# Micro-Climate Computed Machine and Deep Learning Models for Prediction of Surface Water Temperature Using Satellite Data in Mundan Water Reservoir

^{1}

^{2}

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## Abstract

**:**

^{2}of 0.93 RMSE of 0.16 °C, and bias of 0.01 °C). The factors that had a significant effect on the model’s accuracy performance were identified and quantified using a two-factor analysis of variance (ANOVA) analysis. The results demonstrate that the main effects and interaction of the type of machine/deep learning (ML/DL) model and the type of satellite have statistically significant effects on the performances of the different models. The test statistics are as follows: (satellite type main effect p *** ≤ 0.05, F

_{test}= 15.4478), (type of ML/DL main effect p *** ≤ 0.05, F

_{test}= 17.4607) and (interaction, satellite type × type of ML/DL p ** ≤ 0.05, F

_{test}= 3.5325), respectively. The models were successfully deployed to enable satellite remote sensing monitoring of SWT for the reservoir, which will help to resolve the limitations of the conventional sampling and laboratory techniques.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

#### 2.2. Data Collection and Image Preprocessing

_{10}is the brightness temperature at the sensor for L8-TIRS band 10, and a constant factor b

_{γ}= 121.47.

_{11}is representing the brightness temperature of TIRS sensor for band 11, while bands 10 and 11 mean and difference emissivity values for the same L8-TIRS are represented by ε and Δε, respectively.

_{k}(k = 0–7) [28].

#### 2.3. Machine and Deep Learning Algorithms Applied for Regression

- I.
- Gaussian Process Regression (GPR)

- II.
- Support Vector Machine (SVM)

- III.
- Artificial Neural Network (ANN)

- IV.
- Long Short Term Memory (LSTM)

_{(t−1)}, x

_{(t)}] at time step t. The network cell state is denoted by c

_{(t)}. The output vectors passing through the network between consecutive time steps t, t + 1 are denoted by h

_{(t}

_{)}. The forget gate, input gate, and output gate are the three gates that make up an LSTM network and are used to update and control the cell states [38,39,40,41,42]. The gates are customized by hyperbolic tangent and sigmoid activation functions. On the assumption that new information would have entered the network, the forget gate directs that the information in a cell state be forgotten. Its output is computed by the function:

_{(t)}[40,42]. The output gate’s activations are represented as:

- V.
- Convolutional Long Short Term Memory (Conv-LSTM)

#### 2.4. Sliding Window Time Series Cross-Validation and Model Evaluation Metrics

^{2}), root mean square error (RMSE), and uncertainties, i.e., bias-variance trade-off. To rigorously evaluate the performance of our proposed method, cross-validation was performed using the sliding window time series cross-validation (SWTSCV) method, which divided data into a series of overlapping training-testing sets [46]. As shown in Figure 5, each set is moved forward through the time series. SWTSCV is the most appropriate and robust evaluation method because it takes into account time indices and is capable of capturing autocorrelations. The principle is that the model should be trained using time series and its performance should be evaluated using (unseen) test data, which should always be the future data. Each model was evaluated on the test set, and the R

^{2}and RMSE values were recorded. The SWTSCV-model scores were displayed using boxplots, and the average of the recorded and model errors were computed [47]. In our study, we used 10-time series split (i.e., i = 10). Time series cross-validation was selected because it is usually the most effective method for estimating the uncertainty in error statistics and gaining insight into the generalization ability of a model.

#### 2.5. Performance Evaluation Metrics

^{2}), RMSE, and bias-variance trade-offs. Mean absolute error (MAE) measures the extent to which a model is able to predict extreme events or outliers, such as extreme temperature heat wave or cold, and in this study MAE was not a useful metric because our data did not have extreme events or outliers as such.

^{2}is a measure of how simulated variables can be predicted based on measured variables. Its strength ranging from 0 to 1, closer to 0 indicates a lower correlation, while close to 1 represents a high correlation.

^{2}and the lower the RMSE, variance, and bias, the higher the model precision and accuracy for SWT, showing a better fit for the model predictions.

