I am looking for a mathematical expression that accounts for the change in size of paired fires. Ie. there are thousands of fires, all paired (ie. two separate simulations have been run, and each fire in one simulation has a counterpart in the other simulation).
The ratio of one fire to the other only gives me the relative change, but that gives equal weight to fires that grew from 5 to 10 hectares, and fires that grew from 50,000 to 100,000 ha.
I am looking for a metric that can account for:
- the direction of the change (ie. negative if it shrinks, 0 if it stays the same, and positive if it grows),
- the magnitude of the change so that a fire that grows from 1-10 ha gets a much smaller value than a fire that grows from 100-1000 ha.
Hi Chris:
Have you tried comparing the event size distributions? First build the cumulative function of the frequency size distribution. Then fit one parameter Pareto or truncated Pareto models to the log10-log10 transform of the inverse of the cumulative distribution function or the probability density function. You should see straight sloping lines with negative slope values. This will be driven by high frequency small fires and low frequency large fires. Then compare the frequency size distributions (or pdfs) statistically using maximum likelihood estimation (MLE) techniques with at least n=500 to 1000 iterations. This technique will tell you the likelihood that the slopes, the x-min values, and the influence of the largest patch sizes are different or not.
Hi Paul,
Thanks for the suggestion. Initially I was looking at a way to have a univariate measure that I could map. That is to say, for every paired fire to be able to draw the point but scale the point by the magnitude of the change in fire size for that particular fire. However, what you suggest is indeed a better way to examine the actual change in distributions and to determine their significance.