Water Temperature Simulation in a Tropical Lake in South China

water

Article Water Temperature Simulation in a Tropical Lake in South China

Hongbin Gu 1,2, Baohong Lu 1,* , Changjun Qi 1,3,*, Si Xiong 4, Wenlong Shen 1 and Lejun Ma 5

1 College of Hydrology and Water Resources, Hohai University, Nanjing 210098, China; [email protected] (H.G.); [email protected] (W.S.) 2 China Renewable Energy Engineering Institute, Beijing 100011, China 3 Appraisal Center for Environment and Engineering, The Ministry of Ecology and Environment of China, Beijing 100012, China 4 Jiangxi Provincial Water Conservancy Planning Design and Research Institute, Nanchang 330029, China; [email protected] 5 Jinling Institute of Technology, Nanjing 211169, China; [email protected] * Correspondence: [email protected] (B.L.); [email protected] (C.Q.); Tel.: +86-25-6815-6577 (B.L.); +86-25-6815-6577 (C.Q.)

Abstract: To study the vertical water temperature structure and thermodynamic characteristics of tropical lake-like reservoirs, a water temperature model was developed by a vertical one-dimensional numerical model for Songtao Reservoir in Hainan Province, China. The model was verified by the measured water temperature data, and sensitivity analysis of key model parameters was carried out. The results show that water temperature simulated by the model in Songtao Reservoir agreed with the observations quite well, and the model is feasible for water temperature simulations in large reservoirs in tropical zones. The sensitivity of vertical water temperature structure to different model parameters varied. For example, the extinction coefficient greatly affected surface water Citation: Gu, H.; Lu, B.; Qi, C.; temperature, which is important for the formation and development of the surface water temperature Xiong, S.; Shen, W.; Ma, L. Water hybrid layer. The vertical mixing coefficient significantly influenced the inflection point position and Temperature Simulation in a Tropical thickness of the thermocline. The vertical water temperature structure in Songtao Reservoir was Lake in South China. Water 2021, 13, stratified. Reservoir surface water temperature varied from 19.4 ◦C to 33.8 ◦C throughout a year. The 913. https://doi.org/ hypolimnion mainly appeared in elevation below 150 m, where the water temperature is basically 10.3390/w13070913 maintained at 19 ◦C throughout the year. This study also found that the surface water temperature of Songtao Reservoir in the tropical zone was higher than the air temperature throughout a year, with Academic Editors: Michele Mistri and an annual average of 3.5 ◦C higher than that of air temperature. The preliminary analysis found out Naicheng Wu that the higher surface water temperature may be caused by the strong air temperature and solar

Received: 24 January 2021 radiation in tropical zones, in addition to the enhanced capacity of heat absorption and heat storage Accepted: 23 March 2021 due to the slow water flow in the reservoir. Published: 27 March 2021 Keywords: tropical zone; lake-like reservoir; vertical one-dimensional numerical model; vertical Publisher’s Note: MDPI stays neutral water temperature structure with regard to jurisdictional claims in published maps and institutional affil- iations. 1. Introduction Reservoir water temperature has been studied in China since the 1960s. With a deep understanding of reservoir water temperature mechanism, hydropower resources develop- Copyright: © 2021 by the authors. ment at present focuses on solving a series of environmental problems caused by reservoir Licensee MDPI, Basel, Switzerland. water temperature stratification [1,2], and many studies on reservoir water temperature This article is an open access article simulation and mitigation measures have been carried out. The cases of reservoir wa- distributed under the terms and ter temperature simulations were mainly studied in subtropical, temperate, and plateau conditions of the Creative Commons mountainous climate regions in China. By contrast, studies on the distribution of reser- Attribution (CC BY) license (https:// voir water temperature in tropical zones are less common. Previous studies in different creativecommons.org/licenses/by/ regions showed that air temperature [3,4] and solar radiation have a positive correlation 4.0/).

Water 2021, 13, 913. https://doi.org/10.3390/w13070913 https://www.mdpi.com/journal/water Water 2021, 13, 913 2 of 18

with water temperature [5]. However, the studied water bodies (lakes and reservoirs) are located in different climatic regions, and their morphologies, depths, and water quality are different, which leads to large differences in the spatiotemporal characteristics of water temperature [6,7]. Reservoir water temperature is an important factor in reservoir water resources management in China. Reservoir water temperature presents seasonal stratification in the vertical direction, and there is a great difference between surface water temperature and bottom water temperature. In the situation in which the location of reservoir water intakes is low, the low-temperature water discharge from the reservoir affects normal habitat and breeding of downstream aquatic organisms. To mitigate the impact of low-temperature water discharge, layered water intake structures are often adopted at hydropower stations according to the vertical water temperature structure. Therefore, accurately capturing the vertical structure of water temperature is key to understanding the design of intake structures. Experts in related industries also pay great attention to the research in this aspect and have carried out many studies in different climatic zones. According to the existing water temperature observation data of the reservoir, the range of reservoir water temperature change in different climatic zones in China is approximately 15 ◦C. The reservoir bottom water temperature is approximately 4.0 ◦C in Fengman Reservoir in Jilin Province [8,9], 6.0 ◦C in Longyangxia Reservoir in Qinghai Province [10,11], 10 ◦C in Xinanjiang Reservoir in Zhejiang Province [12,13], 10–11.5 ◦C in Ertan Reservoir in Sichuan Province [14,15], 16 ◦C in Guangzhao Reservoir in Guizhou Province [16], and 17 ◦C in Nuozhadu Reservoir in Yunan Province [17,18]. However, the bottom water temperature of Songtao Reservoir in Hainan Province located in the southern tropical zone of China is approximately 19 ◦C, which is obviously higher than those in other regions. Influenced by the unique climatic conditions in tropical zones, water temperature structure and thermodynamic characteristics of reservoirs in tropical zones might be different from those in other regions. Therefore, reservoir water temperature simulation in tropical areas can further reveal the distribution of reservoir water temperature in tropical areas. Based on a few laboratory and field findings, the dynamic reservoir simulation model (DYRESM) provides a complete set of optional parameters. Thus, this model has been widely used all over the world. Han et al. [19] simulated three-year water temperature change in Sau Reservoir in northeast Spain by the DYRESM model. Gideon et al. [20] used the DYRESM model to simulate the changes in water temperature and salinity in a period of 45 months in Kinneret Lake in northern Israel. Laurie et al. [21] simulated the seasonal change of water temperature and salinity in Dexter Pit Lake in Nevada, USA. David et al. [22] simulated three-year water quality change in Rotorua Lake in northern New Zealand by coupling DYRESM with the computational aquatic ecosystem dynamics model (CAEDYM), and Asaeda et al. [23] simulated the mechanism of two vertical curtains in Terauchi Reservoir in Japan with the DYRESM model to reduce algae outbreak. In China, the DYRESM model has also been widely used. Chen et al. [24] simulated the annual water temperature change in Taihu Lake in 2005, and the modeling results well reflected the daily water temperature change in Taihu Lake. Xie et al. [25] established a DYRESM– CAEDYM one-dimensional (1D) water quality model for Chaohu Lake, calibrated the model parameters using measured data of water quality, hydrology, and meteorology and put forward the water quality model parameters suitable for characterizing the water environment in Chaohu Lake. Chen [26] used the DYRESM model to investigate the stratification and other thermodynamic conditions in Lugu Lake in southwest China. In this study, Songtao Reservoir in Hainan Province, China, was selected as the study area. Subsequently, a reservoir water temperature model was established to investigate the water temperature distribution in a tropical reservoir. Finally, the thermodynamic characteristics of water temperature in Songtao Reservoir were analyzed. The findings of this study are expected to provide scientific guidelines for formulating ecological environmental protection measures according to local conditions. Water 2021, 13, x FOR PEER REVIEW 4 of 21

