Testing the Beta-Lognormal Model in Amazonian Rainfall Fields Using the Generalized Space q-Entropy

Hernán Salas,Oscar Mesa,Germán Poveda

doi:10.3390/e19120685

Abstract

We study spatial scaling and complexity properties of Amazonian radar rainfall fields using the Beta-Lognormal Model (BL-Model) with the aim to characterize and model the process at a broad range of spatial scales. The Generalized Space q-Entropy Function (GSEF), an entropic measure defined as a continuous set of power laws covering a broad range of spatial scales, S q ( λ ) ∼ λ Ω ( q ), is used as a tool to check the ability of the BL-Model to represent observed 2-D radar rainfall fields. In addition, we evaluate the effect of the amount of zeros, the variability of rainfall intensity, the number of bins used to estimate the probability mass function, and the record length on the GSFE estimation. Our results show that: (i) the BL-Model adequately represents the scaling properties of the q-entropy, S q, for Amazonian rainfall fields across a range of spatial scales λ from 2 km to 64 km; (ii) the q-entropy in rainfall fields can be characterized by a non-additivity value, q s a t, at which rainfall reaches a maximum scaling exponent, Ω s a t; (iii) the maximum scaling exponent Ω s a t is directly related to the amount of zeros in rainfall fields and is not sensitive to either the number of bins to estimate the probability mass function or the variability of rainfall intensity; and (iv) for small-samples, the GSEF of rainfall fields may incur in considerable bias. Finally, for synthetic 2-D rainfall fields from the BL-Model, we look for a connection between intermittency using a metric based on generalized Hurst exponents, M ( q 1 , q 2 ), and the non-extensive order (q-order) of a system, Θ q, which relates to the GSEF. Our results do not exhibit evidence of such relationship.

Highlights

Results show that the histograms of β and σ2 are statistically different for both climatic regimes, and, that the Cumulative Distribution Functions (CDFs) of the parameter β for the Easterly and Westerly regimes are significantly different according to a k-sample test, based on the likelihood ratio [66] at 95% confidence level, but no so for the parameter σ2
Using 2-D radar rainfall fields from Amazonia, we investigate the spatial scaling and complexity properties of Amazonian rainfall using the Generalized Space q-Entropy Function (GSEF), defined as a set of continuous power laws covering a broad range of spatial scales, Sq (λ) ∼ λΩ(q), to test for the validity of the random multiplicative cascade BL-Model model (BL)-Model in representing 2-D properties of observed rainfall fields
Our results show that for both climate regimes the GSEFs are not statistically different whereas the BL-Model parameters σ and β are statistically different

Summary

Introduction

[19] found that 2-D rainfall fields over Amazonia exhibit multiscaling properties in space, which means that the relationship Mr (λ) ∼ λ−τ (r) exhibits a non-linear behavior, where λ is the spatial scale, r the order of the statistical moment and τ (r ) is the r-th moment scaling exponent. They show that both the diurnal cycle and the predominant atmospheric regime of Amazonian rainfall (Easterly or Westerly) exert a strong control on the scaling properties of Amazonian.

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