Calibration of NSRP Models from Extreme Value Distributions

De Luca De Luca,Galasso Galasso

doi:10.3390/hydrology6040089

Abstract

In this work, the authors investigated the feasibility of calibrating a model which is suitable for the generation of continuous high-resolution rainfall series, by using only data from annual maximum rainfall (AMR) series, which are usually longer than continuous high-resolution data, or they are the unique available data set for many locations. In detail, the basic version of the Neyman–Scott Rectangular Pulses (NSRP) model was considered, and numerical experiments were carried out, in order to analyze which parameters can mostly influence the extreme value frequency distributions, and whether heavy rainfall reproduction can be improved with respect to the usual calibration with continuous data. The obtained results were highly promising, as the authors found acceptable relationships among extreme value distributions and statistical properties of intensity and duration for the pulses. Moreover, the proposed procedure is flexible, and it is clearly applicable for a generic rainfall generator, in which probability distributions and shape of the pulses, and extreme value distributions can assume any mathematical expression.

Highlights

For many locations of interest, the sample sizes of continuous data with a high resolution are usually short, or they are not available, and only annual maximum rainfall (AMR) series exist, but they are often not so long at the finest time scales (1 or 5 min). These usual data deficiencies, together with the necessity to obtain perturbed time series, that can be representative of future rainfall fields at hydrological scales, induced the development of stochastic rainfall generators (SRGs), which are characterized by simple mathematical formulations and low computational costs, allowing for the quick generation of large ensembles of long precipitation time series
This work remarked that seasonality is not essential for intensity and duration of the rectangular pulses, but it could be necessary for other parameters, mainly for a good modeling of dry/wet periods, not investigated here. This described work constitutes the first step of an interesting research, aimed to investigate the possibility of a good calibration for models such as the Neyman–Scott Rectangular Pulses (NSRP), suitable for the generation of continuous high-resolution rainfall series, by using only data from annual maximum rainfall (AMR) series at fine scales, which are usually longer than continuous sub-hourly series, or they are the unique available data set for many locations
The obtained results highlighted the crucial role of high-resolution extreme value distributions as important signatures for defining the statistical properties of intensity and duration for rectangular pulses, without considering continuous high-resolution rainfall data

Summary

Introduction

Long continuous high-resolution series of rainfall are more and more necessary for many hydrological purposes, in particular for applications related to small urban catchments.for many locations of interest, the sample sizes of continuous data with a high resolution are usually short, or they are not available, and only annual maximum rainfall (AMR) series exist, but they are often not so long at the finest time scales (1 or 5 min).These usual data deficiencies, together with the necessity to obtain perturbed time series, that can be representative of future rainfall fields at hydrological scales, induced the development of stochastic rainfall generators (SRGs), which are characterized by simple mathematical formulations and low computational costs, allowing for the quick generation of large ensembles of long precipitation time series.A review of all these SRGs is provided in [1,2]. For many locations of interest, the sample sizes of continuous data with a high resolution are usually short, or they are not available, and only annual maximum rainfall (AMR) series exist, but they are often not so long at the finest time scales (1 or 5 min). These usual data deficiencies, together with the necessity to obtain perturbed time series, that can be representative of future rainfall fields at hydrological scales, induced the development of stochastic rainfall generators (SRGs), which are characterized by simple mathematical formulations and low computational costs, allowing for the quick generation of large ensembles of long precipitation time series. Many applications of these models regarded England [5,8,11,12,13], Scotland [14], Belgium [7], Switzerland [15], Germany [9], Spain [16], Ireland [16], South Africa [17], New Zealand [18], Australia [19,20,21], Greece [22], Italy [23,24], United States [3,4,23,25,26,27], and Korean Peninsula [28]

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