Wavelet coupled MARS and M5 Model Tree approaches for groundwater level forecasting

Abstract

In this study, two different machine learning models, Multivariate Adaptive Regression Splines (MARS) and M5 Model Trees (MT) have been applied to simulate the groundwater level (GWL) fluctuations of three shallow open wells within diverse unconfined aquifers. The Wavelet coupled MARS and MT hybrid models were developed in an attempt to further increase the GWL forecast accuracy. The Discrete Wavelet Transform (DWT) which is particularly effective in dealing with non-stationary time-series data was employed to decompose the input time series into various sub-series components. Historical data of 10years (August-1996 to July-2006) comprising monthly groundwater level, rainfall, and temperature were used to calibrate and validate the models. The models were calibrated and tested for one, three and six months ahead forecast horizons. The wavelet coupled MARS and MT models were compared with their simple counterpart using standard statistical performance evaluation measures such as Root Mean Square Error (RMSE), Normalized Nash-Sutcliffe Efficiency (NNSE) and Coefficient of Determination (R2). The wavelet coupled MARS and MT models developed using multi-scale input data performed better compared to their simple counterpart and the forecast accuracy of W-MARS models were superior to that of W-MT models. Specifically, the DWT offered a better discrimination of non-linear and non-stationary trends that were present at various scales in the time series of the input variables thus crafting the W-MARS models to provide more accurate GWL forecasts.