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Spatial patterns of humidity, fuel moisture, and fire danger across a forested landscape van der Kamp, Derek W. 2017

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Spatial patterns of humidity, fuel moisture, and firedanger across a forested landscapebyDerek W. van der KampBSc., Physics and Ocean Sciences, University of Victoria, 2005MSc., Geography, The University of British Columbia, 2008A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Geography)The University of British Columbia(Vancouver)August 2017c© Derek W. van der Kamp, 2017AbstractSpatial variability in fuel moisture driven by changes in microclimate is an im-portant bottom-up factor determining spatial wildfire behaviour, as fuel moistureimpacts fire intensity, severity, and spread probability. However, few studies haveexamined how landscape scale patterns in near-surface microclimates impact fuelmoisture patterns. This study quantified patterns of near-surface atmospheric con-ditions within a heterogeneous forested landscape, and determined how those pat-terns impact the spatial variability of fuel moisture and fire danger across the land-scape. Observations across a forested landscape demonstrated that, in general,spatial variability in near-surface relative humidity and temperature was highestduring dry, clear-sky conditions. However, daytime relative humidity was an ex-ception, being relatively homogenous across the landscape and only weakly relatedto weather conditions. Canopy cover and above-canopy radiation load predicteda significant portion of the spatial patterns in relative humidity and temperature.Changes in canopy cover had the largest impact on near-surface conditions. Opensites saw higher relative humidity, on average, due to nocturnal longwave cooling.A novel fuel moisture model was presented that predicted between 76% and 93%of the variance in observations from independent sites or time periods, which is animprovement on a more complex model currently used operationally. This modelwas combined with meteorological observations to quantify spatial patterns in fuelmoisture and potential fire danger across the landscape. Daytime fuel moisture andpotential fire danger exhibited low spatial variability, regardless of weather con-ditions, and only 1-hour fuel moisture was related to canopy cover or radiationload. Fuel moisture and potential fire danger were more variable at night and thatvariability increased during cool, moist periods with low wind speeds. Patterns iniifuel moisture and potential fire danger were dominated by differences in noctur-nal longwave cooling due to changes in canopy cover. Open sites had lower dailymean potential fire danger. When fire danger was extrapolated over a larger studyregion, daytime conditions remained homogenous. Moreover, radiation load andcanopy cover did not have a large enough direct influence on daytime fuel moistureto generate patches within the landscape that remain significantly wetter than thesurrounding landscape.iiiLay SummaryFires play an important role in forests, and it is important to understand how firesspread and how the severity and intensity of a fire changes across a forest. The goalof this thesis was to determine how fuel moisture, which has a significant influenceon fire behaviour, changes across a forested landscape due to changes in aspect andthe density of the canopy. It was found that the density of the canopy had an impacton fuel moisture. Open sites had wetter fuels and lower fire danger due to increasedcooling at night. Terrain aspect had a secondary impact on the moisture of smallerfuel elements, but not on fire danger. In general, however, fuel moisture did notvary substantially across the landscape during the afternoon, suggesting that aspectand canopy density alone cannot create significant changes in fuel moisture acrossthe landscape.ivPrefaceThe following thesis was completed under the supervision of Dr. R. Dan Mooreand Dr. I.G. McKendry. Dr. Moore and Dr. McKendry provided guidance andsuggestions on the study design and analyses, as well as editorial revisions. Derekvan der Kamp was the lead author and led the conceptualization, design, data col-lection, data analyses and writing of this thesis.A version of Chapter 4 has been published as:van der Kamp, D. W., Moore, R.D., and McKendry, I.G. 2017 A model for simulat-ing the moisture content of standardized fuel sticks of various sizes. Agriculturaland Forest Meteorology 236: 123-134.vTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of symbols for Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . xxiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . 41.2.1 Processes impacting fuel moisture . . . . . . . . . . . . . 41.2.2 Modelling fuel moisture . . . . . . . . . . . . . . . . . . 51.2.3 Spatial variability of microclimate and fuel moisture at thelandscape scale . . . . . . . . . . . . . . . . . . . . . . . 81.3 Thesis objectives and outline . . . . . . . . . . . . . . . . . . . . 112 Field site and methodology . . . . . . . . . . . . . . . . . . . . . . . 14vi2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Field site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3 Field methodology . . . . . . . . . . . . . . . . . . . . . . . . . 162.4 Supplementary weather observations . . . . . . . . . . . . . . . . 203 Spatial variability of near-surface temperature and humidity acrossa heterogeneous forested landscape . . . . . . . . . . . . . . . . . . . 233.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.3.1 Quantifying variability in near-surface humidity and tem-perature and the impact of weather conditions . . . . . . . 303.3.2 Quantifying the impact of radiation load and canopy cover 383.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.4.1 Quantifying variability in near-surface humidity and tem-perature and the impact of weather conditions . . . . . . . 393.4.2 Quantifying the impact of radiation load and canopy cover 423.4.3 Implications for fuel moisture . . . . . . . . . . . . . . . 443.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 444 A model for simulating the moisture content of standardized fuelsticks of various sizes . . . . . . . . . . . . . . . . . . . . . . . . . . 474.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.2 Model description . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 504.2.2 Shortwave radiation . . . . . . . . . . . . . . . . . . . . 534.2.3 Longwave radiation . . . . . . . . . . . . . . . . . . . . . 534.2.4 Sensible heat flux . . . . . . . . . . . . . . . . . . . . . . 544.2.5 Water vapour and latent heat flux . . . . . . . . . . . . . 554.2.6 Conduction and diffusion . . . . . . . . . . . . . . . . . 584.2.7 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . 594.3 Model calibration and evaluation . . . . . . . . . . . . . . . . . . 604.3.1 Model sensitivity analysis . . . . . . . . . . . . . . . . . 63vii4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 755 Modelling the spatial variability of fuel moisture and fire dangeracross a heterogeneous forested landscape . . . . . . . . . . . . . . . 775.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 825.2.1 Analysis overview . . . . . . . . . . . . . . . . . . . . . 825.2.2 Precipitation interception model . . . . . . . . . . . . . . 855.2.3 Shortwave radiation interception model . . . . . . . . . . 895.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.3.1 Model evaluation . . . . . . . . . . . . . . . . . . . . . . 915.3.2 Spatial variability of fuel moisture and fire danger . . . . 955.3.3 Influence of canopy cover on below-canopy fuel moisture 995.3.4 Modelling spatial patterns in fuel moisture and potentialfire danger with canopy cover and radiation load . . . . . 1005.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.4.1 Spatial variability of fuel moisture and potential fire danger 1015.4.2 Influence of canopy cover on below-canopy fuel moisture 1035.4.3 Modelling spatial patterns in fuel moisture and potentialfire danger with canopy cover and radiation load . . . . . 1055.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066 Modelling high resolution fire danger rasters across a large studyregion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1176.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 1206.2.2 Spatial input data . . . . . . . . . . . . . . . . . . . . . . 1246.2.3 Modelling details . . . . . . . . . . . . . . . . . . . . . . 1246.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.3.1 Temperature/humidity model . . . . . . . . . . . . . . . . 126viii6.3.2 Relative impact of factors influencing the spatial variabilityof potential fire danger . . . . . . . . . . . . . . . . . . . 1276.3.3 Spatial patterns of potential fire danger across the studyregion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1296.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1306.4.1 Temperature / humidity model . . . . . . . . . . . . . . . 1306.4.2 Simulated potential fire danger maps . . . . . . . . . . . . 1316.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1337 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1457.1 Summary of key findings . . . . . . . . . . . . . . . . . . . . . . 1457.2 Implications of findings . . . . . . . . . . . . . . . . . . . . . . . 1477.3 Suggestions for future research . . . . . . . . . . . . . . . . . . . 150References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153A Temperature, humidity, and fuel moisture bias correction . . . . . . 168A.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168A.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169A.2.1 Logtag bias corrections . . . . . . . . . . . . . . . . . . . 169A.2.2 Fuel moisture sensor bias corrections . . . . . . . . . . . 171B Fuel moisture model details . . . . . . . . . . . . . . . . . . . . . . . 175B.1 Stick specific heat calculation . . . . . . . . . . . . . . . . . . . . 175B.2 Division of shortwave radiation into diffuse and direct components 175B.3 Absorbed radiation . . . . . . . . . . . . . . . . . . . . . . . . . 177C Supplementary information for Chapter 6 . . . . . . . . . . . . . . . 179ixList of TablesTable 2.1 Site characteristics. . . . . . . . . . . . . . . . . . . . . . . . 22Table 3.1 Daily standard deviation (SD) and maximum range (Range) oftemperature and humidity variables averaged across each monthand across all days with and without rain. . . . . . . . . . . . . 35Table 3.2 Results of model selection. Standardized regression coefficientsare shown in the Canopy Gap and Rad Load columns. Boldvalues indicate the predictor with the strongest single variablemodel as determined by the coefficient of determination. Miss-ing values indicate that the addition of the predictor did not sub-stantially improve the model performance. Standard error of theestimate is provided in the units of the predictor (Temperature:◦C, Relative Humidity: %, Vapour Pressure: kPa). . . . . . . . 46Table 4.1 Optimal parameter values for all calibration site/size combinations 65Table 4.2 Skill of optimal models applied to calibration data. Compari-son statistics used are: the Log-transformed Nash-Sutcliffe ef-ficiency, coefficient of determination, root-mean-square error,bias, and bias for all data with observed moisture below 30%.The units of Bias and RMSE are percent moisture content. . . . 65Table 4.3 Model evaluation with independent time period: models are cal-ibrated on 1997 Oklahoma data and evaluated using 1996 data.The units of Bias and RMSE are percent moisture content. . . . 66xTable 4.4 Model evaluation with independent sites: models calibrated atone site are evaluated at the other two sites. All models aretrained using the 10-hour fuel size. The units of Bias and RMSEare percent moisture content. . . . . . . . . . . . . . . . . . . 68Table 4.5 Comparison of model skill between the Nelson model and themodel presented here when applied to the Carlson dataset. Theunit for Bias is percent moisture content. . . . . . . . . . . . . 73Table 5.1 Precipitation interception model statistics: Coefficient of deter-mination, model bias and root mean square error. . . . . . . . . 92Table 5.2 Shortwave interception model statistics: Coefficient of determi-nation, model bias and root mean square error. . . . . . . . . . 93Table 5.3 Daily standard deviation (SD) and maximum range (Range) ofdaily minimum and maximum 1-hour fuel moisture (1-hmin and1-hmax), 1000-hour fuel moisture (1000-hmin and 1000-hmax),and ERC (ERCmin and ERCmax) averaged across each monthand across all days with and without rain. . . . . . . . . . . . . 96Table 5.4 Results of model selection. Standardized regression coefficientsare shown in the Canopy Gap and Rad Load columns. Boldvalues indicate the predictor with the strongest single variablemodel as determined by the coefficient of determination. Miss-ing values indicate that the addition of the predictor did not sub-stantially improve the model performance. The standard errorof the estimate is also provided in units of the predictand (ERC:unitless, FMC: %). . . . . . . . . . . . . . . . . . . . . . . . . 109Table 6.1 Skill of models applied to evaluation data. Comparison statis-tics used are: root-mean-square error, bias, and coefficient ofdetermination. Results are provided for evaluation across bothtime and sites. . . . . . . . . . . . . . . . . . . . . . . . . . . 127xiTable 6.2 Comparison statistics between modelled ERC forced by ob-served meteorology and modelled ERC forced by simulatedmeteorology. Comparison statistics used are: root-mean-squareerror, bias, and coefficient of determination. Results are pro-vided for evaluation using both independent time-period andindependent sites. . . . . . . . . . . . . . . . . . . . . . . . . 127Table A.1 LogTag vs. Rotronic comparison statistics for both relative hu-midity and temperature. Values provided for before and afterthe bias adjustment. . . . . . . . . . . . . . . . . . . . . . . . 170Table A.2 Intercomparison of moisture sensors after the bias adjustmentusing both comparison periods. Statistics are calculated for databelow and above the Fibre Saturation Point as well as for all thedata. Comparisons are made between sensors 1 and 2 (‘1v2’), 1and 3 (‘1v3’) and 2 and 3 (‘2v3’). . . . . . . . . . . . . . . . . 173xiiList of FiguresFigure 2.1 Map of study area, including the Field site location (purpletriangle), the Sparks Lake fire weather station used in Chapter5 (yellow square) , and the study region (green square) andKamloops Airport weather station (red circle) used in Chapter6. The location of the study area within BC is indicated by theblack point in the map at top. . . . . . . . . . . . . . . . . . 17Figure 2.2 Detail of the field site. Top: aerial photography of site. Bottom:radiation load averaged over the entire field season (calculatedusing a 30-m resolution digital elevation model developed byRosin (2010)). Sites referred to in text are indicated by colour. 18Figure 2.3 Field instrumentation. Left: Base Station; Top Right: Log-Tag Haxo-8 humidity and temperature sensor; Bottom Right:Radiation screen installed at Site 6. Instrumentation was sur-rounded by chicken wire to protect against grazing cattle. . . . 20Figure 3.1 Daily relative humidity, vapour pressure, and temperature ob-servations. The thick black lines are the daily intersite means.The grey ribbons show the intersite range of the daily mini-mum and maximum values. Hourly precipitation observationsat the Base Station are presented in bottom plot. . . . . . . . 31Figure 3.2 A sample of hourly relative humidity, vapour pressure, tem-perature, and precipitation (bottom) observations for all sites(grey lines). Fuel Moisture 2, Site 22, and Site 4 are highlighted. 32xiiiFigure 3.3 Daily anomalies from the intersite mean for maximum andminimum relative humidity and temperature, and daily meanvapour pressure at all sites (grey lines). As in Figure 3.2, FuelMoisture 2, Site 22, and Site 4 are highlighted. . . . . . . . . 34Figure 3.4 Range (black line) and standard deviation (grey line) of dailymaximum and minimum relative humidity (A, B), mean vapourpressure (C), and maximum and minimum temperature (D, E).Hourly precipitation (F), and daily average wind speed (G) arealso provided. Precipitation amounts are also shown with ma-roon shading. . . . . . . . . . . . . . . . . . . . . . . . . . . 36Figure 3.5 Daily standard deviation of maximum and minimum humidity(top two rows) and minimum and maximum temperature (bot-tom two rows) plotted against days since rain (first column),solar radiation (second column), daily precipitation (third col-umn), and mean wind speed (fourth column). Days are dividedinto days with rain (blue points) and without (red points). Formaximum humidity and minimum temperature solar radiationis calculated as a running average of the current and followingdays. Loess curves with a two-degree polynomial are fit to therelations with days since rain while linear regressions are fit tothe solar radiation plots (solid blue lines) The 95% confidenceintervals for these fits are included (grey ribbons). . . . . . . . 37Figure 3.6 Average anomalies of daily maximum and minimum relativehumidity (top row) and temperature (bottom row) for all non-rain days plotted on the radiation load - canopy gap fractionparameter space. The right column shows daytime conditions(maximum temperature and minimum relative humidity), whilethe left column shows night time conditions (minimum temper-ature and maximum relative humidity). The anomaly valuespredicted by the linear regression models summarized in rows1-4 of Table 3.2 are indicated by the contour lines. Specificsites are highlighted as in Figures 3.3 and 3.2: Site 22 (yel-low), Fuel Moisture 2 (red), and Site 4 (green). . . . . . . . . 40xivFigure 4.1 Schematic of model showing all components of the moistureand energy budgets. Please refer to the list of symbols for anexplanation of the labels. . . . . . . . . . . . . . . . . . . . 51Figure 4.2 The impact of surface fuel moisture on surface relative humid-ity for different values of A and B. The fibre saturation pointof 30% is shown by the vertical dashed grey line. . . . . . . . 57Figure 4.3 Comparison of co-located fuel moisture observations by thesensors used at sites BS and FM2. A 1:1 line is provided as areference. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Figure 4.4 Comparison of modelled and observed fuel moisture at the Ok-lahoma site for 1996. The models used were calibrated foreach size separately using the 1997 data. A) 1-hour fuel size,B) 10-hour fuel size, C) 100-hour fuel size, and D) 1000-hourfuel size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 4.5 Example time series of modelled fuel moisture (grey lines)generated by 1997 Oklahoma models and observed fuel mois-ture (black line) at the Oklahoma site during 1996 for the A)1-hour fuel size, B) 10-hour fuel size, C) 100-hour fuel size,and D) 1000-hour fuel size. Note the varying y-axis limits. . . 67Figure 4.6 Comparison of modelled 10-hour fuel moisture with observa-tions when the model is calibrated and evaluated at differentsites. A) Calibrated at BS and evaluated at BS, B) Calibratedat FM2 and evaluated at BS, C) Calibrated at Oklahoma andevaluated at BS, D) Calibrated at BS and evaluated at Oklahoma. 69Figure 4.7 Example time series of observed (black) and modelled (grey)10-hour fuel moisture when the model is calibrated and eval-uated at different sites. A) Calibrated at BS and evaluated atBS, B) calibrated at FM2 and evaluated at BS, C) calibrated atOklahoma and evaluated at BS, D) Calibrated at BS and eval-uated at Oklahoma. Note that BS data are from 2014 while theOklahoma data are from 1996. . . . . . . . . . . . . . . . . . 70xvFigure 4.8 A comparison of modelled 10-hour fuel moisture generated atBS using the 10-hour Oklahoma model forced by screen-levelobservations (grey) and near-surface observations (black). . . 71Figure 4.9 Comparison statistics when comparing original fuel moisturemodel output at BS with model output when one of the forcingvariables (downwelling diffuse and direct shortwave, down-welling longwave, relative humidity, air temperature, and wind-speed) is randomized across days. Mean bias is provided onthe left and the coefficient of determination is provided on theright. Results for all four fuel sizes are provided. . . . . . . . 72Figure 5.1 Schematic of the rutter precipitation interception model. Adaptedfrom Valente et al. (1997) . . . . . . . . . . . . . . . . . . . 86Figure 5.2 Hemispherical photos overlayed with radial grids with a 5 de-gree resolution (top row), and thresholded hemispherical pho-tos (bottom row). Examples provided are from Sites 15 (leftcolumn) and 23 (right column). . . . . . . . . . . . . . . . . 90Figure 5.3 Scatter plots of daily modelled and observed precipitation. Re-gression lines are provided (Black Lines), and 1:1 lines are pro-vided for reference (grey lines). . . . . . . . . . . . . . . . . 93Figure 5.4 Time series of modelled and observed daily shortwave radia-tion at Fuel Moisture 1 and Fuel Moisture 2. . . . . . . . . . . 94Figure 5.5 Scatter plots of modelled and observed hourly and daily short-wave radiation at Fuel Moisture 1 and Fuel Moisture 2. A 1:1line is included for reference (dashed line). . . . . . . . . . . 95Figure 5.6 Two months of modelled and observed fuel moisture for theFuel Moisture 1 site using the precipitation and radiation canopyinterception models and the fuel moisture model. . . . . . . . 97Figure 5.7 Scatter plot of modelled and observed fuel moisture for theFuel Moisture 1 site using the precipitation and radiation canopyinterception models. Data from the entire season are used here.A 1:1 line has been added for reference (black line). . . . . . 98xviFigure 5.8 Observed hourly 10-hour fuel moisture at all three sites (A),along with daily maximum (B) and daily minimum (C) values.Observed precipitation at the Base Station is also provided (D). 110Figure 5.9 A sample of modelled hourly 1-hour and 1000-hour fuel mois-ture, modelled ERC for for all sites (grey lines), and observedprecipitation at the Base Station. Fuel Moisture 2, Site 22, andSite 4 are highlighted. . . . . . . . . . . . . . . . . . . . . . 111Figure 5.10 Daytime and night-time ERC for all sites. As in Figure 5.9,Fuel Moisture 2, Site 22, and Site 4 are highlighted. The greyribbon indicates the range between the median and 95th per-centile ERC calculated at the Sparks Lake station over 26 sea-sons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Figure 5.11 Daily standard deviation of maximum and minimum ERC plot-ted against daily minimum and maximum relative humidityand temperature, daily mean wind speed, daily mean sortwaveradiation, and Days Since Rain. Regression lines and the coef-ficient of determination (R2) are included for plots where nullhypothesis that the regression coefficient is equal to zero wasrejected at the 95% confidence level (blue lines). . . . . . . . 113Figure 5.12 Modelled fuel moisture biases (compared to the original model)at Site 4 for all four sizes when removing one or all of thecomponents of the canopy model: Longwave, shortwave, orprecipitation. Note the varying scales of the y-axes. . . . . . . 114Figure 5.13 Daily mean ERC biases (compared to the original model) atSite 4 when removing one or all of the components of thecanopy model: Longwave, shortwave, or precipitation. Hourlyprecipitation at the Base Station is included. . . . . . . . . . . 115Figure 5.14 Second principal component of ERC for all 24 sites plottedagainst canopy gap fraction and radiation load. As in Figures5.9 and 5.10, Fuel Moisture 2, Site 22, and Site 4 are highlighted.115Figure 5.15 A month of ERC values for all 24 sites (grey lines). The siteswith the three highest PC2 loadings (blue lines) and the siteswith the three lowest PC2 loadings (orange lines) are highlighted.116xviiFigure 6.1 Procedure used to generate fire danger rasters. Variables areshown as squares and models are shown as green circles. Vari-ables are either time-varying spatial rasters (yellow squares),constant spatial rasters (purple squares), or non-spatial timeseries (grey squares). . . . . . . . . . . . . . . . . . . . . . . 121Figure 6.2 Procedure used to generate relative humidity and temperaturerasters. Variables are shown as squares and models are shownas green circles. Variables are either time-varying spatial rasters(yellow squares), constant spatial rasters (purple squares), ornon-spatial time series (grey squares). . . . . . . . . . . . . . 123Figure 6.3 Canopy Gap, Radiation Load, and Elevation rasters used asinput layers for relative humidity and temperature models. . . 135Figure 6.4 Both observed and modelled daily minimum and maximumrelative humidity and temperature at Site 10, which was notpart of the subset of sites used to train the model. . . . . . . . 136Figure 6.5 Example comparisons of ERC generated using observed mete-orological conditions and ERC generated using simulated con-ditions. Results for daily maximum and minimum ERC areshown. A subset of four sites not used for training the hu-midity and temperature models are shown here. 1:1 lines isprovided for reference. . . . . . . . . . . . . . . . . . . . . . 137Figure 6.6 Afternoon and nighttime ERC for all grid points within thestudy region. The dashed horizontal line indicates an ERCvalue of 60. . . . . . . . . . . . . . . . . . . . . . . . . . . . 138Figure 6.7 Standard deviations of nighttime and afternoon ERC across theentire study region. The results from four different simulationsare shown here: three runs in which all but one of the three spa-tial factors were kept constant, and one when all three factorsvaried across the study region. The magenta points indicatethe two days which are shown as rasters in Figures 6.8 and 6.9 139Figure 6.8 Rasters of afternoon ERC for two different days (columns, in-dicated in Figure 6.7). Rasters driven by all factors, and thethree factors individually (rows) are provided. . . . . . . . . . 140xviiiFigure 6.9 As in Figure 6.8, but for nighttime ERC. . . . . . . . . . . . 141Figure 6.10 As in Figure 6.7, but for the variogram range of the ERC rasters.142Figure 6.11 Relationship between the mean ERC, the standard deviation ofERC, and the variogram range of ERC across the landscape forboth afternoon and nighttime ERC. Two example days whenthe fire danger was both high and variable are highlighted andthe rasters for these two days are shown in Figure 6.12. . . . . 143Figure 6.12 Example rasters for both an afternoon and nighttime case inwhich the fire danger is both high as well as variable. The twoexample cases are highlighted in Figure 6.11. . . . . . . . . . 144Figure A.1 Comparison of all co-located LogTag and Rotronic tempera-ture and relative humidity observations. The red line is thesmoothed GAM function. A 1:1 line is provided for reference. 170Figure A.2 Example relative humidity measurements by the Rotronic andLogTag sensor at the Base Station along with bias-adjustedLogTag data. . . . . . . . . . . . . . . . . . . . . . . . . . . 171Figure A.3 Early and late-season comparison of co-located moisture sen-sors before bias adjustment. . . . . . . . . . . . . . . . . . . 172Figure A.4 Early and late-season comparison of co-located moisture sen-sors after bias adjustment. . . . . . . . . . . . . . . . . . . . 174Figure B.1 Integral geometry for the absorption of diffuse radiation by thefuel moisture stick. . . . . . . . . . . . . . . . . . . . . . . . 178Figure C.1 Change in ERC at the Base Station resulting from the adjust-ment of wind speed by constant factors of 0.1 and 10. . . . . . 180xixFigure C.2 Standard deviations of afternoon and nighttime relative humid-ity across the entire study region. The results from four differ-ent simulations are shown here: three runs in which all but oneof the three spatial factors were kept constant, and one whenall three factors varied across the landscape. The points indi-cate the two days which are shown as rasters in Figures 6.8 and6.9 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181Figure C.3 As in Figure 6.7, but for temperature . . . . . . . . . . . . . . 182Figure C.4 Rasters of afternoon relative humidity for two different days(columns, indicated in Figure 6.7). Rasters driven by all fac-tors, and the three factors individually (rows) are provided. . . 183Figure C.5 As in Figure 6.8, but for nighttime relative humidity. . . . . . 184Figure C.6 As in Figure 6.8, but for afternoon temperature . . . . . . . . 185Figure C.7 As in Figure 6.8, but for nighttime temperature. . . . . . . . 186xxList of symbols for Chapter 4Variablesα Albedoβ Cloud type constantε Emissivityκ Thermal diffusivity of air (1.9 ×10−5 m2 s−1)λ Energy required to transition a unit mass of water to vapour (J Kg−1)ν Kinematic viscosity of air (1.51×10−5 m2 s−1)Ω Aerodynamic resistance ( sm−1)φ Solar elevation angle (rad)ρ Density (kg m−3)σ Stephan-Boltzmann constant (5.67 × 10−8 W m−2 K−4)τ Atmospheric transmissivityθ Angle relative to the horizontal (rad)a Surface area (m2)A,B Empirical constants related to the equilibrium moisture contentC Conduction into the core (W)xxic Specific heat (J K−1 kg−1)D Diffusion into the core ( kg s−1)d Bulk moisture diffusion coefficient (m2 s−1)E Moisture flux between the outer layer and the atmosphere ( kg s−1)f Fraction of the stick volume taken up by the outer layerg Specific gravity of the stickI Isotropic diffuse radiation (W m−2)K Shortwave radiation (W m−2)k Bulk conductivity ( J m−1 s−1 K−1)L Longwave radiation (W m−2)l Length of the stick (m)M Molecular mass of water ( 0.0180 kg mol−1)m Cloudiness factorm Moisture content (% of oven-dry weight)n Clearness indexNu Nusselt numberP Precipitation ( kg s−1)Q Turbulent heat flux (W m−2)q Vapour density(kg m−3)r Radius of stick (m)R Gas constant (8.314 ×10−3 kPa m3 mol−1 K−1)Re Reynolds numberxxiiRH Relative humidity (%)s Canopy view-factorT Temperature (K)u Wind speed (m s−1)V Volume (m3)w Precipitable water content (cm)Subscriptsa Ambient airabs Absorbed by stickc Inner core of stickd Downwelling radiationdi f f Diffuse radiation componentdir Direct radiation componente latent heat fluxemitt Emitted by stickf sp Fibre saturation pointg Groundh Sensible heat fluxinc Incidentmax Maximum allowable valuemid Mid-point radius (m)o Outer layer of stickxxiiis Entire sticksat Saturationsur f At the stick surfaceu Upwelling radiationxxivAcknowledgmentsI want to begin by thanking my co-supervisors, Dan Moore and Ian McKendry, fortheir support and encouragement throughout my thesis. They provided me withboth the freedom to develop and pursue my own research direction, as well asuseful guidance when I needed it. I couldn’t have asked for better supervisors.As well, my committee members, Meg Krawchuk and Steve Mitchell, providedme with very useful advice at the outset of the project. This thesis also benefitedimmensely from their careful reading and thoughtful comments. I would also liketo thank Meg for letting me tag along to her field sites so that I could “smell thenumbers.” It was great to be able to work on this thesis alongside my good friendsand officemates, Joel Trubilowicz and Jason Leach who provided me with a lot ofgreat advice and timely distractions. Thanks to my parents and family for all thesupport over the years.I am grateful to J.D. Carlson for providing us with the Oklahoma fuel moisturedataset. Thanks to Dr. Christopher A. Fiebrich of the Oklahoma ClimatologicalSurvey for providing the Oklahoma Mesonet data. Thanks also to Lawrence Birdfor his assistance in the field. Funding for this research was provided by the NaturalScience and Engineering Research Council. NSERC provided me with a CanadaGraduate Scholarship and Discovery Grants to both Dan Moore and Ian McKendry.Dan K. Thompson and Ralph M. Nelson provided useful comments on an earliermanuscript of Chapter 4.Finally, I want to thank Alison for all her support. I am so lucky that I had mybest friend and partner just down the hall over the last few years.xxvChapter 1Introduction1.1 MotivationWildfire is a significant source of disturbance in many ecosystems and the spatialpatterns that fires leave on a landscape affect both ecosystem structure and ecosys-tem function (McKenzie et al., 2011). For instance, the successional pathway of aforested ecosystem following fire is strongly dependent on burn severity patterns.Species richness and community composition are impacted by the size and severityof burned patches (Turner et al., 1997). Patterns in post-fire seedling establishmentcan be influenced by the location of stands of surviving mature trees that act asseed sources (Pierce and Taylor, 2011), or by burn severity patterns in organicsoils (Johnstone and Chapin, 2006). The heterogeneity and connectivity of veg-etation patterns resulting from fires are also important in creating suitable habitatfor fauna; a more heterogeneous landscape provides species with a larger range ofhabitat conditions (Smith et al., 2000). Wildfire patterns also influence subsequentfire activity (Parks et al., 2014).Understanding the spatial behaviour of fires is important from a managementperspective, as accurate predictions of fire behaviour are crucial for protecting livesand values at risk. As well, current management practices emphasize that reducingsuppression efforts and allowing more fires to burn will help achieve managementgoals and create more resilient forests (Stephens and Ruth, 2005; Canadian Councilof Forest Ministers, 2005). Increasing our understanding of fire behaviour across1the landscape will increase the confidence of fire managers to allow more fires toburn (Collins et al., 2007). The planning and execution of prescribed fires and fueltreatments would also benefit from an increased ability to predict the patterns andecological consequences of wildfires.The spatial behaviour of wildfire across a landscape is dependent on the threeelements of the “fire triangle”: fuels, topography, and weather, all of which varyat multiple scales (McKenzie et al., 2011). At the finer scales, fire patterns areinfluenced by patterns in fuel type, fuel amount, and connectivity across differentslope aspects (Lertzman et al., 1998); the impact of slope steepness on firelineintensity (Cohen and Deeming, 1985); and the influence of terrain on local windfields (Sharples, 2009).A number of researchers have identified patterns in fuel moisture driven bychanges in microclimate across different slope aspects as an important bottom-upfactor determining spatial wildfire behaviour (e.g., Heyerdahl et al. 2001). It hasalso been postulated that reduced wind speeds and radiation below dense forestcanopies lead to cool moist microclimates and wetter fuels (Collins et al., 2007). Anumber of studies have pointed to variability in fuel moisture across the landscapeas a driver of burn severity patterns derived from satellite imagery (e.g., Holdenet al. 2009; Birch et al. 2015; Kane et al. 2015; Dillon et al. 2011). Spatial patternsin fuel moisture may also alter fire spread probability. In the extreme case wherethe landscape is homogeneously dry, a fire can spread unimpeded through a region.However, in moderate fire weather conditions, particular areas of the landscapemay be dry enough to support fire spread while other areas are too wet, and inthis case the pattern of fuel moisture becomes important. If fuel moisture changesgradually across the landscape, a fire will be more likely to spread across the drierportion of the region, given ideal weather conditions and fuel types. Alternatively,if the fuel moisture pattern is patchier, a fire will be less likely to move across theentire landscape as patches of wet fuels will impede its progress (Miller and Urban,2000; Littell and Gwozdz, 2011).Patterns in microclimates impact fuel moisture directly though changes in radi-ation, wind speed, cold air pooling, or soil moisture. They can also have an indirecteffect through their influence on vegetation density and composition. Cool, north-facing slopes may have increased biomass in both the overstory and understory that2decreases the amount of solar radiation and wind speed available to dry out surfacefuels (Zou et al., 2007; Birch et al., 2015). Increased vegetation may, in turn, in-crease near-surface humidity through enhanced transpiration (Renaud et al., 2011;Estes et al., 2012). Nyman et al. (2015b) demonstrated that the influence of aspecton fuel moisture is significantly enhanced by the indirect influence of increasedvegetation, and deeper, wetter soils on cooler slopes. In this way the indirect ef-fects and direct effects compound one another. However, this relationship betweenthe direct and indirect impact may be decoupled due to disturbance history, or inwetter, energy-limited forests that often have homogeneous vegetation across dif-ferent aspects (Ohmann and Spies, 1998). It would therefore be useful to decouplethese direct and indirect impacts of microclimate patterns on fuel moisture andexamine each factor in isolation.That fuel moisture is a primary driver of wildfire patterns is a reasonable con-clusion, considering that moisture has a strong influence on the energy released bythe propagating fire front (Rothermel, 1972) and the amount of forest floor duffand larger fuel elements that are consumed (Sandberg, 1980, Knapp et al., 2005).However, limited work has been done directly measuring patterns in fuel moistureacross forested landscapes, and many of the studies that are available have foundlow variability, especially during dry periods (Whitehead et al., 2006; Estes et al.,2012; Banwell et al., 2013; Gibos, 2010). As well, even though the literature oftencites microclimate as a primary driver of fuel moisture patterns, there are few stud-ies that examine landscape scale patterns in microclimate with the explicit purposeof determining how these patterns in near-surface conditions, in turn, influence fuelmoisture patterns. For instance, previous analyses have primarily focused on tem-perature, rather than relative humidity, which is a primary driver of fuel moisture(Viney, 1991).Given that 1) patterns in fuel moisture are often considered to be a primarydriver of fire behaviour, 2) direct observations of fuel moisture variability are lim-ited, and 3) few studies in microclimate