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Predicting time-since-fire from forest inventory data in Saskatchewan, Canada Schulz, Rueben J. 2008

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PREDICTING TIME-SINCE-FIRE FROM FOREST INVENTORY DATA IN SASKATCHEWAN, CANADA by Rueben James Schulz B.Sc.F., The University of British Columbia, 2001 Dipl. T., The British Columbia Institute of Technology, 2002  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in  THE FACULTY OF GRADUATE STUDIES (Forestry)  THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver)  December 2008  © Rueben James Schulz, 2008  Abstract Time-since-fire data are used to describe wildfire disturbances, the major disturbance type in the Boreal forest, over a landscape. These data can be used to calculate various parameters about wildfire disturbances, such as size, shape and severity. Collecting time-since-fire data is expensive and time consuming; the ability to derive it from existing forest inventory data would result in availability of fire data over larger areas. The objective of this thesis was to explore the use of forest inventory information for the prediction of time-since-fire data in the mixedwood boreal forests of Saskatchewan. Regression models were used to predict time-since-fire from forest inventory variables for each inventory polygon with a stand age. Non-water polygons with no stand age value were assigned values from neighbouring polygons, after splitting long polygons that potentially crossed many historic fire boundaries. This procedure filled gaps that prevented polygons from being grouped together in latter analysis. The predicted time-since-fire ages were used to generate wildfire parameters such as age-class distributions and fire cycle. Three methods were examined to group forest inventory polygons together to predict fire event polygons: simple partitions, hierarchical clustering, and spatially constrained clustering. The predicted fire event polygons were used to generate polygon size distribution wildfire metrics. I found that there was a relationship between time-since-fire and forest inventory variables at this study site, although the relationship was not strong. As expected, the strongest relationship was between the age of trees in a stand as indicated by the inventory and the time-since-fire. This relationship was moderately improved by including tree species composition, harvest modification value, and the ages of the surrounding polygons. Assigning no-age polygons neighbouring values and grouping the forest inventory polygons improved the predicted time-since-fire results when compared spatially to the observed time-since-fire data. However, a satisfactory method of comparing polygon shapes was not found, and the map outputs were highly dependent on the grouping method and parameters used. Overall it was found that forest inventory data did not have sufficient detail and accuracy to be used to derive high quality time-since-fire information.  ii  Table of Contents Abstract .......................................................................................................................................................... ii Table of Contents .......................................................................................................................................... iii List of Tables.................................................................................................................................................. v List of Figures ............................................................................................................................................... vi Acknowledgments ........................................................................................................................................ vii 1 Introduction ................................................................................................................................................. 1 1.1 Background .......................................................................................................................................... 1 1.1.1 Ecosystem Management ................................................................................................................ 1 1.1.2 Time-Since-Fire Data and Wildfire Parameters ............................................................................ 3 1.2 Objectives............................................................................................................................................. 5 1.3 Thesis Organization.............................................................................................................................. 5 2 Methods ....................................................................................................................................................... 7 2.1 Study Area............................................................................................................................................ 7 2.2 Data ...................................................................................................................................................... 9 2.2.1 Time-Since-Fire Data .................................................................................................................. 10 2.2.2 Forest Inventory Data .................................................................................................................. 11 2.3 Analysis .............................................................................................................................................. 14 2.3.1 Data Preparation .......................................................................................................................... 14 2.3.2 Descriptive Data Analysis ........................................................................................................... 18 2.3.3 Prediction Modelling ................................................................................................................... 18 2.3.4 Fire Cycle Calculations ............................................................................................................... 22 2.3.5 Grouping Inventory Polygons into Fire Events ........................................................................... 22 3 Results ....................................................................................................................................................... 26 3.1 Descriptive Data Analysis .................................................................................................................. 26 3.2 Prediction Modelling .......................................................................................................................... 28 3.2.1 Single-Age Prediction Models..................................................................................................... 28 3.2.2 Multi-Age Prediction Models ...................................................................................................... 30 3.2.3 No-Age Models ........................................................................................................................... 31 3.3 Model Application.............................................................................................................................. 32 3.4 Fire Cycle Calculations ...................................................................................................................... 35 3.5 Grouping Inventory Polygons into Fire Events .................................................................................. 36 4 Discussion ................................................................................................................................................. 46 4.1 Descriptive Data Analysis .................................................................................................................. 46 4.2 Prediction Modelling .......................................................................................................................... 49 4.2.1 Regression Models ...................................................................................................................... 49 4.2.2 No-Age Models ........................................................................................................................... 51 4.2.3 Model Evaluation and Use........................................................................................................... 52 4.3 Grouping Inventory Polygons into Fire Events .................................................................................. 53 5 Summary and Conclusions ........................................................................................................................ 56 5.1 Summary of Findings ......................................................................................................................... 56 5.2 Future Research Opportunities ........................................................................................................... 56 5.3 Conclusion.......................................................................................................................................... 57 References .................................................................................................................................................... 59  iii  Appendix 1 Forest Inventory Codes in Presented Models............................................................................ 64 Appendix 2 Regression Model Parameters................................................................................................... 65 Single-age Regression Model Parameters ................................................................................................ 66 Multi-age Regression Model Parameters.................................................................................................. 68 Appendix 3 Regression Model Residuals..................................................................................................... 69 Single-age Regression Model Residuals .................................................................................................. 69 Multi-age Regression Model Residuals.................................................................................................... 71 Appendix 4 Fire Event Groups..................................................................................................................... 73  iv  List of Tables Table 2-1: Percent area covered by the leading tree species in the forest inventory dataset. ........................14 Table 2-2: Inventory groups for modelling and descriptive analysis.............................................................16 Table 2-3: Single-age regression model variables.........................................................................................20 Table 2-4: Additional multi-age regression model variables.........................................................................20 Table 2-5: Output fire events from grouped forest inventory polygons. .......................................................23 Table 3-1: Comparison between inventory age and time-since-fire age values for different subsets of the data. ...........................................................................................................................................26 Table 3-2: Single-aged models for predicting time-since-fire and fit statistics. See Table 2-3 for variable descriptions........................................................................................................................29 Table 3-3: Multi-age models for predicting time-since-fire and fit statistics. See Table 2-3 and Table 2-4 for variable descriptions............................................................................................................31 Table 3-4: RMSE for four methods of assigning neighbouring values, by no-age inventory category. .........................................................................................................................................................32 Table 3-5: Fire frequency estimates for observed time-since-fire age, oldest forest inventory age, and predicted time-since-fire age. ...................................................................................................35 Table A1-1: Definitions of the forest inventory modification codes. ............................................................64 Table A1-2: Definitions of tree species codes. ..............................................................................................64 Table A2-1: Regression model parameters for the single-aged models. .......................................................66 Table A2-2: Regression model parameters for the single-aged models, continued.......................................67 Table A2-3: Regression model parameters for the multi-aged models..........................................................68 Table A2-4: Regression model parameters for the multi-aged models, continued........................................68 Table A4-1: Output groupings from the simple 10-year partition with no-age values assigned. ..................73 Table A4-2: Output groupings from the hierarchical cluster with a 5-year cluster width. ............................73 Table A4-3: Output groupings from the hierarchical cluster with a 10-year cluster width. ..........................74 Table A4-4: Output groupings from the spatially constrained hierarchical cluster with a distance penalty weight of 0.0002.................................................................................................................74 Table A4-5: Output groupings from the spatially constrained hierarchical cluster with a distance penalty weight of 0.0005.................................................................................................................74 Table A4-6: Output groupings from the spatially constrained hierarchical cluster with a distance penalty weight of 0.001...................................................................................................................75  v  List of Figures Figure 2-1: Study area location. ......................................................................................................................7 Figure 2-2: Ecodistricts within the study area (black boundary). ....................................................................8 Figure 2-3: Time-since-fire data symbolized by predominant fire year. .......................................................11 Figure 2-4: Forest inventory data symbolized by the oldest origin year........................................................13 Figure 2-5: Three inventory polygons on either side of a fire boundary (black line) labeled with their overlap area ratios. All three polygons had overlap area ratios below the threshold and were not used for model building. ...........................................................................................................17 Figure 2-6: Assigning no-age polygons predicted time-since-fire values from neighbours, after splitting............................................................................................................................................20 Figure 3-1: Origin-class distributions for the forest inventory and time-since-fire datasets..........................27 Figure 3-2: Polygon size distributions for the forest inventory and time-since-fire datasets.........................28 Figure 3-3: Fitted line plot between time-since-fire age and the maximum inventory age (solid) and a 1 to 1 line (dotted), for single-aged polygons. Random noise, from a uniform distribution between ± 5, was added to the age variables to spread them out and to make them visible. ..........30 Figure 3-4: Map of predicted time-since-fire age for the entire study area. ..................................................33 Figure 3-5: Origin-class distributions, in 10-year classes, for the observed time-since-fire and predicted time-since-fire ages. ........................................................................................................34 Figure 3-6: Polygon size distributions for the observed time-since-fire, predicted time-since-fire, and forest inventory polygons with age values. ..............................................................................34 Figure 3-7: Time-since-fire estimated from a negative exponential model fitted to the observed time-since-fire age, oldest forest inventory age, and predicted time-since-fire age. .......................36 Figure 3-8: Map of observed time-since-fire (a), simple 10-year partitioning (b), 5-year hierarchical clustering (c), 10-year hierarchical clustering (d), constrained clustering with a 0.001 distance penalty (e), and constrained clustering with a 0.0005 distance penalty (f). ......................37 Figure 3-9: Polygon size distributions for partitioned predicted time-since-fire (with and without no-age values) and partitioned oldest forest inventory ages............................................................38 Figure 3-10: Origin-class