Abstract
After we modified raw data for anomalies, we conducted spectral analysis using the data. In the frequency, the spectrum is best described by a decaying exponential function. For this reason, stochastic models characterized by a spectrum attenuated according to a power law cannot be used to model precipitation anomaly. We introduced a new model, the e-model, which properly reproduces the spectrum of the precipitation anomaly. After using the data to infer the parameter values of the e-model, we used the e-model to generate synthetic daily precipitation time series. Comparison with recorded data shows a good agreement. This e-model resembles fractional Brown motion (fBm)/fractional Lévy motion (fLm), especially the spectral method. That is, we transform white noise Xt to the precipitation daily time series. Our analyses show that the frequency of extreme precipitation events is best described by a Lévy law and cannot be accounted with a Gaussian distribution.
Highlights
Just as turbulence and clouds have been described using fractals, geoscientific fields such as topographical fields, temporal or spatial rainfall fields, and earthquake-slip fields are often modeled using fractals (Gagnon, et al [1]; Lavallée and Archuleta [2]; Lavallée [3]; Lovejoy and Schertzer [4]; Schertzer and Lovejoy [5]; Tchiguirinskaia, et al [6])
A similar behavior has been observed for all the other observation stations considered in this study. These results suggest that stochastic process characterized by a spectrum attenuation given by a power law—for instance, fractional Brown motion (fBm), fractional Lévy motion (fLm) and other multifractal models (e.g. fractional integrated flux model (FIF))—cannot properly model the average spectrum E( ) observed for the anomaly R considered in this study
We strove to apply a stochastic model to daily precipitation time series recorded at 51 observation stations in Japan
Summary
Just as turbulence and clouds have been described using (random) fractals, geoscientific fields such as topographical fields, temporal or spatial rainfall fields, and earthquake-slip fields are often modeled using fractals (Gagnon, et al [1]; Lavallée and Archuleta [2]; Lavallée [3]; Lovejoy and Schertzer [4]; Schertzer and Lovejoy [5]; Tchiguirinskaia, et al [6]). If we examine simulations of temporal or spatial rainfall field as one example, two approaches might be used (Over and Gupta [7]): stochastic approaches, or physical or dynamical approaches. Regarding the former, many stochastic models of temporal and spatial rainfall fields have been developed. Several mono-fractal or multifractal models have been used to model the scaling property of rainfall fields
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