# Spot initialization

Probability of new spots initialization is calculated by multiple linear regression. Age of forest stand, volume per hectare, stand density, distance to the edge of forest, vegetation index NSC2 and annual potential solar radiation are independent variables. Whole procedure of calculation is represent on figure below.

In first step the softwe derive actual mask of forest stand. Spots of bark beetle development are then subtract from this mask of forest stands. Distances to the forest edge is calculated on the basis of the subtract mask of forest stand. Result layer is one of the input for multiple linear regression.
Multiple linear regression is calculated in samples of randomly generated points. Same number of samples from last year is generate for bark beetle outbreaks as for forest areas unaffected by bark beetle outbreaks. For areas with bark beetle outbreaks is value 1 prescirebed and for areas unaffected by bark beetle outbrakes is value 0 prescribed.

Whereas the unaffected areas of forest by bark beetle have not usually the same size as bark beelte outbrakesÂ  areas over the last year, therefore it is not possible to use this areas for multiple linear regression. Situation where one of this areas is much bigger than the other causes that the probability function derived from multiple linear regression will be constant. For this is reason values from generated random samples are used to derive probability function. Maximal number of samples is entered by user or it is derived automaticaly from input layers.

Input rasters of independent values are containing values with different sizes. For example values of total annual solar radiation is many times bigger than values of stand density or age of forest stand. Then the coefficient that is derived by multiple linear regression from layer with higher values seems like it is zero. For this reason relative values are used for linear regression and not absolute values. Before the calculation of multiple linear regression all values are set to range from 0 to 1.

Coefficients of multiple linear regression are calculated for data from generated random samples. Coefficients are used to calculate the probability of spot initialization layer. The multiple linear regression function does not guarantee values just from 0 to 1. Output raster contain negative values also values higher than 1.

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