models, lack important spatial, successional, and evolutionary dynamics. Future work may blend forest dynamics and physical processes through data assimilation in new hybrid model architectures. New models may rely on deep learning for modeling complex spatiotemporal patterns, such as wildfire spread and forest growth, trained on spaceborne remote sensing time-series. For such applications, generative adversarial networks hold particular promise (Goodfellow et al., 2014a).  Forest landscape models simulate dynamic changes in the composition, structure, and function of forests, typically at a species taxonomic resolution, based on classical Linnaean taxonomic classification schemes rather than modern genomics data. Forest dynamics thought to be most impacted by global change are the focus of this thesis. In the foothills region of Alberta, anthropogenic changes to climate and fire are two such dynamics. Warming is predicted to alter the mortality and establishment rates of trees (Brubaker, 1986; Allen et al., 2010; Luo & Chen,  12 2013), which may explain a recently observed demographic shift in Alberta’s forests (Zhang et al., 2015). While regeneration rates are likely to decline in some areas, a number of models predict that fire frequency, size, intensity, and thus tree mortality rates (severity), will likely increase under warming (Flannigan et al., 2001; Ali et al., 2012; de Groot et al., 2013). The combined effect of these dynamics is the subject of this research, focusing on potential impacts to understory irradiation, which is an important predictor of understory plant productivity.  In northern forests, fire and climate mediate the pace of forest compositional change through the effects of growth and mortality events on successional pathways (Gavin et al., 2013). Changes to light availability may regulate the capacity of understory plants to respond to climatic change through migration by altering the likelihood of successful germination and establishment. While previous modeling efforts represent many of these dynamics individually, statically (e.g., bioclimatic envelope models), or mechanistically (e.g., gap models), there is a need to simulate the interaction of these processes at the landscape scale under global change conditions. This interaction may serve to amplify or attenuate forest compositional, structural, and functional changes to forests in the coming decades (Nilsson & Wardle, 2005; Hart & Chen, 2006; Gracia et al., 2007; Smith, 2011; Wing et al., 2012).  An appropriate forest landscape model should incorporate salient spatial and aspatial dynamics of succession and disturbance, including ageing, competition, dispersal, mortality, regeneration, and fire spread. Such a model should incorporate physiological changes to germination and establishment, based on soil attributes in relation to the timing of seasonal weather events and species-specific tolerances. The model should represent fire ignition, initiation, and fuels- and  13 weather-modified spread rates, in accordance with observations. The model will need to simulate changes to understory light conditions, directly or indirectly. Based on the above model selection criteria, LANDIS-II (Landscape Disturbance and Succession model, variant II, version 6.0) was parameterized, optimized, and used to simulate forest processes in western Alberta.  The LANDIS family of models, including LANDIS-II (Scheller et al., 2007; Sturtevant et al., 2009) and LANDIS PRO (Wang et al., 2013, 2014b), following the original LANDIS work (He & Mladenoff, 1999; He et al., 1999; Mladenoff & He, 1999; Sturtevant et al., 2004; Yang et al., 2004), is unique in its ability to represent stochastic, mechanistic, logical, and probabilistic processes through a number of user-provided extensions in an open-source software framework. Of these models, LANDIS-II has the most active user community and provides the most user-developed sub-models. LANDIS-II and other cellular automaton-based hybrid models extend from empirical growth-and-yield equations, mechanistic gap models, and classical fire models (Scheller et al., 2007).  To reduce components of stand competition to a network of logical operations, LANDIS-II incorporates ecological succession through species life history strategies. For model initialization, LANDIS-II requires parameters for tree species life history attributes, tree species distributions, landcover classes, age classes, biogeoclimatic regions, regeneration probabilities, and, optionally, disturbance regimes. Of these parameters, regeneration probabilities are frequently the most difficult to attain. These values are typically imported from a separate ecophysiological model of planet regeneration, such as PnET-II (Aber & Federer, 1992; Aber et  14 al., 1995, 1997; Gustafson et al., 2014) or TACA-GEM (Nitschke & Innes, 2008; Mok et al., 2012; Erickson et al., 2015).  Combined with the latest ecophysiological regeneration models, such as the updated TACA-GEM model presented herein (Chapter 4), LANDIS-II can simulate forest dynamics at a stand resolution and landscape scale. A hybrid modeling approach provides greater representation of salient dynamics than models that rely purely on correlative relationships, lending to a theoretically greater ability to extrapolate beyond past conditions. LANDIS-II is designed to model at the species taxonomic resolution, necessary given evidence of historical no-analogue species assemblages (Urban et al., 2011). Details on the design of TACA-GEM and LANDIS-II are provided in Chapter 2.  1.5.2 Airborne Laser Scanning Models of Canopy Light Transmission The distribution and intensity of understory light provides a physical control on the establishment and production of understory plants (Hart & Chen, 2006). Along with soils, understory light is a major source of uncertainty in modeling understory plant distributions. Understory light is a product of solar radiation propagation, transmittance, reflectance, and extinction within forest canopies (Ligot et al., 2014). In boreal forests, understory light is primarily a function of canopy light transmission resulting from structural and compositional forest conditions related to climate and fire history (Gavin et al., 2013). Tree canopy properties that vary with stand composition (e.g., leaf area index, leaf angle distribution, canopy bulk density, leaf chemistry) play an important role in controlling the quantity and quality of understory light (Niinemets, 2010a; Ishii et al., 2012; Niinemets et al., 2015).  15 Following a landmark study in ecophysiology (Monsi & Saeki, 1953, 2005), a suite of methods exist to estimate canopy light transmission. Here, I develop models of canopy light transmission from convex spherical densiometer measurements and airborne laser scanning data. New methods are provided for mapping and simulating changes to canopy light transmission across forested landscapes. While previous studies model canopy light transmission using 3-D forest growth models and ray-tracing (Casella, 2008; Lintunen et al., 2013), such gap model simulations are difficult to extend beyond the stand scale.  In recent years, a number of studies have utilized light-detection-and-ranging (LiDAR) for mapping understory light conditions. With airborne laser scanning  (ALS), off-nadir scan angle pulse penetration used to represent angular canopy closure and on-nadir pulse penetration used to represent vertical canopy cover (Korhonen & Morsdorf, 2014). LiDAR systems can be single-return, multiple-return, or full-waveform digitizing systems. Typical ALS systems for terrestrial applications consist of a 1064 nm near-infrared neodymium-doped yttrium aluminum garnet (Nd:YAG) LASER source, avalanche photodiode detector with telescopic receiving optics, oscillating mirror or rotating polygon scanning device, precision inertial measurement unit (IMU) and global positioning system (GPS) receiver, and data recording device, mounted in an aircraft system (Baltsavias, 1999; Wehr & Lohr, 1999). Precise localization of points is achieved with IMU-GPS sensor fusion, typically using a variant of the Extended Kalman Filter (Caron et al., 2006). Sorties are flown at a velocity, altitude, and side-lap designed to reach a given target point density with even sampling.   16 Compared to ground-based approaches, ALS methods provide more robust and efficient estimation of canopy light transmission at broader scales (Lieffers et al., 1999). ALS methods of estimating light transmission in forests are rooted in geometry (Alexander et al., 2013), statistics (Morsdorf et al., 2006), the physical Beer-Lambert Law (Hopkinson & Chasmer, 2009), or a combination of the three, as exhibited by gap fraction, leaf-area index, and canopy light transmission (Richardson et al., 2009; Korhonen & Morsdorf, 2014). By characterizing canopy light transmission for different forest types and stages of development along productivity gradients, and connecting these values to dynamically simulated forest attributes and a bare-earth solar irradiation model, it may be possible to forecast changes to understory solar irradiation and thus plant productivity. While machine learning provides a promising approach of connecting empirical measurements to dynamic vegetation model, linear regression may be sufficient. In order to integrate remote sensing regression models with dynamic vegetation models, the same predictor variables must be available in each, constraining variable selection.  1.6 Research Overview This work is based on linking together a series of models to predict changes to understory global solar irradiation under the continuation of historical climate and fire trajectories. These models are complex and require a copious number of parameters, which are often process-specific, derived from data or the literature. Estimating reliable parameters is a central limitation of modeling studies, particularly for longer simulation durations whereby model behavior may overcome landscape initialization. A tradeoff was observed between the resolution and scale of parameters available for Canada. While there is ample field data for certain species, times, and places, gridded nationwide data are seldom available. This is particularly true for tree species,  17 given the specificity of parameters required. While spatiotemporal variation in species attributes linked to genetic or gene expression variation (Aitken et al., 2008) is not included here, organismal plasticity under the assumption of optimality is motivating the development of next-generation dynamic global vegetation models (Strigul et al., 2008; Franklin et al., 2012; Scheiter et al., 2013; Falster et al., 2017).  Models of forest dynamics are typically spatial (sites interact) while regeneration models lack spatial interaction, similar to other process-based models (e.g., dynamic global vegetation models). These models are designed for a range of scales and resolutions. Forest landscape models (e.g., LANDIS-II or LANDIS PRO) are designed to operate at a stand resolution (~ 1 ha) and landscape scale (~ 106 ha), unlike gap models designed for an organismal resolution and stand scale (Bugmann, 2001). Size- and age-structured models using partial differential equations have also emerged, which operate at an organismal resolution and up to global scale (Moorcroft et al., 2001; Purves et al., 2008; Strigul et al., 2008; Medvigy et al., 2009; Xu et al., 2016). These are the first gap model derivatives that can be applied for terrestrial biosphere modeling. Meanwhile, regeneration models operate at resolutions ranging from individual trees to landscapes and are effectively scale-free, limited by the resolution- and model-dependent accuracy of climate, soils, and species parameters.  While the majority of regeneration models infer establishment suitability from photosynthetic limitations (e.g., LINKAGES, PnET, and 3-PG-based models), the TACA family of models builds on this approach by explicitly modeling a number of regeneration processes. The latest TACA version, presented herein, incorporates germination processes and extreme events, in  18 addition to phenology. Given the substantial number of tree species parameters required for the TACA and LANDIS-II models, values used in previous studies and the literature were relied upon. Additional parameters were calculated from available geospatial soils, climate, fire, site index, elevation, and tree species distribution, and landcover data. While each of these data represent different spatiotemporal resolutions and scales, sources used were selected for their compatibility with the study design. Model spin-up was used to generate the initial age distribution, as this information was not available and LANDIS-II may be insensitive to spatial parameters when stochastic model components are used (Davis, 2013).  Unknown errors likely exist in the parameterization data, contributing noise to the simulation results. The contribution of such noise to the results requires additional research on specific model components, as well as overall model outputs; statistical models may be used to link the two, as is performed herein for the TACA model. Bayesian methods (e.g., Gaussian process regression) offer a promising approach of quantifying uncertainties in stochastic simulations (Green et al., 2000; van Oijen & Thomson, 2010). The LANDIS family of models was designed to facilitate such inquiries into interchangeable model components (He et al., 2002), allowing it to be used as a tool for ecological inquiry (Davis, 2013). While model parameter sensitivity and validation studies have been conducted for specific components and regions for TACA (Nitschke & Innes, 2008; Mok et al., 2012) and LANDIS-II (Sturtevant et al., 2009; Xu et al., 2009; Davis, 2013; Simons-Legaard et al., 2015), global model validation, parameter optimization, and parameter sensitivity analyses should be conducted.   19 Finally, the designs of the two models undoubtedly contribute errors, as such models represent coarse simplifications of natural systems. The model simplifications used are detailed in the following chapter. While it is often assumed that compute poses the main limitation, contemporary model design is limited by data first, ingenuity second, and compute third. Nevertheless, detailed simulations for broad scales and/or long durations using physical models (e.g., classical gap models) remain compute-limited. This has motivated the development of hybrid models such as LANDIS-II (Scheller et al., 2007) and SORTIE-PPA (Purves et al., 2008; Strigul et al., 2008).   20 Chapter 2: Model Data and Descriptions  2.1 Introduction A considerable portion of this research involved locating and pre-processing datasets for model parameterization. A major goal of this work was to develop a model parameterization methodology utilizing tree species, fire history, soil, and climate data available Canada-wide, in order to facilitate future simulations at the national scale as computational resources improve. It is important to document these datasets separate from the research chapters in order to facilitate both reproducibility and extensibility. In this chapter, datasets used for model parametrization are described. First, fire history data are presented. Next, TACA-GEM model data are discussed, followed by LANDIS-II model data. For each model, distinct classes of parameters are grouped. For LANDIS-II, separate sections are provided for the succession and disturbance submodels. Tree species attributes are presented separately for each model, as they often differ in source and type. Finally, ALS data used to develop regression models of canopy light transmission are described.  2.2 Fire History Data To estimate parameters for historical fire regimes, the latest Canadian Forest Service National Fire Database (NFDB) spatial wildfire polygon and point data were used (Canadian Forest Service, 2015). The NFDB was formerly known as the Large Fire Database, or LFDB. While the LFDB was previously limited to fires greater than or equal to 200 ha in size, the NFDB contains fires of all size classes. The NFDB data used contains fires from 1919 through 2014, covering 97% of the area burned in Canada (Stocks et al., 2002; Bond-Lamberty et al., 2007). The dataset  21 was assembled from a variety of sources and underwent extensive validation. The NFDB represents the best long-term fire data available for Canada, combining a variety of data and methods commonly used to map disturbances (Stocks et al., 2002; Goetz et al., 2006; Parisien et al., 2006; Gralewicz et al., 2012; Canadian Forest Service, 2015).  The NFDB contains geolocated fire perimeters mapped by the thirteen fire management agencies (provinces, territories, and Parks Canada) using aerial photography and passive optical spaceborne remote sensing (i.e., Landsat and MODIS). The mapping methods vary by source and year (Parisien et al., 2006; Canadian Forest Service, 2015). The data show expected patterns of improved monitoring coverage over time, particularly with the addition of Landsat and MODIS in recent decades. Spaceborne remote sensing provides greatly improved temporal resolution and coverage of fire disturbances compared to airborne remote sensing, at the cost of spatial resolution. The impact of this change in data sources on recorded fire regimes is briefly assessed in Chapter 3. The NFDB also contains ancillary information reported by the fire management agencies, such as the date and severity of disturbances.  2.3 Tree Regeneration Model Two versions of the Tree and Climate Assessment (TACA) tree regeneration model were applied, TACA-EM and TACA-GEM. Recent advances to the TACA-GEM model are presented in Chapter 4. This section describes data used to parameterize each version of the TACA model.   22 2.3.1 Model Description The TACA model is designed to assess climate change impacts on the regeneration niche of trees, the niche most sensitive to climatic change (Nitschke & Innes, 2008). In the TACA model, each year is simulated at a daily resolution to capture phenologically-driven regeneration events. Phenology poses fundamental limitations on species distributions (Chuine & Beaubien, 2001) and plant fitness (Chuine, 2010), thus its inclusion may improve model performance. Regeneration carries particular importance in global change studies, as it regulates forest change at a low level (Fisichelli et al., 2014), providing an important climatic feedback.  The TACA regeneration model simulates tree species regeneration as a function of climatic and edaphic conditions relative to species biophysical constraints (Nitschke & Innes, 2008; Erickson et al., 2015). TACA was originally based on regeneration and phenology functions within the forest gap model, ZELIG++ (Burton & Cumming, 1995; Cumming & Burton, 1996). The TACA model relies upon empirically derived biophysical relationships for regeneration in a process-based approach. Modeled species must navigate seasonal biologically relevant physical thresholds in order to regenerate each year. The regeneration probability output for a species is the sum of each annual probability divided by the number of scenarios in each simulation, producing an average probability for a given decade. Unlike statistical approaches, TACA explicitly models biological processes, enabling more robust extrapolation to novel conditions.  The TACA Germination and Establishment Model (TACA-GEM) builds on the TACA Establishment Model, TACA-EM (Nitschke & Innes, 2008), by including a germination submodel. The latest TACA-GEM version presented herein builds on previous versions  23 (Nitschke et al., 2012) with four improvements. The growing-degree-day (GDD) response functions from Zelig++ (Burton & Cumming, 1995), JABOWA (Botkin et al., 1972) and FORÊT (Shugart & West, 1977) are used to determine annual establishment suitability as a probabilistic function of temperature, rather than binary responses to GDD and drought conditions for a given year. Second, drought is now calculated based on the proportion of the year where soil water potential is equal or below the turgor loss point (permanent wilting) for a given species, instead of the portion of the year where water deficit occurs per the actual-to-potential-evapotranspiration (AET:PET) ratio. This provides a more physiological basis for drought.  Third, soil water potentials are calculated from soil water availability and soil texture classes, using a reformulation of the van Genuchten soil water model (van Genuchten, 1980). Species regeneration suitability is equal to one in years with no water deficit and declines to zero if the proportion of the year under water deficit exceeds a species-specific threshold. Ponding depth is not explicitly modeled. The fourth improvement to the model is the development of an extreme events module. The extreme events module modifies species regeneration by eliminating seedlings that regenerate in favorable years but are subjected to prolonged and/or extreme drought or frost events, which result in mortality over decadal periods. A diagram of TACA-GEM is provided (Figure 2.1). Additional factors such as seed source and canopy conditions are modeled within LANDIS-II, into which TACA-GEM establishment probabilities are integrated. 24  Figure 2.1 TACA-GEM model diagram (Erickson et al., 2015); germination niche dormancy refers to embryo dormancy 25 2.3.2 Data Requirements In addition to species biophysical parameters, the TACA model requires daily weather, soil, and solar radiation parameters for each site modeled. These parameters are decadal-scale daily resolution temperature minima and maxima, precipitation, soil moisture regime, soil texture, rooting zone depth, coarse fragment percent, percolation rate, an optional nitrogen modifier for productivity, and latitude, used in solar modeling. As the following TACA model configuration was designed for integration within LANDIS-II simulations, shared regions were used consisting of the Natural Subregions of Alberta (Natural Regions Committee, 2006). While this reduces site-scale variability in climate and soils, it was necessary for the purposes of this research.  2.3.3 Daily Weather Most bioclimatic studies use monthly means of weather variables averaged over a climate normal period, typically 30 years. The major factor influencing the selection of this temporal resolution is the widespread availability of monthly resolution general circulation model projections (Intergovernmental Panel on Climate Change, 2014). The use of daily resolution data improves the results of phenological models applied for ecological forecasting (Cook et al., 2010; Richardson et al., 2013). The TACA model was designed to use daily resolution weather data to model soil moisture conditions and species regeneration responses. Acquiring daily resolution climate projections typically involves the use of stochastic weather generators or other statistical disaggregation approaches. Meanwhile, daily resolution historical weather station measurements provide the most robust model data for phenology.   26 Data from the National Oceanic and Atmospheric Administration (NOAA) Global Historical Climate Network Daily (GHCN-D) version 3.11 were used to parameterize daily minimum and maximum temperature, and total daily precipitation, in the TACA model. The GHCN-D dataset is a global weather station database subjected to uniform quality assurance (Menne et al., 2012). Using R (R Core Team, 2015), daily weather values were computed for the median decade of interest within 30-year periods, averaged across each Natural Subregion within the study area for each day, in order to provide results comparable to other vegetation modeling studies. Missing values were imputed using a multivariate expectation-maximization (EM) algorithm with bootstrapping, commonly applied to climate variable imputation, using the R FastImputation package (Honaker et al., 2011; Lounici, 2012). Stations missing 50% or more observations were discarded; this low threshold was used for the regional averaging methods employed, as multiple stations exist per Natural Subregion. Imputed values, which followed the central tendency of time-series, were considered preferable to unduly weighting values for distant stations. Simplified versions of the GHCN-D processing functions and an interface to the NOAA API are available in the rnoaa package for R (Chamberlain et al., 2016).  2.3.4 Soil Textural Classes Biogeoclimatic Natural Regions and Subregions of Alberta (Natural Regions Committee, 2006) were overlaid onto the Soil Landscapes of Canada (SLC) v3.2 database (Soil Landscapes of Canada Working Group, 2010) to generate soil textural class parameters for each modeled region in TACA (Figures 2.2 and A.3; Table A.1). Soils were characterized for each subregion based on the dominant soil type. Soil texture, rooting zone depth, percentage of coarse fragment material,  27 available water holding capacity (AWHC), and derived percolation rate (Derr et al., 1969) were calculated based on corresponding values from the SLC lookup table.   Figure 2.2 Alberta study area overlaid on NASA SRTM version 2 (National Geospatial Intelligence Agency corrected) elevation in NAD83 UTM 11N (meters) coordinates; (a) Natural Subregions of Alberta; (b) Natural Regions of Alberta; (c) soil available water holding capacity; points denote locations of NOAA GHCN-Daily weather stations; refer to Figure 1.1 for geolocation information  Soil moisture levels and mean elevation parameters were obtained from the subregional summaries (Natural Regions Committee, 2006). The soil textural classification for SLC values was based on Agriculture and Agri-Food Canada particle size classes (Soil Classification Working Group, 1998), which follows the USDA Textural Soil Classification pyramid. Soils were classified into textural groups based on SLC values for percent sand, silt, and clay, filtered (a) (b) (c)  28 by parent material texture. Organic soils were designated as the dominant soil type for one subregion, based on the biogeoclimatic region summary (Natural Regions Committee, 2006).  Table 2.1 Soil texture and latitudinal parameters used with TACA-GEM version 4.4; AWSC = Available Water Storage Capacity; L = Loam; CL = Clay loam; SiCL = Silty clay loam; Latitude = centroid Natural Subregion latitude rounded to nearest 5° in WGS84 projection Natural Subregion Soil Texture Rooting Zone Depth (m) Coarse Fragment % AWSC (mm/m) Field Capacity (mm/m) Percolation (mm/day) Latitude Alpine - - - - - - - Central Mixedwood SiCL 1.0 5% 452 560 93.1 55˚ Central Parkland CL 1.0 5% 341 470 122.6 50˚ Dry Mixedwood CL 1.0 5% 341 470 122.6 55˚ Foothills Fescue CL 1.0 5% 341 470 122.6 50˚ Foothills Parkland CL 1.0 20% 341 470 103.2 50˚ Lower Boreal Highlands CL 1.0 20% 341 470 103.2 55˚ Lower Foothills CL 1.0 5% 341 470 122.6 55˚ Mixedgrass CL 1.0 5% 341 470 122.6 50˚ Montane L 1.0 20% 377 460 66.4 50˚ Peace River Parkland CL 1.0 5% 341 470 122.6 55˚ Subalpine L 1.0 20% 377 460 66.4 50˚ Upper Boreal Highlands CL 1.0 20% 341 470 103.2 55˚ Upper Foothills CL 1.0 5% 341 470 122.6 55˚   2.3.5 Species Biophysical Attributes Tree species biophysical parameters were derived from the literature and regional databases, following previously applied methods (Nitschke & Innes, 2008; Nitschke et al., 2012). Existing species compendiums may benefit from updates including genomics information. Sources for species biophysical parameters used in the TACA-GEM model are as follows:    29 Table 2.2 Source of tree species parameters used in the TACA model; Burns & Honkala (1990) and Thompson et al. (1999) cover North America, Klinka et al. (2000) covers British Columbia, other sources vary; several parameters adopted by Nitschke & Innes (2008) from the original Zelig++ work (Burton & Cumming, 1995; Cumming & Burton, 1996) were derived from range data; LANDIS-II simulations used only dominant species, listed in Table 2.3 Species Data Source Abies balsamea (Balsam fir) (Burns & Honkala, 1990; Thompson et al., 1999; Greenwood et al., 2008) Abies grandis (Grand fir) (Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008) Abies lasiocarpa (Subalpine fir) (Edwards, 1982; Leadem, 1989; Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Nitschke et al., 2012) Betula papyrifera (White birch) (Bevington & Hoyle, 1981; Bevington, 1986; Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Grenier & Sirois, 2009) Larix laricina (Tamarack) (Pitel & Cheliak, 1986; Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000) Larix lyallii (Subalpine larch) (Shearer, 1961; Burns & Honkala, 1990; Carlson, 1994; Thompson et al., 1999; Klinka et al., 2000) Larix occidentalis (Western larch) (Burns & Honkala, 1990; Sorenson, 1990; Carlson, 1994; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008) Picea engelmannii (Engelmann spruce) (Woodard, 1983; Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008) Picea engelmannii x glauca (Hybrid white spruce) (Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Renault et al., 2000; Nitschke & Innes, 2008; Nitschke et al., 2012) Picea glauca (White spruce) (Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Renault et al., 2000; Nitschke & Innes, 2008; Nitschke et al., 2012) Picea mariana (Black spruce) (Farmer et al., 1984; Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Sirois, 2000; Meunier et al., 2007; Nitschke & Innes, 2008) Pinus albicaulis (Whitebark pine) (Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Tomback et al., 2001; Nitschke & Innes, 2008; Bower et al., 2011) Pinus banksiana (Jack pine) (Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Renault et al., 2000; Greenwood et al., 2002) Pinus contorta (Lodgepole pine) (Barton, 1930; Woodard, 1983; Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Nitschke et al., 2012) Pinus flexilis (Limber pine) (Barton, 1930; Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000) Pinus monticola (Western white pine) (Barton, 1930; Leadem, 1985; Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Feurtado et al., 2004; Nitschke & Innes, 2008) Populus balsamifera (Balsam poplar) (Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Wolken et al., 2010; Nitschke et al., 2012) Populus tremuloides (Trembling aspen) (Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Wolken et al., 2010; Nitschke et al., 2012) Populus trichocarpa (Black cottonwood) (Burns & Honkala, 1990; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Wolken et al., 2010; Nitschke et al., 2012) Pseudotsuga menziesii (Douglas fir) (Burns & Honkala, 1990; Li et al., 1994; Thompson et al., 1999; Klinka et al., 2000; Nitschke & Innes, 2008; Boberg et al., 2010)    30 TACA parameters for a subset of species used for model integration in the LANDIS-II simulations are located in Table 2.3. These simulations utilized the original version of the TACA model (TACA-EM) that does not include a germination sub-model. Species parameters for TACA-EM and TACA-GEM were generously provided by Dr. Craig Nitschke.  Table 2.3 TACA-EM parameters used in the LANDIS-II simulations Species Model Code Physiological Base Temperature (°C) Heat Sum for Bud Burst (GDD) Chilling Requirement (Days) Minimum Temperature (°C) Drought Tolerance GDD (5°C) Minimum GDD (5°C) Maximum Frost Tolerance Frost Season Wet Soils Heat Moisture Index Abies balsamea Sp01 2.8 121 49 -62 0.20 560.0 2,386 0.9 305 0.55 41.4 Abies lasiocarpa Sp02 2.6 119 70 -67 0.25 197.6 5,444 0.9 320 0.75 28.7 Betula payrifera Sp03 3.7 231 77 -80 0.30 236.8 4,122 0.9 285 0.30 40.0 Larix laricina Sp04 2.9 111 42 -76 0.20 150.8 3,331 0.9 300 0.75 33.8 Picea engelmannii Sp05 3.1 145 49 -64 0.25 74.4 2,150 0.9 335 0.50 28.7 Picea glauca Sp06 2.7 147 42 -69 0.34 129.6 3,459 0.9 305 0.50 43.2 Picea mariana Sp07 3.0 123 56 -69 0.30 144.0 3,060 0.9 305 1.00 42.7 Pinus banksiana Sp08 2.8 108 56 -85 0.50 830.0 2,216 0.9 320 0.30 37.9 Pinus contorta Sp09 2.9 116 63 -85 0.42 185.6 3,374 0.9 320 0.50 37.9 Populus balsamifera Sp10 2.1 93 49 -80 0.13 126.0 7,852 0.9 290 0.55 59.0 Populus tremuloides Sp11 3.5 189 70 -80 0.40 226.8 4,414 0.9 284 0.30 40.0  Parameters used in the updated TACA-GEM model, including a germination submodel, are in Table 2.4. These parameters were used to model regeneration responses to climatic change in the standalone application of TACA presented in Chapter 4. Parameters for drought tolerance, wet soils, frost tolerance, heat-moisture index, germination moisture threshold, and nitrogen availability are unitless coefficients described in previous works (Fuchigami et al., 1982; Urban, 1990; Burton & Cumming, 1995; Nitschke & Innes, 2008; Mok et al., 2012). While Abies grandis, Larix occidentalis, Pinus monticola, and Pinus ponderosa are not commonly found in  31 Alberta, they were included in TACA-GEM as future migrants to assess potential for compositional change. Abbreviations used in Table 2.4: GDD = growing-degree days; P50 = leaf water potential causing a 50% decline in hydraulic conductivity; TLP = turgor loss point; threshold = model bounds; b0-b2 parameters for the impact of chilling on breaking physiological seed dormancy; b0-b3 = parameters for germination amount and timing based on GDD accumulation. 32 Table 2.4 Tree species biophysical parameters used in TACA-GEM; continued on the next page   Species Abies balsamea Abies grandis Abies lasiocarpa Betula papyrifera Larix laricina Larix lyallii Larix occidentalis Picea engelmannii Picea glauca Picea glauca x engelmannii Picea mariana Physiological Base Temperature (°C) 5 4.3 2.6 3.7 2 2.7 3.4 3.1 2.7 2.9 3 Heat Sum for Bud Burst (5°C GDD) 98 307 119 231 111 146 180 145 147 146 123 Chilling Requirement (days) 60 91 60 77 42 56 70 49 42 45 56 Minimum Temperature (°C) -42 -35 -67 -80 -76 -60 -42 -50 -70 -58 -69 Drought Tolerance 0.25 0.4 0.25 0.3 0.2 0.2 0.4 0.25 0.34 0.3 0.3 Wet Soils 0.9 0.3 0.9 0.9 0.9 0.9 0.7 0.9 0.9 0.9 0.9 5°C GDD Minimum (days) 164 206.4 197.6 236.8 150.8 160 163.2 74.4 129.6 139.2 144 5°C GDD Maximum (days) 3364 3877 5444 4122 3331 2650 3057 2150 3459 3331 3060 Frost Tolerance 0.75 0.55 0.75 0.3 0.75 0.75 0.05 0.4 0.5 0.45 1 Frost Season 285 305 320 285 300 320 305 335 305 320 305             Heat-Moisture Index 43.6 41.4 28.7 40 33.8 18.4 38.7 28.7 43.2 43.2 42.7             Heat Sum (GDD 5°C) 64 127 160 75 106 135 133 82 175 175 114 Stratification (days) 7 0 28 0 0 28 7 0 0 0 0 Chilling x Heat Sum Factor (linear model) 0 -0.0173 -0.0066 -0.0449 -0.0075 -0.0111 -0.0085 0 -0.0016 -0.0016 0 C x H Factor Threshold (days) 40 28 28 7 30 30 80 30 60 60 60 Germination Moisture Threshold -0.5 -0.5 -0.5 -0.1 -0.5 -0.5 -1 -0.5 -0.5 -0.5 -0.5 Min Temperature for Germination 5 5 5 5 5 5 5 5 5 5 5 Max Temperature for Germination 35 35 35 35 35 35 35 35 35 35 35             b0 0.1922 0.9571 0.257743 1 1 0 0.0753 1 1 1 1 b1 0.0127 0.0008 0.005005 0 0 0.0147 0.023 0 0 0 0 b2 0 0 -0.000011 0 0 0 0 0 0 0 0 Threshold 40 28 364 30 30 80 40 30 60 60 60             b0 -0.158618 -0.532881 -0.358261 -0.50382288 -1.157836759 -0.031503408 -1.732323493 -2.648495123 -1.777235311 -1.777235311 -4.182342657 b1 0.003008 0.005202 0.003631 0.010126041 0.013978789 0.000245723 0.018922241 0.054610675 0.01501801 0.01501801 0.051122351 b2 -8.52E-6 -7.74E-06 -0.00000552 -5.10789E-05 -2.84902E-05 -8.54172E-08 -4.43156E-05 -0.000316429 -2.7636E-05 -2.7636E-05 -0.000125243 b3 6.28E-9 0.00000000 0 7.57734E-08 0 0 0 5.54355E-07 0 0 0 Minimum Threshold 64 127 160 75 106 135 133 82 175 175 114 Maximum Threshold 500 545 529 267 385 2742 294 209 369 369 294             Seedfall Julian Date 258 258 288 258 258 258 258 258 258 258 245 Seed Viability (days) 360 360 360 180 300 300 300 300 300 300 300 Photoperiod (days) 275 275 275 275 275 275 275 290 290 290 290             Vegetative Reproduction None None None Sprouting None None None None None None Layering             Low Nitrogen Availability 0.55 0.05 0.55 0.25 0.3 0.25 0.3 0.55 0.3 0.425 1 Medium Nitrogen Availability 1 0.5 1 1 1 1 1 1 1 1 0.5 High Nitrogen Availability 0.75 1 0.75 0.75 0.75 0.3 0.75 0.5 0.75 0.625 0.05             P50 / TLP Minimum -2.86  -3.27 -2.33 -3.35 -3.35  -4.18 -3 -3.59 -3.3 P50 / TLP Maximum -2.86  -3.27 -2.33 -3.35 -3.35  -4.18 -3 -3.59 -3.3   33 Species Pinus albicaulis Pinus banksiana Pinus contorta Pinus monticola Pinus ponderosa Pinus flexilis Populus balsamifera Populus tremuloides Populus trichocarpa Pseudotsuga menziesii Physiological Base Temperature (°C) 3 5 2.9 4.4 3.9 5 2.1 3.5 4.6 3.4 Heat Sum for Bud Burst (5°C GDD) 120 196 116 468 250 70 93 189 175 255 Chilling Requirement (days) 70 60 63 98 77 70 49 70 70 56 Minimum Temperature (°C) -55 -65 -85 -40 -41 -40 -80 -80 -60 -47 Drought Tolerance 0.4 0.42 0.42 0.25 0.6 0.5 0.13 0.4 0.13 0.5 Wet Soils 0.9 0 0.9 0.75 0.7 0.05 0.9 0.9 0.5 0.75 5°C GDD Minimum (days) 216 327 185.6 211.2 280.8 109 126 226.8 257.6 176.8 5°C GDD Maximum (days) 3352 3237 3374 3554 5656 4291 7852 4414 5263 3261 Frost Tolerance 0.05 0.9 0.5 0.5 0 0.9 0.55 0.3 0.55 0.25 Frost Season 320 315 320 305 275 320 290 284 295 300            Heat Moisture Index 34.2 36.8 37.9 25.8 65.9 93.3 59 40 62.3 61.9            Heat Sum (5°C GDD) 194 96 141 116 21 151 5 5 5 58 Stratification (days) 60 0 0 21 7 28 0 0 0 7 Chilling x Heat Sum Factor (linear model) 0 -0.0122 -0.0126 -0.0065 -0.0116 -0.0042 0 0 0 -0.0215 C x H Factor Threshold (days) 60 14 21 21 21 84 30 30 30 21 Germination Moisture Threshold -1 -1 -1 -1 -1.1 -1 -0.2 -0.4 -0.2 -1 Min Temperature for Germination 4 5 5 5 5 5 5 5 5 5 Max Temperature for Germination 35 35 35 35 35 35 35 35 35 40            b0 -0.2 1 0.9684 0.153446077 0.8441 0.516 1 1 1 0.8626 b1 0.0067 0 0.0015 0.014395893 0.0073 0.0202 0 0 0 0.003 b2 0 0 0 -0.00014212 0 -0.0002 0 0 0 0 Threshold 120 14 21 90 21 84 30 30 30 21            b0 -0.147452534 -1.298055 -3.362802616 -0.418418034 -0.248791734 -0.147996 0 -0.010558767 0 -0.28611 b1 0.000878443 0.019592 0.040247169 0.004664458 0.014040249 0.001205 0.01401 0.015174407 0.01401 0.005681 b2 -6.20703E-07 -0.00007 -0.000135697 -9.0252E-06 -8.5889E-05 -1.49E-6 -0.000132 -0.000139067 -0.000132 -0.000012 b3 1.15925E-10 7.27E-8 1.38078E-07 0 0 0.00E0 0 0 0 0.00E0 Minimum Threshold 194 96 141 116 21 151 1 1 1 58 Maximum Threshold 2299 378 355 401 143 658 106 108 106 400            Seedfall Julian Date 244 230 230 274 295 244 152 152 152 244 Seed Viability (days) 360 300 300 300 300 360 180 180 180 300 Photoperiod (days) 290 290 290 290 290 290 275 275 275 290            Vegetative Reproduction None None None None None None Sprouting None Sprouting/ Fallen Branches None            Low Nitrogen Availability 0.3 0.75 0.75 0.05 0.25 0.25 0.05 0.3 0.05 0.3 Medium Nitrogen Availability 1 0.5 1 0.5 1 1 0.5 1 0.5 1 High Nitrogen Availability 0.25 0 0.3 1 1 0.3 1 0.75 1 0.75            P50 / TLP Minimum -3.63 -3.9 -3.9 -3.9 -4.05 -5.1 -1.9 -2.74 -1.9 -4.59 P50 / TLP Maximum -3.63 -3.9 -3.9 -3.9 -4.05 -5.1 -1.9 -2.74 -1.9 -4.59  34 2.4 LANDIS-II Forest Landscape Model This section describes the design of the LANDIS-II model and data used for parameterization.  2.4.1 Model Description Following the original LANDIS model, LANDIS-II is based on the JABOWA-FORET genre of gap models and LANDSIM (Mladenoff & He, 1999). Rather than using the mechanistic formulation of gap models, LANDIS-II closely follows the vital attributes/fuzzy systems approach of LANDSIM. This efficient approximation enables LANDIS-II to model salient spatial and non-spatial forest dynamics at a stand resolution and landscape scale. The LANDIS-II model core is the central hub of a modular system that allows users to specify submodels at a user-defined time-step. In LANDIS-II, each grid cell in the landscape matrix is either active or inactive. Inactive cells are static and active cells are dynamic. Active grid cells can be forested or non-forested. Grasslands are typically the only active non-forested cells, where trees may establish provided seed and favorable conditions for regeneration. Each active forested grid cell represents a stand of trees comprised of horizontally homogeneous species-age cohort classes (Scheller et al., 2007). To better represent regional variation in climate, soils, and fire patterns, I divided the simulation landscape into biogeoclimatic regions. In the simulations, I utilize three submodel configurations: Age-Only Succession, Succession with Base Fire, and Succession with the Dynamic Fuels and Fire System.  