# Forecasting Water Temperature in Cascade Reservoir Operation-Influenced River with Machine Learning Models

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Methodology

#### 2.2.1. Decision Trees (DT)

#### 2.2.2. Random Forest (RF)

#### 2.2.3. Gradient Boosting (GB)

#### 2.2.4. Adaptive Boosting (AB)

#### 2.2.5. Support Vector Regression (SVR)

#### 2.2.6. MultiLayer Perceptron Neural Network (MLPNN)

## 3. Results

#### 3.1. Importance Ranking of Variables

^{2}all above 0.96 and Nash efficiency coefficient (NSE) [43] no less than 0.96; the best-fitting model was GB, which was almost completely accurate for all training data. In the test data, the prediction accuracy of the six models decreases to some extent. However, the overall RMSE of all models was below 0.64 °C, the R

^{2}was above 0.93, and the NSE was no less than 0.92. The RF model achieved the highest precision among all of them, with an RMSE of only 0.203 °C. All of the above indicate that the constructed model is robust in terms of variable screening.

#### 3.2. Prediction Results of Each Model

^{2}and NSE, were used to compare the various machine learning models. To calibrate and validate the models used for water temperature prediction, the data were randomly divided into a calibration and validation period at a ratio of 6:4. That is, we use the first 60% of the data as input to train the models and then use the remaining 40% to test the model’s performance. This is a widely used paradigm for model development.

^{2}values for each model version in the training set are 0.200 °C and 0.980, 0.044 °C and 0.996 and 0.017 °C and 0.998, respectively. While the RMSE and R

^{2}values for each model version in the test dataset are 0.554 °C and 0.943, 0.330 °C and 0.966 and 0.359 °C and 0.963, respectively. Specifically, DT achieves greater accuracy in versions 2 and 3, both of which improve by approximately two percentage points over version 1. This demonstrates that including Flow as a predictor aids in reducing forecast error. Switching from version 2 to version 3 and including factors other than DOY and Flow as input variables improved the performance of DT slightly. The scatterplot and comparison between observed and predicted WT for the three-model version are shown in Figure 7. As illustrated in the figure, the graphs for all three cases fit reasonably well, and the scatter on the regression curves is relatively concentrated.

^{2}and NSE values (R

^{2}≈ 0.950, NSE ≈ 0.949) and a low error value: RMSE ≈ 0.201 °C. In addition, the modeling findings reveal that version 3 greatly outperformed the other models. In fact, RF2 increased the model’s accuracy by reducing the RMSE of RF1 by 49.73 percent, while RF3 enhanced the model’s accuracy by reducing the RMSE by about 74.39 percent. This proportion is altered to 51.52 percent and 58.12 percent in the test set, demonstrating that the RF3 and RF2 models perform comparably. The accuracy of the three models as a whole demonstrates that version 3 outperforms all other models. Figure 8 illustrates the scatterplots and comparison of observed and predicted WT.

^{2}and NSE values (R

^{2}≈ 0.980, NSE ≈ 0.980) and a low error value: RMSE ≈ 0.194 °C. Additionally, the modeling results indicate that version 3 outperformed the previous versions significantly. Indeed, GB2 reduced the root mean square error of the GB1 by 99.69 percent, and GB3 increased the model’s accuracy by reducing the root mean square error by approximately 100.0 percent in the training set. This percentage is changed to 48.28 and 47.32 percent in the test set, indicating a small performance difference between the GB3 and GB2 models. The accuracy of the three models as a whole demonstrates that version 3 outperforms all other models; Figure 9 illustrates the scatterplots and comparison of observed and predicted WT.

^{2}value of 0.978 while operating alone (version 1) in the exercise set. When the Flow is added to DOY (version 2), the model’s performance is improved slightly. In the test set, a similar phenomenon is observed, but with a lower RMSE and a higher R

^{2}value (RMSE = 0.292 °C, R

^{2}= 0.970) for version 2.

^{2}value of 0.971. When the Flow is added to DOY (version 2), the model’s performance slightly degrades, with the RMSE increasing to 0.345 °C and the R

^{2}value decreasing to 0.965. In the test set, a similar phenomenon is observed, but with a lower RMSE and a higher R

^{2}value (RMSE = 0.323°C, R

^{2}= 0.967) for version 1.

