Quantification of land-surface heterogeneity via entropy spectrum method

Surface heterogeneity is present on every scale of the land surface. However, its role in the exchange processes between the land surface and the atmosphere is still an open question. In this paper, we present a method, which combines the decomposition of land-surface heterogeneity into fine and coarse structures with the quantification of the structures using information entropy. The resulting entropy spectrum allows the assessment of the amount of information on different scales. The wavelet transformation and the most frequent-value method are used as filters for the decomposition. We also derive an analytical formula for estimation of the probability density function (PDF) of filtered random surface parameters using the most frequent-value method. By analyzing the entropy spectrum of synthetic data, we derive rules for the interpretation of the entropy spectrum. We then apply them to real data and appraise, which scale of the heterogeneity is important for land surface and atmosphere interactions.