The Age-Only Succession submodel was used to model light, reproduction, ontogeny, senescence, seed dispersal, and interspecific competition, accepting external parameters for tree species regeneration. In LANDIS-II, light is internally modeled as a logical function of the  35 maximum shade tolerance for sexually mature species present at a site. The presence of shade tolerant species is used as an indicator of low-light conditions. A tradeoff was observed here between shade and fire tolerance (R2 = 0.58; p < 0.001). Accordingly, when fires initiate within a cell, younger and more shade tolerant species-age cohorts have higher mortality rates, increasing modeled light values post-disturbance.  Reproduction is limited by propagule presence and light availability provided regeneration probabilities output from a separate model, such as TACA-EM or PnET-II. Fire directly interacts with regeneration through mortality, resprouting, and serotiny. Age-related mortality is a function of species maximum age, with an increasing probability of mortality once species reach 80% of their maximum age. Seed dispersal is represented by a two-part negative exponential probability distribution with a leptokurtic dispersal kernel (Ward et al., 2004), based on observed migration rates (Clark et al., 1998). Interspecific competition occurs through the intersection of species life history attributes (e.g., reproductive timing, vegetative reproduction, serotiny, and tolerances to fire and shade), establishment probabilities, and local disturbance patterns.  We apply two conceptually different LANDIS-II extensions for modeling wildfire: Base Fire and the Dynamic Fuels and Fire System (Dynamic Fire). Base Fire is an empirically-driven stochastic fire-growth model that reproduces parameterized statistical distributions, with variability a result of its stochastic core. In contrast, Dynamic Fire is a semi-mechanistic stochastic fire-growth model that uses topography, fuel conditions, fire weather, and empirical fire distributions to shape fire patterns. The Dynamic Fire model is conceptually analogous to Prometheus in Canada (Tymstra et al., 2010) and FARSITE in the US (Finney, 2004), which are  36 based on the Fire Behavior Prediction (FBP) System (Forestry Canada Fire Danger Group, 1992) and BEHAVE (Andrews & Chase, 1989), respectively. In both LANDIS-II fire models, fires begin through separate ignition and initiation events (Yang et al., 2004). Mean fire return intervals (Pickett & Thompson, 1978) are used to represent fire frequency.  In the Base Fire model, the frequency of ignitions follows a Poisson distribution. Fire initiation is based on Bernoulli trials, with ignition probability a function of time-since-last-fire. Fire sizes are drawn from a log-normal distribution (Yang et al., 2004), producing episodic large fires. The fire shape is a product of a stochastic percolation algorithm representing wind vectors. Inactive cells may act as fire breaks, stopping fire spread before reaching its target size. Fire severity is determined by fuel and wind curves representing fuel buildup and decay; a site’s position on these curves is determined by time-since-last-fire. Fire is modeled as a bottom-up disturbance, whereby younger cohorts have a higher probability of mortality (He & Mladenoff, 1999). This dynamic is well-established and is correlated with tree height, depth-at-breast-height, and bark thickness (Regelbrugge & Conard, 1993; Whittier & Gray, 2016). While some fire models use a uniform fire frequency distribution and exponential fire size distribution (Yang et al., 2004), the Base and Dynamic Fire models use Poisson and log-normal distributions, respectively. A log-normal size distribution has been empirically shown to hold for many regions of the world (Hantson et al., 2016), including for Canada (Appendix A).  The Dynamic Fire model is a process-based fire model that uses a semi-mechanistic representation of fire growth (Sturtevant et al., 2009). Similar to Base Fire, the ignition frequency follows a Poisson distribution, with cells in each fire region selected stochastically.  37 Unlike Base Fire, fire initiation is modeled probabilistically based on site fuel conditions, calculated using cohort information and daily weather data within FBP and Fire Weather Index (FWI) Systems equations (Van Wagner, 1987; Forestry Canada Fire Danger Group, 1992). Fire sizes are drawn from a lognormal distribution; users can alternatively specify duration-based sizes. Fire shape is modeled using fuel-specific rate-of-spread equations (Hirsch, 1993) and a modified minimal-travel-time cost-path method. The minimum-travel-time method is based on Huygens’ Principle of wave propagation, also used in Prometheus and FARSITE. LANDIS-II utilizes the most efficient algorithm implementation of the three fire simulators (Finney, 2002).  In the Dynamic Fire model, the fire spread algorithm contains two core components: wind bias and fuel conditions. Wind bias has an ellipsoidal shape with the length and width based on the magnitude of a wind velocity vector (Finney, 2002). Fuel-based spread is a function of fuel class, wind speed, and topography, using FBP System fuel classes. A cost surface is created using the inverse rate-of-spread to calculate a minimum-travel-time path. The cumulative minimum-travel-time and fire size selected determine the shape of each fire, producing improved disturbance pattern realism.  The probabilities of fire sizes being selected from the lognormal size distribution are classified into five equally spaced fire weather bins, based on the logic that larger fires occur during more severe fire weather conditions. The fire weather bins are typically parameterized by classifying fire weather index (FWI) values. The seasonal distribution of fire frequency is represented probabilistically, incorporating leaf status. Detailed model information and equations are  38 provided in the literature (Forestry Canada Fire Danger Group, 1992; Finney, 2002; Sturtevant et al., 2009).  2.4.2 Data Requirements The LANDIS-II model core requires a list from the literature containing life history attributes for tree species, including longevity, sexual maturity age, shade tolerance, fire tolerance, seed dispersal, vegetative reproduction, and serotiny (Scheller et al., 2007). The model core also requires a matrix and lookup table specifying tree species-age cohort classes present in each cell. Cohort classes are dynamically updated at each time-step. A biogeoclimatic regions matrix and corresponding lookup tables are optional. A succession model table requires species regeneration probabilities; these values can be unique for each bioregion to represent local climatic patterns.  The Base Fire model requires statistical fire distributions for fire regions, typically set to the biogeoclimatic region matrix. Base Fire requires parameters for the mean, minimum, and maximum event size, ignition probability (λ), and the mean fire rotation period for each of the fire regions. These parameters require adjustment to reproduce empirical fire distributions, typically achieved by manual approximation of the ignition probability and fire rotation period parameters (Syphard et al., 2007). Fit is difficult to achieve if the empirical fire size distribution differs substantially from a lognormal distribution.  The Dynamic Fire model similarly requires fire regions, also typically using the biogeoclimatic region matrix, and a corresponding lookup table. The model requires the expected mean (µ), standard deviation (σ), and maximum fire size for a lognormal distribution. The model requires  39 low and high averages of seasonal foliar moisture content (FMC), proportion of fires during high FMC conditions, open fuels class designation, and the annual frequency of fire initiation for each region. A fire seasonality table containing leaf status, proportion of fires, percent curing, and fire-day-length-proportion parameters for each season is also needed. Additional parameters include a fuel-type table based on FBP System classes, which consist of parameters for base type, surface type, initiation probability, three fuel type-specific rate-of-spread constants, buildup index (BUIS in the FBP System), maximum buildup effect (q in the FBP System), and crown base height, which are used to modify the initial spread index. The equations implementing these parameters have previously been described (Forestry Canada Fire Danger Group, 1992; Finney, 2002; Sturtevant et al., 2009).  The Dynamic Fire model’s damage table requires parameters for the upper bound of the cohort age range and the minimum difference between fire severity and tolerance for mortality to occur. An initial weather database incorporating daily fire weather data, including fine-fuel moisture code, buildup index, wind speed velocity, fire weather index, fire weather index bin, season, and bioregion, is used to modify fuel conditions. To model the effects of topography on fire shape, users may input percent-slope and upslope-azimuth matrices, which are included here using 90-meter NASA SRTM elevation data (Farr & Kobrick, 2000).  The Dynamic Fire model requires a fuel coefficient for each species and a maximum-site-hardwood-percentage, a classification threshold for the coniferous fuel group. The optional Dynamic Fuels submodel, which is applied herein, requires a fuel type classification table in order to reclassify site fuel conditions following succession and/or disturbance. The table  40 contains parameters for base fuel type, age range, and species presence/absence. A disturbance conversion table can optionally be used to allow other disturbance types to modify the site fuel classification (Sturtevant et al., 2009).  To produce the desired fire regimes at high accuracy, a new fire model parameter optimization method based on stochastic gradient descent (Widrow & Hoff, 1960) was developed and applied to both fire models. Using this method, the error between model results and empirical values is used as an objective function for iterative minimization. The fire simulations are repeated using this error coefficient to update the fire distribution parameters until the error reaches a minimum. Specifically, the ignition probability is adjusted for each region until the simulated fire frequency is within 1% of the target range before the same optimization process is applied to k values, equivalent to the fire rotation period. Pareto optimality is approximated by adjusting each parameter separately in this order. The stochastic nature of the model prevents local minima trapping, as is commonly done for model training in deep learning (LeCun et al., 2015).  Firest, coarse-resolution (500 m cell) simulations are run for the maximum duration (~1,000 years) to quickly estimate the fire regime signal for a given parameter space. Next, final parameter optimization is computed by running simulations at full resolution for the target duration. The new method reliably produces fire frequencies within ±1% of empirical values and an area burned R2 of 0.96, compared to standard values of ±20% and 0.82, respectively. If fire regimes deviate significantly from a lognormal size distribution, Base Fire will be limited in its ability to reproduce them, due to the shape of distribution used for the model (Scheller et al., 2007; Sturtevant et al., 2009).  41 2.4.3 Model Core To parameterize the LANDIS-II model core, local species parameters were derived from the literature and species compendiums (Burns & Honkala, 1990; Farrar, 1995a; Klinka et al., 2000). Ward’s leptokurtic double-exponential seed dispersal algorithm was applied in the succession model (Ward et al., 2004), as previously noted. To parameterize the initial landscape, a rule-based classification of modeled species abundance for western North American tree species was applied (Gray & Hamann, 2012).  Modeled species abundance values were used to classify the landcover using FBP System classes (Forestry Canada Fire Danger Group, 1992). Forested sites were binned into the following classes (FBP System code): Aspen (D-1); Boreal Spruce (C-2); Lodgepole or Jack Pine (C-3/C-4); Douglas-fir (C-7); Boreal Mixedwood (M-1/M-2). Each site was set to even age classes of 0, 30, 60, and 90 years, relying on model spin-up (running the model for a period) to produce desired forest structure patterns, given an absence of reliable forest age maps. In the absence of validation data, I relied on model behavior to produce realistic age patterns. For biogeoclimatic regions, a provincial classification scheme was used (Natural Regions Committee, 2006).  Landcover for Agricultural Regions of Canada (Agriculture and Agri-Food Canada, 2012) and Earth Observation for Sustainable Development of Forests (Wulder et al., 2007) data were combined and reclassified, each set to year 2000 conditions. Three base cell states were used for the model: active-treed, active-untreed, and inactive. The initial landscape was classified as active-treed cells where tree species cohorts were present. Herb, grassland, and shrubland landcover classes were set to active-untreed, while setting agriculture, annual cropland, perennial  42 crops and pasture, wetland, water, exposed land, snow/ice, rock/rubble, and built-up cells to inactive. Hence, forests and fires could expand into open natural areas given suitable conditions, but not into developed or resource-limited sites.  As TACA and LANDIS-II require qualitatively different tree species parameters, additional data sources were located for LANDIS-II. Tree species life history attributes for LANDIS-II were derived from the following sources (Table 2.5):  Table 2.5 Sources of life history attribute species parameters used in LANDIS-II Species Data Source Abies balsamea (Balsam fir) (Xu et al., 2010) Abies lasiocarpa (Subalpine fir) (Burns & Honkala, 1990; Farrar, 1995a) Betula papyrifera (Paper birch) (Peterson et al., 1997; Government of Alberta, 2009) Larix laricina (Larch) (Burns & Honkala, 1990; Farrar, 1995a) Picea engelmannii (Engelmann spruce) (McCune & Allen, 1985; Burns & Honkala, 1990; Government of Alberta, 2009) Picea glauca (White spruce) (Dobbs, 1976; Groot et al., 2003; Government of Alberta, 2009) Picea mariana (Black spruce) (Stanek, 1961; Burns & Honkala, 1990; Government of Alberta, 2009) Pinus banksiana (Jack pine) (Flannigan & Wotton, 1994; Farrar, 1995a; Government of Alberta, 2009) Pinus contorta (Lodgepole pine) (Lotan & Perry, 1983; Parminter, 1984; Burns & Honkala, 1990; Farrar, 1995a) Populus balsamifera (Balsam poplar) (Burns & Honkala, 1990; Farrar, 1995a) Populus tremuloides (Trembling aspen) (DeByle & Winokur, 1985; Burns & Honkala, 1990; Huang et al., 1992; Jelinski et al., 1992; United States Forest Service, 2013)  The tree species life history attributes derived from these sources for use in LANDIS-II are as follows (Table 2.6): 43 Table 2.6 Tree species life history attributes used in LANDIS-II simulationsSpecies Longevity Sexual Maturity Age Shade Tolerance Fire Tolerance Effective Seed Dispersal Distance Maximum Seed Dispersal Distance Vegetative Reproduction Probability Sprouting Minimum Age Sprouting Maximum Age Post-Fire Regeneration Abies balsamea 150 25 5 1 30 160 -1 -1 -1 None Abies lasiocarpa 200 20 4 2 30 80 0.05 20 200 None Betula papyrifera 150 15 2 1 100 200 0.5 1 200 Resprout Larix laricina 150 10 1 3 38 60 0.05 10 150 None Picea engelmannii 720 15 3 2 46 183 0.05 15 720 None Picea glauca 350 25 3 2 100 300 0.05 25 350 None Picea mariana 150 30 4 1 260 260 0.05 30 200 Serotiny Pinus banksiana 200 10 2 4 37 60 -1 -1 -1 Serotiny Pinus contorta 200 5 2 4 27 200 -1 -1 -1 Serotiny Populus balsamifera 200 9 2 3 50 3000 0.5 1 200 Resprout Populus tremuloides 200 2 1 4 uni 5000 0.95 1 200 Resprout  44  2.4.4 Base Fire For Base Fire, historical fire data were used from the Canadian National Fire Database (Canadian Forest Service, 2015) for 1923 to 2014. For the fire regions, the Natural Subregions of Alberta were used. The default fuel curve table values were used to represent five fire severity classes, as it was created for Canadian forests. I wrote functions in R (R Core Team, 2015) to calculate the mean, minimum, and maximum fire size, ignition probability, and fire rotation period for each fire region.  2.4.5 Dynamic Fuels and Fire System For Dynamic Fire, the expected mean, standard deviation, maximum fire size, and annual fire frequency were calculated using R for each region and period. Functions derived from the FBP System were used to calculate seasonal foliar moisture content (FMC) values. To do so, the regional minimum FMC date was calculated, based on the mean latitude, longitude and elevation, before calculating the mid-season FMC using ordinal dates for the vernal equinox, summer solstice, autumnal equinox, and winter solstice. These values were used to calculate the proportion of fires occurring during the high FMC period. Low and high FMC thresholds were set to 25% and 75% of the maximum, respectively, which is the default model configuration (Sturtevant et al., 2009).  Subregions were used as the fire regions matrix. For percent ground slope and uphill azimuth, NASA SRTM version 2 data were processed using standard techniques (Reuter et al., 2007). For the fire seasons table, the leaf status for spring, summer, and fall were set to leaf-off, leaf-on, and leaf-off, respectively, to represent phenological periods of full dormancy, growing season (full  45  leaf emergence), and leaf abscission (early dormancy) for deciduous species. The proportion of fires during each season were calculated by using a subset of the fire database, with dates converted to ordinal dates and seasons. The percent curing values for open/grassland fuel types (Wotton et al., 2009) were calculated as a function of FMC values, using a grassland curing index equation (Dilley et al., 2004), with the mean index value used to represent each season. Fire day-length proportion was set to the standard value of one.  An initial fire weather database was calculated using Alberta Agriculture and Rural Development’s historical fire weather station data. Fire weather stations were selected with the shortest Euclidean distance to the centroid of each region. Daily resolution fire weather data were used for the April 2012 through March 2013 fire weather season to represent recent climatic influences on fuels; historical fire weather data was otherwise unavailable for the region. The weather metrics used include precipitation, mean temperature, mean humidity, wind speed at 10 m above ground, and wind direction at 10 m above ground. The R mtsdi package (Junger & de Leon, 2012) was used to impute missing values for the period, using the default expectation-maximization algorithm and splines method. The R fwi.fbp package (Wang et al., 2014c) was used to calculate daily fine fuel moisture content, build-up index, and fire weather index using standard equations (Van Wagner, 1987). Fire weather index values were segmented into five bins based on quantile groups using the R Hmisc package (Harrell & Dupont, 2015).  To parameterize the fuel type table, FBP System fuel classes and parameters developed for Canada were used (Forestry Canada Fire Danger Group, 1992). These parameters include base type, surface type, initiation probability, a, b, and c rate-of-spread parameters, a q depth dryness  46  parameter, build-up index, maximum build-up effect, and crown base height. Fuel types not currently present in the landscape were set to inactive. A standard fire damage table was used, with probability of mortality inversely related to cohort age. The table includes species-specific fire tolerances, with standard transitions at 20%, 50%, 85% and 100% age percent of longevity. The optional Dynamic Fuels submodel was used, reclassifying site fuel conditions at the end of each simulation year based on species-age cohorts. This enables fire behavior to more realistically respond to succession and disturbance. To parameterize the fuels model, species were assigned an even fuel reclassification weighting coefficient of 1.0. Deciduous stands were given a standard maximum conifer composition threshold of 10%, which is the standard threshold used in the model. The fuel type reclassification table was based on the FBP System, utilizing its definitions for species composition and age classes (Forestry Canada Fire Danger Group, 1992).  2.5 Airborne Laser Scanning Data Airborne laser scanning (ALS) data was provided by Foothills Research Institute on behalf of Hinton Wood Products, a subsidiary of West Fraser. The sorties were conducted by a Canadian remote sensing company, Airborne Imaging, in the mid-2000s near Hinton, Alberta in the foothills of the Canadian Rocky Mountains. Airborne Imaging used an Optech Airborne Laser Terrain Mapper (ALTM) 3100 mounted aboard a twin-engine fixed-wing Piper Navajo aircraft with an Applanix precision global positioning system-inertial navigation system (GPS-INS) position-orientation system utilizing sensor fusion. Flights were conducted with 50% sidelap between flight lines at an estimated mean velocity of ~ 160 knots (296 km h-1) and altitude of ~ 1,400 m above-ground-level (AGL), yielding an estimated mean point spacing of 0.75 m and  47  theoretical minimum vertical accuracy between 10 and 15 centimeters (±1 sigma). The Optech ALTM 3100 emitted near-infrared (1,064 nm) photons at a pulse rate of 70 kHz, using a maximum scan angle from nadir of ~ 14 degrees (0.24 radians), scan rate of 33 Hz, and a sawtooth scanning pattern. While the Optech ALTM 3100 is one of the first commercial ALS systems capable of full-waveform digitization, the system used in this study is a discrete-return system, recording up to four returns for every laser pulse, each with 12-bit dynamic range intensity information (Hilker et al., 2013).  Ground and non-ground returns were classified using Terrasolid TerraScan version 0.6 consumer-off-the-shelf (COTS) software, which applies previously demonstrated methods (Kraus & Pfeifer, 1998). The pre-processed LiDAR data were delivered in standard American Society of Photogrammetry and Remote Sensing (ASPRS) laser (LAS) file specification. The estimated final horizontal and vertical positional accuracy was 0.45 m and 0.3 m, respectively, based on a large sortie conducted on November 19, 2007 (Hilker et al., 2013). A total of 18.6 billion points were collected at a mean point density of 1.64 points m-2 for the 1,100 km2 Hinton area, based on calculations with LAStools software (Isenburg, 2015).      48  Chapter 3: Past-century Fire Regimes of Western Alberta, Canada  3.1 Introduction The evolutionary history and paleorecord of North America’s boreal forests reflect millennia of cold, dry, and fiery conditions (Hu et al., 2006; Gavin et al., 2007; Tinner et al., 2008; He et al., 2012; Kelly et al., 2013). Global change in the Anthropocene (Crutzen & Stoermer, 2000) has shifted each of these three conditions. Over the past half-century, boreal forests warmed at twice the rate of the global mean (Intergovernmental Panel on Climate Change, 2014). In southwestern Canada, recent climatic change produced warmer and wetter conditions, significantly reduced snowfall, and related reductions in cryomass (Intergovernmental Panel on Climate Change, 2014), or total mass of surface and ground water in a frozen state. Warming is projected to accelerate in the near-term (Smith et al., 2015), with the highest rates of warming expected to occur in mountainous regions (Miller, 2013) and higher latitudes. The northernmost regions are experiencing the most severe temperature extremes of the past 600 years through polar amplification (Miller, 2013; Tingley & Huybers, 2013).  The North American boreal is projected to migrate northward under warming, inducing a net terrestrial loss of carbon storage (Scheffer et al., 2012; Koven, 2013). At lower elevations and latitudes, extant tree species are expected to regenerate less frequently following disturbance under warming, due to an increased frequency and magnitude of physiological drought (Nitschke et al., 2010; Barichivich et al., 2014; Intergovernmental Panel on Climate Change, 2014). Together, changes to regeneration and fire regimes may explain diminished recruitment rates observed for Canada in recent years (de Lafontaine & Payette, 2011; Boisvert-Marsh et al.,  49  2014; Zhang et al., 2015). A reduction in area burned, without a compositional shift toward deciduous trees, may further accelerate warming through reduced albedo (Amiro et al., 2006).  Large stand-replacing fires have characterized circumpolar boreal forests for millennia, reflected in the fire-resisting, -avoiding, and -embracing evolutionary strategies of the resident tree species (Kelly et al., 2013; Rogers et al., 2015). Changes to fire regimes carry particular importance in the North American boreal, where fire has been shown to regulate carbon flux (Bond-Lamberty et al., 2007), energy partitioning (Amiro et al., 2006), compositional change, and tree migration (de Lafontaine & Payette, 2011; Gavin et al., 2013). Warming has increased the severity of fuel conditions in the boreal by increasing evaporative demand (Barichivich et al., 2014; Intergovernmental Panel on Climate Change, 2014) and permafrost thaw (Camill, 2005; Baltzer et al., 2014), accelerating carbon loss through an increased depth of ground-layer burning, particularly for peatlands (Turetsky et al., 2011, 2015).  Recent burn rates for the North American boreal have been reported in excess of Holocene (~11.7 kybp) fire regime limits (Kasischke & Turetsky, 2006; Kelly et al., 2013; Marlon et al., 2013). The global area burned rapidly accelerated with the Industrial Revolution before declining over the past century (Marlon et al., 2008, 2013). Unprecedented high burn rates (short fire rotation periods) are evident for the Alaskan boreal in recent years (Turetsky et al., 2011; Kelly et al., 2013). Yet, Alaska shows little agreement with other regions of the North American boreal. The eastern Canadian boreal shows a fire frequency and biomass burning maximum ~ 4.5 kybp and a steady decline thereafter, currently at a 7,000-year low, due to decreased insolation, shorter fire seasons, and increased precipitation (Marlon et al., 2008, 2013). More recently, early  50  season warming has produced an increase in spring fire size, with variation in fire patterns attributable to climate-related water table changes and post-glacial topography (Ali et al., 2009, 2012). Regions of the western Canadian boreal similarly show declines in area burned linked to increased precipitation over the past century (Meyn et al., 2013). These studies indicate that co-varying patterns of solar radiation, temperature, precipitation, physiological drought, and human activity explain global variability in the area burned, with human activity playing an increasingly important role post-industrialization (Marlon et al., 2008). The critical role of human activity is shown by a recent analysis of global burned area (Andela et al., 2017). While short-term efficacy of fire suppression was shown for Alberta (Cumming, 2005), long-term efficacy remains poorly understood.  In Scandinavia, boreal fire regimes shifted to their present state in the 17th century, due to increased human activity (Niklasson & Granström, 2000). In Niklasson & Granström (2002), the fires-per-unit-area-time metric was used to indicate physical energetic constraints in the configuration of fire regimes, based on fire frequency, size, and area burned per unit time, following research on phase transitions in the classical Forest Fire Model (Drossel & Schwabl, 1992; Malamud et al., 1998). A recent analysis of global fire regimes supports the presence of both physical energetic constraints and human-dominated fire regimes (Archibald et al., 2013). Archibald et al. (2013) estimated energetic constraints from an expanded feature set that includes fire frequency, size, intensity, season length, return interval, and area burned per unit time.  Similar to Niklasson & Granström (2000), Archibald et al. (2013) demonstrate that fire frequency and size are inversely proportional for a given area burned per unit time. Fire  51  frequency strongly regulates fire intensity, while areas with shorter fire return intervals have higher area burned per unit time. Longer fire seasons are related to higher human activity levels, although difficult to uncouple from anthropogenic warming. Maximum fire size is characterized by exponential decay and has a logarithmic relationship with area burned per unit time that quickly approaches an asymptote (Archibald et al., 2013).  These findings reflect fundamental relationships between fire, climate, vegetation, and human activity, supporting the theory of dual energetic controls (fuels and weather) on area burned per unit time along productivity gradients (Meyn et al., 2007, 2010; Archibald et al., 2013). These studies also indicate that human activity poses a third fundamental energetic constraint on fire regimes in the Anthropocene, alongside fuels and weather. Human activity may explain recent changes to fire regimes in actively managed forests of southwestern Canada by providing greater energetic inputs (ignitions), producing many small fires near human hotspots, while reducing energy stores and spread potential (harvest, fuels management, and fire suppression). These past-century changes to management are hypothesized to be evident in the historical fire record.  Following pan-boreal (Bradshaw et al., 2009; Laurance et al., 2014) and regional trends (Linke & McDermid, 2012; Braid & Nielsen, 2015), previous work has shown that increased economic development in the Alberta study area expanded the road network into formerly remote areas, facilitating increased access and use for economic and recreational purposes. Expanded human activity is further evident in an increase in other linear features, such as oil and gas pipelines, seismic lines, and power lines, as well as point features including one-hectare well-sites (Linke & McDermid, 2012). While a number of studies have assessed disturbance patterns here (Forest  52  et al., 2008; Nielsen et al., 2008; Laberee et al., 2014), existing studies do not explain the drivers of long-term disturbance variability critical to predicting future patterns in simulation studies. Existing datasets may contain valuable information for discerning relationships in space and time between human activity and fire, necessary for simulating disturbance-related changes to understory solar irradiation. In the following sections, the effects of past-century warming and increased human activity on fire regimes are assessed.  3.2 Methods Here, changes in the statistical patterns of historical wildfire data within the Alberta study area and across Canada are analyzed. The analysis focuses on climatic and anthropogenic changes to fire, including variation in elevation, latitude, cause, size, frequency, and area burned along multiple temporal resolutions, including annual, seasonal, monthly, and daily intervals. Fire seasons were calculated as meteorological quarterly seasons. The analysis is structured to focus on proxies of climatic change and human activity, based on known historical changes and the findings of previous studies in the region. Although there exists significant variation in fire regimes across Canada, national fire patterns provide a baseline for separating regional variation from overall trends.  For the regional analysis, three data sources were used: the latest Canadian National Fire Database (NFDB) fire perimeter data, NASA Shuttle RADAR Topography Mission (SRTM) version 2 data processed using standard correction techniques (Reuter et al., 2007), and Natural Regions and Subregions of Alberta for the biogeoclimatic zones (Natural Regions Committee, 2006). The data were subset to the Alberta study area and zonal statistics calculated for the  53  minimum, mean, and maximum elevation, as well as slope and aspect for each fire. The latitude and longitude for each fire centroid was also calculated. The NFDB contains many relevant fire attributes including the year, month, day, cause, source, and size. Using the year, month, and day values, the ordinal date and season of fires were calculated. Using values for the elevation, latitude, and ordinal date of each fire, foliar moisture content (FMC) was calculated for each fire. To calculate FMC values, standard equations were applied from the Canadian Fire Behavior Prediction (FBP) System (Hirsch, 1993).  Fire rotation period (FRP), or fire cycle, is a commonly applied metric to indicate the rate of burning, with lower values indicating greater severity (Wagner, 1978). FRP is the average time required for the sum of fire sizes within an area to equal the area in size, calculated over a given time interval. FRP is often presented alongside the mean fire return interval (MFRI), the average time interval between fires for a given area or site, as well as time-since-last-fire.  FRP = time interval / (sum of fire sizes burned in area / area size) MFRI = time interval / number of fires in site or area  Hence, FRP is the area-normalized MFRI. Applied to individual sites, FRP is equal to MFRI. By normalizing for area, FRP provides more information about fire regimes at scales greater than the individual site. MFRI values calculated for areas of different sizes are not directly comparable, unless normalized for area, which yields FRP. FRP is applied in the historical fire regime analysis. While other changes in the distribution of fires provide additional information, FRP provides a single robust metric for fire regimes.  54  Fire size distributions were analyzed to detail variation in regional (Alberta study area) and national patterns, as well as changes to fire regimes between periods. This work follows a study on lightning-caused fires in the boreal mixedwood region of Alberta, using the former LFDB (Cumming, 2001) that showed that fire models should use a truncated exponential distribution to prevent over-predicting large fires. Here, a Weibull distribution was fit to log-transformed fire sizes. A right-tail Anderson-Darling maximum-goodness-of-fit estimation was used to adjust for power-law behavior at the tail of the distribution. Hartigan’s dip test was used to test for bimodality. The expectation-maximization (EM) algorithm and Bayesian Monto Carlo Markov Chain (MCMC) simulations were used to fit a mixed normal distribution. Changes to fire size distributions were confirmed by Kullback-Leibler divergence and the Earth Mover’s Distance (EMD), or Wasserstein metric, commonly used for comparing empirical probability mass functions (Gottschlich & Schuhmacher, 2014).  Fire regimes were temporally segmented using the binary segmentation algorithm (Scott & Knott, 1974). While other change-point detection algorithms were tested, including pruned exact linear time (Killick et al., 2011), e-divisive (Matteson & James, 2013), and e-divisive with medians (James et al., 2014), binary segmentation showed optimal sensitivity to small variations in the given task. Thus, binary segmentation was applied to classify fire regime periods. First, fire regime periods were classified with a priori knowledge on changes to management and climate. Periods of 30 years are used for compatibility with studies using 30-year climate normal data. The four a priori fire regime periods are as follows:  Pre-Suppression (1923-1952); Early Suppression (1953-1982); Global Change (1983-2012); and, overlapping the Global Change period, the Most Recent Decade (2003-2012). The Global Change period corresponds to an  55  acceleration of global change conditions (Steffen et al., 2007). The most recent decade is included to represent recent trends independent of the three 30-year periods.  Software used to conduct this work includes ArcGIS 10.2 for spatial analysis, ENVI-IDL 5.2 for processing synthetic aperture RADAR data, R 3.1 for statistical analysis, and Python 2.7 for automation. The seas package for R was used for date-time conversion (Toews et al., 2007), while the fwi.fbp package for R was used to calculate FMC values (Wang et al., 2014c). The changepoint (Killick & Eckley, 2014), ecp (James & Matteson, 2015), and BreakoutDetection (James et al., 2014) packages for R were used to test change-point algorithms for classifying fire regime periods.  3.3 Results Across the full 90-year period in the Alberta study area, mean, maximum, and minimum fire sizes declined. Fire frequency initially declined at an inflection point near 1950 before increasing rapidly since approximately 1990. On average, over the 90-year period, fires declined in size by 142.6 ha per year, annual area burned declined by 3,450 ha per year, and fire frequency increased by 5.44 fires per year (Figure 3.1).   56   Figure 3.1 Mean annual trends for fires in the Alberta study area, 1919 to 2012: (a) log of area burned; (b) fire frequency; (c) log of fire size; (d) latitude in WGS84 (decimal degrees) coordinates; loess smoothing with 95% confidence interval shown  In the Alberta study area, comprised predominantly of boreal forests, an inflection point in fire regimes is apparent near 1970, with patterns in area burned, mean fire size, and mean fire latitude changing thereafter; a rapid rise in fire frequency began a decade later (Figure 3.1). The abruptness of the ~ 1970 and 1990 inflection points suggest a change in management, the former potentially linked to an increase in oil and gas development in the boreal known to occur at the time. An observed linear decrease in area burned and increase in fire frequency was independent of elevation (high-elevation mean = -4607 ha/year, +3.3 fires/year; low-elevation mean = -29643 ha/year, +2.2 fires/year) and latitude (high-latitude mean = - 31211 ha/year, +3.0 fires/year; low-(a) (b) (c) (d)  57  latitude mean = - 3039 ha/year, +2.4 fires/year), based on median fire elevation and latitude. FRP increased by 298% between the Pre-Suppression (1923-1952) and Global Change (1983-2012) periods, indicating a three-fold reduction in fire regime severity during a period of warming (Intergovernmental Panel on Climate Change, 2014).  FRP increased by 166% between the Pre-Suppression and Early Suppression (1953-1982) periods, before increasing by another 50% between the Early Suppression and Global Change periods. FRP in the Most Recent Decade (2003-2012) reflects patterns of the Global Change period it overlaps, shorter by 0.1% at 923.9 years (Table 4.2). However, Most Recent Decade fires were approximately twice as frequent and half the size of Global Change period fires (MFRI ∆ = -45%; annual frequency ∆ = +82%; MFS ∆ = -43.3%). The stability of FRP values between the Global Change and Most Recent Decade periods is indicative of the temporal depth of past-decade trends (Table 3.1).  