Estimation of the distribution of annual runoff from climatic variables using copulas

Abstract

An approach of deriving the annual runoff distribution using copulas from an annual rainfallrunoff model is proposed to provide an alternative annual runoff frequency analysis method in case of changing climatic variables. The annual rainfall-runoff model is established on the basis of the Budyko formula to estimate annual runoff, with annual precipitation and potential evapotranspiration as input variables. The model contains one single parameter k that guarantees that annual water balance is satisfied. In the derivation of the annual runoff distribution, annual precipitation, annual potential evapotranspiration, and parameter k are treated as three random variables, while the annual runoff distribution is obtained by integrating the joint probability density function of the three random variables over the domain constrained by the annual rainfall-runoff model using the canonical vine copula. This copula-based derivation approach is tested for 40 watersheds in two large basins in China. The estimated annual runoff distribution performs well in most watersheds. The performance is mainly related to the accuracy of the marginal distribution of precipitation. The copula-based derivation approach can also be used in ungauged watersheds where the distribution of k at the local site is estimated from the regional information of the k variable, and it also has acceptable performance in most watersheds, while poor performance is observed in a few watersheds with low accuracy in the Budyko formula.

A framework of change‐point detection for multivariate hydrological series

“…Before applying the CLR method described above to the multivariate series consisting of more than two random variables, a crucial issue should be considered, that is, choosing a proper copula model to construct the dependence structure of the multivariate series. For the high‐dimensional hydrological series, i.e., , the joint distribution can be built by at least three copula models, i.e., symmetric copula [ Joe , ; Nelsen , ; Zhang and Singh , ; Aas and Berg , ], asymmetric copula [ Joe , ; Nelsen , ; Grimaldi and Serinaldi , ; Serinaldi and Grimaldi , ; Aas and Berg , ], and pair‐copula [ Aas et al ., ; Aas and Berg , ; Xiong et al ., ]. Figure displays the structures of symmetric copula, asymmetric copula and pair‐copula for trivariate case.…”

“…Thus, choosing a proper copula model to construct the dependence structure of these variables is very crucial before applying the CLR method to multivariate (more than two random variables) hydrological series. As far as we know, there have been at least three kinds of copula model that can be applied to construct the dependence structure of multivariate hydrological series, i.e., symmetric copula [ Joe , ; Nelsen , ; Zhang and Singh , ; Aas and Berg , ], asymmetric copula [ Joe , ; Nelsen , ; Grimaldi and Serinaldi , ; Serinaldi and Grimaldi , ; Aas and Berg , ], and pair‐copula [ Aas et al ., ; Aas and Berg , ; Xiong et al ., ]. In this study, these three kinds of copula model will be investigated for their suitability to capture the dependence structure in multivariate series when the CLR method is used to detect change‐point in the dependence structure of multivariate series.…”

Identification of hydrological model parameter variation using ensemble Kalman filter

“…Li et al, 2013;Zhang et al, 2013;Xiong et al, 2014). The inputs of the model include monthly areal precipitation and potential evapotranspiration.…”

A continuous rainfall model based on vine copulas

“…Nikololoupoulos et al (2012);Zhang (2014); Mendes and Accioly (2014)) and geophysics and hydrology (see e.g. Gräler (2014); Xiong et al (2014); Gyasi-Agyei and Melching (2012); Gräler et al (2013)). …”