Machine Learning Methods for Improved Understanding of a Pumping Test in Heterogeneous Aquifers
Abstract
:1. Introduction
2. Materials and Methods
2.1. Study Area
2.2. Pumping Tests
2.3. Methods
2.3.1. Pearson Correlation Analysis
2.3.2. Cluster Analysis
2.3.3. Time-Series Analysis Method of Drawdowns within Pumping Wells
2.3.4. Forecasting Method for Groundwater Levels among Observation Wells
2.3.5. Linear Graphic Method in the Theis Model
3. Results
3.1. Distribution of Maximum Drawdown
3.2. Relationship of Water Levels between Observation and Pumping Wells
3.3. Predictions of Drawdowns within Pumping Wells
3.4. Predictions of Drawdowns in Observation Wells
4. Discussion
5. Conclusions
- (1)
- Rather than the mere contour map of the maximum drawdowns, the relationships of the drawdown over the period of pumping tests between wells provide a visual picture using ML methods, and the cluster of Pearson correlation coefficient shows the hydraulic connections between wells;
- (2)
- The ARIMA method can be used to effectively predict the time-series changes of drawdowns in three pumping wells. In the hypothetical Theis model, the relative error of drawdowns is only 0.86% after 1.37 × 109 years. The predicted maximum drawdown in well P01, P02, and P03 after 3 years is 64.53 m, 52.50 m, and 92.88 m, respectively;
- (3)
- Trained ANN, SVR, and RF models can reasonably capture the change of drawdowns in 25 observation wells induced by pumping; however, SVR and RF models provide better estimates, with average RMSE values for drawdowns of 0.13 m;
- (4)
- K-means clustering using the Pearson correlation coefficient, the maximum drawdown, and well depth visually shows a preferable pathway, with the good permeability under depths ranging from 250 m to 350 m;
- (5)
- Model parameters have certain influences on the simulated drawdowns for ANN, SVR, and RF models, but the RF model shows the least sensitivity to the value of the parameters, and has the best performance when compared with observed results;
- (6)
- With the assumption of the Theis model, the linear regressive method may be used to roughly estimate the value of hydraulic conductivity, and the results in this paper are consistent with the previous studies.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Series (From Young to Old) | Formation | Local Name | Brief Description | Approximated Thickness (m) | |
---|---|---|---|---|---|
Kundelungu | Kundelungu | Ku | Sediments | 3000–5000 | |
Nguba | Nguba | Ng | Sandstone, shale | 200–500 | |
Upper Roan (R) | R4 | Mwashya | shale, siltstone, sandstone, dolomites | 50–100 | |
R3-2 | Dipeta | Sandy shales | about 1000 | ||
R3-1 | Roches Greseuse Superior (RGS) | Grey shales | 100–200 | ||
Lower Roan | R2-3 | Mines Group | Calcaire á Minerals Noirs (CMN) | Black calcareous siltstone | 130 |
R2-2 | Schistes Dolomitic Superior (SDS) | Dolomitic shales, black ore mineral zone (BOMZ) | 50–80 | ||
R2-1 | Schistes de Base (SDB) | Dolomitic shales, black ore mineral zone (BOMZ) | 10–15 | ||
Roches Silicieuses Cellulaire (RSC) | Siliceous, vuggy dolomite | 12–25 | |||
Roches Silicieuses Feuilletees (RSF) | Bedded dolomitic siltstone | 5 | |||
Dolomie Stratifiee (DSTRAT) | Grey talcose sandstone | 3 | |||
Roches Argileuses Talceuse (RAT) GRISES | Grey talcose sandstone | 2–5 | |||
