Performance evaluation of spectral vegetation indices using a statistical sensitivity function

A great number of spectral vegetation indices (VIs) have been developed to estimate biophysical parameters of vegetation. Traditional techniques for evaluating the performance of VIs are regression-based statistics, such as the coefficient of determination and root mean square error. These statistics, however, are not capable of quantifying the detailed relationship between VIs and biophysical parameters because the sensitivity of a VI is usually a function of the biophysical parameter instead of a constant. To better quantify this relationship, we developed a “sensitivity function” for measuring the sensitivity of a VI to biophysical parameters. The sensitivity function is defined as the first derivative of the regression function, divided by the standard error of the dependent variable prediction. The function elucidates the change in sensitivity over the range of the biophysical parameter. The Student's t- or z-statistic can be used to test the significance of VI sensitivity. Additionally, we developed a “relative sensitivity function” that compares the sensitivities of two VIs when the biophysical parameters are unavailable.