variability are designed with fuel moisturein mind, it would be worthwhile to examine, in detail, how microclimatic condi-tions vary across forested landscapes, and how that variability translates into fuelmoisture patterns. In the following section, a brief literature review will summarizethe processes impacting fuel moisture, provide an overview of different approaches3to fuel moisture modelling, and discuss how microclimates and fuel moisture mayvary across a forested landscape.1.2 Literature review1.2.1 Processes impacting fuel moistureDead fuel moisture content plays a significant role in determining the rate andintensity of fire spread as the latent heat of vaporisation represents a significantportion of the energy required to bring a fuel to ignition (Rothermel, 1972). Deadsurface fuels gain and lose moisture through a number of processes. Fuel elementscan gain moisture through the adsorption of water vapour from the surroundingair by cell walls via molecular bonding, or through absorption, in which liquidwater is drawn into cavities within the fuels though capillary flow. Adsorptioncan only raise moisture up to a “fibre saturation point” (around 30% of the dryweight of the fuel), beyond which moisture must be gained through the absorptionof liquid water (Viney, 1991). When liquid water is introduced to a fuel element,rapid absorption occurs within the first few hours, after which the absorption ratedecreases as the fuel reaches saturation, which can range anywhere from 150 to400% of the dry weight of the fuel (Simard, 1968). Previous research suggeststhat waxy resins on the surface of the elements can reduce moisture absorption.As fuels decompose, this wax coating is lost, and the rate at which fuel elementsabsorb moisture increases (Van Wagner, 1969). These processes will continuallymove fuel moisture towards an equilibrium moisture content (EMC). The EMCfor a particular meteorological condition is the moisture content reached by a fuelelement if it is given enough time to come to an equilibrium with that condition.Precipitation has an obvious impact on fuel moisture. However, the amount ofincident precipitation that is actually absorbed by fuel elements is dependent onintensity and antecedent moisture (Nelson, 2000); precipitation will more readilybe absorbed by fuels if the rate of precipitation is low, and if the fuels are dry.Condensation can also signficantly increase fuel moisture in the absence of pre-cipitation (Viney, 1991). There is also evidence that surface fuels gain moisturefrom underlying wet soils due to capillary draw (Hatton et al., 1988; Samran et al.,41995). Fuel elements lose moisture through gravitational drainage of liquid waterfrom larger pores and the evaporation of liquid water from the fuel surface and freeliquid water drawn to the surface via capillary forces. Evaporation of liquid wateris followed by the desorption of bound water from the cell walls (Viney, 1991).Free liquid water within the cells and surfaces of the fuel elements is likelypresent only during brief windows following precipitation, snowmelt or condensa-tion (Van Wagner, 1979; Viney, 1991). As liquid water is quickly removed from thefuel elements, the fibre saturation point is reached and adsorption and desorptionthen become dominant and represent the primary method of moisture exchangethroughout the fire season. This transfer of water vapour to and from molecularlybound water in the cell walls of fuel elements is thermodynamically different thanevaporation and condensation, as bound water within cellulose has a lower energystate than liquid water (Skaar, 1988), i.e., it takes more energy to remove the waterfrom the fuel element.1.2.2 Modelling fuel moistureNumerous researchers have developed models for simulating fuel moisture (seeViney (1991) and Matthews (2013) for reviews). These models can be dividedinto two broad categories: empirical models and process-based models. Empiricalmodels are often generated by regressing measured fuel moisture content againsta suite of meteorological and site variables (e.g., McArthur 1962; Pook and Gill1993; Marsden-Smedley and Catchpole 2001; Ferguson et al. 2002; Lin 2004;Alves et al. 2009). Matthews (2013) reviewed the literature to determine predictorsof fuel moisture commonly used by these regression models. Relative humiditywas the most common predictor, followed by temperature.A number of empirical models of EMC have been developed. Van Wagner(1972) let different fuel types come to equilibrium with conditions precisely con-trolled in a drying chamber. The author found that the EMC was a sigmoidal func-tion of atmospheric relative humidity, and that the shape of the function changedwith temperature and fuel type. Importantly, fuel moisture exhibited a hysteresisbehaviour: the shape of the function also depended on whether the fuel was dry-ing towards the EMC or getting wetter. Van Wagner (1972) fit a semi-empirical5function to the data. This sigmoidal behaviour, along with the presence of hystere-sis has been repeated in other studies (e.g., Anderson 1990b), and is a part of thefuel moisture indices within the Canadian Fire Weather index system (Van Wagner,1987). Nelson (1984) developed a semi-physical model for EMC based on ther-modynamic arguments. At the core of the model is the assumption that the changein the Gibbs free energy that occurs when liquid water becomes molecularly boundwithin the cellulose of the fuel is an exponential function of the fuel moisture. Us-ing this assumption, Nelson (1984) derived a sigmoidal EMC function similar towhat was found in previous empirical studies.The EMC can be used to model actual fuel moisture using the differential equa-tion:dmdt=me−mτ(1.1)where m is the fuel moisture content given as a percentage of the dry weight, meis the EMC, and τ is the response time of the fuel, which determines how quicklythe fuel approaches the EMC. This formulation has been used by a number ofresearchers (e.g., Fosberg et al. 1981; Catchpole et al. 2001), is utilized by theCanadian Fire Weather Index system (Van Wagner, 1987), and has recently beenintegrated into a coupled fire-weather model (Vejmelka et al., 2016). Numerousstudies have measured the response time, τ , of various fuels and attempted to re-late these drying rates to weather conditions (e.g. Anderson 1990a; Hille and denOuden 2005). Van Wagner (1979) demonstrated that the drying rate increases withtemperature and decreases with relative humidity, although that relationship is lessclear below 60% relative humidity. Van Wagner (1979) also found that the dryingrate increases with wind for low wind speeds (<2 km/h), but is relatively insensi-tive to speeds above that threshold.The Canadian Fire Weather Index system (Van Wagner, 1987) is used oper-ationally in Canada and globally to estimate fire weather severity. At the coreof this system are three moisture indices: the Fine Fuel Moisture Code (FFMC),the Duff Moisture (DMC) Code, and the Drought Code (DC). The FFMC repre-sents small diameter surface litter, such as needles, cured grasses, and small twigs,the DMC represents the layer of decomposing, loosely packed organic material,6and the DC represents the moisture of the deep layer of compact organic material.These indices are calculated using an accounting approach whereby yesterday’sfuel moisture is increased though precipitation, or reduced via drying. The FWIsystem uses the approach outlined in Equation 1.1, and the response time of thefuel is smallest for the FFMC, and largest for the DC. In the case of the FFMC,the drying rate calculation uses the relationships found by Van Wagner (1979) andthe EMC is a sigmoidal function of relative humidity. In contrast, the DMC hasa constant EMC of 20%, and the logarithm of the drying rate has a positive linearrelationship with temperature and the length of day, and is negatively related torelative humidity. Daily moisture loss for the DC is estimated from temperatureonly, using a empirical linear relationship.A crucial component of the American National Fire Danger Rating System(NFDRS) is the four fuel moisture variables: 1-hour, 10-hour, 100-hour, and 1000-hour fuel moisture (Cohen and Deeming, 1985). These metrics were developedto simulate the moisture of standardized fuel sticks of various sizes. They wereassumed to, in constant conditions, behave according to equation 1.1 and approachthe equilibrium moisture content, me, along an exponential curve defined by theresponse time of the fuel, τ , which was independent of conditions, and increasesfrom 1 hour to 1000 hours.Fuel moisture for the 1-hour and 10-hour fuel sizes are calculated using theapproach of Fosberg and Deeming (1971). The authors developed a differentialequation that related the change in moisture content with the trend in me over thelate morning and early afternoon. Using climatological data from a single study,Fosberg and Deeming (1971) developed equations in which the mid-afternoon 1-hour and 10-hour fuel moisture was a simple linear function of the mid-afternoonme. It is important to note that these two metrics are not related to precipitation.For the 100-hour and 1000-hour fuels the NFDRS follows the procedure outlinedby Fosberg et al. (1981) whereby the change in moisture from some initial value isdirectly related to the difference between that initial moisture content and the me,and τ . For the 100-hour fuel, the day’s moisture content is calculated using the pre-vious day’s value and the average me for the last 24 hours, while for the 1000-hourfuel the moisture content from seven days ago is used along with the me averagedover the last week. The influence of precipitation is included by increasing me by7an amount dependent on precipitation amount.Nelson (2000) developed a sophisticated model for simulating the moisture ofstandardized fuel sticks as an alternative to the relatively simple approach usedpreviously in the NFDRS. This model is used operationally by a number of firemanagement agencies. It simulates the energy and moisture exchange at the surfaceas well as the transport of moisture and heat within the interior of the stick. Themodel uses a linearised energy budget in which net longwave radiation is estimatedas a function of the difference between the stick temperature and the apparent skytemperature.1.2.3 Spatial variability of microclimate and fuel moisture at thelandscape scaleAll of the processes influencing fuel moisture will vary spatially at a host of dif-ferent scales. For instance, fuel moisture is heavily influenced by near-surfacetemperature and humidity, which can vary significantly in complex terrain. Tem-peratures generally decrease with altitude due to adiabatic cooling (Barry, 2008)and increase with increasing radiation load (Geiger, 1965; Barry, 2008). A numberof studies have examined the influence of terrain on surface conditions and fuelmoisture. Hayes (1941) found that, in the absence of a canopy, fuel moisture wasalways higher on north slopes. However, Gibos (2010) found no significant differ-ence between a north and south aspect under dense canopy. Nyman et al. (2015a)found that, in both dry or wet forests where canopy is either homogeneously denseor open, aspect had little effect on fuel moisture, as radiation was either consistentlylow, or high across sites. Aspect had the largest impact in a forest with moderatecanopy cover. Sullivan and Matthews (2012) used a model validated on field datato simulate differences in fuel moisture across different aspects. They found thatdifferences in modelled fuel moisture mainly occurred during the morning on steepslopes due to lower morning sun angles. Holden and Jolly (2011) used empiricalrelationships between terrain indices and weather observations to model fire dan-ger across complex terrain. Their analysis indicated that south facing slopes haddrier fuels, due, in part, to increased radiation.Stand structure can have a significant influence on near-surface microclimatesduring the fire season. Near-surface temperatures are often lower than above canopy8conditions during the day and warmer at night (Fridley, 2009). Wind speeds dimin-ish with increased canopy cover (Oke, 1990). However, significant evaporation canoccur when large eddies penetrate the canopy and ventilate the surface with rela-tively warm or dry air (Denmead and Bradley, 1985). The presence of a signifi-cant understory will enhance both the decreased ventilation and decreased moisturedeficit directly above the forest floor. Within the understory, moisture levels are of-ten near saturation and wind speeds can be close to zero (Oke, 1990). As well,net radiation levels are obviously controlled by canopy and understory structure.Studies examining the influence of canopy cover on temperature have found that,overall, a forest canopy acts to reduce diurnal variability in temperature by reduc-ing incoming solar radiation and nocturnal radiative cooling (Chen et al., 1999).The influence of canopy cover on relative humidity is partly driven by tempera-ture variability. Compared to open sites, cooler daytime conditions below densecanopies lead to higher relative humidity while relative humidity is lower at nightwhen nocturnal cooling is reduced (Chen et al., 1993; Renaud et al., 2011). How-ever, this effect is more modest and less consistent than for temperature. A handfulof studies have examined the influence of canopy cover on fuel moisture (e.g.,Whitehead et al. 2006; Estes et al. 2012; Banwell et al. 2013). Generally, it wasfound that canopy cover has the strongest impact on fuel moisture during periodsof low to moderate fire weather; extreme fire weather leads to more homogeneousmoisture levels.Variability in canopy cover and precipitation interception will impact spatialpatterns in fuel moisture. The amount of interception by vegetation is strongly de-pendent on antecedent precipitation (dry canopies have a higher capacity to retainmoisture than wet canopies), wind speeds, and air temperature, which influenceevaporation and precipitation rates. Mean annual interception rates are dependenton canopy densities and weather and range from 3 to 30% of total precipitation,depending on forest stand characteristics and climate conditions (Winkler et al.,2010). The amount of infiltrating precipitation that will be stored within the lit-ter layer is dependent on antecedent moisture conditions and precipitation rates.Sato et al. (2004) found that the rate of moisture accumulation fell quickly uponinitiation of precipitation, plateauing at a maximum storage amount that was itselfdependent on the precipitation rate. Within the Canadian Fire Weather Index sys-9tem, precipitation adds moisture content to the fine fuels at a rate that decreaseswith increasing precipitation rate and initial moisture content (Van Wagner, 1987).Mesoscale air flows driven by buoyancy differentials can also change surfaceclimates. For instance, the negative buoyancy experienced by cool surface airforms down-slope katabatic drainage flows during clear nights. This will leadto cooler air with higher relative humidity levels pooling in valley bottoms andhollows (Lundquist et al., 2008). Simulated maps of fire danger generated for amountainous terrain by Holden and Jolly (2011) found that nocturnal drainage ledto diminished fire danger in valley bottoms. A similar pattern of relatively low firedanger in valley bottoms was found by Schunk et al. (2013).High fuel moisture may also be found in topographically convergent and/orpoorly drained areas within a landscape. Late-successional stands with lower firefrequencies are more likely to occur within riparian zones (Camp et al., 1997;Dwire and Kauffman, 2003). Lateral flows of water through the duff and litterlayers themselves are more ephemeral and occur at a smaller spatial scale than lat-eral flow within mineral soils (Kim et al., 2005; Keith et al., 2010b). It is likely,therefore, that any hydrological impact on fuel moisture patterns is due to lateralflow within the underlying mineral soil, which then influences fuel moisture.Such an influence could happen in a number of ways. Fuels could be inundatedif the water table reaches the surface. High water tables mainly occur in regions ofhydrological accumulation such as regions of confluence, on perched water tables,or within valley bottoms (Winkler et al., 2010). This effect may be reduced duringdry periods; Dyer (2009) found that cool climates found in valley bottoms are lesspronounced during the growing season. Secondly, as mentioned in the previoussection, it may be possible for the moisture of surface fuels to be influenced by theunderlying soil moisture through upwards capillary draw, although the literatureis unclear on this topic. While a few observational studies have indicated thatsurface fuels gain moisture from the underlying soils (Hatton et al., 1988; Samranet al., 1995; Nyman et al., 2015b), exclusion experiments by Keith et al. (2010a)indicated that during dry conditions diurnal cycles in duff moisture were driven byevaporation from the surface; capillary draw had no impact. A number of modelsof litter moisture (Oge´e and Brunet, 2002; Matthews, 2006) assume no upwardscapillary draw.10Hydrology may also have an indirect control of fuel moisture by first influ-encing near-surface atmospheric conditions. Temperatures have been found to belower near streams (Bolstad et al., 1998; Lookingbill and Urban, 2003; Fridley,2009) due to increased evaporative cooling. Moreover, Dobrowski (2011) pointedout that relatively moist soils can temper the diurnal range of near-surface temper-ature due to increased thermal inertia. The cooler, more slowly varying microcli-mates found above moist soils could, in turn, lead to slowly varying fuel moisture.1.3 Thesis objectives and outlineFrom the overview of the literature presented above, it is clear that there are a num-ber of research gaps that have yet to be filled. Specifically, it is unclear whetherchanges in near-surface atmospheric conditions can lead to substantial variabil-ity in fuel moisture and fire danger over a forested landscape within complex ter-rain. There is also little information about the relative influence of different fac-tors controlling fuel moisture patterns. Finally, there has been a lack of researchon separating the direct and indirect impacts of microclimates on fuel moisture.Therefore, the overall objective of this thesis is to quantify the spatial variability innear-surface atmospheric conditions, examine how this variability translates intopatterns in fuel moisture and fire danger, and determine the relative influence ofcanopy cover, radiation load, and elevation on these patterns.Radiation load is defined here as the intensity of solar radiation on the for-est floor if the canopy were to be removed, and will vary with slope and aspect.Canopy cover is defined here in terms of a canopy gap fraction estimated fromhemispherical photos. In the interest of producing a focused study, and given re-source limitations, the potential influences of cold-air pooling and groundwaterpatterns on fuel moisture patterns are not examined here.As mentioned above, wind, slope and fuel amount influence fire danger inaddition to fuel moisture. However, this thesis will focus on the contribution offuel moisture to fire danger rating. Consequently, the Energy Release Component(ERC) of the US National Fire Danger Rating System will be used as a metric forpotential fire danger. The ERC is strongly dependent on fuel moisture, and is notrelated to wind or slope. The ERC is used operationally in the United States as a11metric for potential fire behaviour.The thesis objectives will be addressed through four analysis chapters. Fol-lowing a description of the field site and methodology in Chapter 2, the analysisin Chapter 3 focuses on the spatial patterns of observed near-surface temperatureand relative humidity. Specifically, a network of humidity and temperature sen-sors was established at sites representing a range of both radiation load and canopycover. The locations were chosen so that the two dimensional parameter spacedescribed by canopy cover and radiation load was sampled as evenly as possible.This sampling approach allows for the influence of both factors to be assessed in-dependently and for their relative influence to be compared. The objective of thischapter is to quantify the amount of spatial variability in near-surface atmosphericconditions that is seen across a small (<4 km2) forested landscape, how weatherconditions control that variability, and the relative influence of radiation load andcanopy cover on spatial patterns in near-surface conditions. Sites were chosen withconsistent understory vegetation in order to focus on the direct impacts of changingradiation loads on fuel moisture.In order to determine how micrometeorological conditions impact fuel mois-ture, a novel fuel moisture model was developed that explicitly simulates heatand moisture exchange between the atmosphere and standardized fuel sticks. Thismodel is described and evaluated in Chapter 4. The new model builds on the modelused operationally by fire management agencies by increasing the sophistication ofthe treatment of radiative and turbulent heat transfers. This increased sophisticationwill allow for a more detailed examination of how changing micrometeorologicalconditions alter fuel moisture. A focus on elevated fuel moisture sticks avoids therequirement to simulate the potential influence of underlying soil moisture on fuelmoisture.In Chapter 5 the network of near-surface weather observations presented inChapter 3, and the fuel moisture model presented in Chapter 4, are combined tosimulate fuel moisture variability across the field site. These data are then usedto examine the influence of micrometeorology and site characteristics on spatialpatterns in fuel moisture and fire danger. As in Chapter 3, the spatial variabilityin fuel moisture and fire danger is quantified, and the relative influence of canopycover and radiation load is assessed. This chapter examines if either radiation load12or canopy cover have the ability to create significant patterns in fuel moisture andfire danger that persist over multiple days. In order to examine how changingmicroclimates on different slope aspects directly impact fuel moisture, a samplingapproach will be used which separates the influence of radiation load and canopycover and uses sites with consistent understory. Chapter 5 also attempts to quantifythe relative influence of precipitation and radiation on fuel moisture and fire danger.Finally, in Chapter 6 rasters of fuel moisture are developed to examine patternsin fire danger across a larger study region of 140 km2. In this way the analysisof spatial patterns in fire danger and fuel moisture is extended beyond point mea-surements made within a small (<4 km2) area. Additionally, this final analysisintroduces the impact of elevation. The required rasters of relative humidity andtemperature are estimated using a non-linear machine learning approach that istrained on the near-surface observations used in Chapter 3.Final conclusions are provided in Chapter 7, beginning with a summary ofmajor findings. This is followed by a discussion of the implications of the findingsand potential future research directions.13Chapter 2Field site and methodology2.1 OverviewA network of near-surface humidity and temperature sensors was established acrossa forested landscape with a wide range of both radiation load and canopy cover.In order to isolate the influence of these two factors, and given the focus on thelandscape scale, the network sampled a relatively small area (<4 km2) with littlechange in elevation. This sampling design ensured that there were no larger scaleclimatic gradients, and that all sites were forced by the same above-canopy condi-tions. Sites were selected so as to sample as much of the two dimensional spacedescribed by canopy cover and radiation load as possible, which helped to avoidcollinearity and its effects on the stability of estimated regression coefficients. Asmentioned in the introduction, this thesis will attempt to isolate the direct impactof patterns in microclimate on fuel moisture due to increased radiation from theindirect impacts, which are attributable to the fact that vegetation is often denserin cooler and wetter microclimates. Therefore, sites were chosen which had rel-atively consistent vegetation with little understory vegetation. As a complementto this network, fuel moisture, solar radiation, precipitation, and wind speed weremeasured at a subset of sites.142.2 Field siteThe field location was selected based on several criteria. At a broad scale, theInterior Douglas-fir (IDF) Biogeoclimatic Ecological Classification (BEC) zone(Pojar et al., 1987) was chosen as a suitable ecosystem type for this field work forseveral reasons. Firstly, this region is characterized by relatively long seasons ofintense fire weather and was likely to provide a wide range of conditions includingprotracted dry periods. Secondly, this BEC zone is characterized by a relativelysparse understory which allowed me to focus on the influence of the overstoryindependently of the influence of shrubs and understory trees. At a finer scale, Ifocused on locating regions of Crown land that were accessible by major loggingroads but were not being actively logged. Finally, I looked for regions characterizedby high spatial variability in canopy cover and radiation load so that a wide rangeof these factors could be sampled within a relatively small area.Based on these criteria, a broader region of interest was selected located 20km north-west of Kamloops, just west of the Lac du Bois Grasslands Protectedarea with an average elevation of 1170 m. The plateau region exhibits a rollingterrain, and logging activity has left a mosaic of stand structures. Within the drierregions of BC, such as the IDF and Ponderosa Pine BEC zones, canopy coverincreases with decreasing radiation load due to decreased water deficit. However,the logging at the field location has, to a certain extent, decoupled this relationship;logging on cool north facing slopes has provided sites with low radiation load andlow canopy cover. This decoupling provided an opportunity to sample the entirecanopy cover/radiation load parameter space.A smaller field site was then selected within this broader region. Its locationis shown in Figure 2.1. Using Landsat imagery, the Vegetation Resource Inventorydatabase (http://www., and Google Earth, canopy cover wasmapped across the broader region. Combining these layers with maps of radiationload calculated using ArcGIS 10 (ESRI), the region was divided into 16 strata, eachwith a unique combination of low, low-moderate, high-moderate, and high levels ofboth canopy cover and radiation load. A smaller region was then identified withinwhich as many of the 16 strata as possible were represented. Having selected thespecific study area, these strata were then used to to select individual measurement15sites so that as much of the two-dimensional parameter space was sampled as pos-sible. In Chapter 6 I produce 30-m resolution rasters of fire danger across a 34 km2study region centred around the field site. The location of this study region is alsoshown in Figure 2.12.3 Field methodologyThe network of stations comprised 24 sites, each of which had a LogTag Haxo-8relative humidity/temperature sensor, which took measurements every 30 minutes.A detailed map of the field area along with the site locations is shown in Figure2.2, and site characteristics are provided in Table 2.1. Site locations were chosento minimize among-site variation in understory structure, with a preference forsites dominated by a needle bed interspersed with grasses and/or mosses. Shrubsand thick understory vegetation were avoided as much as possible. Observationswere made from May 6 to September 22, 2014. The field site was established soonafter the area was accessible, and ended when the likelihood of a period of highfire danger occurring had diminished. Each LogTag was placed within a customradiation screen constructed from corrugated plastic sheets and reflective foil tape,based on the design by Holden et al. (2013). As these data will be used to drivethe fuel moisture stick model developed in Chapter 3, the sensors were placed 30.5cm above the ground, which is the standard measurement height for fuel moisturesticks.At each site, hemispherical photos of the canopy were taken to estimate canopycover. A Nikon FC-E8 fisheye lens and a Nikon Coolpix 4500 4.0 mega pixel cam-era were used to take the images at the highest image quality. These images wereprocessed with the Gap Light Analyser software (Frazer et al., 1999), which gener-ated canopy gap fractions as a function of zenith angle and azimuth. A total canopygap fraction, which was taken to represent canopy cover, was then generated by in-tegrating over the half sphere. The hemispherical photos were also used to modelbelow-canopy shortwave radiation load. The details of this modelling are providedin Chapter 5. Aspect was estimated at each site using a compass, and slope gra-dients were estimated at each site by averaging both the downslope and upslopegradient over a distance of 10 m using an inclinometer. Aspect and slope were then16lSparks LakeField SiteKamloops AirportStudy Region0km 10km 20km50.650.750.850.9−120.8 −120.6 −120.4LongitudeLatitudelFigure 2.1: Map of study area, including the Field site location (purple tri-angle), the Sparks Lake fire weather station used in Chapter 5 (yellowsquare) , and the study region (green square) and Kamloops Airportweather station (red circle) used in Chapter 6. The location of the studyarea within BC is indicated by the black point in the map at top.17Figure 2.2: Detail of the field site. Top: aerial photography of site. Bottom:radiation load averaged over the entire field season (calculated usinga 30-m resolution digital elevation model developed by Rosin (2010)).Sites referred to in text are indicated by colour.18used to calculate radiation load at each site using the equations of Iqbal (1983). Ateach site, flux densities of solar radiation parallel to the forest floor were calculatedassuming clear sky conditions and no canopy cover. These hourly data were thenaveraged over the entire field season to generate average radiation loads for eachsite.At three of the sites, Fuel Moisture 1, Fuel Moisture 2, and the Base Station,Campbell Scientific CS506 Fuel Moisture Sensors made 10-hour fuel moisture ob-servations at a standard height of 30.5 cm. This sensor is composed of a time do-main reflectometer probe embedded within a standard moisture stick with a radiusof 0.65 cm and a length 50.8 cm. Co-located with each fuel moisture sensor was aRotronic HC-S3 humidity and air temperature sensor (also at a height of 30.5 cm),a Rainwise tipping bucket raingauge, and a Kipp And Zonen CM3 pyranometer. Inaddition, at the Base Station wind speed was measured by a Met One anemometer,which has a stall speed of 0.4 m s1, and temperature and humidity measurementswere also taken at a height of 1.62 m. Wind speed was interpolated to 30.5 cmfrom 1.62 m using a neutral logarithmic wind profile. The aerodynamic roughnesslength was set to 0.01 m, which is appropriate for short grass (Oke, 1990). Fuelmoisture, temperature, humidity, wind speed, and solar radiation measurementswere made at 10 minute intervals. Finally, precipitation was also measured at Site8 and at Site 1. Example photos of the instrumentation are shown in Figure 2.3.A number of steps were taken to assess the accuracy of the Logtag sensors.Firstly, to assess any intrinsic biases of individual sensors, the LogTags were setto measure ambient temperature and humidity in the lab for three days before andafter the field season. Secondly, the LogTag observations were compared to higherquality co-located Rotronic HC-S3 observations made at three of the sites. Resultsfrom this analysis can be found in Appendix A.Even though the pine dowels used in the automatic fuel moisture sensors arecarefully selected and standardized, it is likely that the sensors used here wouldprovide slightly different results. With respect to sensor accuracy, the manufacturerreports that the root mean square error is± 0.74% for moisture content below 10%,± 0.90% for moisture between 10% to 20%, ± 1.94% for moisture between 20%and 30% and± 2.27% for values above 30% (Campbell Scientific, 2015). To checkthe consistency between the sensors, two comparison periods were undertaken on19Figure 2.3: Field instrumentation. Left: Base Station; Top Right: LogTagHaxo-8 humidity and temperature sensor; Bottom Right: Radiationscreen installed at Site 6. Instrumentation was surrounded by chickenwire to protect against grazing cattle.either end of the field season in which the sensors were co-located for a total of35 days. Using these co-located data, biases between the sensors were calculatedand then removed to bring the three sensors into agreement. Details of this fuelmoisture sensor calibration is detailed in Appendix A.2.4 Supplementary weather observationsIn order to provide context for the single season of fire danger estimated at the fieldsite in Chapter 5, 26 years of fire weather data from a nearby British Columbia20Wildfire Management Branch fire weather station, Sparks Lake, were used to gen-erate a regional climatology of fire danger. The station’s location, shown in Figure2.1, is at a similar elevation and forest type as the field site. The data, whichwere taken from Pacific Climate Impact Consortium’s Data Portal (, include hourly observations of wind speed, precipitation,and relative humidity and temperature at a screen height of 2 m. Shortwave ra-diation was not measured at these stations and was therefore extracted from theDaymet dataset, which is a 1-km resolution daily interpolated weather dataset(Thornton et al., 1997). Daily mean shortwave radiation was converted to the re-quired hourly resolution using the technique outlined by Liu and Jordan (1960).Any fire season (May 15th to October 1st) that had a data gap wider than four dayswas not used in the analysis and any data gap less than four days was in-filled usinglinear interpolation. Although this is not a particularly accurate method, it does notlikely have a large impact on the resulting fire danger climatology derived from 26fire seasons.The analysis in Chapter 6 requires the calculation of temperature and humiditylapse rates. These lapse rates were calculated using the field observations com-bined with observations at the Kamloops Airport, which is at an elevation of 345 mabove sea-level, compared to the field site’s elevation of 1170m (See Figure 2.1 forlocation). The Kamloops Airport data were produced by Environment and ClimateChange Canada and also acquired via the Pacific Climate Impact Consortium’sData Portal.21Table 2.1: Site characteristics.Site Name Longitude Latitude Radiation Canopy Gap Aspect Slope(Degrees) (Degrees) Load (Wm−2) Fraction (%) (Degrees) (Degrees)Site 1 -120.5991 50.7969 293 32 239 17Site 2 -120.5967 50.7969 282 28 294 5Site 3 -120.5930 50.7942 291 18 241 25Site 4 -120.5873 50.7989 208 16 21 29Site 5 -120.5886 50.7997 223 18 22 25Site 6 -120.5896 50.7995 291 31 227 4Site 8 -120.5953 50.7988 268 60 44 11Site 9 -120.5956 50.8011 268 30 22 9Site 10 -120.5970 50.8014 241 28 8 18Site 11 -120.5976 50.8018 245 47 28 18Site 12 -120.5994 50.8023 266 46 332 10Site 13 -120.6033 50.8024 294 21 232 29Site 14 -120.6067 50.8030 262 32 307 15Site 15 -120.6042 50.8046 274 46 299 10Site 16 -120.6029 50.8040 268 17 27 9Site 17 -120.6032 50.8034 238 14 12 19Site 18 -120.6037 50.8033 265 32 27 10Site 19 -120.6028 50.8032 246 14 34 18Site 21 -120.5898 50.7920 294 33 237 19Site 22 -120.5899 50.7913 232 10 10 21Site 23 -120.5895 50.7989 232 19 41 24Base Station -120.6058 50.8008 298 68 216 11Fuel Moisture 1 -120.5925 50.7984 237 18 47 24Fuel Moisture 2 -120.5972 50.7990 303 52 207 1522Chapter 3Spatial variability of near-surfacetemperature and humidity acrossa heterogeneous forestedlandscape3.1 IntroductionNear-surface atmospheric conditions drive fuel drying rates (Cohen and Deeming,1985; Van Wagner, 1987) and can vary significantly at a range of scales within aheterogeneous forested landscape. Spatial patterns in near-surface conditions canbe due to a number of factors including aspect and elevation (Barry, 2008), cold-airpooling (Holden et al., 2011b), patterns in canopy cover due to natural and anthro-pogenic disturbances (Chen et al., 1999), precipitation, and soil moisture dynamics(Lookingbill and Urban, 2003). Any large fire (>1 km2) will likely encounter amosaic of conditions as all of these factors vary at a range of scales, leading tocomplex patterns in fire behaviour and effects. It is therefore important to under-stand what are the most important drivers of patterns in near-surface conditions atthe scale of large fires (1 km2 to 100 km2), how weather conditions enhance ordiminish their effects, and how the impact of elevation, aspect, cold-air-pooling,23canopy cover, precipitation, and soil moisture interact.Relative humidity is often taken to be the master variable that determines fuelmoisture (Viney, 1991; Matthews, 2013). Fuel moisture is primarily driven byadsorption and desorption, especially at lower moisture levels. These sorptionprocesses are constantly moving fuel towards some equilibrium moisture content,which is the moisture level the fuel would obtain if left to come into equilibriumwith some constant atmospheric condition. By analysing the thermodynamics ofsorption, Nelson (1984) demonstrated that this equilibrium moisture content is di-rectly related to relative humidity. This dependence on relative humidity is animportant distinction that sets sorption apart from evaporation and condensation,which are more strongly related to humidity deficits: vapour pressure deficit orvapour density deficit (Oke, 1990). Consequently, relative humidity will be theprimary focus of this study. However, variability in relative humidity is, to a largeextent, driven by variability in temperature, particularly at the daily time scalewhere vapour pressure is less variable. Temperature also has a direct but secondaryimpact on fuel moisture (Viney, 1991). Temperature will therefore be included inthis analysis primarily because it provides insight into the observed trends in rela-tive humidity. Due to its direct impact on relative humidity, absolute humidity willbe examined here as well using vapour pressure.The relative influence of canopy cover and radiation load on near-surface con-ditions will be examined in this study. Canopy cover and radiation load also meritstudy due to possible interactions (Nyman et al., 2015b). The influence of aspect islikely diminished below dense canopies, and canopy cover may not be as importanton very cool terrain facets where radiation levels are already low.In general, temperatures increase with increasing radiation load (Geiger, 1965;Barry, 2008). Within open sites there is a positive linear relationship between ra-diation load and surface temperatures (Chung and Yun, 2004; Vercauteren et al.,2013) (unless otherwise stated, the literature reviewed here examines mid-latitudetemperate forests). This influence of solar radiation is seen primarily during theday (Bolstad et al., 1998; Lookingbill and Urban, 2003; Dingman et al., 2013).This influence of aspect is strongest during winter months when lower sun angleslead to larger spatial variability in radiation load (Smith, 2002; Dobrowski et al.,2009), and is reduced during cloudy conditions (Dobrowski, 2011; Suggitt et al.,242011). Dingman et al. (2013) found that the impact of radiation load on tempera-ture increased closer to the ground.There is little evidence in the literature of any significant impact of aspect onabsolute humidity. In many cases the dewpoint temperature is assumed to equalthe daily minimum temperature (e.g., Thornton et al. 1997). Given the lack of vari-ability in nocturnal temperatures across different terrain facets, this approach im-plicitly assumes that there is no influence of aspect on absolute humidity. Changesin relative humidity with aspect are therefore driven largely via its impact on tem-perature. For instance, given constant absolute humidity, one would expect thatdaytime minimum relative humidity would be lower on warmer slopes. Indeed,Holden and Jolly (2011) found that, averaged over the fire season, daytime relativehumidity levels were lowest on south-west facing slopes.Canopy cover also has a significant impact on forest floor conditions. Overall, aforest canopy acts to reduce diurnal variability in temperature by reducing incom-ing solar radiation and nocturnal radiative cooling (Chen et al., 1999). Stathers(1989) found that the probability of seedling frost damage was reduced belowdense canopies. Because of counteracting effects of longwave cooling and solarheating, canopy cover has less impact on daily mean temperatures. Canopy influ-ence is most strongly felt near the ground (Whitehead et al., 2006; Suggitt et al.,2011), during summer months due to increased sun angles (Suggitt et al., 2011;Smith, 2002), and during fair weather conditions (Chen et al., 1993). Working inNew South Wales, Australia, Ashcroft and Gollan (2011) demonstrated that canopycover is more important than both elevation and distance to the coast in determin-ing a site’s extreme temperatures. However, this influence is only seen at very highcanopy densities. An opposite result was obtained by Vanwalleghem and Meen-temeyer (2009) where stand density played only a minor role in determining thespatial variability of temperature at monthly, daily, and sub-daily time scales.As with aspect, the influence of canopy cover on relative humidity is partlydriven by temperature variability. Compared to open sites, cooler daytime condi-tions below dense canopies lead to higher relative humidity while relative humid-ity is lower at night when nocturnal cooling is reduced (Chen et al., 1993; Renaudet al., 2011). However, this effect is more modest and less consistent than fortemperature. Meyer et al. (2001), Whitehead et al. (2006), and Brooks and Kyker-25Snowman (2008) all found little to no impact of canopy cover on relative humiditydifferences, while Latif and Blackburn (2010) found lower nocturnal relative hu-midity within natural treefall gaps. Chen et al. (1993) found that absolute humiditywithin a forested site was higher during the day and lower during the night ascompared to an open site, suggesting that some of the variability in relative hu-midity was due to changes in absolute humidity. Again, this is not a robust resultas Valigura and Messina (1994) found no real impact of canopy cover on absolutehumidity.Fridley (2009) and Dobrowski (2011) demonstrated that relatively moist soilscan temper the diurnal range of near-surface temperature due to increased thermalinertia. These results are echoed by Ashcroft and Gollan (2013a), who found thatcanopy cover only gains importance as a factor for near-surface conditions duringdrier situations.The above literature leaves room for further research aimed at a specific goalof this thesis: the quantification of spatial variability in near-surface conditionsat the landscape scale, with an emphasis on humidity and fuel moisture. For in-stance, many of the above mentioned studies have focused on screen-level mea-surements. However, conditions can change significantly within the first few me-tres of the atmosphere (Oke, 1990). Both Dingman et al. (2013) and Suggitt et al.