distributions, in 10-year classes, for partitioned predicted time-since-fire (with and without no-age values) and partitioned oldest forest inventory ages. .............................39 Figure 3-11: Map of predicted fire ages, grouped with a simple 10-year partition, with (a) and without (b) no-age values filled in, in the southwest corner of the study area. ...............................40 Figure 3-12: Polygon distributions for hierarchical clusters and simple 10-year partition............................41 Figure 3-13: Origin-class distributions, in 10-year classes, for hierarchical clusters and simple 10-year partition. .............................................................................................................................43 Figure 3-14: Polygon distributions for spatially constrained clusters............................................................44 Figure 3-15: Origin-class distributions for spatially constrained clusters, in 10-year classes. ......................45 Figure A3-1: Single-age model 1 residual values..........................................................................................69 Figure A3-2: Single-age model 2 residual values..........................................................................................69 Figure A3-3: Single-age model 3 residual values..........................................................................................69 Figure A3-4: Single-age model 4 residual values..........................................................................................69 Figure A3-5: Single-age model 5 residual values..........................................................................................70 Figure A3-6: Single-age model 6 residual values..........................................................................................70 Figure A3-7: Single-age model 7 residual values..........................................................................................70 Figure A3-8: Single-age model 8 residual values..........................................................................................70 Figure A3-9: Single-age model 9 residual values..........................................................................................70 Figure A3-10: Single-age model 10 residual values......................................................................................70 Figure A3-11: Multi-age model 1 residual values. ........................................................................................71 Figure A3-12: Multi-age model 2 residual values. ........................................................................................71 Figure A3-13: Multi-age model 3 residual values. ........................................................................................71 Figure A3-14: Multi-age model 4 residual values. ........................................................................................71 Figure A3-15: Multi-age model 5 residual values. ........................................................................................72 Figure A3-16: Multi-age model 6 residual values. ........................................................................................72 Figure A3-17: Multi-age model 7 residual values. ........................................................................................72 Figure A3-18: Multi-age model 8 residual values. ........................................................................................72  vi  Acknowledgments There are many people I would like to thank for helping me complete this thesis. Thank you Dr. Peter Marshall, my thesis supervisor, for encouraging me to finish and for prompt editorial feedback on draft documents. Also, I was greatly aided by the feedback on the first draft from Dr. Valerie LeMay and Dr. David Tait. I would also like to thank Dr. David Andison for providing the project that this work was based on, and Marie-Pierre Rogeau and the field crews for collecting the time-since-fire data. A Natural Sciences and Engineering Research Council of Canada (NSERC) scholarship and funding from the Sustainable Forest Management Network (SFMN) were also greatly appreciated and helped to make this work possible. Finally, I would like to thank Dr. Cindy Prescott for granting me an extension to finish this thesis and to Forest Ecosystem Solutions Ltd. for allowing me to spend the fall finishing it instead of working.  vii  1 Introduction 1.1 Background 1.1.1 Ecosystem Management Recent trends in forest management have been towards incorporating more ecosystem management principals (Johnson and Agee 1988, Galindo-Leal and Bunnell 1995, Christensen et al. 1996, Franklin 1997). Ecosystem management involves managing ecosystems to assure their sustainability in terms of ecosystem composition, structure, and function (Christensen et al. 1996, Franklin 1997). Under this style of management, timber products are a secondary consideration and their output is adjusted to meet the primary objective of environmental sustainability (Christensen et al. 1996). The focus on sustainability will ensure long term benefits, but could demand some short term costs such as lower harvests or using more complex silvicultural systems (Cissel et al. 1999). One of the components used in ecosystem management is the natural range of variation (NRV), as this approach recognizes that the processes that generate disturbances should be maintained and used as a coarse filter (Christensen et al. 1996, Tomas 1996, Landres et al. 1999). The NRV is the "ecological conditions, and the spatial and temporal variation in these conditions, that are relatively unaffected by people, within a period of time and geographical area appropriate to an expressed goal" (Landres et al. 1999). One way of quantifying this variation is with the parameters of a disturbance regime. A disturbance regime can be characterized by its frequency, size, and severity. Aside from abiotic differences across a landscape, a disturbance regime is the main driver that creates forest landscapes composed of patches (Franklin and Forman 1987, Bergeron et al. 2002, Andison 2003). The pattern of landscape patches is dependent on the disturbance type and its parameters. Since a coarse filter “establish[es] a set of reserves containing representative examples of all the various types of communities in a given area” (Hunter 1991), the patterns produced by a natural disturbance regime would act as coarse filter. Maintaining historic landscape patterns through historic levels of disturbance will help species adapted to these patterns to survive (Hunter 1991, Galindo-Leal and Bunnell 1995).  1  The pattern at the landscape and stand levels can be directly related to habitat needed by different species. At a stand level, remnants from previous stands, such as snags, create habitat elements necessary for some species (Franklin et al. 1997). The amount of habitat and its spatial arrangement impacts the population levels for different species (Turner 1989, Gustafson 1998, Harrison and Bruna 1999). Therefore, creating the same patterns in the future can help maintain populations and may lead to understanding why species are present on a landscape historically. The approach of focusing on a coarse filter may be more successful, and achievable, given our knowledge limitations, than managing many species individually (Franklin 1993). Using the NRV in management implies using past conditions as a baseline for current management (Christensen et al. 1996, Andison 2003); however, there are limits to this approach. The extremes of historic disturbance regimes, such as high severity, large, frequent fires, will not be mimicked due to political and economic constraints (Andison and Marshall 1999, Cissel et al. 1999, Bergeron et al. 2002). Also, additional goals such as managing for a single endangered species or economic considerations may prevent managers from strictly implementing such a system (Lorimer and White 2003). As Bergeron et al. (2002) stated, “[ecosystem based management] is aimed rather at defining a socially and economically acceptable compromise within the limits of historic variability that will reduce the risk of negatively affecting biodiversity." Information about historic disturbance regimes may be collected from a number of sources. The variety of disturbance regimes across the landscape makes it difficult to extrapolate from one area to another, requiring that this information be collected multiple times (Bergeron et al. 2002). Sources of this information include sedimentary pollen and charcoal, pre-settlement land survey records, descriptions by travelers, naturalists and foresters, reconstruction of disturbance histories in old growth stands, modern records and aerial photos (including time-since-fire records), and computer modelling. Generally, it is necessary to synthesize more than one source of information to correctly describe a disturbance regime (Lorimer and White 2003). Using historic disturbance conditions as a reference for forest management plans has been  2  evaluated to provide guidelines on appropriate patch sizes, rotation ages, and retentions. For example, Cissel et al. (1999) and Bergeron et al. (2002) explored using NRV techniques for fire-dominated ecosystems. They found that employing these techniques can create a management plan with more variety in patch size, rotation ages and overstory retention, at the cost of less harvested volume. Lorimer and White (2003) described pre-settlement disturbance regimes (caused by wind, fire, ice storms, and insects) on forests in northeastern USA. Their work was done to examine the amount of young forest stands over the landscape that was needed for certain endangered species. Ott and Juday (2002) characterized small gap disturbance in Alaska. 1.1.2 Time-Since-Fire Data and Wildfire Parameters The primary historic disturbance in the boreal forests of Saskatchewan has been wildfire. A time-since-fire dataset records the year of the last known stand-replacing fire 1 for areas within a landscape and represents the history of wildfire disturbance for a landscape. Time-since-fire data minimally consist of a series of records each detailing the year, the area, and optionally the location, of the last fires that burned over the entirety of a study area. Non-adjacent fires occurring in the same year are recorded as separate records. Stand replacing fires consume evidence of previous fires limiting time-since-fire datasets to only the last fire for most locations of a landscape. However, the heterogeneous nature of fire behaviour results in some trees surviving a fire disturbance, allowing information to be collected about previous fires for some areas. Time-since-fire data are sometimes displayed as a stand origin map (Johnson 1992). Collecting time-since-fire data is time-consuming and expensive. Data collection often involves delineating fire boundaries from aerial photographs and then collecting extensive ground information to improve the boundaries and assign ages to each fire (Johnson 1992, Andison 1999a, Andison 1999b, Weir et al. 2000, Rogeau 2003). The ground information collected relies on the age of trees that regenerated after the last disturbance and information from any veteran trees that survived the last disturbance. Veteran trees within or beside a disturbance may provide fire scars (from cores and cross-sections) and release 1  The year of the last stand-replacing fire is easily converted to time-since-fire (a.k.a. fire age) by subtracting the year of the fire from a base year.  3  information from cores. A wildfire disturbance regime on a landscape is described by several parameters. Fire cycle (average fire interval) is the time, usually in years, it would take for the area of the entire landscape to be burned by wildfire (Van Wagner 1978, Johnson and Van Wagner 1985). The inverse of fire cycle is the fire frequency or the probability of an area burning per unit time (Johnson and Van Wagner 1985). Disturbance sizes (i.e., the sizes of fire events) is another important wildfire disturbance parameter (Cissel et al. 1999, Bergeron et al. 2002). Finally, fire severity, the level of overstory tree mortality caused by fire (Cissel et al. 1999, Bergeron et al. 2002), is also sometimes used to describe a wildfire disturbance regime. Both disturbance sizes and fire severity are distributions that may also be described by parameters such as the average and variance. Additionally, there are other parameters people have examined at the landscape level that describe the spatial pattern of disturbances (Wier et al. 2000). Time-since-fire datasets are one of the main sources of information for calculating wildfire disturbance parameters, although forest inventory data and the other sources mentioned above may also be used. Aspatial area versus age class curves from time-since-fire or forest inventory ages can be used to calculate the fire cycle (Van Wagner 1978), assuming the forest inventory dataset reflects regeneration from fire disturbances. Time-since-fire or forest inventory datasets may also be used to calculate fire size. Both datasets cannot easily be used to calculate fire severity, since the spatial resolution needed to determine the proportion of trees killed in a fire is usually not present in landscape level datasets. While forest inventories can be used to calculate disturbance parameters, the accuracy of the parameters “relies heavily on spatially complete and accurate stand age data [and] poor or incomplete age data can lead to misrepresentation of age-class structure, patch size distribution, and even patch shapes” (Andison 1999a). Previous projects were undertaken to collect time-since-fire data and to derive fire disturbance parameters in the boreal forest. For example, complete time-since-fire datasets were collected in the Boundary Waters Canoe Area (Minnesota), Lake St. Joseph (Ontario), Ruttledge Lake (NWT), and Porcupine River (Alaska) (Johnson 1992). Weir et al. (2000)  4  used time-since-fire to explore how fire frequency changed over time and how the spatial pattern of patches changed throughout Prince Albert National Park, Saskatchewan. Andison (2000) calculated age class distributions and fire frequency, while Andison (2003) compared historic 1950 landscape patterns to 1995 patterns that were affected by human management, using forest inventory and time-since-fire data in the Foothills Model Forest in Alberta.  1.2 Objectives The primary objective of this thesis is to derive time-since-fire information from existing forest inventory datasets in the mixedwood boreal forest of northwestern Saskatchewan. An important secondary objective is to evaluate the usefulness of the derived time-since-fire data for use in ecosystem management, as compared to using the baseline forest inventory age data. The outcome of these objectives is important to people who need wildfire disturbance information in the boreal forest. The expense of collecting time-since-fire data means that it can only be gathered for limited areas. If strong relationships can be established between time-since-fire and forest inventory datasets, then this capability can be used to cheaply generate disturbance parameters from available datasets.  1.3 Thesis Organization This thesis is arranged into five chapters. This chapter contains background information about ecosystem management and time-since-fire datasets. This background explains why time-since-fire data is needed by forest managers and how this information requirement is related to the objectives of this thesis. The second and third chapters contain the methods and results, respectively. The methods chapter overviews the study area and datasets used for the analysis. It also describes the methods used for data preparation, the models used to predict time-since-fire from forest inventory variables, fire cycle calculations, and groupings of forest inventory polygons into fire events. The results chapter presents the outcome of the analyses described in Chapter 2. The fourth chapter contains a discussion of the results. The fifth and final  5  chapter contains some suggestions for future research and some overall conclusions from this thesis.  6  2 Methods 2.1 Study Area The 90,000 ha study site is centered at 109.60 degrees west longitude and 54.65 degrees north latitude (NAD 83 datum). This is northwest of Meadow Lake, Saskatchewan, north of Meadow Lake Provincial Park and south of the Cold Lake Air Weapons Range. Cold Lake, Alberta is outside of the study area to the west (Figure 2-1). The project site falls entirely within Mistik Management Ltd.’s forest management area.  Figure 2-1: Study area location.  