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    Multiple threshold method for fitting the generalized Pareto distribution and a simple representation of the rainfall process

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    Abstract. Previous studies indicate the generalized Pareto distribution (GPD) as a suitable distribution function to reliably describe the exceedances of daily rainfall records above a proper optimum threshold, which should be selected as small as possible to retain the largest sample while assuring an acceptable fitting. Such an optimum threshold may differ from site to site, affecting consequently not only the GPD scale parameter, but also the probability of threshold exceedance. Thus a first objective of this paper is to derive some expressions to parameterize a simple threshold-invariant three-parameter distribution function which is able to describe zero and non zero values of rainfall time series by assuring a perfect overlapping with the GPD fitted on the exceedances of any threshold larger than the optimum one. Since the proposed distribution does not depend on the local thresholds adopted for fitting the GPD, it will only reflect the on-site climatic signature and thus appears particularly suitable for hydrological applications and regional analyses. A second objective is to develop and test the Multiple Threshold Method (MTM) to infer the parameters of interest on the exceedances of a wide range of thresholds using again the concept of parameters threshold-invariance. We show the ability of the MTM in fitting historical daily rainfall time series recorded with different resolutions. Finally, we prove the supremacy of the MTM fit against the standard single threshold fit, often adopted for partial duration series, by evaluating and comparing the performances on Monte Carlo samples drawn by GPDs with different shape and scale parameters and different discretizations. </jats:p

    Multifractal analysis and simulation of rainfall fields in space

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    Statistical downscaling of precipitation from the large scales of meteorological models to the characteristic response scales of small catchment basins needs to correctly preserve the anomalous scaling laws observed in real rainfall. Multifractal behaviour of precipitation in space is investigated on a set of rainfall fields obtained by a high resolution simulation with a limited area model for numerical weather prediction and on two sets of radar measures of it rainfall during the GATE campaign. Some sets of synthetic rainfall fields were generated applying a multifractal model based on a wavelet expansion with coefficients extracted by a log-Poisson random cascade, and results of comparisons with the GATE rainfall fields are presented.73-78Pubblicat
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