Water 2021, 13, 913 3 of 18 and a total reservoir capacity of 3.345 × 109 m3. Its normal water level is 190 m, the maximum dam height is 80.1 m, and the installed capacity is 44.85 MW. After Songtao Reser- voir began to store water,2. Materials a lake and with Methods a water surface area of approximately 144 km2 and a backwater length of2.1. approximately Study Area and Temperature 51 km was Monitoring formed in the upper reach of the Nandu River. Songtao Reservoir, located in Danzhou City, Hainan Province, is the earliest large-scale water-control project developed in the Nandu River basin (Figure1). The main use for this To conduct a scientificreservoir study is irrigation on the needs. vertic Moreover,al structure the reservoir of water has comprehensivetemperature in benefits Song- such as tao Reservoir, three powervertical generation, water temperatur flood control,e andobservation water supply. lines The were reservoir set wasup in started different in 1958 and regions of Songtao Reservoirwas completed on in26 1968, April and 2016 the entire and reservoir13 June was 2016. finished The inmonitoring 1970. Songtao points Reservoir is 9 3 are shown in Figurein 1. multi-yearFigure 2 regulationdemonstrates mode, the with measured a mean annual vertical runoff water of 1.622 temperature× 10 m and at a total reservoir capacity of 3.345 × 109 m3. Its normal water level is 190 m, the maximum dam the three observation lines. The measured data show that water temperature in Songtao height is 80.1 m, and the installed capacity is 44.85 MW. After Songtao Reservoir began to Reservoir basically presentedstore water, an a lake isothermal with a water distribution surface area in of the approximately same horizontal 144 km plane,2 and a and backwater water temperature stratificationlength of approximately only appeared 51 km was in formedthe vertical in the upperdirection. reach of the Nandu River.

Figure 1. Study area andFigure water 1. Studytemperature area and watermonitoring temperature points. monitoring points.

To conduct a scientiﬁc study on the vertical structure of water temperature in Songtao Reservoir, three vertical water temperature observation lines were set up in different regions of Songtao Reservoir on 26 April 2016 and 13 June 2016. The monitoring points are shown in Figure1. Figure2 demonstrates the measured vertical water temperature at the three observation lines. The measured data show that water temperature in Songtao Reservoir basically presented an isothermal distribution in the same horizontal plane, and water temperature stratiﬁcation only appeared in the vertical direction.

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0 0

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20 20 Depth(m) Depth(m) 30 30 Point 1 Point 1 Point 2 Point 2 Point 3 Point 3

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50 50 15 20 25 30 35 15 20 25 30 35 Water temperature(degrees Celsius) Water temperature(degrees Celsius) 26 April 2016 13 June 2016

Figure 2. DistributionFigure 2. Distribution of measured of measured water temperature water temperature in Songtao in Songtao Reservoir. Reservoir.

2.2. Reservoir Water2.2. Reservoir Temperature Water TemperatureModel Model 2.2.1. Model Selection 2.2.1. Model SelectionCompared with physical models, numerical models are more convenient to rationally Comparedinvestigate with physical the pattern models, of reservoir numerical water models temperature are more change. convenient Reservoir to water ration- tempera- ture models include vertical 1D, cross-sectional two-dimensional, and three-dimensional ally investigate the pattern of reservoir water temperature change. Reservoir water tem- models. According to reservoir morphological characteristics, regulation mode, and hy- perature modelsdrodynamic include conditions,vertical 1D, a suitablecross-sectional model with two-dimensional, satisfactory accuracy and andthree-dimen- high calculation sional models.efficiency According should to bereservoir selected [morpho27]. Givenlogical that Songtao characteristics, Reservoir regulation is a typical lake-like mode, reser- and hydrodynamicvoir in conditions, a multi-year a regulation suitable modemodel with with relatively satisfactory slow wateraccuracy flow and in the high reservoir cal- area, culation efficiencythe vertical should 1D be models selected with [27]. good Given accuracy that Songtao and high Reservoir calculation is efficiencya typical arelake- suitable like reservoir forin a water multi-year temperature regulation prediction mode in with such relatively reservoirs. slow As shownwater flow in Figure in the2, theres- water ervoir area, thetemperature vertical 1D of models Songtao with Reservoir good basically accuracy presents and high an isothermal calculation distribution efficiency in are the same suitable for waterhorizontal temperature plane, and prediction water temperature in such stratificationreservoirs. onlyAs shown appears in in theFigure vertical 2, the direction. Therefore, it is reasonable to use the vertical 1D models to simulate the vertical water water temperature of Songtao Reservoir basically presents an isothermal distribution in temperature change in Songtao Reservoir. the same horizontalThe plane, vertical and 1D water numerical temperature models usually stratification divide aonly reservoir appears into in several the verti- horizontal cal direction. Therefore,thin layers alongit is reasonable the vertical to direction. use the Thesevertical models 1D models assume to that simulate water temperaturethe ver- in tical water temperatureeach layer ischange evenly in distributed, Songtao Reservoir. and the change of vertical water temperature structure is The verticaldescribed 1D numerical by the transformation models usually of the divide wind-mixing a reservoir turbulent into several kinetic energyhorizontal and water thin layers alongpotential the vertical energy. Thedirection. 1D models These comprehensively models assume consider that the water influence temperature of reservoir in inflow each layer is evenlyand outflow, distributed, wind mixing, and the and chan waterge surface of vertical heat exchangewater temperature on reservoir structure water temperature is described by thestratification. transformation The assumption of the wind-mixing of horizontal turbulent isothermal kinetic layers hasenergy been and proved water by many measured data. These models can produce good simulation results when model parameters potential energy. The 1D models comprehensively consider the influence of reservoir in- are accurately calibrated. Typical vertical 1D water temperature models include the water flow and outflow,resources wind engineering mixing, and model water (WRE) surface [28], heat the Massachusetts exchange on Institute reservoir of Technologywater tem- model perature stratification.(MIT) [29], The and theassumption DYRESM modelof horizontal [30,31]. Inisothe this study,rmal thelayers DYRESM has been model proved was used to by many measuredsimulate data. water These temperature models incan Songtao produce Reservoir. good simulation results when model parameters are accurately calibrated. Typical vertical 1D water temperature models include the water resources engineering model (WRE) [28], the Massachusetts Institute of Technology model (MIT) [29], and the DYRESM model [30,31]. In this study, the DYRESM model was used to simulate water temperature in Songtao Reservoir.