Industrial impacts on this region are relatively recent. Limited harvesting started in the 1960s and most natural wildfires have been suppressed since the 1950s. This leaves much of the historic fire history on this landscape intact, making the area suitable for this project. Two different forest ecosystem classifications exist in Saskatchewan: ecoregions (Acton et  7  al. 1998) and forest regions (Rowe 1972). Both systems are used here to describe the ecology of the study area. The study site is located within the Boreal Plains ecozone and the Mid Boreal upland ecoregion (Acton et al. 1998). The lower half of the study area lies within the E10 Mostoos Escarpment ecodistrict, while the upper half lies mostly within the E8 Mostoos Upland ecodistrict (Figure 2-2). A small portion of the northern section of the study area falls within the E9 Primrose Plain ecodistrict. Using Rowe’s 1972 ecosystem classification, the study site is located within the Mixedwood Section of the Boreal Forest Region, the largest forest region in Canada extending from Newfoundland and Labrador to the Yukon. The Mixedwood Section extends from southwest Manitoba to northeastern British Columbia, and is north of the Aspen Grove section, which forms the border between the boreal forest and prairie grassland. The Boreal Mixedwood Section is contained within the Boreal Plains ecozone.  Figure 2-2: Ecodistricts within the study area (black boundary).  8  The relief of the boreal mixedwood is not extreme (Rowe 1972). The southern section of the study area in the Mostoos Escarpment ecodistrict is on the south facing slopes of the Mostoos Hills. These hills range in elevation from 525 m to 750 m. The northern half of the study area within the Mostoos Upland ecodistrict is relatively flat, with the Primrose Plain ecodistrict areas situated at a slightly lower elevation (Acton et al. 1998). The Mid Boreal upland ecoregion experiences a sub-arctic climate (Acton et al. 1998). The nearest climate station is Cold Lake, Alberta, which has a mean (1971-2000) annual temperature of 1.7 C. The coldest monthly average (1971-2000) temperature of -16.6 C was found for January and the warmest monthly average, at 16.9 C, occurred in July. The mean (1971-2000) annual precipitation was 426.6 mm (Environment Canada 2004). The boreal forest is dominated by wildfire (Swan and Dix 1966, Johnson 1992, Bergeron 2000). Overlapping fires have resulted in a mosaic of stands with different times since they last burned (Johnson 1992). This favours tree species that regenerate quickly after fire, such as trembling aspen (Populus tremuloides Michx.) and jack pine (Pinus banksiana Lamb.) (Rowe 1972, Bergeron 2000). The characteristic trees species on well-drained uplands in the mixedwood boreal forest is a mixture of trembling aspen, balsam poplar (Populus balsamifera L.), white birch (Betula papyrifera Marsh.), with white spruce (Picea glauca (Moench) Voss) and balsam fir (Abies balsamea (L.) Mill.) in older stands. Jack pine is present on drier sites, and black spruce (Picea mariana (Mill.) Britton, Stems & Poggenburg) and tamarack (Larix laricina (Du Roi) K. Koch) are present on wetter sites (Rowe 1972, Swan and Dix 1966, Acton et al. 1998).  2.2 Data Two datasets were used in this analysis: (1) time-since-fire and (2) forest inventory. Both datasets were provided as 12, 10 by 10 km, mapsheets with accompanying attribute data. These mapsheets were combined to form each of the datasets. A NAD 83, UTM zone 12 coordinate reference system was used for both.  9  2.2.1 Time-Since-Fire Data The time-since-fire dataset was produced in two phases, primarily during the summer of 2002 2 . In the first phase, aerial photos were used to establish possible fire boundaries and to determine where ground plots should be located. The second phase used ground plots where tree measurements were recorded. Final delineation of the fire boundaries was recorded on mylar mapsheets, using 2001 forest inventory orthophotos (1:12,500 scale) as a base (Rogeau 2003). The mapsheets were digitized in April 2003. Fire boundary mapping was done using 1:60,000 scale aerial photos from 1954 for the entire area and 1:20,000 scale photos from 1949 for the more complex eastern portion. Different textures and patterns in the imagery, along with knowledge of how fires spread, were used by the interpreter to locate fire boundaries (Rogeau 2003). Areas for which the interpreter needed a fire age, or was unsure about the boundary, were targeted for ground sampling (Rogeau 2003). In total, 223 stands were visited. At each stand, four or five trees were sampled for their age since germination. Most of the samples collected were increment cores, but some cross-sections of fire scared trees were also taken. Tree ages that were measured 20 cm or more above the ground were corrected to ground age by applying developed correction factors. Ages were measured in a lab using a microscope and release information was also determined from the cores. The collected information was used to generate the fire history for each plot location and a list of fire ages for each mapsheet. The time-since-fire dataset showing the year of the last wildfire is displayed in Figure 2-3. Where evidence was available (e.g., fire scars), up to two earlier fire dates for a location were also recorded. The dataset contained 940 polygons (covering approximately 90,800 ha), 68 of which were lakes (covering approximately 2,500 ha). Of the remaining 872 polygons, 811 had a single time-since-fire age (covering approximately 83,500 ha), 40 had two time-since-fire ages (covering approximately 2,800 ha) and 21 had three time-since-fire ages (covering approximately 2,100 ha). The oldest fire recorded in the  2  A pilot study was conducted during the summer of 2001 on a small portion of the overall area to refine the sampling methodology employed.  10  dataset was from 1790, determined from a tamarack in a heavily treed muskeg (Rogeau 2003). The youngest recorded fire was from 1945; after this point, fire suppression effectively controlled most fires on this landscape. The smallest polygon distinguished in the time-since-fire dataset was 0.08 ha, with 185 polygons below 1 ha in size.  Figure 2-3: Time-since-fire data symbolized by predominant fire year.  2.2.2 Forest Inventory Data Forest inventories contain information about forest conditions needed by resource managers and researchers. They typically include information about tree species composition, age, height, and density. Information may also be recorded about silvicultural treatments and other interventions of interest to forest managers. The forest inventory data used in this project were provided by Mistik Management Ltd. and collected by Silvacom Ltd. These data were collected using photographic interpretation of 1:15,000 scale aerial photographs, with some ground plots used for calibration and additional data collection. Generally photo-interpreters use the colour and  11  texture of areas within a photograph, along with an understanding of the disturbance history of the landscape, to demarcate similar areas into polygons. While some polygon characteristics such as tree species can be assessed from the air photo, others like herb species require ground surveys (Saskatchewan Environment 2004). The records in the forest inventory dataset were collected in 2002 and conform to the Saskatchewan Forest Vegetation Inventory (SVI) standard (Saskatchewan Environment 2004). The forest inventory divided the landbase into homogeneous stands (polygons) and recorded information for each polygon and for layers within each polygon. The layers recorded for each forest inventory polygon included up to: three tree layers, a shrub layer, an herb layer, and an aquatic layer. Attributes of each tree layer included crown closure, height, origin year, and canopy pattern class. Origin years were usually recorded in 10-year classes, with a few origins recorded to an exact year. Each tree layer recorded up to six tree species and their accompanying percent cover. While the inventory standard allows for up to three origin years and 18 species to be recorded for each polygon, stands will typically only have one or two layers and a few species. The shrub and herb layers may contain up to 10 species, while the aquatic layer was limited to three species. Information about human land-use, non-forest descriptions (e.g., water), and stand disturbance (modification) values were also provided for each inventory polygon. Disturbances values record human activities or natural disturbances that occurred within an inventory polygon within the last 30 years and are described in Table A1-1 in Appendix 1. The minimum mapping unit (MMU) for the SVI standard varied between 1 and 10 hectares and was a function of the difference between a potential inventory polygon and adjacent areas. As the size of a potential polygon decreases, the difference between it and its neighbours must increase for it to be separated and mapped as an individual polygon. The minimum size of polygons distinguished in the inventory was 1 ha for water bodies and clearings. For other situations, the minimum mapping unit can be 4 ha, if two characteristics differ between adjacent areas, or 10 ha if one characteristic differs. These characteristics include age differences of 20 years, canopy closure differences of 20 percent, and tree height differences of 3 m.  12  The forest inventory dataset contained 10,299 polygons (covering approximately 90,700 ha) that covered the same region as the time-since-fire dataset (Figure 2-4). Of these polygons, 339 (about 3,500 ha) had a non-forest or land-use attribute, meaning they were roads, lakes, rivers, flooded areas, gas lines, mining areas, or built-up areas. Not including the non-forest or land-use polygons, 1458 polygons (approximately 9400 ha) had no primary tree species recorded, and hence no stand origin values. These polygons were mostly (all but 14.7 ha) covered by aquatic, shrub or herb species, and many had a modification value recorded. Overall, 4,721 inventory stands had a single age value (approximately 38,200 ha), 3,342 stands had two age values (approximately 32,700 ha), and 439 had three origin age values recorded (about 6,800 ha). The breakdown of the leading species (the species with the largest crown closure in the tallest tree layer) in the forest inventory dataset is displayed in Table 2-1.  Figure 2-4: Forest inventory data symbolized by the oldest origin year.  13  Table 2-1: Percent area covered by the leading tree species in the forest inventory dataset. Leading Tree Species Trembling Aspen Jack Pine Tamarack Black Spruce White Spruce Balsam Poplar White Birch None  Scientific Name Populus tremuloides Michx. Pinus banksiana Lamb. Larix laricina (Du Roi) K. Koch Picea mariana (Mill.) Britton, Sterns & Poggenburg Picea glauca (Moench) Voss Populus balsamifera L. Betula papyrifera Marsh.  Percent of Study Area 44.3 15.8 11.5 10.6 2.7 0.4 0.1 14.6  2.3 Analysis There were four main steps for predicting time-since-fire ages for the inventory polygons and grouping them into fire events. First the forest inventory was classified into four categories: single-age, multi-age, no-age, and water. Next, regression models were built to predict time-since-fire values for the single-age and multi-age polygons. The third step was to assign a time-since-fire value for the no-age polygons using the predicted time-since-fire values of neighbouring single-age or multi-age polygons. Lastly, the forest polygons were grouped into clusters, based on their predicted time-since-fire values, to create fire event polygons. Data manipulation, regression modelling, and clustering were completed using SAS software (SAS Institute Inc. 2000). Spatial operations were done using tools and custom scripts within the ArcGIS 8.3 geographic information system (GIS) 3 (Environmental Systems Research Institute, Inc. 2004). 2.3.1 Data Preparation For of the purpose of describing the data and modelling, the forest inventory dataset was partitioned into four major categories: (1) single-aged inventory polygons; (2) multi-aged inventory polygons; (3) inventory polygons with no ages; and (4) water polygons. Water polygons, such as rivers and lakes were excluded from this analysis since they are not  3  A GIS is a computer system used to display, store, and manipulate spatial data (Heywood et al. 1998).  14  predicted to burn. The determination of the number of ages in an inventory polygon was done after removing young tree layers and by classifying ages into 10-year age classes. The age of an inventory polygon’s tree layer was calculated as the year of the inventory origin subtracted from a base year of 2000. To remove the effect of recent disturbances from the forest inventory, forest inventory polygon tree layers with an age less than a threshold of 31 years (1969) were removed from the polygon before classifying the polygon into one of the three non-water categories. The threshold was chosen as the age of the air photos used for fire boundary mapping (1949) plus 20 years to cover regeneration delay. It recognises the fact that inventory polygons with ages younger than this threshold likely resulted from logging or a non-historic wildfire disturbance. Additionally, forest inventory polygon tree layers with ages recorded to an exact year were assigned to a 10-year decadal class before the classification was done. Single-aged inventory polygons had the same age for all of their layers, after removing layers below the young age threshold. Multi-aged inventory polygons had more than one age value in their layers. Polygons with no ages generally were young stands that were recently disturbed (i.e., with a tree layer younger than the threshold), or were areas without trees (roads, gas lines, muskegs, etc.). Each of the three non-water categories were further divided into three or four sub-categories based on the presence or absence of: (1) tree layer ages less than the young age threshold; and (2) a recorded forest inventory disturbance (modification) value. No-age forest inventory polygons with a young age present were those that had an inventory tree layer with an age less than the 31-year age threshold. All of the polygons with disturbances in the no-age category had tree layers with young ages present, resulting in this category only being divided into three sub-categories. This resulted in the inventory ultimately being divided into the 11 groups shown in Table 2-2. For modelling and analysis purposes, each of these groups was labeled with a sub-category code value.  15  Table 2-2: Inventory groups for modelling and descriptive analysis. Category Single-age  Multi-age  No-age  Water  Young age present no no yes yes no no yes yes no yes yes  Modification recorded no yes yes no no yes yes no no yes no  Sub-Category Code 10 11 12 13 20 21 22 23 30 31 32  Percent Of Total Area 37.01 4.61 0.75 1.12 39.34 1.28 0.03 1.00 11.71 0.06 0.49 2.60  Number of Polygons 4370 261 45 105 3509 71 2 45 1722 13 81 75  To model time-since-fire from the forest inventory inputs, the observed time-since-fire age for each forest inventory polygon was determined. As with the inventory age, the time-since-fire age was calculated as the year of the fire event subtracted from a base year of 2000. To deal with boundary errors in both datasets, which made it difficult to determine which time-since-fire polygon covered each forest inventory polygon, time-since-fire values were rated for each forest inventory polygon. The rating process involved calculating the areas of one or more time-since-fire polygons that overlapped each forest inventory polygon, using an overlay function in a GIS. The ratio of the area of each time-since-fire polygon that overlapped the area of the forest inventory polygon was then calculated for every forest inventory polygon. The time-since-fire age of the time-since-fire polygon with the maximum overlap area ratio was assigned to the forest inventory polygon and used for model creation. Forest inventory polygons having a maximum overlap area ratio below an arbitrary cut-off of 0.8 were excluded from the model building and descriptive analysis, since it was hard to say which fire event covered the inventory polygon. An example of some of the forest inventory polygons that were on either side of a time-since-fire boundary, and hence possessed low overlap area ratios, is shown in Figure 2-5. In the few cases where there was more than one time-since-fire age for a time-since-fire polygon, the most recent fire age was used.  16  Figure 2-5: Three inventory polygons on either side of a fire boundary (black line) labeled with their overlap area ratios. All three polygons had overlap area ratios below the threshold and were not used for model building.  To reduce the number of variables representing tree species in the regression models, primary and secondary tree species were calculated for each forest inventory polygon. The primary species was considered to be the species with the largest percent cover and crown closure, summing over the three inventory layers. The secondary species was that with the second largest percent cover and crown closure, also summed over all three tree layers. The amount of a species in a forest inventory polygon tree layer was calculated as the crown closure (as a ratio) multiplied by the species percent (also as a ratio). Some models employed in the analyses required information about forest inventory ages of neighbouring polygons. The average, minimum, and maximum of neighbouring forest inventory polygon ages were calculated using a script within the GIS that identified the forest inventory polygons adjacent to, within 200 metres of, and within 400 metres of the forest inventory polygon of interest. In cases were there were multiple ages for a neighbouring forest inventory polygon, the oldest age from that polygon was used as the age of the neighbouring forest inventory polygon.  