Research papers
A C-vine copula framework to predict daily water temperature in the Yangtze River

https://doi.org/10.1016/j.jhydrol.2021.126430Get rights and content

Highlights

  • A C-vine copula framework is developed to predict river water temperature.

  • The framework can better capture water temperature variation downstream of a reservoir.

  • Suitable discharge ranges for ecological water temperature are recommended by habitat.

Abstract

The thermal regime of rivers plays a crucial role in chemical, biological and ecological processes. Effectively predicting water temperature is a key issue related to environment management. This study develops a probabilistic model based on C-vine copulas for water temperature prediction. The proposed framework is applied to forecast daily water temperature in the Yangtze River, considering long-term effects of preceding air temperature and daily discharge. The prediction performance of this framework is compared with the logistic regression model (LogR) and generalized regression neural network (GRNN). The results of this study indicate that the proposed C-vine copula framework and GRNN model provide better forecasting of stream temperature with weak human-related disturbances than LogR model. The outperformance of C-vine framework is reflected by its ability to accurately capture variations in the water temperature greatly affected by the Three Gorges Reservoir (TGR). This steady and reliable framework is further applied for the conservation of Chinese Sturgeon to estimate the range of suggested discharge, given the daily air temperatures, to adjust the water temperature within 18–20 °C at Yichang station during the spawning season. This application is verified to be more effective, providing indications for reservoir management to lower water temperatures by regulating river flow to ensure the occurrence of spawning activities. The results of this study may provide a scientific reference for the ecological operation of reservoirs in regulated rivers.

Introduction

Water temperature is a key factor for the overall health of aquatic ecosystems. Most aquatic organisms have a specific range of temperatures that they can tolerate, and variations in the riverine thermal regime directly influence the growth rates, behavior and distributions of aquatic species (Caissie, 2006). It is essential to have access to current and projected water temperature dynamics and to have a good understanding of the thermal constraints of different aquatic species for effective fisheries management as well as for conducting environmental impact assessments.

Various kinds of models used for water temperature prediction have been developed so far and can be classified into two main categories: physically based deterministic models and statistical models (Cole et al., 2014, Zhu et al., 2019). Deterministic models generally require a mathematical representation of both hydrological processes occurring in the catchment and heat exchange processes occurring between the river and the surrounding environment (Piccolroaz et al., 2016). They have an advantage of being applied in well monitored locations and at different spatial scales (Caissie, 2006, van Vliet et al., 2012, Piotrowski and Napiorkowski, 2019). However, many predictor variables (e.g., fluvial topography, a full set of meteorological variables, and the hydraulic properties of the river), which are frequently unavailable, are required to predict water temperature. As such, the applicability of deterministic models for regions with limited data is impractical, so flexible statistical models are promising alternatives. Various forms of regression models (Mohseni et al., 1998, Webb et al., 2003, Piotrowski and Napiorkowski, 2019), artificial neural networks (ANN) (Zhu et al., 2019), and hybrid statistical-physical-based models (Toffolon and Piccolroaz, 2015, Piccolroaz et al., 2016) have been proposed and implemented successfully. In most statistical models, air temperature is commonly viewed as a predictor variable for water temperature because it can be used as a surrogate for the net changes in heat flux that affect the water surface and because it approximates the equilibrium temperature of a water course (Webb et al., 2003, Webb et al., 2008). In addition, models commonly link water temperature to changing volumes of runoff, which significantly affect water temperatures due to changes in thermal capacity and travel time, and the dilution capacity of thermal effluents (Webb et al., 2003, van Vliet et al., 2011, van Vliet et al., 2012). However, water temperature is a product of multiple factors, triggered by both anthropogenic perturbations (e.g., thermal pollution, water withdrawals, and deforestation) and climate change (Caissie, 2006, Piccolroaz et al., 2016). Many uncertainties may arise in simulations of temperature processes in regulated rivers using traditional statistical models. Therefore, a probabilistic model based on vine copulas, which is a promising tool for addressing uncertainties, will be proposed in this research.

To consider the uncertainty of the design variables, multivariable frequency analyses are always conducted in hydrology and water resource management (Yu et al., 2019). A copula is a multivariate probability distribution in which the marginal probability distribution of each variable is uniform; a copula describes the dependence structure among the marginal distributions of individual variables (Liu et al., 2017). Vine copulas, which focus on problems with large dimensions, are based on hierarchical models by sequentially employing bivariate copulas as the building blocks for constructing a higher-dimensional copula (Liu et al., 2016). There is an increasing number of vine copula applications for predicting various factors in hydrology, such as stream flow and water level (Liu et al., 2015, Liu et al., 2016, Yu et al., 2019). In addition, little attention has been given to the probabilistic prediction of water temperature using the vine copula method.