(2011) demonstrated that the landscape-scale variability in temperature seen nearthe surface was largely absent at heights above 1.5 m. Consequently, since surfacefuel moisture is driven by conditions at the forest floor, results based on screen-level measurements may be misleading. Another gap in the literature is that mosttopoclimatology studies focus on large (>100 km2) areas and elevation gradients,while a spreading fire interacts with the mosaic of terrain, fuels, and moisture ata smaller scale of around 1 km2. As well, while the literature focuses on temper-ature, fuel moisture is primarily driven by relative humidity, which can have dif-ferent spatial patterns and driving factors than temperature. In addition, there hasbeen little focus on the impact of weather events on spatial patterns. In most casesthe focus has been on long-term or monthly averages, which removes the impactof shorter-term weather variability that drives extreme fire weather conditions.Finally, few studies have attempted a focused and systematic analysis of therelative impact of aspect and canopy cover or their interaction. Vanwalleghem and26Meentemeyer (2009) found that the spatial pattern of temperature across a 274km2 study area was more closely related to stand structure than radiation load atmonthly time scales, while the opposite was true at daily time scales. However,these were just two of a number of different explanatory variables examined. Sug-gitt et al. (2011) found that the monthly mean temperature differences betweensouth and north-facing slopes were similar to the differences between open andforested sites, although these results were from two different study regions. Zouet al. (2007) measured shortwave radiation at sites with different combinations ofaspect, slope, and canopy cover. The results suggest an interaction between radi-ation load and canopy cover during the summer. The impact of aspect on below-canopy solar radiation was muted under dense canopies, and canopy cover had alarger impact on south aspects compared to north aspects.Given the gaps in the literature and the goals of this thesis, this chapter willaddress the following research questions:1. How much variability is seen in near-surface temperature and humidity at thelandscape scale across a heterogeneous forested environment with complexterrain?2. How do weather conditions act to either enhance or diminish this spatialvariability in near-surface temperature and humidity?3. What is the relative influence of radiation load and canopy cover on spatialpatterns in near-surface temperature and humidity, and do these two factorsinteract?The analysis will be guided by the following specific hypotheses that are basedon results from the literature and preliminary analysis of the field data:1. Spatial variability in near-surface conditions is enhanced during fair-weather,dry conditions.2. canopy cover and radiation load have an interacting influence on spatial pat-terns of near-surface temperature and relative humidity.3. canopy cover and radiation load are better predictors of spatial patterns innear-surface temperature than relative humidity.27This chapter begins with a description of the analysis methods in Section 3.2.Results presented in Section 3.3 include quantification of the variability of near-surface humidity and temperature (Section 3.3.1) and analysis of the relative influ-ences of radiation load and canopy cover on these near-surface conditions (Section3.3.2). This is followed by a discussion of results in Section 3.4 and conclusions inSection 3.53.2 MethodsAcquisition and processing of field data are described in Chapter 2. The first step inthe analysis for the current chapter involved calculating the daily mean, maximum,and minimum values for relative humidity, vapour pressure, and temperature ateach of the 24 sites described in Chapter 2.2. These data were originally measuredat 30 minute intervals. Spatial variability was quantified by calculating daily site-specific anomalies from the daily intersite mean for each of the variables. Thedaily anomaly time-series of these nine variables formed the core of this chapter’sanalysis. For the purpose of calculating the maximum and minimum values, theday was taken to start at sunrise rather than midnight. That is, the hours beforesunrise are assumed to belong to the previous day. During a particularly cold night,the temperature and humidity at midnight could be more extreme than the previousmorning’s conditions. In this case, ending days at midnight would lead to a doublecounting of these extreme conditions for both days. Ending the day at sunriseavoids this truncation issue.Due to the strong diurnal cycles in temperature and relative humidity, max-imum and minimum values were chosen as indicators of daytime and nocturnalextremes. Daytime extremes are important as they provide an indication of howsevere the afternoon fire weather will become. It is often during the afternoon thatthe most intense fire behaviour occurs. The nocturnal extremes are important be-cause they indicate the extent to which fuel moisture can increase, or recharge,during the night. The daily mean values were highlighted as they indicate the av-erage seasonal trends in relative humidity and temperature, which play a large rolein determining the seasonal trends in fuel moisture, especially for the larger fuelelements.28To address the first two research questions, anomalies were compared acrosssites to identify the variables and periods of the day that exhibited the widest spreadacross stations. This spread was quantified by calculating, for each day and for eachof the nine variables, both the standard deviation and the maximum range (that is,the difference between the warmest and coolest site, or the wettest and driest site)of the variables. These daily standard deviations and ranges were averaged foreach month and for all days with and without rain. To specifically address thesecond research objective, daily time series of these ranges were compared to timeseries of weather variables measured at the Base Station that could potentially beinfluencing temporal changes in the the spread of conditions across sites.To address the third research question, longer term averages of the anomalieswere calculated over the entire field season for days with and without rain, and foreach month, resulting in seven averaging periods (five months + all rain days + alldry days). For each combination of the nine variables and the seven averaging pe-riods, optimal linear regression models were developed using canopy gap fraction,radiation load, and their interaction as possible predictors of these average anoma-lies. Collinearity between predictors was assessed by calculating variance inflationfactors (VIF). As well, exploratory analysis using Cook’s distance suggested thatSite 22 was a significant outlier during the night time and was therefore excludedfrom the following analysis. Consequently, these 23 data points were used to fitthe models. An examination of bi-plots between predictors and predictands did notuncover any obvious non-linear relationships. Therefore, no transformations weredeemed necessary.The optimal models were selected using the following stepwise approach. First,single predictor models were developed for both explanatory variables. Second,starting with the strongest single predictor model, analysis of variance was usedto determine if the addition of the second predictor, and then an interaction term,significantly improved the model. That is, for each additional term, the null hy-pothesis that the term’s regression coefficient was equal to zero was tested. Theterm was added to the optimal model only if the null hypothesis was rejected at the95% confidence level.In order to compare the relative influence of canopy gap fraction and radiationload, the predictors and predictands were first normalized by subtracting the mean29and dividing by the standard deviations. In this way the relative sizes of the esti-mated regression coefficients indicated the relative influence of each predictor onthe spatial patterns in near-surface conditions.Throughout this analysis two sites were chosen to represent end-members ofthe sample. Site 4 was located on a steep north-facing slope with a closed-canopy.The Fuel Moisture 2 site was in an open location on a south-facing slope. Thesesites are highlighted in the results section. In addition, Site 22 was identified as asignificant outlier due to its unusual nocturnal conditions relative to other similarlyplaced sites. This site was also singled out in the following results.3.3 Results3.3.1 Quantifying variability in near-surface humidity andtemperature and the impact of weather conditionsThe seasonal trends in near-surface conditions are presented in Figure 3.1. Therewas a warming trend through May, June, and into July with cooling through Augustand September. There was also an unseasonally cool period in the second half ofJuly centred around a significant precipitation event. Absolute humidity remainedrelatively steady during the first three months of the season. In August there was asubstantial increase in vapour pressure, which was followed by a drying trend intoSeptember. Relative humidity generally decreased through May, June, and July.Two low-humidity periods occurred in mid-July and late July / early August. Thelast dry period ended with the increase in vapour pressure. In general, precipitationwas associated with high relative humidity values across all sites.Figure 3.2 shows 29 days of humidity and temperature data for all 24 sites at aresolution of 30 minutes. Both relative humidity and temperature had large diurnalcycles while for vapour pressure the diurnal signal was weaker. The largest amountof spatial variability occurred during the afternoon and early morning. Nocturnalvariability in relative humidity across sites was particularly large. At times thedifferences between sites were over 40%. For all three variables the spatial vari-ability among sites tended to increase during warm, dry periods with no rain, whileprecipitation acted to collapse the spread among stations. Fuel Moisture 2, which30Figure 3.1: Daily relative humidity, vapour pressure, and temperature obser-vations. The thick black lines are the daily intersite means. The greyribbons show the intersite range of the daily minimum and maximumvalues. Hourly precipitation observations at the Base Station are pre-sented in bottom plot.had little canopy cover, was consistently warmer during the day and cooler at nightcompared to the closed canopy Site 4. There was no consistent difference betweensites. The Fuel Moisture 2 site also saw larger diurnal cycles in relative humiditywith wetter nights and drier afternoons. Compared to the similarly placed Site 4,the diurnal cycle was much larger at Site 22 due to its cool and wet nocturnal con-ditions. Indeed, the nocturnal conditions at Site 4 were similar to those at the openFuel Moisture 2 site.31Figure 3.2: A sample of hourly relative humidity, vapour pressure, temperature, and precipitation (bottom) observationsfor all sites (grey lines). Fuel Moisture 2, Site 22, and Site 4 are highlighted.32The spatial variability in temperature and humidity is highlighted in Figure 3.3.A summary of these anomalies is presented in Table 3.1. In general, variability in-creased over the first three months of the season. The daily mean values saw lessspread across sites while nocturnal conditions were generally the most variable, es-pecially for relative humidity. Other than minimum relative humidity, precipitationacted to reduce the spread across stations.Figure 3.3 also demonstrates the consistent warm/dry daytime conditions andcool/wet nocturnal conditions at the Fuel Moisture 2 site seen in Figure 3.2. Itfurther demonstrates that the anomalies in daytime conditions (Figures 3.3B andD) were relatively steady throughout the field season, regardless of weather condi-tions. This consistent variability is in contrast to the nocturnal conditions (Figures3.3A and E), which exhibited obvious shifts between periods of low and high vari-ability. Figure 3.3 demonstrates that the role of precipitation in reducing spatialvariability was strongest at night.Anomalies in mean vapour pressure (Figure 3.3C) were less consistent thanfor relative humidity and temperature. However, daily mean vapour pressure wasgenerally lower at Site 4 while the last half of the season saw a large moist anomalyat Site 22. July exhibited two periods of more significant spread in vapour pressurewhich coincided with similar large ranges in the nocturnal relative humidity andtemperature.Even though the outlying Site 22 was similar to Site 4 in its placement (north-facing closed-canopy), it was generally much cooler with higher relative humidityat night. Site 22 also consistently had the lowest temperature and highest relativehumidity of all sites during the day. Absolute humidity at Site 22 did not showsuch strong anomalies, although it exhibited relatively high vapour pressure duringAugust, July, and September.The spread in near-surface conditions and the influence of rain events are high-lighted in Figure 3.4. The impact of precipitation is easily identified here. For mostvariables, rain events acted to reduce the spatial variability, reflecting the results inTable 3.1. The impact of precipitation is most evident during the night (Figures3.4A and E) when rain created substantial reductions in the spatial range of maxi-mum relative humidity and minimum temperature. A similar but less severe patternis seen in the maximum temperatures (Figure 3.4D). Precipitation had the opposite33Figure 3.3: Daily anomalies from the intersite mean for maximum and mini-mum relative humidity and temperature, and daily mean vapour pressureat all sites (grey lines). As in Figure 3.2, Fuel Moisture 2, Site 22, andSite 4 are highlighted.34Table 3.1: Daily standard deviation (SD) and maximum range (Range) oftemperature and humidity variables averaged across each month andacross all days with and without rain.RHmin Tmax RHmax Tmin RHmean Tmean(%) (◦C) (%) (◦C) (%) (◦C)Period SD Range SD Range SD Range SD Range SD Range SD RangeMay 3.9 16.1 1.5 5.6 4.2 15.5 0.9 3.2 2.8 11.3 0.5 2.2June 3.3 13.0 1.7 6.0 6.4 22.5 1.3 4.5 3.5 12.2 0.5 2.3July 3.4 14.0 2.1 7.6 8.5 28.6 1.9 6.3 3.9 14.4 0.7 3.4Aug. 4.5 19.3 2.0 6.9 6.2 21.4 1.6 5.2 3.6 14.5 0.6 2.9Sept. 5.7 23.0 2.0 7.5 7.8 28.6 1.8 5.8 5.0 19.8 0.9 3.8Dry Days 4.0 16.4 2.0 7.4 8.1 27.4 1.8 5.8 4.1 15.5 0.7 3.4Rain Days 4.3 17.6 1.5 5.4 3.9 15.1 1.1 3.7 3.0 11.8 0.4 2.0impact on minimum relative humidity, which generally became more variable aftersignificant rain (Figure 3.4B). Examination of Figure 3.3B demonstrates that thesesignificant increases in the total range were primarily due to the outlying Site 22.However, post-rain increases are seen to a certain degree in the standard deviationas well, suggesting that this effect was felt broadly across all sites. The impactof precipitation on vapour pressure (Figure 3.4C) is less clear; rain acted to bothincrease and decrease variability while in other cases there did not seem to be anyimpact.The influence of weather conditions on the spread across stations is furtherdemonstrated in Figure 3.5 where the daily standard deviation of maximum andminimum relative humidity and temperature (the grey lines in Figures 3.4A, B, D,and E) are plotted against days since rain, solar radiation (Kd), daily precipitationamounts, and daily mean wind speed. Again, the impact of precipitation is clear. Inaddition, the left column of Figure 3.5 demonstrates that the homogenising impactof precipitation on nocturnal conditions and daytime temperatures was felt acrossthe landscape for a number of days after precipitation ended. However, as seen inFigure 3.4B and Table 3.1, precipitation had the opposite impact on minimum rela-tive humidity where the spread across stations was highest during and immediatelyafter precipitation.Increased solar radiation was associated with increased variability for all butminimum relative humidity, for which there was a small negative relationship (mid-dle column). The relationship was strongest for daytime temperatures (bottom35Figure 3.4: Range (black line) and standard deviation (grey line) of dailymaximum and minimum relative humidity (A, B), mean vapour pressure(C), and maximum and minimum temperature (D, E). Hourly precipita-tion (F), and daily average wind speed (G) are also provided. Precipita-tion amounts are also shown with maroon shading.36llllllllllll lllll llllllllllll lllllllllllllllllllllll llllllllllllllllllllllllllllll lllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllll llllllllll lllll lllll llllll llllllllllllllllll lllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllll llllll l ll l llllllllll l ll l l ll lll l l ll llll l ll llllllll lllllllll llllll lll ll llllllllllllllllllllll lllllllll lllllllllllllllll l ll lllll llll lllll llll l llllllll llllllllllllllllllllllll lllllllllllllll llllllll lllll lll ll llll lllllllllllllllllllllll llllllllllll l llll llll lll llllllllllllllll lllllllll llll ll lll llllll ll l llllllllllllll llllllllllllllll llllllllllllllllllllllllllllll llllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllll llllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllll lllllllllllllllllllllllllllllllllllllllllllll lllllllllll llllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllll llllllllllllll llllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllll l lll lllllllllll lllllll lllllll lll lll l lllllll lllll ll l lllllllllllllllllllllllll lllllllll lllllllll llllllll llllllllllllllllllllllllll lllllllll lllllllllllll llllllllllllllllllllllllllllll ll lllllllllllllllllllllllllllllllllllllllllll llllllll llll llllll lllll llllllllllll lll llllllllllllllllllllllllllllllllllllllllll llllll llllll llllllllllllllllllllllll llllllllllllll llll051015051015012301230 5 10 15 100 175 250 325 0 5 10 15 20 0.751.001.251.500 5 10 15 100 175 250 325 0 5 10 15 20 0.751.001.251.500 5 10 15 100 175 250 325 0 5 10 15 20 0.751.001.251.500 5 10 15 100 175 250 325 0 5 10 15 20 0.751.001.251.50Days Since Rain Kd (Wm−2) P (mm) wind speed (m/s)RHmax S.D. (%)RHmin S.D. (%)T min S.D. (oC)T max S.D. (oC)Figure 3.5: Daily standard deviation of maximum and minimum humidity(top two rows) and minimum and maximum temperature (bottom tworows) plotted against days since rain (first column), solar radiation (sec-ond column), daily precipitation (third column), and mean wind speed(fourth column). Days are divided into days with rain (blue points) andwithout (red points). For maximum humidity and minimum tempera-ture solar radiation is calculated as a running average of the current andfollowing days. Loess curves with a two-degree polynomial are fit tothe relations with days since rain while linear regressions are fit to thesolar radiation plots (solid blue lines) The 95% confidence intervals forthese fits are included (grey ribbons).37row). For the nocturnal variables (top row and third row) solar radiation is calcu-lated as an average of the current day and the following day and can be thought of asa metric of “sky clearness” and radiative cooling at night. Consequently, the physi-cal link to near-surface variability is less direct than for maximum temperature, forwhich solar radiation is for the current day only, leading to decreased correlationsin the nocturnal case. The spread in nocturnal conditions is reduced during periodswith heavy precipitation or high wind speeds, especially for nocturnal conditions.3.3.2 Quantifying the impact of radiation load and canopy coverThe correlation between radiation load and canopy cover ranged from 0.44 to 0.56,depending on the averaging period chosen. VIFs (Montgomery and Peck, 1992)for all averaging periods remained below 2 in all cases, suggesting that collinearityis not a major concern (Zuur et al., 2007).The results of the model selection procedure are shown in Table 3.2. In allcases, an interaction term did not improve the model at the 95% confidence leveland is therefore not included in the following analysis. For the sake of brevity,results are presented only for June, September, and the full season. The relationshipbetween predictands and predictors is generally what would be expected. Coolerconditions with higher relative humidity are found at north-facing, closed-canopysites during the day and at open canopy sites during the night. Notably, there isa relatively strong positive relationship between maximum vapour pressure andcanopy gap fraction; higher vapour pressure is generally found at open sites.Overall, canopy gap fraction was the strongest predictor. That is, for almostall cases, canopy gap fraction explained more of the spatial pattern in near-surfaceconditions and had larger or comparable standardized regression coefficients thanradiation load. However, it is important to note that radiation load was a strongpredictor of minimum relative humidity. On average, the temperature models werethe most skillfull (assessed using the coefficient of determination), while the vapourpressure models performed the poorest. Models of daily mean values were gener-ally poorer than for maximum and minimum values. Indeed, the two variables hadno significant explanatory power (at the 5% confidence level) for average temper-atures during periods of rain.38The models for “All Dry Days” summarized in Table 3.2 are shown graphicallyin Figure 3.6. In general, there was a wider range in nocturnal conditions than dur-ing the day, which is consistent with Figure 3.3. canopy cover had a significanteffect on both daytime and nocturnal conditions. Moreover, compared to radia-tion load the influence of canopy cover was stronger for daytime temperatures andapproximately equal for daytime relative humidity. The abnormal nocturnal condi-tions seen at Site 22 (which was not included in the regression analysis) are clearfrom this figure. Compared to similar sites surrounding it within the parameterspace, it was cooler and had higher relative humidity levels.3.4 DiscussionThere were a number of significant findings from this study. Firstly, near-surfaceconditions were generally more heterogeneous during dry, clear-sky conditions,and spatial variability was reduced during, and for a few days following, precip-itation. In particular, spatial variability in daytime relative humidity was low andrelatively unaffected by weather conditions. Secondly, while canopy cover hadweak drying effect on daytime humidity due to solar heating, canopy cover alsohad a stronger impact on nocturnal relative humidity, which was higher at opensites due to longwave cooling. Consequently, open sites experienced higher dailymean relative humidity.3.4.1 Quantifying variability in near-surface humidity andtemperature and the impact of weather conditionsSignificant variability was seen across the relatively small study area, especiallyat night. For instance, the daily ranges in both minimum and maximum temper-atures were often comparable to over a kilometre of elevation change, assuminga typical lapse rate of ca. 6◦C per kilometre. In some cases, nocturnal relativehumidity was close to 100% at open sites but around 50% at closed-canopy sites.Spatial contrasts in daytime relative humidity were less pronounced. Some of theabove results reflect similar findings in the literature. For instance, the presence ofa canopy significantly reduced the diurnal variability of relative humidity and tem-perature (Chen et al., 1993), and higher temperatures were found on south-facing39lllllll llllllllllllllllRHminlllllll llllllllllllllllRHmaxlllllll llllllllllllllllTmaxlllllll llllllllllllllllTmin22525027530022525027530020 40 60 20 40 6020 40 60 20 40 60Canopy gap fraction (%) Canopy gap fraction (%)Canopy gap fraction (%) Canopy gap fraction (%)Radiation load (Wm−2 )Radiation load (Wm−2 )−10−5051015RHAnomaly (%)−4−202TemperatureAnomaly( oC)Figure 3.6: Average anomalies of daily maximum and minimum relative hu-midity (top row) and temperature (bottom row) for all non-rain daysplotted on the radiation load - canopy gap fraction parameter space.The right column shows daytime conditions (maximum temperatureand minimum relative humidity), while the left column shows nighttime conditions (minimum temperature and maximum relative humid-ity). The anomaly values predicted by the linear regression models sum-marized in rows 1-4 of Table 3.2 are indicated by the contour lines.Specific sites are highlighted as in Figures 3.3 and 3.2: Site 22 (yellow),Fuel Moisture 2 (red), and Site 4 (green).40slopes (Barry, 2008).As was hypothesized, variability was generally enhanced during dry, clear-skyconditions, although this study revealed further details and caveats that expandon this relatively simple prediction. For instance, the impact of precipitation isstrongest for nocturnal relative humidity and temperature. As well, this homoge-nizing influence of precipitation persisted for a number of days following rain. It islikely that increased moisture following precipitation led to increased thermal in-ertia of near-surface conditions (Fridley, 2009; Dobrowski, 2011), which, in turn,reduced heterogeneity across the landscape. As well, variability in daytime min-imum relative humidity increased during and immediately after rainfall and wasnegatively related to solar radiation, supporting what was seen in Figure 3.4.It is likely that some of the fluctuation between high and low variability of max-imum relative humidity is due to the 100% saturation ceiling. That is, precipitationfollowed by nocturnal cooling will bring many of the sites to saturation, decreas-ing variability substantially. This saturation effect explains the strong relationshipbetween precipitation amount and the spread in maximum humidity seen in Figure3.5.Site 22 is an interesting outlier in this dataset. Even though it had the dens-est canopy of any site, its nocturnal conditions were similar to that of an opensite: cool with high relative humidity. It also saw a substantial cold/wet daytimeanomaly compared to all other sites. The sensor in this case was located within 15m of a draw that remained wet throughout the season. It is likely that an elevatedwater table at the site led to enhanced near-surface moisture, leading, in turn, to ele-vated relative humidity compared to other closed-canopy locations. Indeed, duringthe last half of the season when the rest of the sites dried out, this extra sourceof moisture kept vapour pressure anomalously high at Site 22 (see Figure 3.3C),explaining the elevated relative humidity throughout the day. The cold anomalycould be attributed to evaporative cooling that would occur as drier surrounding airwas advected through the site. The cold anomaly could also be partially explainedby the fact that groundwater is typically cooler than summer air temperatures. An-other potential explanation is that cool air was draining downslope from an openarea located upslope of the site. However, because this cold advection would haveonly occurred during clear nights, it cannot explain the consistent cold anomaly41present during all times of day and weather conditions.3.4.2 Quantifying the impact of radiation load and canopy coverIn most cases, canopy gap fraction and radiation load were able to account for alarge amount of the spatial variability of near-surface conditions. The fitted rela-tions were stronger during the night than during the day. The best results wereachieved for nocturnal temperature during dry conditions, for which the model ex-plained up to 85% of the spatial variability. Canopy gap fraction emerged as themost important predictor, even for daytime temperature and daytime relative hu-midity during days with rain. Even for variables with radiation load as the strongestsingle predictor, the standardized regression coefficient values where comparablebetween the two predictors. This suggests that the amount of solar radiation be-ing absorbed at a particular site is more dependent on canopy interception thanthe solar angle relative to the slope of the forest floor. Considering that the im-pact of radiation load increases closer to the forest floor (Dingman et al., 2013), itis also possible that skin temperatures of the forest floor would be more stronglyinfluenced by radiation load, and that this impact is diminished at the 30.5 cmmeasuring height used here.It was hypothesized that canopy cover and radiation load would be strongerpredictors of temperature than humidity. This prediction is borne out in the re-sults where the temperature models were the most skillfull, followed by relativehumidity and then vapour pressure. It is possible that variability in humidity ismore dependent on site characteristics such as the amount and type of understoryvegetation and the resulting rates of transpiration. Although an effort was made tomaintain consistent understory vegetation across sites, the variability that did occurmay have been enough to increase unexplained variability in relative humidity.The analysis also revealed higher vapour pressure at more open sites, especiallyfor mean and maximum vapour pressure. This result is slightly counter-intuitive,as one might expect that more open canopies would allow for greater mixing withdrier air aloft, leading to a negative relationship. However, it is also possible that ascanopy cover decreases, the amount of moisture removed from the forest floor viatranspiration within the overstory would also decrease. It is unlikely that increased42precipitation at open sites led to increased vapour pressure as these results demon-strated that precipitation had little impact on vapour pressure. It may also be thecase that heating of the Logtag sensors by solar radiation led to a positive bias intemperature and vapour pressure at open sites. However, if this radiation influencewere present, one would expect a bias at higher temperatures. Yet, following theremoval of temperature biases in the Logtag sensors (see Appendix A), no suchbias was apparent.An important result here is the homogeneity of daytime humidity, which wasrelatively constant regardless of weather conditions. For instance, in contrast tothe other variables, precipitation did not act to decrease the variability in minimumrelative humidity across sites while solar radiation had a small negative impact (seeFigure 3.5). The positive relationship between canopy gap fraction and vapourpressure may explain this reduced spatial variability in daytime relative humidityand its weak relationship with canopy gap fraction. That is, higher levels of vapourpressure at open sites were balanced by higher daytime temperatures, resulting inless variability in minimum relative humidity across sites.It is significant that daily mean relative humidity and temperature are gener-ally less variable across sites and were more poorly predicted than minimum andmaximum values. Indeed, during periods of rain the spatial pattern in daily meantemperatures was not related to either explanatory variable. Chen et al. (1999)suggested that due to the counteracting impact of canopy cover on daytime versusnocturnal conditions, average conditions will likely be less related to canopy coverand will therefore be less spatially variable.The lack of interaction between the two predictors is also notable. It was origi-nally hypothesized that increased canopy cover would diminish the impact of radi-ation load on near-surface conditions, while canopy cover would be less importanton cool north-facing aspects where the radiation load is already low. However, noevidence for this was found in this study, although it is possible that a larger datasetwould produce significant interaction terms.433.4.3 Implications for fuel moistureThese findings have a number of implications for fuel moisture. With respect torelative humidity, which is the primary driver of fuel moisture, the spread acrosssites is smaller during the day than at night. Therefore, in the afternoon, whenfires are often the most active, spatial variability in fuel moisture may be small.As well, relative humidity patterns across the landscape are not strongly dependenton weather conditions, suggesting that the daytime spatial variability in dryingpotential may not increase during particularly dry periods.Air temperature does have a secondary impact on fuel moisture. However,these results suggest that the nocturnal and daytime variability of near-surface tem-perature (both of which are driven primarily by canopy cover) are of equal mag-nitude but opposite sign. This balance between daytime and nocturnal conditionsmeans that there would be no persistent temperature anomaly that could drive asignificant divergence in fuel moisture across sites.This behaviour is in contrast to that of relative humidity, which varied moreat night than during the day, leading to the positive relationship between canopygap fraction and daily mean relative humidity seen in Table 3.2. Therefore, as willbe hypothesized in Chapter 5, nocturnal moisture recharge may overwhelm thedaytime drying at the open sites, leading