Copula and ARMA based study of controlled outflow at Farakka barrage

Abstract

Abstract. In this study, 25 years mean monthly out flow discharge data of Farakka barrage was used (i.e., from 1949 to 1968). Farakka barrage is located between on Ganga River. Spatial and temporal variation in flow rate for any particular area is very common due to various meteorological and other factors existing in nature. But large variations in these factors cause extreme events (e. g., floods and droughts). Monthly outflow discharge for a particular critical month are predicted using statistical models (ARMA Model and Copula Model). Different Copulas (i.e., Normal, t, Frank, Clayton, Gumbel–Hoggard, Ali–Mikhail–Haq) are used for this purpose and the copula model is selected based on distribution functions (Normal distribution, Lognormal distribution, Extreme value type-1 distribution, Generalized Extreme value type, Gamma distribution, Weibull distribution, Exponential distribution). The distribution is selected based on the Mean square error (MSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC). The model parameters were computed using the Maximum Likelihood (ML) estimation method.

Dependence structure analysis of multisite river inflow data using vine copula-CEEMDAN based hybrid model

“…Overall it is concluded that for the significant correlation among rivers, our proposed C-Vine based CEEMDAN-R-MM and for the non-significant association between rivers, our first-stage proposed model CEEMDAN-R-MM performs well over the works of Ledolter (1978) and Singh et al (2018). It is concluded that the performance of multi-site river inflow data can enhance by providing the maximum information which exists between complex multivariate time series data.…”

“…However, for the Jhelum and the Chenab rivers inflow as they did not provide any significant correlation among pairs of variables as depicted in Fig. 9, only the first-stage model (CEEMDAN-R-MM; Nazir et al, 2019), provides satisfactory results for Jhelum and Chenab rivers inflow than all other existing work of Ledolter (1978) and Singh et al (2018) and two-stage novel C-Vine based CEEMDAN-R-MM model. It can be observed from our results that by utilizing important information that is present in data, one can enhance the quality of complex hydrological time series data.…”

“…The proposed model is compared with three benchmark models described as following: First, the Vector Autoregressive (VAR) model of Ledolter (1978) is considered where the dependance structure of multi-site rivers inflow is modeled directly without assuming their multi-scale and joint probabilistic structure. Second, the copula-based ARMA model of Singh et al (2018) is selected for the comparison of the proposed model. The copula-based ARMA model only considers the joint dependance structure of multi-site rivers inflow without assuming the multi-scale characteristics into account.…”

“…Second, the copula-based ARMA model of Singh et al (2018) is selected for the comparison of the proposed model. The copula-based ARMA model only considers the joint dependance structure of multi-site rivers inflow without assuming the multi-scale characteristics into account.…”

“…They concluded that IID transformations through ARMA-GARCH are imperative before modeling multivariate dependance structure between hydrological data to avoid bias induced due to volatile dependance. Singh et al (2018) also developed a hybrid copula-based model for seasonal data. They incorporated ARMA with Copula to effectively filter out the inter-dependence, which are proved fruitful in accurately simulating pre and post-monsoon data.…”