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Open AccessArticle

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

Facultad de Minas, Departamento de Geociencias y Medio Ambiente, Universidad Nacional de Colombia, Sede Medellín, Carrera 80 # 65-223, Medellín 050041, Colombia
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Entropy 2017, 19(12), 685; https://doi.org/10.3390/e19120685
Received: 9 October 2017 / Revised: 28 November 2017 / Accepted: 8 December 2017 / Published: 13 December 2017
(This article belongs to the Special Issue Entropy Applications in Environmental and Water Engineering)
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. View Full-Text
Keywords: hydrology; tropical rainfall; statistical scaling; Tsallis entropy; multiplicative cascades; Beta-Lognormal model hydrology; tropical rainfall; statistical scaling; Tsallis entropy; multiplicative cascades; Beta-Lognormal model
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Salas, H.D.; Poveda, G.; Mesa, O.J. Testing the Beta-Lognormal Model in Amazonian Rainfall Fields Using the Generalized Space q-Entropy. Entropy 2017, 19, 685.

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