to higher fuel moisture at open sites.Being quicker to respond, the smaller fuel elements will likely follow this dielcycle of relative humidity: increased moisture and spatial variability at night fol-lowed by drier, less variable fuel moisture during the day. For the larger fuel ele-ments with their longer response times, the impact of increased daily mean relativehumidity at open sites, integrated over time, may actually lead to higher fuel mois-ture at open sites. In any case, canopy cover, being a stronger predictor of relativehumidity anomalies than radiation load, will, in turn, be the primary driver of spa-tial patterns in fuel moisture.3.5 ConclusionsThe largest variability in near-surface conditions was seen at night, while dailymean values were less variable than both daily minimum and maximum values.At night, sites with dense canopies remained warmer than open sites due to down-44welling longwave radiation. Consequently, there were some instances in whichopen sites were near or at saturation while relative humidity was around 50% atclosed-canopy sites. During the day, cool, north-facing slopes were often signifi-cantly cooler than nearby warm south-facing slopes. For temperature and noctur-nal relative humidity, precipitation acted to reduce variability across the landscapewhile variability increased during clear sky conditions. However, radiation andprecipitation had the opposite impact on daytime relative humidity variability. Thehomogenizing influence of precipitation persisted for a number of days after rainceased, and the impact of weather conditions on spatial variability was largest atnight. One site, located next to a draw that remained wet throughout the season,recorded anomalously wet, cool conditions relative to other similarly placed sites.As other sites dried out over the course of the season, the site’s high water tableprovided a source of moisture, which also led to evaporative cooling.Together, canopy gap fraction and radiation load predicted up to 85% of thespatial variability in near-surface climate. Patterns in temperature were better pre-dicted than relative humidity, while vapour pressure was poorly predicted. Overall,canopy gap fraction was a better predictor of average near-surface conditions thanradiation load. Notably, mean relative humidity was positively correlated withcanopy gap fraction during both dry and wet conditions, suggesting that open sitesare on average wetter than closed sites, even after periods with no rain.The results of this study have a number of implications for fuel moisture.Firstly, spatial variability in daytime relative humidity is relatively limited and notstrongly impacted by weather conditions, suggesting that afternoon fuel moisturewill remain homogenous across the landscape and throughout the fire season. Sec-ondly, because open sites are wetter compared to closed-canopy sites, it is possiblethat open sites will see higher fuel moisture. Finally, areas where a high watertable persists throughout the season will likely have wetter fuels relative to thesurroundings.The implications for fuel moisture will be studied in more detail in Chapters 5and 6 where the fuel moisture model developed in Chapter 4 will be combined withthe above dataset and canopy interception models of precipitation and radiation togenerate modelled patterns of fuel moisture across the landscape.45Table 3.2: Results of model selection. Standardized regression coefficientsare shown in the Canopy Gap and Rad Load columns. Bold values indi-cate the predictor with the strongest single variable model as determinedby the coefficient of determination. Missing values indicate that the ad-dition of the predictor did not substantially improve the model perfor-mance. Standard error of the estimate is provided in the units of the pre-dictor (Temperature: ◦C, Relative Humidity: %, Vapour Pressure: kPa).Predictand Period Canopy Gap Rad Load Adj. R2 Std. ErrorRHmin All Dry Days -0.39 -0.56 0.64 1.66Tmax All Dry Days 0.64 0.36 0.74 0.89RHmax All Dry Days 0.78 0.23 0.82 3.50Tmin All Dry Days -0.82 -0.2 0.85 0.72RHmean All Dry Days 0.83 0.68 1.84Tmean All Dry Days -0.61 0.34 0.34emin All Dry Daysemax All Dry Days 0.74 0.53 0.03emean All Dry Days 0.56 0.28 0.02RHmin All Rain Days -0.59 -0.43 0.76 1.33Tmax All Rain Days 0.74 0.25 0.76 0.64RHmax All Rain Days 0.75 0.54 2.40Tmin All Rain Days -0.92 0.84 0.44RHmean All Rain Days 0.59 0.32 1.82Tmean All Rain Daysemin All Rain Days -0.43 0.15 0.02emax All Rain Days 0.76 0.56 0.03emean All Rain Days 0.52 0.23 0.02RHmin June -0.46 -0.49 0.65 1.36Tmax June 0.81 0.64 0.88RHmax June 0.85 0.71 3.04Tmin June -0.92 0.85 0.48RHmean June 0.77 0.57 1.77Tmean Juneemin Juneemax June 0.83 0.68 0.03emean June 0.73 0.51 0.02RHmin September -0.77 0.57 2.83Tmax September 0.56 0.54 0.85 0.68RHmax September 0.84 0.69 3.83Tmin September -0.92 0.84 0.68RHmean September 0.73 0.51 2.52Tmean September -0.71 0.48 0.40emin September -0.53 0.25 0.02emax Septemberemean September46Chapter 4A model for simulating themoisture content of standardizedfuel sticks of various sizes4.1 IntroductionDead fuel moisture is an important determinant of wildfire behaviour as it influ-ences a fire’s intensity and rate of spread (Rothermel, 1972). Metrics of fuel mois-ture are at the core of both the Canadian and U.S. fire danger rating systems (Cohenand Deeming, 1985; Van Wagner, 1987). Moisture content of the 1-hour, 10-hour,100-hour and 1000-hour fuel sizes is a major component of the American NationalFire Danger Rating System and is used to estimate, among other things, ignitionpotential, fireline intensity, flame length, and rate of spread. Given constant envi-ronmental conditions, fuel elements are assumed to dry following an exponentialdecay to some equilibrium moisture constant. The names of the fuel sizes are inreference to the decay constant of these exponential drying curves.Traditionally, the moisture of the smaller two fuel sizes was estimated byweighing standardized Pinus ponderosa (ponderosa pine) dowelling. Recently, au-tomated measurements have become more common in which moisture sensors areintegrated directly into the fuel sticks, allowing for remote real-time observations47(Nelson, 2000). However, fuel moisture observations are not always available, es-pecially for larger fuel sizes. Simple models were therefore developed within theNational Fire Danger Rating System that related fuel moisture to the equilibriummoisture constant by assuming exponential drying curves (Cohen and Deeming,1985). These models used climatological data from a single study to estimate mois-ture. Consequently, the diurnal cycle forcing the model is assumed to be constanteven though the model is applied across a range of sites and weather conditions.A more sophisticated process-based model was developed by Nelson (2000),which simulates the moisture content of the fuel sticks at sub-daily resolution (re-ferred to here as the Nelson model). An updated version of the Nelson model isa component of the FlamMap (Finney, 2006) and FARSITE (Finney, 2004) firemodelling tools that are used by a number of fire management agencies to simulatespatial patterns in fuel moisture and fire behaviour. The Nelson Model is also inte-grated into the USDA Weather Information Management System. Andrews (2014)suggested that the Nelson model be used within the BehavePlus fire modellingsystem.The Nelson model simulates the energy and moisture exchange at the surfaceas well as the transport of moisture and heat within the interior of the stick. In-ternal moisture transport can occur within the model through the diffusion of wa-ter vapour, the diffusion of bound water, or capillary flow. It also includes semi-empirical modelling of rainwater absorption.The radial and temporal variation of moisture and heat within fuel sticks canbe described by a two-dimensional partial differential equation expressed in ra-dial coordinates. In order to simplify the problem, the Nelson model uses a lin-earised energy budget in which net longwave radiation is estimated as a functionof the difference between the stick temperature and the apparent sky temperature.The model assumes two constant apparent sky temperatures, one for the daytimeand one for the nighttime. However, the accuracy of the linearised energy budgetdiminishes when the difference between the fuel temperature and apparent atmo-spheric temperature increases. Indeed, during periods of high radiation this tem-perature difference exceeds 30 ◦C.Moreover, a linearized energy budget does not allow for variations in down-welling longwave radiation due to canopy coverage or changes in sky conditions48such as cloud cover. Including the impact of the canopy on longwave radiation maybe particularly important for simulating the impact of changing canopy cover onthe spatial patterns of fuel moisture across forested landscapes. However, becauseFARSITE and FlamMap use the Nelson model, they are not able to include varia-tions in longwave radiation due to canopy coverage because the Nelson model, asmentioned above, does not have this functionality.In addition, the transport of moisture between the stick surface and the atmo-sphere is modelled by assuming that the fuel stick acts as a wet bulb. That is, it isassumed that sensible and latent heat flux are the only components of the energybudget, and all sensible heat is converted to latent heat, driving evaporation. How-ever, if the stick is exposed to direct sunlight, shortwave radiation would dominatethe energy budget, and the wet-bulb assumption becomes invalid.This chapter presents a model for simulating the fuel moisture of standard fuelsticks. The model uses a linear approximation of the internal transport of heatand moisture but solves the energy and moisture budgets numerically, whereas theNelson model uses a linear form of the energy budget and solves the internal trans-port equations numerically. By solving the energy and moisture budgets numeri-cally, incoming and outgoing longwave radiation can be modelled directly. Thisapproach allows for the incoming radiation to vary due to both canopy coverageor changing sky conditions. As well, the transport of moisture to and from thesurface of the stick, and its corresponding latent heat flux, is calculated using anaerodynamic resistance approach. This approach avoids the assumption made inthe Nelson model that the stick acts like a wet-bulb. However, it does require theinclusion of wind speed as an input variable, which is avoided in the Nelson model.With respect to internal transport, the new model divides the stick into two layersand calculates an energy and moisture budget for each layer at every time step.Moisture observations of fuel sticks are used to calibrate and evaluate themodel. Two independent datasets were used: a previous dataset of moisture contentof 1-hour, 10-hour, 100-hour, and 1000-hour fuel sticks used to evaluate the Nelsonmodel, and the observations of 10-hour fuel stick moisture content collected at theBase Station and Fuel Moisture 2 site (see Chapter 2). An additional analysis willexamine the sensitivity of the model to its forcing variables.This chapter begins with a full description of the model in Section 4.2 (a list49of symbols is provided at beginning of the thesis), followed by a description ofthe model calibration and evaluation and sensitivity analysis in Section 4.3. Modelevaluation results are then presented and discussed (Sections 4.4 and 4.5), followedby conclusions in Section Model description4.2.1 OverviewThe model requires hourly values of air temperature, relative humidity, precipita-tion, shortwave radiation, and wind speed. The stick is assumed to be suspended ata standard 30.5 cm above the forest floor. The stick is divided into two zones: a thinouter layer that reacts to atmospheric forcing, and a larger central core. The thick-ness of the outer layer changes with the different stick sizes, but remains below 8mm. This division will allow the model to respond to changes in atmospheric con-ditions at the hourly scale as well as over multiple days. Temperature and moistureare assumed to be spatially constant within the outer layer and core. The averagestick temperature, Ts (K), and moisture, ms (kg of H2O), are calculated as:Ts = f To+(1− f )Tc (4.1)ms = f mo+(1− f )mc (4.2)where To, Tc, mo, and mc are the temperature and moisture of the outer layer andinner core, respectively, and f is the fraction of the stick volume taken up by theouter layer. The variable f will be estimated via calibration.The model is based on the assumption that diffusion and conduction only occurradially, and that transfers of heat and moisture to and from the stick only occurbetween the outer layer and the environment; the core will only gain or lose energyand moisture through conduction and diffusion from the outer layer. This assump-tion simplifies the problem and was also made by the Nelson model. Figure 4.1provides a model schematic.The model is composed of four differential equations which represent the en-50CLemittKabs,diffKabs,dirLabsCPDQhE/QeCentral	CoreOuter	Layermc TcmoToFigure 4.1: Schematic of model showing all components of the moisture andenergy budgets. Please refer to the list of symbols for an explanation ofthe labels.ergy and moisture budgets for each of the two zones. The energy budget for theouter layer, solved for the rate of temperature change, is:dTodt=1csρsVo(Labs+Kabs,di f f +Kabs,dir−asLemit −asQh− (as−2pir2)Qe−C)(4.3)where Labs is the absorbed longwave radiation (W) , Kabs,di f f and Kabs,dir are theabsorbed diffuse and direct shortwave radiation, respectively (W), Lemit is the emit-ted longwave radiation (W m−2), Qh is the sensible heat flux (W m−2), Qe is thelatent heat flux (W m−2), C is the conduction into the stick’s core (W), cs is thestick specific heat (J K−1 kg−1), which is a function of the stick moisture and tem-perature (see Appendix A for details), ρs is the stick density (400 kg m−3, Nelson,2000), Vo is the volume of the outer layer, and as is the surface area of the entirestick.The energy budget of the core is composed solely of conduction from the outerlayer:51dTcdt=CcsρsVc(4.4)where Vc is the volume of the core.The moisture budget for the outer layer is composed of three components: ab-sorbed precipitation (Pabs), evaporation/desorption (E), and diffusion (D) into thecore:dmodt= Pabs− (as−2pir2)E−D (4.5)All three terms on the right-hand side are in units of kg s−1. Evaporation is propor-tional to the latent heat flux (details below), which connects the moisture and theenergy budgets.The moisture budget for the core is composed of diffusion only:dmcdt= D (4.6)Of note here is the use of the total stick surface area minus the area of the stickends (as− 2pir2) when calculating latent heat flux and evaporation. For the twosmallest fuel sizes, the 1-hour and 10-hour fuel sticks, the area of the stick ends issmall relative to their total surface area and can therefore be ignored (see Section4.3). Moreover, the two larger 100-hour and 1000-hour fuel moisture sticks usedfor calibration and evaluation had wax coating their ends. This would have blockeddesorption or adsorption at the stick ends. For these reasons, the latent heat fluxand evaporation terms were calculated using only the lateral stick surface.In contrast, the full surface area, as, is used when calculating emitted longwaveand sensible heat flux as it is assumed that the wax did not impact the conductivityor emissivity of the stick ends. However, it is also assumed that there is onlyradial transport of heat and moisture within the stick. Therefore, while the energyexchanged between the surroundings and the stick ends is ignored, it is assumedthat this energy will be exchanged via the outer layer. In effect, the outer layer hasan “effective” outer surface area equal to the area of the entire stick.The model was written in Fortran and makes use of the ODEPACK libraryof differential equation solvers (Hindmarsh, 1983). The deSolve package in R52(Soetaert et al., 2010) was used to initialize the model and input the forcing data.4.2.2 Shortwave radiationBecause the stick is suspended above the ground, radiation inputs must be calcu-lated from both directions. When discussing radiation components, the subscript“d” indicates downwelling inputs, “u” indicates upwelling inputs from the ground,and “emitt” indicates emitted radiation from the stick.The downwelling shortwave radiation Kd (W m−2) is divided into its diffuse,Kd,di f f , and direct, Kd,dir, components following Erbs et al. (1982). Details ofthese calculations are presented in Appendix A. The upwelling shortwave input iscalculated as Ku = αgKd , where αg is the ground albedo which is taken to be 0.185,based on values reported by Eck and Deering (1992) and Smith and Goltz (1994).The direct solar radiation absorbed by the stick, Kabs,dir (W), is calculated as:Kabs,dir = ashadow(1−αs)Kd,dir (4.7)where αs is the stick albedo. A constant albedo value of 0.65 (Nelson, 2000) isassumed. ashadow is the area of the shadow cast by the stick on a horizontal planeand is a function of the sun position:ashadow = 2rl cscφ(1− cos2 φ cos2ψ)0.5+pir2 cotφ cosψ (4.8)where φ is the solar elevation angle and ψ is the solar azimuth angle, both inradians (Monteith and Unsworth, 2008). This approach is more sophisticated thanthe approach by Nelson (2000), where ashadow was assumed to be constant.Appendix A provides details on the calculation of diffuse solar radiation ab-sorbed by the stick, Kabs,di f f (W).4.2.3 Longwave radiationIn our model, downwelling longwave radiation, Ld , varies with changing sky con-ditions, temperature, and canopy coverage. Changing sky conditions are accountedfor with a varying atmospheric emissivity, εa (See Appendix A for details). Canopycoverage is accounted for using a sky-view factor, s, which is the proportion of the53sky hemisphere which is open to the atmosphere. Ld is calculated as:Ld = (sεa+(1− s)εcanopy)σT 4a (4.9)where ecanopy is the canopy emissivity, and σ is the Stephan-Boltzmann constant(5.67× 10−8 W m−2 K−4). This approach expands upon the Nelson model, whichused two constant values for downwelling longwave, one during the day and oneat night, and did not allow for a changing canopy. However, because the evaluationdataset that was used to test both the present model and the Nelson model wascollected only at open sites, and in the interest of providing a focused study here,the model evaluation presented below does not include an assessment of our canopytreatment. The impact of canopy on fuel moisture will be examined in Chapter 5.The upwelling longwave input from the ground and longwave output from thestick are calculated as:Lu = εgσT 4a , Lemitt = εsσT4o (4.10)where εg = 0.95 (Monteith and Unsworth, 2008) and εs = 0.85 (Nelson, 2000) arethe emissivities of the ground and stick, respectively. Although the emissivity maychange when liquid water is present on the stick surface, this only occurs duringbrief periods directly following precipitation. Therefore, Following Nelson (2000),the stick emissivity is assumed to remain constant. Here it is also assumed that thethe ground temperature is equal to the air temperature, Ta. While this assumptionis likely not valid during clear sky conditions (due to solar heating and longwavecooling), the resulting bias was not deemed large enough to warrant increasingmodel complexity in order to simulate the forest floor temperature.As with diffuse shortwave radiation, Appendix A provides details on how thelongwave radiation absorbed by the stick, Labs (W), is calculated.4.2.4 Sensible heat fluxSensible heat flux is calculated using an aerodynamic resistance approach:Qh = ρacaTo−TaΩ(4.11)54where ρa is the density of air (1.093 kg m−3) and ca is the specific heat of air (1005J kg−1 K−1). Ta is the temperature of the ambient air and Ω is the aerodynamicresistance (sm−1), which is calculated following Monteith and Unsworth (2008):Ω=2rκNu(4.12)where r is the radius of the stick (m), κ is the thermal diffusivity of air ( 1.9×10−5m2 s−1), and Nu is the Nusselt number, which, in the case of a cylinder exposed tothe range of wind speeds observed in the field, can be assumed to be a function ofthe Reynolds Number, Re:Nu = 0.17Re0.62 (4.13)whereRe =u2rν(4.14)where u is the wind speed (m s−1) and ν is the kinematic viscosity of air (1.51×10−5m2 s−1). When the wind speed fell below the stall speed of the anemometer (0.4m s−1), the wind speed was set to the stall speed. The approach may have over-estimated evaporation during low wind conditions. However, as will be shownlater in this chapter, fuel moisture was relatively insensitive to wind speeds, so thisapproximation likely did not have a significant impact on model output.4.2.5 Water vapour and latent heat fluxThe mass flux of water vapour to and from the stick, E (kg m−2 s−1), is computedas:E =qsur f −qaΩ(4.15)where qa is the vapour density of the ambient air (kg m−3) and qsur f is the vapourdensity at the stick surface. Here the aerodynamic resistance of water vapour isassumed to be the same as the resistance for sensible heat flux, Ω.In order to calculate qsur f , desorption and adsorption within the stick needs55to be accounted for. These sorption processes were included using the followingapproach. When the stick’s moisture content is above the fibre saturation point of30%, the stick surface is near or at saturation, and it is assumed that liquid water ispresent, and evaporation occurs as from a liquid surface. Below the fibre saturationpoint desorption processes begin to dominate and resistance to moisture removalincreases. This resistance occurs because an increasing proportion of the moisturewithin the stick would be composed of bound water, which requires extra energyto convert to water vapour and diffuse out towards the surface (Viney, 1991).Adsorption and desorption constantly move the moisture of a fuel towards anequilibrium moisture content, which is a function of the temperature and relativehumidity at the fuel surface. To account for these sorption processes it will beassumed that the surface of the stick is always at the equilibrium moisture con-tent. Following Matthews (2006), this assumption allows us to invert the equationfor the equilibrium moisture content given by Nelson (1984) to calculate the rela-tive humidity of the air right at the stick surface, RHsur f , for a given stick surfacetemperature, Tsur f (K), and moisture content, msur f (%) :RHsur f = exp(−4.19MRTsur fexp(msur f B+A))(4.16)where M is the molecular mass of water ( 0.0180 kg mol−1), R is the gas constant(8.314 ×10−3 kPa m3 mol−1 K−1), and B and A are unitless empirical constants,which will be treated as adjustable parameters during model optimization. Thefactor of 4.19 is required to convert the original equation of Nelson (1984) to S.I.units. RHsur f can then be combined with the saturation vapour density, qsat , tocalculate qsur f :qsur f = qsat RHsur f (4.17)which can then be used in Equation 4.15 to calculate evaporation rates.The impact of ms on RHsur f is presented in Figure 4.2 for a range of possi-ble curves using A and B values suggested by the experimental work of Anderson(1990b). The influence of temperature on RHsur f is relatively weak, and it is ig-nored in this figure by setting temperature to a constant 15◦C. Here we see the56aforementioned relationship between surface humidity and fuel moisture content.Above the fibre saturation point of 30%, the relative humidity at the surface is ator near 100% and evaporation is not limited. As moisture decreases below 30%,the relative humidity quickly decreases, and the resistance to moisture removalincreases as sorption processes begin to dominate. 0.25 0.50 0.75 1.00msRHsA=5.3 / B=−21 A=5.5 / B=−17 A=4.6 / B=−15Figure 4.2: The impact of surface fuel moisture on surface relative humidityfor different values of A and B. The fibre saturation point of 30% isshown by the vertical dashed grey line.Here it will be assumed that the surface moisture and temperature are equalto the average moisture and temperature of the outer layer. In the final model,the outer layer represents a thin outer shell, whose thickness increases with fuelsize but remains below 8 mm for the largest size. Therefore, this assumption isreasonable as the moisture and temperature within the thin outer layer will notlikely deviate significantly from the mean value. Indeed, Matthews (2006) made57the same assumption when modelling the moisture content of eucalyptus litter ele-ments, which also have a small but finite thickness. This approximation simplifiesthe model considerably by avoiding the calculation of moisture right at the surface.In order to calculate the latent energy flux, Qe (W m−2), from the vapour massflux, E, the lower energy state of the bound water within cellulose material com-pared to liquid water has to be accounted for (Skaar, 1988). Consequently, theenergy required to transition a unit mass of water from its bound state to vapour (inJ kg−1) is the sum of the latent heat of vaporisation, λvap, and the differential heatof sorption, λsorp, so that:Qe = (λvap+λsorp)E (4.18)Sorption processes should become insignificant as the fuel moisture contentapproaches and exceeds the fibre saturation point of 30% and moisture loss is dueto evaporation only. Therefore, λsorp is modelled as an exponentially decayingfunction of fuel moisture content (Nelson, 2000):λs =21000Me−14ms (4.19)The dependence of λvap on temperature (Stull, 1988) is also accounted for:λvap = 2.501×106−2.37×103 (Ta−273.15) (4.20)4.2.6 Conduction and diffusionDiffusion and conduction within the stick are computed using a bulk transport ap-proach, assuming that each layer has a constant temperature and moisture content.Using a radial coordinate system, the flux of heat between the two layers, C (W),is given as:C = 2pi lks (To−Tc)ln( ro,midrc,mid )(4.21)where ro,mid is the mid-point radius of the outer layer, rc,mid is the mid-point radiusof the core, and ks ( J m−1 s−1 K−1) is the bulk conductivity of the stick which is58calculated as an empirical linear function of the stick moisture:ks = g(0.1941+0.004064ms)+0.01864 (4.22)where g is the specific gravity of the stick, equal to 0.42 (Simpson and Tenwolde,1999).The rate of diffusion into the core from the outer layer, D (kg s−1), is computedasD = 2pi ldsρs(mo−mc)ln( ro,midrc,mid )(4.23)where ds, the bulk diffusion coefficient of the stick (m2 s−1), will be determinedthough model calibration. The stick density, ρs, is required to convert the moisturefrom a fractional weight to kg m−3.In actuality, the diffusivity will change with moisture content, and is governedby three different processes: bound water diffusion, vapour diffusion, and capil-lary flow (Nelson, 2000). Using a single constant parameter for controlling internalmoisture transport is therefore a significant simplification. Consequently, ds shouldbe seen as an empirical parameter that describes the rate at which the stick respondsto external forcing. Therefore, during model calibration ds will be allowed to movebeyond the range of diffusivity values reported in the literature. This reduced com-plexity is warranted based on the relatively simple application. Moreover, analysisnot shown here demonstrated that calculating ds as a function of the average stickmoisture did not increase the skill of the model.4.2.7 PrecipitationThe amount of precipitation absorbed by the outer layer, Pabs (kg s−1), is calculatedfrom the incident precipitation rate, Pinc (kg s−1 m−2), and the dimensions of thestick:Pabs = 2r l Pinc (4.24)Here it is assumed that all precipitation intercepted by the stick is absorbed, and59no precipitation is intercepted by the stick ends. The moisture content of the outerlayer is limited to a maximum value, mmax. Any precipitation above this amount isassumed to run off the stick. The value of mmax will be determined through modelcalibration.4.3 Model calibration and evaluationTwo datasets were used to calibrate and evaluate the model. The first dataset wascomposed of observations from the Base Station (BS) and Fuel Moisture 2 site(FM2), which were the two sites with open canopies and a full suite of meteoro-logical and fuel moisture measurements. Each site had one fuel moisture sensor.An analysis of forest canopy impacts on fuel moisture will be left for Chapter 5.Consequently, the closed-canopy Fuel Moisture 1 site was not used in this chapter.Each site had a single fuel moisture sensor. The Rotronic HC-S3 Temperature andRelative Humidity measurements from both the 30.5 cm and 1.62 m heights wereused here. Wind speed was interpolated to 30.5 cm from 1.62 m using a neutrallogarithmic wind profile. The aerodynamic roughness length was set to 0.01 m,which is appropriate for short grass (Oke, 1990). Wind speed was assumed to bethe same across the two sites because FM2 did not have an anemometer. Althoughthe pine dowels used in the automatic fuel moisture sensors are carefully selectedand standardized, it is likely that the two sensors used here would provide slightlydifferent results. With respect to sensor accuracy, the manufacturer reports that theroot mean square error is ± 0.74% for moisture content below 10%, ± 0.90% formoisture between 10% to 20%, ± 1.94% for moisture between 20% and 30% and± 2.27% for values above 30%. To check the consistency between the two sensors,two comparison periods were undertaken on either end of the field season in whichthe two sensors were co-located for a total of 35 days.The second dataset was collected between April 1996 and December 1997 in anagricultural field in Oklahoma and is described in detail by Carlson et al. (2007).This dataset was originally used to evaluate and train the Nelson Model. In thiscase, fuel moisture for the 1-hour, 10-hour, 100-hour, and 1000-hour fuel sizes wasestimated by twice-daily field weighings of ponderosa pine dowels of increasingradii: 0.2, 0.64, 2.0, and 6.4 cm. The 10-hour dowels had a length of 50 cm while60the other three sizes had lengths of 41 cm. The three smaller sizes were weighed tothe closest 0.1 g, while the 1000-hour fuel was weighed to the closest gram. Theabsolute accuracy of these measurements is therefore less than 1% moisture con-tent. For the two smallest fuel sizes standard arrays of four connected dowels wereweighed. An average weight across three separate dowels was used for the twolargest sizes. To minimize the impacts of weathering on moisture measurements,the 1 and 10-hour dowels were replaced every three months while the 100-hourdowels were replaced every six months. The 1000-hour dowels were not replacedduring the two years. Forcing data were taken from a nearby weather station runby Oklahoma Mesonet. Air temperature and humidity were measured at a standardscreen height. Wind speed was measured at 10 m and was also interpolated to 30.5cm.The model was optimized by adjusting five parameters: A, B, Km, mmax, andf . Based on work by Anderson (1990b), potential values ranged from 4.4 to 6.7for A and -22 to -10 for B. Diffusivity values reported in the literature ranged from0.1 ×1010 to 2 ×1010 m2 s−1 (Fosberg, 1970; Deeming et al., 1977; Avramidisand Siau, 1987; Anderson, 1990a; Wadso¨, 1993). This range was used as a startingpoint. However, as previously mentioned, ds was not required to remain withinthis range. The value of mmax was allowed to vary between 30% and 150% andthe value of f varied from 0.05 to 0.90. To find optimal parameter sets, a particle-swarm optimization routine (Clerc, 2010) implemented in R was used ( Default values were used for all settings, except theswarm size was increased from the default of 13 to 32 as this was found to im-prove the stability of the search results.Initial evaluation runs indicated that letting f vary across different stick sizesdid not increase the optimal model skill but significantly reduced the ability of themodel to predict moisture at different sites. A a single value of f was thereforeused across all models. This was done by initially calibrating all models with anadjustable f . A final constant value of 0.22 was then calculated as the average ofall optimal f values. The other four parameters were then optimized using thisconstant f value.The Nash-Sutcliffe efficiency (NSE) was used to determine the skill of eachmodel run. It is a measure of how close the modelled output is to a 1:1 agree-61ment with observations, and accounts for both bias and correlation. The NSE iscomputed as:NSE = 1− ΣNt=1(mtm−mto)2ΣNt=1(mto− ‘)2(4.25)where mtm and mto are the modelled and observed values, respectively, at time t,mo is the mean of the observations, and N is the total number of time steps. NSEranges from negative infinity to 1. A value of 1 indicates perfect agreement, whilea negative value indicates that the average of the observations is more skillful thanthe model output. The optimal parameter set was assumed to be reached when thevalue of NSE did not improve by more than 10−4 over 20 consecutive iterations ofthe particle swarm algorithm.In optimizing the model a priority was placed on accurate simulation of mois-ture values below the fibre saturation point of 30%. This was done for a number ofreasons. Firstly, periods of low moisture are particularly important when estimat-ing wildfire potential. Secondly, the accuracy of electronic fuel moisture sensorsabove the fibre saturation point has not been thoroughly determined, and manualmoisture measurements decrease in reliability at higher moisture levels (Nelson,2000). Therefore, a log transformation was applied to both the observations andmodel output before the NSE was calculated, creating a new NSElog. This met-ric increases the influence of the dry periods and was used by the particle-swarmroutine to find the optimal model.Two approaches were used to test the transferability of the calibrated modelacross time and different sites. First, for each fuel size the model was calibratedusing just the 1997 Oklahoma data and then evaluated using the 1996 Oklahomadata. In the second approach individual models were calibrated at all three sites(the two BC sites and the Oklahoma site) and then evaluated at the other sites.As well, in order to assess the influence of measurement height, predictions weremade at BS using both the near-surface and screen-level temperature and humiditymeasurements.During both calibration and evaluation the model was initialized using the firstobserved moisture value. Consequently, the first portion of the model output is nottruly independent of the observations. However, analysis not shown here indicated62that for all but the 1000-hour fuel the choice of initial value has an negligible impacton the model output because the model quickly comes to equilibrium with theforcing data. For the 1000-hour model the impact of the initial value was felt forthe first 20 days of the simulation. Therefore, the initial 20 days were used asa spin-up period in the 1000-hour simulations and were removed before modelstatistics were calculated.4.3.1 Model sensitivity analysisTo determine the sensitivity of the model to each forcing variable, a series of modelruns were undertaken in which each variable was randomized in turn and then in-put, along with the other, non-randomized, variables into the model. If the modelwas relatively insensitive to a forcing variable, then there should be little differ-ence between the original model output and the output generated when the indi-vidual variable was randomized. Diffuse and direct downwelling shortwave radia-tion, downwelling longwave radiation, relative humidity, air temperature, and windspeed were all randomized. Precipitation was not included in this analysis as thediscrete nature of the variable and its lack of a consistent diurnal trend does notlend itself to a comparison with the other forcing variables.In detail, the time series of the variable to be randomized was divided into days,and those days were randomized across the season. In this way, the randomizedvariable still had realistic diurnal trends and the correlation structure across thevariables was maintained. The sensitivity of the model to each forcing variablewas quantified by calculating the bias and coefficient of determination between therandomized model runs and the original, non-randomized model run.4.4 ResultsBefore evaluating the model, the accuracy of the fuel moisture sensors used at theBC sites were examined. The BC sensors were installed at the same site, both 30.5cm above the ground, for 20 days at the beginning and 15 days at the end of thefield season. A comparison of the observations from these two periods is presentedin Figure 4.3. The root mean square error between the two sensors was larger thanthe accuracy reported by the manufacturer (Section 4.3): 2.56% for moisture levels63below 10%, ± 3.58% for moisture between 10% to 20%, ± 3.55% for moisturebetween 20% and 30% and ± 5.00% for values above 30%. However, at the lowermoisture values the sensors were strongly correlated and much of the error was dueto a consistent bias. As moisture levels increased, the spread increased and the biaschanged sign.02040600 20 40 60FM2 Obs Fuel Mois (%)BS Obs Fuel Mois (%)Figure 4.3: Comparison of co-located fuel moisture observations by the sen-sors used at sites BS and FM2. A 1:1 line is provided as a reference.The optimal parameter values for all site and size combinations are presented inTable 4.1. The diffusivity coefficient, ds, increased with increasing fuel size from2.61 ×10−10 m2 s−1 for the 1-hour model to 3.45 ×10−9 m2 s−1 for the 1000-hour model. The optimal ds values were above the range of values provided in theMethods section. This is not unexpected as a “bulk” approach was used to calculatediffusion in which the two layers are assumed to have constant temperature andmoisture. The maximum allowable moisture content, mmax, was smaller for thelarger fuel sizes. Parameters A and B did not show any apparent relationship tofuel size.Model performance during calibration is summarized in Table 4.2. Althoughthe model was optimized using NSElog, the coefficient of determination, R2, the64Table 4.1: Optimal parameter values for all calibration site/size combinationsCalibration Calibration A B ds mmax fSize (hour) Site (m2 s−1) (%)1 OK 4.00 -12.00 2.61e-10 79.3 0.2210 BS 4.98 -18.80 3.01e-10 76.8 0.2210 FM2 4.70 -22.00 2.92e-10 90.6 