Micro-Climate Computed Machine and Deep Learning Models for Prediction of Surface Water Temperature Using Satellite Data in Mundan Water Reservoir
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Data Collection and Image Preprocessing
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)
- V.
- Convolutional Long Short Term Memory (Conv-LSTM)
2.4. Sliding Window Time Series Cross-Validation and Model Evaluation Metrics
2.5. Performance Evaluation Metrics
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
- 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 R2 and as well as lower RMSE values when comparing the five generated models, achieving the highest accuracy in testing data. In terms of R2 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 R2 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 (H0), 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 H0, 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.
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 () 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
4.5. Spatio-Temoporary Variation Thermal Maps for Mundan
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 R2, RMSE, and bias-variance trade-off evaluators;
- (4)
- The maximum prediction accuracy was achieved by the ConvLSTM based on L8-TIRS data, with R2 = 0.93, RMSE = 0.15 °C.
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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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 |
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 |
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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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
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 StyleMukonza, 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