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2.2.2. Model Theory DYRSEM is a 1D hydrodynamic model for lakes and reservoirs, which was developed by the Water Research Center of the University of Western Australia. Based on the assumption that vertical changes in water temperature and water quality are dominant, the DYRESM model can simulate vertical changes and structural characteristics of water temperature, salinity, and density in lakes and reservoirs [32]. The DYRESM model adopts the Lagrangian layered mode with variable layer thickness, which can adapt to the vertical structure of the lake. This is an advantage of this model in simulating the vertical changes of water temperature and water quality, and users may adjust the vertical layer number of lakes and reservoirs according to their own needs [33]. The DYRESM model mainly uses the laws of water balance and heat balance. The model assumes that lakes and river beds are adiabatic with no heat transfer to the water body. It mainly considers the heat transfer caused by vertical flow, heat exchange at water–air interface, molecular and turbulent diffusion, heat transfer caused by inflow and outflow, and solar radiation absorbed by water. The governing equations of the model are as follows (1): ∂T ∂ TQV 1 ∂ ∂T B 1 ∂(Aϕ z) + = A(Dm+E) + (u iTi−uo T)+ , (1) ∂A ∂t A A ∂z ∂z A ρACP ∂z where t denotes time, z is elevation, B is the average width of horizontal stratification layers, T is the temperature of horizontal stratification layers, A is the horizontal area at the elevation z, QV is the vertical convective flow through the upper boundary of horizontal stratification layers, ρ is the density of stratification layers, CP is the specific ◦ heat of water (4184 J/(kg· C), Dm is the molecular diffusion coefficient, E is the vertical turbulent diffusion coefficient, ui is the inflow velocity, uo is the outflow velocity, Ti is the inflow water temperature, and ϕz is the solar radiation absorbed by water body. QV can be obtained by the mass balance of horizontal stratification as follows (2):

 z z  Z Z Qv= B ui(z, t)dz− uo(z, t)dz. (2) 0 0

Water balance demonstrates the change of water level and storage capacity caused by the imbalance of inflow and outflow. In unit time, the change of water storage in a certain layer is inflow minus outflow, and the vertical convective flow is also considered. The water balance formula is as follows (3):

∂V N = Q −Q +Q , (3) ∂t i,N o,N v,N−1

where N is the layer number, Qi,N is the inflow of the layer N, Qo,N is the outflow of the layer N, and Qv,N-1 is the vertical flow through the N and N-1 layers.

2.3. Modeling Scheme 2.3.1. Boundary Conditions The model mainly requires inflow, outflow, inflow water temperature, and meteorological data as the boundary conditions. The simulation period was from 2 March 2016 to 1 March 2017. The inflow, outflow, and inflow water temperature of Songtao Reservoir were collected as the hydrological and water temperature boundary conditions for the model. The meteorological data included six input variables—short-wave radiation, long-wave radiation, air temperature, vapor pressure, wind speed, and precipitation. Long-wave radiation was calculated by cloud cover, and vapor pressure was estimated by relative humidity and air temperature. The meteorological data were downloaded from the National Meteorological Science Sharing Service Network of China (http://data.cma.cn, accessed on: 16 September 2019 to 30 November 2019). The model used daily intervals, and the Water 2021, 13, x FOR PEER REVIEW 7 of 21

wave radiation was calculated by cloud cover, and vapor pressure was estimated by relative humidity and air temperature. The meteorological data were downloaded from the National Meteorological Science Sharing Service Network of China (http://data.cma.cn, accessed on: 16 September 2019 to 30 November 2019). The model used daily intervals, Water 2021, 13, 913 6 of 18 and the input data were daily average or daily accumulated values. The meteorological data were obtained at the Danzhou meteorological station, which is nearest to the reservoir. inputThe data measured were daily inflow average and or outflow daily accumulated from 2 March values. 2016 to The 1 March meteorological 2017 were data selected were obtained at the Danzhou meteorological station, which is nearest to the reservoir. as the boundary conditions of the model. As shown in Figure 3, on 17–19 August 2016 and The measured inflow and outflow from 2 March 2016 to 1 March 2017 were selected as13–19 the boundaryOctober 2016, conditions inflow ofsharply the model. increased. As shown It was in much Figure larger3, on than 17–19 the August annual 2016 average and 13–19flow, and October the maximum 2016, inflow flow sharply was 4930 increased. m3/s on It was18 October much larger 2016. thanUnder the the annual regulation average of 3 flow,Songtao and Reservoir, the maximum the outflow flow was process 4930 m was/s onrelatively 18 October flat, 2016.and the Under maximum the regulation discharge of Songtao Reservoir, the outflow process was relatively flat, and the maximum discharge 3 was 52.6 mm3/s on on 14 14 February February 2017. 2017.

6000 60 inflow 5000 outflow 50

4000 40 3 3 3000 30 Inflow(m /s)

2000 20 Outflow(m /s)

1000 10

0 4 5 6 7 8 9 1 1 1 1 2 0 3/ / / / / / / 0 1 2 / / 2 20 20 20 20 20 20 /2 /2 /2 20 20 01 1 1 1 1 1 1 0 0 0 1 1 6 6 6 6 6 6 6 16 16 16 7 7 Month/Year Figure 3. InﬂowInflow and outﬂowoutflow processes inin simulationsimulation period.period.

2.3.2. Initial Conditions In termsterms ofof initialinitial profile profile data, data, a seta set of of elevation–water elevation–water temperature temperature relationship relationship arrays ar- from reservoir bottom to water surface (initial water surface height) was needed. The rays from reservoir bottom to water surface (initial water surface height) was needed. The measured water temperature in Songtao Reservoir on 2 March 2016 was used as the initial measured water temperature in Songtao Reservoir on 2 March 2016 was used as the initial input condition. Figure4 demonstrates the initial water temperature distribution. It input condition. Figure 4 demonstrates the initial water temperature distribution. It shows shows that water temperature stratification appeared in Songtao Reservoir in early March. that water temperature stratification appeared in Songtao Reservoir in early March. The The thermocline was from the water surface to the water depth of 8.81 m, and the water thermocline was from the water surface to the water depth of 8.81 m, and the water tem- temperature decline rate was 0.13 ◦C/m. perature decline rate was 0.13 °C/m. 2.3.3. Model Parameters The DYRESM model has many parameters, but most parameters are universal to a certain extent. A total of 15 model parameters require calibration. These parameters are (sw) aerodynamic transmission coefficients (CL, CS, and CM), average water surface albedo ra , extinction coefficient ηA, etc. Satisfactory simulation results can be obtained by using the default model parameters [24]. The model can provide accurate simulations of water temperature structure in medium and small reservoirs [34,35]. However, for the simulations in large reservoirs, parameters such as vertical mixing coefficient C, allowable maximum layer thickness, minimum layer thickness, and turbulence kinetic energy conversion efficiency require recalibration [36]. Given that the DYRESM model is less used to simulate water temperature in tropical zones, model parameters were calibrated using the measured water temperature data in Songtao Reservoir. Table1 demonstrates the calibrated model parameter values. WaterWater 20212021, ,1313, ,x 913 FOR PEER REVIEW 8 7of of 21 18