0.2210 OK 4.96 -20.10 5.39e-10 66.3 0.22100 OK 5.11 -22.00 5.46e-10 48.6 0.221000 OK 4.81 -18.40 3.45e-09 44.0 0.22root mean square error, and the model bias were also provided. Here the model biasis calculated as the mean difference between the modelled and observed values. Apositive bias indicates that the model was, on average, wetter than the observations.At the Oklahoma site, model skill increased with increasing fuel size, while themodel was more skillful in simulating the BC sites than the Oklahoma site. Themodels had a dry bias across all sites and sizes.Table 4.2: Skill of optimal models applied to calibration data. Comparisonstatistics used are: the Log-transformed Nash-Sutcliffe efficiency, coeffi-cient of determination, root-mean-square error, bias, and bias for all datawith observed moisture below 30%. The units of Bias and RMSE arepercent moisture content.Calibration Calibration NSElog R2 RMSE Bias Bias (<30%)Size (hour) Site (%) (%) (%)1 OK 0.28 0.78 7.50 -0.04 0.5810 BS 0.90 0.92 3.19 -0.38 0.0710 FM2 0.93 0.94 2.86 -0.09 0.2210 OK 0.85 0.85 4.01 -0.30 -0.05100 OK 0.84 0.85 1.86 -0.08 -0.031000 OK 0.87 0.89 1.18 -0.07 -0.07Results of calibrating using the 1997 Oklahoma data and evaluating on the1996 data are presented in Table 4.3. Compared to the optimal results in Table 4.2,the model lost little predictive skill when applied to an independent time period.65Again, model skill generally increased with fuel size. Most of the reduction inskill from the optimal results was seen in the biases. Scatter plots for this modelevaluation are presented in Figure 4.4, while example time series are presentedin Figure 4.5. In particular, high moisture levels for the 1-hour fuel were poorlysimulated.Table 4.3: Model evaluation with independent time period: models are cali-brated on 1997 Oklahoma data and evaluated using 1996 data. The unitsof Bias and RMSE are percent moisture content.Evaluation NSElog R2 RMSE Bias Bias (<30%)Size (Hour) (%) (%) (%)1 0.14 0.72 9.37 0.83 1.9410 0.84 0.90 3.18 0.80 1.01100 0.82 0.84 1.98 0.53 0.581000 0.89 0.90 1.21 -0.44 -0.44A BC D02550751000255075100025507510002550751000 25 50 75 100 0 25 50 75 1000 25 50 75 100 0 25 50 75 100Observed fuel moisture (%)Modelled fuel moisture (%)Figure 4.4: Comparison of modelled and observed fuel moisture at the Ok-lahoma site for 1996. The models used were calibrated for each sizeseparately using the 1997 data. A) 1-hour fuel size, B) 10-hour fuelsize, C) 100-hour fuel size, and D) 1000-hour fuel size.66ABCD030609020406010203010152025Jun Jul Aug SepFuel moisture (%)Fuel moisture (%)Fuel moisture (%)Fuel moisture (%)Figure 4.5: Example time series of modelled fuel moisture (grey lines) gener-ated by 1997 Oklahoma models and observed fuel moisture (black line)at the Oklahoma site during 1996 for the A) 1-hour fuel size, B) 10-hourfuel size, C) 100-hour fuel size, and D) 1000-hour fuel size. Note thevarying y-axis limits.The second evaluation approach found optimal models for the 10-hour fuelsize at all three sites and evaluated those models at the other sites. The models for10-hour sticks, calibrated using the BC data set, were applied to the 10-hour andthe 1-hour Oklahoma data to mirror the methods of Carlson et al. (2007). Theseresults are presented in Table 4.4. As expected, model skill was high between the67two BC sites. Significantly, compared to the calibration results (Table 4.2), theskill of the Oklahoma model was not substantially reduced when applied to the BCsites. Indeed, it achieved higher R2 values when modelling the independent data.This is in contrast to the BC model, which, when applied to the Oklahoma site,produced poorer predictions than during the calibration runs.Table 4.4: Model evaluation with independent sites: models calibrated at onesite are evaluated at the other two sites. All models are trained usingthe 10-hour fuel size. The units of Bias and RMSE are percent moisturecontent.Calibration Evaluation Evaluation NSElog R2 RMSE Bias Bias (<30%)Site Site Size (hour) (%) (%) (%)BS FM2 10 0.75 0.94 3.90 1.96 2.79BS OK 1 0.22 0.77 7.47 0.53 1.67BS OK 10 0.79 0.82 4.49 1.15 1.42FM2 BS 10 0.68 0.90 4.54 -2.48 -2.54FM2 OK 1 0.26 0.76 8.05 -1.83 -1.26FM2 OK 10 0.74 0.79 5.40 -1.16 -1.32OK BS 10 0.80 0.91 4.04 -2.26 -1.76OK FM2 10 0.83 0.93 3.70 0.29 1.15Much of the reduction in skill was due to larger biases. The BS model produceda wet bias at the other two sites, while the Fuel Moisture 2 model produced drybiases when applied to the BS and OK sites. These biases are apparent in Figure4.6, where scatter plots compare modelled moisture to observations. Figure 4.6Bmirrors the results shown in Figure 4.3. That is, compared to the BS sensor, theFuel Moisture 2 sensor had a dry bias for lower moisture and a wet bias duringwetter conditions. Consequently, the Fuel Moisture 2 model had a similar biaswhen predicting at BS: the Fuel Moisture 2 model underpredicted fuel moistureat low moisture values and overpredicted at the highest levels. As was the casefor the cross-time evaluation results (Figure 4.4), model error was highest whensimulating higher moisture values at the Oklahoma site (Figure 4.6D).Figure 4.7 presents sample time series of modelled and observed 10-hour fuelmoisture at BS and Oklahoma sites. The model calibrated at FM2 overpredictedduring precipitation events due to its higher mmax value (see Table 4.1). The drybias of the Oklahoma model is apparent in Figure 4.7C. At the lower moisture lev-68A BC D0204060800204060800204060800204060800 20 40 60 80 0 20 40 60 800 20 40 60 80 0 20 40 60 80Observed fuel moisture (%)Modelled fuel moisture (%)Figure 4.6: Comparison of modelled 10-hour fuel moisture with observationswhen the model is calibrated and evaluated at different sites. A) Cali-brated at BS and evaluated at BS, B) Calibrated at FM2 and evaluatedat BS, C) Calibrated at Oklahoma and evaluated at BS, D) Calibrated atBS and evaluated at Oklahoma.els, this bias is due to larger diurnal cycles and excessive drying during the day,leading to daytime moisture minima that were almost always lower than the obser-vations. The Oklahoma 10-hour model had a higher diffusivity value compared toBS model. Consequently, the model responded more quickly to the diurnal cycleleading to these larger amplitudes in moisture. The opposite is true in Figure 4.7Dwhere the Oklahoma observations were modelled by the BS model.To test the influence of measurement height, humidity and temperature weremeasured at the near-surface (0.305 m above the ground) as well as the screen-level (1.62 m) at BS and the 10-hour Oklahoma model was forced with both. Whenforced with the near-surface observations, the model generated consistently higherfuel moisture than when the screen-level data were used. In particular, diurnal cy-cles were larger and nocturnal maxima were noticeably higher during fair-weatherconditions. Overall, the model output based on near-surface forcing data has apositive 1.1% bias compared to screen-level forced output. This bias is evident in69ABCD020406080020406080020406080020406080Jun Jul Aug SepFuel moisture (%)Fuel moisture (%)Fuel moisture (%)Fuel moisture (%)Figure 4.7: Example time series of observed (black) and modelled (grey) 10-hour fuel moisture when the model is calibrated and evaluated at dif-ferent sites. A) Calibrated at BS and evaluated at BS, B) calibrated atFM2 and evaluated at BS, C) calibrated at Oklahoma and evaluated atBS, D) Calibrated at BS and evaluated at Oklahoma. Note that BS dataare from 2014 while the Oklahoma data are from 1996.the sample time-series presented in Figure 4.8. As well, the near-surface condi-tions were, on average, wetter than at screen level, with a 0.05 kPa bias in absolutehumidity and a 2.9% bias in relative humidity.The results of the model sensitivity analysis are presented in Figure 4.9. Thefuel moisture model is substantially more sensitive to relative humidity than to any70204060Jul 14 Jul 21 Jul 28 Aug 04 Aug 11Fuel moisture (%)Figure 4.8: A comparison of modelled 10-hour fuel moisture generated at BSusing the 10-hour Oklahoma model forced by screen-level observations(grey) and near-surface observations (black).other variable. Air temperature and longwave radiation have a secondary impacton the model output. Significantly, this analysis suggests that diffuse shortwaveradiation and wind speed have very little influence on the model output.Table 4.5 provides a comparison of our model skill, given as R2 values, with theresults of Carlson et al. (2007), who used the same Oklahoma data to evaluate theNelson model. As our model was trained at both BS and FM2, Table 4.5 includestwo different R2 values for the 1-hour and 10-hour fuels. The parameters usedby Carlson et al. (2007) for the 1-hour and 10-hour sizes were identical and hadpreviously been calibrated using a separate dataset. Therefore, their test of the 1-hour and 10-hour model mirrors our evaluation of the 10-hour model calibrated atthe two BC sites using the Oklahoma data. For the Nelson model, the regressionsof simulated against observed values had R2 values of 0.64 and 0.79 for the 1-hourand 10-hour fuel sizes, respectively. When applied to the same data our modelachieved higher R2 values of 0.77 and 0.76 for the 1-hour fuel size. For the 10-hour fuel size our model improved or matched the skill of the Nelson model withR2 values of 0.82 and 0.79. The biases produced by our model are dependent onthe calibration site. The BS model produced a smaller bias for the 1-hour fuel size(0.53% compared to 1.4% reported by Carlson et al. 2007) while the FM2 modelproduced a larger bias of -1.83%. For the 10-hour fuel size, Both BC modelsproduced a larger bias (1.15% and -1.16% compared to 0.1%).Carlson et al. (2007) used the Oklahoma data set for both calibration and eval-71Figure 4.9: Comparison statistics when comparing original fuel moisturemodel output at BS with model output when one of the forcing vari-ables (downwelling diffuse and direct shortwave, downwelling long-wave, relative humidity, air temperature, and windspeed) is randomizedacross days. Mean bias is provided on the left and the coefficient ofdetermination is provided on the right. Results for all four fuel sizes areprovided.uation of their 100-hour and 1000-hour models. In this case it is most appropriateto compare their results to the model skill achieved by our optimized models. TheNelson model achieved R2 values of 0.77 and 0.56 for the 100-hour and 1000-hourfuel sizes, respectively. Our model improves on this, with optimal R2 values of0.85 and 0.89 for the same sizes. Additionally, our optimized models produced bi-ases of -0.08% and -0.07 % for the 100-hour and 1000-hour fuel sizes, respectively.This is also an improvement on the Nelson model biases: 0.6% for the 100-hourmodel and -0.2% for the 1000-hour model.The skill of the new model can also be compared to that of Resco de Dioset al. (2015), who developed a simple model for simulating daily minimum 1-hour72Evaluation R2 Bias (%)Size (hour) Nelson Current Nelson Current1 0.64 0.77, 0.76 1.4 0.53, -1.8310 0.72 0.82, 0.79 0.1 1.15, -1.16100 0.77 0.85 0.6 -0.081000 0.56 0.89 -0.2 -0.07Table 4.5: Comparison of model skill between the Nelson model and themodel presented here when applied to the Carlson dataset. The unit forBias is percent moisture content.and 10-hour fuel moisture content. The authors evaluated their model using obser-vations from a previous version of the Campbell Scientific 10-hour fuel moisturesensor (the CS505). When evaluating their model with an independent dataset theyachieved an R2 value of 0.67 and a bias of 0.73%. Our model improves on theseresults as well, with higher correlations and comparable biases. However, some ofthe sensors used for evaluation by Resco de Dios et al. (2015) were placed on theground, while their calibration sensors were suspended 30.5 cm above the ground.This difference in placement could have led to a reduction in their model skill.4.5 DiscussionThe model presented here improved on the skill achieved by the Nelson modelwhen applied to the same dataset and has additional features that allow for a morerealistic treatment of canopy coverage and changes in sky conditions. Fuel mois-ture simulated by the new model had consistently higher correlations with obser-vations compared to the Nelson model, suggesting that the new model would bebetter at simulating seasonal and diel trends in fuel moisture.This study has demonstrated that when simulating the moisture of standardfuel sticks, more sophisticated treatments of internal moisture transport, precipita-tion interception, and the transfer of moisture to and from the atmosphere do notnecessarily increase the skill of the model. If the model was intended to be appliedto a range of fuel types with varying characteristics, then a more detailed process-based model may indeed be more appropriate. However, the simple characteristicsof the moisture sticks lend themselves to a less complex formulation such as ours,73especially if it can be calibrated to observations.A portion of the model bias seen in the evaluation results can be explained byintrinsic differences between individual sensors or sticks. That is, model skill waslimited by inconsistent observations across sites. The comparison of co-locatedfuel moisture sensors (Figure 4.3) demonstrated that significant biases can existeven between sensors sourced from the same manufacturer. Even though Carlsonet al. (2007) averaged over multiple sticks that were periodically replaced, the typesof sticks used in that study may have exhibited a systematic bias compared to theBC sensors.These results point to the importance of having co-located meteorological ob-servations; small changes in local conditions could reduce the maximum achiev-able model skill. Overall, the BC sites, which had co-located weather observations,yielded better calibration results. When applied to the BC sites, the performance ofthe Oklahoma model was not significantly reduced from the calibration run. Thisfinding suggests that the benefit of having co-located measurements at the BC sitescompensated for the inevitable reduction when the model was applied to the inde-pendent dataset. Indeed, the opposite was not true; the BC models yielded largerreductions in skill when applied to the Oklahoma site.The model had the most difficulty predicting high moisture levels. There are anumber of reasons for this. Firstly, as previously mentioned, the reliability of stan-dardized fuel moisture sticks is reduced during wet conditions. Consequently, thelack of dependable observations could have led to modelling error. Secondly, therate at which the stick loses and gains moisture increases with increasing moisture.Therefore, any error in the modelled response time or differences in conditions be-tween the weather station and the fuel sticks would be magnified at these higherlevels of moisture.These issues become particularly important for the smaller fuel sizes, whichlikely explains why the 1-hour model had the poorest results and high RMSE val-ues: the rapid moisture changes are more difficult to predict, the stick is moreoften at elevated moisture levels, and the lack of co-located weather observationswould be particularly detrimental in this case. However, this reduction in skill athigher moisture levels is less of a concern as it is the simulation of low-moistureconditions that is most important for fire management purposes.74Forcing the model with near-surface observations (0.305 m above the ground)led to a wet bias relative to the screen-level measurements (1.62 m). It was alsoshown that near-surface conditions were consistently wetter than at screen height.This vertical gradient likely explain the biases between the two tests.As previously mentioned, our model is capable of including the impact ofcanopy cover on downwelling longwave radiation. However, because Carlson et al.(2007) only made measurements at open sites, and for the sake of brevity, the im-pact of canopy coverage was not assessed here, even though a closed canopy wouldlikely increase the amount of downwelling radiation substantially and increase noc-turnal stick temperature, especially during clear nights. Based on Equation 4.16,this would lead to increased stick moisture. Yet, it should be mentioned that thesensitivity analysis results suggest that, compared with relative humidity, longwaveradiation has little impact on fuel moisture. The influence of canopy coverage onfuel stick moisture will be examined in Chapter 5.In contrast to the Nelson model, our model requires wind speed as a forcingvariable. However, the sensitivity analysis demonstrated that the model is insensi-tive to winds speeds. This lack of influence was expected, because at lower mois-ture levels the rate at which the stick exhanges moisture with the atmosphere islimited by sorption processes within the stick (that are not influenced by wind),as opposed to turbulent fluxes within the atmosphere (see Section 4.2.5). Conse-quently, using a constant aerodynamic resistance would remove wind speed fromthe list of required forcing variables and may do little to alter model skill, especiallyat lower moisture levels.4.6 ConclusionsThe model developed in this chapter differs from the Nelson model (Nelson, 2000)in a number of ways. It simplifies the treatment of the internal transport of moistureand heat, the capture of precipitation, and the transfer of moisture between the stickand the atmosphere, while its treatment of longwave and shortwave radiation ismore sophisticated: it avoids linearising the net longwave component and allowsfor variations in sky condition and canopy coverage. As well, it does not assumethat the stick acts like a wet bulb, as this assumption does not hold true when the75stick is exposed to direct sunlight. This model can be applied operationally usingstandard weather observations.The model was evaluated to determine its transferability across different timeperiods and different sites. The model lost little skill when applied to an inde-pendent time period. It was also demonstrated that the 10-hour fuel model retainsmuch of its predictive skill when it is calibrated at one site and evaluated at an inde-pendent site. However, in some cases the model did exhibit relatively larger biaseswhen applied to the evaluation dataset. This could partly be due to intrinsic differ-ences in the observation technique: one dataset used manually weighed fuel stickswhile the other used automatic fuel moisture sensors. Our results also suggest thathaving co-located weather observations at the same height as the moisture stickimproves model results. The skill of our model improved on the performance ofthe Nelson model (as presented by Carlson et al. 2007) when predicting the sameset of fuel moisture measurements.In the next chapter the model will be applied to the field observations describedin Chapter 2, along with modelled below-canopy precipitation and radiation, tosimulate fuel moisture and fire danger at all 24 sites. The modelled dataset willthen be used to examine the spatial variability of fuel moisture and fire dangeracross a forested landscape. The model will also be used to examine the influenceof canopy cover on simulated fire danger.76Chapter 5Modelling the spatial variabilityof fuel moisture and fire dangeracross a heterogeneous forestedlandscape5.1 IntroductionA number of studies have examined the influence of terrain on surface conditionsand fuel moisture. Hayes (1941) measured the fuel moisture at open sites on nearbynorth-facing and south-facing slopes. Fuel moisture was always higher on the northslope. Conditions were wetter at lower slope positions where the average differ-ence was 1.9% moisture content. Stambaugh et al. (2007) also found that decidu-ous litter was drier on south-facing slopes under most conditions, but the impact ofaspect was absent during the wettest and driest conditions. Gibos (2010) examinedthe influence of aspect on fine fuel moisture within montane spruce stands. Theabsence of a significant difference between a north and south aspect was attributedto high canopy coverage at both sites, which reduced radiation levels by around90%. Nyman et al. (2015b) reported that fuel moisture was higher on cooler as-pects, although the cooler aspects also had increased canopy cover and understory77vegetation, and thicker organic soils which retained moisture.Sullivan and Matthews (2012) modelled forest floor fuel moisture for differ-ent aspect and slope combinations. Differences in modelled fuel moisture mainlyoccurred during the morning on steep slopes due to lower morning sun angles.Holden and Jolly (2011) used a network of temperature and humidity sensorsacross a region of complex terrain to create high resolution maps of the estimatedfire danger, which is strongly impacted by fuel moisture. There was significantvariability in fire danger and these patterns changed over the fire season. Specif-ically, south facing slopes had drier fuels, due in part to increased radiation. Aswell, the distribution of early season fire danger was bi-modal, reflecting signifi-cantly different drying rates between different facets and elevations.Others have examined the impact of stand structure on fuel moisture. Coun-tryman (1977) demonstrated that within-stand variability in fuel moisture was de-pendent on the integrated amount of direct sunlight experienced by a particularlocation; more radiation led to decreased moisture. Observations by Whiteheadet al. (2006) indicated that lower moisture content was found in thinned standscompared to unthinned stands. However, these differences diminished as the fuelsdried out and were not significant during the driest periods of the season. In a sim-ilar study by Estes et al. (2012), moisture levels were measured for fuel sticks ofvarious sizes placed on the forest floor of thinned and unthinned stands. Overall,the drying impact of a reduced canopy cover was small with the only significantinfluence occurring for large 10,000-hour fuels early in the season. Pook and Gill(1993) found that fine fuel moisture within Pinus radiata stands was most sensitiveto canopy coverage and density during wetter periods. Both Banwell et al. (2013)and Faiella and Bailey (2007) could not identify any significant differences in fuelmoisture across sites with differing canopy cover. A slightly different result wasobtained by Tanskanen et al. (2006) who also observed increased drying rates inopen stands as compared to mature closed stands. However, the differences be-tween sites increased over the season, which the authors attributed to the enhancedlight interception by the canopy with decreasing solar angle.Rothermel et al. (1986) created a model that simulates the impact of bothcanopy cover and aspect on fuel moisture. Their model uses empirical relation-ships between radiation levels, wind speed, and fuel moisture developed by Byram78and Jemison (1943). These relationships were established using a “weather simu-lator” whereby surface fuels were encompassed in a large box in which radiationlevels and wind speeds were controlled by lights and fans. Changing light lev-els were used to simulate the impact of changing radiation loads with aspect andslope. These empirical relationships suggested that radiation load has a significantimpact on fuel moisture. However, their model underestimated moisture levels athigh radiation levels, possibly because the authors did not include the impact ofevaporative cooling or resistance due to sorption processes in their calculations.Rothermel et al. (1986) also developed a canopy shading algorithm that directlycalculated shading cast by the canopy, taking into account canopy height, tree type,aspect and slope. They found that their model was more accurate than the FFMC(see Chapter 1) when predicting fuel moisture in direct sunlight.There are a number of gaps in the literature that will be addressed in this chap-ter. Firstly, when examining the spatial patterns of fuel moisture, most studies usedobservations with approximately a weekly resolution. Some studies made dailymeasurements, but this is still too coarse to resolve diurnal trends. As well, to myknowledge, the relative impact of canopy coverage and aspect on fuel moisture hasnot been examined. As mentioned in Chapter 1, aspect can impact fuel moisturedirectly through changes in radiation, but it also has an indirect effect by affect-ing understory and overstory vegetation cover and soil type. In order to accuratelypredict fuel moisture patterns across the landscape, it will be important to disentan-gle these direct and indirect effects, especially if disturbance history decouples therelationship between radiation load and vegetation. To my knowledge, only oneother study (Nyman et al., 2015a) has attempted to separate the effects of radiationload and canopy cover on fuel moisture. Their results suggested that the impact ofaspect was primarily an indirect effect due to increased vegetation on cooler slopes.This study will examine the spatial patterns and temporal trends of observedand modelled fuel moisture and fire danger across a heterogeneous forested land-scape and address these knowledge gaps. Using hourly resolution data will allowfor an analysis of diurnal trends, nocturnal conditions, and the impact of synopticweather variability on fuel moisture. This chapter will isolate the direct impact ofradiation load on fuel moisture. In this study, the isolation of the direct effect ofradiation load will be accomplished by (1) choosing sites with homogenous un-79derstory vegetation, (2) sampling across the entire parameter space described bycanopy cover and radiation load (see Chapter 3), and (3) focusing on elevated fuelsticks that are not impacted by underlying soil moisture.As a fire moves across a landscape, the speed and intensity of the propagatingfront of the fire is dependent, not just on fuel moisture, by also on wind speed,fuel amount, and the slope of the terrain (Rothermel, 1972). Consequently, spa-tial patterns in fire intensity (the amount of heat released by the fire), and the fireseverity (the resulting impact of the fire) will not be entirely dictated by patterns infuel moisture. For instance, a fire may burn more intensely as it moves up slope,and local wind fields can have a significant impact on patterns as well (McKenzieet al., 2011). However, this chapter will focus on the contribution of fuel moistureto fire danger. To this end, the Energy Release Component (ERC) of the US Na-tional Fire Danger Rating System Cohen and Deeming (1985) will be used here asa metric for potential fire danger. The ERC is strongly dependent on fuel moisture,and does not account for the impact of wind speed or the influence of slope onthe propagating fire. The ERC is related to the total available energy per unit areathat could potentially be released by the fire front and provides an indication ofseasonal wetting and drying cycles.The results from Chapters 3 and 4 suggest a number of possible outcomes forthis chapter. (1) It was shown in Chapter 3 that relative humidity, which is the maindriver of fuel moisture, was relatively homogeneous during the day, regardless ofweather conditions, while the opposite was true at night. One would thereforeexpect similar homogeneous fuel moisture during the day, with elevated variabilityat night. (2) During days without rain, open sites had, on average, higher levels ofrelative humidity, suggesting that open sites may have wetter fuels. (3) It is likelythat conditions will be anomalously wet at the outlying Site 22 where there was anelevated water table throughout the season. (4) Given its strong performance as apredictor of near-surface climate, one would expect that canopy gap fraction willbe a better predictor of patterns in fuel moisture than radiation load. (5) Modelsensitivity analysis in Chapter 4 demonstrated that modelled fuel moisture wasprimarily driven by relative humidity. Longwave and shortwave radiation had amuch smaller secondary influence, suggesting that the impact of the canopy onfuel moisture is primarily an indirect one. That is, changes in canopy cover will80impact near-surface conditions, which, in turn, will impact fuel moisture. Changesin the radiation budget of the stick with a changing canopy will only be a secondarydriver of changes in fuel moisture.This chapter will pursue the following research questions and accompanyinghypotheses:• Research Question #1: How much variability in fuel moisture and fire dangeris seen at the landscape scale and how does that variability change with thetime of day and with weather conditions?– Hypothesis #1a: During the day, fuel moisture and fire danger will behomogeneous. Heterogeneity will increase at night, while Site 22 willbe significantly wetter relative to the other sites.– Hypothesis #1b: During the day, variability will decrease with increas-ing solar radiation. Nocturnal spatial variability will be highest duringdry, clear-sky conditions with low winds.• Research Question #2: How do modelled changes in precipitation and/or ra-diation absorbed by the moisture stick impact fire danger and fuel moisture?– Hypothesis #2a: Changes in radiation amounts absorbed by the mois-ture sticks will have little impact on fire danger.– Hypothesis #2b: Changes in precipitation amounts will have a largeinitial impact, but this influence will recede over the course of arounda week.• Research Question #3: What are the relative impacts of canopy coverage andradiation load on spatial patterns in fuel moisture and fire danger?– Hypothesis #3a: Canopy coverage is the dominant factor influencingfuel moisture and fire danger, and this influence is strongest for noctur-nal conditions.– Hypothesis #3b: Open sites will see wetter fuels relative to closed-canopy sites.81This chapter begins with a description of the methods in Section 5.2, whichincludes an overview of the data analysis (Section 5.2.1), and a description of boththe precipitation and shortwave radiation interception models (Sections 5.2.2 and5.2.3). Results are presented in Section 5.3, followed by a discussion (Section 5.4)and concluding remarks (Section 5.5)5.2 Methods5.2.1 Analysis overviewThe fuel moisture model described in Chapter 4 was forced with meteorologicalobservations described in Chapter 2 to model 1-hour, 10-hour, 100-hour, and 1000-hour fuel moisture at all 24 sites. For the 1-hour, 100-hour, and 1000-hour fuelsizes parameter sets optimized to the Oklahoma dataset (Carlson et al., 2007) wereused. The 10-hour fuel size was modelled using the parameter set optimized to theBase Station (see Chapter 4).The model requires relative humidity, temperature, precipitation, shortwave ra-diation, and wind speed and a sky view factor for each site. Relative humidity andtemperature were measured using the LogTag sensors. The influence of the canopyon precipitation, shortwave radiation, and longwave radiation was also modelled.The precipitation and shortwave components of the canopy model are described inthe next two sections. These models were forced using observations from the BaseStation, which assumes that above-canopy conditions are homogeneous across thesites. As the furthest sites were 1.8 km apart with no significant elevation differ-ences, this estimation should be reasonable. Details of the longwave component ofthe canopy model were provided in Chapter 4. In order to evaluate the full suite ofmodels, below-canopy fuel moisture simulated at the closed-canopy Fuel Moisture1 site was compared to observation.Wind speed was only measured at the Base Station. Although wind speedis reduced within denser canopy (Graefe, 2004), it was shown in Chapter 4 thatthe fuel moisture model is only weakly sensitive to wind speed. Indeed, at lowermoisture levels, wind speed had no discernible impact. Because of this fact, andbecause there were no below-canopy wind observations to evaluate a potential wind82speed model, wind speed was assumed not to spatially vary across sites.Potential fire danger was estimated using the ERC, which is a component of theAmerican National Fire Danger Rating System (Cohen and Deeming, 1985) and isan estimate of the maximum amount of heat that could be potentially released bythe propagating fire front. The ERC is not dependent on slope, wind speed, or fuelamount and is strongly related to the moisture of all four fuel sizes. In the contextof this study the term “potential fire danger” is used synonymously with ERC, andcan be considered as the contribution of fuel moisture to potential fire behaviour,independent of the impacts of weather, fuel amounts, or the impact of slope on firepropagation.The ERC was used by Holden and Jolly (2011) for assessing the heterogeneityof potential fire danger over a large mountainous region. The “G” fuel model wasused to calculate the ERC. This choice, which was also made by Holden and Jolly(2011), was based on maps of fuel models provided by, whichcategorized similar forest types within the states of Washington and Oregon as “G”type fuels. As was mentioned in Chapter 4, a 20 day spin-up period was used whenmodelling 1000-hour fuel moisture to remove any sensitivity to initial conditions.Consequently, modelled ERC presented here begins 20 days after the start of thefield season.To address the first research question regarding spatial variability in fuel mois-ture and potential fire danger, an analysis similar to that of Chapter 3 was used.Daily anomalies from the intersite mean were calculated for daily maximum andminimum modelled fuel moisture (all sizes) and ERC. Daily standard deviationsand maximum ranges were calculated to quantify the spatial variability. Spatialvariability in fuel moisture was also assessed using fuel moisture observations atthe Base Station, Fuel Moisture 1, and Fuel Moisture 2 sites.In order to assess the influence of weather conditions, the daily standard devia-tions were correlated against air temperature, relative humidity, wind speed, short-wave radiation, and Days Since Precipitation. The weather variables were thencombined in a multiple regression to create an optimal model of ERC variability.Analysis of Variance was used to determine whether the inclusion of additionalvariables improved the model. In order to isolate the impact of these weather vari-ables, only days without precipitation were used, as the impact of rain dominates83variability during wet days. As well, the outlier Site 22 was removed from thisanalysis.To address the second research question, precipitation interception, shortwaveradiation interception, and the impact of the canopy on longwave radiation wereremoved from the canopy model one at a time before modelling fuel moisture. Afourth simulation removed all three components from the model. These resultingfuel moisture time series were then compared to the original simulation to deter-mine the relative influence of each component. This analysis was performed usingSite 4, which had one of the densest canopies. It is important to note here that thesame relative humidity and temperature observations were used as inputs into themodel. These observed near-surface conditions were, of course, influenced by thecanopy as well. Therefore, this analysis separates the direct impact that the canopyhas on the fuel moisture stick through changing the incident precipitation and netradiation at its surface, from the indirect impact of the canopy through its influenceon near-surface conditions.The third research question was addressed using a similar analysis to that usedin Chapter 3. Longer term averages of fuel moisture and ERC anomalies werecalculated over the entire field season for days with and without rain, and for eachmonth. Optimal linear regression models were then developed using canopy gapfraction, radiation load, and their interaction as possible predictors of these averageanomalies (see Chapter 3 for further details).The influence of canopy gap fraction and radiation load was also explored usinga Principal Component Analysis (PCA). PCA was applied to the 24 column matrixcomposed of the ERC time-series from all sites, resulting in 24-element componentloading vectors for 24 principal components (PC). Sites with similar componentloading values were assumed to have similarly varying ERC time-series. The com-ponent loading values of the four leading PCs were then regressed against canopygap fraction and radiation load to determine if either of those variables were ableto isolate similarly varying sites.845.2.2 Precipitation interception modelBelow-canopy precipitation was modelled using a simplified sparse-canopy Ruttermodel based on the approach of Valente et al. (1997). This model uses a “water-bucket” approach wherein canopy storage is the net result of incident precipitationminus evaporation from the canopy, drainage to the stems, and drainage directly tothe forest floor. The canopy is modelled as a water-bucket with a maximum storagecapacity. Any additional precipitation above this capacity drains out of the canopy.Above-canopy incident precipitation was assumed to equal the amount measuredat the Base Station. Here precipitation is assumed to fall vertically.Figure 5.1 provides a schematic of the model. Before any interception occurs,a certain amount of the incident precipitation, Pg, falls directly to the forest floorthrough gaps in the canopy. Once the incident precipitation has entered the canopy,evaporation from the canopy, Ec is calculated as:Ec ={(1− ε)E CcSc : Cc < Sc(1− ε)E : Cc ≥ Scwhere E (mm) is the potential evaporation, Cc (mm) is the current amount ofcanopy storage per unit area of covered area, ε is the fraction of total forest standevaporation that occurs from the trunk and stems, and Sc (mm) is the canopy stor-age capacity per unit of covered area, which is calculated as Sc = S/c, where S isthe canopy storage capacity (in mm) and c is the canopy cover fraction. Both S andε are adjustable model parameters.85Figure 5.1: Schematic of the rutter precipitation interception model. Adaptedfrom Valente et al. (1997)The portion of canopy drainage, Dc (mm), that is diverted to stemflow is deter-mined by the stemflow fraction parameter, pd , which is also an adjustable modelparameter. The final precipitation rate at the forest floor, Pf (mm), is the averageof the free throughfall and the canopy drip throughfall, Di,c (mm), weighted by thecanopy cover fraction:86Pf = (1− c)Pg+ cDi,c (5.1)The canopy cover fraction, c, was estimated at each site using hemisphericalphoto analysis described in section 5.2.3. For this application, the canopy coveragewas estimated using a minimum angle above the horizon of 85 degrees. That is,it was assumed that only the canopy directly above the gauge contributed to theprecipitation at a specific point.Following Carlyle-Moses and Gash (2011), potential evaporation from the canopy,E, which assumes a saturated canopy, is modelled using a Dalton-type equation:E =ρacpλγ ra[e∗s − ea] (5.2)where ρa (1.225 kg m−3) is the density of air (which is assumed to be constant), cp(1.00467× 10−3 MJ kg−1 K−1) is the specific heat of air, λ (2.45 MJ kg−1) is thelatent heat of vaporisation, γ ( 0.0665 kPa K−1) is the psychrometric constant, ra (sm−1) is the aerodynamic resistance, e∗s is the saturation vapour pressure (kPa), ea isthe ambient vapour pressure (kPa), and e∗s − ea is the vapour pressure deficit (kPa)between the saturated canopy and the ambient air. In lieu of direct measurementsabove the canopy, screen height measurements from the Base Station were used asa replacement for above-canopy conditions.Aerodynamic resistance is calculated following Rutter et al. (1975):ra =1k2 u(lnz−dzo)2(5.3)where k (0.4) is the von Ka´rma´n constant, u (m s−1) is the windspeed at height z(m), which is 2 m above the canopy, d is the displacement height, which is taken tobe 75% of the canopy height, and zo is the aerodynamic roughness length, whichis taken to be 10% of the canopy height. Canopy height at each site was estimatedusing the Vegetation Resource Inventory database ( The average canopy height of 20 m was used in all cases.The screen-height wind speed measured at the Base Station, uscreen, was inter-polated to the above-canopy height, z, using the approach of Rutter et al. (1975):87u = ln(z−dzo)(0.818+ ln(a+4.75))−1uscreen (5.4)where a is the anemometer height (1.62 m).There are three adjustable parameters in this model: the maximum canopystorage capacity, S, the proportion of canopy drainage diverted to stemflow, pd ,and the proportion of total stand evaporation that comes from stems and trunks,ε . Average values for S (1.54 mm), pd (0.05), and ε (0.02) were calculated fromvalues reported by the literature for forest types similar to the study site (Rutteret al., 1975; Whitehead and Kelliher, 1991; Loustau et al., 1992; Klaassen et al.,1998; Spittlehouse, 1998; Iroume and Huber, 2002; Link et al., 2004; Pypker et al.,2005) and used here. Parameter calibration was not attempted as there was onlyone site with below-canopy precipitation measurements and therefore not enoughdata to perform accurate model calibration.Modelled precipitation was compared to observations at Fuel Moisture 2, Site8, Site 1, and Fuel Moisture 3. The first three sites were assumed to be openlocations as there was no canopy coverage for altitudes of 85◦ above the horizontalat these rain gauges. Consequently, the model assumed that there was no canopyinterception, and these sites therefore tested the assumptions that above-canopyprecipitation was homogeneous across all sites and that precipitation at a givenpoint on the forest floor is determined only by the amount of canopy directly above.The rain gauge at Fuel Moisture 1 was below the canopy and was used to evaluatethe interception model.Because only one closed-canopy site was used, the skill with which the modelpredicts spatial patterns in below-canopy precipitation cannot be tested here. How-ever, the sparse-canopy Rutter model is a widely accepted approach and the param-eters values used are based on optimal values taken from the literature. Moreover,as will be seen in the results, fuel moisture is relatively insensitive to precipitationamounts, especially during dry periods.885.2.3 Shortwave radiation interception modelThe canopy interception of shortwave radiation was modelled by combining thehemispherical photos described in Chapter 2 with solar geometry calculations fol-lowing the technique of Moore et al. (2005). As a first step, above canopy radiationis assumed to equal measured radiation at the Base Station and is divided into itsdirect, (Kdir) and diffuse (Kdi f f ) components using the procedure detailed in Ap-pendix B. To generate gap fraction as a function of zenith angle, θ , and azimuth,ψ , each hemispherical photo was converted to grayscale and a brightness thresholdwas chosen to demarcate pixels of open sky from pixels of canopy. The image wasthen divided into 5◦ by 5◦ segments, which were each assigned a gap fraction fromthe proportion of open sky pixels to total pixels. Figure 5.2 provides examples ofboth original and processed hemispherical photos.Time series of the solar zenith and azimuth angle were calculated using theequations of Iqbal (1983). At each time step this information was used to place thesun within a particular 5◦ by 5◦ segment of the hemispherical photo. The above-canopy direct radiation was then reduced by that segment’s gap fraction to generatea time series of below-canopy direct radiation, Kbc,dir(t).Below-canopy diffuse radiation was modelled using a sky-view factor calcu-lated by integrating f (θ ,ψ) over the the half sphere:fv =1pi∫ 2pi0∫ 2pi0f (θ ,ψ)cosθ sinθ dθ dψ (5.5)This integral was estimated numerically using the 5◦ resolution gap fraction.The total below-canopy downwelling shortwave radiation was calculated as:Kbc(t) = Kbc,dir(t)+ fv Kdi f f (t) (5.6)where Kbc(t) is the time series of total below-canopy solar radiation at the forestfloor.The model was evaluated by comparing modelled Kbc at Fuel Moisture 1 and 2to the measured below-canopy shortwave radiation at those two sites. Daily valueswere used for the evaluation. This choice of resolution was made for a numberof reasons. Firstly, hourly values of modelled shortwave radiation are impacted by89Figure 5.2: Hemispherical photos overlayed with radial grids with a 5 de-gree resolution (top row), and thresholded hemispherical photos (bot-tom row). Examples provided are from Sites 15 (left column) and 23(right column).90the location of individual sun flecks and are therefore sensitive to the exact positionthat the hemispherical photo was taken. In this case, the hemispherical photos weretaken directly above the Logtag sensors rather than the pyranometers. Therefore,at the hourly scale, there was a significant amount of model error. However, thismodel error was reduced at the daily time scale. Secondly, given the slow responsetime of fuel moisture, it is less important to model hourly variations in radiationthan it is to simulate daily and seasonal variability.The one adjustable parameter in the model is the brightness threshold usedto demarcate open sky pixels from canopy pixels. The modelled radiation wasfound to be sensitive to this threshold. Therefore, for the two evaluation sites, thebrightness threshold was adjusted to obtain the lowest model bias, following theprocedure of Leach and Moore (2010).5.3 Results5.3.1 Model evaluationBelow-canopy precipitation modelModelled below-canopy precipitation was compared to observations at Fuel Mois-ture 1, Fuel Moisture 2, Site 8, and Site 1. Model skill statistics are presentedin Table 5.1. Scatter plots of modelled versus observed precipitation are shown inFigure 5.3. Both Fuel Moisture 2 and Site 1, which had gauges below open canopy,showed low model biases with RMSE values less than 1 mm, supporting the as-sumption that precipitation was relatively uniform across the study area. However,the other open site, Site 8, had a large negative model bias. It is not likely that thiserror was due to an intrinsic bias of the rain gauges, as they were calibrated in thelab. It is also unlikely that the bias was due to a spatial gradient in rainfall intensity,as Site 8 was located within 250 m of Fuel Moisture 2, which did not experience thesame bias. It is possible that there was wind-induced undercatch of precipitationat the Base Station (Mekonnen et al., 2015), which was more exposed than Site8 and consequently likely experienced higher wind speeds. At Fuel Moisture 1,which had a canopy coverage of 57% directly above the rain gauge, the simulated91precipitation had a bias of 0.04 and an RMSE of 0.6 mm. This model accuracy iscomparable to the open sites Fuel Moisture 2 and Site 1.Table 5.1: Precipitation interception model statistics: Coefficient of determi-nation, model bias and root mean square error.Site R2 Bias RMSE(mm) (mm)Fuel Moisture 1 0.93 -0.04 0.60Fuel Moisture 2 0.94 -0.01 0.66Site 1 0.99 0.01 0.34Site 8 0.91 -0.36 1.12Shortwave interception modelThe optimal brightness threshold that minimized the error in modelled below canopyshortwave radiation at Fuel Moisture 1 was 210. For Fuel Moisture 2, model biasdecreased as the brightness threshold increased. However, once the brightnessthreshold was increased beyond 141, portions of the open sky began to be incor-rectly masked out as “canopy.” Therefore, 141 was used as the optimal brightnessthreshold for Fuel Moisture 2. For all other sites, 210 was used as the optimalbrightness threshold unless the same incorrect masking of the open sky occurred.If this erroneous masking did occur, the optimal threshold was taken to be thehighest possible value before the masking of open sky occurred.Modelled below-canopy shortwave radiation was compared to observations atFuel Moisture 1 and Fuel Moisture 2. Model skill statistics are presented in Table5.2. Time series and scatter plots of modelled and observed shortwave radiationare shown in Figures 5.4 and 5.5, respectively. The model accuracy was high forFuel Moisture 2. The bias was -3.4 Wm−2, or 2% of the seasonal average, whilethe RMSE was 9.9 Wm−2. Model bias at Fuel Moisture 2 became more negative asthe season progressed. Figure 5.5 demonstrates that, as previously discussed, themodel did a substantially better job at simulating daily data than hourly data. Thelarger scatter of hourly observations is likely due to the fact that the hemisphericalphotos were taken above the LogTag sensors, and not the pyranometer. The twolocations would have experienced slightly different insolation at short time scales92Figure 5.3: Scatter plots of daily modelled and observed precipitation. Re-gression lines are provided (Black Lines), and 1:1 lines are provided forreference (grey lines).as sun flecks moved across the forest floor. The model was less accurate for FuelMoisture 1. However, the model bias of -7.0 Wm−2, was still only 9% of theseasonal average.Table 5.2: Shortwave interception model statistics: Coefficient of determina-tion, model bias and root mean square error.Site R2 Bias RMSE(Wm−2) (Wm−2)Fuel Moisture 1 0.86 -7.03 12.87Fuel Moisture 2 0.99 -3.44 9.8893Figure 5.4: Time series of modelled and observed daily shortwave radiationat Fuel Moisture 1 and Fuel Moisture 2.Combined model of below-canopy fuel moistureA two-month sample of modelled and observed fuel moisture at Fuel Moisture 1 ispresented in Figure 5.6, while a scatter plot of the entire season’s data is providedin Figure 5.7. Overall, the model accurately simulated the seasonal pattern of fuelmoisture. Model accuracy improved with decreasing moisture content. The modelhad a bias of -1.4%, an RMSE of 4.3% and an R2 of 0.88. For moisture below30% the bias and RMSE decreased to -0.5% and 2.1%, respectively, while the R2decreased to 0.85. Much of the error during the drier periods was due to largersimulated diurnal cycles, particularly during early August.94Figure 5.5: Scatter plots of modelled and observed hourly and daily short-wave radiation at Fuel Moisture 1 and Fuel Moisture 2. A 1:1 line isincluded for reference (dashed line).5.3.2 Spatial variability of fuel moisture and fire dangerObserved 10-hour fuel moisture from the Base Station, Fuel Moisture 1, and FuelMoisture 2 is presented in Figure 5.8 as hourly (5.8A), daily maximum (5.8B),and daily minimum values (5.8C). Overall, the three stations maintained similarmoisture levels throughout the season, particularly during the day when conditionswere dry. However, Fuel Moisture 1 had a dry nocturnal bias and smaller diurnalvariability during dry conditions. Consequently, the fuel sticks were, on average,wetter at the the open sites.A sample of hourly modelled 1-hour fuel moisture, 1000-hour fuel moisture,and ERC is presented in Figure 5.9. The same sites highlighted in Chapter 3 arealso highlighted here: the south-facing open canopy Fuel Moisture 2 site, the north-facing closed-canopy Site 4, and the anomalously wet Site 22. Similar to observedfuel moisture, all 24 sites had similar seasonal trends in modelled fuel moistureas well as ERC, and nocturnal differences were larger than during the day. Theopen canopy south-facing Fuel Moisture 2 site exhibited wetter fuels and lower95ERC at night than the closed-canopy Site 4. As the sites dried out during theday, the 1-hour fuel moisture responded quickly and became drier at the open siteduring the day, while the more slowly varying 1000-hour remained consistentlywetter at the open site; the nocturnal cooling overwhelmed the daytime heatingfor the larger fuel size. Although not shown here, daytime 10-hour and 100-hourfuel moisture were also higher at open sites. Consequently, daytime ERC wasoften similar between the open and closed sites. Finally, the moist Site 22 had aconsistently low ERC, particularly during the day. Site 22 and Fuel Moisture 2experienced similar nocturnal conditions, despite the large differences in canopycover.Spatial heterogeneity across stations is explored in more detail in Table 5.3.Fuel moisture and ERC were consistently more homogeneous during the day thanat night, and larger fuels were less variable than smaller fuels. Precipitation in-creased variability, particularly for the smaller fuels.Table 5.3: Daily standard deviation (SD) and maximum range (Range) ofdaily minimum and maximum 1-hour fuel moisture (1-hmin and 1-hmax),1000-hour fuel moisture (1000-hmin and 1000-hmax), and ERC (ERCminand ERCmax) averaged across each month and across all days with andwithout rain.ERCmax ERCmin 1-hmax 1-hmin 1000-hmax 1000-hmin(%) (%) (%) (%)Period Range SD Range SD Range SD Range SD Range SD Range SDMay 21.4 5.4 5.8 1.6June 9.4 2.1 18.0 4.5 17.0 4.4 2.3 0.6 2.0 0.5 1.6 0.4July 11.8 2.6 15.5 4.0 10.8 2.7 3.8 0.9 1.9 0.5 1.7 0.4Aug. 12.9 2.6 18.1 4.8 19.7 5.0 3.5 0.8 2.1 0.5 2.0 0.4Sept. 14.9 3.6 20.1 5.1 21.9 5.0 5.7 1.3 2.6 0.7 2.3 0.6Dry Days 11.9 2.6 17.9 4.6 14.2 3.6 2.8 0.7 2.0 0.5 1.9 0.4Rain Days 12.5 2.8 17.3 4.5 24.4 6.0 6.3 1.5 2.3 0.7 1.9 0.496Figure 5.6: Two months of modelled and observed fuel moisture for the FuelMoisture 1 site using the precipitation and radiation canopy interceptionmodels and the fuel moisture model.97Figure 5.7: Scatter plot of modelled and observed fuel moisture for the FuelMoisture 1 site using the precipitation and radiation canopy interceptionmodels. Data from the entire season are used here. A 1:1 line has beenadded for reference (black line).Afternoon and early morning ERC time-series are shown in Figure 5.10 and arecompared to the ERC climatology for Sparks Lake, which was located at a standardopen site. The reduced variability in daytime ERC is evident here. Daytime fuelmoisture at Site 22 decreased at a slower rate than the other sites. During the driestperiods, the nocturnal spread across sites was comparable to the difference betweenthe median and 95th percentile modelled at the open Sparks Lake site. Again, apartfrom Site 22, there is less spread in daytime ERC.Daily standard deviations of minimum and maximum ERC are plotted againstweather variables in Figure 5.11. Changes in the spatial variability of daytime po-tential fire danger were correlated only with wind speed at the 95% confidencelevel; higher wind speeds led to a more homogeneous landscape. Nocturnal firedanger variability was most strongly correlated with wind speed and relative hu-midity. At night the landscape was more homogeneous during days with high rel-ative humidity and low wind speed. Temperature, shortwave radiation, and DaysSince Rain were all negatively related to nocturnal ERC variability, although these98correlations are weak. Modelling the standard deviation of nocturnal ERC withmaximum relative humidity and wind speed resulted in an R2 value of 0.46. Theaddition of the remaining variables did not improve model performance at the 95%confidence level.5.3.3 Influence of canopy cover on below-canopy fuel moistureThe impact of removing components of the canopy model on fuel moisture is pre-sented in Figure 5.12. When the canopy did not absorb or emit longwave radiation,fuel moisture increased. In contrast, removing shortwave canopy interception ledto dry biases. As would be expected, removing precipitation interception led to wetbiases. Overall, the largest biases occurred during and immediately after rain, par-ticularly for the smaller fuel sizes. For the 1-hour fuels, these biases disappearedalmost immediately after rain, but the 1000-hour fuel remained anomalously wetfor at least ten days following rain. When the canopy was removed entirely, theinfluence of the increased shortwave radiation was generally larger than both thedecreased longwave and increased precipitation, leading to a dry bias overall. Anexception was during periods of rain or low amounts of shortwave radiation.The impact of canopy removal on ERC is presented in Figure 5.13. The re-moval of shortwave interception from the model increased the ERC by 7.0 on av-erage, which is a mean relative bias of 13.1%. During periods of high ERC thebias decreased to around 5. Removing the canopy impact on longwave radiationdecreased ERC on average by -4.0 (-7.4%). Removing precipitation interceptiondecreased the ERC on average by -2.0 (-3.6%). The decrease in ERC due to in-creased precipitation was only comparable to the radiation terms during and imme-diately following periods of rain. When the influence of the canopy was removedentirely, the ERC bias was almost always positive with an average ERC bias of 1.9(3.5%). The one exception was during a period of persistent rain in late Augustand early September.995.3.4 Modelling spatial patterns in fuel moisture and potential firedanger with canopy cover and radiation loadThe results of the model selection procedure are provided in Table 5.4. Canopygap fraction was almost always the best single predictor and the addition of radi-ation load as a second predictor only improved the model (at the 95% confidencelevel) for daytime 1-hour fuel moisture. Daytime ERC and 1000-hour fuel mois-ture were not significantly related to either canopy gap or radiation load. Overall,the strongest models were for daytime and nocturnal 1-hour fuel moisture. Noctur-nal ERC was also relatively well predicted. Spatial patterns were generally poorlypredicted during periods of rain.Conditions were wetter at more open sites during the night. Daytime 1-hourfuel moisture was lower at open sites, while canopy gap did not impact daytime1000-hour fuel moisture. Although not shown in Table 5.4, both 10-hour and 100-hour fuel moisture had weak positive relationships with canopy gap during the day,suggesting that only the smallest fuel size dried quickly enough to recover fromthe wetter nocturnal conditions. Daytime 1-hour fuel moisture was also lower onsouth-facing slopes. This relationship was particularly strong at the end of the fireseason in September. Daily mean fuel moisture was generally higher and ERClower at open sites.The first PC of the ERC time series reflected the average seasonal trend in ERC.Canopy gap fraction was weakly correlated with the loading values of the first PC(R2 = 0.31). Loading values of the second PC were strongly correlated with canopygap fraction with an R2 = 0.84 (Figure 5.14). Radiation load was weakly correlatedwith the second PC (R2 = 0.31), but did not improve predictive skill (at the 95%confidence level) when added as a second predictor along with canopy gap fraction.The two predictors were not significant predictors of any of the higher PCs.Apart from the outlier Site 22, the sites with the three lowest and three highestPC2 loading values also had the highest and lowest canopy gap fraction. Thesesix sites are highlighted in Figure 5.15, in which two months of ERC data arepresented. The closed-canopy sites (high PC2) saw smaller changes in ERC overthe day compared to the open canopy sites (low PC2).1005.4 DiscussionOverall, daytime fuel moisture and potential fire danger exhibited low spatial vari-ability, regardless of weather conditions, and daytime ERC was not related to eitherradiation load or canopy cover. Fuel moisture and fire danger were more variableat night and that variability increased during cool, moist periods with low windspeeds. Patterns in fuel moisture and fire danger were dominated by differences innocturnal longwave cooling due to changes in canopy cover. Consequently, opensites had lower daily minimum and daily mean fire danger, and radiation load didnot have a significant impact on ERC.As mentioned in the introduction of this chapter, the ERC, which is used hereas a metric for fire danger, does not include the impact of slope, wind speed, orfuel amounts on fire behaviour. Rather, the ERC represents the seasonal cycle offire danger due to the drying and wetting of fuels. Consequently, patterns in thefire behaviour and resulting fire effects of an individual fire will also be dictatedby variability of the wind field, and patterns in fuel amounts. For instance, windspeeds are generally lower below dense canopy (Oke, 1990), which may counter-act the elevated ERC found under denser stands. As well, even though ERC wasnot related to aspect, warmer, south facing aspects may experience increased up-slope flows and more intense fire behaviour. Landscape patterns in fuel type andamount are also impacted by stand density, slope, and aspect, and can also impactpatterns in fire behaviour (McKenzie et al., 2011). However, fuel moisture is animportant driver of fire behaviour (Rothermel, 1972), and the patterns in ERC thathave been presented here will likely play an important role in determining both thebehaviour of an individual fire, as well as the pattern of long-term fire potential orburn likelihood.5.4.1 Spatial variability of fuel moisture and potential fire dangerNocturnal variability was higher than daytime variability, consistent with Hypoth-esis #1a. Excluding Site 22, variability in daytime conditions was small relativeto the interannual variability recorded at the Sparks Lake fire weather station (seeFigure 5.9). These results suggest that, apart from areas with an additional sourceof moisture due to a higher water table (such as Site 22), the study landscape dries101out during the day at a similar rate following rain, regardless of canopy cover oraspect.During dry periods, open canopy sites had moist nocturnal conditions similarto median conditions modelled at Sparks Lake, while nocturnal conditions at thedry closed canopy sites were comparable to the station’s most extreme years (seeFigure 5.10). The average difference in ERC between the driest and wettest siteranged from 15 to 20, depending on the time of year. This range can be comparedto the results of Holden and Jolly (2011) who modelled daily ERC over a largermountainous region (>400 km2) with an elevational range of over 1400 m. Intheir study, the range of ERC across the study region was comparable to what wasfound here. Therefore, the current study demonstrates that, at the landscape scale,variability in nocturnal fire danger can be significant for areas with a mosaic ofcanopy cover.Hypothesis #1a also correctly predicted the wet conditions exhibited by Site22. These results suggest that locations with a supply of subsurface moisture willhave a relatively cool, wet near-surface climate that, in turn, will lead to reducedpotential fire danger relative to surrounding areas. Previous work supports thisconclusion. Duff moisture is generally higher at the bottom of hillslopes (Samranet al., 1995; Keith et al., 2010b; Vo, 2001), and Camp et al. (1997) found thatfire refugia were most likely to occur in regions with a large contributing upslopearea, such as regions of confluence, over perched water tables, and within valleybottoms.Overall, variability in modelled daytime ERC was not strongly related to weathervariables (Figure 5.11). This is not unexpected, as the spatial variability across sitesduring the day is low (see Table 5.3. Wind speed was the one variable with a sig-nificant but weak impact on the spatial variability of ERC: variability was lower onwindier days. Based on the results of Chapter 3, Hypothesis #1b incorrectly pre-dicted that increased solar radiation would lead to increased daytime ERC variabil-ity. However, it is possible that increased modelling accuracy would have revealedsuch a relationship.The low variability in daytime fuel moisture and ERC reiterates what wasfound in previous studies (e.g., Chrosciewicz 1989; Whitehead et al. 2006; Faiellaand Bailey 2007; Estes et al. 2012; Banwell et al. 2013). These studies also sug-102gested that daytime variability is higher during moist conditions and following rain.In contrast, the results of the current study suggest that, during the day, the spatialvariability of ERC is relatively insensitive to weather conditions.Hypothesis #1b predicted that, as was found for relative humidity and temper-ature in Chapter 3, ERC would also become less variable during cool and moistconditions. However, these results found the opposite: nocturnal ERC variabilityis highest during cool, moist conditions. Unlike near-surface climate, the amountof below-canopy precipitation directly impacts fuel moisture and ERC. From Fig-ure 5.13 it is clear that the impact of precipitation on ERC persists for around aweek. Therefore, it is likely that variations in canopy interception across sites ledto higher nocturnal variability in ERC. Indeed, when precipitation interception wasremoved from the model, relative humidity lost much of its impact on nocturnalERC variability and the negative relationship with Days Since Rain disappearedcompletely.Increased wind speed reduces nocturnal variability in ERC. It is likely that thisrelationship was not due to the direct impact of wind speed on the fuel stick, asChapter 4 demonstrated that this impact was small. Rather, wind speed primar-ily influences fuel moisture and ERC indirectly though its impact on near-surfaceconditions. Indeed, nocturnal relative humidity was also more homogeneous dur-ing days with high wind speeds (see Chapter 3).5.4.2 Influence of canopy cover on below-canopy fuel moistureSetting the canopy to be transparent to longwave radiation decreased the energyabsorbed by the stick. When the stick was saturated immediately following rain,this reduction in net radiation reduced the amount of energy available for evapora-tion, leading to wet fuels. When the stick was below the fibre saturation point andsorption processes dominated, the decreased longwave radiation led to lower sticktemperatures, which, in turn, led to higher equilibrium moisture content and highermoisture overall (see Figure 5.12). The opposite was true for shortwave radiation;removing shortwave interception led to a dry bias relative to the full model. It isclear from Figure 5.12 that biases due to changes in radiation interception weremuch larger during wet periods following precipitation. Resistance to moisture re-103moval increases as the stick dries out. Consequently, changes in the energy budgethave the most impact on fuel moisture during wetter periods.Removing shortwave radiation interception by the canopy led to an averageERC bias of 7.0, which is comparable to, or larger than, the average spatial anoma-lies reported in Table 5.3. Therefore, in contrast to what was predicted in Hypothe-sis #2, the impact of changing a stick’s radiation budget is not negligible. However,it is still of secondary importance compared to the impact of near-surface relativehumidity (See Chapter 4).It was hypothesized that precipitation would have a large impact during rainevents, but that this impact would recede over the course of a week after rainceased. It was indeed the case that the wet bias due to increased precipitationwas largest during rain events and that this bias decreased over the course of aweek. However, in most cases increased precipitation had a smaller impact thanchanges to the radiation components, and the ERC was lowered by less than 5units, or on the order of a few percentage points of relative change. The impact ofchanging below-canopy precipitation was largest during a period of moderate butpersistent rain in late July and early August, suggesting that the duration of a rainevent is more important than rain amount. This is because persistent low-intensityprecipitation will readily be intercepted and evaporated from the canopy.The simulated removal of the dense canopy from Site 4 increased daily precip-itation by, on average, 1.0 mm, which, in turn, decreased the average ERC at thesite by 3.6% but had little impact on ERC during dry periods. The average error forthe precipitation interception model was less than 0.66 mm (Table 5.1). Therefore,the accuracy of the model was high enough for the purpose of simulating potentialfire danger, especially during extended dry periods. The same reasoning extendsto the shortwave interception model. Removing the canopy from Site 4 increasedthe average shortwave radiation by 180 W m−2, leading to an ERC bias of 13%.The much smaller errors of the interception model (Table 5.2) would therefore re-sult in only minor errors in ERC. Based on these comparisons, it is likely that thecomplexity of both interception models could be reduced without diminishing theaccuracy of modelled potential fire danger, especially during dry conditions, and ifobservations of near-surface humidity and temperature are available.1045.4.3 Modelling spatial patterns in fuel moisture and potential firedanger with canopy cover and radiation loadBased on the results from Chapter 3, it was predicted in Hypothesis #3a that canopycover would be the dominant factor in determining spatial patterns in fuel moistureand potential fire danger. This hypothesis has been confirmed here. Apart from 1-hour fuel moisture, canopy gap fraction was the best single predictor, and radiationload did not improve the models when added as a second predictor. The dominantimpact of canopy cover was reiterated by the PCA. Canopy cover is the most im-portant determinant of diurnal variability in ERC. These results demonstrate thatthe direct impact of aspect on fuel moisture through changes in radiation load islikely secondary to the indirect impact of increased canopy cover. This conclusionwas also reached by Nyman et al. (2015a), who found that the impact of aspect wasprimarily an indirect effect due to increased vegetation on cooler slopes.It was also hypothesized that predictive skill would be larger during the night.This prediction was true for the 1000-hour fuel moisture and ERC, neither of whichwere related to either factors during the day. However, the daytime and nocturnal1-hour fuel moisture models were equally skillful.Only the 1-hour fuel size was drier at open sites and south-facing slopes duringthe day. In fact, daytime 10-hour and 100-hour fuel moisture was higher at opensites. Consequently, as predicted in Hypothesis #3b, open sites had, on average,higher modelled fuel moisture and lower potential fire danger, although the rela-tionships were weak with relatively low R2 values. Observed 10-hour fuel moisturewas also wetter at open sites.There are a number of possible reasons why ERC was lower at open sites.Firstly, an examination of Figure 5.9 suggests that, because of their longer responsetimes, the larger fuel sizes were not able to dry out quickly enough at open sitesto reverse the nocturnal pattern when fuels were wetter at open sites. In contrast,1-hour fuel moisture responded quickly enough so that it mirrored the daytime rel-ative humidity patterns seen in Chapter 3, with drier conditions at open sites andsouth-facing slopes. Secondly, Chapter 3 demonstrated that canopy gap fractionhad a much larger impact on relative humidity patterns at night, and that daily meanabsolute humidity was also higher at open sites. Thirdly, Figure 5.12 demonstratedthat 100-hour and 1000-hour fuel moisture were elevated for a few days follow-105ing rain. Consequently, precipitation patterns may have counteracted patterns indaytime solar radiation and enhanced patterns in nocturnal cooling for these largerfuels. It is possible that previous results pointing to a small or insignificant impactof canopy cover on fuel moisture (Faiella and Bailey, 2007; Estes et al., 2012; Ban-well et al., 2013) could be explained by this counteracting effect of solar heatingand nocturnal cooling.5.5 ConclusionsCanopy interception models of precipitation and shortwave radiation were reason-ably accurate, especially for the purpose of modelling below-canopy fuel moisture.The suite of models developed here was able to accurately simulate the observedseasonal trends in below-canopy fuel moisture. The models produced a bias of1.4%, and RMSE of 4.3% and an R2 of 0.88, although these results improved dur-ing dry periods.Compared to longwave radiation and precipitation, shortwave radiation had thestrongest direct impact on fuel moisture. Precipitation interception had the small-est impact on fuel moisture and ERC, especially during dry periods. The impactof precipitation became negligible around a week following rain. As previouslymentioned, it is important to note this analysis separates the direct impact that thecanopy has on the fuel moisture stick through changing the incident precipitationand net radiation at its surface, from the indirect impact of the canopy through itsinfluence on near-surface conditions.Both observed and modelled fuel moisture and potential fire danger were rel-atively homogeneous across the landscape during the day; daytime variability inmodelled fuel moisture was comparable to the model error. This lack of daytimevariability agrees with previous studies and may be a result of the counteractingeffects of nocturnal cooling and increased precipitation versus daytime solar heat-ing. Daytime ERC variability was not strongly influenced by weather conditions.This result is in contrast to previous studies, which generally concluded that theimpact of canopy cover on fuel moisture is diminished during dry periods. Whiledaytime 1-hour fuel moisture was related to canopy cover and radiation load, pat-terns in daytime ERC were not related to either canopy cover or radiation load. At106the anomalously moist Site 22, an elevated water table likely contributed to lowERC throughout the season.Fuel moisture and potential fire danger were more variable at night. Comparedto a climatology of ERC modelled at a nearby long term station, the wettest siteswere comparable to a median season, while the driest sites had ERC levels similarto the 95th percentile. The variability in nocturnal ERC was comparable to thevariability in average ERC found across a much larger mountainous region (Holdenand Jolly, 2011), suggesting that a mosaic of canopy cover can lead to significantvariability in nocturnal ERC at the landscape scale.Nocturnal fire danger was also more strongly influenced by weather conditions.Specifically, the landscape became more variable during cool and moist periods,and during periods with low wind speeds. This is in contrast to the near-surfaceclimate which was relatively homogeneous during cool and moist conditions. Thedifference is likely due to variations in below-canopy precipitation, which has astronger, direct impact on fuel moisture. Spatial patterns in nocturnal ERC andfuel moisture were correlated with canopy cover but not radiation load. Thesecorrelations were strongest for the smaller fuel sizes.Overall, open sites saw significant nocturnal longwave cooling and increasedprecipitation. Because these impacts persisted within the slowly varying larger fu-els, fuel moisture and ERC patterns were dictated by canopy cover with wetteraverage conditions at open sites. Only the 1-hour fuel size reacted quickly enoughto mirror the drier and warmer daytime conditions at open sites and south-facingslopes. Finally, these results demonstrate that the direct impact of aspect on fuelmoisture through changes in radiation load is likely secondary to the indirect im-pact of increased canopy cover.The assessment of spatial patterns in potential fire danger presented here waslimited to point measurements across a small field site. This analysis will be ex-tended to a larger scale in the following chapter, where the suite of models pre-sented here will be used to generate high-resolution rasters of ERC across a large(140 km2) region with a significant elevational gradient. This approach will allowfor a comparison of the relative influence of not just radiation load and canopycover, but elevation as well. Moreover, simulating high-resolution rasters will al-low for a more detailed analysis of patterns in ERC to determine if there are patches107within the landscape that remain moist relative to their surroundings.108Table 5.4: Results of model selection. Standardized regression coefficientsare shown in the Canopy Gap and Rad Load columns. Bold values indi-cate the predictor with the strongest single variable model as determinedby the coefficient of determination. Missing values indicate that the ad-dition of the predictor did not substantially improve the model perfor-mance. The standard error of the estimate is also provided in units of thepredictand (ERC: unitless, FMC: %).Predictand Period Canopy Gap Radiation Load R2 Std. ErrorERCmin All Dry Days -0.86 0.72 2.351-h FMmax All Dry Days 0.89 0.78 1.401000-h FMmax All Dry Days 0.69 0.46 0.30ERCmax All Dry Days1-h FMmin All Dry Days -0.61 -0.43 0.78 0.231000-h FMmin All Dry DaysERCmean All Dry Days -0.7 0.46 1.761-h FMmean All Dry Days 0.84 0.70 0.511000-h FMmean All Dry DaysERCmin All Rain Days -0.68 0.43 3.131-h FMmax All Rain Days 0.64 0.39 3.741000-h FMmax All Rain Days 0.54 0.25 0.52ERCmax All Rain Days1-h FMmin All Rain Days -0.77 0.58 0.561000-h FMmin All Rain DaysERCmean All Rain Days -0.5 0.21 2.531-h FMmean All