Statistical Analysis of Mesoscale Rainfall: Dependence of a Random Cascade Generator on Large-Scale Forcing

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

“…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.…”

“…Therefore, we analyze the model output using spatial moment and fractional wetted area (FWA) analyses, treating the output as though it were stochastic. Scaling features under these analyses were observed by Gupta and Waymire (1993) and Over and Gupta (1994)in the Global Atmospheric Research Program (GARP) Atlantic Tropical Experiment rainfall data sets (GATE; Hudlow and Patterson, 1979). Our model can be formally, but not physically, compared to other models that have been investigated in statistical mechanics and nonlinear chaotic dynamical systems, where the chaotic nature of dynamical output is analysed using stochastic methods; see Beck and Schlogl (1993) for an excellent introductory reference on this topic.…”

“…Waymire et al, 1984;Eagleson and Qinliang, 1985;Gupta and Waymire, 1987;Kavvas et al, 1987;Phelan and Goodall, 1990;Cox and Isham, 1988), and scale invariant (e.g. Lovejoy, 1981Lovejoy, , 1982Lovejoy and Schertzer, 1990;Gupta and Waymire, 1990;Over and Gupta, 1994;Perica and Foufoula-Georgiou, 1996;Foufoula-Georgiou, 1998;Jotithyangkoon et al, 2000); and on determining the extent to which they exhibit certain features of data. However, stochastic models models have faced the difficult problem of determining a relationship between model parameters and the underlying physical processes governing rainfall.…”

“…Lovejoy, 1981Lovejoy, , 1982Lovejoy and Schertzer, 1990;Gupta and Waymire, 1990;Over and Gupta, 1994;Perica and Foufoula-Georgiou, 1996;Foufoula-Georgiou, 1998;Jotithyangkoon et al, 2000). These 'scaling models', in contrast to the scale-dependent models, generally required only a few parameters to relate the statistics of rainfall fields among different scales.…”

Imperfect scaling in distributions of radar-derived rainfall fields

“…Empirical investigation of the scaling behaviour does indeed show that not all rainfall fields obey the basic assumption that the increments of ε between scales are i.i.d. Divergences from this behaviour were described by various authors who observed that the increments were dependent on factors such as large-scale rainfall intensity (Deidda, 2000;Over and Gupta, 1994) and pixel size (Menabde et al, 1997;Over and Gupta, 1994;Paulson and Baxter, 2007). Additionally, scaling behaviour was found to differ with the intensity of storms (Venugopal et al, 2006) and thus the nonraining intervals do not scale (Olsson, 1998).…”