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

Kuk-Hyun Ahn

doi:10.5194/hess-25-4319-2021

Abstract

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.

Highlights

Hydrological observation records covering long-term periods are instrumental in water resources planning and management, including the design of flood defense systems and irrigation water management (Aissia et al, 2017; Beguería et al, 2019)
This study focuses on drawable vines (Dvines) since they are more widely used in practice (Daneshkhah et al, 2016)
The maximum root mean squared error (RMSE) of MDvine is less than the maximum RMSE of MKraus

Summary

Introduction

Hydrological observation records covering long-term periods are instrumental in water resources planning and management, including the design of flood defense systems and irrigation water management (Aissia et al, 2017; Beguería et al, 2019). Missing data are observed in remote catchments where equipment failures are repaired only after significant delays following extreme events, which can be crucial for hydrological frequency analysis. Hydrologists often rely on simulated sequences to infill missing data in partially gaged catchments (Booker and Snelder, 2012) by using two primary modeling approaches, such as (1) process-based models (i.e., estimating streamflow based on a conceptual understanding of hydrological processes) and (2) transfer-based statistical models (i.e., transferring information from gaged to ungaged catchments; Farmer and Vogel, 2016). Over the past few decades, a variety of statistical models, including simple drainage area scaling (Croley and Hartmann, 1986), the spatial interpolation technique (Pugliese et al, 2014), a regression model (Beauchamp et al, 1989), and flow duration curves (FDCs; Hughes and Smakhtin, 1996), have been developed. If the target watershed is completely gaged, FDCs can be established using regres-

Methods

Results

Conclusion