GEOG 566

         Advanced spatial statistics and GIScience

April 22, 2018

Mapping fire extent from binary point data

Filed under: Exercise/Tutorial 1 2018 @ 11:25 am

(Please click the links to view all figures.  They aren’t very clear or large in the post!)

Question that you asked?

My overall objective is to build a predictive model of the annual spatial distribution of fire across my fire reconstruction area.  This will inform how fire extent and distribution were related to climate, topography, and fuels. Prior to doing this I need to answer these questions:

  1. What is the best method for mapping fire boundaries from binary point data?
  2. What do these maps indicate about spatial patterns of historical fires?

Dataset – I reconstructed fire history at 31 sampling points evenly distributed on a 5km grid, and 21 points that encircled landscaped patches of lodgepole pine forest (Figure 1). Point samples were denser near lodgepole pine forests because they may limit fire spread due to slow fuel recovery. At each sampling point I collected 3-6 cross sections from fire-scarred trees (194 trees total). All cross sections were precisely dated, and 1,969 fire scars were assigned to the calendar year of their formation. At each sample point individual tree records were composited into a record of fire occurrence at the sample point. Pyrogeographers composite fire records at points because most trees that survive fire do not form and preserve fire scars even when directly in the path of fire, and recorder trees record fire events over different time periods. Obtaining a full census of fire events at a sample point (e.g. figure 2) requires sampling multiple recorder trees within a defined search radius (250 meters in my study). I eliminated 89 scars that occurred on only one tree or could have been attributed to lightning, mechanical, or insect damage.

Figure 1 Point samples and recorder trees across the study area

Figure 2. Top panel –  individual recorder trees at a sample point, Bottom panel – composite records at each sample point. Vertical slashes on timelines indicate fire events.


Name of the tool or approach that you used?

Question 1 – I compared three different tools for mapping fire extent from binary point data. This has also been done by Hessl et al. 2008, but for a different study landscape using a smaller sampling grain over smaller areas.

  1. Thiessen polygons are polygons whose boundaries define the area that is closet to a sample point. Using thiessen polygons to map fires assumes the best evidence of fire or no fire at an unsampled point is the record at the nearest sampled point. Thus all unsampled areas are assigned the record of the nearest sampled point.
  2. Kriging is an optimal interpolation method that uses a linear combination of weights at know points to estimate the value at an unknown point (Burrough and McDonnel 1998).
  3. Inverse Distance Weighting (IDW) is a deterministic interpolation method that calculates the value of an unsampled cell as a distance-weighted average of sample points within a specified neighbor (Burrough and McDonnel 1998).

Question 2 – To assess spatial variation in mapped fires and the sum of all fires that occurred I used three approaches

  1. I created an animation of fires from 1700 – 1925 using the Time Slider tool in arc map to visualize each fire event using the thiessen polygon mapping method
  2. I mapped fire history statistics (e.g. mean, maximum, interval, CV of interval, fire size) at each point using the Thiessen Polygon and Kriging methods
  3. I performed cluster analysis on the occurrence of fire from 1700-1918, and then mapped the fire groups.


Brief description of steps you followed to complete the analysis?

All mapping approaches were testing in ArcMap.

Question 1

1a. I used the create thiessen polygons tool with my sample points as the input. Make sure to click environments to specify the processing extent or you will likely get unintended results! Outer polygons extend infinitely, and need to be clipped. I clipped them using my study area boundary (2.5km from any sampled point).

To map fires for each year, I used R to subset my fire year data for each tree to a composite at each sample point.  In Arc map, I joined this data to my sample points and thiessen polygons surrounding each sample point

1b and c. Prior to Kriging and IDW I created a binary matrix of fire occurrence for each fire year at each plot. Rows were plots and columns were fire years (52 rows by 132 columns). For both Kriging and IDW the input features were my sample points, and the value field was the binary presence/absence of the fire year I wanted to map.

I initially used the default settings for Kriging and IDW. After comparing results with the Thiessen polygon method I adjusted the importance of near versus far points by adjusting the search radius. For IDW you can also adjust the power parameter. As power increases IDW approximates the Thiessen polygon method where the interpolated value takes on the value of the nearest known point.

Kriging settings: method = ordinary semivariogram, model = spherical, search radius variable, number of points = 12.

IDW settings: power = 2, search radius variable, number of points = 12.

Question 2

2a. ArcMap has a convenient time slider that allows you to move through time to visual temporal variation in spatial data. I simply followed a tutorial to use the tool.

Make sure that you store all shapefiles that depend on an animation in a file geodatabase or the animation and Time Slider will not function correctly. The nice feature about enabling time is that any joins you make are dynamic and info tables update with each time step, but only if you store files in a geodatabase!

2b. I calculated summary statistics the fire record at each plot from 1700-1918 using the ddply package in R. This helpful package allows you to apply a set of functions to a group identifier (plot) within a data frame.  I’m happy to share the code if this is useful for someone in the class. After the summary table was created I joined this to my shapefile of sample points in Arc map to map variation in summary statistics. I used Thiessen polygons and Kriging to spatially represent variation in the statistics.

2c. Taylor and Skinner (2003) used cluster analysis to identify and map spatial patterns of fire occurrence. Similarly, I created a binary matrix of fire occurrence where rows were sample points and columns were fire years.  Cluster analysis was performed in PC-ORD using a Sorensen distance measure with a flexible beta method of β = 0.25. The resulting dendrogram was pruned by examining stem length and branching distribution to identify nodes that maximized both within-group homogeneity and between-group differences, while minimizing the number of groups (McCune and Grace 2002).