^{2}values for each model version in the training set are 0.275 °C and 0.972, 0.236 °C and 0.976 and 0.190 °C and 0.981, respectively. While the RMSE and R

^{2}values for each model version are 0.311 °C and 0.968, 0.281 °C and 0.971 and 0.386 °C and 0.960, respectively, in the test dataset. It is clear that MLPNN performs better in version 2 than in version 1, with both versions improving by approximately 0.5 percentage points over version 1 in both datasets. This demonstrates that including Flow as a predictor aids in reducing forecast error. Switching from version 2 to version 3, with input variables other than DOY and traffic, improves accuracy slightly on the training set while decreasing it slightly on the test set. As illustrated in Figure 11, the graphs for all three cases fit reasonably well, and the scatter on the regression curves is relatively concentrated.

^{2}and NSE values and lower RMSE (°C) values. The AB model performed best in version 2 (when DOY and Flow were used as predictors), while the model SVR performed better in version 1 (with DOY as an input variable only). On the test dataset, the six models produced results that were inconsistent with those obtained on the training set. Version 2 (with combined DOY and Flow inputs) had the highest fitting accuracy for models AB, DT, GB and MLPNN, while version 3 had the best result for RF and version 1 had the best result for model SVR.

^{2}and NSE values as well as lower RMSE values. On average, the six models performed well in predicting river water temperature, with an R

^{2}value greater than 0.95 and an NSE value greater than 0.95. The DT and GB models fit curves more precisely than the others, especially at peaks and troughs. Their performance varies significantly in the test data. RF performed well in forecasting WT, with an R

^{2}greater than 0.97; AB, DT, GB and MLPNN models performed slightly worse but still exceeded 0.96; and SVR performed poorly in both cases. One possible explanation is that the data pre-processing and parameter selection algorithms (normalization range, dimension reduction algorithm and optimal parameter selection algorithm) are not well adjusted.

## 4. Discussion

^{2}= 0.93, NSE = 0.92). Eventually, we did not find a definite answer about a single optimal machine learning algorithm when using the same input variables, indicating that our selected machine learning models all capture the nonlinear dynamics of the water temperature fairly well. The most parsimonious models were then developed based on six machine learning models using a combination of the three most important inputs. Comparing their performance according to statistical metrics, the results showed that GB3 and RF3 produce the highest prediction accuracy on the training dataset and the test dataset, respectively (Table 8). This also suggested that choosing the appropriate minimum number of input variables is sufficient for the machine learning model to obtain acceptable prediction results. On the other hand, we can see from Figure 7, Figure 8, Figure 9, Figure 10, Figure 11 and Figure 12 that as the water temperature increases (>18 °C), more discrete points appear near the fitting curve. The challenge here is that 18 °C is a threshold of great importance for fish spawning. The four major carp species only started spawning when the water temperature increased to 18 °C in April [46]. The results suggested that gaining further insight into physical dynamics remains the most essential factor for the successful exploitation of ML to better predict water temperature.

## 5. Conclusions

^{2}and NSE values. The DOY is the most significant factor in all forecast models, while air temperature, flow and dew temperature are secondary aspects connected to water temperature variations. This is possibly due to the cascaded reservoir operating on a year-round basis that affects the annual cycle of downstream river water temperature. As a result, the DOY may be more precise in its prediction of river water temperature downstream of the reservoir; the modeling performance indicates that the machine learning model developed in this study is capable of accurately predicting river water temperature under the influence of a cascaded reservoir.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Distribution map of main dams (blue circle) and hydrological monitoring points (red triangles) in the study area.

**Figure 2.**Time series plot of water temperature (red lines), mean air temperature (black lines), and discharge (blue lines).

**Figure 3.**Workflow summarizing the steps of the comparative analysis of the performance of the different ML methods.

**Figure 4.**Permutation importance in DT and RF; DT, decision trees, RF, random forests. (DT on the

**top**, RF on the

**bottom**, WT: °C).

**Figure 5.**Permutation importance in GB and AB; GB, gradient boosting regression, AB, adaptive boosting regression. (GB on the

**top**, AB on the

**bottom**, WT: °C).

**Figure 6.**Permutation importance in SVR and MLPNN; SVR, support vector regression, MLPNN, multilayer perceptron neural networks. (SVR on the

**top**, MLPNN on the

**bottom**, WT: °C).

**Figure 7.**Model fitting results—DecisionTree Regressor, blue dot: X coordinate (observed data), Y coordinate (predicted data); black line: y = x; red dotted line: the regression curve of the blue dots. (

