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In this section, the effect of parametric scheme optimization of vertical thermal diffusivity (
$ K $ ) in WRF-lake on water temperature simulation is discussed. Some earlier studies modified the parameterization for$ K $ in WRF-lake and proved that an increase in$ K $ could improve the model simulation for deep lakes (Subin et al., 2012; Gu et al., 2015; Xu et al., 2016; Fang et al., 2017). Wang et al. (2019) added a diffusion enhancing term into the model for applications in reservoirs and lakes deeper than 100 m, referring to the suggestions of Ellis et al. (1991), Subin et al. (2012), and Fang et al. (2017). We compared the simulated temperatures by different versions of WRF-lake, including the latest version (W0) (Wang et al., 2019) and the modified version described in section 2.2 of this paper (W1).Curves of 2015 surface water temperature simulated by different models, including the two versions of WRF-lake and Delftf3D-Flow, are shown in Fig. 4. Root-mean-square errors (RMSEs) and mean absolute errors (MAEs) are shown in Table 1. The results from Delft3D-Flow are the simulated water temperatures near the Nuozhadu dam. It can be seen that the simulated results of the latest WRF-lake version (Wang et al., 2019) have obvious errors during the large flow rate months, i.e., from May to August. The modification performed in this study eliminated this defect, and the performance was improved significantly because the larger flow rate caused stronger vertical mixing of the water body. Additionally, the downward energy transfer was strengthened, which resulted in lower surface water temperature. The W1 model has a larger
$ K $ value than the W0 model in the large flow rate period because of considering the influence of flow rate on vertical diffusivity. Therefore, surface temperatures were simulated lower and closer to the measured data and results of Delft3D-Flow (Fig. 5).WRF-lake [by Wang et al. (2019)] WRF-lake (modified) Delft3D-Flow Surface water temperature RMSE (°C) 1.50 1.08 1.19 MAE (°C) 0.35 0.15 0.10 Vertical water temperature profile RMSE (°C) 1.13 1.01 1.10 MAE (°C) 0.94 0.70 0.60 Table 1. The RMSE and MAE of the WRF-lake model version by Wang et al. (2019), the modified WRF-lake model used in this paper, and the Delft3D-Flow model used in surface water temperature and vertical temperature profile simulation near the dam.
Figure 5. Simulated surface water temperature in 2015, including the results of the WRF-lake model version by Wang et al. (2019) (blue solid line), the modified WRF-lake model used in this paper (blue dotted line), and the Delft3D-Flow simulation (black solid line), with the observed data (red dots) as reference.
The vertical profiles of water temperature and diffusion coefficient (
$ K $ ) in the 12 months are shown in Figs. 6(a) and 6(b). The W0 model underestimated vertical mixing in the whole vertical profile during the period from May to August, which was enhanced by large water flow through the reservoir. The revision (W1) of vertical thermal diffusivity in this paper solved this problem, leading the vertical temperature profiles to become more reasonable.Figure 6. (a)Vertical water temperature profiles of the WRF-lake model version by Wang et al. (2019) (blue lines) and the modified WRF-lake model used in this paper (black lines). The dots represent observed data. (b) Diffusion coefficient profiles of the WRF-lake model version by Wang et al. (2019) (blue lines) and the modified WRF-lake model used in this paper (black lines).
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It has been acknowledged that a vertically 1D model can be applied to a lake-shaped reservoir like the Miyun reservoir (Guo et al., 2022). But it is not clear whether the vertically 1D WRF-lake model can also be applied to a riverine reservoir as long as the Nuozhadu reservoir. Therefore, a 3D model, Delft3D-Flow, was utilized in this study, and the 3D results served as a reference for WRF-lake. Since WRF-lake only considers vertically 1D characteristics, the water temperature variation along the longitudinal direction is discussed in this section.
Figure 7 shows water temperature isotherms in different months in 2015, including April, July, September, and December, representing spring, summer, autumn, and winter, respectively, simulated by the Delft3D-Flow model. It can be seen that the Nuozhadu Reservoir, with a hydraulic residence time of 180 days, has a significant vertical thermal stratification. This is consistent with previous studies that have found that reservoirs with hydraulic residence times of more than 100 days are usually stably stratified (Straškraba et al., 1993; Owens, 1998; Nowlin et al., 2004; Li et al., 2016). The thermal stratification exists in all four seasons. The water at the surface is always warmer than at the bottom, and the water temperature under 100-m depth remains about 15°C year-round. The longitudinal temperature variation mainly exists in the upstream, within a length of about 50 km, which is 25% of the total length of the reservoir. From the midstream to the dam, the isotherms are relatively horizontal, and the longitudinal water temperature variation is less than 1.5°C with length of 100 km. The isotherms are nearly horizontal near the dam. As a whole, for the large riverine reservoir with hydraulic residence time of 180 days, in more than half of its length, the isotherms are relatively horizontal, and the longitudinal water temperature variation is quite small in all four seasons, which is meaningful for the WRF-lake 1D model application.