Brief description of the results you obtained? (I went overboard on what I included, but its all useful at this stage)

I obtained maps of all fire events using Thiessen Polygons, and maps of selected fires using Kriging and IDW for comparing the methods. In these maps red indicates area burned and blue indicates unburned.  The gradient between indicates uncertainty for Kriging and IDW. Trees that recording fire are represented by black points and trees that did not are represented by white points.

1918 map of fire extent comparing interpolation methods

1829 map of fire extent comparing interpolation methods

A movie of fire events based on Thiessen Polygon Mapping this file is too large to attach 🙁

FireMetrics mapped using thiessen polygons

FireMetrics_Kriging Metrics mapped using Kriging

FireGroups Fire occurrence groups identified through cluster analysis

I was also able to calculate and graph Fire Extent by year using the Theissen polygon method


Critique of the method- what was useful, what was not?

 Fire mapping techniques – The advantage of the Kriging and IDW techniques are that multiple data points are used to interpolate fires, whereas Thiessen polygons are informed only by the nearest point. Additionally Kriging and IDW are able to represent uncertainty of fire perimeters while Thiessen polygons produce abrupt fire boundaries that are an artifact of the sample distribution.

Kriging produced the most seemingly realistic and attractive fire maps for many fires (e.g. 1918).  However, Kriging poorly represented several large fires with irregular un-burned patches (e.g. 1829). Kriging requires the spatial variation in the variable represented can be similarly observed at all locations (requires spatial homogeneity), and performs best with uniform sampling density. Irregular unburned patches occur in several of the large fires that occurred in my study landscape. Logically they occur where fire burned and removed fuel in the years preceding the fire of interest.  For example, the large unburned area in 1829 on the East side of the study landscape burned in 1827. In combination, irregular burn probabilities and non-uniform sampling limit the utility of Kriging to consistently represent fire perimeters for my data and study landscape.

IDW was not similarly limited by irregular burn patterns. However, IDW creates a bullseye pattern of high to low burn probability where sample points are isolated or are on burn perimeters.  This imputes lower burn probability in the area between the somewhat isolated point and the main mass of the fire.  When all points within a large area recorded fire, IDW imputes a higher burn probability to the unsampled area at the center of the sampled points that actually recorded fire. In reality we know the sampled points burned, and they should not have lower burn probability than the unsampled points. IDW’s representation of fire can be improved by decreasing the search neighborhood or increasing the power function. However, this approaches the Thiessen polygon interpolation technique (see 1829 map).

Both Kriging and IDW are time intensive and would require a different and subjective threshold to be applied to each fire map to delineate burned and unburned area. The Thiessen polygon method ultimately provides the most efficient, objective, and parsimonious method to map fire perimeters based on the distribution of my sample points. After watching the animation of fire events mapped with Thiessen polygons the most important pattern that appeared was a consistent lag between fires that prevented reburn within short (<5 year) time periods.  Thus, fuel recovery after fire may constrain fire extent, and time since fire may be an important predictor of the annual spatial distribution of fire in the landscape. Kriging and IDW assume higher likelihood of fire at points where no fire was recorded that are surrounded by points that did record fire.  This provides another rationale for using the binary Thiessen interpolation method.

In making my choice to use the Theissen polygon method I also considered that area burned and fire metrics were highly and significantly recorded across all interpolation techniques (Hessl et al. 2007). Furthermore, Thiessen polygons accurately represented burn perimeters and fire frequency through a validation using known modern day fire perimeters (Farris et al. 2010).

Mapping Fire Metrics

I preferred the Kriging method to identify regions of the landscape with distinct fire regime metrics.  The Kriging method incorporates more than just the sample point allowing regions with higher or lower values for a metric to be clearly represented. The Southeast region of the study area burned with lower frequency, longer maximum intervals, and higher variability. This area has a high concentration of low productivity and relatively fuel limited lodgepole pine forest.

Identifying and Mapping Fire Types

Cluster analysis of fire years appears to be a promising technique for identifying regions with a similar history. The FireGroups were geographically clustered in the study landscape.  It may be possible to use these fire types to identify landscape features that constrain fire. This map suggests that the similarity or spatial auto correlation of fire history varies depending on position within the landscape.  This suggests a non uniform distribution of landscape features that constrain fire.


See this link for more about Kriging

Burrough P and McDonnel R. 1998. Principles of geographical information systems. Oxford: Oxford University Press.
Dieterich JH. 1980. The composite fire interval: a tool for more accurate interpretation of fire history. USFS GTR- RM-81.
Farris CA, Baisan CH, Falk DA, Yool SR, Swetnam TW (2010) Spatial and temporal corroboration of a fire-scar based fire history in a frequently burned ponderosa pine forest. Ecological Applications 20(6):1598-1614.
Hessl A, Miller J, Kernan J, Keenum D, McKenzie D. 2007. Mapping Paleo-Fire Boundaries form Binary Point Data: Comparing Interpolation Methods. The Professional Geographer 59:1, 87-104.
Taylor AH, and CN Skinner (2003) Spatial Patterns and Controls on Historical Fire Regimes and Forest Structure in the Klamath Mountains. Ecological Applications 13(3):704-719.
Farris CA, Baisan CH, Falk DA, Yool SR, Swetnam TW (2010) Spatial and temporal corroboration of a fire-scar based fire history in a frequently burned ponderosa pine forest. Ecological Applications 20(6):1598-1614.

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