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FigureFigure 4. 4. InitialInitial water water temperature temperature distribution distribution for for water water temperature temperature simulations. simulations. Table 1. Calibrated model parameter values in Songtao Reservoir. 2.3.3. Model Parameters No.The DYRESM model has Parameters many parameters, but most parameters Unit Calibrationare universal Value to a −3 certain1 extent. Aerodynamic A total transmissionof 15 model coefficients parameters (C Lrequire, CS, CM )/calibration. These parameters1.5 × 10 are (sw) (sw) aerodynamic2 transmissionAverage water coefficients surface albedo (CL, CSr,a and CM), average/ water surface albedo 0.09 ra , extinction3 coefficient Long-wave ηA, emissivityetc. Satisfactory at water simulation surface εw results can/ be obtained by 0.96 using the default4 model parameters Critical [24]. wind The speed modelUcir can provide accuratem/s simulations of 3.00 water tem- perature5 structure Entrainment in medium coefficient and small constant reservεoirs [34,35]. However,/ for the 0.05simulations 6 Light plume entrainment coefficient α / 0.083 in large reservoirs, parameters such as vertical mixing coefficient C, allowable maximum 7 Coefficient of shear energy generation efficiency ηk / 0.06 layer8 thickness, Coefficient minimum of potential layer energy thickness, mixing an efficiencyd turbulenceηp kinetic/ energy conversion 0.5 effi- ciency9 require Coefficient recalibration of wind [36]. disturbance Given that efficiency the DYRESMηs model/ is less used 0.85to simulate 2 7 water10 temperature Coefficient in tropical of effective zones, surface model area parametersAC were mcalibrated using10 the meas- 2 −5 ured11 water temperature Top diffusion data in coefficientSongtao KReseBBL rvoir. Table 1 mdemonstrates/s 1.4 the× calibrated10 model12 parameter values. Vertical mixing coefficient C / 50 13 Minimum layer thickness Hmin m 0.5 14 Maximum layer thickness Hma m 2 Table 1. Calibrated model parameter values in Songtao Reservoir. −1 15 Extinction coefficient ηA m 0.70 No. Parameters Unit Calibration Value 2.4.1 Parameter Aerodynamic Sensitivity transmission Analysis coefficients (CL, CS, CM) / 1.5 × 10−3 ()sw 2 Extinction coefficientAverage waterηA, also surface called albedo attenuation ra coefficient,/ refers to the0.09 attenuation degree3 of solar Long-wave radiation enteringemissivity the at water water surface body ε alongw its depth, / and it was 0.96 calculated by the4 Beer–Lambert formula.Critical wind This speed coefficient Ucir directly affects m/s the distribution 3.00 of solar radiation5 along its Entrainmentdepth, controls coefficient the on-way constant attenuation ε of heat / after entering 0.05 the water body,6 and further Light impacts plume the entrainment vertical structure coefficient of α reservoir water / temperature. 0.083 7 Vertical Coefficient mixing coefficientof shear energyC is generation a non-universal efficiency parameter, ηk / and it is 0.06 a constant in the8 relational Coefficient expression of potential between energy effective mixing vertical efficiency diffusion ηp / and lake index 0.5 LN in the thermocline,9 which Coefficient is expressed of wind disturbance by (4): efficiency ηs / 0.85 10 Coefficient of effective surface area AC m2 107 11 Top diffusion coefficientK KBBLC m2/s 1.4 × 10−5 Z = , (4) 12 Vertical mixing coefficientKM CL N / 50 13 Minimum layer thickness Hmin m 0.5 where14 KZ is the effective Maximum vertical layer diffusion thickness coefficient, Hma LN is the m lake index [37 2 ,38], KM is −7 2 the15 molecular thermal diffusionExtinction coefficient coefficient (1.4ηA × 10 m /s), m and−1 C is the vertical0.70 mixing coefficient. Given LN, the value of vertical mixing coefficient C affects the effective vertical

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diffusion intensity of thermocline. For simulations in a different lake, the value of this coefficient is different. For example, the calibrated value for Kinneret Lake was 200 [37], those for Wanaka and Wakaitipu Lakes were 1500 [39], and the value for Geneva Lake was 700 [35]. In this study, many parameter values were selected for calibration, and the best calibrated vertical mixing coefficient for Songtao Reservoir was 50. The model controls the vertical grid size by defining the maximum layer thickness Hmax and minimum layer thickness Hmin. In the simulation, if the grid size of a certain layer is lower than the defined minimum layer thickness, this layer is merged with the adjacent layer. On the contrary, if the grid size of a layer is larger than the maximum allowable layer thickness, this layer is divided into several layers with the same temperature, and the thickness of new layers should be within the allowable layer thickness. The maximum and minimum layer thickness follows the principle of Hmax > 2Hmin. Layer thickness is very important to the simulation of the thermocline. If layer thickness is too large, the simulated water temperature is vertically homogenized, and the inflection point of thermocline may not be accurately simulated. This further affects the vertical water temperature structure. However, if the layer thickness is defined to be too small, the model efficiency is affected.

3. Results 3.1. Model Verification 3.1.1. Water Level The observed reservoir inflow and outflow from 2 March 2016 to 1 March 2017 were used as the hydrological boundaries (Figure3). Figure5 demonstrates the measured and simulated water levels in the simulation period. The figure shows that the simulated water level process agreed with the observations quite well, with a root mean square error of 0.18 m. Water level verification shows that under the measured inflow and outflow conditions, the simulated reservoir operation, and the regulation process were in line Water 2021, 13, x FOR PEER REVIEW with the actual situation, and the inflow water volume was balanced with the outflow.10 of 21 Therefore, the model can accurately simulate the water quantity and water level processes in Songtao Reservoir.

190

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170 measured values simulated values

165 3 4 5 6 7 8 9 1 1 1 1 2 / /2 /2 /2 /2 /2 /2 0 1 2 /2 /2 20 0 0 0 0 0 0 /2 /2 /2 0 0 1 16 16 16 16 16 16 01 01 01 17 17 6 6 6 6 Month/Year FigureFigure 5. 5. ObservedObserved and and simulated simulated water water level level processes processes in in Songtao Songtao Reservoir. Reservoir. 3.1.2. Water Temperature 3.1.2. Water Temperature The observed water temperature data in Songtao Reservoir on 26 April 2016 and 13 The observed water temperature data in Songtao Reservoir on 26 April 2016 and 13 June 2016 were used to verify the simulated water temperature. Figure6 compared the June 2016 were used to verify the simulated water temperature. Figure 6 compared the simulated vertical water temperature structure with the observations. It shows that the simulated vertical water temperature structure with the observations. It shows that the model simulated the vertical water temperature stratiﬁcation characteristics in Songtao model simulated the vertical water temperature stratification characteristics in Songtao Reservoir quite well and had a good ﬁt to the observed water temperature structure. Reservoir quite well and had a good fit to the observed water temperature structure.

190 190

180 180

170 170

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150 150 Elevation(m) Elevation(m)

140 140 measured values measured values simulated values simulated values 130 130

120 120 15 20 25 30 35 15 20 25 30 35 Water temperature(degrees Celsius) Water temperature(degrees Celsius)

(a) 26 April 2016 (b) 13 June 2016 Figure 6. Verification of vertical water temperature structure in Songtao Reservoir: (a) Comparison of simulated water temperature and measured water temperature on 26 April, 2016; (b) Comparison of simulated water temperature and measured water temperature on 13 June, 2016.

To analyze the accuracy of the simulated water temperature further, the thickness and water temperature of surface temperature layer, thermocline depth, the temperature gradient of the thermocline, and water temperature of hypolimnion were selected as the characteristic values of vertical water temperature distribution, and the simulated values were compared with the observations. As shown in Table 2, the overall error was low for

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190

185

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175 Water level(m)

170 measured values simulated values

165 3 4 5 6 7 8 9 1 1 1 1 2 / /2 /2 /2 /2 /2 /2 0 1 2 /2 /2 20 0 0 0 0 0 0 /2 /2 /2 0 0 1 16 16 16 16 16 16 01 01 01 17 17 6 6 6 6 Month/Year Figure 5. Observed and simulated water level processes in Songtao Reservoir.

3.1.2. Water Temperature The observed water temperature data in Songtao Reservoir on 26 April 2016 and 13 June 2016 were used to verify the simulated water temperature. Figure 6 compared the simulated vertical water temperature structure with the observations. It shows that the Water 2021, 13, 913 model simulated the vertical water temperature stratification characteristics in Songtao9 of 18 Reservoir quite well and had a good fit to the observed water temperature structure.