17  2.3.2 Descriptive Data Analysis A descriptive analysis of the differences between forest inventory ages and time-since-fire age was used to provide a baseline with which to compare the modelling results, and to suggest model forms that might be effective. Root mean square error (RMSE), Equation 1, and average differences, Equation 2, were used in the comparison. These measures summarized the differences between the time-since-fire and forest inventory age for each single-age and multi-age category forest inventory polygon that had a determined time-since-fire age (overlap area ratio above 0.8). For multi-age polygons there were more than one age with which to compare, so the inventory age also included the minimum, maximum, and average age of the layers in the polygon, as well as the age of the tree layer with the largest crown closure. n  RMSE =  ∑ (InventoryAge i =1  i  − FireAgei )  [1]  n −1 n  Avg. Difference =  2  ∑ (InventoryAge i =1  i  − FireAgei )  n  [2]  In addition to looking at the difference between the time-since-fire and inventory ages for each polygon, the age and polygon size distributions for the forest inventory and time-since-fire datasets were examined. The time-since-fire and forest inventory age areas, grouped within 10-year age classes, were plotted against one another for the study area. In cases where the forest inventory polygons had more than one age, the oldest age was used. The polygon size (patch) distributions of each dataset were also plotted against one another. 2.3.3 Prediction Modelling  Models were developed to predict time-since-fire ages from the forest inventory data, using the individual inventory polygons as the units of observation. Because different variables were available depending on the number of age variables present in an inventory polygon, the models were split into three groups to match the inventory polygon  18  categories: (1) single-aged inventory polygon models; (2) multi-aged inventory polygon models; and (3) models for inventory polygons with no ages. The union of the outputs from the three model groups resulted in predicted time-since-fire values for the entire vegetated area. Regression models were used to predict the time-since-fire ages for those inventory polygons that had age values (Categories [1] and [2]). The training data used to fit the models for these categories were the subset that had an area overlap ratio greater than 0.8, which allowed the associated fire age to be determined. The fitted models were applied to all forest inventory polygons within these two categories to generate a predicted time-since-fire age for all forest inventory polygons with valid stand ages older than the threshold age of 31 years. The model forms explored were based on various assumptions about relationships between time-since-fire and inventory variables, the patterns seen in scatter plots between these sets of variables, and the results of the descriptive analysis. Most of these models were linear and fit using the GLM procedure in SAS software (SAS Institute Inc. 2000), with categorical inputs treated as dummy variables. Table 2-3 describes some of the variables used in the single-age models. Models for the multi-aged inventory polygons were similar; however, the multiple ages within these polygons allowed additional age-related variables to be used (Table 2-4).  19  Table 2-3: Single-age regression model variables. Variable Name Time-since-fire Age Forest Inventory Age Modification Primary Species Secondary Species Sub-Category Code Avg. Weighted Age (400m)  Variable Definition The first recorded age of the fire event. The only age for a single-aged inventory polygon. Silvicultural modification value (cutover, burn over). Primary species within all inventory tree layers. Secondary species within all inventory tree layers. A division of the dataset based on the presence or absence of modification and young age values below the threshold age. The average age, weighted by area, for forest inventory polygons neighbouring within 400 m. The oldest age was used in the average if neighbouring polygons had more than one age.  Table 2-4: Additional multi-age regression model variables. Variable Name Max. Inventory Age Min. Inventory Age Avg. Inventory Age Large Inventory Age Avg. Oldest Age (400m)  Variable Definition The oldest age of tree layers in an inventory polygon. The youngest age of tree layers in an inventory polygon. The average age for the tree layers in an inventory polygon. The age of the tree layer with the largest crown closure. The average of the oldest age for neighbouring forest inventory polygons within 400 m.  Polygons with no age values (Category [3]) were assigned a predicted time-since-fire age based on the predicted time-since-fire for neighbouring polygons in Categories [1] and [2]. There were two steps in this process: (1) splitting long polygons; and (2) assigning the time-since-fire value based on predicted time-since-fire values of neighbouring polygons. Figure 2-6 illustrates this process for a road polygon, where the road was split into smaller polygons and the neighbouring polygons, four of which are marked with arrows, were used to fill in the age value for the newly created polygons.  Figure 2-6: Assigning no-age polygons predicted time-since-fire values from neighbours, after splitting.  20  Long polygons, such as roads and gas lines, required splitting because they crossed considerable areas of the dataset and possibly many separate fire events. These polygons were split by joining nodes 4 from opposite sides of the polygon to form new boundary lines. The splitting procedure resulted in many smaller polygons being generated from a single large polygon. Once the splitting was done, all of the newly created polygons and the other smaller, unsplit polygons with no ages were assigned a predicted time-since-fire value. The assigned value came from a neighbouring polygon in Categories [1] or [2], which had a predicted time-since-fire value from the regression models. Four methods were explored to assign these values: (1) the largest neighbour; (2) the neighbour with the largest shared boundary; (3) the oldest neighbour; and (4) the youngest neighbour. Where polygons lacked neighbours with predicted time-since-fire values, the assignment was iterative; all polygons with neighbours with predicted values were assigned values first and then the process was repeated for the polygons that did not have an assigned value after the initial pass. This served to make the predictions as complete as possible, and was useful when latter comparing predicted time-since-fire event polygons. The predicted time-since-fire values for the single-age, multi-age, and no-age categories of forest inventory polygons were evaluated by comparing them to the observed time-since-fire values. This comparison was only done on the subset of the inventory polygons with an observed time-since-fire value and an overlap ratio greater than 0.8. The regression models were compared by examining their R2 values, RMSEs (in this case, time-since-fire relative to estimated time-since-fire), and plots of residuals. The four methods used to assign predicted time-since-fire values for polygons with no inventory ages were evaluated by examining the RMSE between the predicted and observed time-since-fire values. Age class distributions of the model outputs were also compared with distributions based on the observed time-since-fire values.  4  A node is a line endpoint that is shared by 3 or more lines that form polygon boundaries.  21  2.3.4 Fire Cycle Calculations  Calculated fire cycle was also used to evaluate model outputs. Area versus age class data from the observed time-since-fire age, predicted time-since-fire age, and oldest forest inventory age were fitted to simple negative exponential models. The negative exponential model assumed that the risk of an area burning did not change over time (Van Wagner 1978). The negative exponential model was fit with a maximum likelihood estimator, which had a fire recurrence parameter (equal to the fire cycle) that was calculated as the sample average of the time-since-fire data (Van Wagner 1978, Johnson and Van Wagner 1985). The average of the time-since-fire data was weighted by the forest inventory polygon areas. Since fire suppression has affected the area since 1950, young age classes are under represented and were removed from the fire cycle calculation as done in Yarie (1981). Fifty five years of age (1945) was used as the cutoff since no historic wildfires were recorded in the time-since-fire dataset younger than this age. Predicted time-since-fire age class distributions for the study area, starting at age 55, were calculated based on the fire cycles from the negative exponential models fitted to the observed time-since-fire age, predicted time-since-fire age, and oldest forest inventory age. These age class distributions were displayed in 10-year classes, with boundaries four years below the mean and five years above it. These boundaries were chosen to match the forest inventory age class boundaries. For calculating the time-since-fire age class distributions, the fitted models were used to predict the proportion of a population that would survive each 10-year period and this proportion was then converted to an area. 2.3.5 Grouping Inventory Polygons into Fire Events  Several partitioning techniques were used to group forest inventory polygons with similar predicted time-since-fire values and locations into fire events. Most of the groupings were based on the predicted time-since-fire values, from the best of the regression model outputs, with the no-age category of polygons given predicted time-since-fire values from their neighbours. One grouping of predicted time-since-fire values did not assign a predicted time-since-fire age to no-age polygons. Another of the output groupings was based on forest inventory ages, with no-age category polygons assigned a forest inventory age from  22  neighbouring polygons. The grouping methods used were: (1) simple 10-year wide partitions; (2) hierarchical clustering; and (3) spatially constrained hierarchical clustering. Adjacent forest inventory polygons assigned to the same group were merged into a single output polygon using a standard GIS dissolve function. The merged output polygons were assigned a time-since-fire using the average predicted time-since-fire (or forest inventory age for the grouping based on inventory ages) from the polygons that were merged into the group. The groupings of forest inventory polygons that were produced and evaluated are listed in Table 2-5. Table 2-5: Output fire events from grouped forest inventory polygons. Source Dataset Forest Inventory Forest inventory with no-age polygons split and filled with neighbouring predicted T-S-F or inventory age values (using the largest shared boundary method)  Grouping Name Predicted T-S-F, simple 10yr partition, no-age not filled Forest Inventory Age, simple 10yr partition  Predicted T-S-F, simple 10yr partition Predicted T-S-F, hierarchical cluster 5yr Predicted T-S-F, hierarchical cluster 10yr Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.001 Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.0005 Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.0002  Description Simple partition of predicted T-S-F age with 10-year classes without no-age polygons having a predicted value Simple partition of forest inventory age with 10-year classes. No-age polygons were assigned neighbouring values (largest shared boundary method) Simple partition of predicted T-S-F age with 10-year classes Hierarchical clustering of predicted T-S-F age with 5-year cluster widths Hierarchical clustering of predicted T-S-F age with 10-year cluster widths Spatially constrained clustering with a 10-year cluster width and distance penalty weight of 0.001 Spatially constrained clustering with a 10-year cluster width and distance penalty weight of 0.0005 Spatially constrained clustering with a 10-year cluster width and distance penalty weight of 0.0002  Simple 10-year partitions were applied to the predicted time-since-fire ages and forest inventory ages as a comparison with other clustering techniques. These partitions divided inventory polygons into equally sized decadal classes based on either their predicted time-since-fire age or their oldest forest inventory age. Class boundaries extended from four years below the mean to five years above it; for example the class boundaries for the 1900 origin-class were from 1896 to 1905, which match the boundaries used for the forest inventory origin classes. For one of the partitions based on the time-since-fire age, the  23  no-age category of polygons were not assigned neighbouring values allowing it to be compared to the other partition that did use neighbouring values to fill in no-age polygons. The partition based on forest inventory ages had values assigned to no-age polygons, but only assigned ages to no-age polygons without any stand age. Young polygons, below the 31-year age threshold, were left in the list of ages that were grouped. Hierarchical and spatially constrained clustering of the entire forest inventory dataset, with split no-age category polygons, was not possible using SAS. Clustering required an n2 distance matrix, where n is the number of polygons, which would contain over 100 million elements for this case. To complete the clustering, the predicted time-since-fire values were rounded to a single year and neighbouring forest inventory polygons with the same year were grouped with a GIS dissolve operation. This grouping step reduced the forest inventory dataset to a size manageable by the SAS cluster procedure, and created an output grouped forest inventory dataset. The SAS clustering procedure allowed the use of an input distance matrix, which only needed to be calculated once and could be re-used. This distance matrix contained the Euclidean distance, measured in years, between each input-grouped forest inventory polygon’s predicted time-since-fire age and every other input polygon’s predicted time-since-fire age. This distance matrix was subsequently modified for use in the spatially constrained hierarchical clustering. Hierarchical clustering used a centroid method (also called group average linkage) to further group the grouped forest inventory polygons based on the similarity of their predicted time-since-fire ages (Manly 1994). This is a multi-step, agglomerative clustering method that starts with each grouped forest inventory polygon in a separate cluster and joins the closest clusters together at each step, until all the data is in one cluster. The centroid method used the average of the predicted time-since-fire ages within a cluster as the value to compare clusters against one another when determining which should be joined. The closest clusters, based on a squared Euclidean distance measure between the average predicted time-since-fire ages for the clusters, were joined at each step in the clustering procedure. In the event of ties, where more than one group could be joined at the  24  same step, the SAS implementation joined the clusters together that had the minimum dataset record number. The output of the clustering procedure was a dendrogram that recorded the distance between each cluster joined at each step of the clustering procedure. A critical distance (referred to in Table 2-5 as cluster width) was used to specify the height on the output dendogram used to group polygon records together. Clusters, which may be individual forest inventory polygons, separated by distances (in time-since-fire age units) over this critical distance were not joined together. The critical distances presented were 5 and 10 years. When the forest inventory polygons in a single cluster were merged into output polygons with a GIS dissolve function, non-adjacent groups of polygons within the same cluster were separated into different output polygons. Spatially constrained hierarchical clustering was employed to force clusters to only group polygons with similar time-since-fire values and similar locations (Legendre 1987, Legendre and Fortin 1989, Gordon 1996). A second distance matrix containing the Euclidean distance, in metres, between all of the grouped inventory polygon centroids (centre coordinate) was calculated. This matrix was then multiplied by a distance penalty weight and the result added to the predicted time-since-fire age distance matrix used in the hierarchical clustering. The resulting distance matrix combined the differences between the predicted time-since-fire ages of input polygons with their differences in spatial locations. This distance matrix was then used as an input to a clustering procedure that used a centroid method to produce an output dendrogram, similar to the hierarchical clustering. The addition of the distance penalty values prevented polygons that were far apart, with similar predicted time-since-fire values, from being clustered together. Three approaches were used to evaluate and compare the output of the groupings to the observed time-since-fire dataset: (1) plots of the area of the landscape versus origin-class; (2) plots of the number of polygons versus size classes; and, (3) visual comparisons of mapped outputs. All plotted origin values were grouped into 10-year classes to simplify the charts presented. Both the area versus origin-class and polygon size class distribution plots do not contain values from polygons that did not have a predicted time-since-fire age, or forest inventory age for the case where grouping was done on inventory age.  25  3 Results 3.1 Descriptive Data Analysis There were a total of 10,299 forest inventory polygons, covering an area of approximately 90,700 ha. Of these, 4,223 single-aged polygons (covering approximately 33,500 ha) and 3,196 multi-aged polygons (covering approximately 32,400 ha) were used in building regression models. A further 989 polygons (approximately 11,400 ha) fell below the 0.8 overlap area ratio and were not used in model creation. There were 1,816 polygons (covering approximately 11,100 ha) in the no-age category. The remainder of the inventory dataset consisted of 75 polygons (approximately 2,400 ha) recorded as lakes or rivers. Summaries of the differences between the observed time-since-fire age and the inventory age values for the same locations (polygon by polygon), broken down by inventory category, are given in Table 3-1. Comparisons were done for the single and multi-age category forest inventory polygons that had an overlap area ratio over 0.8. This provides a baseline for regression model comparisons. For the multi-age polygons, the maximum forest inventory age was closest to the observed time-since-fire age.  