Table 3.1 Fire regime statistics by period for the western Alberta study area; mean fire return interval (MFRI) is shown in years for the full region rather than the mean site value, where Burned = 1 / MFRI * MFS * Years; FRP = Area / Burned * Years Period Burned (ha) Area (ha) Fire Rotation Period (FRP, years) Mean Fire Return Interval (MFRI, years) Mean Fire Size (MFS, ha) 1923-1952 3,224,691 24,972,634 232.3 0.011 1,148.4 1953-1982 1,211,806 24,972,634 618.2 0.020 811.1 1983-2012 809,967 24,972,634 925.0 0.020 545.1 2003-2012 270,287 24,972,634 923.9 0.011 308.9   58  Differences in the mean and variance of fire size between Early Suppression and Global Change periods were not statistically significant at a p-value threshold of 0.05 (t = 1.69, p-value = 0.09; F = 1.19, p-value = 0.06). Area burned declined substantially between these periods (BurnedES = 1,211,806 ha, BurnedGC = 809,967 ha, ∆ = -33.1%), even though remote monitoring improved. While MFRI remained stable across the Early Suppression and Global Change periods (MFRIES = 0.0201, MFRIGC = 0.0202, ∆ = +0.5%), mean fire size (MFS) declined at a rate equivalent to that of area burned (MFSES = 811 ha, MFSGC = 545 ha, ∆ = -33%). Thus, a decline in mean fire size best explains the reduction in area burned under warming in the Alberta study area. This is particularly evident in the Most Recent Decade, where FRP (area burned) was similar to the Global Change period it overlaps (∆ = -0.2%) as MFRI (fire frequency) increased by 81.8%.  In the Alberta study area, the ratio of human- to lightning-caused fires increased from 0.93:1 to 1.39:1 (+33%) between the 1970s and 2000s. A spatial analysis of historical ignitions in the study area using NFDB point data demonstrates the proximity of small fires to areas of human activity, typically major roads and river valleys (fire distance from roads: mean = 2.2 km, standard deviation = 4.8 km; fire distance from roads or surface water: mean = 297 m, standard deviation = 363 m), supporting a human origin (Figure 3.2).   59   Figure 3.2 Fire adjacency to roads by cause overlaid on SRTM 90 m elevation data in the vicinity of Hinton, Alberta in NAD83 UTM 11N coordinates with WGS84 graticules: light blue = human-caused; magenta = lightning-caused; green = roads; top = north   Between the 1980s and 2000s, as Alberta’s population doubled, the mean distance of fires from roads declined by 40%, from 2.3 to 1.4 km. The mean distance of fires from roads or surface water (rivers and lakes; proxies of human activity) declined by 32% across the same 30-year period, from 318 to 216 meters. Concurrently, annual fire frequency increased by 33%, from 6,035 to 9,054 fires, in the point data. The increasing influence of human activity in Alberta’s  60  fire regimes is apparent in the percentage of the total area burned attributable to sources over the past three decades (Figure 3.3).   Figure 3.3 Decadal area burned by fire source for the Alberta study area; (a) absolute area burned (ha); (b) percent of total area burned (ha); most fires were unknown in origin (not shown); H = human-caused; H-PB = prescribed burn; L = lightning  A decline in the relative influence of lightning on the total area burned in Alberta was offset by an increase in the percentage of area burned explained be human-caused fires. Between the 1970s and 2000s, the area burned increased by 34% in summer, fire frequency increased in (a) (b)  61  spring and summer, and mean fire size increased by 83% in fall and decreased by 60% in spring for the Alberta study area (Tables 3.2 and 3.3).  Table 3.2 Fire regime change by season Season Area Number Mean Size Spring -6.8% +13.5% -60% Summer +7.6% +1% +16.6% Fall -2.2% -18.2% +82.9%  Table 3.3 Fire seasonality Season Area Number Mean Size Spring 63.2% 51.2% 123% Summer 33.8% 39.2% 86% Fall 2.4% 6.8% 35%   An analysis of fire seasonality related to the ‘spring dip’ in foliar moisture content (FMC) using standard formulations from the Canadian Fire Behavior Prediction System (Forestry Canada Fire Danger Group, 1992; Wotton et al., 2009), shows that the standard FMC equations are not suitable for the Alberta study area. Here, the modeled spring dip in FMC occurs approximately two months after the peak in fire frequency and size (Figures 3.4a and 3.4c) that likely corresponds to the true spring dip (Tymstra et al., 2007; Alexander & Cruz, 2013). The log of fire size shows the strongest density at 138 DOY (late April), followed by a second peak ~ 1 week later at a substantially larger fire size (Figure 3.4a). Meanwhile, modeled spring dip occurs at 200 DOY (Figure 3.4c). Across the full time period, fires declined in size following a structural change around 1990 (Figure 3.4b). In recent years, fires were most frequent and concentrated earlier in the season, with longer fire seasons (Figure 3.4d).     62          Figure 3.4 Two-dimensional kernel density estimation for fire frequency by ordinal date and year for the Alberta study area, 1919 to 2012: (a) log of mean fire size by ordinal date; (b); log of mean fire size by year (c) modeled foliar moisture content (FMC) by ordinal date; (d) fire ordinal date by year  Across Canada, an increasing rate of area burned declined at a similar inflection point around 1990, when mean fire size and latitude declined as fire frequency rapidly increased (Figure 3.5). Between the 1990s and 2000s, fires nationwide declined in mean latitude at a rate of 14 km/year while fires in the Alberta study area declined at a rate of 24.4 km/year. Nationwide and in Alberta, lightning-caused fires decreased and human-caused fires increased in mean latitude during the period (nationwide = -6/+1.6 km/year; Alberta = -5.9/+1.5 km/year). Characteristic of (a) (b) (c) (d)  63  the boreal, large lightning-caused fires >= 200 ha increased in mean latitude by 5.4 km/year nationwide and decreased by 10.1 km/year in Alberta. Since 1920, fires >= 200 ha shifted northward at a mean rate of 5.2 km/year (R2 = 0.13; p < 0.001) nationally.   Figure 3.5 Mean annual trends for fires Canada-wide, 1919 to 2012: (a) log of area burned; (b) fire frequency; (c) log of fire size; (d) latitude in WGS84 (decimal degrees) coordinates; loess smoothing with 95% confidence interval shown; NFDB data prior to 1960 are known to be incomplete  For the a priori classification in the Alberta study area, the Pre-suppression period (1923-1952) is characterized by frequent fires and the largest annual area burned, while the Early Suppression period (1953-1982) shows a sharp decrease in fire frequency and annual area burned, with the (a) (b) (c) (d)  64  lowest overall rates of each. The Global Change period (1983-2012) exhibits a rapid increase in fire frequency but a relatively flat annual area burned. The Most Recent Decade (2003-2012), shows the most rapid increase in fire frequency and the most rapid decline in mean fire size, accompanied by a decline in area burned.  For the Alberta study area and Canada, fire regime period classification using the binary segmentation change-point detection algorithm produced fire regime periods distinct from the a priori classification. In Alberta, based on time-series of annual area burned and fire frequency (Figures 3.6a and 3.6b), the algorithm shows an initial fire regime segmentation from the late 1930s to the early 1960s, followed by another regime from the 1960s to the 1990s, and final regime characterized by an increase in fire frequency from the 1990s to 2012. For Canada-wide fires, the algorithm shows little consistency between fire regimes for the univariate annual area burned and fire frequency time-series (Figures 3.6c and 3.6d). Nevertheless, the annual area burned time-series shows approximate agreement with the a priori classification, with regime periods falling from the early 1920s to ~ 1950, ~ 1950 to late 1960s, 1960s to late 1970s, and late 1970s to 2012.   65          Figure 3.6 Fire regime change-point segmentation using the binary segmentation algorithm: (a) Alberta fire frequency by year; (b) Alberta total area burned by year; (c) Canada-wide fire frequency by year; (d) Canada-wide total area burned by year  Fire regime periods differed for the two scales. Canada-wide, the 1940s through 1970s were characterized by infrequent fires and a steadily increasing area burned, while the inverse was true for Alberta. Nationwide, the first broad shift in fire regimes occurred during the 1970s with a spike in fire frequency and area burned. Yet, area burned was flat from ~ 1980. In the Alberta (a) (b) (c) (d)  66  study area, similar to nationwide patterns, fire frequency increased rapidly beginning ~ 1990. Yet, Alberta showed little change in area burned from 1960 to 2012, despite strong variability within the period (Figure 3.6).  Over the 90-year period, in the Alberta study area, fire seasons lengthened by ~ 60 days, or two months (mean = +1.2 days/year), due to more frequent human-caused fires (mean = +9.2 fires/year) earlier and later in the season (Figure 3.7a). The fire season experienced a lower rate of lengthening nationwide (Figure 3.7b). At both scales, lightning-caused fires were concentrated in summer, while human-caused fires were concentrated in the spring and fall (Figure 3.7).      Figure 3.7 Fire regime patterns nationwide and Alberta study area changes in seasonality with linear models and 95% confidence intervals: (a) Alberta study area fire ordinal date by year and season; (b) Canada-wide ordinal date by year, season, and cause; salmon = human; aqua = lightning; linear regression with 95% confidence interval shown  (a) (b) Fall Summer Spring Fall Summer Spring  67  Within the Alberta study area, the largest fire sizes and area burned occurred in the boreal, followed by the foothills and Rocky Mountain regions. Within the boreal region, the lowland mixedwood subregions experienced a greater area burned than the highland subregions. Yet, mean fire size and annual area burned declined in the boreal across the study period. Canada-wide, the log-transformed fire size distribution for fires > 2 ha showed reasonable fit with a Weibull distribution (K-S = 0.02; ω = 1.60; A2 = 27.34; AIC = 174679.6; BIC = 174696.8), with fit improving with the right-tail second-order Anderson-Darling (AD2R) statistic due to power-law behavior at the tail (Appendix A). While the distribution of fire sizes nationwide showed unimodality per Hartigan’s dip test (D = 0.003, p-value = 0.11) despite visual evidence of bimodality, fire sizes in the Alberta study area showed significant bimodality (D = 0.02, p-value = 0.002). Using a mixed Gaussian model for Alberta study area fire size, the two modes centered on µ of 1.2 and 6.2 log ha, with Expectation-Maximization (EM) and Bayesian Markov Chain Monte Carlo (MCMC) algorithms each converging to these values (Appendix A). This implies that there are two dominant fire regime phases in Alberta.  A further analysis reveals distinct changes in the fire size distribution over time. While previous periods showed approximately Gaussian fire size distributions without skew, fires in the Global Change period were strongly skewed toward smaller values (Appendix A). Bimodality of fire sizes for all years in the Alberta study area is comprised of two distinct components: (1) frequent large fires in 1923-1952; (2) frequent small fires in 1983-2012. The Most Recent Decade showed the second greatest K-L divergence (DKL = 0.84, after the Pre-Suppression period (DKL = 1.05), and greatest distance from, the fire size distribution for all years, based on the Earth Mover’s  68  Distance (EMD) or Wasserstein metric (EMD = 5.15). Fire regimes in Alberta thus reached a novel state in recent years.  For Canada, monthly aggregations show mean fire size and total area burned were typically largest in June, followed by July and May. Fire frequency peaked in July, followed by June and May (Figures 3.8a – c). These findings are supported by daily resolution data. Given increased temporal resolution, Gaussian and splines models indicate a typical fire frequency peak between 184-185 DOY, mean fire size peak between 172-178 DOY, and area burned peak between 171-178 DOY (Figures 3.8d – f). The splines models shows early season spikes in fire frequency and areas burned corresponding with the ‘spring dip’ in foliar moisture content indicated in Figure 3.4c – a sharp early season increase in the frequency and size of fires (Van Wagner, 1967) – as well as a skewed fire frequency distribution. The log of mean daily fire size centers at ~ 5.5 ha, while the log of mean daily area burned centers at ~ 6.5 ha. The log of daily fire frequency shows a negative exponential distribution with a large λ value (Figures 3.8g – i). This matches the typical model for the probability distribution of time-since-event for Poisson processes, such as the probability of fire events, as in LANDIS-II (Yang et al., 2004; Sturtevant et al., 2009).         69          Figure 3.8 Monthly and daily patterns of fire frequency, mean fire size, and total area burned Canada-wide: (a) total area burned by month; (b) mean fire size by month; (c) fire frequency by month; (d) total area burned by ordinal date; (e) mean fire size by ordinal date; (f) fire frequency by ordinal date; (g) log of daily area burned; (h) log of daily mean fire size; (i) log of daily fire frequency; recorded fire detection dates are used to calculate DOY values; blue and red lines in (d-f) are cubic splines and a Gaussian distribution fit, respectively, while the red line in (i) is an exponential distribution fit  (a) (b) (c) (d) (e) (f) (g) (h) (i) Total Area Burned (ha) Mean Fire Size (ha) Number of Fires Total Area Burned (ha) Mean Fire Size (ha) Number of Fires Area Burned Density Fire Size Density Fire Events Density  70  3.4 Discussion The distribution of fire sizes follows well-documented power-law behavior common to self-organized systems (Malamud et al., 1998; Reed & McKelvey, 2002), showing a heavy-tailed distribution. Previous theoretical work suggested that fire size distributions should fit a truncated Pareto distribution (Strauss et al., 1989). However, an empirical study of the boreal mixedwood region of Alberta, using the former Large Fire Database for 1980-1998, showed optimal model fit with a truncated exponential distribution (Cumming, 2001). The above results suggest that the use of the AD2R goodness-of-fit statistic yields reasonable model fit with a Weibull distribution for the logarithm of fire sizes.  The results illustrate that the Alberta study area experienced a sharp rise in human-caused fires and area burned since 1990. This rise in human-caused fires likely combined with warming to facilitate lengthening fire seasons in both early spring and late fall (spring mean = +0.26 days/year; fall mean = +0.67 days/year; R2 = 0.83; p < 0.001), in agreement with previous observations (Stocks et al., 2002; Kasischke & Turetsky, 2006). The combined lengthening of fire seasons by 0.93 days/year is approximately five times faster than the Canada-wide average of 0.2 days/year (spring mean = +0.07 days/year; fall mean = +0.13 days/year; R2 = 0.57; p < 0.001). This difference in fire season lengthening rates is likely attributable to rapidly increasing human activity in the study area. From the 1970s to the 2000s, human-caused fires accounted for a growing proportion of both annual fires (+9.8%) and area burned (+38.9%) for fires of known cause.   71  While the majority of area burned continues to be produced by lightning-caused fires nationally, this work observed a southern boreal shift to human-driven regimes characterized by more frequent, smaller fires near human activity earlier and later in the year. Climatic warming and a growing human presence are combining to create longer fire seasons, known to have challenged managers in recent years (Tymstra et al., 2007). Fire frequency, area burned, and mean fire size were greatest in spring for all regions, representing 51% of fires and 63% of area burned, except the Rocky Mountain region, where fire frequency and size are greatest in summer due to temperature constraints. The largest fires occurred in May, consistent with a ‘spring dip’ in foliar moisture content. Although this episodic decline in foliar moisture content remains under investigation (Jolly et al., 2014), it is an important physiological phenomenon in these forests (Little, 1970; Alexander, 2010; Finney et al., 2013; Jolly et al., 2014). Spring dip typically corresponds to intense crown fire activity, producing the largest and most severe fires of the fire season, which these data support.  Boreal fire regimes appear to be tracking a northward shift of boreal climatic conditions (Koven, 2013), reducing the size and severity of fires in the study area, as southern boreal ecosystems transition to Anthropocene fire regimes. Data from southeastern Canada indicate that the in-migration of temperate species into the southeastern reaches of the American boreal is already underway (Fisichelli et al., 2014). Fisichelli et al. (2014) proposes that the reduced size of boreal fires, despite warming, is attributable to four key factors: (1) reduced surface fuel loads from frequent small human-caused fires; (2) increased fire suppression; (3) reduced crown fuels and/or forest fragmentation due to extractive industry activities; (4) a northward shift of boreal climatic  72  conditions, evidenced by changing wildfire patterns and climate-analogue vectors (Koven, 2013).  A recent study shows demographic ageing for the region (Zhang et al., 2015), which may further reduce surface fuels prior to gap formation and understory reinitiation. Previous studies argue little effect of fire suppression on fire regimes in boreal and subalpine systems, as fuel moisture shows greater importance than fuel load in models, while neither fire frequency nor crown-fire potential were correlated with stand age (Johnson et al., 2001). Nevertheless, a shift toward more frequent and smaller fires is evident for fire suppression regions (Kasischke & Stocks, 2000). Subsequent analyses of Ontario and Alberta provide contrasting views on the effectiveness of fire suppression in Canada (Bridge et al., 2005; Cumming, 2005).  The increasing extent and magnitude of industrial activity, recreational usage, and road network expansion in formerly remote areas are combining with record temperature anomalies (Kamae et al., 2014) to produce frequent ignitions and small fires around areas of human activity. Harvest operations are widespread in these forests, reducing canopy fuels while providing new ignition sources. A temporal lag of large fires following periodic pulses in pest populations (Kurz et al., 2008) may amplify fuel conditions, fire regimes, and forest transition rates. Increasingly warm and wet conditions may favor deciduous species in the southern boreal (Terrier et al., 2012), producing a negative climatic feedback through increased summer albedo (Amiro et al., 2006) while reducing the rate of fire spread (Dash et al., 2016).   73  An increase in fire suppression corresponds to an increasing human presence in previously remote forested regions, related to a 619% increase in Alberta’s population during the 1921-2011 period (Statistics Canada, 2011) and economic growth from extractive industry activity (Cross & Bowlby, 2006). The advent of fire suppression is indicated in the historical record by reduced fire activity in the mid-20th century, following the 1950 Chinchaga wildfire in northwestern BC and western Alberta, the largest recorded wildfire in North American history. The disturbance legacy of this large fire is evident in the fire data, with few fires in its recovery zone since, while surrounding boreal areas have burned frequently. This may partially explain the observed decline in mean fire size, but does not explain accelerated decay in recent decades. The mean area burned by fires followed a similar trend, only rising in 1998 at the beginning of an exponential-like increase in fire frequency, as described for other regions of the boreal (Kasischke & Turetsky, 2006; Kelly et al., 2013). Research for Alberta, conducted parallel to this work, selected a similar fire exclusion period start date of 1948, chosen for its correspondence with the establishment of the Eastern Rockies Forest Conservation Board. This work also shows a general lengthening of fire rotation periods compared to historical burn rates (Rogeau, 2016).  While one may infer that increased fire detection by satellites in recent decades (e.g., Landsat and MODIS) explains the observed rapid increase in fire frequency, decrease in fire size, and increase in latitude of large lightning-caused fires during this period, an analysis of the reported detection source rejects this hypothesis. Recent studies elsewhere in the boreal have shown the effect of human activity on fire frequency (Gaglioti et al., 2016). While disturbance detection source or instrument (spaceborne remote sensing versus traditional air and ground methods)  74  shows a statistically significant relationship for fire size (p < 0.001) and latitude (p < 0.001), it is not enough to explain recent fire regime changes.  Mean decadal fire frequency and area burned show little change due to inclusion of spaceborne remote sensing over the past three decades (Figures 3.9a and 3.9b). Only mean fire latitude and size were significantly impacted by detection source (Figures 3.9d and 3.9c), with the effect greater for median values; an ANOVA indicates that latitude was more strongly affected than fire size (p = 7.39e-05; p < 2e-16). Since the 1970s, spaceborne detection methods appear to have substituted for traditional methods in northern regions. The mean decadal latitude of lightning-caused fires > 200 ha peaked in the 1970s, prior to broad use of spaceborne monitoring. Large lightning-caused fires were 2 degrees further north on average than fires £ 200 ha, with a maximum of 5.3 degrees higher in the 1970s (WGS84 coordinates).   75       Figure 3.9 Fire statistics by reported detection source Canada-wide: (a) fire frequency by decade; (b) area burned by decade; (c) mean fire size by decade; (d) mean fire latitude by decade in WGS84 (decimal degrees) coordinates; blue = traditional detection source; red = modern remote sensing instruments  Thus, the contribution of spaceborne instruments to observed fire patterns remains small relative to traditional methods. In the 2000s, spaceborne monitoring was used to detect less than 9% of recorded fires in Canada, despite reliable Landsat and MODIS coverage for the period (Fensholt (a) (b) (c) (d)  76  & Proud, 2012; Wulder et al., 2016). Even though spaceborne detection methods often produced a mean fire size twice that of traditional sources during the past decade, likely due to the a combination of the coarse resolution of the MODIS hotspot product (Hantson et al., 2013) and increased coverage in the north, combined mean fire size sharply declined from 1990 onward. Furthermore, a rapid increase in the frequency of small human-caused fires in recent decades may drive the mean fire latitude southward toward population centers. While this is evident for fires of all sizes, large lightning-caused fires > 200 ha representative of classical boreal fire regimes generally increased in latitude over the past 90 years, indicative of high-latitude warming and an increased human presence in the north; disentangling these two factors, as well as the inherent sampling bias of non-satellite detection methods, presents an opportunity for future research. Nonetheless, a poleward shift of boreal fire regimes may correspond to a northward migration of boreal forests under warming (Koven, 2013; D’Orangeville et al., 2016). Further research leveraging the Landsat or AVHRR record is required to confirm this dynamic.  While the inclusion of satellite disturbance detection data in recent decades should increase the apparent area burned, the opposite is observed across regional and national scales. At its peak prior to the current decade, in the 2000-2009 decade, spaceborne observations represented 8% of fire observations and 19.4% of the total area burned; omitting these observations leaves observed patterns generally intact. At its latitudinal peak in the 1990-1999 decade, spaceborne observations were 14% further northward on average compared to traditional detection methods. However, the true northward bias of spaceborne observations is likely greater than 14%, due to the range and thus inherently low variation of latitudinal values, which begin at the 49th parallel  77  and end near the 66th. Future studies of fire regime migration should rescale latitude values into local Cartesian coordinates using pan-boreal biome bounds.  For the study area in western Alberta, where recent changes to fire regimes are greater than national patterns, the detection source of fire observations shows no effect. According to the National Fire Database, none of the fires in the study area were sourced from modern remote sensing instruments. Hence, the analysis and related conclusions at the national and regional scales remain valid. At the national scale, while the subtraction of remote sensing detected fires would further increase FRP (reduce the rate of burning) during the Most Recent Decade, such large fires were often drawn on a map by hand in previous decades. Absent additional information, I estimate the historical fire size detection threshold at > 40 ha for the study area, based on strong correspondence to a gamma fire size distribution at this threshold (K-S = 0.028 ω = 0.231; A2 = 1.621). Individual fire sizes between periods did not significantly differ in the mean, but did significantly differ in variance (t = 0.750, p-value = 0.454; F = 301.180, p-value < 2.2e-16).  Despite declines in fire size, latitude, and area burned for lightning-caused fires Canada-wide between the 1990s and 2000s reported here (mean = -422 ha/year; mean = -15.6 km/year; mean = -744,674 ha/year), a recent analysis of long-term warming suggests that these changes are not climatic (Karl et al., 2015). Results for the study area show a regime shift toward human-dominated fires in recent decades. By the 2000s, human-caused fires accounted for 58.1% of fires and 70.8% of area burned in the study area, surpassing the millennia-old dominance of large  78  lightning-caused fires. These findings contrast with Canada-wide changes during the same period, where human-caused fires declined in contribution to the area burned from 9% to 6%. While human activity has long played a role in fire regimes in the boreal (Bowman et al., 2011), Anthropocene conditions have recently combined to produce fire regimes without historical analogue along the southern boreal. By analyzing fires > 200 ha before the 2000s, due to limitations in the former national fire database, previous studies (Stocks et al., 2002; Kasischke & Turetsky, 2006) were unable to detect this regime shift. Fires < 200 ha in size represent 46.6% of fires in the study area (0.6% of area burned) and 59.3% of fires Canada-wide (0.9% of area burned). Thus, while large fires continue to explain the area burned, they fail to explain variation in fire frequency. As was shown, recent dramatic changes to fire frequency are not explained by the inclusion of spaceborne detection methods.  The Alberta study area results contrast to previous studies suggesting that lightning maintains a dominant role in annual area burned throughout the North American boreal (Stocks et al., 2002; Kasischke & Turetsky, 2006). Here, more effective fire suppression (Cumming, 2005) appears overwhelmed by a combination of warming and increased human activity, beginning at an inflection point ~1970. At higher latitudes and elevation in Canada, warming has been shown to increase biomass production (Hantson et al., 2015; D’Orangeville et al., 2016), partially explaining an increased area burned here under the assumption of fuel limitations.  An increased annual rate of fire frequency since 1980 corresponds with population growth and increased economic activity in Alberta (Statistics Canada, 2011) combined with rapid warming (Karl et al., 2015). Regional and national warming is evidenced by IPCC findings  79  (Intergovernmental Panel on Climate Change, 2014), previous fire regime analyses (Wotton & Flannigan, 1993; Tymstra et al., 2007), and indirectly by aforementioned observed changes to fire regimes Canada-wide. Human activity may explain most of the increase in the frequency of small fires near roads and surface water, while warming also increases the frequency of lightning strikes and severity of fire weather conditions (Krawchuk et al., 2009).  Although mean annual fire size and area burned declined in the study area over the past decade, the effects of warming on burning appear to have been amplified, rather than attenuated, by human activity. The data do not appear to support a previously reported non-linear U-shaped relationship between human activity and the frequency of fire ignitions (Syphard et al., 2007; Parisien et al., 2012). Due to the relative remoteness of Alberta's burnable land and small urban areas (compared to populous regions, such as California), there appears to be an approximately linear, rather than a U-shaped, distribution between fire frequency, area burned, and human activity. The study area results appear similar to findings for the Alaska boreal (Gaglioti et al., 2016). Successful fire suppression efforts (Cumming, 2005) may partially account for the decline in mean fire size nationally and in Alberta, as well as a declining national annual area burned, despite warmer conditions with more frequent human-caused ignitions. High-frequency small fires and extractive activities have likely also reduced forest fuels, which may together explain an observed demographic shift in these forests (Zhang et al., 2015).  These patterns differ from other recent studies in the North American boreal including Alaska (Stocks et al., 2002; Kasischke & Turetsky, 2006), which show a rapid rise in mean fire size and annual area burned, based on analyses of previous historical fire database versions. The results  80  presented herein contradict both of these notions across regional and national scales, showing greater agreement with paleoreconstructions from Alaska (Kelly et al., 2013), studies on the relationship between human activity and fire frequency in the Alaskan boreal (Gaglioti et al., 2016), and recent analyses indicating the presence of negative wildfire feedback mechanisms in the North American boreal (Héon et al., 2014; Rogers et al., 2015).  Future studies should assess whether these trends are prominent across North America and northern forests globally. A coupled climatic-human activity dynamic appears to explain the observed changes in fire distribution. This is supported by a recent study showing a global human-driven reduction in burned area (Andela et al., 2017). Studies should seek to better delineate the causes of these patterns in terms of the precise roles of climatic, human, and forest fuels mechanisms responsible. Of primary interest is the unexplained inflection point observed around 1990, for both the Alberta study area and across Canada, related to a rapid increase in fire frequency, reduced mean fire size, and reduced area burned, despite warming. This poorly understood change-point appears to explain many observed dynamics. While historical landcover and demographic change undoubtedly also play a critical role in explaining variations in fire patterns, a dearth of detailed historical maps makes it difficult to assess, with remote sensing records absent earlier than a few decades into the past. Future studies should investigate the coupling of climatic change and human activity to better understand present and future conditions, until more precise maps of landcover history are available.  Results indicate that the application of historical climate-fire correlations to general circulation model projections, absent anthropogenic trajectories, carries diminished predictive power in the  81  Anthropocene. Short-term boreal ecological forecasts should include spatially explicit dynamics of human-caused ignitions, fire suppression, and structural-demographic changes to forest fuels related to increasing human activity. Long-term forecasts should further include compositional change impacts on fuel conditions (Terrier et al., 2012), as well as coupled climate feedbacks (Amiro et al., 2006).  These requirements may motivate the development of new terrestrial biosphere models incorporating disturbance, succession, and energy partitioning processes, similar to recent hybrid models (Bond-Lamberty et al., 2005; Scheller et al., 2007). The anthropogenically focused Community Earth System Model (CESM1) revisions (Li et al., 2013a) and Human-Earth System Fire (HESFire) model (Le Page et al., 2015) represent such an approach, as do physically based three-dimensional regional models such as WRF-Fire (Coen et al., 2012) and HIGRAD/FIRETEC (Colman & Linn, 2007). New hybrid models may rely on partial differential equation representations of individual tree dynamics (Moorcroft et al., 2001; Purves et al., 2008; Strigul et al., 2008; Medvigy et al., 2009), as well as the use of machine learning to represent pattern-based processes, as first presented herein. In the following chapter, I assess the effects of warming on tree species regeneration to account for potential long-term changes in canopy light transmission.  3.5 Limitations This research relies on the best available fire history data for Canada (Stocks et al., 2002; Parisien et al., 2006; Burton et al., 2008). Yet, the data contain known sampling biases toward lower latitudes, larger fires of longer duration, and years subsequent to ~ 1960, particularly for  82  data on fire seasonality and cause. Accordingly, 95% confidence intervals are used for regression models to display the relative uncertainty in model estimates over time. For improved estimates of parameter uncertainty or model error, future studies may rely on Bayesian methods (e.g., Gaussian process regression or Hamiltonian Monte Carlo). These methods are also useful for parameter estimation and uncertainty analysis with ecosystem models (Kennedy & O’Hagan, 2001; Larocque et al., 2008; Nagel, 2017). While modern spaceborne imaging systems such as Planet Doves (Hand, 2015) and recent computer vision techniques (LeCun et al., 2015) are poised to alleviate sampling biases in historical fire maps over time by improving the spatiotemporal resolution of detection accuracy, the temporal depth of this remote sensing record remains limited.   83  Chapter 4: Tree Species Regeneration Modeling1  4.1 Introduction Tree development and phenology are related to climate through evolutionary controls, influencing the early niche space of trees, with plasticity potentially providing a buffer to maintain fitness (Aitken et al., 2008; Vitasse et al., 2013). Important tree development and phenology events include germination, establishment, bud burst, growth, bud set, leaf senescence, seed fall, and dormancy, among others (Walck et al., 2011; Richardson et al., 2013). Climatic change can uncouple the phasing of fine-scale seasonal weather variations with developmental processes and phenology beyond the range of plasticity, reducing regeneration rates (Fridley, 2012; Richardson et al., 2013). This phase uncoupling can alter the duration of important phenological processes and timing of phenological events.  The widespread adaptation of trees to local climatic conditions (Alberto et al., 2013) indicates that tree phenology is intricately tuned to optimize fitness for local environmental conditions through gene expression, posttranslational modification, and, genetic and epigenetic inheritance (Liu et al., 2010; Cooke et al., 2012; Matzke & Mosher, 2014). Environmental effects are estimated to exert greater influence on plasticity than genetics in northern forests (Vitasse et al., 2013), while phenotypic variation reflecting phylogeographic origins (Alberto et al., 2013) is not necessarily adaptive (Duputié et al., 2015). Extreme weather events, such as frost or drought,                                                 1 This chapter is published in Ecological Modelling: (Erickson et al., 2015)   84  occurring at critical times during tree development can have strong demographic effects on forests. Given the importance of fine-scale climatic and phylogenetic variability, high temporal resolution climate data (Cook et al., 2010) along with a range of aggregate species tolerances can aid in the modeling of these dynamics at the landscape scale, where individual- or population-level data is seldom attainable.  Here, it is hypothesized that warmer conditions combined with changes in soil water balance (Dobrowski et al., 2013; Piedallu et al., 2013) and more rapid and severe extreme weather events (Allen et al., 2010; Kamae et al., 2014; Trenberth et al., 2014) are altering regeneration patterns in northern forests. Recent empirical evidence suggests that this shift is already occurring (Lenoir et al., 2009; Urbieta et al., 2011; Boisvert-Marsh et al., 2014; Zhang et al., 2015). However, direct measurement remains confounded by forest turnover, which can increase the amount of space available for recruitment (Zhu et al., 2012, 2014; Park Williams et al., 2013; Woodall et al., 2013). Additional confounding factors include patterns of fine-scale climate (Dobrowski et al., 2013) and ontogenetic niche variation, whereby the niches of species can change throughout development (Cavender-Bares & Bazzaz, 2000; Eriksson, 2002; Donohue et al., 2010; Niinemets, 2010b; Bertrand et al., 2011a; Urbieta et al., 2011).  Here, it is suggested that changes to tree regeneration throughout northern forests in recent decades have been driven by interactions between climatic change and local soil patterns. To test this hypothesis, a species-specific ecophysiological model that explicitly represents major tree regeneration processes is used, based on forest gap models. The model is parameterized for tree species and soil textural classes across a 25.2 million ha study area in Alberta, Canada,  85  encapsulating an important elevational and latitudinal gradient. Daily resolution historical weather station data is used for three decadal periods over the last century, and for the most recent decade, to model the effects of climatic change on forest regeneration throughout the past 90 years. A previous version of the TACA model used in this study is combined with LANDIS-II to model forest dynamics in Chapter 5. Subsequent chapters develop and apply models for the dynamic simulation of understory irradiation.  4.2 Methods The methods and Alberta study area are described in previous chapters. A model parameterization diagram is provided below (Figure 4.1), showing alternate climate data sources for the use of monthly or daily temporal resolutions (Erickson et al., 2015). Here, daily weather station data was used to provide the most representative conditions, important for phenological models. In summary, historical daily weather station data was acquired from the NOAA Global Historical Climatology Network Daily (GHCN-D) data set. The data was processed using custom scripts available in reduced form in the rnoaa package for R (Chamberlain et al., 2016).   86    Figure 4.1 TACA-GEM parameterization scheme for Canada  Weather stations were spatially filtered and aggregated within each Natural Subregion of Alberta (Natural Regions Committee, 2006), before calculating median daily weather station values for each of these biogeoclimatic regions. Soil textural class information for each biogeoclimatic region was calculated from the CanSIS Soil Landscapes of Canada (SLC) v3.2 data set. Additional values used from SLC data include soil rooting zone depth, coarse fragment percent, available water storage capacity, and derived percolation rate. Latitude values are used for solar modeling in the Hargreaves-Samani soil moisture submodel.   87  A regression analysis was conducted to determine the relative importance of different mechanisms in explaining regeneration values, filtering covariates at a threshold of |r|>0.7  (Dormann et al., 2013), before filtering variables at a significance threshold of p ≤ 0.05.  I utilized R2 partitioned by averaging over orderings of regressors (LMG) and proportional marginal variance decomposition (PMVD) with the R relaimpo package (Grömping, 2006) to determine predictor variable relative importance in linear regression.  