Scaling statistics in a critical, nonlinear physical model of tropical oceanic rainfall

Abstract

Abstract. Over the last two decades, concepts of scale invariance have come to the fore in both modeling and data analysis in hydrological precipitation research. With the advent of the use of the multiplicative random cascade model, these concepts have become increasingly more important. However, unifying this statistical view of the phenomenon with the physics of rainfall has proven to be a rather nontrivial task. In this paper, we present a simple model, developed entirely from qualitative physical arguments, without invoking any statistical assumptions, to represent tropical atmospheric convection over the ocean. The model is analyzed numerically. It shows that the data from the model rainfall look very spiky, as if generated from a random field model. They look qualitatively similar to real rainfall data sets from Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment (GATE).A critical point is found in a model parameter corresponding to the Convective Inhibition (CIN), at which rainfall changes abruptly from non-zero to a uniform zero value over the entire domain. Near the critical value of this parameter, the model rainfall field exhibits multifractal scaling determined from a fractional wetted area analysis and a moment scaling analysis. It therefore must exhibit long-range spatial correlations at this point, a situation qualitatively similar to that shown by multiplicative random cascade models and GATE rainfall data sets analyzed previously (Over and Gupta, 1994;Over, 1995). However, the scaling exponents associated with the model data are different from those estimated with real data. This comparison identifies a new theoretical framework for testing diverse physical hypotheses governing rainfall based in empirically observed scaling statistics.

Annual and interannual (ENSO) variability of spatial scaling properties of a vegetation index (NDVI) in Amazonia

“…Scaling theories have provided important clues towards understanding and modelling the space-time dynamics of diverse bio-geophysical processes, such as vegetation surface fluxes (Katul et al, 2001), tropical convective storms (Yano et al, 2001), modeling of rainfall fields through fractal, multi-scaling, and random cascade models (Lovejoy, 1981(Lovejoy, , 1982Lovejoy & Schertzer, 1991Gupta & Waymire, 1990;Over & Gupta, 1994;Perica & FoufoulaGeorgiou, 1996;Foufoula-Georgiou, 1998;Deidda et al, 1999;Harris et al, 2000;Jotithyangkoon et al, 2000;Nordstrom & Gupta, 2003), maximum annual river flows (Gupta & Waymire, 1990;Gupta & Dawdy, 1995;Goodrich et al, 1997;Ogden & Dawdy, 2003), infiltration in porous media (Barenblatt, 1996), low river flows (Furey & Gupta, 2000), ecological processes (Tilman & Kareiva, 1997; Bascompte & Sole, 1998), and vegetation dynamics (Harte et al, 1999;Milne & Cohen, 1999;Milne et al, 2002). For instance, in the study of river floods, Gupta (2004) has explained how scaling statistics in maximum annual river flows can be used to test different physical hypotheses covering complex runoff dynamics on channel networks.…”

Complejidad de la estructura espacio-temporal de la precipitación

“…Desde la base conceptual de los modelos que hasta aquí se han mencionado, es claro que no han considerado, en principio, las bases físicas de los procesos de precipitación, sin embargo otras investigaciones como las realizadas por Nordstrom & Gupta (2003);Marzan, Schertzer & Lovejoy. (1996);Perica & Foufoula-Georgiou (1996b), han hecho esfuerzos por definir relaciones teóricas entre la física y la formulación matemática de los modelos descriptivos de la estructura espacio -temporal de la precipitación.…”

“…Entre los modelos de base física y construidos sobre ecuaciones dinámicas, se encuentra el modelo introducido por Nordstrom & Gupta (2003). Este modelo es construido para estudiar la lluvia convectiva tropical sobre el océano, independiente de consideraciones estadísticas y se interesa en entender el origen físico del escalamiento estadístico de las observaciones de precipitación.…”

Diurnally driven scaling properties of Amazonian rainfall fields: Fourier spectra and order‐q statistical moments

“…Scaling theories have provided important insights toward understanding and modeling the space‐time dynamics of rainfall, including (multi‐)fractal, multiscaling, and random cascade models [ Lovejoy , 1982; Lovejoy and Schertzer , 1991, 1993; Gupta and Waymire , 1990; Over and Gupta , 1994; Perica and Foufoula‐Georgiou , 1996a, 1996b; Foufoula‐Georgiou , 1998; Deidda et al , 1999; Yano et al , 2001; Harris et al , 2001; Jotithyangkoon et al , 2000; Nordstrom and Gupta , 2003; Nykanen , 2008]. Diverse multiscale statistical techniques have been used to characterize and quantify the scale dependence of rainfall fields, including the Fourier spectra and the order‐ q statistical moments function.…”