R1 | Roches Argileuses Talceuse (RAT2) | Talcose sandstone | 190 | ||
Roches Argileuses Talceuse (RAT1) | Talcose sandstone | 40 |
ID | Well Name | X Coordinate (m) | Y Coordinate (m) | Well Depth (m) | Maximum Drawdown (m) |
---|---|---|---|---|---|
1 | P01 | 332,585.13 | 8,817,317.16 | 310.20 | 61.21 |
2 | P02 | 332,754.99 | 8,817,435.06 | 251.51 | 45.08 |
3 | P03 | 332,259.70 | 8,817,203.31 | 325.00 | 57.70 |
4 | O01 | 332,466.69 | 8,817,664.79 | 110.39 | 0.42 |
5 | O02 | 332,522.15 | 8,817,498.36 | 300.20 | 1.22 |
6 | O03 | 332,061.84 | 8,817,135.65 | 330.19 | 22.35 |
7 | O04 | 331,489.21 | 8,816,936.91 | 150.56 | 1.39 |
8 | O05 | 333,045.08 | 8,817,509.79 | 300.05 | 7.55 |
9 | O06 | 333,190.69 | 8,817,610.82 | 110.03 | 0.59 |
10 | O07 | 332,821.69 | 8,816,666.56 | 150.95 | 0.27 |
11 | O08 | 332,805.85 | 8,816,292.67 | 102.25 | 0.15 |
12 | O09 | 330,946.09 | 8,817,636.84 | 100.25 | 0.13 |
13 | O10 | 331,761.74 | 8,817,414.28 | 100.42 | 0.68 |
14 | O11 | 330,483.97 | 8,817,678.42 | 150.00 | 0.48 |
15 | O12 | 330,483.97 | 8,817,678.42 | 50.00 | −0.13 |
16 | O13 | 332,594.98 | 8,817,275.07 | 400.07 | 18.16 |
17 | O14 | 332,856.15 | 8,817,437.12 | 344.13 | 37.27 |
18 | O15 | 332,253.28 | 8,817,166.53 | 324.75 | 27.81 |
19 | O16 | 332,709.88 | 8,817,245.02 | 450.20 | 3.84 |
20 | O17 | 332,475.42 | 8,817,329.49 | 330.51 | 18.20 |
21 | O18 | 332,546.68 | 8,817,209.31 | 602.00 | 2.94 |
22 | O19 | 332,442.94 | 8,817,113.78 | 658.00 | 1.81 |
23 | O20 | 332,778.77 | 8,817,213.32 | 346.00 | 4.86 |
24 | O21 | 332,735.77 | 8,817,305.28 | 442.00 | 4.38 |
25 | O22 | 332,515.40 | 8,817,012.31 | 612.00 | 2.26 |
26 | O23 | 331,833.07 | 8,816,934.75 | 281.05 | 3.01 |
27 | O24 | 332,026.27 | 8,816,985.75 | 50.00 | −0.17 |
28 | O25 | 332,026.27 | 8,816,985.75 | 150.00 | 8.95 |
Models | Parameters | RMSE (m) | Average Relative Error (%) | |||
---|---|---|---|---|---|---|
Well O15 | Well O19 | Well O15 | Well O19 | |||
ANN Model | number of the first and the second hidden layers | (2, 2) | 5.1972 | 0.3516 | 90.64 | 220.01 |
(5, 5) | 0.8717 | 0.1834 | 9.66 | 195.83 | ||
(10, 10) | 0.5844 | 0.1998 | 16.30 | 84.34 | ||
(100, 100) | 0.5085 | 0.1237 | 10.56 | 89.60 | ||
SVR Model | kernel function (the radial basis function (rbf) and linear) and parameter c | rbf, c = 10 | 1.1462 | 0.0941 | 76.40 | 96.87 |
rbf, c = 100 | 0.0926 | 0.0941 | 1.90 | 96.87 | ||
rbf, c = 1000 | 0.0926 | 0.0941 | 1.90 | 96.87 | ||
linear, c = 1000 | 2.6271 | 5.4130 | 58.95 | 2443.24 | ||
RF Model | number of trees (n) | n = 5 | 0.2429 | 0.0551 | 14.13 | 22.01 |
n = 50 | 0.2071 | 0.0468 | 11.57 | 13.38 | ||
n = 500 | 0.1842 | 0.0416 | 11.17 | 14.84 | ||
n = 5000 | 0.1853 | 0.0394 | 10.91 | 15.17 |
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Fan, Y.; Hu, L.; Wang, H.; Liu, X. Machine Learning Methods for Improved Understanding of a Pumping Test in Heterogeneous Aquifers. Water 2020, 12, 1342. https://doi.org/10.3390/w12051342
Fan Y, Hu L, Wang H, Liu X. Machine Learning Methods for Improved Understanding of a Pumping Test in Heterogeneous Aquifers. Water. 2020; 12(5):1342. https://doi.org/10.3390/w12051342
Chicago/Turabian StyleFan, Yong, Litang Hu, Hongliang Wang, and Xin Liu. 2020. "Machine Learning Methods for Improved Understanding of a Pumping Test in Heterogeneous Aquifers" Water 12, no. 5: 1342. https://doi.org/10.3390/w12051342