Improving Forecasting Accuracy of Multi-Scale Groundwater Level Fluctuations Using a Heterogeneous Ensemble of Machine Learning Algorithms
Abstract
:1. Introduction
- Performance evaluation of the seven ML-based individual models to forecast multi-step ahead GWL fluctuations.
- Development of a heterogeneous ensemble of the GWL forecast models using the BMA approach and comparison of the performance of the ensemble with that of the standalone forecast models.
2. Materials and Methods
2.1. Study Area and the Data
2.2. Machine Learning-Based Models
2.2.1. Adaptive Neuro-Fuzzy Inference System (ANFIS)
2.2.2. Bagged and Boosted RF
2.2.3. Gaussian Process Regression (GPR)
2.2.4. Bidirectional Long Short-Term Memory (Bi-LSTM) Network
- A sequence input layer, which matched the number of input variables or features.
- A Bi-LSTM layer, whose units corresponded to the number of hidden units.
- A fully connected layer, tailored to the number of output variables or response variables.
- Finally, a regression layer.
2.2.5. Multivariate Adaptive Regression Spline (MARS)
2.2.6. Support Vector Regression (SVR)
2.3. Modeling Techniques
2.3.1. Data Preprocessing
2.3.2. Selection of Input Variables
2.3.3. Standardization of Data
2.3.4. Development of Individual Models
2.3.5. Development of Ensemble Models
2.4. Model Performance Evaluation
2.5. Variable Importance
3. Results and Discussion
3.1. Performance of the Individual Forecasting Models during Training and Validation
3.2. Performance of the Standalone and Ensemble Models on the Independent Test Dataset
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Observation Well | Mean | STD | Skewness | Kurtosis |
---|---|---|---|---|
GT8134017 | 6.796 | 2.797 | −0.172 | −0.446 |
GT8134020 | 7.735 | 2.683 | −0.043 | −0.596 |
GT8134021 | 6.612 | 2.555 | −0.457 | −0.535 |
GT8134022 | 6.534 | 2.274 | −0.218 | −0.557 |
Model | Parameters |
---|---|
ANFIS | Number of clusters: GT8134017-GWL (t + 1) = 6, GT3330001-GWL (t + 2) = 3, GT3330001-GWL (t + 3) = 3 GT8134020-GWL (t + 1) = 3, GT3330002-GWL (t + 2) = 2, GT3330002-GWL (t + 3) = 4 GT8134021-GWL (t + 1) = 6, GT3330020-GWL (t + 2) = 3, GT3330020-GWL (t + 3) = 5 GT813402-GWL (t + 1) = 5, GT3330020-GWL (t + 2) = 4, GT3330020-GWL (t + 3) = 3 Initial FIS: Fuzzy partition matrix exponent = 2 Maximum number of iterations = 500 Minimum improvement = 1 × 10−5 ANFIS: Maximum number of epochs: 500 Error goal = 0 Initial step size = 0.01 Step size decrease rate = 0.9 Step size increase rate = 1.1 |
Bagged RF | Number of variables to sample = all Predictor selection = interaction-curvature Method = bag Number of learning cycles = 200 Learn rate = 1 |
