| Water temperature is a key physical factor to river ecosystems, as well as to water quality. It has great influences on river the eco-environment. Thus it is of important theoretical value and practical significance to perform the simulation and estimation of river water temperature. Based on previous studies, this study carried out the simulation and estimation of river water temperature in the Yellow River, especially in the data-scarce regions, using one-dimensional mathematical and statistic methods. Major results are listed as follows:(I) A one-dimensional river water temperature model was built based on the one-dimensional convection-diffusion equation, and was solved by the finite difference and sweep methods. The measured data from the Wujinxia and Anningdu hydrological stations in the Upper Reaches of the Yellow River were used to validate the model. Results show that the three metrics of mean absolute error(MAE), root mean square error(RMSE), and Nash-Sutcliffemodel efficiency(NSE) for the Wujinxia and Anningdu stations are 1.5 ℃ and 1.6 ℃, 0.86 and 0.91, and-0.11 and-0.22, respectively. The simulation results approach to the observed values.(II) Air temperature is found to be a key factor to influence the water temperature in terms of the correlation analysis between meteorological factors and water temperature. The observed data in 2009 from the hydrologic stations of Huangheyuan, Jimai, Jungong, Mentang, Tangnaihai, and Lanzhou in the upper main stream of the Yellow River were employed to build three kinds of statistic functions, i.e., quartic polynomial, cubic polynomial, and power. They were validated by the observed data series in 2010 and 2011. Results show that the three metrics of MAE, RMSE, and NSE from the quartic polynomial in the daily scale in 2010 and 2011 are 0.99, 0.68, 0.10, and 0.80, 0.57, 0.55, respectively, which are better than those from the cubic polynomial and the power function. In contrast, the three metrics of MAE, RMSE, and NSE from the power function in the monthly scale in 2010 and 2011 are 0.91, 0.55, 0.73 and 0.97, 0.65, 0.59, respectively, which are better than the results from the other two functions.(III) The observed data in 2009 from the hydrologic stations of Minhe and Xining in the tributary of the Upper Yellow River were employed to build three kinds of statistic functions, i.e., quartic polynomial, cubic polynomial, and power. They were validated by the observed data series in 2010 and 2011. Results indicate that the three metrics of MAE, RMSE, and NSE from the power function in the daily scale in 2010 and 2011 are 0.75, 0.66, 0.24 and 1.10, 0.66, 0.62, respectively, which are better than those from the quartic polynomial and the cubic polynomial. In addition, the power function in the monthly scale in 2010 and 2011 also has better metrics of MAE, RMSE, and NSE of 0.65, 0.60, 0.70 and 0.59, 0.26, 0.85, respectively, which are better than the results from the other two functions.(IV) The daily-scale simulation results in the data-scarce regions demonstrate that the quartic polynomial and the power function have high precision in the forecasts of daily average water temperature in the main stream and the tributary, respectively. They can be applied to the simulation of river water temperature in the data-scarce regions of the upper reaches of the Yellow River. In contrast, the monthly-scale results show that the power function has higher accuracy to simulate the river water temperature in the tributary than the quartic polynomial and the cubic polynomial.(V) Comparisons between the one-dimensional river water temperature model and the statistic method were carried out. The simulated average water temperature in daily scale from the quartic polynomial in the main stream of the Upper Yellow River has better metrics of MAE, RMSE, and NSE of 0.99, 0.68, and 0.10 than those of 1.55, 0.88 and-0.17 from the one-dimensional river water temperature model. The statistic method has higher accuracy and needs less data support than the one-dimensional river water temperature model to simulate the daily river water temperature in the main stream of the Upper Yellow River. |
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