Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective |
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| Authors: | Francesco Serinaldi |
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| Institution: | (1) Dipartimento di Idraulica Trasporti e Strade, “Sapienza” Università di Roma, Via Eudossiana 18, 00184 Rome, Italy;(2) H2CU - Honors Center of Italian Universities, “Sapienza” Università di Roma, Via Eudossiana 18, 00184 Rome, Italy |
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| Abstract: | A comprehensive parametric approach to study the probability distribution of rainfall data at scales of hydrologic interest
(e.g. from few minutes up to daily) requires the use of mixed distributions with a discrete part accounting for the occurrence
of rain and a continuous one for the rainfall amount. In particular, when a bivariate vector (X, Y) is considered (e.g. simultaneous observations from two rainfall stations or from two instruments such as radar and rain
gauge), it is necessary to resort to a bivariate mixed model. A quite flexible mixed distribution can be defined by using
a 2-copula and four marginals, obtaining a bivariate copula-based mixed model. Such a distribution is able to correctly describe
the intermittent nature of rainfall and the dependence structure of the variables. Furthermore, without loss of generality
and with gain of parsimony this model can be simplified by some transformations of the marginals. The main goals of this work
are: (1) to empirically explore the behaviour of the parameters of marginal transformations as a function of time scale and
inter-gauge distance, by analysing data from a network of rain gauges; (2) to compare the properties of the regression curves
associated to the copula-based mixed model with those derived from the model simplified by transformations of the marginals.
The results from the investigation of transformations’ parameters are in agreement with the expected theoretical dependence
on inter-gauge distance, and show dependence on time scale. The analysis on the regression curves points out that: (1) a copula-based
mixed model involves regression curves quite close to some non-parametric models; (2) the performance of the parametric regression
decreases in the same cases in which non-parametric regression shows some instability; (3) the copula-based mixed model and
its simplified version show similar behaviour in term of regression for mid-low values of rainfall.
An erratum to this article can be found at |
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| Keywords: | 2-Copula Zero-inflated data Bivariate mixed model Rainfall Regression Inter-gauge distance Time scale |
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