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I am trying to determine the relationship between multiple factors (slope(from dem-raster), aspect(from dem-raster), proximity to settlements (buffers-polygon)) with fire events(point data, with date attribute) spatially and temporally.

I have classified the multiple factors as a ranking between 1-10 (10 being the most likely to increase fire risk) but would like to quantitatively and spatially assess the relationship between the ranking and fire events.

I don't know which technique will provide me with what I want. Does anyone have any ideas of how I can investigate and represent this relationship in ArcGIS?

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Perhaps a heat-map type analysis would be suitable. You could convert the proximity to settlements into a raster (with the ranking score being the raster value). After that you could then use the weighted sum tool, or perhaps perform the calculations yourself in raster calculator to create a final raster that displays a score that is derived from the multiple fire risk factors.

If you haven't already taken care of it in your ranking methodology, you could weigh these factors accordingly as well (e.g. is proximity to settlements more of a contributor to fire risk than slope?). So in the end you would have a raster which would display a low score if significant slope (or lack of?) and settlements are not nearby but display a high score if they are. You could then overlay your historical fire event points over that raster and see how it lines up with your findings.

If you choose to use the weighted sum tool, keep in mind that it will constrain its output to the extent of the smallest raster in the analysis by default, though this can be changed.

  • A "heat-map" is produced by a kernel density function. It is dangerous advice suggesting using this approach in a statistical model. The relationships could easily be the result of the kernel smoothing and not the actual functional relationship. Results can also change dramatically, depending on the specification of the kernel size and sigma. – Jeffrey Evans Dec 16 '16 at 16:35
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In determining correlation between layers, one method to use is the "point data" and "rank field" you have in your attribute data. For suitable assessment, i suggest your points should not be less than 30. You can use "Incremental Spatial auto correlation" in Arc Map. This tool will need your "point data", and "ranked field" to produce probability value( p or z value) against distances. There are set of value for "p" or "z" to accept correlation or to consider it null.

see the image below of an incremental spatial auto correlation.

enter image description here

The distances in graph that has trends has their points in the graph circled blue. Trace the distances from the blue circled points, to generate a hot or cold spot analysis map. The hot or cold spot map including graph from incremental spatial auto correlation will help interpret the map where there are increased and low fire risk.

 Hotspot analysis map image.(The traced distance from the graph will be used for Hotspot Analysis map)

enter image description here

You can get this tools from,

Incremental spatial Auto correlation > Arc Toolbox > Spatial Statistics > Analyzing Patterns >Incremental Spatial Auto correlation (Please take output Report, that is the graph).

Hotspot Analysis Map>Arc Toolbox > Spatial Statistics > Analyzing Patterns > Hotspot Analysis (self potential field = distance from Incremental spatial autocorrelation)

  • This does not address the question! Quantifying autocorrelation would indicate the global spatial structure of a given variable but is univariate and does not quantify any correlative relationships. The local autocorrelation is a measure of nonstationarity and also does not indicate an functional relationship between variables. BTW, "incremental spatial autocorrelation" is made up ESRI language, the correct term is a correlogram which has been a long standing methodology in spatial statistics. – Jeffrey Evans Dec 16 '16 at 16:33

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