#### 2.6. Hypothesis Testing (Two-Factor ANOVA) and Post-Hoc Scheffe

## 3. Results

#### 3.1. Descriptive Statistics

#### 3.2. Long Term Atmospheric Air and Surface Water Temperature Trends for Mundan Water Reservoir (1993–2020)

#### 3.3. Exploratory Data Analysis–Correlation between Different Variables

#### 3.4. Machine Learning Models

## 4. Discussion

#### 4.1. Factors Affecting the Accuracy of SWT Predictions

^{2}= 0.81; RMSE = 0.15; Turbidity: R

^{2}= 0.86; RMSE = 0.95); the other models linear regression (LR), SVM, and random forest regressor (RFR) trailed behind. In another separate but similar study, water reflectance data obtained from both a hand-held spectroradiometer and satellite data was used to examine four ML approaches for retrieving three water quality parameters (Chl-a, SS, and turbidity) over the coastal waters of Hong Kong [53]. They also mapped the spatial distribution of these parameters. According to the results of cross-validation, ANN was able to reach the highest levels of accuracy for the water quality indicators for both in situ reflectance data (0.89 Chl-a, 0.93 SS, and 0.82 turbidity) and satellite data (0.91 Chl-a, 0.92 SS, and 0.85 turbidity). Further comparisons were made between the water quality characteristics retrieved by the ANN model and those retrieved by the standard C2RCC-Nets processing chain model for Case-2 Regional/Coast Color (C2RCC). The results of the standard Case-2 Regional/Coast Color (C2RCC) processing chain model C2RCC-Nets and the ANN model were further compared with station-based water quality data using a different set of satellite data. The potential of using ML and neural networks (NNs) for the retrieval of water quality metrics is demonstrated by all of the studies that have been cited [53]. This has only been applied to optically active and inactive water quality parameters. Our work expands the scope of this research to include thermal infrared channels for determining the thermal properties of surface water.

- The five models tested performed well on both the test and training sets (accuracy > 0.67 for S3 and >0.71 for L8). Refer to Figure 8;
- DL models outperformed all other models in terms of greater R
^{2}and as well as lower RMSE values when comparing the five generated models, achieving the highest accuracy in testing data. In terms of R^{2}and RMSE, 1D-ConvLSTM performed ahead of every other model for both satellites following the descending order: 1D-ConvLSTM > LSTM > ANN > SVM > GPR (Figure 8); - Two deep-learning architectures (LSTM and 1D-ConvLSTM) performed relatively better than conventional and simple ANN architectures on test data used to evaluate different models. LSTM layers provide an added advantage over conventional model architecture when working with time series data since they are made up of memory cell blocks (known as hidden units in simple hidden layers). The hidden memory cell blocks can store information for longer time interval [58]. Deep-learning architectures needed more time to train than basic ML structures despite having superior predictive accuracy because they had more trainable parameters. Although adopting techniques, such as transfer learning or graphics processing unit (GPU) computing, can help to reduce training times;
- For all the evaluated models, the median R
^{2}values ranged from 0.67 to 0.92, while the median RMSE scores ranged from 0.16 to 3.4 °C. In addition, L8 models performed better than their S3 corresponding models. It is also important to note that for both satellites, DL models performed better than conventional ML techniques. Similarly, this trend is also observed for the RMSE metric.

- Furthermore, the results of the two sample t-tests confirm the null hypothesis (H
_{0}), which states that the average RMSE score for Landsat-8 is assumed to be less than or equal to the average of Sentinel-3’s RMSE score, with equal or pooled variance (p-value = 0.9453, (p(x ≤ T) = 0.05). This means that the probability of a type I error, which involves rejecting the correct H_{0}, is too high: 94.53% for the 50 samples. This is further evidence that L8 SWT estimates are more precise than S3 estimates; - These sensor performances may be attributed to the following factors: sensor characteristics, L8 has a higher spatial resolution compared to S3, data processing, season, day-night changes (in the case of Sentinel-3), and atmospheric correction.

^{2}and RMSE of every model in each subplot.

#### 4.2. Hypothesis Testing: Two-Factor ANOVA

- Type of ML/DL main effect (F = 17.4607, p = 4.001 × 10
^{−12}***); - The satellite type main effect (F = 15.4478, p = 0.0001208 ***);
- Interaction effect (satellite type × type of ML/DL) (F = 3.5325, p = 0.008399 ***);
- The results indicate that both factors and their interaction have an impact on model performance;
- An increasing effect based on the factorial analysis of variance using effect size estimates (${\eta}_{p}^{2}$) was observed in the following descending order: type of ML/DL > interaction > type of satellite;
- According to the two-factor ANOVA design approach, the selection of ML/DL is therefore more significant than the type of satellite used. The model score for S3 is improved by using DL models as shown by diverging or crossing lines, which shows evidence of interaction between the two factors (Figure 10);

