# Sensitivity of Optical Satellites to Estimate Windthrow Tree-Mortality in a Central Amazon Forest
## 2 Materials and Methods
### Remote Sensing Estimates of Windthrow Tree Mortality  
We fitted a Generalized Linear Model (GLM) [88] relating NPV with field-measured windthrow tree-mortality (see Section 2.1). The GLMs were fitted for each satellite. We described the distribution of residuals using the binomial family, and used the _logit_ link function, in which linear predictors must be reversed to the scale of the observations by means of an inverse function [88].  
We used the field subplots only for model fitting, thus avoiding overfitting problems for the cases in which the validation was performed using the same subplots [89]. Virtual subplots were not used for validation/training; we focused on evaluating the performance of the models, and also assessed the Residual Deviance using Analysis of Variance (ANOVA). For each model we calculated the Akaike Information Criteria (AIC, [90]). Standard Error of the Estimates (S\({}_{\text{yx}}\)), Root Mean Square Error (RMSE), Residual Standard Deviation (Sigma), and the Adjusted Coefficient of Determination (R\({}^{2}\)) computed with the Kullback-Leibler divergence formula (R\({}^{2}\)KL, [91]). The R\({}^{2}\)KL is suitable for exponential family models (e.g., logit), which retains the informative properties of the fit due to the inclusion of regressors [91,92]. Unlike the linear model, which is based on the Ordinary Least Squares (OLS) approach, R\({}^{2}\) in these models does not represent the proportion of variability explained, because the binomial distribution does not have the same variability structure as the normal distribution used in simple linear regression [93]. For this reason, some methods for measuring the goodness-of-fit of GLM models, in particular for log-link families (e.g., binomial, exponential, gamma), have been constructed to express one more diagnostic measure of the nonlinear models. Among the available methods, the R\({}^{2}\)KL (Kullback's formula) provides a measure of the divergence between the distribution of observed and estimated values [91,92]. This measure can be used analogously to the R\({}^{2}\) for quantifying how much of the variation of field-measured tree mortality was captured by the fitted models [94]. The best model was the one with the lower Residual Deviance, AIC, S\({}_{\text{yx}}\), RMSE, Sigma, and higher R\({}^{2}\)KL.  
We assessed the precision (i.e., minimum [Min], maximum [Max], median, and mean) and accuracy (i.e., standard deviation [SD], standard error [SE], and 95% confidence interval of the mean [hereafter referred to as 95% CI]) of remote estimates of tree mortality. For comparing our results with those reported for other Amazon regions [2,4], we also expressed windthrow tree-mortality as categories of severities: old-growth/undisturbed forest [\(\leq\)4% of windthrow tree mortality]; low windthrow severity [4% < windthrow tree mortality \(\leq\) 20%]; moderate windthrow severity [20% < windthrow tree mortality \(\leq\) 40%]; high windthrow severity [40% < windthrow tree mortality \(\leq\) 60%]; and extreme windthrow severity [>60% of windthrow tree mortality]).