4.3 Results The results show that tree regeneration suitability, modeled as the probability of reaching an age of ten years, declined across the 1923-2012 period for most species in the Alberta study area (Figure 4.2). The establishment of new cohorts for most species was increasingly unlikely. Adding extreme climatic events (i.e., drought and frost) further reduced regeneration conditions, which were poorest in recent decades. It is estimated that the regeneration niches of extant and adjacent tree species are largely out of equilibrium with climatic conditions and have been for decades, with regeneration conditions likely to worsen in the coming years. The frequency and magnitude of drought following germination was the most limiting factor affecting regeneration conditions, due to reduced soil moisture.   88   Figure 4.2 Modeled mean change in species regeneration across regions for the full period; probabilities were output from TACA-GEM simulations for a 10-year period  The most recent period modeled, 2003 to 2012, shows a slight deceleration in the rate of regeneration suitability change, likely attributable to a slowdown in warming (Kosaka & Xie, 2013). A significant mean decline in regeneration suitability was predicted across the full study period. Compared to simulations without extreme events, including extreme events in the simulations marginally decreased the probability of establishment (mean = 0.085, σ = 0.220; mean = 0.059, σ = 0.216) and the change in establishment across the full study period (mean = -0.138, σ = 0.228; mean = -0.142, σ = 0.248). More frequent drought, diminished germination success, and lengthened bud dormancy resulted in an overall decline in regeneration suitability. Species regenerational responses varied across space and time, often responding similarly in direction to climatic and edaphic conditions within regions and time periods (Figure 4.3). These  89  trends are indicative of directional climate change, evident in a similar direction of species responses across regions.   Figure 4.3 Mean change in species regeneration probability, 1923-1952 to 1983-2012 period, including extreme events for the five regions; species that consistently failed to regenerate appear unchanged; a value of 1.0 represents a 100% change in regeneration probability; probabilities were output from TACA-GEM simulations for a ten year period; solid red = -1.0; none = 0; solid green = 1.0   90  The boreal forest and foothills regions showed a transition in the regeneration niche of species toward deciduous poplar species, with improved suitability for Engelmann spruce (Picea engelmannii), a high altitude montane species. Other regions indicated regenerational improvements for pine species that are more resilient to drought. The grassland region, which has the lowest regeneration suitability overall due to high hydraulic conductivity, showed a transition toward grand fir (Abies grandis), trembling aspen (Populus tremuloides), and whitebark pine (Pinus albicaulis). The parkland region showed the strongest net improvement in regeneration conditions overall, transitioning toward grand fir, ponderosa pine (Pinus ponderosa), and limber pine (Pinus flexilis). The Rocky Mountain region showed the most widespread regenerational decline, symptomatic of relatively severe soil moisture limitations. Overall, the highest elevations experienced the greatest regenerational decline, due to a shift in soil water availability toward lower elevations.  The impact of directional warming on species-specific physiological drought frequency varied considerably across regions, due to interactions with regional soil properties, precipitation patterns, and snowmelt timing. Results indicate that in the boreal forest, grassland, and Rocky Mountain regions, the 1983 to 2003 period crossed species drought tolerance thresholds with the greatest frequency, while showing an increased incidence of frost after bud flush, indicative of increased temperature variability. Modeled regeneration suitability for the 2003 to 2012 period reflects a temporary slowdown in warming combined with increased high-precipitation events, in agreement with Clausius-Clapeyron scaling based predictions under warming and observations for the region (Trenberth et al., 2003; Wentz et al., 2007; Allan & Soden, 2008; Trenberth, 2011).  91  The biophysical niche space of species (e.g., species tolerances) accounted for a significant amount of variation in regeneration responses (p ≤ 0.001). However, species often responded with similar directionality to climatic and edaphic changes, particularly for drought and turgor loss. While inter-specific variability was clearly present (mean σ = 0.179), changes to regeneration suitability were better explained by spatiotemporal variation (p ≤ 0.001; mean σ = 0.198). In terms of regeneration, gymnosperms fared similarly to angiosperms across all periods and regions (gymnosperm mean = 0.18, σ = 0.225; angiosperm mean = 0.14, σ = 0.198), while the difference diminished with the inclusion of extreme effects (gymnosperm, mean = 0.14, σ = 0.221; angiosperm, mean = 0.12, σ = 0.197). Species, regions, and time periods showed greater distributional heterogeneity than differences between conifers and angiosperms.  A fixed-effects analysis of variance (ANOVA) showed a significant relationship between variance in regeneration probabilities and species, period, region, subregion, growing degree days, killing frosts, drought frequency, germination frequency, germination events, and stratification (p ≤ 0.001), and a less significant relationship with spermatophyte taxon, ordinal date of bud break (p ≤ 0.01), and physiological dormancy (p ≤ 0.05). Chilling requirements met, frost frequency, frost days, frost events, and turgor loss point frequency did not show a significant relationship with species regeneration probabilities (p > 0.05). The frequency of germination success for species varied across the study period, while generally declining. ponderosa pine (Pinus ponderosa), an arid fire-adapted specialist, experienced the greatest reduction.   92  With extreme events for all species and periods, both metrics indicated that germination frequency (LMG = 0.28; PMVD = 0.31), drought frequency (LMG = 0.08; PMVD = 0.16), number of growing degree days (LMG = 0.06; PMVD = 0.07), and turgor loss point frequency (LMG = 0.05; PMVD = 0.001) were the most important mechanisms determining regeneration responses, providing details that were absent in the previously described ANOVA. From these metrics, a multi-decadal climatic warming signal is evident, with heterogeneous regional implications.  The modeled frequency of reaching species’ turgor loss point and exceeding physiological drought tolerances increased for most species in most regions over the full study period. Turgor-loss-point frequency was relatively homogeneous across species, exhibiting a generalized model response of turgor loss point and leaf water potential at 50% loss of hydraulic conductivity, measures of leaf vulnerability to cavitation that are functions of xylem structure (Bartlett et al., 2012). Species physiological drought frequency was heterogeneous across regions and homogeneous within regions. Specific regeneration probabilities fluctuated primarily in response to climatic change relative to soil moisture conditions. Black cottonwood (Populus trichocarpa) and balsam poplar (Populus balsamifera) exhibited the greatest sensitivity to drought, as shown in empirical studies (Nitschke et al., 2012). Douglar-fir (Pseudotsuga menziesii) and ponderosa pine were the most tolerant of increasingly frequent and severe drought conditions. Species regeneration values varied by species, region, and time period (Figure 4.4).   93   Figure 4.4 Regeneration probability boxplots: (a) by period; (b) by region; (c) by species; boxplots include native species and potential migrants; boxplots display the median, hinges as the first and third quartiles, whiskers as the product of 1.5 and the interquartile range, and outlier points  At higher elevations and latitudes, modeled frost events following both bud flush and germination events declined in the most recent decades. However, frost events more frequently (a) (b) (c)  94  exceeded specific frost tolerance threshold parameters, indicative of warming and greater temperature variability. More frequent and severe modeled physiological drought conditions were the main factor limiting modeled establishment values in the boreal, grassland, and parkland regions, with modeled soil moisture particularly meager in the latter two regions due to the high hydraulic conductivity of glacial and aeolian deposits. The inclusion of extreme weather events particularly reduced modeled establishment conditions for fir and spruce species with lower drought tolerance – but similar frost tolerance – than pines. The modeled number of growing degree days and probability of germination success also declined. In essence, a phase decoupling of climatic patterns and species phenology in time and space seems likely from our model results for multiple regenerational processes.  4.4 Discussion Warmer and more variable climatic conditions are diminishing the conditions for extant tree species regeneration in Alberta, Canada. As multi-decadal warming continues unabated, modeled tree species are likely to fail to regenerate. An increasing magnitude of climatic disequilibrium is likely to reduce forest regeneration, which may be initiated through climate-driven changes to disturbance regimes (Magnani et al., 2007). Some studies indicate that forest regeneration conditions should be improving at higher elevations and latitudes (Brubaker, 1986; Lenoir et al., 2009) and declining in lower elevation forests (Loarie et al., 2009; Bertrand et al., 2011b), while others provide mixed results potentially related to changes in human activity (Boisvert-Marsh et al., 2014). Here, the findings support a relative improvement in regeneration conditions in low-elevation northern forests (Crimmins et al., 2011; Zhu et al., 2012, 2014; Dobrowski et al., 2013). It was found that changes to soil moisture conditions drove species regeneration niches  95  toward the foothills and parkland regions, indicating that changes to soil water balance may drive future species migrations under warming (Crimmins et al., 2011; Piedallu et al., 2013). The inclusion of soil water balance is particularly important in mountain watersheds (Hwang et al., 2014) and in the Canadian boreal forest (Barnett et al., 2005), as it is the key limiting factor driven by climate. The model results provide a potential explanation of complex tree regeneration patterns observed in previous studies (Urbieta et al., 2011; Zhu et al., 2012, 2014; Woodall et al., 2013; Boisvert-Marsh et al., 2014; Zhang et al., 2015), providing direction for future empirical work.  A recent study (Zhang et al., 2015) provides empirical support for the modeling results. Using permanent sample plot data for western Canada, their study shows that competition plays a stronger role in local forest dynamics than climate, long demonstrated in gap and hybrid model studies based on theoretical and empirical formulations (Shugart, 1984; Deutschman et al., 1997; Schumacher et al., 2004). The Zhang et al. (2015) study also modeled trends in recruitment rates for western Canadian provinces, based on empirical data. The study shows an overall decline in recruitment across regions, with a linear decline exhibited in Alberta. In agreement with the results presented here and contrary to findings for the Sierra Nevada range (Dolanc et al., 2013), the most dramatic reduction in recruitment and growth rates occurred in the high-elevation montane Cordillera region (Zhang et al., 2015). The present study indicates that this reduction in recruitment is likely due to changes in soil water balance, driven by the interaction of warming and soil textural properties.   96  In the coming years, increases in the frequency of anthropogenic disturbances (Kurz et al., 2008; Park Williams et al., 2013) may accelerate the currently delayed regenerational response of forests by increasing the number of sites available for recruitment. Concurrently, warmer and wetter conditions projected for northern forests (Trenberth, 2011) may accelerate recruitment by increasing the rate of forest turnover (Zhu et al., 2014). Due to the long-lived nature and relatively rapid dispersal ability of trees (Clark et al., 1998), future compositional changes will likely occur in pulses as climatic change intensifies. Directional changes to the region’s forests may occur through rare long-distance migration events (Clark et al., 1998) by species better adapted to low soil moisture, producing no-analogue communities.  Future empirical studies should investigate evidence of regenerational change in northern forests with ground plot data in connection with directly measured local climate data. Future modeling studies should incorporate important forest dynamics, such as competition, dispersal, and disturbance by fusing theoretical and empirical formulations with detailed remote sensing structural measurements. An improved understanding of forest regeneration may help forest managers to meet multiple-use goals, while providing a more complete picture of biospheric climate feedbacks. In the next chapter, we fuse the TACA model with LANDIS-II to simulate a full suite of forest dynamics in the western Alberta study area.  4.5 Limitations The TACA-GEM model application presented herein relies on species-specific parameters that include observations and species for adjacent regions, including southeastern British Columbia. Some of these species may be adapted to different conditions than those of Alberta, due to  97  variation in genes or their expression. Other species parameters for TACA-GEM were roughly estimated from species ranges for previous studies (Burton & Cumming, 1995; Cumming & Burton, 1996). Meanwhile, a number of parameters were derived from species compendiums that provide single values for the continent or country (Burns & Honkala, 1990; Farrar, 1995a; Klinka et al., 2000), which is biologically unrealistic regardless of the metric. The effect of these species parameter simplifications is unknown, but may potentially reduce the number of realized niches due to convergence in the parameter space.  Soil and daily weather data used to calculate parameters for TACA also contain limitations. Soil data (Soil Landscapes of Canada Working Group, 2010) was compiled from existing soil survey maps (gridded plot data) at a representative fraction of 1:1000000. Meanwhile, statistically filtered GHCN-Daily weather data (Menne et al., 2012; Hausfather et al., 2016) still contains stations with sporadic temporal coverage in the region; these stations were filtered out if more than half of the observations were missing, while smaller gaps were imputed. Both data may also contain unknown sources of noise or bias (e.g., the proximity of weather stations to roads or non-anthropogenic low albedo surfaces, or topographic effects on solar radiation). As such, a considerable degree of uncertainty is expected for TACA model parameters. Again, Bayesian methods should be used in future studies to jointly estimate parameters and their uncertainties.  Validation of TACA-GEM results was limited to an analysis of general trends provided in Appendix F, which may be expanded in future work. The validation exercise was complicated by changes in forest canopy conditions over the period, lending additional uncertainty to the results. Meanwhile, validating each component of TACA-GEM for each species and bioregion is  98  currently infeasible. Other likely sources of TACA-GEM model error stem from the simplification of complex physical processes into logical or linear model components, as well as knowledge gaps for specific processes; such errors may propagate within the model, requiring further analysis. To account for variation internally, the TACA model is probabilistic rather than deterministic. As such regeneration models grow in complexity, parameter and model uncertainties warrant greater consideration.   99  Chapter 5: Forest Landscape Modeling  5.1 Introduction Seasonal fire and climate cycles played a central role in the evolution of boreal forests. Here, large stand-replacing fires have been the dominant disturbance type for millennia (Rowe & Scotter, 1973; Davis & Shaw, 2001; Rogers et al., 2015), while temperature conditions can be severe. In North America, boreal tree species evolved a diversity of adaptations to fire, including vegetative resprouting, cone serotiny, aerial seed banks, fire-enhanced regeneration, and increased flammability (Schwilk & Ackerly, 2001; Keeley et al., 2014; Pounden et al., 2014; Rogers et al., 2015). These adaptations are believed to impart trees with a competitive advantage in the successional phases of disturbance and regeneration.  Trees in the Canadian boreal have high intraspecific genetic variation, exhibiting a high degree of local adaptation (Davis & Shaw, 2001). Trees respond to periodic climatic cycles in situ via phenotype plasticity (e.g., gene expression) and to long-term climatic change through migration (Aitken et al., 2008; Matzke & Mosher, 2014). Extreme events beyond physiological tolerances produce mortality. While the distribution of tree species correlates well with historical climate at coarse spatiotemporal scales, disturbance responses dominate fine-scale dynamics (Prentice, 1986). Trees often lag behind climate-space optima (Bertrand et al., 2011b), requiring mortality and recruitment to transition forest composition toward optimality.  When temperature shifts outpace the availability of open niches for plant regeneration given seed dispersal rates (Clark et al., 1998), climatic change may occur too rapidly for migration to track  100  warming. Given migration failure, in situ regeneration conditions can become increasingly suboptimal (Nitschke & Innes, 2008). When multiple species fail to track warming, absent new migrants, short-term forest decline can result, which may explain recent empirical observations (Hogg et al., 2008; van Mantgem et al., 2009; Allen et al., 2010; Mascaro et al., 2011; Michaelian et al., 2011; Martínez-Vilalta et al., 2012; Vilà-Cabrera et al., 2013; Worrall et al., 2013; Cohen et al., 2016). Over longer time-scales, short-term forest decline may give way to compositional or landcover change. A reduction in mortality rates (e.g., due to fire suppression) may temporarily inhibit these changes, obfuscating the latent processes in empirical data.  Given previous results (Chapters 3 and 4), these observations, and, recent climate and fire trends, a decline in regeneration potential is hypothesized to intensify the reduction in total forested area produced by severe burning. Due to an unavailability of empirical plot data and the challenge of controlling variables in these data, this hypothesis was tested with a numerical simulation model. The limitations of this work stem from the uncertainties of this experiment design related to model simplification, parameterization, and optimization.  Due to an accelerated pace of high-latitude warming, boreal climatic conditions are shifting northward at a rate of 430 m yr-1 (Loarie et al., 2009; Hamann et al., 2015). The high rate of recent warming surpasses paleo-rates of species range shifts inferred from the pollen record, while landscape fragmentation may pose a constraint on migration (Lazarus & McGill, 2014). While direct measurements of species migrations and other forest dynamics remain limited by the long timescales of the biological processes involved, simulation models provide an attractive tool for inference. A combination of simulations and adaptive management (Holling, 1978) may  101  eventually facilitate ecological optimization to achieve management goals, such as maximizing carbon storage.  Here, forest compositional and structural changes arising from past-century climate and fire trends are simulated for the Alberta study area. A hybrid forest landscape model is initialized at year 2000 conditions using modeled tree species distributions (Gray & Hamann, 2012) classified into Canadian landcover classes. Four historical climate, fire, and human activity periods were used to simulate past-century forest successional trajectories. Differences in stand conditions are assessed after fifty years of simulation, allowing for ten years of model spin-up. By simulating the historical scenarios, the resilience of extant forests to the persistence of past-century climate and fire conditions is determined.  5.2 Methods The Alberta study area is detailed in previous chapters. Using the Natural Regions and Subregions of Alberta (Natural Regions Committee, 2006), the majority of the study area is located in the Boreal region (46.2% of the study area), followed by the Foothills (25.5%) and Rocky Mountain (19.5%) regions. The Parkland and Grassland regions together comprise less than 10% of the study area, making over 90% of the study area boreal and montane, characterized by a strong elevational gradient.  The Tree and Climate Assessment (TACA) establishment model (Nitschke & Innes, 2008; Mok et al., 2012) was combined with the Landscape Disturbance and Succession (LANDIS-II) model (Scheller et al., 2007) to simulate forest dynamics across the 25.2 million hectare study area at  102  one-hectare resolution. Model parameterization is detailed in Chapter 2. While the study area comprises 25.2 million one-hectare cells, 18 million of these cells are active (containing natural vegetation), after masking out developed land, waterbodies, and bare rock.  TACA and LANDIS-II previously underwent validation and sensitivity analysis in North America (Mladenoff et al., 1993; Scheller & Mladenoff, 2004; Scheller et al., 2007; Nitschke & Innes, 2008; Nitschke et al., 2008, 2012; Simons-Legaard et al., 2015). Thus, given a paucity of validation data for Alberta, many model subsystems were not locally validated. Within LANDIS-II, two types of wildfire models are applied: (1) a statistical fire-spread model; (2) a semi-mechanistic cost-path fire-spread model incorporating fire weather inputs and landcover change to dynamically update site fuel conditions. The semi-mechanistic fire model was developed from forest fire data for Canada (Wagner, 1977; Van Wagner, 1987, 1989; Forestry Canada Fire Danger Group, 1992). For each fire model, a new optimization algorithm based on stochastic gradient descent (Widrow & Hoff, 1960) is applied for parameter tuning, overcoming a long-standing practical limitation of implementing large simulations (He & Mladenoff, 1999). The parameterization and simulation framework is shown below (Figure 5.1).   103   Figure 5.1 Model parameterization, fusion, and optimization of TACA-EM and LANDIS-II  TACA was run separately for each of the climate scenarios and biogeoclimatic regions (see previous chapter). Resultant tree species establishment probabilities were input into LANDIS-II with other required parameters for each scenario. Simulations were run for a duration of 50 years, with the first 10 years used for model spin-up, in order to produce empirical disturbance-related age class patterns. This produced more realistic-appearing initial stand conditions, given the absence of age class data for the region and the importance of fire in shaping age class patterns (Boychuk & Perera, 1997).   104  The LANDIS-II model was initially run at 500 m resolution to accelerate convergence of parameter optimization using an algorithm based on stochastic gradient descent (Widrow & Hoff, 1960), shown in yellow in Figure 5.1. The algorithm relies on principles similar to other iterative gradient-based optimization methods. Parameter values are updated in the direction and magnitude of reduced model error (e.g., using only positive first-derivatives), iteratively updated based on previous simulations. The optimization method is widely used alongside the backpropagation algorithm (Dreyfus, 1962; Linnainmaa, 1970) in deep learning for hyperparameter tuning (LeCun et al., 2015). Final model runs were conducted at 100 m resolution to balance computational cost and grain size needed to capture the effects of fine-scale disturbance patterns, approaching the precision limits of model design. The parameter optimization technique dramatically reduced the error of fire simulations ("#	= 0.96; ΔR2 = +0.14), returning values nearing Pareto optimality for the two model parameters without the computational expense of exhaustive grid search.  5.2.1 Historical Fire Regimes Regional fire regime parameters were derived from an analysis of Canadian National Fire Database (NFDB) spatial wildfire data, presented in Chapter 3. These data were produced from an analysis of aerial and satellite imagery together with field plot data.  5.2.2 Model Scenarios Fourteen 50-year simulations were run at an annual resolution, corresponding to four historical periods, three model configurations, and two extremes scenarios, to determine forest resilience under the persistence of past-century climate and fire trends. A 50-year simulation duration was  105  selected for its relevance to management timescales and balance between initial conditions and model behavior (e.g., equilibrium at 500-year timescales), as error is known to propagate over time in simulations, increasing uncertainty. Historical climate and fire conditions were classified into the following three 30-year periods: Pre-Suppression Era (1923-1952), Early Suppression Era (1953-1982), and Global Change Era (1983-2012), corresponding to changes in fire suppression, climate, and human activity. A Most Recent Decade (2003-2012) scenario was included to encapsulate current regimes, based on an observed inflection point in fire frequency and size.  With the exception of the Extremes scenarios, each of the four scenarios was run under three different model configurations: (1) Succession only (ao); (2) Succession with Base Fire (ao-bf); (3) Succession with Dynamic Fire (ao-dffs). This was done to control for the effects of climate and fire on forest structural and compositional change. For the two Extremes scenarios, Pre-Suppression Era fire regimes – the most severe burn rate – were applied to Most Recent Decade climatic conditions – the warmest conditions – to determine the relative contributions of climate and fire on forest compositional and structural change in the most extreme cases. The simulation scenarios (configuration and period combinations) are abbreviated as shown below (Table 5.1).        106  Table 5.1 Simulation scenario codes based on model configuration and period LANDIS-II Configuration Period Abbreviation Age-only succession 1923-1952 ao-1923-1952 Age-only succession 1953-1982 ao-1953-1982 Age-only succession 1983-2012 ao-1983-2012 Age-only succession 2003-2012 ao-2003-2012 Age-only succession with base fire 1923-1952 ao-bf-1923-1952 Age-only succession with base fire 1953-1982 ao-bf-1953-1982 Age-only succession with base fire 1983-2012 ao-bf-1983-2012 Age-only succession with base fire 2003-2012 ao-bf-2003-2012 Age-only succession with dynamic fire 1923-1952 ao-dffs-1923-1952 Age-only succession with dynamic fire 1953-1982 ao-dffs-1953-1982 Age-only succession with dynamic fire 1983-2012 ao-dffs-1983-2012 Age-only succession with dynamic fire 2003-2012 ao-dffs-2003-2012 Age-only succession with base fire Extremes ao-bf-extremes Age-only succession with dynamic fire Extremes ao-dffs-extremes  For each scenario, spatiotemporal metrics indicative of directional change at the landscape scale are tracked, including latitudinal and elevational variation in species regeneration and relative abundance, as well as changes to forest structure (inferred from site age classes) and area. A focus on climate and fire is intended to represent changes related to these two fundamental drivers of boreal forest ecosystems.   107  5.3 Results Adjusted for area, across all periods, the Boreal region had the shortest fire rotation period (FRP), followed by the Foothills and Rocky Mountain regions. The lower-elevation Parkland region had the longest FRP, followed by the Grassland region (Figure 5.2f). The Boreal shows the greatest area burned and, by a lower margin, greatest proportion of the study area (Figures 5.2d and 5.2c). FRP increased across the three periods, indicative of diminished burning (Figure 5.2e). Between the Pre-suppression and Global Change Eras, FRP lengthened the most in the Boreal and Foothills regions while declining the most in the Parkland and Rocky Mountain regions (Figure 5.2b). An analysis at the finer scale shows an acute increase in the FRP for the Peace River Parkland and Dry Mixedwood subregions, while the Upper Foothills subregion declined. All higher elevation subregions showed intensifying burning indicative of warming (Figure 5.2a).   108   Figure 5.2 Historical fire statistics by region and time period; change metrics are computed between the periods 1923-1952 and 1983-2012: (a) Fire rotation period (FRP) change by subregion; (b) FRP change by region; (c) proportion of study area by region; (d) area burned by region; (e) FRP by period; (f) FRP by region; Montane region = Rocky Mountain; red = decline; green = increase (a) (b) (c) (d) (e) (e)  109  The stochastic gradient descent-based optimization algorithm greatly improved fire model calibration ("#	= 0.96; Δ"# = +0.14), yielding simulation results closely matching observations from the Canadian National Fire Database. Based on a visual analysis of simulation results for maximum cohort age classes resulting from fire region parameterizations, the boreal region exhibited the greatest fire-related structural (i.e., mean and standard deviation of site age class) change across scenarios. Frequent large fires during the Pre-Suppression Era produced a homogeneous structural patchwork of forests, while frequent small fires in the two most recent scenarios produced a diffuse forest landscape age pattern and decline in area burned, corresponding to observed empirical changes.  While base fire better fit aggregate 30-year statistics for observed fire regimes, time-series comparisons between simulated and observed regimes showed that dynamic fire better captured the mean and variability for both annual fire frequency and area burned. Wavelet spectra for annual 1-D time-series showed higher and lower wavelet dissimilarity (Rouyer et al., 2008) for dynamic fire area burned and fire frequency, respectively, compared to base fire (Table 5.2). Wavelet spectra decompose the variance of 1-D time-series over a 2-D time-frequency plane and can be used to analyze the covariance of non-stationary signals with noise (Rouyer et al., 2008).        110  Table 5.2 Simulated and observed fire time-series statistics; WD = wavelet dissimilarity Period Simulation Meanarea SDarea rarea WDarea Meanfreq. SDfreq. rfreq. WDfreq. 1923-1952 Base Fire +70,282 +375,027 -0.10 49.594 +696.8 +82.9 0.42 46.976 1923-1952 Dynamic Fire -18,385 -168,825 -0.14 48.496 +54.3 -8.8 0.05 39.841 1953-1982 Base Fire -27,265 -66,458 0.25 46.235 +357.6 +17.5 -0.29 42.179 1953-1982 Dynamic Fire -3,338 -59,027 0.07 48.456 +39.9 -2.7 0.11 40.394 1983-2012 Base Fire -20,689 -51,047 0.21 47.059 +202.3 -5.7 0.68 38.613 1983-2012 Dynamic Fire -1,529 -46,255 -0.02 47.939 +55.4 -14.9 0.17 36.923 2003-2012 Base Fire -18,363 -40,783 -0.06 15.150 +352.4 -4.6 0.07 14.528 2003-2012 Dynamic Fire -5,121 -31,994 -0.58 15.377 +152.6 +42.8 0.13 14.360  In the dynamic fire model results, iteratively updated landscape fuel conditions, based on 2012-2013 fire weather, reduced fire frequency and area burned in each scenario compared to base fire. For the most severe fires, in the Pre-Suppression Era, base fire model results showed large fires during the initial simulation year and relatively flat activity until simulation year ~ 45. The temporal distribution of fire frequency was more stable and realistic in the dynamic fire scenarios due to the fuel-limited semi-mechanistic model design, while base fire exhibited brute-force application of initial model parameters (Figure 5.3c).   111   Figure 5.3 Simulated annual fire regimes by period (above) and scenario (below): (a) annual simulated area burned by period; (b) annual simulated fire frequency by period; (c) annual simulated area burned by scenario; (d) annual simulated fire frequency by scenario; refer to Table 5.1 for scenario codes  TACA model results indicate that conditions for tree regeneration were increasingly suboptimal, declining across the 1923-2012 study period (Chapter 4). Optimal regeneration conditions occurred most frequently in the Rocky Mountain, Parkland, and Foothills regions. The Boreal region remained the most stable, while Montane regions maintained higher overall regeneration potential. An increased frequency and depth of modeled drought, due to changes to soil water balance, most limited regeneration conditions in the Grassland region, where fluvial and aeolian (a) (b) (c) (d)  112  soils are abundant. These results were critical to changes observed in LANDIS-II simulations, due to interactions between fire and regeneration.  LANDIS-II model results showed a decline in forested area for the most severe fires and an increase in forested area for mild disturbance scenarios. Forest decline indicates a failure to regenerate post-disturbance and/or an annual rate of burning outpacing the rate of regeneration. Resprouting and serotinous species regenerate post-fire each simulation year, the latter requiring that seed availability and establishment conditions be met. An initial rapid increase in forested area for most scenarios is attributable to recruitment into sites classified as open (i.e., untreed active cells) in the initial landscape. The maximum total forested area was 38% greater than the minimum area, resulting from differences in both fire regime severity and regeneration suitability. For the Pre-Suppression Era and Extremes scenarios, base fire produced the largest disturbances and thus the greatest change in forested area. While greater fire disturbances removed more species-age cohorts, warming climatic conditions reduced post-fire regeneration, further diminishing the forested area (Figure 5.4).   113   Figure 5.4 Simulated annual total forested area (sum of 1 ha pixels) by year and scenario; includes forests of all age classes; refer to Table 5.1 for scenario codes  While warming reduced the likelihood of regeneration over the simulation period, variation in fire regimes produced more rapid changes, with the interaction of the two processes explaining changes in forested area. Results showed minor declines in the abundance of Picea, Larix, and Betula genera, and minor increases in Pinus, across the simulation period. Species richness declined for all scenarios, declining the most under more severe disturbances (Figure 5.5a). The mean number of age classes present at one-hectare sites followed similar patterns, but recovered over time for succession-only scenarios (Figure 5.5b). The central tendency (i.e., median) of the spatial distribution of forests mildly increased in latitude and elevation under the most severe disturbances. While the mean forest latitude increased for all scenarios modeled, mean forest elevation was generally flat or declined (Figures 5.5c and 5.5d).   114   Figure 5.5 Individual and ensemble (i.e., simulation mean) model results by scenario and species: (a) species richness by scenario; (b) age class count by scenario; (c) mean forest latitude by scenario in WGS84 decimal degrees; (d) mean forest elevation by scenario; (e) incremental mean forest latitude change by species in WGS84 decimal degrees; (f) incremental mean forest elevation change by species; refer to Table 5.1 for scenario codes (a) (b) (e) (f) (c) (d)  115  A downhill mean forest distribution shift was shown for the Global Change and Most Recent Decade periods (Figure 5.5d). This is explained by an increase in high-elevation burning and reduction in regeneration suitability here, due to modeled water holding capacity limitations of rocky soils for the Montane region. Available water storage capacity was the most important model predictor of regeneration, as described in Chapter 4. In the Pre-Suppression and Extreme scenarios, the spatial distribution of forests shifted uphill on average due to high fire mortality rates at low elevations that surpassed the rate of regeneration. The difference in mean forest elevation between the two scenarios indicates that warming climatic conditions slowed rather than accelerated an uphill mean distribution shift (Figure 5.5d).  Latitudinal and elevational changes were produced by the spatiotemporal distribution of fire mortality more than climate over the 50-year simulation period. This is evidenced by large incremental changes in species elevation and latitude in the initial simulation years (Figure 5.5e and 5.5f), when disturbances were greatest in magnitude. While this spin-up period is often omitted from simulation studies, it is shown here to make model behavior transparent. The weaker effect of warming is also evident in a comparison of Extremes scenarios with Pre-suppresion Era fire scenarios, which differed only in climate. Species responses varied in mean latitudinal and elevational distribution shifts resulting from fire. Rather than attributable to life history strategy or functional type, differences in species response appear primarily attributable to the initial location of species. This is evidenced by the observation that the greatest mean species distribution shifts were shown by species endemic to the boreal region, in the northeastern portion of the study area, where the rate of burning was greatest. These changes were particularly evident for the large fires of the base fire scenarios (Figures 5.5e and 5.5f).  116  A reduction in the annual area burned slowed changes to the central tendency of the spatial distribution of forests. In the full ensemble results (the mean of all scenarios), the mean latitude of forests shifted mildly poleward while the mean elevation was static (mean latitude = +111 m yr-1; mean elevation = -0.02 m yr-1). All periods showed agreement in a mean latitudinal increase in forests, which may partially be explained by recruitment during the model spin-up period. Forest composition remained stable under the two most recent scenarios (Global Change and Most Recent Decade), but less stable during previous scenarios (Pre-Suppression and Early Suppression) due to greater disturbances. Extreme scenarios combining the most area burned with the warmest climatic conditions showed the most rapid changes in forest demographics (Figure 5.5b) and composition (Figure 5.6).   117   Figure 5.6 Simulated annual incremental change in species abundance by scenario; refer to Table 5.1 for scenario codes  Ensemble model results showed agreement in forested area decline (Figure 5.7a). An analysis of simulated annual mean incremental changes in area burned, fire frequency, and, forest latitude and elevation (Figure 5.7b) using Spearman’s rank correlation coefficient (ρ) to probe for monotonocity showed that latitudinal and elevational changes were strongly correlated (ρ = 0.71), positively correlated with area burned (ρ = 0.49; ρ = 0.34), and negatively correlated with fire frequency (ρ = -0.34; ρ = -0.50). Total forested area was negatively correlated with fire frequency more than area burned (ρ = -0.54; ρ = -0.11) (Figure 5.7c).  