Application of copula‑based and ARCH‑based models in storm prediction

Abstract

In this study, Vector Autoregressive-Generalized Autoregressive Conditional Heteroskedasticity (VAR-GARCH), copula, and copula-GARCH models were used for joint frequency analysis of storms in the Aras river basin in northwestern Iran in period of 1998–2018. The heteroskedasticity in the series was considered using the vector autoregressive model. Two-dimensional copulas were also used for bivariate analysis. After confirming the correlation between the pair variables of storm with one event lag (S1) and storm with no lag (S0), bivariate frequency analysis was performed. In the simulation step, the residual series of the VAR model was extracted and fitted to the GARCH model. Then, the residual series of the GARCH model was modeled using the copula model. Finally, storm with no lag (S0) affected by storm with one event lag (S1) was simulated by VAR-GARCH, copula, and copula-GARCH models. According to the coefficient of determination (R2) and Nash–Sutcliffe Efficiency coefficient (NSE) and root mean square error (RMSE), the VAR-GARCH model had higher accuracy than copula and copula-GARCH models. The RMSE in the simulation of storm height using the VAR-GARCH model was estimated to be 18% and 11% less than copula and copula-GARCH models, respectively. The VAR-GARCH model provided higher accuracy in the simulations due to the consideration of different lags in the simulations and modeling the variance of the residual series. According to the Taylor diagram, the certainty of all three models in simulating storm height are acceptable. Finally, by two-dimensional analysis of pair variables of storm height and storm duration, typical curve was produced that can estimate the storm duration with different probabilities. In fact, having the storm information that has happened in the present can accurately predict the next storm information. It can be very useful in flood management and the generated curves can be used as a flood warning system in the basin.