Rain Days1000-h FMmean All Rain DaysERCmin June -0.73 0.51 2.961-h FMmax June 0.84 0.68 2.051000-h FMmax JuneERCmax June1-h FMmin June -0.68 -0.33 0.79 0.191000-h FMmin JuneERCmean June -0.45 0.16 2.211-h FMmean June 0.74 0.53 0.801000-h FMmean JuneERCmin September -0.8 0.63 3.251-h FMmax September 0.78 0.58 3.101000-h FMmax September 0.67 0.42 0.51ERCmax September1-h FMmin September -0.75 0.54 0.531000-h FMmin SeptemberERCmean September -0.66 0.40 2.891-h FMmean September 0.64 0.39 1.50109Figure 5.8: Observed hourly 10-hour fuel moisture at all three sites (A), along with daily maximum (B) and dailyminimum (C) values. Observed precipitation at the Base Station is also provided (D).110Figure 5.9: A sample of modelled hourly 1-hour and 1000-hour fuel moisture, modelled ERC for for all sites (greylines), and observed precipitation at the Base Station. Fuel Moisture 2, Site 22, and Site 4 are highlighted.111-Figure 5.10: Daytime and night-time ERC for all sites. As in Figure 5.9, Fuel Moisture 2, Site 22, and Site 4 arehighlighted. The grey ribbon indicates the range between the median and 95th percentile ERC calculated at theSparks Lake station over 26 seasons.112Figure 5.11: Daily standard deviation of maximum and minimum ERC plotted against daily minimum and maximumrelative humidity and temperature, daily mean wind speed, daily mean sortwave radiation, and Days Since Rain.Regression lines and the coefficient of determination (R2) are included for plots where null hypothesis that theregression coefficient is equal to zero was rejected at the 95% confidence level (blue lines).113Figure 5.12: Modelled fuel moisture biases (compared to the original model)at Site 4 for all four sizes when removing one or all of the componentsof the canopy model: Longwave, shortwave, or precipitation. Note thevarying scales of the y-axes.114Figure 5.13: Daily mean ERC biases (compared to the original model) at Site4 when removing one or all of the components of the canopy model:Longwave, shortwave, or precipitation. Hourly precipitation at theBase Station is included.Figure 5.14: Second principal component of ERC for all 24 sites plottedagainst canopy gap fraction and radiation load. As in Figures 5.9 and5.10, Fuel Moisture 2, Site 22, and Site 4 are highlighted.115Figure 5.15: A month of ERC values for all 24 sites (grey lines). The siteswith the three highest PC2 loadings (blue lines) and the sites with thethree lowest PC2 loadings (orange lines) are highlighted.116Chapter 6Modelling high resolution firedanger rasters across a largestudy region6.1 IntroductionWildfire behaviour depends on a complex combination of fuels, topography andweather, all of which vary at multiple scales. Consequently, the spatial patternof wildfires and their ecological impact across the landscape is heterogeneous(McKenzie et al., 2011). Determining the drivers of this spatial behaviour willaid in predicting the spatial pattern of fire effects, which can, in turn, influencesuccessional trajectories and ecological processes (Romme et al., 2011). Under-standing what drives the spatial behaviour of fires is also significant from a firemanagement perspective if the goal is to create more resilient ecosystems in theface of a changing climate by introducing more fire onto the landscape (Holdenet al., 2011a).Patterns in fuel moisture likely influence fire spread (Littell and Gwozdz, 2011;Miller and Urban, 2000) and burn severity patterns (Alexander et al., 2006; Dillonet al., 2011; Arkle et al., 2012). It is therefore important to assess how fuel mois-ture varies at different spatial scales, and the relative influence of the factors driving117these patterns. In the extreme case where the landscape is homogeneously dry, afire can spread unimpeded through a region, given ideal wind conditions. How-ever, in moderate fire weather conditions, particular areas of the landscape may besusceptible to fire spread while others are not, and in this case the pattern of fuelmoisture becomes important. If fuel moisture changes gradually across the land-scape, i.e. there is a large spatial autocorrelation, a fire can easily spread across thedrier portion of the region. Alternatively, if the fuel moisture pattern is patchier,and the scale of spatial autocorrelation decreases, a fire will be less likely to moveacross the entire landscape without patches of wetter fuels impeding its spread(Littell and Gwozdz, 2011).Results from Chapter 5 suggest that in the dry Interior Douglas-fir forests stud-ied here, daytime variability in fuel moisture and potential fire danger is low, apartfrom locations that are influenced by a high water table. That is, the whole land-scape dries out at a similar rate. Moreover, spatial patterns in daytime fire dangerwere not significantly correlated with either canopy gap fraction or radiation load.Nocturnal fire danger is more variable and significantly impacted by canopy cover.However, the above results were based on point measurements across a smallarea. These data provide limited information about actual landscape patterns orthe potential for areas to remain persistently wet relative to their surroundings. Aswell, the previous chapters were restricted to a relatively small area (approximately1 km2) with little change in elevation. In this chapter the relationships identifiedin previous chapters will be extrapolated to a larger 140 km2 area with a mosaic ofcanopy coverage and radiation load and a significant elevational gradient. Centralto this analysis is the development of non-linear random forest models for pre-dicting near-surface temperature and relative humidity across the landscape usingmeteorological data from a base station along with raster layers of canopy cover,radiation load, and elevation. The final product will be time-varying 30-m resolu-tion rasters of temperature, humidity, and potential fire danger.As described in Chapter 3, high resolution (<1 km) gridded maps of weathervariables have been produced by a number of researchers (Holden et al., 2011a;Holden and Jolly, 2011; Ashcroft and Gollan, 2011; Bennie et al., 2010; Holdenet al., 2015). However, much of this work has focused on temperature rather thanrelative humidity, which is an important driver of fuel moisture. Holden and Jolly118(2011) developed an empirical downscaling approach using Principal ComponentAnalysis and a network of relative humidity sensors that generated 30-m resolutionmaps of relative humidity across a mountainous region. They found that elevationhad a strong influence on relative humidity, while radiation load was a secondarypredictor. However, this approach did not include the impact of canopy coverageand used measurements 2 m above the ground. Ashcroft and Gollan (2011) devel-oped 25-m resolution grids of near-surface humidity and temperature that includedthe influence of canopy coverage. In their analysis, elevation and canopy coverwere strong determinants of relative humidity patterns. However, the grids theyproduced were of long term extreme values; they did not produce time-varyingmaps. This chapter will build on the literature by developing high resolution mapsof both near-surface temperature and relative humidity at a hourly time intervalsthat are dependent on canopy cover, aspect, and elevation.Less work has been done on developing and analysing high resolution mapsof fire danger. As mentioned in Chapter 5, high resolution fire danger maps de-veloped by Holden and Jolly (2011) exhibited spatial patterns that changed overthe fire season. The authors used the Energy Release Component (ERC) to repre-sent potential fire danger. South facing slopes and lower elevations saw higher firedanger. This chapter will expand on these results by providing a novel examina-tion of the relative influence of elevation, canopy cover, and radiation load on thevariability and patterns of both nocturnal and daytime fire danger.This study will pursue three research objectives:• Objective #1: Develop and evaluate models to predict temperature and rela-tive humidity across a forested landscape and use these models, along withmodels for precipitation and radiation canopy interception, to generate dailyrasters of potential fire danger across a large study region (140 km2).• Objective #2: Examine the spatial variability of potential fire danger acrossthe study region and determine the relative influence of canopy coverage,radiation load, and elevation on that variability. The following predictionwill be tested:– Elevation is the most important factor driving the spread in potential119fire danger across the study region, followed by canopy gap fraction,and then radiation load.• Objective #3: Examine the spatial patterns of potential fire danger acrossthe study region and how it changes over the fire season. The followingprediction will be tested:– The impact of canopy cover and radiation load on daytime fuel mois-ture and potential fire danger is not strong enough to create landscapepatches that are significantly wetter than the surrounding area.This chapter begins with a description of the methods and data used, includ-ing: an overview of the methods used to develop rasters of temperature, humidity,and fire danger (Section 6.2.1); a description of the required input rasters (Section6.2.2), and a detailed description of the temperature and humidity random forestmodels (Section 6.2.3). The results section will provide: evaluation results for thehumidity and temperature models (Section 6.3.1, Objective #1); an analysis of therelative influence of elevation, canopy cover and radiation load (Section 6.3.2, Ob-jective #2); and an analysis of fire danger patterns across the study region (Section6.3.3, Objective #3). This is followed by a discussion of results (Section 6.4) andconclusions (Section 6.5).6.2 Methods6.2.1 OverviewIn this study I produced daily 30-m resolution rasters of the relative humidity, tem-perature, and ERC across a 140 km2 study region centred around the study site de-scribed in the previous chapters (See Figure 2.1 for location). Figure 6.1 provides aschematic overview of the procedure. The ERC rasters were calculated by runningthe fuel moisture model (see Chapter 4) and the ERC model (see Chapter 5) ateach 30-m grid cell. This required time-varying input rasters of below-canopy pre-cipitation, below-canopy shortwave radiation, near-surface relative humidity andtemperature, and wind speed. It also required a raster of canopy gap fraction (de-120scribed in Section 6.2.2). As mentioned in Chapter 5, ERC represents the potentialheat released by a propagating fire front and, as such, does not include the impactof wind speed or slope fire danger. Instead, it can be viewed as representing thecontribution of fuel moisture to fire danger.Base	Station	Wind	SpeedBase	Station	Shortwave	RadiationBase	Station	PrecipitationShortwave	Interception	ModelPrecipitation	Interception	ModelCanopy	Cover	RasterBelow-Canopy	Precipitation	RasterBelow-Canopy	Shortwave	Radiation	RasterHumidity	&	Temperature	RastersFuel	Moisture		&	ERC	ModelsERC	RasterFigure 6.1: Procedure used to generate fire danger rasters. Variables areshown as squares and models are shown as green circles. Variablesare either time-varying spatial rasters (yellow squares), constant spatialrasters (purple squares), or non-spatial time series (grey squares).The weather rasters were generated using weather observations from the BaseStation (described in Chapter 2) and rasters of canopy gap fraction and elevation.Specifically, the below-canopy precipitation raster was generated by running theprecipitation interception model described in Chapter 5 at each grid cell, forced121with Base Station precipitation data and using the canopy gap fraction value at eachcell. This approach assumes that above-canopy precipitation is constant across thestudy region. The below-canopy shortwave radiation raster was generated by run-ning a simple empirical shortwave interception model (described below in Section6.2.3) at each grid cell, which was forced with Base Station shortwave radiationobservations and the canopy gap fraction at each cell.Wind speed was assumed to be constant across the study region and was setto be equal to the wind speed observed at the Base Station. This is a signifi-cant simplification as wind speed would be expected to vary significantly acrossa mountainous landscape.However, this simplification was considered to be rea-sonable because, as shown in Chapter 4, modelled fuel moisture was relativelyinsensitive to wind speed. This finding was supported by additional analysis, inwhich ERC was calculated at the Base Station after wind speeds were adjusted bya constant factor, and then compared to the original ERC. Results for this analysisare shown in Appendix C, Figure C.1. Significant adjustments in wind speed didlittle to impact ERC, especially during dry periods. Moreover, estimating below-canopy wind speeds across a mountainous landscape would substantially increasethe complexity of the study.As mentioned in the introduction, rasters of near-surface relative humidity andtemperature were generated by running non-linear random forest models at eachgrid point. A schematic of the procedure used is presented in Figure 6.2. Therequired inputs for these models are: rasters of canopy gap fraction, seasonallyaveraged above-canopy radiation load, and precipitation amount; shortwave radi-ation, temperature, relative humidity, hours since precipitation, and wind speedobserved at the base station; as well as the hour of the day and the day of year. Be-fore the Base Station temperature and relative humidity were input into the model,they were adjusted to the elevation of each grid cell using a time-varying lapserate. The temperature and humidity lapse rates were calculated every hour us-ing observations from the Kamloops Airport, which is at an elevation of 345 mabove sea-level, compared to the Base Station’s elevation of 1170 m (See Figure2.1 for location). The Kamloops Airport data were acquired from EnvironmentCanada and Climate Change via the Pacific Climate Impact Consortium’s DataPortal (	Station	Relative	Humidity	&	TemperatureRelative	Humidity	&	Temperature	ModelsKamloops	Airport	Relative	Humidity	&	TemperatureHourDay	of	YearBase	Station	Wind	SpeedDigital	Elevation	ModelLapse	Rate	AdjustmentCanopy	Cover	RasterElevation-Adjusted	Base	Station	Humidity	&	TemperatureRadiation	Load	RasterHumidity	&	Temperature	RastersBase	Station	PrecipitationBase	Station	Shortwave	RadiationFigure 6.2: Procedure used to generate relative humidity and temperaturerasters. Variables are shown as squares and models are shown asgreen circles. Variables are either time-varying spatial rasters (yellowsquares), constant spatial rasters (purple squares), or non-spatial timeseries (grey squares).To evaluate the relative influence of canopy coverage, radiation load, and ele-vation on the variability and patterns of potential fire danger across the study land-scape, rasters of ERC were generated while setting all but one of the these threefactors to be constant and equal to its average value across the study region.Variogram analysis was used to quantify the spatial autocorrelation of ERC123patterns across the study region. Specifically, the variogram of ERC was calculatedacross the entire study region for each day. A spherical variogram model wasthen fit to the experimental variogram, as analysis not shown here indicated thatit was the most appropriate model in this instance. The variogram range was thenextracted from the spherical model for each day. The variogram range representsthe maximum distance of spatial autocorrelation in ERC. Larger ranges indicate aslowly varying pattern, while patterns with smaller ranges vary at smaller scalesand are more “patchy.”6.2.2 Spatial input dataThe three required input rasters, shown in Figure 6.3, were elevation, canopy gapfraction, and seasonally averaged above-canopy radiation load (indicated as pur-ple squares in Figure 6.2). Elevation data were taken from a 30-m resolutiondigital elevation model (DEM) of BC developed by Rosin (2010). The canopygap fraction raster was derived from the Vegetation Resource Inventory Database(, which contains numerous GIS layers pro-viding information on vegetation type, stand structure, and logging history. Togenerate the canopy gap fraction raster the “Crown Closure” layer was cropped tothe study region and converted to a 30-m resolution raster with the same geome-try as the DEM. The seasonally averaged above-canopy radiation load raster wascalculated from the DEM using the Potential Incoming Solar Radiation tool avail-able within the SAGA-GIS software. The radiation load raster was calculated asthe mean potential incoming solar radiation averaged across the length of the fieldseason (May 10 to September 22).6.2.3 Modelling detailsThe random forest machine learning approach (Breiman, 2001) was used to modelnear-surface temperature and relative humidity across the landscape. Random for-est models are an extension of classification and regression tree (CART) models.A CART model uses an iterative approach in which the set of training observa-tions are split into smaller and smaller subsets based on threshold predictor values.At each iteration the split is made that generates the most homogenous subsets.124CART models have a number of advantages in that they do not make any assump-tions about variable distributions, they can identify non-linear relationships, andare not susceptible to over-fitting. Random forest models generate a “forest” oftrees using a bootstrapping approach in which an ensemble of trees are trained onrandom subsets of the training data and then validated against the remaining data.The results from the ensemble of trees are then aggregated. Random forest modelshave been increasingly used to predict spatial variables where there are non-linearand hierarchical relationships present (Dillon et al., 2011). The R package “ran-domForest” (Liaw and Wiener, 2002) was used with 120 random trees grown foreach model.As previously mentioned, there are three categories of predictor variables:hourly meteorological observations from a single site (precipitation amount, hourssince precipitation, wind speed, temperature, relative humidity, and shortwave ra-diation); spatially varying site characteristics (seasonally averaged above-canopyradiation load, and canopy gap fraction); and two time variables (hour of day andday of year). Because different processes are more or less important depending onthe time of day, separate models were developed for daytime hours and nighttimehours demarcated by sunrise and sunset. As well, seasonally averaged radiationload was not used as a predictor in the nighttime model.The models were trained using the observational dataset described in Chapter2. Near-surface relative humidity and temperature were simulated at the individualLogtag sites and compared to observations. The hourly meteorological input vari-ables were taken from the Base Station. The same site-specific canopy gap fractionand average above-canopy radiation load values used in Chapters 3 and 5 were usedas model inputs here. Due to its outlying behaviour, Site 22 was excluded from thisanalysis.Although the random forest method uses cross validation to test each tree, theobservations are divided randomly, ignoring site and time of year. However, it isimportant to examine how the models performed at independent sites and time pe-riods not used for training. Therefore, two additional cross-validation approacheswere developed. In one case the models were trained at a random subset of half thesites and evaluated using the remaining sites, and in the other case the models weretrained on the first half of the field season, and evaluated on the remaining portion.125As mentioned above, the precipitation interception model, fuel moisture model,and ERC model were all taken, unchanged, from the previous chapters. However,estimating below-canopy shortwave radiation using hemispherical photos as wasdone in Chapter 5 is not feasible when a raster across the whole study region isrequired. Therefore, a simple shortwave interception model was created wherebythe fraction of radiation intercepted by the canopy was modelled as a linear func-tion of canopy gap fraction. The model was developed using three steps. Firstly,the simulated shortwave radiation that was generated in Chapter 5 was taken as aproxy for observations. Secondly, a seasonal average of below-canopy shortwaveradiation was calculated for each site and divided by the average at the Base Sta-tion site. Finally, this ratio of below-canopy radiation to open-site radiation wasregressed against canopy gap fraction. This linear regression was then combinedwith the canopy gap fraction raster and the hourly time-series of shortwave radia-tion measured at the Base Station to generate a time-varying raster of below-canopyshortwave radiation.6.3 Results6.3.1 Temperature/humidity modelTable 6.1 provides cross-validation model skill statistics for both the relative hu-midity and temperature models. Model skill was highest when the evaluation andtraining subsets were split across sites, rather than time. Cross-site model skillwas highest for minimum relative humidity and minimum temperature. Examplecomparisons of modelled and observed daily relative humidity and temperature areshown in Figure 6.4 using data from site 10, which is one of the evaluation sites.The models are able to simulate the seasonal trends well. The large wet bias inmaximum relative humidity seen in Table 6.1 is also apparent in this figure.Modelled relative humidity and temperature, along with modelled below-canopyprecipitation and shortwave radiation, were then used to model fuel moisture andERC. The resulting ERC values were compared to the ERC values generated usingobservations (see Chapter 5) at the evaluation sites. Comparison statistics are pro-vided in Table 6.2. Model root mean square errors were 5.06 and 5.70 for ERCmax126Table 6.1: Skill of models applied to evaluation data. Comparison statisticsused are: root-mean-square error, bias, and coefficient of determination.Results are provided for evaluation across both time and sites.RHmax (%) RHmin (%) Tmax (◦C) Tmin (◦C)Time Site Time Site Time Site Time SiteRMSE 7.23 5.71 4.54 3.50 1.47 1.42 1.74 0.99Bias 2.94 1.03 -2.42 1.45 0.53 -0.36 -0.78 -0.03R2 0.88 0.88 0.95 0.96 0.95 0.95 0.88 0.94and ERCmin, respectively, model bias was 1.51 and 3.26, and R2 values were 0.90to 0.95. Example scatter plots comparing ERC forced by both observed and sim-ulated relative humidity and temperature are shown in Figure 6.5. Only sites notused for model training are shown. The correlations are strong especially at highervalues, although some cases exhibited either negative or positive biases, dependingon the site and time of day.Table 6.2: Comparison statistics between modelled ERC forced by observedmeteorology and modelled ERC forced by simulated meteorology. Com-parison statistics used are: root-mean-square error, bias, and coefficientof determination. Results are provided for evaluation using both inde-pendent time-period and independent sites.ERCmax ERCminTime Site Time SiteRMSE 5.51 5.06 5.43 5.70Bias 3.26 2.68 1.77 1.51R2 0.91 0.90 0.95 0.936.3.2 Relative impact of factors influencing the spatial variability ofpotential fire dangerThe full suite of models shown in Figures 6.1 and 6.2 was applied to all 30-m gridcells within the study region to generate time-varying rasters of nighttime (0400h) and afternoon (1600 h) ERC. These specific hours were used instead of dailymaximum and minimum values for the sake of consistency across the study region.To show both the seasonal trend and spatial variability of ERC across the study127region, time-series from all grid cells are shown in Figure 6.6. To provide context,an ERC value of 60 was highlighted in the plots. Conditions above this thresholdare often associated with extreme fire behaviour (Raymond and Peterson, 2005).As was seen in Chapter 5, afternoon ERC was less spatially variable than nighttimeERC. Nightitme ERC was most variable during moderately dry conditions at thebeginning and end of the fire season.The spatial variability of ERC across the study region is examined in moredetail in Figure 6.7, where the standard deviation of nighttime and afternoon ERCis shown for the entire field season. Also included is the standard deviation ofERC maps generated when only one of the three influencing factors: canopy gap,elevation, or above-canopy radiation load, is allowed to vary across the study region(the other two factors are set to their average values). This isolation of factorsallows for an analysis of the relative influence of these factors, addressing Objective#2 of this chapter.Overall, ERC variability was enhanced by precipitation events, although thisrelationship was not as consistent at night as it was during the day. The spatialvariability of afternoon ERC also was consistently reduced during dry periods.In contrast, the spatial variability of nighttime ERC was much noisier, and theinfluence of weather conditions was less obvious. For instance, in some cases rainacted to increase variability, while in other cases the opposite was true.ERC was consistently more variable across the study region when all threefactors were allowed to vary. As hypothesized, patterns in radiation load had theleast amount of impact, while much of the spatial variability in afternoon ERC canbe attributed to changes in elevation. One exception was during large rain events,when the variability driven by patterns in canopy cover was equal to or larger thanthe influence of elevation. Another exception was during the driest periods (mid-July, Early August, and Late August) when variability was low and all three factorshad a similar influence. Canopy cover had a much larger influence on the spatialvariability of nighttime ERC. Indeed, during the driest periods elevation had littleinfluence on nighttime conditions, and a large majority of the variability was drivenby canopy cover.1286.3.3 Spatial patterns of potential fire danger across the study regionExamples of ERC rasters are provided in Figures 6.8 and 6.9. Two days werechosen: the first day immediately following a large rain event, and 8 days later,after the landscape was able to dry out (both days are indicated in Figure 6.7).Elevation had a dominant influence on the spread of ERC during the first day,but as conditions became drier the impact of elevation was diminished and canopycover became more dominant, especially at night. As the landscape went from anelevation-dominated pattern to a canopy-dominated one, ERC transitioned from aslowly varying pattern with a large spatial autocorrelation scale, to a pattern dom-inated by the smaller scale variability of the canopy mosaic and a small spatialautocorrelation scale. This shift in spatial patterns can be seen in Figure 6.10where the change in the semi-variogram range of both afternoon and nighttimeERC are presented. Between the two example days shown in Figures 6.8 and 6.9,the range transitioned from around 5 km to around 1 km, indicating that the spatialautocorrelation of ERC was substantially reduced as elevation, which has a largeautocorrelation scale, lost influence. There were a number of other cases, gen-erally during dry periods, where the range in ERC was significantly diminished,indicating a transition to a canopy-dominated pattern. In general, there was a trendtowards lower variogram ranges during the middle of the season.The relationship between the mean of ERC across the study region, the stan-dard deviation of ERC, and the variogram range is presented in Figure 6.11. Thevariability in ERC across the study region decreased as the landscape dried out. Itis also evident from Figure 6.11 that most days with a small autocorrelation scalewere also relatively dry with little variability in ERC, especially during the day.There were a few instances in which the region exhibited large variability dur-ing relatively dry periods. Two such days are highlighted in Figure 6.11 and pre-sented as rasters in Figure 6.12. In both cases there was a large amount of spatialheterogeneity in potential fire danger, especially at the higher elevations wherethere is a mosaic of canopy coverage. In the daytime example (June 11th) thelargest fire danger at higher altitudes was in areas with an open canopy, while theopposite was true during the nighttime example (July 15th). However, these in-stances of dry, variable conditions did not persist for multiple days.129Figures 6.7, 6.8, and 6.9 were repeated for both temperature and relative hu-midity and included as supplementary material in Appendix C.6.4 Discussion6.4.1 Temperature / humidity modelChapter 3 demonstrated that spatial patterns in near-surface conditions were stronglydependent on canopy cover, radiation load, and weather conditions. The randomforest models developed in this chapter were able to capture much of those rela-tionships. When applied to independent sites, the models produced errors that werecomparable to the accuracy of the LogTag sensors themselves (See Appendix A),especially for minimum relative humidity and minimum temperature. The non-linearity of the random forest models was important for this application, as it wasable to simulate the interaction between weather patterns and site characteristicsseen in Chapter 3 (specifically, Figure 3.3). It is also interesting to note that modelskill was highest when applied to independent sites, rather than an independenttime period. This result suggests that the relationship between weather conditionsand near-surface conditions changes over the course of the fire season.Even though the modelled relative humidity and temperature had strong R2values when compared to observations, the model did not capture the full obser-vational variability. When comparing the modelled standard deviation of relativehumidity across the entire study region in Figure C.2 to the standard deviation ofERC generated from observations at just the 24 observation sites (Chapter 5, Table5.3), it is clear that the modelled variability is lower than observations, especiallyfor afternoon RH. This diminished variability in model output is unavoidable whena model is fit to observational data.Moreover, model variability was also reduced because the field observationsdescribed in Chapter 2 did not sample as wide a range of radiation load as wasfound across the study region used in this chapter. Specifically, some steep, north-facing facets had average radiation loads lower than what was sampled. The ran-dom forest models interpolated to these lower values by maintaining a constantrelationship between radiation load and near-surface conditions beyond the lowest130radiation load sampled by the field observations. Consequently, the models likelyunderestimated the variability of relative humidity and temperature across the studyregion that is driven by changes in radiation load. These results should therefore beexamined with the understanding that actual variability in near-surface conditionsis larger than what was produced by the suite of models, especially during the day.The unique modelling approach used in the chapter for generating high-resolutionmaps of temperature and relative humidity across a complex landscape has applica-tions beyond the objectives of this thesis. Understanding how temperature and hu-midity change at the local scale is important for determining the location of micro-climates or microrefugias that are suitable for particular species (Dobrowski, 2011;Ashcroft and Gollan, 2013a). This thesis has demonstrated that a host of factorscan interact to determine near-surface conditions at a specific spot on the land-scape. This chapter has shown that the suite of models developed in this chapterhas the ability to capture some of these interactions in order to simulate changingpatterns of relative humidity and temperature across a forested landscape.6.4.2 Simulated potential fire danger mapsIn addressing Objective #2, it was found that afternoon fire danger was relativelyhomogeneous during dry periods, even across the extended study region of 140km2 with an elevation difference of over 1200 m. ERC variability was particularlylow during the peak of the fire season. One driver of these low variability periodsin afternoon ERC was a reduced relative humidity lapse rate; there is a moderate(0.51) correlation between the standard deviation of afternoon ERC using all fac-tors (blue line in Figure 6.7) and the standard deviation of afternoon RH drivenwith just elevation (red line in Figure C.2). It may also be the case that the fuelmoisture model was not able to dry out the fuels below a certain minimum mois-ture level. Consequently, all grid points approached this minimum moisture level,even if there was variability in relative humidity across the study region. In con-trast, nighttime variability is higher, mirroring the results of Chapter 5 where ERCvariability across the observational sites was also higher at night (see Table 5.3).A number of studies have demonstrated that during dry periods fuel moistureis homogenous across a range of canopy cover (Whitehead et al., 2006; Estes et al.,1312012; Banwell et al., 2013) and radiation load (Gibos, 2010), findings which weresupported by the results of Chapter 5. The present analysis expands on those resultsand suggests that during dry conditions fuel moisture and potential fire danger arerelatively homogenous over a large regions on the order of 100 km2 with a widerange of canopy cover, radiation load and elevation.It was determined that, as hypothesized, elevation generally had the largest im-pact on overall fire danger variability, and radiation load had the smallest impact.However, there were a number of exceptions. For instance, canopy cover had alarge influence on afternoon ERC variability during significant precipitation eventswhen precipitation interception became important, although this influence dimin-ished quickly as the landscape dried out. As well, canopy cover played a muchlarger role during the night, reflecting the findings of Chapter 5 where canopy gapfraction was only predictive of the spatial patterns in minimum ERC and had noconnection with daytime patterns. Canopy cover drove the largest amount of night-time variability during dry, clear-sky conditions, when the role of the canopy in de-termining net longwave radiation was most prominent. It should be mentioned thatthere was a small amount of variability in nighttime ERC when only radiation loadvaried. This variability was present, even though radiation load was not includedas a predictor variable in the nighttime temperature and humidity models, becausethe influence of the daytime models persisted into the night due to the “memory”of the fuel moisture model.As mentioned in the previous section, the model underestimated fire dangervariability due to canopy cover and radiation load. In contrast, the impact of ele-vation was not modelled; rather, the lapse rate was calculated directly from obser-vations. Consequently, it is likely that these results overestimated the influence ofelevation as compared to canopy cover and radiation load. However, it is still likelythat elevation was the dominant factor influencing variability, at least for afternoonERC.As was mentioned in this chapter’s introduction, patches of wet fuels within alandscape could act as impediments to fire spread or lead to heterogeneous burnseverity patterns, which has implications for ecological processes and fire suppres-sion practices. Of the three factors controlling fuel moisture patterns in this study,only canopy cover and radiation load vary at spatial scales small enough to gener-132ate such patches. However, as seen in Figures 6.7 and 6.11, these two factors hadthe strongest relative influence during dry periods when ERC variability is low andthe entire landscape is burnable. Moreover, while fire danger variability is largerduring moderately dry conditions, these periods were also characterized by moreslowly varying patterns in fuel moisture (i.e., large variogram ranges) dominatedby changes in elevation. Consequently, these results confirm the second hypothe-sis that changes in near-surface conditions due to variations in radiation load andcanopy cover are not large enough to generate patches that are substantially wetterrelative to their surroundings.Of course, it is possible that factors other than radiation load and canopy covercould lead to patches of anomalously wet fuels. For instance, based on resultsfrom Chapters 3 and 5, it is likely that areas characterized by high water tables canremain wet throughout the fire season. As well, it should be re-iterated that theseresults likely underestimate the influence of radiation load on fire danger patterns.6.5 ConclusionsThe random forest models described in this chapter were able to accurately predictrelative humidity and temperature at independent sites not used for model training.Model accuracy was on par with the accuracy of the LogTag sensors and was thehighest for minimum temperature and minimum relative humidity. These resultsdemonstrated that the random forest model was able to capture the complex inter-action between site characteristics and weather seen in Chapter 3. One limitationof the model was that the observational sites did not cover the full range of radia-tion load within the study region, resulting in an underestimation of the influenceof radiation load across the region. Another limitation was that the tests sites wereat a similar elevation. As the suite of models included the impact of elevation, itwould have been beneficial to have test sites located across a range of elevation.The full suite of models produced simulated ERC at independent sites with rootmean square errors ranging from 5.06 and 5.70, biases ranging from 1.51 to 3.26,and R2 values ranging from 0.90 to 0.95. These values are for the entire indepen-dent evaluation dataset. However, the model exhibited larger biases at individualsites although these biases tended to decrease at higher ERC values.133The modelled rasters of afternoon potential fire danger were relatively homo-geneous during dry periods, even across the extended study region of 140 km2 andwith a difference in elevation of over 1200 m. This low