Spatial error propagation when computing linear combinations of spectral bands: The case of vegetation indices

The collection of accurate and timely information on land use, crops, forest and vegetation are increasingly based on remote sensing spectral measurements produced by satellites. The most recent spacecrafts like the Earth Observing 1 (EO-1) produce a rich source of information being endowed with hyperspectral sensors that can provide up to 200 or more channels. In many instances such a multivariate signal has to be reduced to just one single value per pixel representing a particular characteristic of land. Linear combinations of bands are the general form of many indices. Since each individual image used to construct indices contains errors, when combined they produce a propagation of errors, a process that can distort a final output map. In this paper we measure the extent of error propagation when building linear vegetation indices. We consider three types of indices: the difference vegetation index (DVI), selected Kauth-Thomas indices (SBI, GVI and WET), and principal components, using benchmarking examples taken from the remote sensing literature. The main implication emerging from these examples is that the SBI and the first principal component are the indices more prone to error propagation. The formalization presented here allows a user to derive measures of error propagation in cases where technical characteristics of a sensor and physical characteristics of a landscape are known. These results can help a user to choose between alternative vegetation indices, and to associate a measure of reliability with such indices.