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Abstract:
Grain-size distribution data, as a substitute for measuring hydraulic conductivity (K), has often been used to get K value indirectly. With grain-size distribution data of 150 sets of samples being input data, this study combined the Artificial Neural Network technology (ANN) and Markov Chain Monte Carlo method (MCMC), which replaced the Monte Carlo method (MC) of Generalized Likelihood Uncertainty Estimation (GLUE), to establish the GLUE-ANN model for hydraulic conductivity prediction and uncertainty analysis. By means of applying the GLUE-ANN model to a typical piedmont region and central region of North China Plain, and being compared with actually measured values of hydraulic conductivity, the relative error ranges are between 1.55% and 23.53% and between 14.08% and 27.22% respectively, the accuracy of which can meet the requirements of groundwater resources assessment. The global best parameter gained through posterior distribution test indicates that the GLUE-ANN model, which has satisfying sampling efficiency and optimization capability, is able to reasonably reflect the uncertainty of hydrogeological parameters. Furthermore, the influence of stochastic observation error (SOE) in grain-size analysis upon prediction of hydraulic conductivity was discussed, and it is believed that the influence can not be neglected.
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Key words:
- Grain-size distribution /
- Hydraulic conductivity /
- ANN /
- GLUE /
- MCMC /
- Stochastic Observation Error (SOE)
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Table 1. Parameters in the ANN model
Parameter Physical meaning Value range D2000+ Gravel content, diameter more than 2 mm 0~0.02 D500 Coarse sand content, diameter between 0.5~2 mm 0.01~0.46 D250 Medium sand content, diameter between 0.25~0.5 mm 0.01~0.82 D75 Fine sand content, diameter between 0.075~0.25 mm 0.02~0.51 D5 Silt content, diameter between 0.005~0.075 mm 0.01~0.68 D5- Clay content, diameter less than 0.005 mm 0.01~0.65 N2 The number of hidden layer nodes 7~21 Wpi, j Network weight initial value -1~1 bpi Bias -1~1 
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Table 2. Comparison between the ANN model's output and measured values
Sample number Gravel Coarse sand Medium sand Fine sand Silt Clay Predicted K 10-6 (cm/s) Measured K 10-6 (cm/s) Relative error % > 2 2~0.5 0.5~0.25 0.25~0.075 0.075~0.005 < 0.005 content % zk11-01 1.15 4.05 12.33 5.10 64.06 13.31 18.01 18.33 1.75 zk11-02 0.00 4.10 14.59 8.18 57.12 16.01 13.34 13.59 1.84 zk11-03 0.00 3.35 8.09 10.17 33.12 45.27 2.42 2.98 18.79 zk11-04 0.53 7.26 20.20 4.11 49.07 18.83 9.29 9.10 2.08 zk11-05 0.00 10.32 13.52 24.97 42.15 9.04 28.91 28.47 1.55 zk11-06 0.00 15.16 46.94 28.05 8.14 1.71 602.56 665.30 9.43 zk11-07 0.00 8.20 1.08 3.34 62.30 25.08 2.65 2.51 5.58 zk11-08 1.00 1.13 1.19 5.17 65.40 26.11 3.80 3.92 3.06 zk11-09 0.00 31.22 39.14 1.35 26.54 1.75 536.11 589.78 9.10 zk11-10 0.00 1.26 5.79 1.62 54.45 36.88 1.87 1.97 5.08 zk11-11 0.00 32.49 27.55 6.88 30.87 2.21 410.41 456.98 10.19 zk11-12 0.00 28.01 38.40 10.02 21.91 1.66 445.09 415.70 7.07 zk11-13 0.00 20.34 42.15 4.37 31.51 1.63 404.02 448.31 9.88 zk11-14 0.00 2.30 2.27 13.25 35.90 46.28 2.21 2.89 23.53 zk11-15 0.00 3.36 1.33 1.03 54.73 39.55 1.23 1.36 9.56 zk11-16 0.00 39.22 20.68 7.21 30.70 2.19 394.80 439.18 10.11 zk11-17 0.00 24.98 55.17 11.15 6.97 1.73 589.85 644.71 8.51 zk11-18 0.00 2.24 1.12 2.33 56.66 37.65 1.18 1.05 12.38 zk11-19 0.00 1.27 2.97 2.10 60.15 33.51 0.88 0.92 4.35 zk11-20 2.06 5.10 4.55 8.51 53.28 26.50 5.03 5.24 4.01
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Table 3. The comparison between the ANN model's output and measured values of samples from middle region of NCP
Sample number Gravel Coarse sand Medium sand Fine sand Silt Clay Predicted K 10-6 (cm/s) Measured K 10-6 (cm/s) Relative error % > 2 2~0.5 0.5~0.25 0.25~0.075 0.075~0.005 < 0.005 content % S18-01 0.00 23.52 20.58 33.54 12.25 10.11 17.33 20.17 14.08 S18-02 0.00 25.08 17.41 45.88 9.38 2.25 398.75 475.32 16.11 S18-03 0.00 25.49 22.72 28.10 10.89 12.80 42.36 36.74 15.30 S18-04 0.00 29.37 25.26 21.65 14.17 9.55 31.91 40.47 21.15 S18-05 0.00 28.90 19.21 41.20 8.92 1.77 332.97 412.55 19.29 S18-06 0.00 28.83 19.88 37.21 11.12 2.96 274.10 376.61 27.22 S18-07 0.00 41.28 22.43 17.57 4.22 14.50 13.73 18.39 25.34
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