190 190

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140 140 measured values measured values simulated values simulated values 130 130

120 120 15 20 25 30 35 15 20 25 30 35 Water temperature(degrees Celsius) Water temperature(degrees Celsius)

(a) 26 April 2016 (b) 13 June 2016

FigureFigure 6.6. VeriﬁcationVerification ofof verticalvertical waterwater temperaturetemperature structurestructure inin SongtaoSongtao Reservoir:Reservoir: ((aa)) ComparisonComparison ofof simulatedsimulated waterwater temperaturetemperature andand measuredmeasured waterwater temperaturetemperature onon 2626 AprilApril, 2016; 2016; ( b(b)) Comparison Comparison ofof simulatedsimulated waterwater temperaturetemperature andand measuredmeasured waterwater temperaturetemperature on on 13 13 June June, 2016. 2016.

ToTo analyzeanalyze thethe accuracyaccuracy ofof thethe simulatedsimulated waterwater temperaturetemperature further,further, thethe thicknessthickness andand waterwater temperaturetemperature ofof surfacesurface temperaturetemperature layer,layer, thermoclinethermocline depth,depth, thethe temperaturetemperature gradientgradient ofof thethe thermocline,thermocline, andand waterwater temperaturetemperature ofof hypolimnionhypolimnion werewere selectedselected asas thethe characteristiccharacteristic valuesvalues ofof verticalvertical waterwater temperaturetemperature distribution,distribution, andand thethe simulatedsimulated valuesvalues werewere comparedcompared with with the the observations. observations. As As shown show inn in Table Table2, the2, the overall overall error error was was low low for allfor the ﬁve vertical water temperature distribution characteristic values, and the calibrated vertical 1D numerical model had a satisfactory performance on water temperature simulations in Songtao Reservoir. The simulated surface layer, thermocline, and hypolimnion were ba-

sically consistent with the measured values, and the model could reveal the characteristics and trend of water temperature distribution in Songtao Reservoir.

Table 2. Observed and simulated characteristic values of vertical water temperature distribution.

26 April 13 June Characteristics of Water Temperature Measured Simulated Measured Simulated Error Error Value Value Value Value Thickness of surface temperature layer (m) 3.2 3.4 0.2 4.0 4.2 0.2 Water temperature of surface temperature layer (◦C) 29.1 29.1 0.0 32.1 33.5 1.4 Thermocline depth (m) 9.7 9.1 −0.6 9.0 8.4 −0.6 Temperature gradient of thermocline (◦C/m) 0.9 1.1 0.2 1.3 1.6 0.3 Water temperature of hypolimnion (◦C) 19.0 19.0 0.0 19.1 19.0 −0.1

3.2. Vertical Water Temperature Structure Figure7 shows the vertical water temperature distribution and its inter-annual variation process in Songtao Reservoir. The simulated water temperature on the 15th day of each month during the simulation period of 2 March 2016–1 March 2017 was used for analysis. This ﬁgure indicated that water temperature in Songtao Reservoir has a distinct vertical stratiﬁcation structure. Surface water temperature largely varied on the inter-annual scale, Water 2021, 13, 913 10 of 18

ranging from 19.4 ◦C to 33.8 ◦C, with a range of variation of 14.4 ◦C. The lowest surface Water 2021, 13, x FOR PEER REVIEW water temperature appeared in February, and the highest surface water temperature was12 of 21

found in June. Hypolimnion was located in the regions with the elevation below 150 m, where the water temperature was stable throughout the year, basically maintained at 19 ◦C.

190

180

170

160 March April 150 May Elevation(m) June July 140 August September October November 130 December January February 120 15 20 25 30 35 Water temperature(degrees Celsius)

FigureFigure 7. 7. SimulatedSimulated verticalvertical water water temperature temperature distribution distribution in Songtao in Songtao Reservoir Reservoir on the 15thon the day 15th of day ofeach each month. month.

According to Figure7, the vertical temperature difference and temperature gradient 3.3. Parameter Sensitivity Analysis of each month were analyzed. Large vertical temperature differences mainly occurred in JuneTotally, and July, 15 with model the verticalparameters temperature were calibr differenceated. of During 14.8 ◦C model and 14.3 parameter◦C, respectively, calibration, itand was the found temperature that the gradientwater temperature in both months stru wascture 0.27 in Songtao◦C/m. As Reservoir shown in was Figure sensitive7, to extinctionvertical water coefficient, temperature vertical stratification mixing coefficient, was most obvious and maximum in June and layer July. thickness. In January In all 15 and February, the vertical temperature difference was low, with a vertical temperature modes, this study◦ mainly ◦focused on analyzing the sensitivity of these three◦ parameters todifference water temperature of 1.0 C and structure. 0.4 C, respectively, Five characte and theristic temperature values reflecting gradient was water 0.01 temperatureC/m. This indicates that vertical water temperature stratification was the weakest in January and structure change were selected. They are surface water temperature Tsurface, the thickness February, basically in a mixed structure. of surface water temperature hybrid layer Hsurface, depth of thermocline inflection point D3.3.thermocline Parameter, thermocline Sensitivity thickness Analysis Hthermocline, and hypolimnion thickness Hhypolimnetic. Figure 8 showsTotally, the positions 15 model of parameters characteristic were values. calibrated. During model parameter calibration, it was found that the water temperature structure in Songtao Reservoir was sensitive to extinction coefficient, vertical mixing coefficient, and maximum layer thickness. In all 15 modes, this study mainly focused on analyzing the sensitivity of these three parameters to water temperature structure. Five characteristic values reflecting water temperature structure change were selected. They are surface water temperature Tsurface, the thickness of surface water temperature hybrid layer Hsurface, depth of thermocline inflection point Dthermocline, thermocline thickness Hthermocline, and hypolimnion thickness Hhypolimnetic. Figure8 shows the positions of characteristic values.

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Water 2021, 13, x FOR PEER REVIEW 13 of 21 Water 2021, 13, 913 11 of 18

0 Tsurface 0 Hsurface Tsurface Hsurface

Hthermocline 10 Hthermocline 10

Dthermocline 20 Dthermocline 20

Depth(m) H 30 hypolimnetic Depth(m) H 30 hypolimnetic

40 40

50 15 20 25 30 35 50 Water temperature(degrees Celsius) 15 20 25 30 35 Water temperature(degrees Celsius) Figure 8. Schematic diagram of characteristic values for parameter sensitivity analysis. FigureFigure 8. 8. SchematicSchematic diagram diagram of of characteristic characteristic valu valueses for for parameter parameter se sensitivitynsitivity analysis. analysis. 3.3.1. Extinction Coefficient 3.3.1. Extinction Coefficient 3.3.1. Extinction Coefficient The extinction coefficient ηA was defined as 0.2, 0.4, 0.9, and 2.0. The simulation re- The extinction coefficient ηA was defined as 0.2, 0.4, 0.9, and 2.0. The simulation sults Theusing extinction these parameter coefficient values ηA was were defined compared as 0.2, with 0.4, that 0.9, under and 2.0. the Thebaseline simulation operating re- results using these parameter values were compared with that under the baseline operating conditionsults using ( ηtheseA = 0.7). parameter Figure 9 values demonstrates were comp theared simulated with that water under temperature the baseline using operating differ- condition (ηA = 0.7). Figure9 demonstrates the simulated water temperature using different entcondition extinction (ηA =coefficient 0.7). Figure values. 9 demonstrates the simulated water temperature using differ- extinction coefficient values. ent extinction coefficient values.