#### 4.3. Hypothesis Testing: Scheffe’s Post-Hoc Multiple Comparison

#### 4.4. Bias-Variance Trade-off for the ML/DL Models

^{2}is constrained in its utility as a validation metric score because high R

^{2}does not always imply high accuracy if the estimates are significantly biased [64,65,66]. Nonetheless, it can frequently be applied as an assessment tool to evaluate the algorithm’s consistency across a range of measurements [64,65,66]. The limitation of RMSE estimates is that they do not capture the average error [49]. Therefore, to avoid potentially erroneous interpretations of R

^{2}and RMSE, bias-variance decomposition of the error was used as a tool to simultaneously identify the bias errors (underfitting) and variance errors (overfitting) that prevent supervised learning algorithms from generalizing beyond their training sets. The GPR emerges for having inflated bias across all satellites (Figure 11), which can be explained by the fact that its simple model architecture fails to capture key data regularities, leading to underfitting. Similar to GPR, SVM and ANN are relatively low complexity models that are plagued by the same bias problem, the only difference is that the severity of their bias is significantly diminished. DL models are ideal for solving regression prediction problems for large data samples because, despite them being more complex models than ML, they nevertheless maintained lower bias and variance metrics (Figure 11), making them accurate and precise in determining SWT.

#### 4.5. Spatio-Temoporary Variation Thermal Maps for Mundan

^{2}, a full resolution projected satellite picture of Sentinel-3 resampled at 300 m × 300 m SLSR pixel theoretically yields 13 pixels. Under such circumstances, the accuracy of the results at specific sampling points is likely to be impacted by the effects of neighboring and adjacent pixels and an increased number of mixed pixels. For instance, an error resulting from the patchiness of sporadic blooms in water polluted by algal blooms [68,69]. In contrast, Landsat-8 TIRS pixels can be resampled at a resolution of 30 m × 30 m, covering 1111 pixels for the same 1.13 km

^{2}. Therefore, a sampling point is clearly discernable with minimum effects from its neighboring or adjacent pixels and has less mixed pixels overall. These are some of the possible underlying reasons behind the superior performances by L8.

## 5. Conclusions

- (1)
- The ANOVA result demonstrated that the ML/DL model used had a more significant impact on estimation accuracy than the type of satellite used. However, it demonstrates that both factors had a significant impact in improving SWT’s estimation accuracy;
- (2)
- To further support this, DL models applied to low resolution satellites performed significantly well;
- (3)
- The considered important evaluation metrics for estimation of SWT were R
^{2}, RMSE, and bias-variance trade-off evaluators; - (4)
- The maximum prediction accuracy was achieved by the ConvLSTM based on L8-TIRS data, with R
^{2}= 0.93, RMSE = 0.15 °C.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Location of Mundan water reservoir and Mundan meteorological station (COR 341) with respect to the map of Taiwan, the reservoir is showing the sampling points S1–S3 as indicated on the map (left-side).

**Figure 2.**Workflow to show the process of retrieval of SWT from L8 and S3 images by ENVI 5.3 and SNAP 8.0 software respectively.

**Figure 3.**LSTM building block units redrawn from Yan. S. Medium Review article [42].

**Figure 4.**Diagram of a ConvLSTM cell structure from Iskandaryan and others [45].

**Figure 6.**Trends in annual atmospheric and surface water temperatures recorded by the Mundan microclimate weather station and the Taiwan EPA, respectively, 1993–2021.

**Figure 7.**Correlation matrix for the different variables highlighting pairwise numerical value of ρ, scatterplots, while the diagonal bar charts represent a data distribution pattern for each variable.

**Figure 8.**Distribution of SWTSCV performance metric evaluation scores, 10-R

^{2}, and RMSE scores for each algorithm because the sliding windows were split into 10-time series splits. The subplots column (

**a**,

**c**) are R

^{2}and RMSE for L8, similarly (

**b**,

**d**) shows the same for S3.

**Figure 9.**Observed vs. predicted WST regression scattergrams derived from the ML/DL models test data. The name of the ML/DL, R

^{2}and RMSE are shown in the graph legends. The distribution of the scatter point markers along the line of equality (1:1) are also visualized in the figure; (

**a**) Landsat-8 models are in the left and middle left columns, and (

**b**) Sentinel-3 models are in the middle right and right columns.

**Figure 10.**Line plots showing the outcome of a two factor experiment main and interactive effects of satellite type and type of ML/DL.