118   Figure 5.7 Mean annual simulated forest change: (a) total forested area for all scenarios with a 95% confidence interval; (b) re-scaled forested area, latitude, elevation, area burned, and fire frequency for all scenarios; (c) Spearman’s ρ for re-scaled metrics; (d) Spearman’s ρ for autocorrelations of re-scaled metrics; Abun = forest area; Lat = forest latitude; Elev = forest elevation; Area = area burned; Freq = fire frequency  The periodicity (i.e., autocorrelation) of elevational changes was strongly correlated with changes to fire frequency (ρ = 0.90). The periodicity of changes in total forested area was negatively correlated with changes to area burned, fire frequency, and, latitude and elevation (ρ = (a) (b) (c) (d)  119  -0.32; ρ = -0.31; ρ = -0.06; ρ = -0.24). The periodicity of changes in mean forest latitude and elevation were positively correlated with changes in area burned and fire frequency, with forest elevation and fire frequency showing the highest correlation (Figure 5.7d).  During the model spin-up decade, where age class distributions were initially homogeneous, shifts in distribution occurred at their most rapid rate. This result was produced by a combination of high severity boreal fires given an even availability of fuels and frequent initial recruitment events. Given an even initial age class distribution, the sexual maturity of trees had equally even coverage, facilitating seed dispersal. These spin-up patterns are critical to note for their role in influencing the interpretation of simulation results. Following the 10-year model spin-up period, all scenarios with fire showed a mild decline in forested area (Figure 5.4).  5.4 Discussion The combination of reduced regeneration potential and more severe fires produced a significant reduction to the total forested area in simulations. This suggests that declining modeled regeneration potential together with reduced area burned in the Global Change Era may potentially diminish the ability of tree species to track the velocity of warming. The simulated mean northward shift in forest distribution was 319 m yr-1 slower than the velocity of climate change (Loarie et al., 2009; Hamann et al., 2015), with agreement shown across simulations. Even under the highest burning and thus migration rates, northward forest migration lagged 291 m yr-1 behind warming. As exhibited by the Extremes scenarios, migration rates were highest in periods where disturbance rates were the most severe, despite cooler temperatures. This is indicative of reduced competitive limitations to migration.  120  In the simulations, the central tendency of the spatial distribution of forests varied in response to changes in climate and fire, as did species and age-classes. Changes in the distribution of tree species and forests were primarily attributable to fire. Forests tended to shift toward higher latitudes and lower elevations across simulation scenarios, while higher fire mortality reduced species and age-class diversity. The mean of the spatial distribution of forests increased in elevation and latitude when disturbance severity was highest, facilitating more rapid migrations with the removal of stands. Although shifts in mean spatial distribution were mild, they are notable given the simulation period of fifty years, short relative to the duration of succession processes. Despite being confined within a fixed study area at a regional scale, changes in the mean spatial distribution of forests may be indicative of broader migrational patterns. Changes in the mean spatial distribution of forests are potentially more robust than range minima or maxima as indicators of migrational change, given the larger sample sizes involved and reduced sensitivity to episodic events produced by leptokurtic (heavy-tailed) seed dispersal kernels.  In addition to fire suppression (Cumming, 2005), forest demographics may partially explain the empirically observed increase in fire rotation period in Alberta (Zhang et al., 2015), due to the bottom-up nature of fire mortality (i.e., younger cohorts are more susceptible to mortality for a given fire intensity, limiting fire crowning through ladder fuels in the absence of young trees). Fire suppression, forest aging, reduced recruitment rates, and related fire energetic constraints may together explain the modest increase in area burned under warming (Kelly et al., 2013; Héon et al., 2014; Zhang et al., 2015). This dynamic was reproduced in simulations with the elimination of young trees during the model spin-up period, yielding older and less species diverse stands and a subsequently reduced rate of burning. Simulation results also suggest that,  121  while secondary to fire, declining regeneration potential may play a role in the decline in forested area observed for the Global Change Era in the adjacent montane Western United States (Cohen et al., 2016).  Some studies have indicated increased forest carbon sequestration under global change conditions (Chen et al., 2006; Fang et al., 2014), while a recent tree-ring analysis indicates no effect of warming on biomass increment in the Canadian boreal (Girardin et al., 2016). Current projections do not take into account expected changes to fire regimes and tree regeneration under warming. Empirical evidence shows diminished recruitment rates for the region (Zhang et al., 2015), in agreement with TACA-GEM model results, while burning is widely projected to increase under warming in the short-term (Flannigan et al., 2001; Groot et al., 2003), before being limited by energetic constraints (Héon et al., 2014). The presented simulation results indicate that the interaction of higher burn rates and diminishing regeneration potential may offset any potential gains to carbon storage over centennial time-scales by reducing the forested area. This dynamic may also offset increases to forest biomass attributable to stand ageing (Huang et al., 2013; Uyeda et al., 2017).  Diminished resilience, or capacity of forests in their current state to respond elastically to perturbation, is evidenced by changes to regeneration, which regulates forest change at a base ecological level. Although variability in interspecific regeneration potential was evident for the region, the dominant regeneration signal across the study period was a long-term decrease in forested area, in agreement with recent ground plot- and remote sensing-based findings on recruitment and forest cover (Bond-Lamberty et al., 2014; Zhang et al., 2015; Cohen et al.,  122  2016). While Zhang et al. (2015) attributed reduced growth and recruitment rates in western Canada primarily to competition and secondly to climate, their analysis focused on undisturbed sites, making growth and recruitment rates primarily a function of stand development.  Meanwhile, fire is the dominant driver of mortality in boreal forests (Rowe, 1961; Rowe & Scotter, 1973; Bond-Lamberty et al., 2007), typically providing sites for recruitment (Clark, 1991; Lavoie & Sirois, 1998; Johnstone et al., 2010; Bond-Lamberty et al., 2014), while competition and climate cannot be disentangled. Competitive or mutualistic interactions are a function of climate space, evident in phenotype plasticity (i.e., gene expression) and evolutionary legacies (Aitken et al., 2008). TACA-GEM model results presented herein suggest an alternative interpretation of the results of Zhang et al. (2015), as model results indicate that diminished recruitment rates for recent decades in the western Canadian boreal are due to a climatically-induced decline in regeneration potential.  Combined with available empirical evidence for Canada (Leithead et al., 2012; Fisichelli et al., 2014; Zhang et al., 2015; Cohen et al., 2016), simulation results suggest that a mild decline in forested area observed for some parts of intermountain western North America in recent decades may be attributable to a combination of increased fire regime severity and diminished regeneration potential. Future studies should explore the role of disturbance, regeneration, and demographics in changes to forested area observed for western North America. Empirical studies should focus on biome interfaces experiencing the highest rate of forest change. Simulation studies should expand beyond species ranges to incorporate shifts at the edge of range limits. Improved spaceborne monitoring, data assimilation, and landscape genetics analyses will be  123  important to understanding these dynamics, granting ecological forecasting greater predictive power.  5.5 Limitations Similar to TACA-GEM, the LANDIS-II simulations presented herein rely on parameters from continental- or national-scale species compendiums (Burns & Honkala, 1990; Farrar, 1995a; Klinka et al., 2000). The previously described fire data was utilized for fire model parameterization. Simulations used landcover maps developed from both remote sensing (Wulder et al., 2007; Agriculture and Agri-Food Canada, 2012) and species distribution models (Gray & Hamann, 2012). Model spin-up was used to produce an initial stand age distribution map, as this information was unavailable for Alberta. Simulations were conducted at annual and 1 ha resolution, whereby species-age cohorts were horizontally homogeneous within stands. Direct validation of LANDIS-II simulations was limited to the two classes of fire model.  The LANDIS-II model contains a number of simplified representations of forest dynamics. The effect of competition on regeneration in LANDIS-II is a critical area for future validation studies. The model core is limited to simple assumptions regarding competition and establishment, whereby light required for regeneration is inversely proportional to the shade tolerance of existing trees. This does little to explain vertical stratification of phototrophic or optical types in forests (Gamon, 2014), which may be corrected by new model formulations. Nevertheless, previous studies using gap models have shown that such simplistic representations of light have little effect on succession (Deutschman et al., 1999). Many other model functions are logic-based  124  or game-theoretic in relation to vital attributes (Noble & Slatyer, 1980), with variation represented through stochasticity, facilitating efficient computation at the cost of model realism.  The base fire model contains similar simplifications, as fire regimes can only have a log-normal fire size distribution and interactions with weather and fuels are not represented. While the dynamic fire model improves upon these shortcomings by adding fire weather and dynamic changes to fuels, reliable fuels parameters may be unavailable for some regions. The main factor limiting the development and application of LANDIS-II and other forest landscape models is the availability of empirical data needed to calibrate and validate each of the model components in different regions of the world. Advances in the accuracy of remote sensing classification and regression models will therefore be central to future model development, as such broad spatiotemporal information is otherwise difficult to attain.   125  Chapter 6: Airborne Laser Scanning Models of Canopy Light Transmission  6.1 Introduction The light environment is a critical factor for the structure and function of vegetation communities (Monsi & Saeki, 1953, 2005; Dengel & Grace, 2010; Gamon & Bond, 2013; Gamon, 2014). In northern forests, tree crown geometries are well suited to a low solar elevation, occluding less light from neighboring trees (Aakala et al., 2016). Understory light is an important factor in the successional trajectory of forests through vegetation establishment and growth, making it a critical parameter required to forecast forest ecosystems (Canham et al., 1999). Although understory light is a function of quantifiable variation in local stand geometry, topographic position, atmospheric conditions, and solar position, it remains difficult and costly to measure. While the importance of understory light has long been understood (Monsi & Saeki, 1953), it is notoriously difficult to measure with remote sensing methods. The advent of angular remote sensing technologies such as airborne laser scanning LiDAR (ALS) and photogrammetric computer vision have made it possible to map canopy light transmission as a proxy for understory light by assuming beam canopy penetration equivalent to a Poisson process. Monsi & Saeki (1953) were the first to represent contact frequency as a Poisson process, equivalent to the Beer-Lambert law (Hancock, 2010).  Due to limitations in spaceborne sensor resolution and coverage, given the large footprint and fixed path of single quantum LiDAR sensors such as IceSat GLAS, understory light is difficult to retrieve for broad scales. NASA’s new Global Ecosystem Dynamics Investigation (GEDI) beam-splitting quantum LiDAR instrument for the International Space Station, while improved in  126  coverage, will not likely resolve this fundamental limitation due to its 25 m footprint and limited sampling area (Dubayah et al., 2014; Coyle et al., 2015). Despite recent advances in deriving forest canopy geometry from commercial passive optical spaceborne sensors (Shean et al., 2016), active optical airborne LiDAR systems remain optimal instruments for estimating understory light conditions at the landscape scale, as the aggregate of fine-scale variation. This is due to their precision, coverage, and ability to collected waveform returns, allowing direct measurement of canopy light transmission with multi-angular pulses of near-infrared photons. While atmospheric conditions are known to effect the quantity and quality of understory light (Dengel et al., 2015), I focus on canopy light transmission (T) metrics best captured by LiDAR.  Airborne laser scanning (ALS) is used throughout boreal forests and contains detailed information on forest geometry at scales ranging from stands to landscapes. Recent studies have demonstrated a number of ALS metrics of forest structure over large areas, from area-based to individual tree-based approaches (Lefsky et al., 2002; Popescu et al., 2002, 2004; Zimble et al., 2003; Coops et al., 2007; Hilker et al., 2012; Kaartinen et al., 2012). Studies have also leveraged the increased availability of ALS to estimate understory light regimes in northern forests. Using point-based quantum sensors of photosynthetic photon flux density (PPFD) (Barnes et al., 1993), convex spherical densiometers (Lemon, 1956), or hemispherical photography for ground-level validation, these studies have retrieved a number of relevant metrics from ALS, including canopy transmittance, canopy gap fraction (Po), vertical canopy cover (VCC), angular canopy closure (ACC), effective leaf area index (Le), apparent clumping index (Ωapp), stem density, and basal area (Parker et al., 2001; Popescu et al., 2002; Morsdorf et al., 2006; Richardson et al., 2009; Kaartinen et al., 2012; Alexander et al., 2013; Musselman et al., 2013; Korhonen &  127  Morsdorf, 2014; Parent & Volin, 2014; Eysn et al., 2015; Moeser et al., 2015). Such individual metrics are desirable for their simplicity and physical basis, which aid interpretation efforts.  Many of these ALS metrics may be used to estimate canopy light transmission, individually or in combination. Some of the earliest, simplest, and most effective metrics of ACC and Po are based on the ratio of ground-to-canopy returns (Riaño et al., 2004; Morsdorf et al., 2006; Solberg et al., 2009; Korhonen et al., 2011). The metric of Solberg et al. (2009) differs in that it corrects for pulses that have returns from both the canopy and ground, assigning a partial cover value to these. A pulse intensity-based approach was designed to correct for two-way transmission loss (Hopkinson & Chasmer, 2007), also novel for utilizing target reflectance information. More recent approaches provide hemispherically projected LiDAR metrics comparable to ground measurements (Varhola et al., 2012; Parent & Volin, 2014), while others further utilize geometric operations to improve the estimation of cover (Alexander et al., 2013). An opportunity exists to improve both simple transmission metrics and advanced representations of forest geometry to estimate cover. While future studies should apply supervised 3-D convolutional neural networks for this task, whereby kernels function similar to voxelization, I focus on simple geometric operations here.  Although these studies show strong agreement with ground measurements for a number of ALS metrics of forest structure, many challenges remain. Models of canopy light transmission are often based on ray tracing (Disney et al., 2000), which can be understood as a form of synthetic LiDAR, or derived from simple canopy metrics, such as Lorey’s canopy height or leaf-area index (Niinemets & Anten, 2009). These metrics lack connection to ecosystem processes, are  128  computationally expensive, or do not fully utilize three-dimensional data for sun-view geometry. Radiative transfer models based on ray-tracing may improve the precision of understory light regime estimates at the landscape scale (Reich et al., 2012; Moeser et al., 2014; Gastellu-Etchegorry et al., 2015). Yet, ray-tracing methods typically require high-point-density data from cutting-edge ALS or terrestrial laser scanning (TLS) LiDAR systems, delivered with rich ancillary data beyond standard (x, y, z, intensity) information. Such methods are also computationally demanding, making them time-consuming to apply.  Simple return-ratio approaches of quantifying canopy radiation attenuation may offer improved functioning with low-point-density data, better facilitate wall-to-wall mapping, and be more comparable to historical ground-based methods. These ALS approaches are comparable to methods used in the synthetic aperture RADAR community to estimate forest aboveground volume, such as the semi-empirical Water Cloud Model (Attema & Ulaby, 1978; Graham & Harris, 2003). Hence, ALS canopy radiation attenuation approaches may be extensible to spaceborne RADAR sensors for global forest change studies, despite substantial sensor differences.  Calculations of forest structural parameters from ALS are often distinct from those of traditional ground methods, due to differences in sampling bias, lending to variation in terminology and methodology. Canopy light attenuation calculations based on ALS often assume canopy light transmission (T) equal to canopy gap fraction (Po), each inverses of vertical canopy cover (VCC) and angular canopy closure (ACC), as provided in the following equation (Morsdorf et al., 2006; Hopkinson & Chasmer, 2009; Gonsamo et al., 2013):  129  T = Po = 1-ACC = 1-VCC  Traditionally, VCC quantifies the 2-D areal canopy coverage, while T is a function of incident photosynthetically active radiation (PAR), fraction of absorbed PAR (fPAR) by leaf absorptance, leaf transmissivity, and scattering, incorporating leaf geometry, position, and orientation effects on the bidirectional reflectance distribution function, or BRDF (Gastellu-Etchegorry et al., 1996). While the equivalence of T and Po holds in the absence of detailed information, the two metrics remain distinct, providing different – though complementary – information (Gonsamo et al., 2013).  Although ALS LASER pulses are typically emitted at narrow zenith angles less than 20 degrees from nadir, they provide an empirical test of angular light penetration through the canopy, making ALS suitable for estimating Po. Meanwhile, VCC is often calculated from ALS for each cell using narrow incoming zenith angles between 0 and 10, opposite to scan and beam divergence source angle (Weiss et al., 2004; Morsdorf et al., 2006). Hence, the measurement of VCC with ALS is often a field-of-view, or scope, function (Lee et al., 2008), rather than a true measure of 2-D areal coverage (although simple grid-based methods exist), making it sensitive to neighborhood effects. Here, as with leaf area index (L), gridded ALS-derived metrics (e.g., the ratio of canopy first-returns to ground first-returns) are more compatible with the classical definition of VCC. Similar challenges of sampling bias have been reported for gap fraction (Po) estimates derived from terrestrial laser scanning (TLS) LiDAR (Vaccari et al., 2013).   130  Variation in ALS metric methodology relative to ground methods is primarily due to four attributes of these systems: ALS is (1) active, (2) narrow-angled, (3) exhibits top-of-canopy bias, and (4) historically had point densities as low as ~ 1 point/m2. These differences are also attributable to the desire to harmonize LiDAR forest structural metrics with historical ground-truthing field methods. Modern ALS and TLS systems provide more precise, accurate, and detailed information about forest geometry than ground-based methods used for calibration and validation. While ground methods such as quantum sensor measurements of PPFD provide greater precision, their generalizability is poor given the complexity of dynamics that drive variation in values (e.g., dynamic changes to solar activity, atmospheric conditions, leaf optical properties, and leaf orientation). As it is not a direct measurement technique, photon flux measurements may be strongly affected by noise unrelated to forest geometry.  The objective of this study was to develop new ALS metrics and regression models of T that can be extended to forest landscape models to simulate understory irradiation. Four new ALS metrics for retrieving T are presented, including the hemispherical Voronoi gap fraction (Phv), point-density normalized gap fraction (Ppdn), and their inverses, hemispherical Voronoi angular canopy closure (ACChv) and point-density normalized angular canopy closure (ACCpdn). While Phv and ACChv are intended to improve estimates of canopy light interception from LiDAR with varying sensor properties, Ppdn and ACCpdn are intended to reduce sensor effects by normalizing hemispherical sectors by their surface area and the overall point density. These are the key innovations provided herein.   131  The four new hemispherical canopy metrics (Phv, Ppdn, ACChv, and ACCpdn), nine vertical canopy cover (VCC) metrics, twelve stem and crown metrics, and five other metrics, for a total of 30 metrics (Table 6.1), were validated against traditional coarse-resolution convex spherical densiometer ground measurements of angular canopy closure (ACC), representing the inverse of T. The Phv metric was applied using four different hemispherical lens geometries at canopy height thresholds varying from one meter to five meters in 0.25 m steps, for a total of 68 different Phv configurations for each plot. 132  Table 6.1 Understory light metrics calculated in this study, explained in detail in the following section New Metrics  Vertical Canopy Cover Metrics Tree and Crown Metrics Other Metrics Hemispherical Voronoi gap fraction (Phv) Above-height cover index (VCCaci) Moving window n trees (ITCmw) Beer-Lambert Law gap fraction (Pbl) Point-density normalized gap fraction (Ppdn) Beer’s Law-modified-intensity-return ratio (VCCbl) Moving window crown area (Gmw) Beer-Lambert Law effective leaf area index (Lebl) Hemispherical Voronoi angular canopy closure (ACChv) Cartesian Voronoi fractional cover (VCCcv) Hierarchical moving window n trees (ITChmw) Ground-to-total-return ratio effective leaf area index (Ler) Point-density normalized angular canopy closure (ACCpdn) First-echo cover index (VCCfci) Hierarchical moving window crown area (Ghmw) Contact frequency effective leaf area index (Len)  Canopy-to-total-first-return ratio (VCCfr) Watershed n trees (ITCwat) Apparent clumping index (Ωapp or ACI)  Intensity-return ratio (VCCir) Watershed crown area (Gwat)   Canopy-to-total-pixel ratio (VCCp) Hierarchical watershed n trees (ITChwat)   Canopy-to-total-return ratio (VCCr) Hierarchical watershed crown area (Ghwat)   Solberg’s cover index (VCCsci) Distance and direction to canopy (Cdist, Cdir)    Distance and direction to tree crown (Crdist, Crdir)   133  6.2 Methods Vegetation ground plot measurements were collected in the Hinton Forest Management Area in the early 2000s during summer (leaf-on) conditions (Nielsen et al., 2004, 2006; Nielsen, 2005). Angular canopy closure (ACC), and thus canopy gap fraction (Po = 1-ACC), was measured from breast-height using a convex spherical densiometer. Densiometer measurements were recorded for each of the four cardinal directions and averaged for each plot (Lemon, 1956; Nielsen, 2005). ALS sorties were conducted in the mid-2000s using an Optech ALTM 3100, detailed in section 2.5. For model development, 100 field plots containing both densiometer measurements and complete ALS coverage were randomly sampled. Each plot contained one value for ACC, measured at the plot center, each representing different levels of forest cover. The wide distribution of ACC values represented is evident in Figure 6.5. Following model development, the top metric was validated for all 950 field plots.  6.2.1 Pre-processing Using LAStools (Isenburg, 2015), the ALS tiles were height-normalized before extracting circular field plots with a 50 m radius, based on previous research exhibiting a saturation of edge effects below this threshold (Zhao & Popescu, 2009; Alexander et al., 2013). Normalization consisted of extracting the ground plane from the point data and subtracting the Delaunay triangle-position elevation from each return’s z value. LAStools implements an optimized variant of the best available ground plane extraction algorithm (Axelsson, 1999; Maguya et al., 2014), modified to include Delaunay streaming or triangulated irregular network (TIN) streaming (Isenburg et al., 2006a,b,c) for improved computational efficiency on large datasets. Maximum point height was filtered at 40 m, based on local tree species ground measurements. The ALS  134  plots were processed with a series of point cloud metrics implemented in custom R scripts (R Core Team, 2015), described below. Finally, the top performing ALS metric (VCCfci) was applied to an expanded set of ALS plots to analyze variation related to species composition and age class.  6.2.2 Spike-free Canopy Height Model Algorithm One step of pre-processing required the generation of continuous canopy height models (CHMs) without smoothing- or sampling-related artifacts. This was due to pitting in the simple gridded maxima CHMs given a mean point density below 2 points m-2, known to affect the accuracy of tree detection. In order to improve CHM inputs for individual tree crown (ITC) detection, a layered 2-D adaptation of the spike-free CHM algorithm (Khosravipour et al., 2014, 2016) was implemented. The approach uses vertically stratified 2-D Delaunay triangulation with barycentric interpolation along z-values for triangulated irregular network (TIN) generation. The maximum of resulting vertical surface model layers or slices is then computed, yielding a CHM with reduced spiking.  Equivalent in output, the new algorithm vertically stratifies all returns into user-defined windows or slices to constrain Delaunay triangulations, which can be absolute distances or height percentiles. A 2 m height threshold was used with steps at 5, 10, and 15 m, as in the pit-free CHM work (Khosravipour et al., 2014). Delaunay triangles with edge lengths exceeding a user-defined threshold are filtered to limit smoothing, set to the default value. The final CHM consists of continuous height maxima along raster grid points. This adaptation takes advantage of vertical stratification to generate non-overlapping points necessary for 2-D Delaunay triangulation. The  135  theoretical advantage over the 3-D Constrained Delaunay approach (Khosravipour et al., 2016) is chiefly computational.  At the heart of barycentric interpolation is the local weighted average (Shepard, 1968; Warren et al., 2006). The predicted z-value of a point within a Delaunay triangle is the weighted average of each of three known z-values, with weights determined by the distance to nodes. Given the three barycentric coordinates (x1, x2, x3) of a triangle and the interpolated point x within its interior, barycentric interpolation performs the following to compute the z-value of x:  ! " ≈ $%! "%&%'(   Here, $% > 0 and	 $% = 1, where $% is the barycentric coordinate of triangle point i, used as weights in interpolation. Given a linear function	! " = ./" + 1, the interpolation is exact and able to compute in either a piecewise or highly parallel framework, requiring little memory overhead. 2-D barycentric interpolation benefits from its simplicity compared to streaming 3-D Delaunay triangulation methods. Yet, a caveat exists in that vertically stratified point subsets fed into 2-D barycentric interpolation for hierarchical CHM generation should have no interior overlap. Unlike many other 2-D interpolation functions, barycentric interpolation functions with irregularly spaced sets are common in LiDAR remote sensing. For regularly spaced sets (e.g., raster grids), simpler interpolation methods exist. While this adaptation is chiefly computational in innovation, it is nonetheless an important contribution in this work. These and other functions are provided in the gapfraction package for R (  136  6.2.3 Hemispherical Voronoi Gap Fraction The hemispherical Voronoi gap fraction (Phv) metric represents Po as the areal coverage of Voronoi tessellation cells above a given canopy height threshold from the perspective of standing at the plot center and looking toward the zenith, identical to a traditional hemispherical photograph. The plot center at 3-D local Cartesian coordinate (x=0, y=0, z=0) is set equal to the hemispherical camera model principal point, or intersection of the optical axis and image plane. The ground plane is set equal to the image plane, with the optical axis pointing skyward at the zenith. Once the LiDAR data is pre-processed into normalized heights and local Cartesian coordinates, the first step is to re-project the LiDAR points into image coordinates based on a model of a fisheye (hemispherical) lens.  The projection of a 3-D point Xw = (Xw, Yw, Zw)T into a 2-D image sensor coordinate x’j = (x’j, y’j) requires a mathematical model of a fisheye lens, consisting of a series of transformations with extrinsic and intrinsic camera parameters (Ray, 2002; Abraham & Förstner, 2005). The extrinsic parameters map the real-world coordinates into camera coordinates, while the intrinsic parameters map the camera coordinates onto the image plane. Typically, a distortion model is used to explicitly include optical system discrepancies; this is necessary for improving performance in computer vision applications based on epipolar geometry, such as stereo vision and structure-from-motion (Wallach & O’Connell, 1953; Ullman, 1979; Bolles et al., 1987; Cornelis et al., 2002), but is unnecessary here. This work focuses on the ideal map of the 3-D image sphere projected onto the 2-D image plane, given a virtual fisheye lens without distortion. The image coordinate calculations take the following form (Abraham & Förstner, 2005):   137  x’ = cx cos(φ) r*(θ) + x’H y’ = cy sin(φ) r*(θ) + y’H  Here, cx and cy are the principal distances (this allows for non-square pixels), φ and θ are the azimuthal and polar angles, respectively, r*(θ) is the radial projection function, or mapping function, and, x’H and y’H are the coordinates of the principal point, or the intersection of the optical axis and the image plane. The distortion model parameters used for real-world lenses, Δx’ and Δy’, typically added to the end of their corresponding equations, are omitted. To change to a different hemispherical camera model, the radial projection function can be simply modified.  The classical pinhole camera is described by the perspective projection function of the form r’ = c tan(θ), where r’ is the radial distance from the principal point on the image plane and c is the principal distance, a function of the focal length and focal distance (Fourcade, 1928). Fisheye lenses generally use one of four common radial projection functions: stereographic, equidistant, orthogonal, and equisolid angle. Most consumer fisheye lenses use the equisolid angle projection and have a full-frame design (the picture angle is 180° only when measured diagonally and is smaller elsewhere), while scientific lenses utilized for hemispherical photography typically use the equidistant projection, where the radial distance is equal to the polar angle, and have a circular design (the full 180° hemisphere is recorded within the image plane). Here, all four projections are implemented with a circular design in the gapfraction package for R. The radial projection function, or mapping function, for each projection is as follows (Ray, 2002; Abraham & Förstner, 2005):   138  r’ = c tan(θ/2)   Stereographic projection           r’ = c θ              Equidistant projection                                   r’ = c sin(θ)            Orthogonal projection           r’ = c sin(θ/2)                       Equisolid angle projection  To transform the real-world coordinates to camera coordinates, the normalized point clouds were projected into 3-D local Cartesian coordinates with an (x, y, z) tuple centroid of (0, 0, 0). A function was developed that allows this calculation without plot center geolocation information to ease LiDAR plot processing. The function sets the midpoint of the vector of X and Y values to half of the range, as shown below:   2′ = 	2 −	2567 −	 2582	–	25672   ;′ = 	; −	;567 −	 ;582	–	;5672   To transform the camera coordinates into image plane coordinates, the 3-D local Cartesian coordinates are projected into 2-D polar coordinates (azimuth angle and radial distance, or φ and r) before projecting the 2-D polar coordinates into 2-D Cartesian space with standard trigonometric equations, where x’ = r cos(φ) and y’ = r sin(φ). The calculations were implemented in their normalized image plane form (Abraham & Förstner, 2005), as the 3-D local Cartesian coordinates were normalized to their true distance values in meters, rather than the typical unit sphere. This was done to preserve 3-D Cartesian distances for calculations that do not require hemispherical or image plane projections.  139  Once the LiDAR data were projected onto the 2-D hemispherical image plane, the 2-D Delaunay triangulation and Voronoi tessellation were computed for the planar point sets using the deldir package for R (Turner, 2015), filtering points below a user-defined canopy threshold. The summed area of filtered cells, or gaps, was calculated as a percentage of the overall plot area, providing the hemispherical Voronoi gap fraction (Phv). This assumes 100% light occlusion by non-filtered cells. The implication of this simplification is that light attenuation is overestimated, which can be adjusted by a simple transmissivity coefficient derived from the slope of linear regression. Since this work focuses on correlations and regression model development, calculating such a coefficient was not necessary. To calculate ACChv, Po values were subtracted from 1. Last, a height-threshold sensitivity analysis was conducted by applying the function with each of the four fisheye lens models and each of 17 minimum canopy height thresholds ranging from 1 to 5 m, at a step of 0.25 m, producing 68 unique combinations for each of the 100 plots, for a total of 6,800 iterations.  6.2.4 Point-density Normalized Gap Fraction The point-density normalized gap fraction (Ppdn) is based on partitioning hemispherically projected first-return points into polar and azimuthal sectors, or annuli, then calculating the number of points per sector as a proxy for canopy light occlusion. Removing non-first-returns facilitates the calculation of point-density normalized metrics by evening the point spacing along the Cartesian ground plane, with ground returns representing canopy gaps. Otherwise, the spatial bias of sampling is too high for the normalization procedure. The return values were normalized by the ground point density and the surface area of each hemisphere sector to reduce sensor effects, producing similar Ppdn values for vastly different point densities. This follows the logic  140  that a greater number of points are expected for sections of greater surface area, given evenly spaced sampling and thus a relatively constant point density along the (X, Y) plane. The procedure begins by filtering for first-returns and projecting the 3-D Cartesian coordinates (X, Y, Z) into spherical coordinates (r, φ, θ) using standard equations:  r = 2< + ;< + =< φ = >?@A( BC  θ = D87A( EF   The φ values were rescaled from (-π, π) to the interval (0, 2π) by adding 2π to φ values where φ is less than zero. Based on previous research (Zhao & Popescu, 2009), the spherical coordinates were sectioned at polar and azimuthal increments of 5° and 45°, respectively, producing 18 x 8 sky sectors for a total of 144 sectors. A polar resolution of 15° is also commonly used in LiDAR studies (Korhonen & Morsdorf, 2014), but is likely coarser than necessary for modern sensors. The number of first returns per hemispherical sector was calculated using the following equation:  GCH/ICJKL = 	 M	|	G% 	< 	GP 	< 	G%Q(  RCH/ICJKS = 	 M	|	RT < 	RP < RTQ(  U(WXDYW7@%,T) = 	M	|	M ∈ GCH/ICJKL ∩ RCH/ICJKS    141  Here, U(WXDYW7@%,T) is the number of elements contained in a set defined by the intersection of polar and azimuthal angle subsets, GCH/ICJKL and	RCH/ICJKS, at hemisphere sector intervals defined by steps i and j, respectively. A matrix is produced containing the frequency of returns within each sector of the hemisphere. In order to account for varying sector sizes, the values are adjusted by the hemispherical surface area of each sector. To do so, the surface area of each hemispherical sector is first calculated, as follows:  ^%,T = 	_< sin G%Q( − sin G% RTQ( −	RT    This produces a second matrix of equal dimensions, i x j. Here, Ai,j is the area of a sector for polar angle ϴi and azimuth angle φj at intervals defined by steps i and j, while R is the radius of the sphere. Next, matrix division is performed on the return frequency and surface area matrices, normalized by point density for the full hemisphere along the (X, Y) Cartesian plane. This mitigates issues related to sensor effects (e.g., point density). The filtering of non-first-returns is necessary to also reduce sensor effects along the z-axis, as vertical resolution can vary due to a number of factors. Point-density normalized canopy gap fraction (Ppdn) was calculated with the following equation:  Mcd7 = 	 7e%CK/_XDYW7@6,fgh6W@D_XDYW7@^iX>D?W6,f 	2	 ^iX>D?W6,f^jX56@cℎXWX7f=176=1 	   142  Where 7e%CK/_XDYW7@6,f is the count of first returns in matrix C for hemisphere sector C[i-j],  ^iX>D?W6,f is the surface area in matrix A of sector A[i, j], DFirstReturns is the point density for the full dataset along the Cartesian (X, Y) ground plane, and AHemisphere is the surface area of the full hemisphere. The right-hand side of the summation scales the output by the proportion of the hemisphere occupied by each sector, similar to the scaling of Le by polar angle (Korhonen & Morsdorf, 2014), rather than calculating the mean value without accounting for sector size. In essence, the Ppdn function normalizes the number of returns per sector by the overall point density and the sector surface area, with the output values scaled by hemisphere proportion. Double summation is approximate to a double integral. ACCpdn is merely one minus Ppdn, as its inverse.  6.2.5 Comparison with Other ALS LiDAR Metrics A set of standard metrics were also implemented to assess their performance against new methods and ground measurements. The method comparison framework includes estimates of canopy gap fraction, angular canopy closure, vertical canopy cover, individual tree detection, crown area, distance to crown and canopy, leaf area index, and clumping. First, these methods are described in the following paragraphs.  Based on previous research on the estimation of leaf area index (Miller, 1967; Lang & Yueqin, 1986; Zhao & Popescu, 2009; Ryu et al., 2010), the effective leaf area index (Le) was calculated using the following equation (Korhonen & Morsdorf, 2014):   143  lX = 2 −m7M G6 >?@G @67G6@67Gf7f=176=1   The apparent clumping index (Ωapp) was calculated based on a ratio of two Le estimation methods (Ryu et al., 2010). The previous approach was modified by approximating the integral as a summation, with each  Le method weighted by the sine of the given polar angle, θ (Korhonen & Morsdorf, 2014): Ωapp 	= 	 2 −m7M G6 >?