FigureFigure 9. 9. VerticalVertical water water temperature temperature distribution distribution using using different different extinction extinction coefficients. coefficients. Figure 9. Vertical water temperature distribution using different extinction coefficients. FigureFigure 99 indicates that the greater the extinction coefficient, coefficient, the higher the surface waterwaterFigure temperature, temperature, 9 indicates and and that the the thesmaller smaller greater the the the thic thickness extinctionkness of of surface surfacecoefficient, water water the temperature temperature higher the surfacehybrid hybrid layer.waterlayer. Whentemperature, When the the extinction extinction and the coefficient coefficientsmaller wasthe was thicdef definedinedkness as of 2, as surfacethe 2, surface the water surface water temperature water temperature temperature hybrid was ◦ ◦ thelayer.was highest theWhen highest (33.7 the extinction°C), (33.7 andC), it coefficient was and 1.3 it was°C was higher 1.3 defC thanined higher asthat 2, than inthe the surface that baseline in water the operating baseline temperature condition operating was thecondition highest( (33.7ηA = °C), 0.7). and In this it was situation, 1.3 °C higher almost than no water that in temperature the baseline hybrid operating layer condition appeared on the surface. In the case of the extinction coefficient of 0.2, the reservoir’s surface water

Water 2021, 13, x FOR PEER REVIEW 14 of 21

A Water 2021, 13, 913 (η = 0.7). In this situation, almost no water temperature hybrid layer appeared on12 ofthe 18 surface. In the case of the extinction coefficient of 0.2, the reservoir’s surface water temperature was the lowest (32.0 °C), and it was 0.4 °C lower than that in the baseline operating condition. The thickness of the surface water temperature hybrid layer was the larg- esttemperature (13.1 m). The was inflection the lowest point (32.0 of◦ thermocC), andline it was was 0.4 the◦C deepest lower than(28.7m), that and in the it was baseline 14.0 moperating lower than condition. that in the The baseline thickness operating of the surfacecondition. water Under temperature other working hybrid conditions, layer was excludingthe largest η (13.1A = 0.2, m). the The position inflection of the point thermocline of thermocline inflection was point the deepest remained (28.7m), almost and unit changedwas 14.0 with m lower a slightly than different that in the thickness baseline of operatingthe thermocline condition. layer, Underand the other hypolimnion working thicknessconditions, was excluding basicallyη theA = same. 0.2, the position of the thermocline inflection point remained almostAccording unchanged to the with analysis a slightly results, different the extinc thicknesstion coefficient of the thermocline mainly affects layer, surface and wa- the terhypolimnion temperature, thickness and it also was has basically certain the impa same.cts on the position of the thermocline. How- ever, Accordingit does not to basically the analysis change results, the thewate extinctionr temperature coefficient of the mainly hypolimnion. affects surface When water the extinctiontemperature, coefficient and it also is large, has certain more heat impacts is absorbed on the position by the upper of the thermocline.water body with However, higher it surfacedoes not water basically temperature. change the Meanwhile, water temperature heat is rapidly of the hypolimnion.attenuated with When depth, the leading extinction to acoefficient thinner surface is large, water more temperature heat is absorbed hybrid by laye ther, upperand hence water the body rise withof the higher thermocline. surface However,water temperature. when the Meanwhile,extinction coefficient heat is rapidly is very attenuated small (e.g., with 0.2), depth, more leadingheat is transferred to a thinner tosurface the lower water water temperature body, and hybrid the position layer, and of hencehypolimnion the rise descends of the thermocline. with the decreased However, layerwhen thickness. the extinction Thiscoefficient conclusion is is very basically small (e.g.,consistent 0.2), more with heat the isfinding transferred of Gal to et the al.lower [20], whowater investigate body, and the the water position temperature of hypolimnion structure descends in Kinneret with theLake. decreased layer thickness. This conclusion is basically consistent with the finding of Gal et al. [20], who investigate 3.3.2.the water Vertical temperature Mixing Coefficient structure in Kinneret Lake. 3.3.2.Different Vertical vertical Mixing Coefficientmixing coefficient values (1, 200, 500, 3000, and 5000) were selected and compared with the simulation results in the baseline operating condition (C = 50). Different vertical mixing coefficient values (1, 200, 500, 3000, and 5000) were selected andFigure compared 10 show with thethat simulation the vertical results mixing in thecoefficient baseline C operating had no obvious condition influence (C = 50). on surfaceFigure water 10 temperature show that the and vertical the thickness mixing coefficientof the surfaceC had water no obvioustemperature influence hybrid on layer.surface However, water temperature it significantly and the affects thickness the inflection of the surface point water position temperature and thickness hybrid of layer. the thermocline.However, it significantlyWith the increase affects of the vertical inflection mixing point coefficient position and C, thicknessthe inflection of the points thermo- of thermoclinecline. With the descended increase ofwith vertical a range mixing of 0.0–18.3m, coefficient andC, the the inflection thickness points of thermocline of thermocline in- creaseddescended with with a range a range of 0.0–17.3m. of 0.0–18.3m, When and th thee vertical thickness mixing of thermocline coefficient increased was defined with as a 5000,range the of 0.0–17.3m.depth of inflection When the point vertical (32.8 mixing m) and coefficient thickness wasof thermocline defined as 5000,(25.1 m) the were depth the of largest,inflection and point they (32.8 were, m) respectively, and thickness 18.3 of m thermocline and 17.3 m (25.1 higher m) than were those the largest, in the andbaseline they operatingwere, respectively, condition. 18.3 m and 17.3 m higher than those in the baseline operating condition.

20 Depth(m) 30 1 50 200 500 40 3000 5000

50 15 20 25 30 35 Water temperature(degrees Celsius)

FigureFigure 10. 10. SimulatedSimulated water water temperature temperature distribution distribution stru structurecture using different vertical mixing coefﬁ-coefficients.cients.

This analysis shows that the vertical mixing coefﬁcient has no obvious impact on surface water temperature, and it mainly affects the structure of the thermocline. A larger vertical mixing coefﬁcient leads to a stronger effective vertical mixing in the thermocline,

deeper inﬂection points of the thermocline, and a thicker thermocline. Meanwhile, the Water 2021, 13, x FOR PEER REVIEW 15 of 21

This analysis shows that the vertical mixing coefficient has no obvious impact on surface water temperature, and it mainly affects the structure of the thermocline. A larger Water 2021, 13, 913 vertical mixing coefficient leads to a stronger effective vertical mixing in the thermocline,13 of 18 deeper inflection points of the thermocline, and a thicker thermocline. Meanwhile, the temperature gradient of the thermocline decreases correspondingly, and the slope of the temperature curve vertically decreases. This coefficient is inversely proportional to the thicknesstemperature of hypolimnion. gradient of the The thermocline thickness decreasesof hypolimnion correspondingly, tends to decrease and the with slope the of thein- creasetemperature of this parameter. curve vertically decreases. This coefﬁcient is inversely proportional to the thickness of hypolimnion. The thickness of hypolimnion tends to decrease with the increase 3.3.3.of this Maximum parameter. Allowable Layer Thickness 3.3.3.The Maximum maximum Allowable allowable Layer layer Thickness thickness of 1.0 m, 3.0 m, 4.0 m, and 5.0 m were selected and compared with the simulation results in the baseline operating condition (Hmax The maximum allowable layer thickness of 1.0 m, 3.0 m, 4.0 m, and 5.0 m were selected = 2.0). To analyze the sensitivity of maximum allowable layer thickness, the minimum and compared with the simulation results in the baseline operating condition (H = 2.0). layer thickness was taken as 0.5 m. max To analyze the sensitivity of maximum allowable layer thickness, the minimum layer The analysis shows that the maximum allowable layer thickness affected the thick- thickness was taken as 0.5 m. ness of the surface water temperature hybrid layer and thermocline layer (Figure 11). With The analysis shows that the maximum allowable layer thickness affected the thickness the increase of maximum allowable layer thickness, the thickness of surface water tem- of the surface water temperature hybrid layer and thermocline layer (Figure 11). With the peratureincrease ofhybrid maximum layer allowabledecreased layerwith thickness,a range of the−1.4–3.8 thickness m), and of surface the thickness water temperature of thermo- clinehybrid increased layer decreased with a range with of a 1.4–3.8 range m). of − Howe1.4–3.8ver, m), the and inflection the thickness point position of thermocline of ther- moclineincreased basically with a range remained of 1.4–3.8 unchanged, m). However, and it thehad inﬂection little effect point on positionthe thickness of thermocline of hypolimnion.basically remained unchanged, and it had little effect on the thickness of hypolimnion.