Boosted RF | Method = LSBoost Minimum number of parents = 10 Minimum number of leafs = 5 Maximum splits = 12 Number of learning cycles = 57 Learn rate = 0.1929 |
GPR | Basis function = Linear Kernel function = Rational Quadratic Fit method = Exact, predict method = Exact Beta = 0, Sigma = 0.4081 Optimizer = quasinewton |
MARS | Number of Basis functions at the forward pass = 100 Number of Basis functions at the backward pass = 50 Minimum number of observations between the knots = 3 No penalty is added to the variables to give equal priority to all input variables |
Bi-LSTM | Gradient decay factor = 0.9, Epsilon = 1 × 10−8, Initial learn rate = 0.01 Learn rate drop factor = 0.1, Learn rate drop period = 10, Gradient threshold = 1 L2 regularization = 1 × 10−4, Gradient threshold method = l2norm, Maximum number of epochs = 1000, Mini batch size = 150 |
SVR | Kernel function = linear, Box constraint = 25.4335, Epsilon = 0.1021 Delta gradient tolerance = 0, Gap tolerance = 1 × 10−3, Kernel scale = 7.4663 Solver = SMO, Bias = 6.7549, Iteration limit = 1,000,000 |
Model | GWL (t + 1) | GWL (t + 2) | GWL (t + 3) | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
RMSE | MAE | NS | MBE | RMSE | MAE | NS | MBE | RMSE | MAE | NS | MBE | |
GT8134017 | ||||||||||||
ANFIS | 1.85 | 0.93 | 0.40 | −0.25 | 1.57 | 0.95 | 0.57 | −0.29 | 1.82 | 1.16 | 0.43 | −0.44 |
BaggedRF | 1.59 | 1.01 | 0.56 | −0.86 | 1.83 | 1.33 | 0.41 | −1.17 | 2.03 | 1.56 | 0.28 | −1.41 |
BoostedRF | 1.67 | 1.12 | 0.51 | −0.92 | 2.20 | 1.63 | 0.16 | −1.48 | 2.09 | 1.59 | 0.24 | −1.40 |
GPR | 1.29 | 0.67 | 0.71 | −0.16 | 2.16 | 1.48 | 0.18 | −1.14 | 3.43 | 2.60 | −1.04 | −2.42 |
BiLSTM | 1.38 | 0.80 | 0.67 | −0.67 | 1.49 | 0.98 | 0.61 | −0.68 | 1.47 | 0.98 | 0.63 | −0.59 |
MARS | 1.95 | 1.10 | 0.33 | −0.67 | 8.65 | 5.40 | −12.06 | −5.23 | 8.13 | 5.49 | −10.46 | −5.22 |
SVR | 1.42 | 0.70 | 0.64 | −0.17 | 1.46 | 0.88 | 0.63 | −0.33 | 1.85 | 1.31 | 0.40 | −0.80 |
BMA | 0.87 | 0.50 | 0.87 | 0.00 | 1.13 | 0.68 | 0.78 | 0.00 | 1.23 | 0.77 | 0.74 | 0.00 |
GT8134020 | ||||||||||||
ANFIS | 0.76 | 0.45 | 0.52 | −0.10 | 0.80 | 0.51 | 0.47 | −0.15 | 0.98 | 0.67 | 0.20 | −0.17 |
BaggedRF | 1.17 | 0.89 | −0.15 | −0.84 | 1.25 | 1.00 | −0.31 | −0.96 | 1.42 | 1.19 | −0.70 | −1.16 |
BoostedRF | 1.25 | 0.96 | −0.30 | −0.94 | 1.39 | 1.15 | −0.61 | −1.13 | 1.63 | 1.40 | −1.23 | −1.39 |
GPR | 0.67 | 0.41 | 0.63 | −0.21 | 0.77 | 0.54 | 0.50 | −0.36 | 2.08 | 1.86 | −2.62 | −1.86 |
BiLSTM | 1.46 | 1.16 | −0.77 | −0.98 | 1.21 | 0.90 | −0.23 | −0.83 | 1.40 | 1.08 | −0.64 | −1.00 |
MARS | 1.32 | 0.68 | −0.46 | −0.01 | 1.12 | 0.67 | −0.05 | −0.17 | 1.61 | 0.92 | −1.16 | 0.06 |