Three Gorges Reservoir (TGR), the largest water control project in the middle reach of the Yangtze River, provides comprehensive benefits, such as flood control, power generation, and navigation, and contributes to economic prosperity and social well-being. On the other hand, the construction of the TGR has greatly altered the hydrological and thermal regimes downstream of the reservoir by changing the amount and timing of flow and by releasing hypolimnetic water (Wang et al., 2012, Wang et al., 2019, Long et al., 2016, Cai et al., 2018, Liu et al., 2018). The survival, metabolism, and reproductive success of individual aquatic species as well as the composition of species within the Yangtze River, the location of the most important freshwater fishery in China, have been affected by water temperature changes caused by the TGR (Long et al., 2016, Wang et al., 2017). For these reasons, patterns of water temperature in the middle reach of the Yangtze River have been of considerable interest, and it can be difficult to predict the thermal regime associated with the TGR. A probabilistic model may help improve the understanding of how water temperature fluctuates in this regulated river.

The main objective of this study is to develop a framework to predict daily water temperature in the Yangtze River and explain its potential strengths. To achieve this objective, the study (1) develops a C-vine-based model to predict the daily river temperature given a time series of air temperature and discharge data obtained at Cuntan, Datong and Yichang stations; (2) tests the prediction ability of the proposed framework by comparing with the logistic regression model and generalized regression neural network; and (3) applies the advanced vine-based model to simulate the suggested range of discharge to obtain an ecological water temperature during the spawning season of Chinese Sturgeon. The application of the vine-based model can provide future science-based reservoir management strategies aimed at the protection of important fishes in the Yangtze River.

Section snippets

Study area and data

The Yangtze River, one of the largest rivers in the world, flows eastward 6300 km through 11 provinces in China before debouching into the East China Sea at Shanghai (Li et al., 2011). The Yangtze River Basin is characterized by a subtropical monsoon climate initiated from the Southeast Pacific Ocean and Indian Ocean, with a drainage area of 1,800,000 km2. The TGR is located in the main stream of the Yangtze River and began to impound water in 2003. It has a large storage capacity of 3.93 × 1010

Methodology

In this study, we developed a vine copula framework to predict river water temperature and compared its performance to that of the logistic regression model (LogR) and the generalized regression neural network (GRNN).

Evaluation of water temperature forecasting

First, the long-term effects of preceding air temperature needed to be considered on the thermal regimes of the river, which can improve the accuracy of predictions. In the LogR model, the number of lag days and the parameter f assigned to the exponentially decreasing values of air temperature were chosen by trial and error. The results of the LogR model are shown in Table 3. It can be seen that the average of lag days was 24 days. The impacts of preceding air temperature at Yichang and Datong

Discussion

This study introduces the C-vine copula to forecast the daily water temperature in rivers for the first time. The vine-based model incorporates vine copulas, conditional bivariate copula distributions and a copula-based conditional quantile function. Our past study applied bivariate copulas to observe impacts of reservoirs by changes in the joint dependence structures of air–water temperature and discharge-water temperature between pre-reservoir and post-reservoir periods (Tao et al., 2020b).

Conclusions

In this study, a C-vine copula framework is proposed to produce probabilistic forecasts of water temperature using daily data. To demonstrate its usefulness and applicability, the water temperatures at Cuntan, Datong and Yichang stations in the Yangtze River have been predicted by considering the long-term effect of preceding air temperature and daily discharge. Our results reveal that GRNN model and C-vine copula framework perform better than LogR model when predicting water temperature with

CRediT authorship contribution statement

Yuwei Tao: Methodology, Formal analysis, Writing - original draft, Writing - review & editing. Yuankun Wang: Conceptualization, Writing - review & editing, Supervision. Dong Wang: Writing - review & editing, Project administration. Lingling Ni: Data curation, Investigation. Jichun Wu: Project administration.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was supported by the second Tibetan Plateau Scientific Expedition and Research Program (2019QZKK0203), the National Key Research and Development Program of China (2017YFC1502704), and the National Natural Science Fund of China (51679118, 41571017, and 91647203), and Jiangsu Province“333 Project” (BRA2018060).

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