20 Depth(m) 30 1 2 3 4 40 5

50 15 20 25 30 35 Water temperature(degrees Celsius) FigureFigure 11. 11. SimulatedSimulated water water temperature temperature distribution distribution structure structure using using different different maximum maximum allowable allowable layerlayer thickness. thickness.

ThisThis analysis analysis indicates indicates that that the the effect effect of of maximum maximum allowable allowable layer layer thickness thickness on on water water temperaturetemperature and and the the thickness thickness of of hypolimnion hypolimnion can can be be ignored, ignored, and and it it mainly mainly affects affects water water temperaturetemperature and and the the thickness thickness of of surface surface water water temperature temperature hybrid hybrid layer layer and and thermocline. thermocline. AA smaller smaller maximum maximum allowable allowable layer layer thickness thickness decreases decreases the the spatial spatial iteration iteration step step of of nu- nu- mericalmerical simulations andand givesgives a a ﬁner finer description description of of layer-to-layer layer-to-layer convective convective diffusion diffusion and andvertical vertical water water temperature temperature structure. structure. However, However, it increases it increases the computationalthe computational time. time.

3.4.3.4. Thermodynamic Thermodynamic Characteristics Characteristics of of the the Reservoir Reservoir FigureFigure 1212 showsshows the the monthly monthly mean mean air air temperature, inflow inflow water temperature, and surface water temperature in Songtao Reservoir from 2 March 2016 to 1 March 2017. It surface water temperature in Songtao Reservoir from 2 March 2016 to 1 March 2017. It demonstrates that these three variables were in a consistent trend. January−July was the demonstrates that these three variables were in a consistent trend. January−July was the period of temperature rise, and water temperature increased with the rise of air temperature. Subsequently, a cooling period appeared. As air temperature decreased, water temperature also decreased. According to the correlation analysis, the correlation coefficient between air temperature and the inflow water temperature was 0.98, and that between air temperature and reservoir surface water temperature was 0.97. As expected, a strong correlation existed between air temperature and water temperature. During this period, the monthly Water 2021, 13, 913 14 of 18

maximum, monthly minimum, and annual mean air temperatures were 28.1 ◦C (in June), 17.8 ◦C (in January), and 23.7 ◦C, respectively. The monthly maximum, monthly minimum, and annual mean inflow water temperatures were 28.2 ◦C (in July), 19.3 ◦C (in January), and 24.7 ◦C, respectively. Those for the reservoir’s surface water temperature were 32.9 ◦C (in July), 20.3 ◦C (in January), and 27.2 ◦C, respectively. The inflow water temperature was 1.0 ◦C higher than the air temperature, and the annual variation processes of these two variables were similar. The reservoir’s surface water temperature was much higher than the air temperature, which was 4.9 ◦C, 2.5 ◦C, and 3.5 ◦C higher than the monthly maximum, monthly minimum, and annual mean air temperatures, respectively. Therefore, heat sources of reservoirs in tropical zones are from air temperature, inflow water temperature, and other meteorological elements such as solar radiation, wind speed, cloud cover, and sunshine hours. In addition, after reservoir construction is complete, the flow rate decreases Water 2021, 13, x FOR PEER REVIEW with longer water exchange time. The water body is exposed to strong air temperature17 of 21 and solar radiation for a long time. This enhances the capacity of heat absorption and heat storage. Therefore, high water temperature is maintained all year round.

20 air temperature inflow water temperature

Temperature(degrees Celsius) surface water temperature 15 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month

FigureFigure 12. 12. AnnualAnnual cycle cycle of air temperature, inﬂowinflow waterwater temperature, temperature, and and surface surface water water temperature tempera- turein Songtao in Songtao Reservoir. Reservoir.

4. DiscussionsUnder the thermal effects of air temperature and water temperature, the vertical water temperature structure of Songtao Reservoir changed periodically. From February to July, 4.1. Model Verification and Thermodynamic Characteristics of the Reservoir with the increase of air temperature and solar radiation, heat absorbed by the surface layerWater of the temperature reservoir increased simulation continuously, using the andvertical water 1D temperature numerical model increased agreed gradually. with theHowever, observations the reservoir quite well, has with poor accurate fluidity simulated and weak water vertical temperature diffusion capacity,in Songtao and Reser- heat voir.absorbed The error by the between upper the water measured body cannot and simulated be transferred surface to water the lower temperature water body. was 0 The °C (onwater 26 temperatureApril 2016) and of the 1.4 lower °C (on water 13 June body 2016). was The maintained error between at 19 ◦C, the and measured the vertical and water sim- ulatedtemperature hypolimnion stratification water structuretemperature was was continuously 0 °C (on 26 strengthened, April 2016) and reaching −0.1°C the (on strongest 13 June 2016).stage inAlthough June and the July. error In August,of thermocline air temperature temperature and gradient solar radiation was 0.2 beganm and to 0.3 decrease, m, the largestand inflow relative water error temperature appeared in also the decreased. simulation The results, surface which water were body −19.2% of the and reservoir 19.3%. Thisentered reflects the that heat-losing the model stage, has considerable and the surface uncertainty water temperature in simulating gradually the position, decreased. thickness,Meanwhile, and temperature the upper difference and lower waterof the bodiesthermo begancline. Satisfactory to mix vertically simulations and exchange of the heat.sur- faceAs shown temperature in Figure layer7, inand October, hypolimnion November, were andobtained December, in this a study, water and temperature the temperature hybrid gradientlayer of approximatelyof thermocline 15–30 tended m appearedto be overestimated. below the reservoir This is a surface common layer. problem In January in reser- and voirFebruary, water surfacetemperature water simulation temperature by isthe close DYRESM to reservoir model bottom[35,39–41], water probably temperature, due to andthe problemvertical waterof model temperature structure. structure is mixed. The DYRESM model assumes that the extinction coefficient is a static constant. By contrast,4. Discussions hydrological, meteorological, and other boundary conditions are assumed to change4.1. Model with Verification time. Therefore, and Thermodynamic the constant Characteristics extinction coefficient of the Reservoir might produce errors in the simulationWater temperature of reservoir simulation water temperature using the vertical structure. 1D In numerical this study, model the extinction agreed with coef- the ficientobservations ηA was defined quite well, as a with constant accurate value simulated of 0.7, and water it might temperature impact the in simulation Songtao Reservoir. results. The thermocline depth is affected by the internal wave motion and diurnal temperature difference [42,43]. The internal wave motion can cause the temporary offset of the thermocline. DYRESM is more effective in water temperature structure simulations in small- and medium-sized reservoirs [44]. This is because the horizontal temperature difference in small reservoirs is low, which satisfied the assumption of 1D models. The spatial changes of wind stress and heat source input can cause obvious horizontal water temperature differences in large reservoirs. The thermal response of rivers depends on spatiotemporal scales, and its short-term response relationship is more complex [45]. However, a certain correlation exists between water temperature and air temperature in annual cycles, and it is usually assumed that air temperature is the main driving factor of water temperature change [46–48]. Therefore, ignoring the influence of air temperature may lead to the deviation of simulated reservoir water temperature [49]. Given that meteorological conditions in different geographical dimensions are quite different, it is not easy to quantitatively analyze the contribution of