SVR | 0.71 | 0.41 | 0.58 | −0.18 | 0.84 | 0.58 | 0.41 | −0.39 | 1.07 | 0.81 | 0.04 | −0.63 |
BMA | 0.59 | 0.33 | 0.71 | 0.00 | 0.64 | 0.38 | 0.66 | 0.00 | 0.71 | 0.47 | 0.58 | 0.00 |
GT8134021 | ||||||||||||
ANFIS | 0.85 | 0.60 | 0.79 | −0.35 | 1.15 | 0.88 | 0.62 | −0.65 | 1.30 | 0.97 | 0.52 | −0.59 |
BaggedRF | 1.10 | 0.80 | 0.66 | −0.69 | 1.47 | 1.15 | 0.38 | −1.03 | 1.85 | 1.51 | 0.02 | −1.39 |
BoostedRF | 1.07 | 0.79 | 0.68 | −0.65 | 1.53 | 1.19 | 0.33 | −1.05 | 1.83 | 1.47 | 0.05 | −1.31 |
GPR | 0.78 | 0.54 | 0.83 | −0.29 | 1.11 | 0.85 | 0.65 | −0.66 | 1.42 | 1.13 | 0.43 | −0.96 |
BiLSTM | 0.58 | 0.40 | 0.91 | −0.23 | 1.02 | 0.75 | 0.70 | −0.29 | 1.08 | 0.84 | 0.67 | −0.31 |
MARS | 0.83 | 0.60 | 0.80 | −0.31 | 1.22 | 0.96 | 0.58 | −0.39 | 1.64 | 1.26 | 0.24 | −0.60 |
SVR | 0.78 | 0.51 | 0.82 | −0.12 | 0.98 | 0.73 | 0.73 | −0.46 | 1.28 | 1.02 | 0.54 | −0.82 |
BMA | 0.44 | 0.27 | 0.95 | 0.00 | 0.75 | 0.50 | 0.84 | 0.00 | 0.83 | 0.61 | 0.81 | 0.00 |
GT8134022 | ||||||||||||
ANFIS | 0.63 | 0.45 | 0.92 | −0.23 | 1.02 | 0.73 | 0.81 | −0.42 | 1.35 | 1.07 | 0.66 | −0.61 |
BaggedRF | 0.63 | 0.44 | 0.93 | −0.20 | 1.01 | 0.72 | 0.81 | −0.44 | 1.39 | 1.08 | 0.65 | −0.83 |
BoostedRF | 0.70 | 0.48 | 0.91 | −0.26 | 1.07 | 0.78 | 0.79 | −0.55 | 1.57 | 1.19 | 0.55 | −0.95 |
GPR | 0.82 | 0.63 | 0.87 | −0.49 | 1.41 | 1.15 | 0.63 | −1.00 | 1.70 | 1.37 | 0.47 | −1.20 |
BiLSTM | 0.34 | 0.22 | 0.98 | −0.17 | 0.70 | 0.53 | 0.91 | −0.34 | 0.82 | 0.64 | 0.88 | −0.23 |
MARS | 0.69 | 0.49 | 0.91 | −0.14 | 1.10 | 0.79 | 0.78 | −0.28 | 1.40 | 1.08 | 0.64 | −0.53 |
SVR | 0.62 | 0.45 | 0.93 | −0.23 | 0.99 | 0.80 | 0.82 | −0.52 | 1.26 | 1.02 | 0.71 | −0.66 |
BMA | 0.28 | 0.18 | 0.98 | 0.00 | 0.55 | 0.38 | 0.94 | 0.00 | 0.77 | 0.56 | 0.89 | 0.00 |
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Roy, D.K.; Munmun, T.H.; Paul, C.R.; Haque, M.P.; Al-Ansari, N.; Mattar, M.A. Improving Forecasting Accuracy of Multi-Scale Groundwater Level Fluctuations Using a Heterogeneous Ensemble of Machine Learning Algorithms. Water 2023, 15, 3624. https://doi.org/10.3390/w15203624
Roy DK, Munmun TH, Paul CR, Haque MP, Al-Ansari N, Mattar MA. Improving Forecasting Accuracy of Multi-Scale Groundwater Level Fluctuations Using a Heterogeneous Ensemble of Machine Learning Algorithms. Water. 2023; 15(20):3624. https://doi.org/10.3390/w15203624
Chicago/Turabian StyleRoy, Dilip Kumar, Tasnia Hossain Munmun, Chitra Rani Paul, Mohamed Panjarul Haque, Nadhir Al-Ansari, and Mohamed A. Mattar. 2023. "Improving Forecasting Accuracy of Multi-Scale Groundwater Level Fluctuations Using a Heterogeneous Ensemble of Machine Learning Algorithms" Water 15, no. 20: 3624. https://doi.org/10.3390/w15203624