Quantification of land‐surface heterogeneity via entropy spectrum method

Abstract

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.

Analysis of the Spatial Variability of Land Surface Variables for ET Estimation: Case Study in HiWATER Campaign

“…Thus, modelers are especially interested in the PDF of the surface variable [14,34], which tells how frequent a certain parameter value occurs. For the same variable, if the PDF is narrow, then the surface is more homogeneous, and if the PDF is broad, the surface is more heterogeneous [34].…”

“…Thus, modelers are especially interested in the PDF of the surface variable [14,34], which tells how frequent a certain parameter value occurs. For the same variable, if the PDF is narrow, then the surface is more homogeneous, and if the PDF is broad, the surface is more heterogeneous [34]. PDF can describe heterogeneity in a qualitative manner, however, it is unable to quantify the information content and cannot be used to compare the variability of different variables over the same observed scene [34].…”

“…Other methods involve mathematical models such as wavelet analysis [19] and Fourier transform [32]; moreover, geographically weighted regression has become popular to explore spatial heterogeneity [33]. These methods are mostly used to analyze the heterogeneity of land surface solely, so the spatial patterns of pixels and spatial variability of the variable values both need to be considered [26,34]. The other group focuses only on spatial variability of the variable values and does not consider the spatial patterns.…”

“…The other group focuses only on spatial variability of the variable values and does not consider the spatial patterns. The commonly used methods include the quantile, range, deviation, variance/standard deviation, moment, coefficient of variation (CV) [25], Gini coefficient and entropy [34,35], and these methods are often used for specific purposes (e.g., building models) [36].…”

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“…Surface heterogeneity is one of them by affecting local surface-air interactions [83,84]. Heterogeneity can be characterized by a moving window-based semi-variogram model [85], spatial scale-based entropy spectrum [86], or landscape structure-based indices [87] and may help improve the local Ta estimation considering neighborhood interactions involved in the pixel-station pair correlation. In other words, it alters the representativeness of the station-measured observation at a pixel scale, and thus could be appropriate as a modulator to adjust the spatial distribution of the estimated Ta, as an additional weight to adjust the contributions of spatial predictors [5], or as a reference to limit the regression to the less heterogeneous areas.…”