Abstract
Organizations of many variables in nature such as soil moisture and topography exhibit patterns with no dominant scales. The maximum entropy (ME) principle is proposed to show how these variables can be statistically described using their scale-invariant properties and geometric mean. The ME principle predicts with great simplicity the probability distribution of a scale-invariant process in terms of macroscopic observables. The ME principle offers a universal and unified framework for characterizing such multiscaling processes.
Highlights
Organizations of many variables in nature such as soil moisture and topography exhibit patterns with no dominant scales
The question is: would it be possible to use the known multiscaling moments to determine probability distributions? This study considers a possible approach, i.e., the principle of maximum entropy (ME), to answer that question
The generality and power of ME is rooted in the fact that the Bayesian interpretation of probability allows probability theory to be applicable to any situation where statistical inference based on incomplete information is sought
Summary
Organizations of many variables in nature such as soil moisture and topography exhibit patterns with no dominant scales. In this study we attempt to use the ME theory to characterize some important variables in hydrometeorology: the drainage area of a river network, soil moisture, and topography. We present two cases: (1) drainage area of river network (DARN), and (2) surface soil moisture field (SSM) and topography as captured in a digital elevation map (DEM).
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