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The error between the measured and simulated surface water temperature was 0 ◦C (on 26 April 2016) and 1.4 ◦C (on 13 June 2016). The error between the measured and simulated hypolimnion water temperature was 0 ◦C (on 26 April 2016) and −0.1◦C (on 13 June 2016). Although the error of thermocline temperature gradient was 0.2 m and 0.3 m, the largest relative error appeared in the simulation results, which were −19.2% and 19.3%. This reflects that the model has considerable uncertainty in simulating the position, thickness, and temperature difference of the thermocline. Satisfactory simulations of the surface temperature layer and hypolimnion were obtained in this study, and the temperature gradient of thermocline tended to be overestimated. This is a common problem in reservoir water temperature simulation by the DYRESM model [35,39–41], probably due to the problem of model structure. The DYRESM model assumes that the extinction coefficient is a static constant. By contrast, hydrological, meteorological, and other boundary conditions are assumed to change with time. Therefore, the constant extinction coefficient might produce errors in the simulation of reservoir water temperature structure. In this study, the extinction coefficient ηA was defined as a constant value of 0.7, and it might impact the simulation results. The thermocline depth is affected by the internal wave motion and diurnal temperature difference [42,43]. The internal wave motion can cause the temporary offset of the thermocline. DYRESM is more effective in water temperature structure simulations in small- and medium-sized reservoirs [44]. This is because the horizontal temperature difference in small reservoirs is low, which satisfied the assumption of 1D models. The spatial changes of wind stress and heat source input can cause obvious horizontal water temperature differences in large reservoirs. The thermal response of rivers depends on spatiotemporal scales, and its short-term response relationship is more complex [45]. However, a certain correlation exists between water temperature and air temperature in annual cycles, and it is usually assumed that air temperature is the main driving factor of water temperature change [46–48]. Therefore, ignoring the influence of air temperature may lead to the deviation of simulated reservoir water temperature [49]. Given that meteorological conditions in different geographical dimensions are quite different, it is not easy to quantitatively analyze the contribution of air temperature to reservoir heat. In addition to air temperature, meteorological conditions such as solar radiation, evaporation, wind speed, flow rate, and inflow water temperature also have thermal effects on the water body. It is generally believed that water temperature change is delayed after air temperature variations, and water temperature is slightly higher than air temperature [50,51].

4.2. Parameter Sensitivity This study mainly focused on the sensitivity of extinction coefficient, vertical mixing coefficient, and maximum allowable layer thickness. Each parameter had different effects on vertical water temperature structure. The extinction coefficient largely affects surface water temperature. This is important for the formation and development of the surface water temperature hybrid layer. For example, when ηA was defined as the maximum value of 2, the surface water temperature was the highest among all sensitive analysis conditions for extinction coefficient, and almost no water temperature hybrid layer appeared on the surface. In the case of ηA less than 2, the surface water temperature hybrid layer began to form and develop and reached 13 m (ηA = 0.2). The vertical mixing coefficient significantly influences the inflection point and thickness of the thermocline. With the increase of vertical mixing coefficient, the thermocline inflection point descends, and the thermocline thickness increases. The maximum allowable layer thickness has certain effects on the thickness of surface water temperature hybrid layer and thermocline. However, compared with the extinction coefficient and vertical mixing coefficient, this parameter is less sensitive to the vertical water temperature structure. Certain parameters are often associated with other physical and biochemical processes. For example, the extinction coefficient is related to phytoplankton content, suspended Water 2021, 13, 913 16 of 18

solids, etc. To simulate phytoplankton content and suspended solids, a water quality model should be added. When the hydrodynamic module DYRESM and the water quality module CAEDYM are coupled, the extinction coefficient can be simulated by the concentration of phytoplankton and suspended solids to obtain the time-varying values. In this study, the water quality module of CAEDYM was not included, and the coupling study of parameters in physical and biochemical processes was not carried out. Instead, the extinction coefficient was directly given in the model configuration file. In addition, the influence of fundamental modeling data and model input conditions on water temperature simulation cannot be ignored. Fundamental modeling data normally include terrain, water intake position, reservoir regulation process, etc. Model input conditions include reservoir inflow, outflow, inflow water temperature, air temperature, cloud cover, water vapor pressure, solar radiation, wind speed, precipitation, etc. To ensure the model’s accuracy, the hydrological and meteorological data measured in Songtao Reservoir were collected and analyzed as the model input conditions. However, further analysis on the sensitivity of input conditions is still needed.

5. Conclusions In this study, Songtao Reservoir in Hainan Province, China, was selected as the study area to quantify water temperature structure and thermodynamic characteristics of reservoirs in tropical zones by a vertical 1D numerical model. The constructed model was verified by the measured data, and sensitivity analysis of critical model parameters was performed. The main conclusions are summarized as follows: (1) Water temperature simulated by the vertical 1D numerical model agreed with the observations quite well, with convincing simulated vertical water temperature in Songtao Reservoir. The model is suitable for water temperature structure simulations for large reservoirs in tropical zones with accurate results; (2) The parameter sensitivity analysis shows that the extinction coefficient greatly affected surface water temperature, which is important for the formation and development of the surface water temperature hybrid layer. The vertical mixing coefficient significantly affected the position of the inflection point and the thickness of the thermocline. The vertical water temperature structure was sensitive to these two parameters. Therefore, these parameters require deliberate calibration in the application of vertical 1D numerical models; (3) The vertical water temperature structure in Songtao Reservoir was stratified. Reservoir surface water temperature varied in the range of 19.4–33.8 ◦C within a year. The hypolimnion of the reservoir was located at the elevation below 150 m, where the water temperature was basically maintained at 19 ◦C throughout the year; (4) As expected, the correlation between air temperature and water temperature in tropical zones is similar to that in other regions. However, the air temperature and surface water temperature data in Songtao Reservoir showed that surface water temperature was higher than air temperature all year round, and the annual mean difference between them was 3.5 ◦C. The unique climate in the tropical zone has a strong heating effect on the reservoir water body. In addition, water flow in the reservoir is slow. Thus, the water body can continuously receive heat.

Author Contributions: Conceptualization, H.G. and B.L.; methodology, H.G.; software, C.Q.; val- idation, H.G., C.Q., and S.X.; investigation, B.L. and W.S.; resources, H.G.; data curation, C.Q.; writing—original draft preparation, H.G.; writing—review and editing, C.Q., W.S. and L.M.; supervi- sion, B.L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the National Key Research and Development Program of China (2018YFC1508200) and Key Problems Research for Water Pollution Monitoring and Its Rapid Treatments of Water Resources Allocation Engineering Project in the Pearl River Delta Region of Guangdong Hydropower Planning & Design Institute Co., Ltd. (WW2018233). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Water 2021, 13, 913 17 of 18

Data Availability Statement: The data presented in this study are available on request from the corresponding author. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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