Table 3-1: Comparison between inventory age and time-since-fire age values for different subsets of the data. Forest Inventory Category single-age multi-age  combined  Forest Inventory variable compared to Time-since-fire age Forest Inventory Age Max. Inventory Age Min. Inventory Age Avg. Inventory Age Large Inventory Age Max. Inventory Age  Root MSE (years) 18.13 17.48 27.56 19.93 22.08 17.85  Average Difference (years) -11.34 -2.54 -22.41 -12.60 -14.10 -7.65  Number of Polygons Compared 4223 3196  7419  A comparison of the stand origin distributions for the time-since-fire and the forest inventory datasets, for all polygons in the two datasets with origin values, is given in Figure 3-1. The forest inventory contained 8,502 treed polygons with stand origin values. The oldest origin value was used if the forest inventory polygon had more than one age and polygons with a young age, classified into the no-age category, were included in the  26  display. The time-since-fire dataset had 872 polygons with historic fire values and the predominant fire value was used if a polygon had more than one. The origin values in Figure 3-1, and all other origin distribution graphs, are presented in decadal classes having class boundaries extending from four years below the mean to five years above. While this simplifies their presentation, it can hide some of the details of the comparison. The area of the datasets compared may differ; therefore, the percent area, relative to the total area of the dataset presented, within each origin-class is displayed instead of the raw areas. For Figure 3-1, the time-since-fire dataset area displayed is larger than that of the forest inventory dataset. The origin-class distribution of the forest inventory is younger, and shifted to the right, compared to the time-since-fire origins. 50  Observed Time-Since-Fire Forest Inventory Age  Percent of Area  40  30  20  10  0 1790  1800  1830  1840  1850  1860  1870  1880  1890  1900  1910  1920  1930  1940  1950  1960  1970  1980  1990  Origin Class (10-year)  Figure 3-1: Origin-class distributions for the forest inventory and time-since-fire datasets.  Figure 3-2 compares the polygon size distributions in the two datasets. The same set of forest inventory and time-since-fire polygons displayed in Figure 3-1 (i.e., those with an origin value) were included here. As expected, the forest inventory contained more small polygons than the time-since-fire dataset, since it delineated polygons based on more criteria than only their stand-initiating event. Half of the time-since-fire dataset is  27  represented by polygons larger than 10,000 ha, while the largest forest inventory polygons are all less than 5,000 ha. 5000 4570  4000  Number of polygons  Observed Time-Since-Fire Forest Inventory Age 3000  2000  1877  1798  1000  332  321 122  197 32  34 52  16 8  80 to 200  200 to 600  8  0  3  0  0  4  0  0  0 0 to 2  2 to 10  10 to 40  40 to 80  600 to 2000 2000 to 5000  5000 to 10000  10000 +  Polygon Size Class (ha)  Figure 3-2: Polygon size distributions for the forest inventory and time-since-fire datasets.  3.2 Prediction Modelling 3.2.1 Single-Age Prediction Models  The continuous and categorical variables used in the single-aged regression models and the fit statistics for the models are shown in Table 3-2. There were 4,223 forest inventory polygons in the single-age category with an overlap area ratio over 0.8 that were used for fitting the regression models. Estimated parameters for these models are provided in Tables A2-1 and A2-2 in Appendix 2 and plots of residuals for these models are in Figures A3-1 to A3-10 in Appendix 3. None of the single-age regression models were strong predictors of the variation in the observed time-since-fire ages. There was unequal variance shown in all of the residual plots. Of the ten models presented, single-age model [8] had the lowest RMSE, and was a simpler model than single-age model [9], although the latter had a slightly higher R2 value. Single-age model [8] was the model that was applied for predicting time-since-fire for all single-age category polygons. 28  Table 3-2: Single-aged models for predicting time-since-fire and fit statistics. See Table 2-3 for variable descriptions. Model #  Model Variables  R2  1 2 3 4 5 6 7 8  Forest Inventory Age Forest Inventory Age, Modification Forest Inventory Age, Sub-Category Code Forest Inventory Age, Primary Species Forest Inventory Age, Secondary Species Forest Inventory Age, Primary Species, Secondary Species Forest Inventory Age, Avg. Weighted Age (400m) Forest Inventory Age, Avg. Weighted Age (400m), Modification Forest Inventory Age, Avg. Weighted Age (400m), Modification, Primary Species Avg. Weighted Age (400m)  0.247 0.293 0.271 0.265 0.258 0.275 0.351 0.387  Root MSE (years) 13.06 12.66 12.85 12.91 12.97 12.83 12.12 11.70  0.397  11.70  0.270  12.86  9 10  Of the continuous variables, the forest inventory age was the best variable for predicting time-since-fire, but the relationship between the two variables was not strong as seen in Figure 3-3. Adding the average age of neighbouring polygons to the model improved the fit. The Pearson correlation coefficient between the forest inventory age and the average weighted age (400m) variables is 0. 474, so the use of both these variables together is not redundant. Using categorical variables, such as modification, species, and sub-category code, in the models allowed the intercepts to vary for different classes (Neter et al. 1996). Forest inventory polygons containing white spruce or balsam poplar had time-since-fire ages that were older than polygons with other tree species of the same forest inventory age. Comparing models [1] and [4] shows that the intercepts for other primary species are about the same as the intercept of model [1], which lacks primary species as a variable. Polygons with cutover as a recorded modification had predicted time-since-fire ages 20 years older than other modification classes. Interactions were tested, which allowed the slope of continuous variables to vary for different categories. Interactions between the inventory age and primary species, sub-category code, and modification variables were all found to be significant predictors of time-since-fire age, but made little improvement to the models and were therefore not included.  29  Figure 3-3: Fitted line plot between time-since-fire age and the maximum inventory age (solid) and a 1 to 1 line (dotted), for single-aged polygons. Random noise, from a uniform distribution between ± 5, was added to the age variables to spread them out and to make them visible.  3.2.2 Multi-Age Prediction Models  Table 3-3 gives the variables used in the multi-aged models along with measures of fit for these models. There were 3,196 forest inventory polygons in the multi-age category with an overlap area ratio over 0.8 that were used for fitting the regression models. The estimated parameters for the models are given in Appendix 2, Tables A2-3 and A2-4 and model residuals are given in Appendix 3, Figures A3-11 to A3-18. As with the single-age regression models, none of the multi-age models explain the variation in time-since-fire well and the model residual plots show unequal variance. Multi-age model [8] was chosen for predicting time-since-fire ages.  30  Table 3-3: Multi-age models for predicting time-since-fire and fit statistics. See Table 2-3 and Table 2-4 for variable descriptions. Model # 1 2 3 4 5 6 7 8  Model Variables Avg. Inventory Age Large Inventory Age Max. Inventory Age Min. Inventory Age Max. Inventory Age, Min. Inventory Age Avg. Inventory Age, Modification Avg. Inventory Age, Avg. Oldest Age (400m) Avg. Inventory Age, Avg. Oldest Age (400m), Modification  R2 0.172 0.150 0.137 0.119 0.165 0.207 0.241 0.271  Root MSE (years) 14.93 15.13 15.24 15.40 15.00 14.62 14.30 14.02  The models presented only used age variables and one categorical variable. Based solely on the R2 values, the average age is the best forest inventory age to use for predicting time-since-fire. As with the single-age models, the average age of neighbouring inventory polygons was found to be a significant predictor of time-since-fire ages. The categorical modification value was also found to be a significant predictor of time-since-fire age, as it was for the single-age regression models. Forest inventory polygons with cutover and clearing modifications tended to have older time-since-fire values than other polygons with the same forest inventory ages. Tree species variables were found to be significant predictors of time-since-fire ages, but made very little improvements to the models and were not presented. Interactions between the average inventory age and species variables was also found to be a significant predictor of time-since-fire age, but again provided little improvement to the models at the cost of added complexity. Interactions between average inventory age and the modification variable were not found to be significant predictors of time-since-fire age. 3.2.3 No-Age Models  Splitting long forest inventory polygons lacking tree ages that extended across the landscape resulted in 84 original polygons (approximately 800 ha) being replaced with 1,111 smaller polygons. When these polygons were added to the other no-age inventory polygons, it resulted in a total of 2,843 polygons in the no-age category. Comparisons among the four different methods of assigning predicted time-since-fire values from neighbouring inventory polygons, separated by forest inventory sub-category  31  code are shown in Table 3-4. Removal of the 206 polygons (approximately 2300 ha) that fell below the 0.8 overlap area ratio and eight polygons that were “islands” without neighbours to provide time-since-fire predictions left 2629 polygons for comparisons. The predicted time-since-fire values for neighbouring polygons came from the application of single-age model [8] and multi-age model [8]. There were no large differences among the methods used to assign predicted time-since-fire ages to no-age category polygons and none of the methods worked well for the 10 inventory polygons, in sub-category code 31, with young ages and modification values recorded. The no-age largest boundary assignment did not fit the data as well as using the largest area, but was the method applied since it produced more logical outputs when polygons were grouped into fire events in a later step. Table 3-4: RMSE for four methods of assigning neighbouring values, by no-age inventory category. Sub-Category Code - Description 30 - No Age Value 31 - Young age and modification value 32 - Young age and no modification value  RMSE (years) Largest Area  Oldest  Youngest  Number of Polygons  11.1  11.4  11.2  2550  31.5  31.5  29.3  32.7  10  14.7  12.4  15.2  13.5  69  Largest Boundary 11.0  3.3 Model Application Predicted time-since-fire output from the selected models is shown in Figure 3-4. The predicted values originate from single-age model [8], multi-age model [8], and the no-age largest boundary assignment procedure. After the models were applied, there were 11,243 forest inventory polygons with predicted time-since-fire values. These were composed of 8,408 single-age and multi-age forest inventory polygons, in addition to the 2,835 no-age polygons (after splitting), which had neighbouring values. Areas without a predicted time-since-fire age were either water or the eight no-age polygons without neighbouring values.  32  Figure 3-4: Map of predicted time-since-fire age for the entire study area.  The origin-class distribution for the predicted time-since-fire age was closer to the observed time-since-fire than the maximum forest inventory ages (Figure 3-5). Unfortunately the models failed to predict older fires and predicted the area of the 1930 and 1940 origin classes badly. The polygon distribution for the predicted time-since-fire ages (Figure 3-6), was only slightly different from the polygon size distribution of the original forest inventory dataset presented in Figure 3-2, as no groupings of the polygons were done at this point. The increase in the number of small polygons was caused by no-age polygons now having time-since-fire age predictions and being included in the comparison. Additionally, some of the original no-age forest inventory polygons were split into many small polygons. The increase in the number of polygons in the 200 to 600 ha size class was attributed to former no-age polygons, such as shrub or herb areas, now having a predicted time-since-fire age and being included in the summary.  33  50  Observed Time-Since-Fire Predicted Time-Since-Fire  Percent of Area  40  30  20  10  0 1790  1800  1830  1840  1850  1860  1870  1880  1890  1900  1910  1920  1930  1940  1950  1960  1970  1980  1990  Origin Class (10-year)  Figure 3-5: Origin-class distributions, in 10-year classes, for the observed time-since-fire and predicted time-since-fire ages.  5149  6000  Observed Time-Since-Fire 4570  5000  Predicted Time-Since-Fire  3737  4000  2059 1877  3000  1798  Number of Polygons  Forest Inventory Age  2000  34 60 52  16 11 8  8 0 0  3 0 0  0 0 0  4 0 0  227 197  32  122  321  332  1000  80 to 200  200 to 600  600 to 2000  2000 to 5000  5000 to 10000  10000 +  0 0 to 2  2 to 10  10 to 40  40 to 80  Polygon Size Class (ha)  Figure 3-6: Polygon size distributions for the observed time-since-fire, predicted time-since-fire, and forest inventory polygons with age values.  34  3.4 Fire Cycle Calculations Calculated fire cycles are shown in Table 3-5, based on a negative exponential model fitted to the observed and predicted time-since-fire age, and oldest forest inventory age values. The predicted time-since-fire was based on the predictions of the best regression models, with no-age polygons being assigned time-since-fire values from neighbouring polygons as described in Section 3.3 Model Application. The fire frequency based on the oldest forest inventory ages was less than the fire frequency calculated from the observed time-since-fire. Table 3-5: Fire frequency estimates for observed time-since-fire age, oldest forest inventory age, and predicted time-since-fire age. Dataset Observed Time-Since-Fire Age Oldest Forest Inventory Age Predicted Time-Since-Fire Age  Fire Cycle (years) 21.0 17.6 20.5  Figure 3-7 shows time-since-fire curves based on the calculated fire frequencies. All of the calculated curves overestimate the amount of area in the youngest age class. However, the calculated time-since-fire curves based on fire frequencies from the observed time-since-fire and predicted time-since-fire were similar.  35  50  Observed Time-Since-Fire Estimated T-S-F based on Fire Frequency derived from Observed T-S-F Age 40  Estimated T-S-F based on Fire Frequency derived from Oldest Forest Inventory Age  Percent of Area  Estimated T-S-F based on Fire Frequency derived from Predicted T-S-F Age  30  20  10  0 55 - 64  65 - 74  75 - 84  85 - 94  95 - 104  105 114  115 124  125 134  135 144  145 154  155 164  165 174  175 184  185 194  Time-Since-Fire Age Class  Figure 3-7: Time-since-fire estimated from a negative exponential model fitted to the observed time-since-fire age, oldest forest inventory age, and predicted time-since-fire age.  3.5 Grouping Inventory Polygons into Fire Events The number of forest inventory polygons which were grouped together depended on whether the no-age category polygons were split and assigned neighbouring age values. In the one case where no-age polygons were not assigned a neighbouring value, there were 8,408 forest inventory polygons grouped. In all other cases the number of polygons was 11,243. Forest inventory polygons without predicted age values, such as water or no-age polygons in the one case where they were not assigned an age, were not included in any of the presented graphs. The three grouping techniques used (i.e., 10-year partitions, hierarchical clustering, and spatially constrained clustering) all produced different numbers of grouped polygons as output. Figure 3-8 shows the spatial output of some of the groupings. Appendix 4 contains tables showing information about the output groupings presented, such as the number of separate groupings and the age ranges within each group.  