**Figure 11.**Bias-Variance Trade-offs and MSE bar charts for all the models: (

**a**) L8, and (

**b**) S3 models.

**Figure 12.**Time series for the spatial distribution of SWT based on ConvLSTM predictions smoothened by Kriging interpolation in Mundan water reservoir.

**Table 1.**Descriptive statistics for all the input variables to the data of the models from 1993–2020.

Landsat-8 Data Set | ||||||
---|---|---|---|---|---|---|

Index | RH (%) | WS (m/s) | Precip (mm) | AAT (°C) | SWTL8 (°C) | SWTGT (°C) |

Count (N) | 882 | 882 | 882 | 882 | 882 | 882 |

Mean | 66.8 | 1.42 | 0.10 | 27.4 | 27.7 | 26.0 |

Std. Dev | 19.6 | 1.34 | 0.66 | 4.31 | 3.69 | 3.75 |

Min | 10 | 0 | 0 | 17 | 19.1 | 19.1 |

First Quartile | 57.3 | 0.3 | 0 | 23.6 | 24.7 | 23 |

Median | 69 | 1 | 0 | 27.6 | 27 | 25.9 |

Third Quartile | 80 | 2.4 | 0 | 31 | 30.3 | 28.7 |

Max | 99 | 7.7 | 5 | 36.9 | 37.6 | 36.3 |

Sentinel-3 Data Set | ||||||

Index | RH (%) | WS (m/s) | Precip (mm) | AAT (°C) | SWTS3 (°C) | SWTGT (°C) |

Count (N) | 1050 | 1050 | 1050 | 1050 | 1050 | 1050 |

Mean | 77.9 | 1.39 | 0.07 | 26.0 | 24.1 | 25.1 |

Std. Dev | 13.3 | 1.82 | 0.49 | 4.73 | 4.23 | 4.55 |

Min | 38 | 0 | 0 | 14.4 | 12.4 | 11 |

First Quartile | 67 | 0.1 | 0 | 22 | 21.2 | 21.7 |

Median | 76 | 0.8 | 0 | 27.0 | 24.4 | 25.5 |

Third Quartile | 90 | 1.9 | 0 | 29.1 | 27 | 28.2 |

Max | 100 | 10.1 | 6.5 | 36 | 35.5 | 36 |

**Table 2.**Grid-search range of the parameters of each ML/DL method with test values for the hyper-parameters are sorted in ascending order.

Model | Hyper-Parameter Name | Hyperparameter Description | Grid Search Parameter Values | Optimal Hyper-Parameter Value |

GPR | length_scale | The length-scale of the respective feature dimension is specified. | 0.5, 1, 2, 3 | 1 |

Kernel function | Transforms data that is linearly inseparable into data that is linearly separable and specifies the kernel type to be used in the algorithm. | RBF, Constant, and exponential | RBF | |

n_restarts_optimizer | The number of optimizer restarts required to find the kernel parameters that maximize the log-marginal likelihood. | 5, 7, 9, 11, 13 | 9 | |

SVM | Cost (C) | Regularization parameter | 0.1, 1, 10, 100, 1000 | 10 |

gamma | Kernel coefficient for RBF, poly and Sigmoid | 0.0001, 0.001, 0.01, 0.1, 1 | 0.0001 | |

Kernel function | Transformation of linearly inseparable data to linearly separable ones and specifying the kernel type to be used in the algorithm | RBF, Sigmoid, Linear, and Polynomial | RBF | |

epsilon (ε) | Defines a tolerance margin in which errors are not penalized. | 0.01, 0.1, 1, 1.5 | 0.1 | |

ANN | Activation functions | The activation function compute the input values of a layer into output values | ReLU, Sigmoid, Softplus, and tanh | Sigmoid–hidden layers and ReLU–output layer |

Optimizer | The optimizer changes the learning rate and weights of neurons in the neural network to achieve lowest loss function | Adam, SGD, RMSprop, and Adagrad | Adam | |

Learning rate | Learning rate manipulates the step size for a model to attain the minimum loss function | 0.001, 1 | 0.01 | |

Neurons | The number of neurons in every layer is set to be the same and should be adjusted to the solution complexity | 10, 100 | 65 | |

Epochs | The number of times a whole dataset is passed through the neural network model | 20, 100 | 100 | |

Batch size | Batch size is the number of training data sub-samples for the input. | 50, 500 | 100 | |

