A Hybrid of Copula Prediction and Time Series Computation to Estimate Stream Discharge Based on Precipitation Data

Abstract

Stream discharge is a key hydrological factor for water supply planning, wetland loss investigation, ecological service assessment, and climate change impact estimation. Conceptually, stream discharge is expected to be highly and positively related to precipitation. In reality, however, such a relationship may be weaker because precipitation characteristics are affected by local climate of watersheds. For many watersheds around the world, a vast amount of precipitation data are readily available but the stream discharge data are very limited or unavailable. It would be time-saving and cost-effective to predict stream discharge based on precipitation data. Unfortunately, this task is very difficult to achieve using the traditional methods. Although the copula method is able to establish a good relationship (or a good dependence structure) between discharges and precipitations, this relationship does not include the time series process, and thus is impractical for applications. Therefore, a hybrid of copula prediciton and time series computation was developed (with detailed procedures) here to estimate stream discharge based on precipitation data. The method was validated using the measured daily discharges with the good statistical measures, that is, the Kandell's τ (0.42-0.44), normalized root mean square error (2.19-2.28 m 3 /s), and R 2 (0.66-0.84). This study suggests that the hybrid method is a useful tool to predict stream discharges based on precipitation data.

Quantification of Mountainous Hydrological Processes in the Aktash River Watershed of Uzbekistan, Central Asia, over the Past Two Decades

“…The result demonstrated the daily streamflow had a good linear correlation with the daily precipitation. This pattern was also reported by Ouyang [30] for a watershed in Mississippi, USA. The simulated average daily streamflow from 2003 to 2019 at the ARW was 0.52 m 3 /s, which was consistent with the observed average daily streamflow of 0.41 m 3 /s from 1947 to 1965 at the same basin [23].…”

A Copula Approach for Predicting Tree Sap Flow Based on Vapor Pressure Deficit

“…In this study, we applied the Vine copulas package in the R-Statistics platform to select the best copula out of the five commonly used bivariate copulas, namely the BB8 (Joe-Frank), Clayton, Frank, Gumbel, and Normal copulas, for fitting our sap flow and VPD data. The following six steps were employed to perform the copula analysis [10,13]: i.…”

“…Copula analysis is a multivariate statistical approach used to identify the relationships among random variables that are otherwise difficult (if not impossible) to determine by traditional methods. As an example, Ouyang [13] has successfully applied the couple method to predict stream discharge using precipitation data, which is not possible by using traditional methods. The copula method was first developed by Sklar [14] and has been widely used for multidisciplinary applications, including actuarial science, finance analysis, hydrological modeling, and water resources management [15][16][17][18][19].…”