Streamflow estimation at partially gaged sites using multiple-dependence conditions via vine copulas

Abstract. Reliable estimates of missing streamflow values are relevant for water resource planning and management. This study proposes a multiple-dependence condition model via vine copulas for the purpose of estimating streamflow at partially gaged sites. The proposed model is attractive in modeling the high-dimensional joint distribution by building a hierarchy of conditional bivariate copulas when provided a complex streamflow gage network. The usefulness of the proposed model is firstly highlighted using a synthetic streamflow scenario. In this analysis, the bivariate copula model and a variant of the vine copulas are also employed to show the ability of the multiple-dependence structure adopted in the proposed model. Furthermore, the evaluations are extended to a case study of 54 gages located within the Yadkin–Pee Dee River basin in the eastern USA. Both results inform that the proposed model is better suited for infilling missing values. To be specific, the proposed multiple-dependence model shows the improvement of 9.2 % on average compared to the bivariate model from the historical case study. The performance of the vine copula is further compared with six other infilling approaches to confirm its applicability. Results demonstrate that the proposed model produces more reliable streamflow estimates than the other approaches. In particular, when applied to partially gaged sites with sufficient available data, the proposed model clearly outperforms the other models. Even though the model is illustrated by a specific case, it can be extended to other regions with diverse hydro-climatological variables for the objective of infilling.

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