@G @67G6@67Gf7f=176=12 −m7	M G6 >?@G @67G6@67Gf7f=176=1   Next, the Le vector is used for n polar angles θ to calculate the canopy gap fraction per the Beer-Lambert Law (Monsi & Saeki, 1953, 2005):  M?6 = X2c −lXq G6cos G6   Other metrics include the following vertical canopy cover (VCC) metrics: canopy-to-total-return ratio (VCCr) (Morsdorf et al., 2006), canopy-to-total-first-return ratio (VCCfr) (Morsdorf et al., 2006), intensity-return ratio (VCCir) (Hopkinson & Chasmer, 2009), Beer’s Law-modified-intensity-return ratio (VCCbl) (Hopkinson & Chasmer, 2009) or intensity cover index (ICI) (Korhonen & Morsdorf, 2014), above-height cover index (VCCaci) (Richardson et al., 2009), first-echo cover index (VCCfci) (Korhonen et al., 2011; Korhonen & Morsdorf, 2014), Solberg’s cover index (VCCsci) (Solberg et al., 2009), canopy-to-total-pixel ratio (VCCp) (Parent & Volin,  144  2014), and Cartesian Voronoi fractional cover (VCCcv) (Alexander et al., 2013). These metrics were applied with a canopy threshold of 1.25 m, per two seminal studies demonstrating algorithms that are the primary basis of this work (Morsdorf et al., 2006; Alexander et al., 2013).  Table 6.2 Additional VCC metrics Metric Equation Canopy-to-total-return ratio tUUC = 	 uvww	x	(.<z	{u|}K/ + u~%JwH Canopy-to-total-first-return ratio tUUÄC = 	 uvww	x	(.<z	{ue%CK/  Intensity-return ratio tUU%C = ÅÇCÉIJÑÅvww  Beer’s Law-modified-intensity-return ratio tUUÖw = 	 ÅÇCÉIJÑ	~%JwHÅvww + ÅÇCÉIJÑ	|}K/ÅvwwÅe%CK/ + Å~%JwHÅvww + ÅÜJ/HC{HÑ%}/H + Å|}K/Åvww  Above-height cover index tUU}á% = 	 u~%JwH + uvww	x	(.<z	{ + uÜJ/HC{HÑ%}/H + u|}K/uvww  First-echo cover index tUUÄá% = u~%JwH	x	(.<z	{ + ue%CK/	x	(.<z	{u~%JwH + ue%CK/  Solberg’s cover index tUUKá% = u~%JwH	x	(.<z	{ + 0.5 ue%CK/	x	(.<z	{ + u|}K/	x	(.<z	{u~%JwH + 0.5 ue%CK/ + u|}K/  Canopy-to-total-pixel ratio tUUâ = uäãå	x	(.<z	{uäãå  Cartesian Voronoi fractional cover tUUáç = t Me%CK/	éH/ICJ > 1.25	5  A suite of proxy metrics relevant to the calculation of Po was also tested. These include individual tree crown (ITC) counts using maximum and hierarchical variable-moving-window  145  (ITCmw) (Koch et al.; Popescu et al., 2002) and watershed (ITCwat) algorithms (Hyyppa et al., 2001; Zhao & Popescu, 2007), crown area (G) using detected tree heights with an empirical height-to-crown-radius function, distances and directions to nearest crown (Cdist, Cdir) and canopy pixels (Crdist, Crdir) from the plot center (Moeser et al., 2015), effective leaf area index (Le) based on the Beer-Lambert Law (Monsi & Saeki, 1953; Korhonen & Morsdorf, 2014), Le based on the ground-to-total-return ratio (Richardson et al., 2009), and Le based on contact frequency (Morsdorf et al., 2006), apparent clumping index (Ωapp) (Ryu et al., 2010), and Beer-Lambert Law canopy gap fraction (Pbl) (Monsi & Saeki, 1953, 2005; Ryu et al., 2010).  While these methods have not been locally validated, they were previously validated for boreal and montane forests. A caveat exists in that the low point densities of the ALS data used are likely a source of tree detection error. Yet, meaning is still inferred from these results, regardless of ITC accuracy (it is likely not optimal), as the focus is on a given metric’s ability to faithfully represent T. Furthermore, these algorithms may extract valuable information from ALS data not captured by other approaches. Correlations with convex spherical densiometer measurements were calculated before testing univariate and multivariate linear models with stepwise-AIC and -BIC model selection. While it is possible to build multivariate linear models with fewer degrees of freedom using dimensionality reduction techniques, this was not performed in order to simplify model interpretation.  The effect of filtering sites likely disturbed between spherical densiometer and ALS sampling campaigns was tested, in order to correct for a half-decade mismatch in data collection. This filtering process was also used to correct for discontinuity between ground and remote sensing  146  observations due to seasonal changes in leaf area index, as ground observations were generally collected during summer leaf-on conditions while ALS sorties were conducted in fall leaf-off conditions. The error contribution of leaf state is likely minimal, as the Hinton Forest Management Area is 4.5% deciduous, 8% mixed, and 40% evergreen forest (Nielsen, 2005). Observations with ground-based angular canopy closure (ACC) values below 0.30 were filtered, where disturbances or leaf condition discontinuities were apparent in ground-to-ALS ACC plots.  6.3 Results Estimation of ACC and Po as a proxy for T using ALS showed good performance. Regression models using multiple metrics substantially outperformed any single ALS metric, yet individual metrics have utility for their simplicity and physical basis, facilitating interpretation. Of the individual metrics, VCCfci, showed the best performance.  6.3.1 ALS Estimates of ACC and Po To test for correlations, given the perfectly inverse relationship between gap fraction (Po) and angular canopy closure (ACC), absolute values were used to calculate Pearson’s correlation coefficient (r) against convex spherical densiometer measurements of ACC. The top five results in terms of r were all vertical canopy cover metrics, with the strongest correlation shown for VCCfci (r = 0.61), followed by VCCsci (r = 0.61), VCCfr (r = 0.60), VCCr (r = 0.58), and VCCir (r = 0.57). The two variable-window individual tree crown (ITC) detection algorithms followed, at r = 0.57 for each, demonstrating their utility as a proxy for T, while point-density normalized Po (Ppdn) was the highest performing new metric at r = 0.56.   147  Each virtual fisheye lens model in Phv improved in accuracy as the minimum canopy height increased, with the equisolid angle model showing the poorest results (Figure A2.1). An optimal canopy height threshold was indicated of 5 m for all hemispherical lens models tested, indicative of an under-prediction of ACC. Of all the gap fraction metrics, Ppdn showed the strongest negative correlation and thus closest agreement with ground ACC measurements. VCCfci, which showed the strongest correlation with ground ACC data, was strongly correlated with the following LiDAR metrics: FCfr (r = 0.99); FCsci (r = 0.99); FCr (r = 0.98); FCir (r = 0.97); FCp (r = 0.97). Correlations between all metrics and ground measurements are provided (Figure A2.2).  ITC count methods show a strong negative correlation with the Beer-Lambert Law gap fraction (Pbl), while the point-density normalized gap fraction (Ppdn) shows a strong negative relationship with VCC metrics. Meanwhile, Po and VCC metrics show strong similarity within metrics. The hierarchical clustering of the hemispherical Voronoi gap fraction (Phv) results indicates that correlations are more strongly linked to minimum canopy height than to the fisheye lens model used. A canopy height threshold of 5 m was indicated for all Phv metrics.  ITC counts similarly have a strong negative correlation with Phv metrics with a higher minimum canopy height, but not with lower height thresholds. Meanwhile, metrics such as Ωapp and direction to canopy or crown have very low correlations with other variables, as expected. The strong negative correlation of Ppdn with VCC metrics, and weak correlation with Phv metrics, suggests that the two gap fraction metrics capture fundamentally different properties of forest  148  geometry. Meanwhile, the Beer-Lambert Law gap fraction (Pbl) shows strong correlations with empirical ITC crown area estimates.  Removing post-disturbance sites (sites with ground ACC values of zero and ALS ACC values greater than zero) before sampling the ground plots, the top seven metrics, in terms of univariate linear model fit with ground measurements, were all vertical canopy cover (VCC) metrics (Figure 6.1). Of these, the first-echo cover index (VCCfci) (Korhonen et al., 2011; Korhonen & Morsdorf, 2014) again achieved the highest score. The seven top metrics include VCCfci (R2 = 0.53), VCCfr (R2 = 0.51), VCCir (R2 = 0.51), VCCsci (R2 = 0.51), VCCr (R2 = 0.49), VCCcv (R2 = 0.48), and VCCp (R2 = 0.47). While Ppdn performed well before filtering out sites, at ninth best (R2 = 0.32), it subsequently dropped to eleventh (R2 = 0.38) after filtering sites. Meanwhile, the ITC count metrics and hierarchical watershed-based crown area performed surprisingly well; these metrics produced R2 values for ACC approximately double those of the Phv metrics.   149    Figure 6.1 Univariate linear model angular canopy closure (ACC) model R2 by metric for all sites and without disturbed or temporally non-synchronous sites in terms of LAI seasonality; black = all sites; red = without flagged sites  An equiangular hemispherical lens projection appeared particularly sensitive to the inclusion of sites that were disturbed or temporally inconsistent with ALS sorties, as filtering out these sites substantially improved model performance (Figure 6.2).ACC Model R2  Canopy Light Transmission Metric  150    Figure 6.2 Change to univariate linear model of angular canopy closure (ACC) model R2 by metric due to filtering likely disturbances; red points represent the filtered values; x-axis labels use the following convention: [lens model] [canopy height threshold]; Stereo = stereographic projection; Ortho = orthographic projection; Equidist = equidistant projection; Equiangle = equisolid angle projectionACC Model R2  Phv Metric by Hemispherical Lens Model and Canopy Height Threshold (m)  151  The mean R2 improvement attributable to filtering out disturbances was ΔR2 = +0.05. The largest gains were shown by VCCcv (ΔR2 = +0.20), VCCir (ΔR2 = +0.18), VCCfr (ΔR2 = +0.16), VCCp (ΔR2 = +0.15), and VCCr (ΔR2 = +0.15), while the largest loss was shown by the stereographic and equidistant fisheye lens model Phv metrics at a minimum canopy height of five meters (ΔR2 = -0.01). Overall, VCC metrics, ITC metrics, and the equisolid angle Phv metrics showed the greatest model improvement, indicating sensitivity to disturbance- or leaf area-related noise. Figure 6.3 shows the full Phv calculation process conducted for each site tested.   152   Figure 6.3 Example LiDAR plot process colored by point height (blue < green < red) with the orientation on-nadir and the circle units in radians with an equiangular projection: (a) nadir view of 50 m radius plot in NAD83 UTM 11N (meters) coordinates; (b) hemispherical view from the plot center toward the zenith projected in local coordinates; (c) Delaunay triangulation of hemispherically projected points; (d) Voronoi tessellation of hemispherically projected points  (a) (b) (c) (d)  153  For the hemispherical view, multiple projections were tested, showing a significant impact on the estimation of ACC and Po in the above results. The differences in projection are clearly visible for stereographic and orthographic projections, while subtle between equidistant and equiangular projections (Figure 6.4).  Figure 6.4 Example LiDAR plot demonstrating each of the four hemispherical (fisheye) lens geometries tested; colors represent point heights (blue < green < red); axis values are in radians  Applying the VCCfci calculation to the full dataset of 950 ALS and ground plots, model fit improvement is again exhibited by filtering out disturbances (Figure A2.4). Both second-order  154  polynomial (R2 = 0.39) and exponential (R2 = 0.35) models show reasonable model fit before filtering disturbed sites, followed by a simple linear model (R2 = 0.32). After filtering out disturbed sites, model fit improved for the second-order polynomial model (R2 = 0.43), exponential model (R2 = 0.42), and linear model (R2 = 0.40). Thus, linear and exponential models showed the greatest improvement in model fit, which is logical given their relatively inflexible behavior compared to polynomials.  Meanwhile, Ppdn showed strong linearity with ACC and thus Po (Figure A2.5). Errors were higher at lower values of ACC, with the presence of a few strong outliers. The application of exponential and polynomial linear models were tested in terms of their impact on model performance (Table 6.3). 155  Table 6.3 Comparison of top three univariate ALS models (VCCfci; VCCfr; VCCir) with Ppdn; ACC = ground plot ACC; Exp(ACC) = exponential model ground ACC; Poly(ACC) 1 = first-order polynomial ground ACC; Poly(ACC) 2 = second-order polynomial ACC; Left model values = without filtering sites; Right model values = with filtering sites; standard error shown in parentheses  Dependent variable  VCCfci VCCfr VCCir Ppdn Model 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 ACC 0.382***   0.757***   0.424***   0.770***   0.265***   0.530***   -0.140***   -0.243***    (0.018)   (0.035)   (0.019)   (0.036)   (0.014)   (0.032)   (0.008)   (0.014)                            Exp (ACC)  0.435***   0.435***   0.295***   0.440***   0.310***   0.310***   -0.097***   -0.139*** -0.139***   (0.020)   (0.020)   (0.013)   (0.020)   (0.018)   (0.018)   (0.005)   (0.008) (0.008)                          Poly (ACC)1   -0.351***   -0.303   -0.230***   -0.078   -0.308***   -0.640***   0.061**       (0.070)   (0.186)   (0.076)   (0.189)   (0.056)   (0.165)   (0.030)                             Poly (ACC)2   0.989***   0.950***   0.884***   0.759***   0.775***   1.049***   -0.272***       (0.092)   (0.163)   (0.099)   (0.167)   (0.073)   (0.146)   (0.040)                             b 0.280*** -0.317*** 0.315*** 0.031 -0.317*** 0.301*** 0.334*** 0.041* 0.364*** 0.104*** -0.245*** 0.320*** 0.178*** -0.252*** 0.204*** 0.002 -0.252*** 0.300*** 0.720*** 0.816*** 0.710*** 0.788*** 0.899*** 0.899***  (0.010) (0.038) (0.010) (0.023) (0.038) (0.052) (0.011) (0.022) (0.011) (0.023) (0.038) (0.053) (0.008) (0.034) (0.008) (0.021) (0.034) (0.046) (0.004) (0.009) (0.004) (0.009) (0.015) (0.015)                          N 945 679 945 679 679 679 950 950 950 679 679 679 950 679 950 679 679 679 950 950 950 679 679 679 R2 0.315 0.421 0.390 0.404 0.421 0.432 0.336 0.358 0.387 0.406 0.419 0.424 0.263 0.312 0.342 0.289 0.312 0.340 0.263 0.279 0.297 0.303 0.314 0.314 Adj.R2 0.315 0.420 0.389 0.403 0.420 0.430 0.335 0.358 0.386 0.406 0.418 0.422 0.262 0.311 0.341 0.288 0.311 0.338 0.262 0.278 0.296 0.302 0.313 0.313 RSE 0.174 (df = 943) 0.135 (df = 677) 0.165 (df = 942) 0.137 (df = 677) 0.135 (df = 677) 0.134 (df = 676) 0.185 (df = 948) 0.182 (df = 948) 0.178 (df = 947) 0.138 (df = 677) 0.137 (df = 677) 0.137 (df = 676) 0.138 (df = 948) 0.122 (df = 677) 0.130 (df = 947) 0.124 (df = 677) 0.122 (df = 677) 0.119 (df = 676) 0.073 (df = 948) 0.072 (df = 948) 0.071 (df = 947) 0.055 (df = 677) 0.054 (df = 677) 0.054 (df = 677) F-stat 434.237***(df = 1; 943) 492.101***(df = 1; 677) 301.499***(df = 2; 942) 457.978***(df = 1; 677) 492.101***(df = 1; 677) 256.980***(df = 2; 676) 478.719***(df = 1; 948) 529.045***(df = 1; 948) 298.685***(df = 2; 947) 463.670***(df = 1; 677) 488.157***(df = 1; 677) 248.980***(df = 2; 676) 338.476***(df = 1; 948) 307.218***(df = 1; 677) 246.053***(df = 2; 947) 275.828***(df = 1; 677) 307.218***(df = 1; 677) 174.242***(df = 2; 676) 337.608***(df = 1; 948) 366.773***(df = 1; 948) 200.322***(df = 2; 947) 294.661***(df = 1; 677) 309.682***(df = 1; 677) 309.682***(df = 1; 677)  *p<0.1; **p<0.05; ***p<0.01  156  6.3.2 Point-density Normalized Canopy Gap Fraction The Ppdn algorithm produced reasonable results, showing agreement with other Po estimates and ground-level measurements. A visualization of point-density-normalized gap fraction (Ppdn), Beer-Lambert Law gap fraction (Pbl), and Beer-Lambert Law effective leaf area index (Lebl), and apparent clumping index (Ωapp) are provided for an example ALS field plot (Figure 6.5).    Figure 6.5 Comparison with traditional metrics: (a) point-density normalized gap fraction by zenith angle; (b) Beer-Lambert Law gap fraction by zenith angle; (c) Beer-Lambert Law effective leaf area index by zenith angle, scaled by	"#$ %; (d) apparent clumping index by azimuth angle; y-axes represent respective values while x-axes represent zenith angle for (a), (b), and (c), and azimuth angle for (d) (a) (b) (c) (d) Ppd Pbl L e Ωapp Zenith Angle (&°)	 Zenith Angle (&°)	Zenith Angle (&°)	 Azimuth Angle ((°)	 157  Of the Po metrics tested, the new Ppdn metric showed the best absolute correlation with ground measurements of ACC, topping other Po metrics by a Pearson’s r of nearly 0.2. A similar difference was shown for univariate linear model R2 values, making Ppdn the top performing Po metric tested. Nonetheless, the performance of Po metrics may benefit from large improvements in accuracy by using more advanced models, such as 3-D convolutional neural networks.  6.3.3 Spike-free Canopy Height Model The spike-free CHM algorithm (CHMsf) produced expected results, following previous methods upon which it was based (Khosravipour et al., 2014, 2016). While gridded canopy maxima produced results with many pits, the CHMsf algorithm produced a continuous canopy surface model without pits, spikes, or excessive smoothing (Figure 6.6).   Figure 6.6 ALS canopy height models for an example site, 1 m resolution: (a) standard canopy height model with maxima for each grid cell; (b) spike-free canopy height model; color = height (m); axes = coordinates in NAD83 UTM 11N (meters) (a) (b)  158  While other smoothing algorithms exist, such as the median filter commonly applied in image processing, the benefits of spike-free CHM algorithms over traditional approaches for individual tree detection have been demonstrated (Khosravipour et al., 2014, 2016). The advance provided herein is primarily computational, reducing a 3-D problem to a layered 2-D solution based on voxels (volumetric pixels).  6.3.4 Tree and Crown Metrics In order to perform individual tree crown (ITC) detection and crown area estimation, empirical data from recent research in the study area (Cortini et al., 2011) was applied to model the height-to-crown-area relationship for deciduous and conifer species, as well as all species as one group. The ground data consist of aggregated minima, means, and maxima for major regional tree species height-to-crown-area, with standard deviations provided. Models for height-to-crown-area were developed for aggregated native species in the study area from these statistical moments. Resultant R2 values for both univariate linear and second-order polynomial models ranged from 0.87 to 0.97 while RSE ranged from 0.73 to 0.25 (Table 6.4). All models have p-values < 0.01.         159  Table 6.4 Comparison of height-to-crown-area model results: all species (1:2); deciduous species (3:4); evergreen coniferous species (5:6); each observation is the average of many observations (Ntotal = 17,929); models are built from minima, means, and maxima, with standard deviations reported (Cortini et al., 2011); standard error shown in parentheses  Dependent variable  Crown Area (m2) Model All-Linear All-Polynomial Deciduous-Linear Deciduous-Polynomial Conifer-Linear Conifer-Polynomial # 1 2 3 4 5 6 Height (m) 0.133***  0.168***  0.116***   (0.011)  (0.020)  (0.007)         Poly(Height)1  0.070  0.118  0.036   (0.042)  (0.082)  (0.021)        Poly(Height)2  0.002  0.001  0.002***   (0.001)  (0.002)  (0.001)        b -0.225 0.056 -0.270 -0.046 -0.217 0.146  (0.198) (0.264) (0.368) (0.522) (0.135) (0.131)        N 24 24 8 8 16 16 R2 0.876 0.889 0.921 0.927 0.949 0.977 Adjusted R2 0.870 0.878 0.908 0.898 0.945 0.974 RSE 0.650 (df = 22) 0.630 (df = 21) 0.694 (df = 6) 0.731 (df = 5) 0.363 (df = 14) 0.252 (df = 13) F-Statistic 155.538*** (df = 1; 22) 83.877*** (df = 2; 21) 70.251*** (df = 1; 6) 31.879*** (df = 2; 5) 260.329*** (df = 1; 14) 277.576*** (df = 2; 13)  *p<0.1; **p<0.05; ***p<0.01  First- and second-order polynomial models were chosen based on a visual analysis of plot data (Figure 6.7). Conifer species showed the best model fit, with a linear and polynomial R2 of 0.94 and 0.98, respectively, compared to deciduous model R2 values equal to 0.92 and 0.93. Both linear and second-order polynomial models for all species showed adequate performance (R2 = 0.88; R2 = 0.89). Hence, even though variation attributable to species is evident (Figure 6.7), a single polynomial linear model showing good model performance is used (R2 = 0.89).   160    Figure 6.7 Empirical height-to-crown-area linear models for (a) deciduous species; (b) conifer species; (c) regression models for major tree species located in the study area based on minima, means, and maxima (Ntotal = 17,929)  Variants of the ITC detection algorithms implemented here underwent validation in a number of previous studies (Popescu et al., 2002; Kaartinen et al., 2012). The algorithms were applied to generate predictor variables to test for variable importance in estimating canopy gap fraction (Po), and its inverse, angular canopy closure (ACC). Here, ITC results are treated as features for estimating T, rather than tree crown counts, as the purpose was to extract additional information from ALS data. Hence, the accuracy of their results is not a consideration in this work. From a (a) (b) (c) Crown Area (m2 ) Crown Area (m2 ) Crown Area (m2 ) Height (m) Height (m) Height (m)  161  visual analysis of ITC estimates, reasonable algorithm performance is assumed. The ITC algorithms implemented include standard and hierarchical watershed segmentation, as well as standard and hierarchical variable-size moving window methods (Figure 6.8).   Figure 6.8 Individual tree crown (ITC) detection for an example ALS plot with the standard watershed segmentation ITC detection method; center points indicate the likely stem locations; circle radii are scaled to the estimated crown area; brightness = height (m); coordinates are in NAD83 UTM 11N (meters)  Standard and hierarchical variable-size moving window ITC detection counts of tree crowns performed the best in predicting ACC of the ITC methods, each with an R2 above 0.4, despite not undergoing calibration. While ITC methods were not inferred to be able to predict ACC on their  162  own, as ITC counts and ACC are considered dependent variables (Falkowski et al., 2008; Kaartinen et al., 2012; Wang et al., 2016), they are complimentary to other metrics as an additional feature of forest geometry, as is the apparent clumping index (Ωapp).  6.4 Discussion Following half a century of hemispherical (fisheye) lens photography for estimating light transmission in forests (Evans & Coombe, 1959), based on the seminal work of Monsi and Saeki (1953), this is likely the first work demonstrating the effects of lens geometry on LiDAR calculations of ACC and Po. While not the focus of this study, these results show that hemispherical projections are an important consideration in the implementation of hemispherical view approaches of calculating T from LiDAR or photographic data, as the projections are fundamentally the same. Traditionally, equiangular lenses have been used under an assumption of improved performance (Schwalbe et al., 2009). With mathematical models of lens geometry, ignoring real-world lens distortion due to optical imperfections, this assumption is tested and results presented.  None of the Phv methods tested show strong performance, requiring further development against hemispherical photography measurements closer to the time of ALS acquisition. While step-wise AIC and BIC linear regression models included unacceptably high numbers of coefficients without substantial performance gains, univariate linear models are considered adequate to the task. The overall top three metrics of ACC, VCCfci, VCCfr, VCCir, all show good univariate linear model fit with ground measurements (adjusted R2 = 0.52; 0.51; 0.50) (Figure A2.3).   163  Despite the general good performance of a number of metrics, the temporal mismatch of field campaigns is plainly visible in the data, as many sites were likely disturbed between the ground measurements and ALS acquisition. Strong agreement between multiple LiDAR-derived predictors of ACC showing only moderate agreement with convex spherical densiometer measurements suggests that the LiDAR metrics should be tested against hemispherical photographs collected closer to the time of ALS acquisitions. It is inferred that this temporal mismatch poses a fundamental limitation on algorithm performance here, as top-performing metrics saturate near the same accuracy level (Figure 6.1).  The modified spike-free CHM algorithm exhibited reliable results, providing continuous canopy values and preserving detail with low computation times. This facilitated the application of ITC detection algorithms. Here, ITC results are treated as an additional feature of the data, rather than measures of tree counts. Although ITC results are likely of low accuracy, variable-window ITC approaches in particular show a strong ability for use in the prediction of ACC.  The most promising finding of the study was the strong performance of the new Ppdn metric, which stands as the most accurate of all tested metrics of gap fraction, or Po. The new metric was designed to harmonize ALS and TLS calculations of Po with ground-based methods. Further studies should test this metric against hemispherical photography estimates, for which it was designed. Thus, the Ppdn metric may be considered a step toward the harmonization of ground-based and airborne estimates of Po, which remains an outstanding challenge due to the different nature of ground and LiDAR measurement techniques.   164  While the Phv metric showed disappointing results given the theoretical strength of assumptions of algorithm design, it nonetheless provides important information. Furthermore, its performance may be limited by the low point densities of the ALS data used here. First, the Phv algorithm’s inclusion of different hemispherical lens geometries shows the importance of lens models. Second, this new metric remains robust in concept, with many opportunities to improve performance.  From these results, it is concluded that these ALS-based models of T require further development with higher point densities closer to the time of ground data collection. As such, in the following chapter, we develop models of T directly from the ground measurements and environmental covariates. Those with high point density LiDAR datasets may nonetheless benefit from the methods presented above, necessary for pursuing similar studies in regions where there is limited ground sampling coverage, as is often the case in boreal forests.  6.5 Limitations The main limitation of this work was the half-decade difference in timing between ground and ALS data collection, which produced strong disagreement between ground ACC and ALS metrics for some sites. It was apparent from scatterplots and ALS plot data visualization that disagreement arose from either disturbance or forest regrowth on previously disturbed sites. This temporal mismatch diminished the utility of ground ACC data for use in cross-validation. Meanwhile, even though the ALS data had a low mean point density of 1.64 points m-2, these data may be of greater precision than coarse spherical densiometer measurements of ACC while providing more complete and even sampling coverage. Thus, I question the use of coarse ground  165  measurements of ACC (e.g., spherical densiometers), instead favoring of measurement with modern LiDAR systems, structure-from-motion models, 360-degree spherical imagers, or digital hemispherical imagers. The use of full-waveform data may add state-of-the-art vertical canopy sampling and canopy penetration essential for modeling canopy light transmission. It is perhaps ironic that ground-truth data were the largest source of uncertainty in this work, as it appears to have fundamentally limited the development of models.   166  Chapter 7: Simulation of Understory Global Solar Irradiation  7.1 Introduction Light is a primary source of life for plants, as its physical energy drives the process of photosynthesis, making light a focus of plant resource competition (Hikosaka & Hirose, 1997; Katahata et al., 2005; Ruban, 2009). While plants have developed adaptations that enable them to tolerate fluctuations in the light environment, long-term or directional changes to light conditions can affect lasting change through successional processes. Unlike open sites, forest canopies place strong limitations on the quantity and quality of light, as can local topographic conditions. Understory light, or understory solar irradiation (Iu), plays a critical role in forest succession and community ecology.  Roles in an array of processes from tree regeneration (Greene et al., 1999) and nutrient cycling to fire frequency have been attributed to boreal understory plants, with some suggesting that the understory drives forest succession (Nilsson & Wardle, 2005). Previous studies have shown the importance of Iu in controlling understory plant diversity and production in boreal forests (Aubin et al., 2000; Grandin, 2004; Bartemucci et al., 2006; Beaudet et al., 2011; Reich et al., 2012). Hence, the prediction and management of boreal understory light are important tasks for scientists and managers (Lieffers et al., 1999). Canopy conditions and topography play a central role in controlling understory light in the boreal, due to lower solar elevations at higher latitudes, despite narrow tree crowns here. While changes in forest structure exert a more pronounced control on canopy light transmission, or T (Lieffers et al., 1999; Beaudet & Messier, 2002;  167  Bartemucci et al., 2006), variation is also due to overstory tree species (Canham et al., 1994) or landcover conditions.  While the direct effects of increased solar radiation and warmer air temperatures may be beneficial for understory plant productivity, particularly when met by increases to precipitation (Trenberth, 2011), atmospheric CO2, nitrogen, and phosphorus, long-term increases in evaporative demand may diminish soil water conditions (Bonan, 2008), limiting regeneration and growth. Although currently understudied, recent work for the Swedish boreal attributed an observed reduction in soil water levels to increased Iu levels (Grandin, 2004). Yet, the quality of light may be more important than the quantity to long-term growth processes (Dengel & Grace, 2010). The ability to predict changes to Iu may better nevertheless facilitate the estimation of understory evaporative demand and thus soil water conditions in forests. This line of work is critical to research on global change and is of key importance to biodiversity research.  My previous chapters show the importance of fire in regulating boreal canopy structure and composition, as boreal systems are predominantly driven by climate and fire conditions. Warming is shown to produce complex changes to stand regeneration and fire regimes, resulting in a weak long-term forest decline signal in some regions. The combined effects of these changes on understory light conditions are the subject of this chapter. Here, I hypothesize that a long-term decline in forested area, modeled in Chapter 5, may increase understory light levels in the forested region of western Alberta, Canada. The effect of these changes on understory species may depend on additional local conditions, such as topographic position, soil conditions, and precipitation patterns. This work focuses on modeling combined canopy, topography, and earth- 168  sun position controls on understory light, as the key drivers of Iu variation, using hybrid forest landscape model simulations in connection with regression models of gap fraction (Po).  Landscape changes to Iu are simulated in a model fusion approach. First, linear and machine learning regression models are developed for Po, designed to be compatible with LANDIS-II model outputs. A global solar irradiation model is used to estimate topographic and latitudinal effects on insolation. By combining Po with bare-earth insolation, Iu is calculated. Continuing the previously described simulation work, four model scenario periods are tested for changes to Iu levels: Pre-suppression Era (1923-1952); Early Suppression Era (1953-1982), Global Change Era (1983-2012); and, Most Recent Decade (2003-2012). The effects of different climate and fire scenarios, as well as different fire models, on landscape-scale understory light conditions are also tested. Models were run for 50 years of duration, with the first 10 years used for model spin-up.  7.2 Methods Multiple linear and Random Forest regression models of ACC were developed using ground plot data. 10-fold cross-validation was repeated three times for each of the models to measure performance using robust methods. RMSE, R2, and the standard deviations of each were used to select final regression models. Landcover classification was performed on LANDIS-II model outputs using the ABMI Landcover 2010 scheme. Methodological details are provided below.  7.2.1 Data Plot data used for the development of regression models include area-based canopy and terrain LiDAR metrics calculated with USDA Fusion (McGaughey, 2014), 30-year normal climate  169  variables output from ClimateWNA (Wang et al., 2011a), Alberta Wet Areas maps derived from LiDAR (Arp et al., 2009), Alberta Biodiversity Monitoring Institute (ABMI) Landcover 2010, Canada Land Inventory (CLI) forest site index, bare-earth insolation calculated with ArcGIS, a NASA SRTM digital elevation model (DEM), and ground-level GPS coordinates and vegetation survey data (Nielsen, 2005). The plot data included the following 58 variables:  Easting, northing, elevation, graminoid abundance, ALS return count, ALS height maximum, ALS height mean, ALS height 5th percentile, ALS height 10th percentile, ALS height 25th percentile, ALS height 50th percentile, ALS height 75th percentile, ALS height 90th percentile, ALS height 95th percentile, ALS ratio of returns above 2m, ALS ratio of returns above mean return height, ALS height relative ratio, ALS height skewness, ALS height standard deviation, ALS terrain aspect, ALS terrain slope, ALS terrain elevation, ALS terrain, ALS terrain plan curvature, ALS terrain profile curvature, ALS terrain solar index, wet areas, convex spherical densiometer ACC, percent conifer, regeneration, degree-days below 0, frost days, frost-free period, growing season precipitation, mean annual precipitation, monthly maximum temperature, monthly minimum temperature, July mean temperature, March precipitation, product of May × September precipitation, June precipitation, December precipitation, summer heat moisture index, January minimum temperature, July minimum temperature, herbaceous plant abundance, ABMI landcover, CLI forest site index, shrub abundance, diffuse radiation, global radiation, product of June × August global solar radiation, product of June × September global solar radiation, ALS compound topographic index (CTI), CTI 150m, CTI 90m, topographic position index, ALS canopy equation  170  Example maps of variables used in the regression analysis described in Section 7.2.2 are provided, including ClimateWNA 1961-1990 mean July precipitation and minimum January temperature, and modeled bare-earth global solar irradiation (Figure 7.1). The physically based model used to calculate bare-earth solar irradiation is described in Section 7.2.4.   Figure 7.1 Predictor variable maps for the study area: (a) 1961-1990 mean July precipitation in mm; (b) 1961-1990 minimum January temperature in degrees C; (c) mean annual bare-earth global solar irradiation in Wh m-2 year-1; axis values represent pixel coordinates in NAD83 UTM 11N (meters) coordinates, used for its high positional accuracy at regional scales  7.2.2 Linear and Machine Learning Regression Models of Po Multivariate linear regression follows the classical form:  *+ = -./+. + ⋯+ -2/+2 + 3+ = 4+5- + 3+			678	9 = 1…< (a) (b) (c)  171  Where T denotes the transpose, such that 4+5- is the inner product between /+ and weight or - vectors. The ordinary least squares function is used to solve for weights and the intercept term that minimize error. The Random Forest algorithm applied also follows this classical form (Breiman, 2001). The Random Forest algorithm is based on the construction of decision trees, regression trees in this case, falling under the classification and regression tree (CART) umbrella term (Breiman et al., 1984). The Random Forest algorithm is detailed in Appendix A.  Multivariate linear and Random Forest machine learning regression models of Po were developed. The effects of different predictor variables on model performance were tested. For linear regression, this is done with step-wise AIC and BIC model selection, as well as manual variable selection based on an analysis of variance combined with inference regarding dynamics likely driving variation in Po. For Random Forest models, variable selection is based mostly on variable importance metrics, while inference-based manual variable selection is also used. To assess the performance of each model, 10-fold cross-validation was implemented three times, randomly selecting 75% of the data for model training and 25% for model testing.  7.2.3 Landcover Classification of LANDIS-II Species-age Cohorts To model Po using LANDIS-II outputs, annual simulated species-age cohort maps were classified into landcover classes using the ABMI Wall-to-wall Landcover Map 2010 Version 1.0 scheme (Alberta Biodiversity Monitoring Institute, 2012). Two caveats exist in this data set in that shrubland is often recently disturbed forest and road width is overestimated, lending to an enlarged developed area. This landcover classification scheme and the algorithm used is detailed in Appendix D.  172  First, species-age cohort maps are classified based on the taxonomic group into either evergreen or broadleaved (i.e., angiosperms). The sum of binary presence values at each site for each group is then calculated in order to calculate the site percent evergreen and percent broadleaved, based on the overall number of species present at a site. Immature trees less than ten years of age were filtered out to remove transient dynamics. ABMI Landcover 2010 class values were applied to inactive sites before classifying LANDIS-II species-age cohort outputs into landcover classes. Sites with greater than 75% evergreen trees were classified as Evergreen Forest. Sites with greater than 75% broadleaved trees were classified as Broadleaf Forest. Sites where both evergreen and broadleaved trees represented 25% or more of the site were classified as Mixed Forest. Active sites without any tree species present were classified as Grasslands to capture sites where regeneration failed.  7.2.4 Bare-earth Global Solar Irradiation Model The sum of direct, diffuse, and reflected solar radiation components is known as global solar irradiation, with direct and diffuse radiation comprising the majority of the insolation budget. While direct radiation theoretically reaches the surface unimpeded, diffuse radiation is scattered by molecules in the atmosphere, and reflected radiation is returned by surface features. Although only a fraction of incident radiation can be used by plants in photosynthesis, known as the fraction of photosynthetically active radiation (fPAR), changes to full-spectrum radiation are important for monitoring changes in energy balance (Rich, 1990) that may control evaporative demand and soil water levels. To compute landscape bare-earth global solar irradiation for the study area, ArcGIS Spatial Analyst solar radiation tools (Fu & Rich, 1999) was used with an SRTM RADAR digital elevation model (DEM). The algorithm is detailed in Appendix C.  173  7.3 Results Supporting the hypothesis provided, model fusion suggests that Iu levels increased with a simulated long-term decline in forested area. Multivariate linear and machine learning regression models of ACC with the Random Forest algorithm showed comparable performance. Both model classes performed well with only two predictor variables, Alberta Biodiversity Monitoring Institute (ABMI) Landcover 2010 and Canada Land Inventory (CLI) Forest Site Index. Multiple linear regression with step-wise AIC produced good model fit (multiple and adjusted R2 = 0.949; RMSE = 0.067), but overfit by selecting 25 predictor variables. Step-wise BIC produced comparable results (multiple and adjusted R2 = 0.946; RMSE = 0.069) while selecting only nine predictor variables. An analysis of variance for all predictors allowed the manual selection of two predictors logically complementary in their ability to predict Po: ABMI Landcover 2010 and CLI Forest Site Index. Critically, both variables contain latent information on disturbance legacies, as well as information on regional climate and soil patterns.  