**a**) only one input variable (DOY), (

**b**) two input variables (DOY and Flow), (

**c**) all variables.

**Figure 8.**Model fitting results—RandomForest Regressor, blue dot: X coordinate (observed data), Y coordinate (predicted data); black line: y = x; red dotted line: the regression curve of the blue dots. (

**a**) only one input variable (DOY), (

**b**) with two input variables (DOY and Flow), (

**c**) with all variables.

**Figure 9.**Model fitting results—GradientBoosting Regressor, blue dot: X coordinate (observed data), Y coordinate (predicted data); black line: y = x; red dotted line: the regression curve of the blue dots. (

**a**) only one input variable (DOY), (

**b**) with two input variables (DOY and Flow), (

**c**) with all variables.

**Figure 10.**Model fitting results—AdaptiveBoosting Regressor, blue dot: X coordinate (observed data), Y coordinate (predicted data); black line: y = x; red dotted line: the regression curve of the blue dots. (

**a**) only one input variable (DOY), (

**b**) with two input variables (DOY and Flow), (

**c**) with all variables.

**Figure 11.**Model fitting results—SupportVector Regression, blue dot: X coordinate (observed data), Y coordinate (predicted data); black line: y = x; red dotted line: the regression curve of the blue dots. (

**a**) only one input variable (DOY), (

**b**) with two input variables (DOY and Flow), (

**c**) with all variables.

**Figure 12.**Model fitting results—Multilayer Perceptron Neural Network, blue dot: X coordinate (observed data), Y coordinate (predicted data); black line: y = x; red dotted line: the regression curve of the blue dots. (

**a**) only one input variable (DOY), (

**b**) with two input variables (DOY and Flow), (

**c**) with all variables.

**Table 1.**Performances of six models (DT: decision trees, RF: random forests, GB: gradient boosting regression, AB: adaptive boosting regression, SVR: support vector regression, MLPNN: multilayer perceptron neural networks) in predicting water temperature.

Models | Training Datasets | Testing Datasets | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

DT | 0.0167698 | 0.998298 | 0.998295 | 0.394039 | 0.959443 | 0.959352 |

RF | 0.0513479 | 0.994788 | 0.994694 | 0.203134 | 0.979092 | 0.978487 |

GB | 2.59 × 10^{−19} | 1 | 1 | 0.308065 | 0.968292 | 0.968119 |

AB | 0.0980462 | 0.990049 | 0.989885 | 0.264675 | 0.972758 | 0.972145 |

SVR | 0.3365923 | 0.965837 | 0.960535 | 0.633647 | 0.934781 | 0.922508 |

MLPNN | 0.1896209 | 0.980754 | 0.980438 | 0.385593 | 0.960312 | 0.958261 |

**Table 2.**Performances of DecisionTree Regressor in modeling water temperature (WT: °C), DT1: only one input variable (DOY), DT2: with two input variables (DOY and Flow), DT3: with all input variables.

Model Version | Training Dataset | Test Dataset | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

DT1 | 0.200361 | 0.979664 | 0.979242 | 0.553881 | 0.942991 | 0.941738 |

DT2 | 0.043619 | 0.995573 | 0.995553 | 0.329739 | 0.966061 | 0.966209 |

DT3 | 0.01677 | 0.998298 | 0.998295 | 0.359478 | 0.963 | 0.962799 |

**Table 3.**Performances of RandomForest Regressor in modeling water temperature (WT: °C), RF1: only one input variable (DOY), RF2: with two input variables (DOY and Flow), RF3: with all input variables.

Model Version | Training Dataset | Test Dataset | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

RF1 | 0.200538 | 0.979646 | 0.979199 | 0.485061 | 0.950074 | 0.948793 |

RF2 | 0.100807 | 0.989769 | 0.989547 | 0.23512 | 0.9758 | 0.975281 |

RF3 | 0.051348 | 0.994788 | 0.994694 | 0.203134 | 0.979092 | 0.978487 |

**Table 4.**Performances of GradientBoosting Regressor in modeling water temperature (WT: °C), GB1: only one input variable (DOY), GB2: with two input variables (DOY and Flow), GB3: with all inputs variable.

Model Version | Training Dataset | Test Dataset | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

GB1 | 0.194251 | 0.980284 | 0.979888 | 0.584754 | 0.939813 | 0.938425 |

GB2 | 0.000596 | 0.99994 | 0.999939 | 0.302442 | 0.968871 | 0.968273 |

GB3 | 2.59 × 10^{−19} | 1 | 1 | 0.308065 | 0.968292 | 0.968119 |

**Table 5.**Performances of AdaptiveBoosting Regressor in modeling water temperature (WT: °C), AB1: only one input variable (DOY), AB2: with two input variables (DOY and Flow), AB3: with all inputs variable.