Figure 7. Simulated water temperature distributions in April, July, September, and December of 2015 by Delft3D-Flow, representing spring, summer, autumn, and winter, respectively.
The surface heat flux calculation by different versions of WRF-lake was evaluated with the simulated results of Delft3D-Flow as reference. Figures 8a, b, and c show the longwave radiation, latent heat, and sensible heat values simulated by the latest WRF-lake version (Wang et al., 2019) (W0), the WRF-lake modified in this paper (W1), and the Delft3D-Flow model (D0), respectively. The positive values and negative values represent the reservoir releasing energy to and absorbing energy from the atmosphere. The heat flux of Delft3D-Flow is the average in unit area of the whole reservoir, calculated by the ratio of the total surface heat exchange to the total surface area. Table 2 shows the annual average values of these three kinds of heat fluxes. Compared with the Delft3D-Flow calculation, the three kinds of heat fluxes are overestimated by W0, mainly because W0 underestimates the downward transfer of energy in the reservoir, resulting in more heat remaining at the surface and returning to the atmosphere. The W1 model, which considers the effect of flow rate on vertical thermal diffusivity, produced surface heat flux values that were significantly closer to the results of Delft3D-Flow, especially in the large flow rate period, which means that our modification has improved the performance of WRF-lake in surface water–atmosphere interactions. The improvement of surface heat flux calculation appears mainly in summer, i.e., the large flow rate period.
Figure 8. Different kinds of heat flux per unit area through the water surface, including net longwave radiation, latent heat, and sensible heat calculated by the WRF-lake model version by Wang et al. (2019) (red lines), the modified WRF-lake model used in this paper (blue lines), and the Delft3D-Flow simulation (black lines). Positive values and negative values represent the reservoir releasing energy to the atmosphere and absorbing energy from the atmosphere
Net Longwave Radiation (W m–2) Sensible Heat (W m–2) Latent Heat (W m–2) Whole year Large flow rate period Whole year Large flow rate period Whole year Large flow rate period WRF-lake [by Wang et al. (2019)] 112.3 107.7 17.4 14.3 82.5 86.2 WRF-lake (modified) 100.3 82.2 11.5 5.6 60.9 46.6 Delft3D-Flow 88.4 84.0 9.0 5.9 50.3 48.2 Table 2. Annual average values and average values of the large flow rate period, i.e., from May to August, for different kinds of heat fluxes per unit area through the water surface, including net longwave radiation, latent heat, and sensible heat calculated by the WRF-lake model version by Wang et al. (2019), the modified WRF-lake model used in this paper, and the Delft3D-Flow simulation. Positive values represent the reservoir releasing energy to the atmosphere.
Our results show that although W1 significantly outperformed W0, there were still differences between the heat flux simulated by W1 and that of D0, and this was mainly due to the following two reasons: (1) As shown in Fig. 7, there exists obvious longitudinal water temperature variation along the channel in the upstream because the river runs from high latitude to low latitude and the inflow is always colder. The heat flux in the upstream is smaller than that near the dam because of lower surface temperature, lowering the whole reservoir surface heat flux per unit area, which cannot be considered in the WRF-lake model. (2) The temperature difference between inflow and outflow, which is also not considered by WRF-lake but is considered by Delft3D-Flow, can affect the surface heat flux. The inflow is colder than outflow in winter and warmer than outflow in summer, so the heat release simulated by D0 is less in winter and more in summer compared to W1. Therefore, in future studies, for applications in other reservoirs with larger flow rates, the effect of inflow and outflow temperature changes in the WRF-lake model can be investigated further.
WRF-lake [by Wang et al. (2019)] | WRF-lake (modified) | Delft3D-Flow | ||
Surface water temperature | RMSE (°C) | 1.50 | 1.08 | 1.19 |
MAE (°C) | 0.35 | 0.15 | 0.10 | |
Vertical water temperature profile | RMSE (°C) | 1.13 | 1.01 | 1.10 |
MAE (°C) | 0.94 | 0.70 | 0.60 |