CLI site index is treated as a numeric integer, rather than categorical, variable due to its linear scaling. Using only the above two predictor variables, multiple linear regression showed model performance comparable with substantially more complex models (Table 7.2). Multiple linear regression model robustness was tested for the two predictor variables by performing 10-fold cross-validation repeated three times (R2 = 0.938; RMSE = 0.079), yielding only marginally diminished model performance compared to step-wise AIC or BIC model selection models with many variables.    174  Table 7.1 Multiple linear regression model; LC = landcover; coefficients shown for variables; standard error shown in parentheses; ACC (1 – Po) is the dependent variable  Independent variables Dependent variable   CLI Forest Site Index ACC (1 – Po)    ABMI LC Class 2 -0.126***  (0.002)   ABMI LC Class 3 0.003  (0.011)   ABMI LC Class 4 0.020  (0.016)   ABMI LC Class 5 -0.185***  (0.007)   ABMI LC Class 6 -0.571***  (0.014)   ABMI LC Class 7 -0.157***  (0.017)   ABMI LC Class 8 -0.378***  (0.034)   ABMI LC Class 9 -0.252***  (0.010)   ABMI LC Class 10 -0.504***  (0.012)   ABMI LC Class 11 -0.126***  (0.032)   Constant 0.882***  (0.007)   N 900 R2 0.938 Adjusted R2 0.938 Residual Std. Error 0.075 (df = 888) F-Statistic 1,350.077*** (df = 10; 889)   Note: *p<0.1; **p<0.05; ***p<0.01      175  A Random Forest regression model using all 59 predictor variables, with 10-fold cross-validation repeated three times, only marginally improved upon multiple linear regression with two variables (R2 = 0.944; RMSE = 0.070), despite the substantial increase in model complexity. Three predictors showed particularly high Random Forest variable importance (Figure 7.2): percent conifer, CLI forest site index, and ABMI Landcover 2010.   Figure 7.2 Random Forest variable importance (decrease in node impurities) used for initial feature selection  While percent conifer shows the highest variable importance, better Random Forest model fit was achieved with the two predictors used in multiple linear regression: CLI forest site index (productivity) and ABMI Landover 2010 class. Ten-fold cross-validation was repeated three times to assess Random Forest model performance. Random Forest models including all three variables of the highest importance explained 93.2% of variance, while models including only the CLI and ABMI landcover variables explained 93.6% of variance. For the final two-parameter Random Forest model (R2 = 0.936; RMSE = 0.076), the scale-free variable importance of the  176  two predictors was 18 for CLI forest site index and 68 for ABMI Landcover 2010. Thus, landcover class is inferred to be the most important predictor tested for Po, even though Random Forest is shown to be biased toward both continuous and many-predictor categorical variables (Strobl et al., 2007), which may be corrected with one-hot encoding (a binary class membership schema). As such, this work proceeds with models using only CLI site index and ABMI landcover class as predictors. The final two-parameter Random Forest model showed stability in low error using an ntree parameter of 500, or a forest of 500 regression trees for averaging (Figure 7.3).   Figure 7.3 Random Forest model out-of-bag MSE (Error) by the number of trees parameter  Despite the strong performance of the final two-parameter Random Forest model (R2 = 0.939; RMSE = 0.074), multivariate linear regression produced only slightly diminished model fit (R2 = 0.938; RMSE = 0.079), although a simpler and smaller model. The multivariate linear regression  177  model did not suffer from the bias of the Random Forest model, which underpredicted Po maxima. Hence, the two-parameter multivariate linear regression model was selected as the final model for modeling Po at the landscape scale by applying the ABMI landcover classification scheme to annual LANDIS-II species-age cohort outputs. Using the linear regression model with LANDIS-II species-age cohort landcover classes and a map of CLI forest site index, annual maps of Po were produced to calculate landscape maps of understory global solar irradiation as the multiple of canopy light transmission and bare-earth global solar irradiation (=> ∗ @AB>CDB).  Both the lowest and highest global solar irradiation levels are shown for the Rocky Mountain and foothills region, due to local topographic variation. The foothills region showed the highest forest productivity in the region, while the Rocky Mountain region contains moderate levels of productivity. These patterns are important for the following sections on modeling understory solar irradiation. Here, ALS data were not used as a predictor due to the temporal mismatch between ALS sorties and ground validation data collection. Due to this mismatch, disturbances and recovery broke down the correlation structure between datasets. ALS remains an important predictor of Po due to its broad sampling capabilities, which may provide a more representative picture of forests. Where high point-density or waveform ALS data is available, it is considered preferable to coarse traditional ground measurements.  7.3.1 Simulation of Po and Iu with Model Fusion Using the final two-parameter linear regression model with CLI forest site index and the ABMI Landcover 2010 classification scheme applied to LANDIS-II simulated species-age cohort maps, Po is simulated at a landscape scale (25.2 million ha) and stand resolution (100 m cells) at an  178  annual time-step for a 50-year duration. Annual understory solar irradiation (Wh m-2 year-1), or Iu, is computed by multiplying each annual map of mean simulated Po against the bare-earth mean global solar irradiation map, following a recent approach (Bode et al., 2014). To track landscape-wide changes in Iu over time for each scenario, mean annual understory solar irradiation (@E) is computed for each modeled Iu map (Figure 7.4). The results for each scenario show that simulated changes to @E reflect complex changes to disturbance regimes and climate over the past 90 years.   Figure 7.4 Simulation and modeling of mean landscape full-spectrum understory solar irradiation (FG) for forested cells in the study area for each of the fourteen model scenarios; the legend text format is as follows: [succession model]-[fire model]-[start year]-[end year]; ao = age-only succession; bf = base fire; dffs = dynamic fuels and fire system; extremes = 1923-1952 period climate with 1983-2012 period fire; see Table 5.1   179  Simulation scenarios with a Pre-suppression Era (1923-1952) high burn rate show an initial rapid increase in @E during the model spin-up decade. Meanwhile, all other simulation scenarios show a decline in @E due to demographic changes, as stand development outweighed mortality given diminished disturbances. In the absence of disturbance, changes in regeneration are masked. Simulated reductions to burning, due to fire suppression in recent decades, reduced the mean quantity of understory light in forests at the landscape scale by a maximum of 8%, attributable to this demographic shift. Meanwhile, higher burn rates generally produced higher landscape levels of @E in forests.  Base Fire (bf) model simulations are notable for showing the highest landscape levels of @E in forests. Meanwhile, Dynamic Fuels and Fire System (dffs) model configurations produced substantially lower levels of @E even when parameterized with the same empirical fire regimes. This is due to the semi-mechanistic nature of the dffs fire model, as initial large fires were followed by fuel limitations. The dffs model configuration scenarios surprisingly yielded lower average levels of @E than age-only succession (ao) scenarios, producing the lowest simulated levels of @E  in the dffs extremes scenario (Figure 7.5).  180   Figure 7.5 Mean understory solar irradiation (FG) across all simulation years by scenario; scenario naming conventions follow those of Table 5.1 and Figure 7.4  Low landscape @E produced in the dffs extremes scenario may be explained by rapid forest expansion following initial large disturbances, as space for recruitment expanded before fuel limitations reduced disturbance. This pattern of fuel-limited disturbance regimes is apparent for the dffs scenarios (Figure 7.6). The bf scenarios, which forced the application of empirically derived historical disturbance regimes without fuel or weather limitations, showed an increase in @E for all model scenarios, except for the Early Suppression (1953-1982) and Global Change (1983-2012) Eras. During these two eras, stand development outweighed empirical fire regimes, diminishing the level of @E. In the Most Recent Decade (2003-2012) bf scenario, @E increased with the rise in fire frequency, despite diminished fire size.  181   Figure 7.6 Change in understory solar irradiation (FG) between simulation years 0 and 50 by scenario; the scenario naming conventions again follow Table 5.1 and Figure 7.4  7.4 Discussion Forest stand age, modeled implicitly in the LANDIS-II simulations, plays a central role in landscape levels of @E. Higher historical burn rates produced higher levels of @E in simulations, as mean forest age declined with higher rates of burning. The inclusion of fuels and weather limitations in fire models notably limited the continuation of high rates of burning over multiple decades. Whether fuels and weather conditions here currently impose a fundamental energetic limit on the burn rate requires further research. Previous studies indicate that the rate of burning was likely more severe in previous centuries under cooler and drier climatic conditions, as discussed in Chapter 3, which may be attributable to a difference in fuels.   182  The two fire-climate extreme scenarios yielded divergent responses in landscape @E levels depending on the fire model used, due to the inclusion of fuel limitations in the dffs fire model. It is evident that a decline in forest cover may drive a long-term increase in landscape @E, if stands fail to regenerate under warmer conditions. A long-term decline in regeneration rates in the area may overshadow a demographic shift related to near-term stand development in the absence of fire-related mortality. As the simulations do not include harvest, its contribution to mortality may balance the decline in area burned. The interaction of harvest, fire, and biological disturbance requires further research. In the simulations, sites converted from forestland to grasslands or shrublands due to reduced regeneration rates, caused by modeled soil water limitations under warming. Given the importance of regeneration to the modeling study results, this component requires more extensive regional validation in future studies. While empirical evidence similarly shows a decline in regeneration across the study period, competition appears to be the main driver, with climate inferred to play a weaker role (Appendix F).  The simulated conversion from forest to grassland or shrubland in LANDIS-II explains changes in landscape @E. Annual bare-earth global solar radiation and CLI forest site index were fixed for each site, making @E variation purely a function of the effects of simulated landcover change on modeled Po. Forest demography is not explicitly modeled in the calculation of Po. Immature trees less than ten years of age are omitted, due to a negligible effect on overstory Po conditions and no effect of competition on regeneration. Hence, the effect of new forest growth is not apparent until ten years after disturbance. This produces a lag in @E values and does not explain the observed simulation patterns. Landcover was the only non-static variable for sites in the @E model.  183  Based on simulated rates of forest change described in previous chapters, modeled landscape @E  showed divergent responses to changing fire and climate conditions. Modeled  @E indicated that understory light levels were highest under greater burn rates and warmer climatic conditions. Yet, this result is dependent on the type of fire model applied. It is suggested to apply empirical fire models for historical analyses of simulated fire regimes, particularly if there is an absence of empirical support for the application of complex semi-mechanistic fire models. Meanwhile, studies concerned with forecasting into novel conditions may benefit from the mechanistic aspects of complex fire models that allow theoretically robust extrapolations.  Here, the primary concern was replicating the continuation of recent historical fire patterns for modeling changes to canopy light transmission (T), a task for which both fire models provide useful information. Future studies should extend forest ecosystem simulations over longer (e.g., century) timescales to test for forest decline or compositional change, as model behavior may overcome initial landscape parameterization at century timescales, resulting in eventual equilibrium. Yet, model uncertainty also increases with longer simulation timescales, as errors propagate, motivating the use of half-century simulations. Regardless of temporal scale, most critical are the simulation time-points where regime shifts are likely to occur, which signify transitions in the state-space of forests. Dedicated state-space models designed for linear systems with random disturbances, such as the Extended Kalman filter (Kalman & Bucy, 1961), may be used to model these changes over time.  Based on landscape @E simulations and previously described simulations (Chapter 5), a forest ecosystem state change-point appears to occur near year ten for the study area (Figure 7.5). Yet,  184  this may be attributable to model spin-up. Evidence is provided that a diminished rate of burning likely decreased @E in recent years, attributable to a demographic shift occurring through stand development processes in the absence of fire-related mortality. This is supported by a precursory analysis of Alberta Permanent Sample Plot data for the region, which shows a reduction in regeneration and mean tree height – inferred to correspond to a reduction in mean tree age – across the Global Change Era, likely reducing understory light levels (Appendix F). Yet, future studies must incorporate the effects of harvest and biological disturbance agents with more sophisticated succession models to estimate the effects of each on understory light.  7.5 Limitations In this chapter, a physical solar radiation model was combined with a regression model of Po using forest site index and simulated landcover as predictors. The layering of these models may produce error propagation, common to complex models lacking global parameter optimization (Pacala et al., 1996; Arras, 1998; Larocque et al., 2008). These uncertainties were not explicitly represented given the complexity of models and scope of this research. Additionally, the solar radiation model used in this chapter assumes constant solar output, which is known to be false, but is a reasonable assumption given that work is not concerned with temporal variation in solar activity. Other limitations of the solar radiation model include its reliance on simple geometric relationships and lack of radiative transfer functions related to turbidity or cloud cover.  Of these shortcomings, the absence of cloud cover information is expected to have the largest effect on modeled radiation, as clouds may be the largest source of radiation attenuation in the atmosphere (Hammer et al., 2003). Cloud cover indices derived from geostationary weather  185  satellite data can be used to generate atmospheric clearness indices. Such indices facilitate a simple but effective method of integrating spatiotemporally resolved atmospheric conditions with models of clear-sky solar radiation and LiDAR canopy light transmission (Tooke et al., 2012). Finally, while changes to landcover were dynamically simulated, forest site index was static (Agriculture and Agri-Food Canada, 2016). Future studies should test the application of NDVI, NIRV, or SIF for incorporating dynamic changes to site productivity.   186  Chapter 8: Conclusion  The purpose of this thesis was to investigate past-century changes to regeneration and fire in western Alberta in order to parameterize models for the simulation of understory solar irradiation (@E) trajectories. To achieve the simulation of @E, process-based, hybrid, physical, and regression models were combined through model fusion. This work is intended to provide a currently absent variable (@E) necessary for forecasting changes in the distribution and abundance of understory plants, critical to brown bears (Ursus arctos Linnaeus) and other regionally important species. This thesis poses six fundamental questions regarding past-century changes in forests of western Alberta linked to global change:  1. Have climatic and anthropogenic changes altered fire regimes in western Alberta and do regional historical fire patterns match those of the national scale? 2. Has climate change altered tree species regeneration rates in western Alberta? 3. What are the net effects of recent climate and fire trends on forests in western Alberta? 4. Can new airborne laser scanning (ALS) models provide an improved ability to estimate understory global solar irradiation in western Alberta? 5. Can a forest landscape model be fused with linear or machine learning regression models to simulate dynamics not explicitly represented in the model? 6. Have past-century climate and fire trends changed landscape-level @E in western Alberta?  In Chapter 3, anthropogenic change is shown to combine with warming to produce complex changes to fire regimes. These changes include more frequent, smaller, human-caused fires near  187  areas of human activity. Only a mild increase in annual area burned was shown under warming for the study area while decreasing nationwide, indicating the expansion of suppression efforts in the absence of broad demographic changes. The shift toward novel fire regimes in recent years is better explained by human activity than by warming, both at regional and national scales. Fire seasons lengthened substantially in the region, while changing little nationwide, likely partially attributable to differences in sampling coverage. In western Alberta, mean fire size declined at a constant rate before accelerating at an inflection point in ~ 1990. A strange pattern occurred at this time-point whereby fires nationwide declined thereafter in mean size, latitude, and total area burned, while increasing in frequency. This same pattern is shown for western Alberta, with the exception of annual area burned. The cause of this pattern remains unknown, but appears attributable to human activity rather than to climate or observational methods.  Nationwide, burning showed spikes of high activity in early spring, likely attributable to winter dead fuel load accumulation (Santana & Marrs, 2016) and phenology-mediated early spring photosynthetic production (Richardson et al., 2013) followed by drying events. A ‘spring dip’ in conifer live foliar moisture content has also been shown to stem from foliar physio-chemical changes linked to phenology (Jolly et al., 2016). Cold and damp regions have been shown to have the highest rates of fuels accumulation, as decomposition rates are lowest here (Dodge, 1972), given the temperature and microbia-taxa dependence of decomposition rates (Dioumaeva et al., 2002; Oliverio et al., 2017). Spring fire activity is poised to intensify with increased winter liquid-phase precipitation (Trenberth, 2011; Intergovernmental Panel on Climate Change, 2014; Rocca et al., 2014), earlier snowmelt (Westerling et al., 2006), increased primary production (gross and net) under warming (McMahon et al., 2010; Wang et al., 2011b; Pausas & Ribeiro,  188  2013; Keenan et al., 2014; Liu & Wimberly, 2014), and increased human activity (Balch et al., 2017), which may result in increased burning (Ali et al., 2012).  Nationwide, the largest fires and area burned occurred in June, while fires were most frequent in July. For fires larger than 200 ha, characteristic of typical boreal fire regimes, mean fire latitude increased across the period. This pattern was partially explained by the increased use of satellite disturbance detection since the 1980s. It is inferred from this result and previous work (Scheffer et al., 2012; Koven, 2013) that boreal fire regimes are nevertheless shifting northward due to a combination of warming in the north and more effective short-term fire suppression (Cumming, 2005) in the south. Yet, this hypothesis requires further testing with less spatiotemporally biased remote sensing records.  In Chapter 4, warming is shown to have a negative influence on modeled tree regeneration potential in western Alberta. While soil conditions are shown to play an important role in the regional response of trees to climatic change, the net effect of warming on regeneration was negative across species and regions. Changes in modeled regeneration were primarily attributable to changes in soil moisture, as available water holding capacity (AWHC) is the most sensitive model parameter in TACA-GEM. Despite predictions of improved regeneration conditions in higher elevations under warming, the results show the greatest reduction in regeneration there, due to differences in soil properties. Soil water levels and thus regeneration rates appeared more stable at low elevations, attributable to post-glacial soil textural properties in the boreal and foothills regions.   189  Germination frequency, physiological drought frequency, growing degree days, and turgor loss point frequency were the most important predictors of regeneration success. Results showed that even species in warmer neighboring regions may experience reduced regeneration potential under warming in the region. Meanwhile, a preliminary analysis of plot data for Alberta suggests that competition explains more of the observed decline tree regeneration rates than climate (Appendix F). The contribution of climate to diminished regeneration rates observed for western Alberta also requires further research. Future studies may incorporate gridded climate data, vegetation indices (e.g., Landsat NDVI and fractional cover, or SAR vegetation optical depth), soil grids, and ground plot data to model regional changes to forest regeneration since ~ 1990. Meanwhile, new ALS methods show strong potential for landscape-scale monitoring of forest regeneration at an individual-tree resolution (Yao et al., 2014; Amiri et al., 2015). Time-series methods using low-cost commercial UAS may facilitate an improved spatiotemporal evenness of sampling coverage.  In Chapter 5, a combination of diminished burning and tree regeneration potential in western Alberta is shown to produce a mean decline in forested area across the 50-year simulation period. Here, the TACA-EM tree regeneration model was fused with the Landscape Disturbance and Succession (LANDIS-II) model to simulate forest dynamics for four periods during the past 90 years. The number of forested sites or cells declined for all simulation configurations, except for the succession-only simulations. In succession-only scenarios, forested sites increased in the absence of fires through recruitment into sites classified as open in the initial landscape.   190  The central tendency of the spatial distribution of forests increased in latitude for all simulations and in elevation for simulations with high burn rates, declining slightly in elevation in the absence of large disturbance levels. It is apparent from the pace of change in the spatial configuration of forests that diminished burn rates are inhibiting forests from migrating toward more optimal regeneration conditions. The simulated rate of forest migration lagged the velocity of warming here. The question remains whether the region’s forests may adapt to novel conditions or whether new genotypes may migrate into the region. A reduction in burn rates implies slowed adaptation rates by lengthening the time interval between generations. Future studies should include phenotype plasticity and adaptive capacity in dynamic forest ecosystem simulations.  The choice of fire model is shown to exert substantial influence on simulation results. The statistical fire model brute-forced the parameterized fire regime, while the semi-mechanistic fire model showed strong fuel limitations following large initial fires. An algorithm based on stochastic gradient descent was developed to optimize fire model parameters. The new method was able to quickly converge by optimizing on reduced resolution simulations before refining these parameters on full-resolution simulations. The method overcomes a long-standing challenge in the application of forest fire models across landscapes with millions of interacting cells.  In Chapter 6, new plot-based regression models and ALS metrics were developed for the estimation of canopy gap fraction (Po). The first new ALS metric was the hemispherical Voronoi gap fraction (Phv) and the second was the point-density normalized gap fraction (Ppdn). For the  191  Phv metric, the effects of four different lens geometries were tested. In the process, a 2-D variant of the spike-free canopy height model (Khosravipour et al., 2016) was developed for the application of standard individual tree crown (ITC) detection algorithms. Standard ALS metrics were calculated for comparison of their performance in estimating ACC (1 - Po) and Po. While the new Ppdn metric performed decently (R2 = 0.32), top performing metrics for estimating ACC used existing methods, VCCfci (R2 = 0.53), VCCfr (R2 = 0.51), VCCir (R2 = 0.51), VCCsci (R2 = 0.51).  In Chapter 7, simulation results from Chapters 4 and 5 were combined with the regression model of Po from Chapter 6 and a topographic solar radiation model to simulate changes in mean annual global understory solar irradiation (Iu) for each of the model scenarios. Linear and machine learning regression models of Po were developed from plot and ancillary data, including ALS metrics, for model fusion. Both classes of model showed optimal performance using two predictors: CLI forest site index and ABMI Landcover 2010. While Random Forest produced comparable model fit compared to multivariate linear regression (R2 = 0.939; RMSE = 0.074), the latter produced less bias while benefitting from simplicity (R2 = 0.938; RMSE = 0.079). Thus, a two-parameter linear regression model was used for final model fusion in LANDIS-II simulations. Nevertheless, I demonstrate the first, to my knowledge, fusion of machine learning and forest ecosystem models.  A classification scheme based on ABMI Landcover 2010 was developed for LANDIS-II species-age cohort outputs to model landcover change for each simulation year. Next, the regression model of Po was applied for each timestep using landcover maps as a predictor. A solar radiation  192  model was applied to a NASA SRTM digital elevation model (DEM) to calculate bare-earth global solar irradiation (Iglobal) as the sum of direct and diffuse components. The resulting map of Iglobal importantly showed the ‘feast-or-famine’ light conditions of mountainous regions in the study area, due to topographic position. Finally, each annual map of Po was multiplied against Iglobal to simulate changes to understory global solar irradiation (Iu).  Hybrid model simulations showed that modeled Iu levels increased under Pre-suppression Era and Most Recent Decade conditions using the statistical fire model. Yet, Iu levels declined in each of the other scenarios. The choice of fire model was a key differentiator in model results. Using the extremes scenarios as an example, where the warmest climate conditions were applied with the most severe rates of burning, Iu levels substantially increased with the statistical fire model and decreased with the semi-mechanistic fire model over the 50-year simulation period. In all other scenarios, the recruitment of new cohorts and stand development outweighed disturbance-related mortality, producing demographic ageing and a mean decline in Iu levels.  Explaining these results requires reference to Figure 6.3d, which shows that the statistical fire model consistently produced the parameterized fire regime, while the semi-mechanistic fire model was strongly constrained by fuel limitations. The choice of fire model architecture is a function of the research question. This research applied both types in an effort to better understand forest ecosystem trajectories using ensembles. Using the statistical model with empirical parameters, it was clear that weakened disturbances reduced modeled Iu across the landscape. However, the past decade showed an increase in the rate of burning and thus in Iu,  193  attributable to exponentially increased fire frequency. These patterns may be indicative of future national fire regimes as population levels and temperatures continue to rise in Canada’s forests.  While one may infer that increased satellite coverage in recent decades explains the apparent increase in fire frequency and decrease in mean fire size observed in the Canadian National Fire Database, this assumption did not hold. Mean fire size was larger rather than smaller for satellite observations, likely attributable to the coarse sensor resolution of MODIS and improved coverage in the north, while the contribution of satellite observations to fire frequency was minimal. Satellite observations partially explained the northward migration of boreal fires, while none of the Alberta fires were sourced from satellite imagery. Increases to area burned were not evident for western Alberta or nationally. The implications of novel anthropogenic fire regimes are unknown, requiring forest ecosystem simulations together with remote sensing for the investigation of likely systematic changes to forests.  8.1 Limitations The limitations of the results of this research stem from two fundamental sources: (1) uncertainty in model parameters; (2) uncertainty in modeled processes. Uncertainty in empirical measurements is implicitly included in parameter uncertainty. While some uncertainties are ‘known unknowns,’ or uncertainties that are known to exist, others are ‘unknown unknowns,’ or uncertainties that are not known to exist (US Department of Defense, 2002). Known unknowns include imputed values, omitted processes known to exist (e.g., models of lighting ground-strike frequency or solar activity), scale effects on model and data accuracy, spatiotemporal variation in model parameters, and the measurement accuracy of empirical data. Unknown unknowns  194  involve the omission of unknown factors and thus include processes not known to exist, parameter values not known to exist, or practical issues related to hardware or software not known to exist. Last, there are ‘known knowns,’ or phenomena that are robustly quantified and treated as certain. While there are many known unknowns and few known knowns, it would be paradoxical to quantify the number of unknown unknowns without statistical inference (i.e., inverse modeling). Therefore, the discussion of research limitations presented in each chapter focuses on known unknowns.  Increased geospatial data would have enhanced model development and parameterization. While fire history data for Canada (Stocks et al., 2002; Parisien et al., 2006; Burton et al., 2008) is more robustly described than for many other regions, it remains limited by spatiotemporal biases and substantial variation in detection methods. These issues with sampling appear readily addressed by modern satellite formations (Hand, 2015) together with recent breakthroughs in computer vision (LeCun et al., 2015), which may demand copious computational resources to fully utilize. While mapping fire, biogeoclimatic regions (Natural Regions Committee, 2006), landcover classes (Wulder et al., 2007; Agriculture and Agri-Food Canada, 2012), and climate data (Menne et al., 2012) have received much attention in recent years, medium-resolution (~ 1 ha) maps of tree species distributions, stand demographics (age classes), soil textural properties, and plant traits essential to parameter estimation where species information is lacking remain absent.  A second data gap stems from the multitude of species parameters used in the models. Some parameters are coarsely estimated, necessitating refinement, while others may only be available  195  for well-studied regions. Meanwhile, single trait values are typically used to describe variation within the entire species ranges (Burns & Honkala, 1990; Farrar, 1995a; Klinka et al., 2000), rather than providing probability distributions. Even though a wide degree of variation in genotypes and gene expression exists in nature (Aitken et al., 2008), this variation is seldom represented in existing species compendiums or models. While next-generation dynamic global vegetation models (Scheiter et al., 2013) take such an ecological-evolutionary approach based on an assumption of optimality, most current-generation forest ecosystem models were not designed to model evolutionary processes, given a typical simulation maximum of 1 kyr.  Even though it is possible to reconfigure existing models to incorporate genetic variation using simple modifications, validation data for genotypic and phenotypic variation may be difficult to attain. Nonetheless, rapid growth is foreseen in the collection of genomics data, given advances in next-generation sequencing techniques (Goodwin et al., 2016) and interest surrounding CRISPR-Cas9 (Doudna & Charpentier, 2014; Sander & Joung, 2014) for targeted applications. New tree species compendiums, consisting of bioinformatics databases rather than books, should be established for use in modeling studies. In order to extrapolate genetic information across the landscape, remote sensing studies should predict genetic variation from canopy spectra using recent advances in machine learning (LeCun et al., 2015). Studies utilizing hyperspectral imagery have demonstrated the feasibility of this task (Asner et al., 2014, 2015; Asner & Martin, 2016; Cavender-Bares et al., 2016). Such maps may resolve some of the most difficult aspects of model parameterization and validation.   196  8.2 Research Contributions In Chapter 3, this work showed that fire regimes in western Alberta transitioned from large stand-replacing lightning-caused fires to small frequent human-caused fires in recent decades. This work demonstrated that mean fire size and latitude across Canada steadily declined since the 1990s, irrespective of increased satellite monitoring. Novel anthropogenic fire regimes were characterized for western Alberta and Canada-wide, including changes in size, frequency, seasonality, latitude, elevation, and cause. Fires occurred closer to roads and waterbodies over the past three decades, treated as proxies of human activity. Human-caused fires linearly occurred closer to roads over time, while lightning-caused fires remained at a constant mean distance. This suggests that increased proximity of fires to roads is not due to road expansion, but to an increased number of users on existing road, which is an important distinction for management.  Importantly, this work showed a northward migration of boreal fire regimes, peaking in the 1970s before dipping southward and rising again, only partially explained by spaceborne monitoring. The temporal classification of fire regimes using the binary segmentation algorithm was also demonstrated. A significant bimodality of the fire size distribution was shown for Alberta, explained by the recent emergence of anthropogenic regimes. An anthropogenic theory of energetic constraints to biomass burning was proposed, which includes human activity alongside vegetation and climate as fundamental energetic controls on fire.  A key conclusion of this work is that future wildfire models should define the probability of ignition with raster surfaces, rather than regional coefficients. These raster inputs may be  197  allowed to vary with the simulation time-step, producing realistic ignition patterns over time to facilitate model validation with new satellite data. The input rasters would serve two other key purposes: (1) to model fire adjacency to human activity, as anthropogenic regimes may eventually dominate northwestern North America (Amoroso et al., 2011; Whitman et al., 2015); (2) to realistically model the spatial distribution of lightning strikes, using data from the GOES-R/GOES-16 Geostationary Lightning Mapper (Goodman et al., 2013) or other sensors.  To better capture spatial wildfire patterns, forest fire models may eventually use separate input maps for the probability of ignition based on the cause, as the size and frequency distribution of lightning-caused and human-caused fires differ markedly. As the input of remote sensing products into forest ecosystem models becomes standardized, similar to data assimilation in weather forecasting models, additional processes may be defined and constrained by raster representations, including landcover, photosynthesis, leaf area index, canopy height, and, carbon, water, and nitrogen flux. Model designers may prepare for these changes by increasing reliance on satellite data for model parameterization. Stacked rasters at defined height intervals may allow volumetric representation of height maps (voxels), as optical stereo photogrammetric imagery may provide global 3-D multi-spectral forest dynamics monitoring in the coming decades (Shean et al., 2016). Meanwhile, modelers may rely on synthetic data for development. In Chapter 4, this work contributed to the development of a new process-based tree regeneration model, TACA-GEM. A national parameterization method was developed for TACA-GEM, based on soil textural classes and NOAA GHCN-D climate data scripts available in the rnoaa package for R (Chamberlain et al., 2016). The TACA-GEM modeling results suggested the potential of a decline in tree regeneration in western Alberta under recent climate change, due to  198  changes in germination frequency, drought frequency, and growing season length. The modeling work highlights the importance of the sensitivity of tree regeneration to climate change in forest succession, elucidating an important area of future research.  In Chapter 5, new methods were developed for parameterizing LANDIS-II in Alberta, Canada. The most detailed forest ecosystem simulations were conducted for the region, at one-hectare resolution with 25.2 million interacting stands. An algorithm was developed for fire model parameter optimization, resolving a long-standing challenge in the application of fire models across large areas. This work generally showed a modeled decline in forested area for western Alberta across the study period. This result was mostly a product of the integrated regeneration model, highlighting the importance of regeneration in stand succession. This work also showed differences in results related to the application of different classes of wildfire models. Importantly, model results indicated that decreased disturbance rates may slow changes to the central tendency of the spatial distribution of tree species, increasing in situ climatic disequilibrium. Increased tree longevity also implies reduced in situ adaptation rates, highlighting an important direction for future research.  