36  Figure 3-8: Map of observed time-since-fire (a), simple 10-year partitioning (b), 5-year hierarchical clustering (c), 10-year hierarchical clustering (d), constrained clustering with a 0.001 distance penalty (e), and constrained clustering with a 0.0005 distance penalty (f).  37  For the three groupings that used simple 10-year partitioning, the effects of filling in no-age category polygons with age values, and grouping on predicted time-since-fire ages versus forest inventory ages were examined. Comparisons were made to a 10-year partitioning done on time-since-fire ages with the no-age category of polygons assigned age values. The spatial output of this simple partition is shown in Figure 3-8 (b). There are many small polygons seen on the map and also included in the polygon size distribution of Figure 3-9. The number of separate groups (Appendix 4, Table A4-1) is only eight, but non-adjacent polygons in the same group form multiple output polygons. The origin-class distribution for the 10-year partitioning done on the time-since-fire ages (Figure 3-10) was no different from the previously presented predicted time-since-fire output in Figure 3-5, since the groupings and origin-class distribution used the same category boundaries. 1500  1242  Observed Time-Since-Fire Predicted T-S-F, simple partition 10yr, no-age assigned Predicted T-S-F, simple partition 10yr, no-age not filled Forest Inventory Age, simple partition 10yr, no-age assigned  761  552  533  570  747  Number of polygons  1000  352  200 to 600  600 to 2000  4 2 0 1  8 10 18 8  80 to 200  0 0 2 0  16 31 54 38  40 to 80  3 5 4 6  34 44 61 83  125 32 42 80  122  218  321  332  400  500  2000 to 5000  5000 to 10000  10000 +  0 0 to 2  2 to 10  10 to 40  Polygon Size Class (ha)  Figure 3-9: Polygon size distributions for partitioned predicted time-since-fire (with and without no-age values) and partitioned oldest forest inventory ages.  38  50  Observed Time-Since-Fire Predicted T-S-F, simple partition 10yr, no-age assigned Predicted T-S-F, simple partition 10yr, no-age not filled  40  Percent of Area  Forest Inventory Age, simple partition 10yr, no-age assigned  30  20  10  0 1790  1800  1830  1840  1850  1860  1870  1880  1890  1900  1910  1920  1930  1940  1950  1960  1970  1980  1990  Origin Class (10-year)  Figure 3-10: Origin-class distributions, in 10-year classes, for partitioned predicted time-since-fire (with and without no-age values) and partitioned oldest forest inventory ages.  Assigning predicted time-since-fire values to the no-age polygons made minor changes to the origin-class distribution in Figure 3-10. The slight difference was caused by the neighbours of no-age polygons not being representative of the predicted time-since-fire for the entire area. The increased area with predicted time-since-fire ages, when the no-age polygons were assigned a value, was hidden by plotting the proportion of the total area within each origin-class. The polygon size distribution, seen in Figure 3-9, has less small polygons and an increased number of larger polygons when comparing the grouping of polygons with complete predicted time-since-fire to those that are missing predictions for the no-age category of polygons. The increase in the size of grouped polygons resulted from polygons within the same partition, previously separated by a no-age polygon such as a road, being able to join together once the barrier between them was removed (Figure 3-11).  39  Figure 3-11: Map of predicted fire ages, grouped with a simple 10-year partition, with (a) and without (b) no-age values filled in, in the southwest corner of the study area.  Using the predicted time-since-fire age for grouping, instead of the oldest forest inventory age, also resulted in an increased number of larger output groupings of polygons being formed (Figure 3-9). The predicted time-since-fire ages were more homogeneous than the oldest forest inventory age; an increased number of adjacent polygons had similar predicted time-since-fire values and formed larger polygons when grouped together. The groupings of maximum forest inventory age also had a different age-class distribution than the groupings of predicted time-since-fire ages, as a result of the nature of the forest inventory ages previously shown in Figure 3-1. There were some slight differences between the forest inventory ages in Figure 3-10, compared to Figure 3-1, as polygons without age values were assigned a forest inventory age from a neighbouring polygon. Hierarchical clustering outputs were compared to the simple 10-year partitioning to determine the usefulness of statistical clustering techniques. Comparisons between the two grouping methods are difficult, since the spread of each cluster varies and may be more than the cluster width value that specified the dendrogram height used to group polygons. The spread of a cluster is the difference between the maximum and minimum age values within it and varied among clusters because the centroid clustering method used the average of time-since-fire age inputs when comparing if two clusters should be joined. More large groupings and fewer small ones were formed with the 10-year wide  40  hierarchical clusters than for the 10-year partition, as seen in Figure 3-12, since the clustering allowed inputs to be up to 19.0 years apart for one of the clusters (Appendix 4, Table A4-3). Hierarchical clustering does not place boundaries as arbitrarily as the 10-year partition; for example, polygons with fire ages of 65 and 63 years may be joined together, whereas these will always be separated by the 10-year partitioning method. The output of the 10-year hierarchical cluster was more aggregated than the 10-year partition, as can be seen in Figure 3-8 (b),(d). This was a factor of the hierarchical clustering allowing some predicted time-since-fire ages to be farther apart and still grouped into the same cluster. 1000  Observed Time-Since-Fire  791  800  Predicted T-S-F, simple partition 10yr, no-age assigned  570  Predicted T-S-F, hierarchical cluster 10yr  321  218  250  318  400  348  400  530  600  332  Number of polygons  Predicted T-S-F, hierarchical cluster 5yr  2 to 10  10 to 40  40 to 80  600 to 2000 2000 to 5000  4 2 1 2  0 to 2  0 0 2 1  200 to 600  0  3 5 2 0  16 31 36 13  80 to 200  8 10 21 9  34 44 53 20  26  32 42  74  129  122  200  5000 to 10000  10000 +  Polygon Size Class (ha)  Figure 3-12: Polygon distributions for hierarchical clusters and simple 10-year partition.  The 5-year hierarchical clustering was a division of the 10-year clustering as both outputs were based on the same dendrogram. The 10-year hierarchical clustering allowed a greater spread of predicted time-since-fire ages to be in the same cluster compared to the 5-year hierarchical clustering (Appendix 4, Table A4-2). The differences between the minimum and maximum time-since-fire ages within a cluster for the 5-year clustering varied between 3.0 to 7.0 years, whereas the 10-year clustering ranged from 6.0 to 19.0 years. The  41  hierarchical clustering with a 5-year cluster width produced more small polygons and fewer large polygons than the clustering using a 10-year cluster width (Figure 3-12). This resulted in less aggregation and more individual output clusters for the 5-year clustering, as seen in Figure 3-8 (c). Also, the spatial boundaries of the 10-year hierarchical clustering were all present in the output of the 5-year clustering. The lack of moderate sized polygons, for the 10-year hierarchical cluster, was balanced by a few large output polygons greater than 10,000 ha. However neither of the cluster width parameters used during clustering correctly estimated the number of observed time-since-fire polygons found in the larger polygon size classes. The origin-class distributions for the hierarchical clusters, and the 10-year partition, are shown in Figure 3-13. These three groupings used the same predicted time-since-fire values as their input, so any difference between them results from how the polygons were grouped together. Both the 5-year and 10-year hierarchical clustering had some individual clusters with boundaries spanning the 10-year decadal classes used for the 10-year partition and for displaying the origin classes in Figure 3-13. The averaging of age values within the output clusters, to produce a single age for each group, was dominated by the well represented origin classes. This shifted the output from the rare origin classes to the more numerous 1920 and 1930 origin classes. The 5-year clustering produced more output polygons, which provided more bins to average time-since-fire ages within, preserving more area of the predicted time-since-fire values that were in the 1940 origin-class. The spatially constrained clustering techniques considered the location of polygons, in addition to their predicted time-since-fire ages, when grouping them together. A 10-year height (cluster width) on the output dendrogram was specified to group clusters together. When the distance penalty weight was zero, the output clusters were the same as the hierarchical cluster with a 10-year cluster width. Any positive, non-zero, distance penalty weight resulted in more, smaller clusters forming for spatially constrained clustering than for the 10-year hierarchical clustering. In general, the value of the distance penalty weights roughly corresponded to the maximum distance polygons with the same predicted time-since-fire age could be apart and still be grouped together. Distance penalty weighting values of 0.001 (1 km = a 1-year penalty), 0.0005 (2 km = a 1-year penalty) and 0.0002 (5  42  km = a 1-year penalty) were used. With a 0.001 penalty value and a 10-year cluster width on the output dendrogram, clustered polygons with the same predicted time-since-fire age can be around 10 km apart and still be joined in the same cluster. However, the centroid clustering method will create output clusters with varying spreads. Adjacent polygons had a minor penalty applied to them, since the distance between them was greater than zero when using the centroid for their locations. The forest inventory polygons were generally small, minimizing this issue. 50  Observed Time-Since-Fire Predicted T-S-F, simple partition 10yr, no-age assigned 40  Predicted T-S-F, hierarchical cluster 5yr  Percent of Area  Predicted T-S-F, hierarchical cluster 10yr  30  20  10  0 1790  1800  1830  1840  1850  1860  1870  1880  1890  1900  1910  1920  1930  1940  1950  1960  1970  1980  1990  Origin Class (10-years)  Figure 3-13: Origin-class distributions, in 10-year classes, for hierarchical clusters and simple 10-year partition.  An increase of the distance penalty weight caused smaller output polygons to form, since polygons with similar predicted time-since-fire values must be closer together to be joined in the same cluster. The number of raw output clusters (Appendix 4, Tables A4-4 to A4-6) followed this pattern, and it mostly extended to the polygon size distributions in Figure 3-14. The exception was for the spatially constrained clustering with a 0.001 distance penalty weight, which produced fewer total polygons than the clustering with a 0.0005  43  penalty weight and fewer polygons in the smallest size classes. Even though the lower, 0.0005 distance penalty weight clustering had fewer output clusters, individual clusters were composed of many non-adjacent polygons, which lead to it having more small polygons in the polygon size distribution than the 0.001 penalty weight clustering. The 0.001 distance penalty weight clustering had more polygons in the 600 ha to 10,000 ha size classes and fewer very large polygons, which can be seen in Figure 3-8 (e), where some of the 1920 and 1930 origin-class polygons covered an eighth of the study area. The 1930 origin-class band in the middle of the 0.001 distance penalty weight clustering output was composed of two separate polygons. Figure 3-14 hides some of the larger output polygons from the lower penalty weight clustering in the greater than 10,000 ha size class. The largest output cluster polygons were: 45,738 ha for the 0.0002 penalty weight, 28,140 ha for the 0.0005 penalty weight, and 11,688 ha for the 0.001 penalty weight. In Figure 3-8 (f), the greater than 10,000 ha polygons for the 0.0005 distance penalty extend from the bottom to the top of the study area. 600  490  523  Observed Time-Since-Fire Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.001  Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.0002  10 to 40  4 2 2 2  2 to 10  0 2 0 0  0 to 2  3 7 2 3  80 to 200 200 to 600  0  8 15 11 4  34 34 38 32  40 to 80  16 17 24 16  32 31 42 24  122  200  145  195 199  271  321  361  400 332 329 335  Number of Polygons  Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.0005  600 to 2000  2000 to 5000  5000 to 10000  10000 +  Polygon Size Class (ha)  Figure 3-14: Polygon distributions for spatially constrained clusters.  44  The origin-class distributions for the spatially constrained clustering behaved in a similar manner as the hierarchical clustering, as seen in Figure 3-15. As the distance penalty weight increased, the clustered polygon sizes decreased leading to more polygons and less averaging of the predicted time-since-fire ages. The higher distance penalty weights produced outputs with less distorted predicted time-since-fire and did not pull the origin distribution into the dominating 1920 and 1930 origin classes. Lower distance penalty weights caused more averaging and led to more area in the 1920 and 1930 origin classes. 60  Observed Time-Since-Fire 50  Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.001  Percent of Area  40  Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.0005 Predicted T-S-F, spatially constrained cluster 10yr, penalty weight 0.0002  30  20  10  0 1790 1800 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990  Origin Class (10-years)  Figure 3-15: Origin-class distributions for spatially constrained clusters, in 10-year classes.  45  4 Discussion The purpose of the modelling presented in this thesis was to predict time-since-fire ages from forest inventory data. The model outputs can be used to calculate wildfire disturbance parameters, such as wildfire frequency and size, which are needed for ecosystem management. The regression models and polygon groupings were used to overcome the differences between the forest inventory and time-since-fire datasets.  