variability was partly dueto low relative humidity lapse rates, as well as the fact that modelled fuel moisturehad a lower moisture limit that all grid points reached during dry periods, regard-less of site characteristics. Unlike afternoon ERC, variability in nighttime ERCwas less impacted by weather conditions.Elevation had the largest overall impact on spatial fire danger variability, espe-cially during the day. Canopy cover had a relatively strong influence during largeprecipitation events and at night during fair-weather conditions. Radiation load hadlittle impact on the spatial variability of fire danger across the study region.During dry periods, afternoon ERC transitioned from an elevation-dominatedspatial pattern with a large spatial autocorrelation scale to a “patchy” pattern witha small autocorrelation scale that was dictated by the mosaic in canopy cover.However, these dry periods with patchy patterns were also characterized by lowvariability in potential fire danger. These results suggest that radiation load andcanopy cover do not have a large enough influence on potential fire danger to gen-erate patches within the landscape that are significantly wetter than the surroundinglandscape.1341376000 1380000 1384000652000656000660000Canopy Gap20406080100Canopy Gap Fraction (%)UTM N1376000 1380000 1384000652000656000660000Radiation Load50100150200250300Above−Canopy Radiation Load (W/m2 )UTM N1376000 1380000 1384000652000656000660000Elevation400600800100012001400Elevatioh (m asl)UTM NUTM EFigure 6.3: Canopy Gap, Radiation Load, and Elevation rasters used as inputlayers for relative humidity and temperature models.13540608030507090101520253005101520Jun Jul Aug SepJun Jul Aug SepJun Jul Aug SepJun Jul Aug SepRHmax (%)RHmin (%)T max (o C)T min (o C)Obseved ModelledFigure 6.4: Both observed and modelled daily minimum and maximum rel-ative humidity and temperature at Site 10, which was not part of thesubset of sites used to train the model.136Fuel Moisture 2 Site 10 Site 12 Site 13ll llllllllllllllllllllllll llllllllllllllllllllllllllll llllllllllllll lll lllllllllllllllllllllll llllllllllllllllllll lllll llllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllll lllllllllllllll llllllllllllllllllllllll lllllllllllll llllllllllllllllll lllllllllllllllllllllllllllllllllllllllllllllllll llllllllllllllllllllllllllllllllllllllllllllllllllllll02550750255075Maximum ERCMinimum ERC0 20 40 60 80 0 20 40 60 80 0 20 40 60 80 0 20 40 60 80Observation−Forced ERC (%)Simulation−Forced ERC (%)Figure 6.5: Example comparisons of ERC generated using observed mete-orological conditions and ERC generated using simulated conditions.Results for daily maximum and minimum ERC are shown. A subset offour sites not used for training the humidity and temperature models areshown here. 1:1 lines is provided for reference.137Afternoon ERCNighttime ERC02550750255075Jun Jul Aug SepEnergy Release ComponentFigure 6.6: Afternoon and nighttime ERC for all grid points within the studyregion. The dashed horizontal line indicates an ERC value of 60.138lll lllllll lllllAfternoon ERCNighttime ERC03690369Jun Jul Aug SepERC Standard Deviation0.0 2.5 5.0 7.5 10.0Daily Precip (mm)Varying Factors l l l lCanopy / Radiation Load / Elevation Canopy Elevation Radiation LoadFigure 6.7: Standard deviations of nighttime and afternoon ERC across theentire study region. The results from four different simulations areshown here: three runs in which all but one of the three spatial fac-tors were kept constant, and one when all three factors varied acrossthe study region. The magenta points indicate the two days which areshown as rasters in Figures 6.8 and 6.91392014−07−26 2014−08−03All FactorsCanopy GapRadiation LoadElevation40506070Afternoon ERCFigure 6.8: Rasters of afternoon ERC for two different days (columns, indi-cated in Figure 6.7). Rasters driven by all factors, and the three factorsindividually (rows) are provided.1402014−07−26 2014−08−03All FactorsCanopy GapRadiation LoadElevation203040506070Nighttime ERCFigure 6.9: As in Figure 6.8, but for nighttime ERC.141llllAfternoon ERCNighttime ERC025005000750010000025005000750010000Jun Jul Aug SepVariogram Range (m)Varying Factors l Canopy / Radiation Load / Elevation0.0 2.5 5.0 7.5 10.0Daily Precip (mm)Figure 6.10: As in Figure 6.7, but for the variogram range of the ERC rasters.142l2014−06−11l2014−07−15Afternoon ERC Nighttime ERC2.55.07.510.00 20 40 60 80 0 20 40 60 80ERCERC Standard Deviation200040006000VariogramRange (m)Figure 6.11: Relationship between the mean ERC, the standard deviation ofERC, and the variogram range of ERC across the landscape for bothafternoon and nighttime ERC. Two example days when the fire dangerwas both high and variable are highlighted and the rasters for these twodays are shown in Figure 6.12.143Afternoon ERC2014−06−11Nighttime ERC2014−07−155560657075ERCFigure 6.12: Example rasters for both an afternoon and nighttime case inwhich the fire danger is both high as well as variable. The two ex-ample cases are highlighted in Figure 6.11.144Chapter 7ConclusionsThis thesis quantified spatial patterns in near-surface atmospheric conditions, fuelmoisture, and potential fire danger across a forested landscape, and examined howthose patterns were impacted by weather conditions, canopy cover, radiation load,and elevation. It also identified the degree to which near-surface microclimatesdirectly impact fuel moisture. Presented below are the key findings of the thesis, adiscussion of their implications, and potential future research directions.7.1 Summary of key findingsChapter 3 examined spatial patterns in near-surface temperature and humidity acrossa forested landscape with complex terrain. The objective of the study was to quan-tify the amount of spatial variability in near-surface conditions, determine howweather conditions impact that variability, and determine the relative influence ofcanopy cover and radiation load on spatial patterns of near-surface conditions. Sub-stantial variability was seen across the small (<4 km2) study site. In general, near-surface conditions were more heterogeneous during during dry, clear-sky condi-tions, and spatial variability was reduced during, and for a few days following, pre-cipitation. Weather conditions had the largest impact on nocturnal fuel moisture.An important finding was that the spatial variability in daytime relative humiditywas low and relatively unaffected by weather conditions.Spatial patterns in near-surface conditions were related to both canopy cover145and radiation load, with canopy cover being the more important predictor. Daytimeconditions were drier and warmer on south-facing slopes. Canopy cover had astrong impact on nocturnal relative humidity, which was higher at open sites dueto longwave cooling. Canopy cover had an opposite, but weaker effect on daytimehumidity due to solar heating. Consequently, open sites experienced higher dailymean relative humidity. Finally, one site located near a draw with an inferred highwater table remained anomalously cool and moist throughout the fire season.Chapter 4 described a new model for simulating the moisture content of stan-dardized fuel moisture sticks, which was subsequently used in Chapters 5 and 6 tosimulate fuel moisture across the study landscape. The model included treatmentsof internal heat and moisture transport, radiation and turbulent heat fluxes, atmo-spheric moisture exchange, and precipitation absorption. Compared to the NelsonModel, which is used operationally by fire agencies, this novel model is relativelysimple, apart from its treatment of radiation transfer, which is more sophisticated.When evaluated using both an independent time period and an independentdataset, the optimized model was able to capture 72 to 94% of the variance inobservations. Despite its simplified approach, the model improved on the skillachieved by the Nelson model. Moreover, the model allows for a more realis-tic treatment of canopy coverage and changes in sky conditions, features that areimportant for the simulation of fuel moisture patterns described in Chapter 5. Fi-nally, sensitivity analysis suggested that relative humidity is the dominant driver ofmodelled fuel moisture. The model was relatively insensitive to wind speed andshortwave radiation, suggesting that treatment of these forcing variables could befurther simplified.In Chapter 5, fuel moisture and potential fire danger (represented by the En-ergy Release Component) were simulated across the field site using the new fuelmoisture model, along with models of canopy interception of radiation and precip-itation. This suite of models was able to accurately simulate the observed seasonaltrends in below-canopy fuel moisture. Following model evaluation, the chapter’sobjective was to quantify the spatial variability of fuel moisture and potential firedanger, and determine the relative influence of canopy cover and radiation load.Daytime fuel moisture and fire danger exhibited low spatial variability, regardlessof weather conditions, and daytime fire danger was not related to either factor.146Fuel moisture and ERC were more variable at night and that variability increasedduring cool, moist periods with low wind speeds. Overall, patterns in fuel mois-ture and ERC were dominated by differences in nocturnal longwave cooling dueto changes in canopy cover. Consequently, radiation load only had a secondaryimpact on 1-hour fuel moisture, and open sites had lower daily minimum and dailymean fire danger. At the anomalously moist Site 22, an elevated water table likelycontributed to low potential fire danger throughout the season.Chapter 6 presented a method for producing high-resolution rasters of potentialfire danger over a 140 km2 region with a wide range of canopy cover, radiation load,and elevation. The study’s objective was to assess the relative impact of these threefactors on patterns in fire danger, and examine, in detail, the spatial patterns in firedanger. As part of this procedure a machine learning approach was used whichaccurately simulated spatial patterns in temperature and relative humidity.During dry conditions fire danger was relatively homogenous over the region,which had a wide range of canopy cover, radiation load, and elevation. Change inelevation led to the most variability in potential fire danger across the landscape.While changes in radiation load and canopy cover sometimes led to “patchy” pat-terns in fire danger during dry conditions, these periods also saw little variability infire danger. These results suggest that radiation load and canopy cover do not havea large enough direct influence on daytime fuel moisture to generate patches withinthe landscape that remain significantly wetter than the surrounding landscape.7.2 Implications of findingsIncreased radiation loads on warmer aspects can have a direct impact on fuel mois-ture by increasing drying rates on south-facing slopes. This direct impact is oftencited as a significant factor dictating patterns in historical fire frequency (Heyer-dahl et al., 2001) and burn severity (Holden et al., 2009; Birch et al., 2015; Kaneet al., 2015; Dillon et al., 2011). However, results from this thesis suggest that inthe Interior Douglas-fir forest type studied here the change in radiation load acrossterrain facets is likely a secondary factor in determining spatial patterns in fuelmoisture, following canopy cover. Moreover, chapter 5 demonstrated that, acrossthe study site, daytime ERC was not related to radiation load. Fine, 1-hour fuel147moisture was lower on warmer slopes, but canopy cover still played the dominantrole. Therefore, it may be that indirect impacts of radiation load, though its impacton canopy cover and understory density, may play the larger role in determiningfuel moisture patterns. Indeed, Nyman et al. (2015b) reached a similar conclusion.Consequently, for the purpose of predicting the spatial pattern of fuel moistureacross the landscape, it is as important to have accurate spatial vegetation data asit is to have terrain information. In many forest types aspect and canopy densityare linked (Zou et al., 2007), so that both indirect and direct effects on fuel mois-ture work in concert and fuel moisture would reliably be lower on warmer aspects.However, there are many other factors that influence vegetation density, includ-ing soil properties, groundwater, and disturbance history, that weaken the aspect-vegetation relationship. Indeed, in wetter, energy-limited forests, stand compo-sition is relatively unaffected by aspect (Ohmann and Spies, 1998). These resultssuggest that drier fuels will not necessarily be found on slopes with higher radiationloads.Overall, there was a lack of variability in daytime fuel moisture and ERC acrossthe landscape, supporting previous findings (Whitehead et al., 2006; Faiella andBailey, 2007; Estes et al., 2012). However, this study built on the literature byexamining not just the afternoon conditions, but the entire diurnal moisture cycle.This analysis determined that the lack of variability in afternoon fuel moisture islikely due to a balance between daytime solar heating and nocturnal longwavecooling. Moreover, this significant impact of nocturnal cooling meant that fuelmoisture was, on average, lower at open sites, a result which was seen in bothobserved and modelled fuel moisture.The important role that nocturnal cooling plays in determining fuel moistureis a significant finding, as many fuel moisture models ignore this process. For in-stance, the fire growth simulation model, FARSITE, which is used operationally,includes the impact of canopy cover on daytime solar radiation, but not noctur-nal longwave cooling (Rothermel et al., 1986). However, this study suggests thatchanges in nocturnal longwave cooling can have a dominant impact on spatial pat-terns in fuel moisture, especially for the larger fuel sizes. Consequently, FARSITEmay overestimate the differences in daytime fuel moisture between open and closedsites.148These results may have implications for the management of prescribed files orwildfires that burn for multiple days during moderate conditions. Understandingand predicting the spatial patterns of fire effects can help managers achieve theirspecific management objectives. For instance, even though fine fuels will likely bedrier at open sites during the afternoon, the overall wetter fuels at open sites maymean that, all other things being equal, fires will be less intense and have less se-vere impacts at open sites. Brown et al. (1985) found that 1000-hour fuel moisturewas a strong predictor of duff consumption by prescribed fires, which, in turn, canimpact seedling establishment and post-fire recovery (Johnstone et al., 2010). Con-sequently, results from this thesis have a number of implications for prescribed firemanagement. Firstly, in the drier forest types examined here, and during moder-ate fire weather conditions, canopy cover and aspect may, on their own, have littleimpact on duff consumption during the day, and understory vegetation may be animportant factor dictating burn patterns. Secondly, setting burns during cool moistconditions may lead to a more heterogenous burn pattern.While there has been an effort to thin stands in drier forests in order to re-store pre-settlement forest structure and reduce fire hazards, there is concern thatthese treatments will increase solar radiation penetration and decrease fuel mois-ture. However, results from this study and previous research suggest that theseconcerns may be overstated. In fact, it may be the case that thinning stands willdecrease fuel moisture, especially for the larger fuel sizes.The lack of variability in fuel moisture seen in Chapter 5 and the simulated fuelmoisture patterns generated in Chapter 6 suggest that neither gradients in canopycover nor radiation load have a large enough direct impact on fuel moisture to gen-erate patches of wet fuels that persist into the field season. As long as sites areforced by the same above-canopy conditions, nocturnal recharge will balance day-time drying and not let sites diverge. In order for a site to remain wet, it requiresa substantial source of additional moisture. Site 22 demonstrated that this mois-ture can come from an elevated water table that keeps an area moist throughoutthe season. Consequently, accurately predicting how fuel moisture changes acrossthe landscape requires spatial information about subsurface flow and water tablepatterns.1497.3 Suggestions for future researchOne limitation of this study was that it focused on observed and modelled moistureof elevated fuel sticks. Even though these fuel sticks are the basis of the Amer-ican Fire Behaviour Prediction System, their moisture content may not representthe moisture of fuels on the forest floor. For instance, there may be differences be-tween the microclimate immediately above the forest floor and at a height of 30.5cm, as vertical gradients in temperature and humidity can be significant near theground (Oke, 1990). Indeed, it was found in Chapter 4 that modelled fuel moistureis dependent on the height at which the temperature and humidity measurementsare taken. Moreover, fuel elements on the forest floor may gain moisture fromthe underlying soils (Hatton et al., 1988; Samran et al., 1995), and elevated fuelshave more exposed surface area and may be more efficient at exchanging moistureand heat with the atmosphere. Finally, there are number of methods of measur-ing fuel moisture, including destructive sampling of the litter layer (Gibos, 2010),weighing of dowels placed on the forest floor (Estes et al., 2012), or direct sen-sor measurements of the litter later (Nyman et al., 2015a). Consequently, it wouldbe instructive to systematically compare the moisture of different types of fuels,measurement techniques, and measurement heights. Such comparison would al-low us to compare results from different studies which use different measurementtechniques.As mentioned in Chapter 4, it would be useful to examine, in detail, the sensi-tivity of the fuel moisture model developed here to the different model parametersand forcing variables. Initial sensitivity analysis in Chapter 4 suggested that themodel is strongly dependent on relative humidity and relatively insensitive to windspeed and shortwave radiation. Further analysis could identify elements of themodel that could be simplified without sacrificing model skill. For instance, it islikely that using a constant aerodynamic resistance would not reduce model skilland remove the requirement for wind speed as an input. As well, the model’s com-plex approach to calculating both shortwave and longwave radiation absorptioncould likely be reduced substantially. Such an analysis could result in an updatedversion of the model which would still be more sophisticated and skillful thanmost of the fuel moisture models reviewed in the Introduction, but also be simple150enough to be utilized by other researchers. For instance, when choosing a fuelmoisture model to be used within a coupled fire-atmospheric model, Mandel et al.(2012) opted to use a relatively simple fuel moisture model rather than the modeldeveloped by Nelson (2000), which they deemed to be too complicated.Another limitation of this study is its reliance on a single season of field ob-servations taken across a relatively small area. Future studies could expand onthis work by deploying new networks of near-surface measurements across dif-ferent locations and different forest types. These new datasets could be used totest whether the relationships between near-surface conditions, radiation load, andcanopy cover found here are applicable to other locations. Independent datasetssuch as these could also be used to evaluate the temperature and relative humidityrandom forest models developed in Chapter 6.These networks could also be designed to examine the impact of factors otherthan radiation load and canopy cover on fuel moisture patterns. For instance, ev-idence from Chapters 3 and 5 suggested that relative humidity and fuel moisturelikely increase in the vicinity of streams and regions with elevated water tables. Afuture field project could focus on quantifying gradients in fuel moisture and rela-tive humidity near these wet regions. It would also be useful to determine the scaleat which this influence occurs. That is, what amount of separation from a draw orstream is required before its effect becomes negligible? It is also possible that therewould be a complex interaction between the distance from a saturated area, terrain,and canopy cover that could be explored. The impact of nocturnal katabatic flowsand cold-air ponding on fuel moisture patterns would be another important areato study. Areas that are susceptible to cold-air ponding would likely see elevatedrelative humidity at night. It is unclear how pervasive this impact would be over afire season, and if it is strong enough to impact daytime fuel moisture or generatepatches of anomalously moist fuels. Finally, as mentioned above, atmospheric con-ditions immediately above the forest floor may be different than conditions at the30.5 cm height used in this study. A network of sensors placed a few centimetresabove the forest floor (similar to the measurements by Ashcroft and Gollan 2013b)may help identify those differences and be more applicable to surface fuels.The sites used in this study were purposefully situated in similar areas withlittle understory growth and homogenous surface vegetation. Choosing sites with151consistent understory vegetation allowed for an examination of the direct impactof changes in microclimate on near-surface conditions and fuel moisture, ratherthan its indirect impact through changes in vegetation. However, as suggested byNyman et al. (2015b), these indirect impacts are likely significant. It is important,then, to attempt to quantify these vegetation impacts on dead fuel moisture. Forinstance, a network of sites could be established where sites are chosen acrossgradients of understory and surface vegetation in a region with little variability intopography. Each site would be characterized by percent cover or density of forbs,mosses, dead litter, shrubs, and understory and overstory trees. The impact of thesefactors on fuel moisture could then be assessed. This analysis of vegetation impactswould provide complementary information to the results found in this study.Networks of near-surface observations could also be used to assess the accu-racy of modelling systems used operationally. For instance, the FARSITE (Finney,2004) and FlamMap (Finney, 2006) models both estimate relative humidity, tem-perature, and fuel moisture across forested landscapes using a model developedby Rothermel et al. (1986). This model includes the impact of canopy, slope andaspect, and elevation on near-surface conditions, but does not include nocturnallongwave cooling. Fuel moisture is modelled using both the National Fire DangerRating System (Cohen and Deeming, 1985) and the Nelson Model (Nelson, 2000).A network of near-surface observations could be used to evaluate these models.To my knowledge, no study has evaluated the ability of these models to accuratelysimulate spatial patterns in fuel moisture.Finally, as was mentioned in Chapter 5, fuel moisture is one of a number offactors that will determine the behaviour of an individual fire. Others include windspeed, slope, and fuel amounts. Fire behaviour prediction tools such as FARSITEand FlamMap include treatments of all these processes, but could be improved byincluding some of the insights from this thesis. These tools could then be usedto examine the sensitivity of spatial patterns in modelled fire behaviour to fuelmoisture, wind speed, slope, and fuel amounts, and determine the most importantdeterminant of spatial fire behaviour.152ReferencesAlexander, J. D., Seavy, N. E., Ralph, C. 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Proceedings.–Andrews PL, Butl.BW, eds. → pages 3, 9, 25, 78, 102, 131, 148Wilkes, K. E. 1979. Thermophysical properties data base activities atOwens-Corning Fiberglas. In Proc. ASHRAE/DOE-ORNL Conf. Therm.Perform. Exter. Envel. Build., pages 662–677. → pages 175Winkler, R. D., Moore, R. D., Redding, T. E., Spittlehouse, D. L., Carlyle-moses,D. E., and Smerdon, B. D. 2010. Hydrologic Processes and WatershedResponse. In Compend. For. Hydrol. Geomorphol. Br. Columbia. BC, pages133–178. British Columbia Ministry of Forests and Range, Forest ScienceProgram, Victoria, BC. → pages 9, 10Zou, C. B., Barron-Gafford, G. A., and Breshears, D. D. 2007. Effects oftopography and woody plant canopy cover on near-ground solar radiation:Relevant energy inputs for ecohydrology and hydropedology. Geophys. Res.Lett., 34(24):1–6. → pages 3, 27, 148Zuur, A., Leno, E. N., and Smith, G. M. 2007. Analysing Ecological Data.Springer Science & Business Media, New York. → pages 38167Appendix ATemperature, humidity, and fuelmoisture bias correctionA.1 MethodsThe LogTags were set to measure ambient temperature and humidity in the lab forthree days before and after the field season. For both periods and both variables, anaverage value across all LogTags was calculated and biases from this inter-LogTagmean were calculated for each LogTag. After checking that these biases remainedstable over the field season, that is, the biases were the same for both calibrationperiods, these individual biases of each LogTag were removed.From a brief pre-field test it was apparent that the three fuel moisture sensorsexhibit biases relative to one another when co-located. These biases were removedbefore comparisons were made between fuel moisture measurements at differentsites. This was accomplished with an approach similar to the LogTag bias correc-tion. The three moisture sensors were co-located at the Base Station for the first20 days of the field season. After the field season the moisture sensors were againset up to take co-located measurements at the UBC climate station for an addi-tional 15 days. The first comparison period was used to calculate the biases of thesticks relative to one another. Once these biases were removed, the second com-parison period was used to test the stability of these biases. Here I will focus onreducing the bias during the dry, low-moisture periods with no rain, because these168periods represent the majority of the season and are the most important from a firebehaviour stand point.Pre-field tests also indicated that the LogTags had biases relative to higher-quality sensors. These biases were quantified by comparing the LogTag data tothe data from the co-located high-quality sensors located at Fuel Moisture 1 and2 and the Base Station. Initial analysis indicated that the LogTag biases were notconstant; they changed with the changing humidity and temperature. Moreover,these relationships between the absolute value of the variable and the bias werenon-linear. Therefore, a generalized additive model (GAM) from the R packagemgcv was used to quantify these non-linear relationships. To account for the non-linear relationships, these variables were first passed through a thin plate regressionspline smoothing function. The amount of smoothing was chosen automaticallythrough cross validation. These models were then used to estimate the bias at eachtime step which was then removed from the LogTag data.A.2 ResultsA.2.1 Logtag bias correctionsBased on the two comparison periods, the individual systematic biases of the Log-Tags were stationary throughout the field season, and were within the± 1◦C and±5 % humidity instrument error reported by the manufacturer. Individual humidityand temperature biases averaged across both periods were therefore removed fromeach LogTag before further analysis.Figure A.1 provides a comparison between all Rotronic and uncorrected Log-Tag observations taken at these three sites. The smoothed function fitted by theGAM model is also shown. The humidity bias is most prominent at the highervalues where the LogTag sensors underpredict by a few percentage points. Con-versely, the LogTag sensors overpredict temperature especially at the higher values.This is reflected in the comparison statistics shown in Table A.1.Once the GAM-modelled errors were removed the comparison statistics im-proved, with most of the improvement seen in the biases. Example relative hu-midity time-series are shown in Figure A.2 for both pre and post adjustment while169error statistics are provided in Table A.1. The root mean square errors saw marginalimprovements while the correlations did not change. This is expected as it is ev-ident from Figure A.1 that much of the error is due to the spread rather than anysystematic bias. It is likely that the slower response time of the LogTag sensorsis responsible for much of this error. However, as we are primarily interested indaily ranges and seasonal trends, this error will not impact the final results of thisanalysis.Figure A.1: Comparison of all co-located LogTag and Rotronic temperatureand relative humidity observations. The red line is the smoothed GAMfunction. A 1:1 line is provided for reference.Table A.1: LogTag vs. Rotronic comparison statistics for both relative hu-midity and temperature. Values provided for before and after the biasadjustment.Relative Humidity TemperatureBias Cor. RMSE Bias Cor. RMSE(%) (%) (oC) (oC)Pre-Adj. -0.68 0.98 5.16 0.28 0.99 1.09Post-Adj. 0.00 0.98 4.79 -0.00ww 1.00170Figure A.2: Example relative humidity measurements by the Rotronic andLogTag sensor at the Base Station along with bias-adjusted LogTagdata.A.2.2 Fuel moisture sensor bias correctionsA comparison of un-adjusted co-located fuel moisture data from all three sensors ispresented in Figure A.3. Below the fibre saturation point of 30% moisture content,where liquid water begins to form on the surface of the sticks, the sensors trackeach other very closely with correlations between 0.94 and 0.98. Sensors 1 and 3show little bias between each other (.11 %) while sensor 2 has a consistent negativebias relative to the other two sensors (-3.2 % and -3.1 %). Above the fibre satura-tion point the sensors are much less consistent: the correlations between sticks arelower (r ranges from 0.86 to 0.94) and no one stick shows a consistent bias com-pared to the others. However, the late-season comparison period shows much moreagreement above the fibre saturation point compared to the early-season period.This may be due to the relatively modest rainfall amount during the late-seasonperiod, i.e., as the sensors approach the saturation point of around 60%, agreement171diminishes substantially.Figure A.3: Early and late-season comparison of co-located moisture sensorsbefore bias adjustment.Biases from an inter-sensor mean were calculated for each sensor using theearly-season data. These biases were then removed from the late-season data andcomparison statistics were calculated. In general, when below the fibre saturationpoint, biases between sensors seemed to be consistent over the season, althoughover the course of the season the spread between sensors increased slightly. Whenthe early-season biases were removed the remaining late-season biases between172sensors ranged from 0.18 to 0.65%.Because the biases seemed to be consistent over the season, I calculated season-wide sensor biases from the inter-sensor mean using both comparison periods andremoved these biases from data. Because the periods below the fibre saturationpoint represent the majority of the season and are the most significant to this re-search, I calculated these biases using just the data below the fibre saturation point.Comparison statistics after removing these biases are presented in Table A.2. Theroot mean square error between sensors ranges from 1.52 to 2.25%. The adjustedfuel moisture time-series are shown in Figure A.4.Table A.2: Intercomparison of moisture sensors after the bias adjustment us-ing both comparison periods. Statistics are calculated for data below andabove the Fibre Saturation Point as well as for all the data. Comparisonsare made between sensors 1 and 2 (‘1v2’), 1 and 3 (‘1v3’) and 2 and 3(‘2v3’).Correlation Bias (%) RMSE (%)1v2 1v3 2v3 1v2 1v3 2v3 1v2 1v3 2v3Above FSP 0.94 0.86 0.89 -0.48 4.52 5.00 3.52 6.47 6.79Below FSP 0.98 0.94 0.96 0.00 0.00 0.00 1.52 2.25 1.52All Data 0.99 0.97 0.98 -0.12 1.14 1.26 2.20 3.78 3.65173Figure A.4: Early and late-season comparison of co-located moisture sensorsafter bias adjustment.174Appendix BFuel moisture model detailsB.1 Stick specific heat calculationFollowing Wilkes (1979) the change in cs with moisture and temperature is calcu-lated as:cs =cwood +mcwater1+ms+ cbound (B.1)where m is the average stick moisture, cwater(4200 J K−1 kg−1) is the specific heatof water, and cwood , the specific heat of dry wood, is estimated as :cwood = 103.1+3.867Ts (B.2)cbound accounts for the energy absorbed by the bound water below the fibre satura-tion point and is given as an empirical function of temperature and moisture:cbound ={ (23.55Ts−1320ms−6191)ms : ms < m f sp0 : ms ≥ m f spB.2 Division of shortwave radiation into diffuse anddirect componentsThe ratio of diffuse to total radiation is:175Kd,di f fKd=1.0−0.09n n≥ 0.220.951−0.1604n+4.388n2−16.638n3+12.336n4 0.22 > n≥ 0.800.165 n > 0.80where n, the clearness index, is calculated as the ratio Kd/Kd,max, where Kd,max isthe theoretical maximum solar radiation achievable under a cloud free sky and iscalculated as:Kd,max = Ksolarτ p/psea−level sinφ (B.3)where Ksolar is the solar constant (1367 W m−2), τ is the atmospheric transmissivitywhich is set to 0.75, p and psea−level are the pressure at the site and at sea-level,respectively, and φ is the solar elevation angle.The downwelling longwave radiation, Ld (W m−2), is calculated by estimatingan atmospheric emissivity, ε . Following Prata (1996) we can first calculate a clearsky emissivity, ε0 as:εclear−sky = 1− (1+w)exp(− (1.2+3.0w)0.5) (B.4)where w is the precipitable water content (cm) which is estimated as:w = 465(M qaR)(B.5)We need to account for cloudiness to estimate a final atmospheric emissivity,εa, from the clear-sky case, εclear−sky. Following Arnold et al. (1996), this can bedone by using the clearness index, n, calculated above. Specifically, εa is calculatedas:εa = (1+βm)εclear−sky (B.6)where m is the cloudiness factor and β is a constant based on cloud type. β is takento be a constant value of 0.26 which is an average value for a variety of cloud types(Braithwaite and Olesen, 1990). m is calculated from n:176m ={1−n : n > 0.21 : n≤ 0.2B.3 Absorbed radiationTo calculate the diffuse radiation absorbed by the cylindrical fuel sticks, Labs andKabs,di f f (W), we will first assume that all incoming diffuse radiation is isotropic.We can then integrate the equation for the intensity of diffuse radiation on a inclinedplane over the surface of the cylinder.Iqbal (1983) provided the diffuse radiation intensity, I (W m−2), for an inclinedplane exposed to both upwelling and downwelling isotropic diffuse radiation:Id = I12(1+ cosθ), Iu = I12(1− cosθ) (B.7)where θ is the angle relative to the horizontal. We apply these two equations to theinfinitesimal segment in Figure B.1. For the upper half of the cylinder the radiationabsorbed, Iabs,top (W), will be:Iabs,top = I∫ pi/201+ cos(pi/2−θ)lrdθ (B.8)The symmetry of the problem allows us to double the integral from 0 to pi/2 (whichcancels out the 1/2 factor in equation B.7). For the lower half we use the samegeometry as in Figure B.1 but we take the radiation to be upwelling towards theinfinitesimal segment (i.e., we flip the geometry around the horizontal axis). There-fore, the limits of integration remain the same but we use the equation for Iu instead:Iabs,bott = I∫ pi/201− cos(pi/2−θ)lrdθ (B.9)The total absorbed diffuse radiation, Iabs, (in J s−1) is then:177Iabs = Iabs,bott + Iabs,top+ Iabs,edge =lrI∫ pi/202dθ + I2pir2 = I(pilr+2pir2) (B.10)Iabs,edge is the power absorbed by both stick edges and is derived by applying equa-tion B.7 to those vertical faces. We can apply this result to our problem, and calcu-late the shortwave and longwave diffuse radiation absorbed by the stick using theterms defined in section ??:Labs = (pilr+2pir2)es(Ld +Lu) (B.11)Kabs,di f f = (pilr+2pir2)(1−αs)(Kd,di f f +Ku) (B.12)dx	=	r	dqg =	p /2	-qqdqrFigure B.1: Integral geometry for the absorption of diffuse radiation by thefuel moisture stick.178Appendix CSupplementary information forChapter 61790400 Hour1600 Hour0102001020Jun Jul Aug SepBias in ERC Wind Adj. Factor0.110Figure C.1: Change in ERC at the Base Station resulting from the adjustmentof wind speed by constant factors of 0.1 and 10.180l lllllllll lllllAfternoon RHNighttime RH05100510Jun Jul Aug SepRH Standard Deviation (%)0.0 2.5 5.0 7.5 10.0Daily Precip (mm)Varying Factors l l l lCanopy / Radiation Load / Elevation Canopy Elevation Radiation LoadFigure C.2: Standard deviations of afternoon and nighttime relative humidityacross the entire study region. The results from four different simula-tions are shown here: three runs in which all but one of the three spatialfactors were kept constant, and one when all three factors varied acrossthe landscape. The points indicate the two days which are shown asrasters in Figures 6.8 and 6.9181l lll ll lllll ll lllAfternoon TemperatureNighttime Temperature0123401234Jun Jul Aug SepTemperature Standard Deviation (%)0.0 2.5 5.0 7.5 10.0Daily Precip (mm)Varying Factors l l l lCanopy / Radiation Load / Elevation Canopy Elevation Radiation LoadFigure C.3: As in Figure 6.7, but for temperature1822014−07−26 2014−08−03All FactorsCanopy GapRadiation LoadElevation2530354045Afternoon RH (%)Figure C.4: Rasters of afternoon relative humidity for two different days(columns, indicated in Figure 6.7). Rasters driven by all factors, andthe three factors individually (rows) are provided.1832014−07−26 2014−08−03All FactorsCanopy GapRadiation LoadElevation6080100Nighttime RH (%)Figure C.5: As in Figure 6.8, but for nighttime relative humidity.1842014−07−26 2014−08−03All FactorsCanopy GapRadiation LoadElevation20242832AfternoonTemperature (oC)Figure C.6: As in Figure 6.8, but for afternoon temperature1852014−07−26 2014−08−03All FactorsCanopy GapRadiation LoadElevation5101520NighttimeTemperature (oC)Figure C.7: As in Figure 6.8, but for nighttime temperature.186


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