Drop out | Dropout is another regularization layer. The dropout layer, randomly drops a certain number of neurons in a layer | 0, 2 | 0.9 | |

Dropout rate | The rate of how much percentage of neurons to drop is set in the dropout rate | 0, 0.5 | 0.15 | |

Batch Normalization | The batch normalization layer normalizes the values passed to it for every batch. This is similar to standard scaler in conventional Machine Learning | 0, 1 | 0.90 | |

LSTM | Learning rate | Learning rate controls the step size for a model to reach the minimum loss function | 0.001, 1 | 10^{−3} |

Epochs | The number of times a whole dataset is passed through the neural network model | 20, 100 | 100 | |

Batch size | Batch size is the number of training data sub-samples for the input. | 50, 500 | 100 | |

Drop out | The dropout layer is another name for the regularization layer, which randomly drops a set number of neurons in a layer. | 0, 2 | 0.5 | |

ConvLSTM | Learning rate | Learning rate controls the step size for a model to reach the minimum loss function | 0.001, 1 | 10^{−3} |

Epochs | The number of times an entire dataset is processed through the neural network model. | 20, 100 | 100 | |

Batch size | Batch size is the number of training data sub-samples for the input. | 50, 500 | 100 | |

Drop out | The dropout layer is another name for the regularization layer, which randomly drops a set number of neurons in a layer. | 0, 2 | 0.5 |

**Table 3.**Post-Hoc Scheffe test p-values for all 12 groups’ two level factors (Satellite Type * ML Algorithm) for RMSE.

L8 | L8 | L8 | L8 | L8 | L8 | S3 | S3 | S3 | S3 | S3 | S3 | ||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

SLT | ML/DL | GPR | SVM-RBF | SVM-Lin | ANN | LSTM | ConvLSTM | GPR | SVM-RBF | SVM-Lin | ANN | LSTM | ConvLSTM |

L8 | GPR | ||||||||||||

L8 | SVM-RBF | 0.001 | |||||||||||

L8 | SVM-Lin | 0.001 | 1.00000 | ||||||||||

L8 | ANN | 0.001 | 0.8999947 | 1.00000 | |||||||||

L8 | LSTM | 0.001 | 0.8999947 | 1.00000 | 0.8999947 | ||||||||

L8 | ConvLSTM | 0.001 | 0.8999947 | 1.00000 | 0.8999947 | 0.8999947 | |||||||

S3 | GPR | 0.001 | 0.001 | 0.00000 | 0.001 | 0.001 | 0.001 | ||||||

S3 | SVM-RBF | 0.8999947 | 0.001 | 0.000000 | 0.001 | 0.001 | 0.001 | 0.001 | |||||

S3 | SVM-Lin | 0.8999947 | 0.001 | 0.000000 | 0.001 | 0.001 | 0.001 | 0.001 | 0.00000 | ||||

S3 | ANN | 0.001 | 0.01 | 0.01 | 0.001 | 0.001 | 0.001 | 0.001 | 0.001 | 1.00000 | |||

S3 | LSTM | 0.001 | 0.8999947 | 0.8999947 | 0.8999947 | 0.8999947 | 0.8999947 | 0.001 | 0.001 | 0.999781 | 0.001 | ||

S3 | ConvLSTM | 0.001 | 0.8999947 | 0.8999947 | 0.8999947 | 0.8999947 | 0.8999947 | 0.001 | 0.001 | 0.999974 | 0.001 | 0.8999947 |

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**MDPI and ACS Style**

Mukonza, S.S.; Chiang, J.-L.
Micro-Climate Computed Machine and Deep Learning Models for Prediction of Surface Water Temperature Using Satellite Data in Mundan Water Reservoir. *Water* **2022**, *14*, 2935.
https://doi.org/10.3390/w14182935

**AMA Style**

Mukonza SS, Chiang J-L.
Micro-Climate Computed Machine and Deep Learning Models for Prediction of Surface Water Temperature Using Satellite Data in Mundan Water Reservoir. *Water*. 2022; 14(18):2935.
https://doi.org/10.3390/w14182935

**Chicago/Turabian Style**

Mukonza, Sabastian Simbarashe, and Jie-Lun Chiang.
2022. "Micro-Climate Computed Machine and Deep Learning Models for Prediction of Surface Water Temperature Using Satellite Data in Mundan Water Reservoir" *Water* 14, no. 18: 2935.
https://doi.org/10.3390/w14182935