Application of a stochastic model to precipitation data
Abstract
As presented at the Fall meeting of AGU in 2012, our research objective is the construction of a random process model that generates time-variational (diurnal-variational) precipitation. The conclusions were the following. 1) For the daily precipitation time series (actually, anomaly of precipitation: 'actual precipitation minus normal precipitation'), mono-fractal models (fractional Brownian motion, fBm; and fractional Lévy motion, fLm) and multifractal models are inappropriate. 2) However, we can apply the same method as the method for fBm and fLm (Lavallée's filtering method; Lavallée, 2008). 3) The difference between our method and that of Lavallée (2008) is that a filter for fBm and fLm is the filter for which the relation between ω (angular frequency) and E(ω) (power spectrum) is log - log-linear (power law type), but our model's filter is exponential one. 4) fBm, fLm, and our model generate random process by filtering white noise. The Lévy noises are more appropriate than the Gaussian noises are. Last year, we confirmed the validity of the random process model and the Lévy noise using precipitation time series from five observation stations. This year, we will present more robust results obtained using time series of daily precipitation at 51 observation stations. We will demonstrate the quantitative superiority of the Lévy law over the Gauss law using the coefficient of correlation and slope of regression analyses. Moreover, we present results of a simulation using this model. Although we discussed which probability law, the Gauss law or Lévy law, is appropriate from the viewpoint of the tail's nature of probability distribution after Lavalée (2008), now we are investigating which probability law among more than 20 laws is most appropriate from the perspective of the goodness-of-fit over the whole range of random variables. We will present the results at the meeting. Generalized extreme-value (GEV), generalized logistic (GLO), and log-GLO are candidates at the present stage. Lavallée (2008), Advances in Geophs, 50, chap.16.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFMNG33A1578K
- Keywords:
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- 4499 NONLINEAR GEOPHYSICS General or miscellaneous;
- 1854 HYDROLOGY Precipitation;
- 1869 HYDROLOGY Stochastic hydrology