In Chapter 6, a modified spike-free canopy height model algorithm was developed based on 2-D barycentric interpolation. Two new canopy gap fraction LiDAR metrics were also developed: hemispherical Voronoi gap fraction and point-density normalized gap fraction. An exhaustive comparison of LiDAR metrics of canopy openness (gap fraction and angular canopy closure) was conducted. Empirical tree-height-to-crown relationships were developed for the application of individual tree crown detection methods. An experimental method of individual tree  199  segmentation based on α-shapes was also tested, which showed promising early results (Figure B.6). Importantly, this research demonstrated the effects of hemispherical lens projections on measures of canopy openness from ALS. This work resulted in a second open-source software package, in the gapfraction package in R.  In Chapter 7, using two parameters, linear regression and Random Forest models of angular canopy closure were developed with R2 values of 0.94 each and RMSE of 0.08 and 0.07, respectively. A new landcover classification scheme was developed for LANDIS-II species-age cohort outputs, based on ABMI Landcover 2010. This work developed new methods of simulating landscape change to angular canopy closure and gap fraction with LANDIS-II. This is also the first study to develop external methods of simulating landscape changes to understory solar irradiation in LANDIS-II. Model results suggest that a decline in forested area and ageing may have counteracting effects on understory solar irradiation levels.  8.3 Areas of Future Research This work is the first, to my knowledge, to demonstrate the fusion of a machine learning model with a forest ecosystem model to simulate processes not explicitly represented, in a hybrid modeling approach. This work paves the way for a promising new area of research on the fusion of machine learning and process-based models. Following model training with plot data, machine learning models may run inference on remote sensing or model data. Near real-time applications exists whereby remote sensing inputs may be used to iteratively update online simulations.   200  In deep learning, generative adversarial networks (GANs), convolutional neural networks (CNNs), or recurrent neural networks (RNNs) may be used to facilitate the representation of complex spatiotemporal dynamics (Goodfellow et al., 2014b; LeCun et al., 2015). In recent years, spatiotemporal 3-D CNN and RNN-CNN architectures have been successfully applied to related tasks, such action recognition in video sequences (Ji et al., 2013; Zhao et al., 2017). Meanwhile, 2-D spatial and 1-D temporal sequence generation tasks have been dominated by GANs and CNNs (Ledig et al., 2016; van den Oord et al., 2016a,b; Chen & Tong, 2017). A clear opportunity exists to fuse deep learning and process-based models to implement the first realistic pattern-based models. While I relied on linear regression for the final model in this work given comparable performance to Random Forest, the promise of deep learning for such problem classes is well established (LeCun et al., 2015).  A new class of hybrid model may blend the grid-based spatial interaction of forest landscape models with the within-stand heterogeneity of gap models to produce more realistic forest demographics, energy partitioning, and biogeochemical cycling. These models may benefit from representing individual tree competition with a mathematically tractable model, as with the first-order hyperbolic partial differential equations and integral equation of the perfect-plasticity approximation (Adams et al., 2007; Purves et al., 2007, 2008; Strigul et al., 2008; Weng et al., 2015) or size-and-age-structured equations (Moorcroft et al., 2001; Medvigy et al., 2009). In these works, the temporal dynamics of individual trees are treated as bounded hyperbolic n-dimensional system with probabilistic events, retaining information on the size structure and density of trees within stands. As the name of the former implies, tree crown shapes are plastic, representing neighborhood competition for light.  201  Efficient model reductions may allow better representation of light resources available for regeneration and other physical processes, such as photosynthesis and evapotranspiration, without greatly increasing computational complexity. An alternative approach to systems of partial differential equations may rely on machine learning for model emulation, reducing model dimensionality and complexity while capturing salient dynamics, a common objective in hybrid modeling. Increased use of machine learning may also enable efficient integration of remote sensing products with process-based models.  A new class of hybrid model should be optimized for highly parallel architectures. Yet, a practical challenge exists in overcoming the sequential design of existing process-based models. Heterogeneous architectures, such as CPU-GPU systems, may facilitate efficient computation of sequential and pattern-based processes. These architectures are widely used in modern supercomputers, including ORNL Titan in the United States, Sunway TaihuLight and Tianhe-2 in China, Piz Daint in Switzerland, and forthcoming CSIRO Bracewell in Australia. As of June 2017, the prior four are the world’s fastest supercomputers (Strohmaier et al., 2017), not including Google’s second-generation tensor processing unit (TPU) datacenters.  The use of dedicated GPGPU (e.g., CUDA, ROCm, OpenCL) and multi-core (e.g., Intel MKL, OpenMP) libraries or natively distributed languages (e.g., Go) may allow for more efficient run times. Highly parallel processor architectures are also ideally suited to training and applying deep learning models. Deep learning models may be included within process-based models by adding deep neural network layers with pre-trained weights, similar to popular ImageNet models (Krizhevsky et al., 2012). Users could optionally apply transfer learning to local datasets for  202  model calibration. Sequential architectures such as long short-term memory (LSTM) may be used to represent pattern-based processes with ecological memory, beyond what is feasible with partial differential equations.  A new class of hybrid models may also benefit from the inclusion of genomics, including genotypes, gene expression (e.g., phenotype plasticity), mutation rates, and gene flow through evolutionary algorithms. While historically constrained by data availability, next-generation sequencing techniques may facilitate the widespread collection of genetic information with reduced cost and time limitations. Although data on landscape genomics remains sparse, an increased availability of genetic information is foreseeable for the coming years. In the meantime, models may include these processes based on predefined sub-models of gene expression, mutation, flow, and thus, adaptation. These sub-models may initially use coarse abstractions, such as pre-defined ranges or probability density functions of species trait variations, admixture rates for particular genotypes co-occurring at sites, or simple mutation rate coefficients. These additions may allow for an improved theoretical understanding of changes to forest landscape genetics produced by evolutionary processes.  The incorporation of genomics into models may also facilitate preliminary inquiry into the potential and limitations of genetic modifications to populations for directed evolution. This is a promising new area of research parallel to synthetic ecology, or the design of ecological interactions through genetic modification (Dunham, 2007). While genetically modified trees are increasingly common in plantations globally and may find targeted use in the wild for conservation and/or carbon sequestration applications (Jacobs et al., 2009; Newhouse et al.,  203  2014), current models lack direct representation of genetic information. By modeling the potential effects of genetic admixture, mutation, and precise gene editing based on tools such as CRISPR-Cas9 (Cong et al., 2013; Mali et al., 2013; Doudna & Charpentier, 2014), better safeguards can be formulated.  Targeted inheritance tools such as CRISPR-based gene drives (Oye et al., 2014; Hammond et al., 2016) may be probed numerically for potential effects of genetic isolation (Drury et al., 2016) and evolutionary resistance to inheritance (Unckless et al., 2017). Biogeochemical optimization applications also exist, including maximizing the rate of carbon sequestration (Jacobs et al., 2009) or minimizing methane production (Su et al., 2015) in plantations. These efforts may benefit from numerical experiments to, for example, achieve optimality between terrestrial carbon storage and residence times (Bloom et al., 2016) in relation to the timing of climatic oscillations to maximize a cooling effect. This would necessitate optimal partitioning of carbon at a stand, rather than tree, scale, lending to combinatorial optimization methods, as optimal partitioning among organ types depends on ecological context.  Full-waveform LiDAR systems (Amiri et al., 2015) may overcome the challenge of monitoring tree regeneration remotely (Amiri et al., 2015; Polewski et al., 2016). Small unmanned aircraft systems (UAS) operating below tree canopies can also be used to map the understory in unprecedented 3-D spectral detail using structure-from-motion (Polewski et al., 2016). This opens a window into mapping the distribution, regeneration, and succession of understory plants. Hyperspectral imaging and/or terrestrial laser scanning systems may be installed in situ across  204  FluxNet towers (Baldocchi et al., 2001) to automate the capture of overstory and understory plant succession in order to link this information to biogeochemical cycles.  Using time-series of hyperspectral imagery with deep learning or standard computer vision techniques, spatiotemporal changes in productivity may be monitored in three-dimensional detail. Provided dense temporal point cloud data for plants, specific succession events can be monitored and recorded in high precision (Li et al., 2013b), providing an automated stand monitoring system. Together, these technologies may provide critically absent information on the dynamics of understory disturbance, regeneration, and succession. Meanwhile, an extensive analysis of plot data across Canada may provide new insights into the effects of climate and competition on tree regeneration. Empirical regeneration studies should incorporate gridded climate, fire, and productivity data (e.g., NDVI or fPAR) to disentangle the effects of climate and competition.  Dense point-cloud time-series from ALS, UAS, and spaceborne stereo photogrammetry provide a unique opportunity to monitor forest dynamics, particularly when fused with deep learning. Meanwhile, new CubeSat satellite formations may facilitate near-real-time observation (Hand, 2015). These data may be applied to monitor forest dynamics in high temporal resolution in order to advance the development of sophisticated new dynamic vegetation models. This data may allow the fitting of models to observation data in more informative ways by focusing on temporally dense 2-D and 3-D patterns, rather than aggregated 1-D trajectories. Again, generative adversarial, recurrent, and convolutional neural networks (Goodfellow et al., 2014a;  205  LeCun et al., 2015) show promise for the transfer of spatiotemporal patterns into model behavior.  Data assimilation through machine learning may be critical for the fusion of satellite observations with dynamic global vegetation models (DVGMs), or terrestrial biosphere models. Remote sensing data and DVGMs are likely to merge through deep learning into a new class of hybrid model. This contrasts to the current use of remote sensing merely to parameterize or constrain physical models. While inherently physical processes may remain simple in form, pattern-based dynamics such as fire spread, species distributions, browsing effects, and biotic disturbances may increasingly rely on deep artificial neural networks. This will require large amounts of labeled data to train new supervised learning models. Long-term monitoring ground plot networks, such as Canada’s National Forest Inventory network (Gillis et al., 2005), which match satellite observations in time, position, and scale should be constructed to facilitate the collection of training data for deep learning in remote sensing.  The full Landsat record should also be utilized to characterize fire history in Canada. This will improve the spatiotemporal coverage of wildfire maps, granting unprecedented insight into historical fire patterns not visible in the current Canadian National Wildfire Database. This information may be used in models to produce more realistic initial conditions. Meanwhile, fire maps may be linked to Landsat vegetation indices, climate grids, and topography to decipher to drivers of fire patterns in Canada. Landsat studies should use spatiotemporal deep learning models to improve the detection and attribution of disturbances. While simple spectral indices may be efficient, they discard rich information contained in the latent space of raw spectra. Deep  206  learning may similarly be applied to develop a new class of radiative transfer model with sequence-to-sequence learning, trained on time-series ground validation data, to correct raw spectra before applying supervised classification models.  Finally, the Canadian federal government, provinces, and universities may benefit by collaborating on the development of open cloud computing infrastructure for geospatial data. This would include harmonized remote sensing and gridded climate products for use in ecological forecasting studies, with standard pre-processing applied to provide ready-to-use products. Pre-processing may include pixel quality metrics and interpolation necessary to match a target spatial and temporal resolution. The finest temporal resolutions may correspond to those of FluxNet (Baldocchi et al., 2001) and weather station data. Such a national data cube with processing facilities would support modeling by easing data access while improving study transparency and reproducibility, critically lacking in large ecosystem modeling and remote sensing studies. Important layers for inclusion may be high-resolution soil texture, coarse fragment content, and soil depth maps, valuable for ecological modeling studies in Canada. These data may improve our ability to represent spatiotemporal changes to soil moisture under the effects of warming. 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Remote Sensing of Environment, 87, 171–182.      272  Appendix A: Statistical Analysis of Historical Fire Regimes  Applying the Shapiro-Wilks test, log-transformed fire sizes showed strong normality both nationwide (W = 0.99 p-value > 2.2e-16) and in the Alberta study area (W = 0.97, p-value > 2.2e-16), enabling the application of t-test and F-test statistics. Based on an analysis of individual fire size mean and variance in the study area, using a significance cutoff of p < 0.05, the full 90-year period showed a significant change in variance only (t = 1.918, p-value = 0.056; F = 24.529, p-value > 2.2e-16). While individual fire sizes between the Pre-Suppression and Early Suppression periods showed a significant difference in variance (F = 20.549, p-value < 2.2e-16), differences in the means between these two periods were not statistically significant (t = 1.336, p-value = 0.182). The distribution of log-transformed fire sizes nationwide showed good fit with Weibull and Gaussian distributions (Figure A.1).        273    Figure A.1 Model fit for log-transformed fire sizes Canada-wide: (a) histogram and theoretical PDFs; (b) empirical and theoretical CDFs; (c) Q-Q plot; (d) P-P plot  The robustness of Weibull model fit for log-transformed fire sizes nationwide is confirmed by the application of five Anderson-Darling maximum goodness-of-fit parameter estimation methods using the fitdistrplus package for R (Delignette-Muller & Dutang, 2015). The right-tail second-order Anderson-Darling (AD2R) statistic (Luceño, 2006) shows the best parameter estimations, as it better mitigates truncation at larger fire sizes (Figure A.2).  (a) (b) (c) (d) Log of fire size (ha) Log of fire size (ha)  274    Figure A.2 Anderson-Darling goodness-of-fit Weibull model parameter estimation for log-transformed fire sizes Canada-wide: (a) histogram and theoretical PDFs; (b) empirical and theoretical CDFs; (c) Q-Q plot; (d) P-P plot; ADR = right-tail Anderson-Darling; ADL = left-tail Anderson-Darling; AD2R = right-tail Anderson-Darling second order; AD2L = left-tail Anderson-Darling second order; AD2 = Anderson-Darling second order  The distribution of fire sizes in Alberta showed significant bimodality. Using a mixed Gaussian model for Alberta study area fire size, the two modes centered on µ of 1.2 and 6.2 log ha, with Expectation-Maximization (EM) and Bayesian Markov Chain Monte Carlo (MCMC) algorithms each converging to these values (Figure A.3). Log of fire size (ha) Log of fire size (ha) (a) (b) (c) (d)  275   Figure A.3 Mixed Gaussian model probability density function showing strong bimodality of the log-transformed fire size distribution for the Alberta study area  The fire size distribution for Alberta showed significant bimodality. A further analysis reveals distinct changes in the fire size distribution over time (Figure A.4).   276   Figure A.4 Fire size distribution (log of ha): (a) 1923-2012; (b) 1923-1952; (c) 1953-1982; (d) 1983-2012(a) (b) (c) (d)  277  Appendix B: ALS Models of ACC and VCC  The Phv lens geometries tested showed comparable performance, with the exception of the equiangular projection, which performed poorly in predicting Po. Higher canopy height thresholds showed superior performance for all lens geometries (Figure B.1).   Figure B.1 Pearson’s correlation coefficient (r) for convex spherical densiometer measurements and the ALS hemispherical Voronoi gap fraction (Phv) metric for different canopy height thresholds; Stereo = stereographic projection; Ortho = orthographic projection; Equidist = equidistant projection; Equiangle = equiangular projection; numerical values = height thresholds used to calculate minimum canopy heightACC	Pearson’s	r	Phv Metric by Hemispherical Lens Model and Canopy Height Threshold (m)  278  Pearson correlations with ground ACC measurements showed good performance for a number of methods. Of the Po metrics tested, Ppdn showed the best overall performance (Figure B.2).    Figure B.2 Pearson’s correlation coefficient (r) for convex spherical densiometer ground measurements and ALS metrics; ACC values are omitted, as they are the inverse of Po  Meanwhile, univariate linear regression models that changed the slope and intercept relationships showed markedly better performance of predicting ACC for the VCC metrics, VCCfci, VCCfr, and VCCir (Figure B.3). In these tests, the performance of Ppdn fell behind. ACC	Pearson’s	r	Canopy Light Transmission Metric  279   Figure B.3 Linear regression model fit for the top three univariate models after filtering out observations with likely disturbances: (a) VCCfci; (b) VCCfr; (c) VCCir; the blue line represents the slope and intercept of the univariate regression model, with VCCfr approaching the 1:1 line  Linear, first-order, and second-order polynomial models were fit between ground ACC and VCCfci for plots with and without observations flagged for quality issues (Figure B.4).   Figure B.4 VCCfci model fit for all 950 ground ACC measurement plots; blue = linear; red = second-order polynomial; green = exponential; left = with disturbed sites; right = without disturbed sites  (a) (b) (c) VCCfci VCCfr VCCir VCCfci VCCfci  280  Using on the filtered observations, the same three models were applied to Ppdn for the estimation of ACC. As the scatter plot shows, the relationship between ACC and Ppdn was more linear than the VCC metrics, while the bias was also greater. The variance was greater for higher Ppdn values, corresponding to lower ACC values (Figure B.5).   Figure B.5 Models of Ppdn and ground ACC measurements; blue = linear; red = second-order polynomial; green = exponential  An experimental method for individual tree segmentation with ALS data based on three-dimensional α-shapes was also tested, based on a simple parametric variant of the convex hull. A visualization of one LiDAR test plot is provided (Figure B.6). While the first results appear promising, the method requires further research with validation data, which were unavailable for this study.   281   Figure B.6 Individual tree segmentation with low-point-density ALS data using three-dimensional α-shapes; object class membership is signified by color; the ground plane is visible in chartreuse    282  Appendix C: Random Forest Algorithm  Random Forest builds on the bagging procedure, or bootstrap aggregation, the averaging of many noisy unbiased models to reduce variance, by building a large collection or forest of de-correlated regression trees before performing averaging. Trees are ideal for bagging procedures, as they can capture complex interactions, have low bias, and high noise (Hastie et al., 2009). The bias of bagged trees is identical to that of individual trees, making variance the focus of improvement. Random Forest was designed to improve upon the variance reduction of bagging by minimizing the correlation between trees without substantially increasing the variance. This is achieved by randomly selecting input variables during the tree-growing process. The Random Forest algorithm process functions as described below, adopted from Hastie et al. (2009):              283  Algorithm: Random Forest Algorithm for Regression or Classification 1. For b = 1 to B: a. Draw a bootstrap sample Z* of size N from the training data b. Grow a random-forest tree !" to the bootstrapped data, by recursively repeating the following steps for each terminal node of the tree, until the minimum node size #$%& is reached i. Select m variables at random from the p variables ii. Pick the best variable/split-point among the m iii. Split the node into two daughter nodes 2. Output the ensemble of trees !" '( Following model training, to make a prediction at a new point x: Regression: )*+( , = '( (".' !" ,  Classification: Let /" ,  be the class prediction of the bth Random Forest tree. Then, /*+( , = 01234567	936:	 /" , ('  Here, I focused on the regression case. In short, the Random Forest algorithm creates ntrees decision trees from randomly selected variables with mtry splits at each node. Each of these trees is a weak predictor, combined through averaging to produce predictions.      284  Appendix D: ABMI Landcover 2010 Classification Scheme and Algorithm  The following section describes the lookup table and algorithm used for classifying simulation outputs into landcover classes (Table D.1) at an annual simulation time-step.  Table D.1 ABMI Landcover 2010 classification scheme Value Landcover Class 0 None 20 Water 31 Snow/Ice 32 Rock/Rubble 33 Exposed Land 34 Developed 50 Shrubland 110 Grassland 120 Agriculture 210 Evergreen (Coniferous) Forest 220 Broadleaf Forest 230 Mixed Forest       285  The pixel classification algorithm used to classify LANDIS-II species-age map outputs is described in detail below:  Algorithm: Classification of LANDIS-II species-age cohorts into ABMI landcover classes 1. For each LANDIS-II simulation scenario: a. For each simulation year: i. For each species-age map: 1. Assign pixels to either evergreen or broadleaf classes ii. Count the number of species present for each class iii. Calculate richness as the sum of species present per class iv. Calculate percent evergreen/broadleaf by dividing by species richness v. Classify pixels inactive in LANDIS-II simulations to remove pixels masked in the simulations: 1. Use ABMI Landcover 2010 map to assign values for classes 0-120 vi. Classify pixels active in LANDIS-II simulations, overwriting previous classification values for sites that fail to regenerate post-disturbance: 1. Assign pixels to Evergreen Forest (210) where greater than 75% 2. Assign pixels to Broadleaf Forest (220) where greater than 75% 3. Assign pixels to Mixed Forest (230) where both percent evergreen and broadleaf are greater than or equal to 25% 4. Assign pixels to Grassland (110) where both percent evergreen and broadleaf are equal to zero b. Save the raster time-series of landcover change for use in regression models of Po  286  Appendix E: Bare-earth Global Solar Irradiation Algorithm   Based on previous work (Rich, 1990; Rich et al., 1994; Fu & Rich, 2002), parallel to GRASS r.sun algorithm development (Šúri & Hofierka, 2004), global solar radiation was calculated in the following steps:  1. Calculate the 3-D hemispherical viewshed for a DEM cell to 2-D polar chart 2. Calculate half-hourly sun position polar chart based on solar zenith (;) and azimuth (<) 3. Calculate half-hourly direct solar radiation for sectors in a 2-D polar chart 4. Calculate half-hourly diffuse solar radiation for sectors in a 2-D polar chart 5. Calculate total direct solar radiation by masking sky sectors of (3) with pixels of (1) 6. Calculate total diffuse solar radiation by masking sky sectors of (4) with pixels of (1) 7. Calculate global solar radiation for the cell as the sum of (5) and (6)  Each 2-D polar chart shares the same projection, facilitating simple matrix computations. The computation of the hemispherical viewshed from the perspective of the ground looking toward the zenith is similar to hemispherical photography, convex spherical densiometers, and hemispherical LiDAR approaches of estimating light occlusion, making the solar model compatible with the proposed modeling framework.  The hemisphere calculations used were originally developed for hemispherical photography vegetation studies (Rich, 1990; Fu & Rich, 1999). In the viewshed calculation, twelve equal azimuth angles are searched from the pixel center for computation of the maximum horizon  287  angle (unobstructed zenith). The horizon angles are then converted into a hemispherical coordinate system as zenith (;) and azimuth (<) angle sectors of a polar plot. Each cell within the hemisphere sectors takes one of two binary values, visible or occluded.  The half-hourly sun position is calculated using standard equations (Iqbal, 1983), used for calculating direct and diffuse radiation components. The calculation of direct, diffuse, and global radiation for a given sun position follows previous work (Rich, 1990; Rich et al., 1994; Fu & Rich, 2002). Global solar irradiation (?@AB"CA) is the sum of direct ?D%*EFG and diffuse ?D%++HIE components, ignoring reflected irradiation:  ?@AB"CA = ?D%*EFG + ?D%++HIE  Direct solar irradiation ?D%*EFG is computed as the sum of irradiation for each sector defined by zenith ;  and azimuth <  angles for each hour and month:  ?D%*EFG = ?D%*EFGK,M  The direct solar irradiation for a given zenith and azimuth angle sector is calculated as the solar constant for the mean earth-sun distance (NFB&IG), equal to 1367 W m-2, multiplied by the atmospheric transmissivity for the shortest path raised to the relative optical path length (O$K), the sky sector sun duration (6P,Q), equal to monthly and half-hourly intervals or spherical  288  geometry, the gap fraction for the sun map sector (RP,Q), and the cosine of the angle of incidence between the sky sector centroid and the surface normal (SP,Q):  ?D%*EFGK,M = NFB&IG ∗ O$K ∗ 6P,Q ∗ RP,Q ∗ cos SP,Q  Relative optical path (0P) is calculated based on the cell elevation in meters (X) and solar zenith angle (;):  0P = 	exp −0.000118	 ∗ 	X	 − 	1.638 ∗ 10cd 	∗ 	Xe 	/ 	cos ;  The angle of incidence (SPQ) is calculated based on the solar zenith angle (;), surface zenith angle (gh), and surface azimuth angle (gC):  SPQ 	= 	 cosc' ; ∗ 	cos gh 	+	sin ; 	∗ 	sin gh 	∗ 	cos(< − gC)	  Diffuse solar irradiation ?D%++HIE is computed as the sum of irradiation for each sector defined by 8 zenith ;  and 16 azimuth <  angle divisions:  ?D%++HIE = ?D%++HIEK,M  Unlike direct irradiation, ?D%++HIEK,M sectors are calculated as the rolling sum of half-hourly values for a given time interval, due to the multi-directional nature of diffuse radiation, with each  289  sector predefined rather than based on modeled solar position. The diffuse solar irradiation for a given zenith and azimuth angle sector is calculated as the global normal radiation (k@A") multiplied by the proportion of diffused global radiation flux (lD%++HIE), time interval (6), sky sector gap fraction (RP,Q), weighted proportion of diffuse radiation originating from a sector (mP,Q), and cosine of the angle of incidence (SP,Q):  ?D%++HIEK,M = k@A" ∗ lD%++HIE ∗ 6 ∗ RP,Q ∗ mP,Q ∗ cos SP,Q  Global normal radiation (k@A") is calculated as the solar constant (NFB&IG) multiplied by the sum of the atmospheric transmissivity for the shortest path raised to the relative optical path length (O$K), divided by one minus the proportion of diffused global radiation flux (lD%++HIE) to correct for direct radiation:  k@A" = NFB&IG O$K / 1 − lD%++HIE   The weighted proportion of diffuse radiation originating from a sector (mP,Q) is calculated as the zenith angle range for a sky sector (cos ;e −	cos ;') divided by the number of azimuth divisions in the sky map (nQ): mP,Q 	= 	 (cos ;e −	cos ;')	/	nQ  Each of these calculations was performed automatically for each cell in the DEM using ArcGIS solar analyst tools (Fu & Rich, 1999).  290  Appendix F: Validation of TACA-GEM with Permanent Sample Plot Data  To validate TACA-GEM regeneration model results, I conducted an analysis of Alberta Permanent Sample Plot (PSP) data. This analysis focuses on stand regeneration dynamics and indicators of competitive resource constraints to regeneration (Alberta Sustainable Resource Development, 2005a). Previous versions of these data were used in studies related to stand growth, mortality, and regeneration in the region (Navratil et al., 1991; Stewart et al., 2001; Yang et al., 2003; Stadt et al., 2007). These studies indicate that competition, measured through proxies of stand development and tree growth (e.g., basal area and tree height), plays a key role in inhibiting regeneration success through diminished resource availability. While the TACA-GEM modeling work in Chapter 4 focused on abiotic resource constraints to regeneration (i.e., climate), model fusion with LANDIS-II in Chapter 5 provided competition through logical rules (e.g., an inverse equivalence of understory light levels and the shade tolerance of tree species present in sites). The purpose of this section is to relate TACA-GEM modeling results to empirical observations for the Alberta study area. I infer regeneration changes attributable to abiotic conditions inversely by modeling the effects of competition.  In this analysis, I rely on Permanent Sample Plot (PSP) and Stand Dynamics System (SDS) data from Alberta Sustainable Resource Department (Alberta Sustainable Resource Development, 2005a,b). While the former is intended to provide information on stand growth and yield, and also contains data on mortality and regeneration over time, the latter is designed to monitor post-harvest regeneration dynamics for stands up to age 20 (Alberta Sustainable Resource Development, 2005b). The SDS observations begin in 1984, immediately following stand- 291  replacing harvest. While PSP observations date back to 1960, the regeneration component changed to the present format in 1983. The PSP and SDS datasets are complementary in their focus on overstory and understory dynamics, respectively. Both datasets contain measures of regeneration abundance by height class and proxies for competition, including tree height and diameter-at-breast-height (DBH). Both datasets are limited in temporal scale relative to stand development, making long-term analyses difficult, while lacking information on climate, soils, and solar radiation.  With these limitations in mind, I conduct a two-part analysis of tree regeneration in the Alberta study area. I focus on the Global Change Era (1983-2012) for its overlap with PSP and SDS regeneration data for this period, high sampling coverage (nPSP = 659,607; nSDS = 406,117), and relevance to TACA-GEM model results. While a naïve view of empirical regeneration data shows diminished regeneration rates over time for both datasets, statistical models, previous research (Navratil et al., 1991; Stewart et al., 2001; Yang et al., 2003; Stadt et al., 2007), and forest dynamics theory (Shugart, 1984) suggest that a significant amount of this variation is explained by stand development.  The SDS data show reduced regeneration rates over the period unexplained by sampling frequency bias (Figures F.1a and F.1b). From 1984 to 2013, the rate of regeneration in SDS data declined by 99.9%. A large magnitude effect is expected given the negative relationship between stand development and post-harvest regeneration produced by resource limitations related to competition (Shugart, 1984). Dividing the regeneration rate by the number of observations for  292  each year, a pattern of asymptotic exponential decay is shown for germination frequency under post-harvest stand development (Figure F.1c).       Figure F.1 Changes in regeneration and observation frequency over time in the SDS plot data: (a) germination frequency by year; (b) observation frequency by year; (c) germination frequency divided by observation frequency by year  (a) (b) (c)  293  The reduction in regeneration rates for SDS plots corresponds to changes in stand ageing and height growth (Figures F.2a and F.2b). Linear models show that overstory and understory competition explain 22% and 23% of regeneration variation, respectively, for the SDS data. This suggests that up to ~ 50% of the decline in regeneration may be attributable to abiotic conditions (i.e., climate, soils, and solar radiation). Future studies should directly test this assumption with climate and soils data, which is beyond the scope of this exercise.       Figure F.2 Box plots of (a) mean tree age and (b) tree height for all age classes as proxies of competition for SDS plots; observations begin following stand-replacing harvest  In the PSP data, saplings are binned into five regeneration height classes, ranging from 0.10 m to 1.29 m in height (Alberta Sustainable Resource Development, 2005a). I focus on changes to the smallest height class as indicative of annual germination and regeneration success, using only plots without any treatment applied. The data show a 39% decline in regeneration frequency from 1960 to 2009 and a 6% decline from 1983 to 2009 (Figure F.3a). Temporal autocorrelation suggests periodicity in regeneration change at approximately years four and nine (Figure F.3b), (a) (b)  294  which may correspond to a combination of the Pacific quasi-decadal oscillation, Pacific Decadal Oscillation, and El Niño-Southern Oscillation (Xie et al., 1999; Wang et al., 2014a). The PSP data indicate that understory competition most reduced regeneration rates; changes to regeneration for the smallest height class (the youngest saplings) were inversely proportional to combined changes for all other classes. The phase of regeneration frequency for both groups showed good agreement (Figure F.3c) after removing sampling bias, which suggests a climatic and/or overstory canopy origin of the phasing.           295       Figure F.3 Regeneration changes in the PSP data by year: (a) changes to height class 1; (b) autocorrelation of regeneration changes to height class 1; (c) relation of changes to height class 1 to other classes; red = height class 1; blue = sum of all other height classes  The effects of competition were also apparent in the PSP data. Based on few available samples (n = 46), understory angular canopy closure (ACC) showed an exponential increase over time, while overstory ACC appeared affected by a single large disturbance in ~ 1968 (Figures F.4a and (a) (b) (c)  296  F.4b). Changes in average age for all 915 PSP plots and all age groups (n = 6,584) shows clear stand ageing over the period (Figure F.4c). This finding is in agreement with a recent study of the region showing an ageing signal (Zhang et al., 2015).  However, mean tree height (n = 283,878) is shown to have declined across the period (Figure F.4d). As tree age and height are known to scale well in Alberta (Cieszewski & Bella, 1989), this discrepancy may be due to differences in sampling coverage. As tree height contains over 43 times as many observations as tree age, tree height is considered a more robust indicator of stand development for the region. Mean tree height significantly declined between 1960 and 2009 (p < 0.001), and, between 1983 and 2009 (p < 0.001). This suggests a similar pattern for mean tree age, challenging the recent study of Zhang et al. (2015) for the region. An alternative explanation is that this change in mean tree height is a statistical property whereby stand development results in few tall trees and many small trees, reducing the central tendency of tree height.     297     Figure F.4 Plots for (a) understory and (b) overstory angular canopy closure (ACC) class, (c) mean site tree age, and (d) mean tree height by year for PSP data; few observations of ACC were available  Counterintuitively, competition indicators explained more regeneration variation in PSP than SDS data. Linear models for the PSP data indicate that 75% and 39% of variance in regeneration for the lowest height class is explained by overstory and understory competition, respectively. For the sum of all regeneration height classes in the PSP data, overstory competition (tree height (a) (b) (c) (d)  298  and DBH) explained only 7% of the variance in regeneration rates. Leave-one-out and univariate linear regression models show that changes to total regeneration were strongly correlated with changes to height classes 2 and 3 (Table F.1). The contribution of height class 1 to total regeneration was low, yet critical in that it represents regeneration at a basal level. This low contribution is likely due to low survival rates, as sapling mortality rates have been shown to decline with age (Jones & Sharitz, 1998).  Table F.1 Linear models of total understory regeneration change by individual height classes  Height Class     Leave-one-out R2   Univariate R2  Class 1 0.0005 0.012 Class 2 0.0038 0.989 Class 3 0.0014 0.988 Class 4 0.0001 0.981 Class 5 0.0003 0.621  Correlations with total regeneration were stronger for taller height classes (Figure F.5). Only height class 1 was negatively correlated with the year, indicative of diminished long-term regeneration rates. Changes to the lowest regeneration height class were positively correlated with changes to the tallest regeneration height class (r = 0.41), suggesting vertical partitioning of the understory canopy or the development of small gaps.  299   Figure F.5 Correlations between height classes (ht), total regeneration (net), and year, using Pearson’s r  This analysis can be broken down further into temporal changes for each of the height classes. Locally weighted polynomial regression (LOESS) was applied with a moving window filter to detect minima and maxima change-points in the regeneration time-series for each PSP tree height class and the total regeneration change (Figure F.6). Moving window and LOESS smoother window sizes of 1.0 and 0.1 were used, respectively. While regeneration declined for the lowest height class, it increased for all other height classes, indicating signs of understory ageing modulated by episodic mortality and growth events.   300   Figure F.6 Changes to regeneration by height class in the PSP data; minima and maxima change-points were detected by comparing minima and maxima of a loess smoother to those of a moving window filter  Agreement is shown for change-points at years 1975, 1984, 1985, 1987, 199