A GLM copula approach for multisite annual streamflow generation

Abstract

The research presents a multisite annual streamflow generation model that combines the Generalized Linear Model (GLM), for determining the temporal structure, with copulas, for modelling the spatial dependence joint distributions. The performance of the GLM-Copula model was verified by comparing its ability to preserve historical features and simulate drought events with the multivariate auto regressive moving average (ARMA) model and the copula autoregressive (COPAR) model. The statistical measures adopted for the models’ perfor- mance evaluation include summary statistics (mean, standard deviation, maximum, minimum and skewness coefficient), temporal and spatial correlation, simulation of drought conditions (maximum number of years under drought condition) and copula entropy as a nonlinear measure of total association. The combined GLM- Copula model’s main advantages are that (i) it does not require data normalization; ii) it allows the modelling of the dependence structures with different probability functions; and (iii) it is capable of representing non- conventional parsimonious autocorrelation functions. The ability of the GLM-Copula approach to preserve the summary statistics from the historical data was similar to both benchmark models. However, the GLM-Copula was considerably better in reproducing the longest drought duration that was underestimated by the ARMA model and was better in reproducing the copula entropy than both benchmark models. The approach is proposed in its simplest form but can be easily upgraded by combining GLMs with numerical data or extended to predict future streamflow with the incorporation of exogenous climate variables that affect streamflow. The proposed model may be useful in future studies/applications where data normalization jeopardizes the replication of data or/and in drought dependent stochastic applications, like the definition of optimal operation rules of a perennial reservoir system or long-term hydropower dispatch.