Model Version | Training Dataset | Test Dataset | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

AB1 | 0.202579 | 0.979439 | 0.978967 | 0.535933 | 0.944838 | 0.943332 |

AB2 | 0.15983 | 0.983778 | 0.983445 | 0.291648 | 0.969982 | 0.969293 |

AB3 | 0.20119 | 0.97958 | 0.979129 | 0.538943 | 0.944528 | 0.943291 |

**Table 6.**Performances of SupportVector Regression in modeling water temperature (WT: °C), SVR1: only one input variable (DOY), SVR2: with two input variables (DOY and Flow), SVR3: with all input variables.

Model Version | Training Dataset | Test Dataset | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

SVR1 | 0.288101 | 0.970759 | 0.970421 | 0.323232 | 0.966731 | 0.966283 |

SVR2 | 0.34541 | 0.964942 | 0.959725 | 0.630718 | 0.935082 | 0.923919 |

SVR3 | 0.336592 | 0.965837 | 0.960535 | 0.633647 | 0.934781 | 0.922508 |

**Table 7.**Performances of Multilayer Perceptron Neural Network in modeling water temperature (WT: °C), MLPNN1: only one input variable (DOY), MLPNN2: with two input variables (DOY and Flow), MLPNN3: with all input variables.

Model Version | Training Dataset | Test Dataset | ||||
---|---|---|---|---|---|---|

RMSE (°C) | R^{2} | NSE | RMSE (°C) | R^{2} | NSE | |

MLPNN1 | 0.274755 | 0.972113 | 0.970939 | 0.311318 | 0.967957 | 0.965799 |

MLPNN2 | 0.236238 | 0.976023 | 0.975322 | 0.280818 | 0.971096 | 0.969259 |

MLPNN3 | 0.189621 | 0.980754 | 0.980438 | 0.385593 | 0.960312 | 0.958261 |

**Table 8.**Best version of performance in different models (DT: decision trees, RF: random forests, GB: gradient boosting regression, AB: adaptive boosting regression, SVR: support vector regression, and MLPNN: multilayer perceptron neural networks) in predicting water temperature (WT: °C), 1.only one input variable (DOY), 2. with two input variables (DOY and Flow), 3. with all variables.

Training Dataset | Test Dataset | ||||||
---|---|---|---|---|---|---|---|

Models | RMSE (°C) | R^{2} | NSE | Models | RMSE (°C) | R^{2} | NSE |

DT3 | 0.017 | 0.998 | 0.998 | DT2 | 0.330 | 0.966 | 0.966 |

RF3 | 0.051 | 0.995 | 0.995 | RF3 | 0.203 | 0.979 | 0.978 |

GB3 | 2.6 × 10^{−19} | 1.000 | 1.000 | GB2 | 0.302 | 0.969 | 0.968 |

AB2 | 0.160 | 0.984 | 0.983 | AB2 | 0.292 | 0.970 | 0.969 |

SVR1 | 0.288 | 0.971 | 0.910 | SVR1 | 0.323 | 0.967 | 0.966 |

MLPNN3 | 0.190 | 0.981 | 0.980 | MLPNN2 | 0.281 | 0.971 | 0.969 |

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## Share and Cite

**MDPI and ACS Style**

Jiang, D.; Xu, Y.; Lu, Y.; Gao, J.; Wang, K.
Forecasting Water Temperature in Cascade Reservoir Operation-Influenced River with Machine Learning Models. *Water* **2022**, *14*, 2146.
https://doi.org/10.3390/w14142146

**AMA Style**

Jiang D, Xu Y, Lu Y, Gao J, Wang K.
Forecasting Water Temperature in Cascade Reservoir Operation-Influenced River with Machine Learning Models. *Water*. 2022; 14(14):2146.
https://doi.org/10.3390/w14142146

**Chicago/Turabian Style**

Jiang, Dingguo, Yun Xu, Yang Lu, Jingyi Gao, and Kang Wang.
2022. "Forecasting Water Temperature in Cascade Reservoir Operation-Influenced River with Machine Learning Models" *Water* 14, no. 14: 2146.
https://doi.org/10.3390/w14142146