Concentration functions and entropy bounds for discrete log-concave distributions

Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They are used to derive certain variants of the entropy power inequalities.

High Spatial Resolution Mapping of Glaciers Mass Variations over the Gulf of Alaska Using Spatial Concentration Functions and Monthly GRACE and GRACE-FO Data

<p>The spatial resolutions of GRACE solutions (level-2 dampened by truncation and/or filtering and level-3 called MASCON) are generally too coarse (~300km) to estimate regional changes in the terrestrial water storage (TWS) components. Focusing methods such as constrained forward approach and spatial concentration functions could improve the spatial distribution estimates of concentrated masses (e.g. glaciers, lakes). In this study, we apply spatial concentration functions to create high resolution monthly time-series of glaciers mass changes over the Gulf Of Alaska (GOA). Spatial weighting functions are based on heterogeneous glaciers mass distribution maps called a priori. First, we use three a priori of different spatial resolutions and sources to create different spatial functions. Second, we compare the amplitude of glaciers mass variations with others GRACE TWS components over the GOA, using the same spatial functions, to improve the discrimination of glaciers mass distribution. Third, we use a variety of GRACE solutions with different processing assumptions given identical resolution characteristics to estimate the uncertainties associated with our methodological framework. To analyze the accuracy of our assessments, we also compare trends resulting from the spatial concentration functions and the constrained forward approach. Then, we compare our estimates with three released MASCON solutions and published results over: (i) the GOA, (ii) the Saint-Elias Mountains and (iii) the Upper Yukon watershed. The results indicate that the spatial functions are sensitive to glaciers mass distribution. The signal from the glaciers dominate the GRACE TWS over the GOA. All solutions used, provide comparable glaciers mass variations. The two focusing methods give similar trends, but the constrained forward approach is time-consuming. The results obtained here could provide to be useful to further our understanding of the contribution of the GOA’s glaciers to sea-level rise and to river flows at the regional scale.</p>