Use of Machine Learning Methods to Reduce Predictive Error of Groundwater Models

Abstract

Quantitative analyses of groundwater flow and transport typically rely on a physically-based model, which is inherently subject to error. Errors in model structure, parameter and data lead to both random and systematic error even in the output of a calibrated model. We develop complementary data-driven models (DDMs) to reduce the predictive error of physically-based groundwater models. Two machine learning techniques, the instance-based weighting and support vector regression, are used to build the DDMs. This approach is illustrated using two real-world case studies of the Republican River Compact Administration model and the Spokane Valley-Rathdrum Prairie model. The two groundwater models have different hydrogeologic settings, parameterization, and calibration methods. In the first case study, cluster analysis is introduced for data preprocessing to make the DDMs more robust and computationally efficient. The DDMs reduce the root-mean-square error (RMSE) of the temporal, spatial, and spatiotemporal prediction of piezometric head of the groundwater model by 82%, 60%, and 48%, respectively. In the second case study, the DDMs reduce the RMSE of the temporal prediction of piezometric head of the groundwater model by 77%. It is further demonstrated that the effectiveness of the DDMs depends on the existence and extent of the structure in the error of the physically-based model.

A Comparative Study of Groundwater Level Forecasting Using Data-Driven Models Based on Ensemble Empirical Mode Decomposition

“…Recently, data-driven models such as artificial neural networks (ANN), support vector machines (SVM), adaptive neuro-fuzzy inference systems (ANFIS) and genetic programming (GP), and time series methods such as autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) have been proved efficient in forecasting hydrologic time series (e.g., groundwater level, water demand and inflow) [5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Yoon et al [5] developed ANN and SVM models to forecast groundwater level fluctuations in a coastal aquifer.…”

“…The ARIMA model was proved have better predictive ability compared to the ARMA model. Xu et al [14] built the instance-based weighting and support vector regression data-driven models to reduce the predictive error of groundwater models. The results of two real-world case studies showed that data-driven models can be applied effectively to reduce the root mean square error of the groundwater models.…”

Groundwater Depth Prediction Using Data-Driven Models with the Assistance of Gamma Test

“…( k x is the input vector, k y is the corresponding output value), and the regression function of SVM can be expressed as: (10) where w is a weight vector, ϕ is a nonlinear transfer function that implements transformation the nonlinear to linear relationship of input to output vectors, and b is a bias. Vapnik introduced the …”

Surrogate Models for Sub-Region Groundwater Management in the Beijing Plain, China

“…Therefore, data-driven models are a good choice when data are limited and the groundwater system is very complex [22]. Data-driven models such as multiple linear regression (MLR), Back-Propagation Artificial Neural Network (BP-ANN), Support Vector Machines (SVM) and Power Function Models (PFM), are gradually used for groundwater level prediction, and thus, comparative studies on the above prediction techniques have been widely used and applied by some researchers [23][24][25].…”