4.1 Descriptive Data Analysis A comparison of the forest inventory dataset to the time-since-fire dataset provided a baseline against which to evaluate the subsequent regression modelling and polygon grouping. The age values in the two datasets were expected to be similar, if the germination of current trees promptly followed the last wildfire disturbance, since the Saskatchewan Environment (2004) inventory specification stated the “year of origin is the year in which the trees are believed to have germinated.” As noted in the results (Section 3.1), differences existed between the age values in the forest inventory and the time-since-fire datasets. Previous comparisons (Andison 1999a, Andison 1999b) found differences between forest inventory and time-since-fire values measured at plots. Where there were forest inventory stands with multiple ages, the oldest of the ages was closest to the time-since-fire age, which may indicate that the younger ages came from trees that regenerated some years after the last fire disturbance. Forest inventory and time-since-fire data were collected to help meet the goals of managing natural resources and to aid researchers to understand past fire disturbances, respectively (Johnson 1992). These requirements determined which objects were delineated and measured and the procedures employed. In the case of the forest inventory, the object identified as a polygon was a forest stand or non-forested area, whereas for the time-since-fire data the object identified was a fire disturbance. These different goals accounted for many of the aspatial and spatial differences observed between the two datasets and manifested themselves in the: (1) attributes recorded; (2) polygon sizes identified; and (3) minimum mapping unit (MMU) used. The forest inventory consisted of data about the landscape at the time of inventory. For 46  each object identified, a broad selection of variables was recorded, as previously described in Section 2.2.2. Forest stand ages were recorded at a low resolution that was suitable for meeting management goals, as reflected by the use of 10-year origin classes to define the inventory ages (Andison 1999a, Saskatchewan Environment 2004). The time-since-fire dataset contained fire disturbance objects across the landscape and used older aerial photographs for mapping. Ground plots targeted this single goal and more effort was paid to gathering age measurements reflective of the most recent, and where available previous, fire disturbances. Current features of the landscape such as recent disturbances and non-forest areas, apart from lakes, were not mapped in this dataset. Polygon size distributions within a dataset were also impacted by the different data collection requirements. The larger number of small polygons in the forest inventory, compared to the time-since-fire data, was a product of forest inventory interpreters delineating forest stands into homogeneous areas based on multiple forest attributes such as site quality and tree species, or non-forest attributes (Saskatchewan Environment 2004). In contrast, the time-since-fire data focused on measuring fire disturbance objects that delineated polygons of homogeneous areas based solely on the year of the last fire disturbance. Since most of the disturbances overwrote previous disturbances, the time-since-fire dataset was composed of a few large polygons in addition to small remnants from previous disturbances. A further difference between the two datasets was the minimum mapping unit (MMU) used; this impacted both the polygon sizes and the attributes recorded. The purposes of the data collection determined the MMU used, which was reflected by the scale of the photographs used to collect data. The MMU difference caused situations where objects that were identified and recorded in one dataset were not measured in the other. If a small polygon was identified in the forest inventory dataset, but not the time-since-fire, the time-since-fire data may have only recorded the last disturbance to the majority of the trees in a location, missing the small group below the resolution threshold. This caused situations where different objects were compared to each other when performing the age comparisons. Additionally, the minimum mapping unit of one to four hectares for forested polygons in the inventory placed a constraint on the smallest fire patches that could be  47  identified through modelling based on the forest inventory data. Attribute measurement errors were also present in both datasets. Many other studies found measurement errors in ages and other forest inventory variables. Wong and Lertzman (2001) found large inaccuracies between the true age of trees that regenerated after wildfires and measured ages, even after applying corrections to the measured breast height ages. DesRochers and Gagnon (1997) found differences between the age of black spruce trees, measured by coring at ground level, and their true age, due to adventitious roots causing the root collar to be below ground. Differences in species classification have also been observed between independently gathered forest inventory datasets covering the same location by Joy and Klinkenberg (1996). Simple measurement errors of the age values in the forest inventory (or time-since-fire) added noise to the comparisons between the ages. Errors in polygon positions and the location of their boundaries may have added to the age differences between polygons from the two datasets that were compared in the descriptive analysis. The mapped locations of forest stands and fire disturbance objects that represented the same ground location may be slightly different between the two datasets and lead to different objects being compared against each other. This may be caused by simple errors when the interpreters mapped the boundary or difficulties locating boundaries that are ill defined. Moreover, the accuracy of boundary locations decreases as the photographic scale used for mapping decreases. Problems caused by positional errors were dealt with by employing the overlap area ratio to better ensure the same objects were being compared to each other. Specific cases demonstrated the effect of the different data collection procedures on the age comparisons. Polygons that were recorded as cutovers in the forest inventory were likely old fire disturbances in the time-since-fire data. This led to some of the large differences between ages in the summarized polygon-by-polygon comparison and explained why the forest inventory area versus origin-class curve was shifted towards younger stands when compared to the curve based on the time-since-fire data. The current landscape described in the forest inventory data had no relationship to the historic disturbance in these cases.  48  4.2 Prediction Modelling Modelling was used to establish relationships between the time-since-fire ages and the variables of forest inventory polygons. The relationships were used to adjust for systematic differences between forest inventory ages and time-since-fire ages. The approach addressed the requirement of using accurate time-since-fire data for calculating fire disturbance parameters discussed in Andison (1999a). In addition to the regression models, a simple model based on the predicted time-since-fire of neighbouring polygons was used to assign age values to forest inventory polygons that were non-forested or lacked suitable age values. This procedure created time-since-fire data over the entire study area, necessary for further polygon size analysis (Andison 1999a). 4.2.1 Regression Models  The model fits were poor and showed that the models explained little of the variation in time-since-fire age. The relationships between the forest inventory variables and time-since-fire ages were weaker than initially hoped. The regression models also failed to predict older fires, which covered a small portion of the landscape. However, they did account for some of the differences between the time-since-fire and inventory data and provided insights to determine the causes of these differences. The most significant independent variable in the single-age regression models was the inventory age; this was expected given the definition of this variable. Unexpectedly, stands with an inventory age of zero were not predicted to have time-since-fire ages of zero. The range of the data used to create the models fell between 40 and 130 years old and the linear form of the models is unlikely to last if younger inventory data were included. The multi-age regression models employed more inventory age variables than the single-age models, with the average age of the tree layers producing the best fit. This variable is difficult to interpret; however, since all the multi-age models fit poorly it made little difference which age variable was used. Another age variable that was significant in the models was the average age of the  49  neighbouring forest inventory polygons. The use of this variable provided a slight improvement over using the forest inventory age in isolation. One possible explanation for the improvement was that neighbouring polygons were often initiated from the same fire event. If all of the inventory polygon ages were unbiased, but not precise, estimates of the year of origin, the average would produce a more accurate estimate of the time-since-fire than single forest inventory ages. The average essentially smoothed out some of the errors in the forest inventory ages. The effect would not hold true on the edge of fire boundaries, but much of the study area was disturbed by large fire events and some edge polygons were removed from the model fitting since they were below the overlap area ratio threshold. Alternatively, if MMU differences led to small inventory polygons measuring different fire objects than their associated time-since-fire polygons, the surrounding forest inventory polygons may better represent the measured historic disturbance for the location. Incorporating tree species into the models as categorical variables slightly improved the model fits. Forest inventory stands containing white spruce or balsam poplar had time-since-fire ages that were older, for a given inventory age, compared to other tree species such as trembling aspen, white birch and black spruce. Bergeron (2000) noted that trembling aspen and white birch could regenerate from root suckers, leading to small differences between the ages of those species and the ages for the disturbances that initiated them. This should also hold for black spruce, which has been observed to regenerate quickly after fire disturbances (DesRochers and Gagnon 1997). White spruce, on the other hand, may have its maximum recruitment delayed by 5 years until after the disturbance (Bergeron 2000) and grows very slowly at first. This delay may explain why the relationship between inventory age and time-since-fire age is different for white spruce than for some of the other species. The difference for balsam poplar was unexpected, since Dix and Swan (1970) found that it has an age structure like a pioneer species and should be akin to aspen. The modification variable was also significant in the regression models and helped account for some of the difference between the current landscape recorded in the forest inventory and the historic time-since-fire age. Inventory stands recorded as cut-over, and with ages older than the young age cutoff present, generally had a time-since-fire age 20 years older  50  than other recorded modification types with the same inventory age. Trees left after harvesting may have been younger than the trees that originally initiated the stand and the age of cut-over stands was not a good substitute for time-since-fire age. The input data violated many of the assumptions of regression modelling and the models produced were imperfect. The independent variables, notably forest inventory ages, were likely not measured without errors, as previously discussed. The spatial nature of the input data made it likely that the inputs and model residuals were both spatially auto-correlated, though this was not explored. Furthermore the model residual values indicate non-equal variance and were not normally distributed, but instead slightly skewed. Additionally, the model fitting may have been dominated by small polygons; however, only eight inventory polygons were larger than 200 ha and most polygons were small, making this unlikely to have a large impact on the results. 4.2.2 No-Age Models  Areas in the forest inventory without suitable ages recorded left holes in the predicted time-since-fire output where, logically, an historic fire burnt. The areas missing ages were roads, harvested areas, or other non-treed areas. If the missing areas were biased towards certain age classes, incorrect results may be produced when using the data to generate non-spatial age class distributions (Andison 2000). Bias is likely present here, as the missing harvested areas were generally older than their surrounding polygons. These holes also created difficulties when using the forest inventory data to create fire event polygons for spatial pattern analysis (Andison 1999a); this aspect is discussed below in Section 4.3. Andison (2003) used similar techniques to those employed here to remove gaps from his dataset. There were three issues that impacted on how well the techniques used to fill the no-age areas performed: (1) the veracity of the assumption that adjacent forest inventory polygons were disturbed by the same fire; (2) the accuracy of the neighbouring time-since-fire age values predicted by the underlying regression models; and (3) the method used to assign the neighbouring age values to no-age polygons. Based on the RMSE comparisons shown in the results (Section 3.2.3), the various 51  techniques employed for assigning neighbour values (e.g., largest boundary, largest area) did not have much impact on the output. None of the approaches improved the predictions for forest inventory polygons with young ages and a recorded modification value. Likely, these polygons were clearcuts, where the previous stand was initiated by a fire older than the surrounding polygons used to assign a predicted value. This situation violates the first assumption that adjacent forest inventory polygons regenerated from the same fire disturbance. Alternative methods need to be explored to account for the issue of human disturbed areas representing older wildfire age classes. Missing these older polygons biased the age class distributions slightly, but only over a small area. 4.2.3 Model Evaluation and Use  The quality of the complete predicted time-since-fire ages was evaluated by comparing them to the observed time-since-fire ages, which were assumed to correctly represent wildfires on the landscape. The complete predictions were created by combining the outputs from the two regression models and the no-age models. The metrics chosen for comparison purposes described the wildfire disturbance or could be used to calculate other fire disturbance metrics and allowed the predicted time-since-fire ages to be evaluated in light of their intended use. Comparisons of landscape metrics were employed by others to describe differences between two datasets (e.g., Franklin and Forman 1987, Mladenoff et al. 1993, Weir et al. 2000). Multiple comparison methods were required, since no single metric was found to fully quantify every property of two datasets (Turner et al. 2001). The metrics chosen for comparison were the origin-class distribution and the fire cycle. Polygon size distribution metrics were not useful as no polygon groupings had been done at this point in the analysis and any comparisons would only reveal differences between the observed time-since-fire and the forest inventory. The origin-class distributions from the model outputs contained older areas, and shifted the distribution towards older stands, making it closer to the observed time-since-fire than the forest inventory ages. The class widths of the origin distribution were limited by the 10-year resolution of the input forest inventory ages. The predicted values will not be able to distinguish fires that are less than 10 years apart and lower resolution origin-class distributions should not be used when interpreting the data (Wong and Lertzman 2001).  52  The fire cycle calculated from the predicted time-since-fire ages was also closer to that calculated from the observed time-since-fire ages than the fire cycle that was calculated from the forest inventory ages. This was expected, since the origin-class distribution was the input to the fire cycle calculation. There are further limits to interpretations about wildfires on the landscape that can be made from the predicted time-since-fire age values. The forest inventory stand ages used in the regression models were only influenced by disturbances intense enough to kill and replace stands (Van Wagner 1978). Information about low severity ground fires, which only scar occasional trees, cannot be gained from models based on the forest inventory data. Also, information about low severity fires that only kill a few trees, but are not completely stand replacing, cannot be gained from the presented model outputs, as the spatial resolution is limited to the forest inventory polygon.  