7th Workshop on Forest Fire Management - EARSeL, European ...

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I - PRE-FIRE PLANNING AND MANAGEMENT
2 - Methods
Spatial analysis was used in order to characterize the fire spatial distribution
and to understand if it is random (autocorrelation equal to zero), uniform
(negative autocorrelation) or clustered (positive autocorrelation). Two
indicators of spatial autocorrelation were used, Moran’s Index (I) and the
Getis & Ord’s Index (G).
Moran’s I (Moran, 1948) is a global indicator of spatial autocorrelation, so
it measure the degree of autocorrelation of a point pattern. It is defined
as:
where N is the number of events, Xi ed Xj are intensity values taken by,
respectively, the point i and the point j and is the mean of the considered
variable. Wij is one element of the weights matrix, that contains spatial
relationships between events because each element of the matrix represents
the spatial weight of each single event, defined according a fixed
proximity criterion. One of the most common criterion is the Fixed Distance
Band Method: if an event is included in the fixed distance band it will be
considered in the calculation, otherwise it will be excluded.
Moran’s I is included between the interval [-1; 1]. If the index is less then
0 the point pattern is negatively autocorrelated; if it converges to 0, the
spatial distribution is random; if I is greater than 0 there are some cluster
in the distribution.
Getis & Ord’s G is instead a local indicator of spatial association. It allows
us to understand where clusters are located. It is defined by the equation
(Getis and Ord, 2001):
where N is the number of events, Xi and Xj are intensity values taken by,
the point i and the point j, respectively, is the mean of the considered variable,
wi(d) is one element of the weight matrix.
Elements with low intensity are autocorrelated if they have also a low G
value; in the same way, if they have a high intensity, they should have a
high G, to be clustered.