4.3 Grouping Inventory Polygons into Fire Events Assuming the forest inventory boundaries were a subdivision of the fire event boundaries, grouping polygons with similar predicted time-since-fire values can produce fire event polygons. This assumption is reasonable, since the data collection procedures for the forest inventory should result in stands being subdivisions of historic fire events. The predicted fire event boundaries can subsequently be used for landscape polygon size analysis (Andison 2003). None of the grouped polygon outputs closely matched the observed time-since-fire dataset and none of the methods or parameters used produced as many large polygons (over 10,000 ha) as were observed in the time-since-fire data. Spatially constrained clustering incorporated the assumption that fires generally spread out from one location and are an autocorrelated process. In contrast, hierarchical clustering ignored the spatial information in a dataset (Gordon 1996). Assuming that observations were created by an autocorrelated process, constrained clustering is more likely to uncover the correct structure because it can reduce the clustering results to those that are geographically meaningful (Legendre 1987, Legendre and Fortin 1989). While the spatially constrained methodology produced output that was more logical in this context, higher distance penalty weights produced  53  output that was too compact and constrained the maximum size of the output polygons. The grouping methods and the parameters employed created different outputs. With similar cluster width parameters, the hierarchical clustering produced more large polygons than the partitioning method, as the hierarchical clustering allowed a greater spread of ages to be within a group than the specified cluster width parameter. Lowering the hierarchical clustering cluster width parameter to 5 years produced more polygons than the 10-year partition, as the spreads of ages within a group were less than 10 years on average. In comparison, the spatially constrained clustering method produced more output clusters than the hierarchical clustering method, given the same cluster width parameter and a non-zero distance penalty parameter. Varying the methods and parameters changed the size and shape of the predicted fire events, but determining the best parameters was problematic. The penalty weights used in the constrained clustering are difficult to objectively specify (Gordon 1996) and those that are “best” for one area are not likely to be “best” for another. Using the predicted time-since-fire ages, compared to the forest inventory ages, and assigning values to the no-age polygons improved the polygon size distributions produced by the groupings. Grouping uncorrected forest inventory ages, with polygons lacking ages assigned age values from their neighbours, produced patch distributions with more small polygons than groupings based on the predicted time-since-fire ages. This was attributed to the uncorrected forest inventory ages exhibiting less similarity between adjacent polygons than the predicted time-since-fire values for these polygons, making adjacent polygons less likely to be grouped together. Additionally, the forest inventory ages included young polygons, which were likely different from their neighbours and placed into separate output groups. In the predicted time-since-fire ages, these young forest inventory polygons were classified as no-age polygons and assigned neighbouring ages, further reducing the age differences between adjacent polygons and leading to larger output polygons. Assigning no-age polygons values from neighbouring polygons also produced larger output grouped polygons. This was attributed to human disturbances, such as roads, breaking up larger fire events and preventing polygons on either side of the no-age polygons from being grouped together. However, it should be noted that the method used  54  to assign values led to larger polygons than may otherwise have been, as it ensured that no-age polygons were always grouped with their neighbours. The best age to assign to the output clusters was not determined; the average age was used in this analysis. Different grouping techniques and parameters resulted in various sized groups composed of different sets of inventory polygons, and changed the landscape origin-class distribution for each output when ages were averaged within groups. Decreasing the number of output polygons caused the average time-since-fire ages assigned to each group to be dominated by the more numerous origin classes and decreased the representation of rarer classes. The average age may not be the best estimate of the time-since-fire age for an output polygon and using an alternative method, such as the age of known fires, may prove better. The assigned age does not impact on using the outputs for patch analyses, since these analyses examine the predicted polygon sizes and shapes. The spatial resolution of the predicted fire events needs to be considered when examining polygon sizes. The spatial resolution of the predicted time-since-fire polygons was limited by the MMU of the input forest inventory dataset. Also, the output spatial resolution was affected by the grouping technique and parameters used, as well as the resolution of the predicted time-since-fire ages. For example, a clustering method with a wide cluster width will tend to produce larger fire events of lower spatial resolution and not be able to separate fire events that are close in age. The output clusters are unlikely to support a high spatial resolution patch analysis and the number of small fire patches predicted is likely underestimated. This makes the output clusters unsuitable for calculating fire severity, which requires single tree measurements and datasets collected with a smaller MMU.  55  5 Summary and Conclusions 5.1 Summary of Findings This research found a relationship between forest inventory variables and the time-since-fire age, which was used to predict time-since-fire information from the forest inventory dataset. As expected, the strongest relationship was found between the forest inventory polygon age and the time of the last wildfire. Another important predictor variable was the age of neighbouring polygons, which may indicate most neighbouring polygons regenerated after the same fire disturbance. The tree species present in the forest inventory also contributed to the relationship. Finally the forest inventory modification variable helped explain the predicted time-since-fire age for polygons that were harvested and contained residual trees. Model forms were not vastly different between single-age and multi-age polygons, apart from multi-aged polygons providing more age values to use in the models. Groupings of forest inventory polygons were employed to produce spatial fire event information. The output was affected by the presence of no-age polygons, like roads, which required assigning predicted time-since-fire ages to them, before grouping. Longer no-age polygons were split into multiple polygons before assigning ages, since they potentially crossed many fire boundaries. Using the neighbouring predicted time-since-fire value to fill in polygons that did not contain ages was generally found to be satisfactory. The exception was for harvested stands, since they likely regenerated after older fire disturbances and their historic tree ages did not match their neighbours. Various methods were used to group polygons together into fire events, with the constrained clustering method (Legendre 1987, Gordon 1996) producing more logical groupings since fire is an autocorrelated process. However, specifying parameters was difficult and no outputs closely matched the observed time-since-fire polygons.  5.2 Future Research Opportunities Historic forest cover information from older inventories or silvicultural data may provide better ages to use for predicting the time-since-fire age of cutover, no-age polygons. The multiple fire ages available in the time-since-fire dataset should also be incorporated into  56  the analysis. Additional metrics can be employed to compare the predicted time-since-fire polygons to the observed time-since-fire polygons, such as measures of polygon shape, fractal dimension, or similarities of attributes between adjacent polygons (Mladenoff et al. 1993, Wier et al. 2000). Large-scale fire parameters, such as fire severity, might also be predicted from forest inventories. The forest inventory lacks the spatial resolution for this application, but may record veteran trees and their cover pattern within a tree layer. Future work in entirely different directions could be undertaken. A possible area of study is to determine how to best target sampling for information used to train regression models to predict time-since-fire age. Inclusion of elevation or climate data might improve the prediction of time-since-fire values, since topography and weather control fire behaviour. There is no straightforward way to include these variables in regression models and their inclusion will require different modelling techniques than those used in this study. One potentially promising technique would be to examine raster-based models of fire spread to predict fire event polygons, such as those provided by the Spatially Explicit Landscape Event Simulator (Fall and Fall 2001).  5.3 Conclusion While the goal of producing time-since-fire output was met, the quality of the output was relatively poor. The model fits were mediocre, and the relationships between forest inventory data and time-since-fire data were not strong. No satisfactory method was found to specify correct parameters for grouping polygons into fire events. Forest inventory data were found to lack the detail and accuracy in ages required to derive accurate time-since-fire information. This is not unexpected given that the two types of datasets were collected for different purposes. Based on the results of this study, the forest inventory data is only of limited, rough use for deriving time-since-fire information over landscapes. This conclusion matches that of Rogeau (2003) who cautioned against using forest inventory age data for creating fire origin maps. The uses of stand origin information to calculate fire cycle by Van Wagner (1978) are only applicable if the forest has not encountered human disturbances and the ages accurately reflect the tree ages. These requirements did not hold for the forest  57  inventory used in this study. 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Canadian Journal of Forest Research 11: 554-562.  63  Appendix 1 Forest Inventory Codes in Presented Models Table A1-1: Definitions of the forest inventory modification codes. Modification Code BO CL CO CW NTA SF SN  Definition Burnover Clearing Cutover Cut windthrow No modification recorded Seasonal Flood Snags  Table A1-2: Definitions of tree species codes. Species Code NTA bP bS jP tA tL wB wS  Common Name No species recorded Balsam poplar Black spruce Jack pine Trembling aspen Tamarack White birch White spruce  Scientific Name Populus balsamifera L. Picea mariana (Mill.) Britton, Stems & Poggenburg Pinus banksiana Lamb. Populus tremuloides Michx. Larix laricina (Du Roi) K. Koch Betula papyrifera Marsh. Picea glauca (Moench) Voss  64  Appendix 2 Regression Model Parameters The following tables contain parameters used to predict time-since-fire age for the presented regression models. Tables 1 and 2 list parameters for single-age regression models and Tables 3 and 4 give parameters for multi-age models. The intercepts of the models are given in the first row. Parameters for continuous variables, without class values, are model slopes. Parameters for categorical variables with class values are added to the intercept depending on the category of the variable. Variables without parameters were not included in the presented model. The variables used are described in Table 2-3 and Table 2-4. The meaning of the modification and species codes are described in Tables A1-1 and A1-2 in Appendix I, while the meanings of the sub-category codes are described in Table 2-2. No typing available (NTA) values signify that there was no value recorded.  65  Single-age Regression Model Parameters Table A2-1: Regression model parameters for the single-aged models. Variable Intercept Forest Inventory Age Avg. Weighted Age (400m) Modification  Sub-Category Code  Primary Species  Secondary Species  Class Value  BO CL CO NTA SF SL SN 10 11 12 13 bP bS jP tA tL wB wS NTA bP bS jP tA tL wB wS  Model 1  Model 2  Model 3  Model 4  Model 5  37.34  34.16  33.57  45.92  41.65  0.60  0.57  0.57  0.59  0.60  1.38 1.00 22.83 4.59 3.34 -3.46 0.00 5.01 11.26 24.25 0.00 0.44 -8.29 -9.48 -7.82 -12.47 -9.22 0.00 -5.09 -2.29 -4.30 -3.72 -3.91 -7.57 -2.16 0.00  66  Table A2-2: Regression model parameters for the single-aged models, continued. Variable Intercept Forest Inventory Age Avg. Weighted Age (400m) Modification  Sub-Category Code  Primary Species  Secondary Species  Class Value  BO CL CO NTA SF SL SN 10 11 12 13 bP bS jP tA tL wB wS NTA bP bS jP tA tL wB wS  Model 6  Model 7  Model 8  Model 9  Model 10  49.49  6.76  3.21  10.93  13.18  0.60  0.39  0.37  0.37  0.64  0.61 2.74 3.30 22.20 6.19 4.19 1.42 0.00  0.60 3.50 2.95 21.92 5.87 3.56 1.08 0.00  0.53 -7.23 -9.50 -7.95 -11.97 -9.34 0.00 -4.71 -2.26 -3.56 -4.09 -4.04 -8.19 -2.83 0.00  0.91  -6.98 -6.86 -6.61 -7.08 -10.42 -10.22 0.00  67  Multi-age Regression Model Parameters Table A2-3: Regression model parameters for the multi-aged models. Variable Intercept Avg. Inventory Age Large Inventory Age Max. Inventory Age Min. Inventory Age Avg. Oldest Age (400m) Modification  Class Value  Model 1  Model 2  Model 3  Model 4  36.05 0.63  48.22  44.88  46.23  0.45 0.43 0.56  BO CL CO CW NTA SF SN  Table A2-4: Regression model parameters for the multi-aged models, continued. Variable Intercept Avg. Inventory Age Large Inventory Age Max. Inventory Age Min. Inventory Age Avg. Oldest Age (400m) Modification  Class Value  Model 5  Model 6  Model 7  Model 8  36.96  12.60 0.64  7.67 0.33  -15.04 0.34  0.70  0.68 23.41 39.88 55.07 29.00 22.84 24.37 0.00  0.30 0.32  BO CL CO CW NTA SF SN  22.28 43.60 57.08 31.80 22.68 20.10 0.00  68  Appendix 3 Regression Model Residuals Single-age Regression Model Residuals  Figure A3-1: Single-age model 1 residual values.  Figure A3-2: Single-age model 2 residual values.  Figure A3-3: Single-age model 3 residual values.  Figure A3-4: Single-age model 4 residual values.  69  Figure A3-5: Single-age model 5 residual values.  Figure A3-6: Single-age model 6 residual values.  Figure A3-7: Single-age model 7 residual values.  Figure A3-8: Single-age model 8 residual values.  Figure A3-9: Single-age model 9 residual values.  Figure A3-10: Single-age model 10 residual values. 70  Multi-age Regression Model Residuals  Figure A3-11: Multi-age model 1 residual values.  Figure A3-12: Multi-age model 2 residual values.  Figure A3-13: Multi-age model 3 residual values.  Figure A3-14: Multi-age model 4 residual values.  71  Figure A3-15: Multi-age model 5 residual values.  Figure A3-16: Multi-age model 6 residual values.  Figure A3-17: Multi-age model 7 residual values.  Figure A3-18: Multi-age model 8 residual values.  72  Appendix 4 Fire Event Groups The following tables show the output groupings of the 10-year partitioning, hierarchical clustering, and spatially constrained clustering. The number of output polygons was greater than the number of output groups because many polygons within a group were not adjacent. Only adjacent polygons in the same group were joined together by the dissolve operation used to produce the output fire event polygons. Table A4-1: Output groupings from the simple 10-year partition with no-age values assigned. Group ID  Avg. group time-since-fire age (years)  Spread within group (years)  1 2 3 4 5 6 7 8  120.8 109.9 99.7 89.7 79.8 71.1 63.2 54.3  5.6 9.4 9.9 10.0 10.0 10.0 9.9 6.0  Number of Area (ha) polygons within group 40.8 538.9 2,939.7 8,141.4 27,137.6 37,806.8 11,527.0 227.6  6 51 303 1033 3660 4610 1569 11  Table A4-2: Output groupings from the hierarchical cluster with a 5-year cluster width. Group ID  Avg. group time-since-fire age (years)  Spread within group (years)  1 2 3 4 5 6 7 8 9 10 11  59.6 64.9 70.7 77.3 85.0 91.3 97.1 103.7 110.0 120.7 50.0  7.0 5.0 5.0 7.0 7.0 3.0 7.0 5.0 7.0 6.0 0.0  Number of Area (ha) polygons within group 2325.0 14377.8 23947.1 29275.9 11771.8 2208.3 3080.7 873.6 456.0 40.8 2.9  175 913 1436 2088 929 250 245 60 31 6 1  73  Table A4-3: Output groupings from the hierarchical cluster with a 10-year cluster width. Group ID  Avg. group time-since-fire age (years)  Spread within group (years)  1 2 3 4 5 6  67.8 79.6 94.2 105.8 120.7 50.0  19.0 15.0 11.0 13.0 6.0 0.0  Number of Area (ha) polygons within group 40649.9 41047.7 5289.0 1329.6 40.8 2.9  2524 3017 495 91 6 1  Table A4-4: Output groupings from the spatially constrained hierarchical cluster with a distance penalty weight of 0.0002. Group ID  Avg. group time-since-fire age (years)  Spread within group (years)  1 2 3 4 5 6 7  93.5 80.9 69.5 108.1 121.0 117.0 50.0  18.0 12.0 22.0 12.0 6.0 4.0 0.0  Number of Area (ha) polygons within group 7860.9 29294.5 50284.3 852.3 39.5 25.5 2.9  670 2083 3322 51 5 2 1  Table A4-5: Output groupings from the spatially constrained hierarchical cluster with a distance penalty weight of 0.0005. Avg. group Group ID time-since-fire age (years) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22  89.7 76.9 76.2 67.3 86.4 79.9 61.8 97.9 102.0 97.7 73.1 60.3 85.5 108.1 97.3 121.0 109.8 117.0 109.0 101.0 115.0 50.0  Spread within group (years) 13.0 17.0 13.0 20.0 13.0 12.0 11.0 14.0 9.0 11.0 12.0 9.0 10.0 8.0 4.0 6.0 9.0 4.0 0.0 0.0 0.0 0.0  Number of Area (ha) polygons within group 4079.4 22503.0 3112.1 30650.1 4838.1 8889.6 520.1 3150.6 133.7 295.5 6753.9 1323.6 1297.9 612.0 54.6 39.5 14.9 25.5 41.1 13.7 8.0 2.9  370 1621 235 1954 403 661 28 215 14 41 382 69 80 39 6 5 4 2 2 1 1 1 74  Table A4-6: Output groupings from the spatially constrained hierarchical cluster with a distance penalty weight of 0.001. Group ID  Avg. group time-since-fire age (years)  Spread within group (years)  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  86.2 89.2 75.4 78.4 78.2 71.8 70.8 85.5 66.9 64.7 78.1 78.3 80.1 63.2 70.6 62.4 99.9 101.8 74.8 64.4 98.1 64.2 81.5 68.0 90.7 81.3 72.6 82.9 89.4 69.9 91.1 88.2 96.8 91.6 107.8 95.1 91.7 105.9 97.8 84.4 55.5 121.0 110.0 109.8 96.5 117.0  2.0 15.0 24.0 14.0 10.0 11.0 14.0 14.0 17.0 12.0 15.0 13.0 9.0 12.0 14.0 9.0 10.0 9.0 13.0 18.0 10.0 9.0 15.0 7.0 8.0 8.0 11.0 13.0 8.0 8.0 9.0 5.0 13.0 5.0 8.0 9.0 11.0 9.0 4.0 6.0 1.0 6.0 5.0 9.0 3.0 4.0  Number of Area (ha) polygons within group 11.5 4837.1 11911.0 6909.1 1220.3 4421.6 3877.4 4582.4 10491.9 2518.8 4470.0 1780.3 943.5 2751.6 6886.6 257.5 1638.4 82.6 4796.4 3733.7 263.8 437.9 1619.5 270.4 153.8 848.9 2633.1 280.1 220.9 676.1 331.2 23.9 905.3 174.7 305.9 153.4 356.6 39.3 37.8 33.6 44.8 39.5 220.0 14.9 16.8 25.5  6 447 827 538 108 313 181 367 701 171 390 171 78 172 370 9 129 9 299 252 37 36 83 25 24 71 65 32 24 28 25 5 23 16 23 12 18 8 4 7 2 5 7 4 2 2  75  Group ID  Avg. group time-since-fire age (years)  Spread within group (years)  47 48 49 50 51 52 53 54  91.0 109.0 109.0 102.0 101.0 115.0 50.0 60.0  0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0  Number of Area (ha) polygons within group 9.9 1.3 39.8 24.7 13.7 8.0 2.9 10.2  1 1 1 1 1 1 1 1  76  

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