Nonlinear time-series modeling of unconfined groundwater head

This paper presents a nonlinear transfer function noise model for time-series modeling of unconfined groundwater hydrographs. The motivation for its development was that existing groundwater time-series models were unable to simulate large recharge events and multiyear droughts. This was because existing methods do not partition rainfall to runoff and do not account for nonlinear soil water drainage. To account for these nonlinear processes, a vertically integrated soil moisture module was added to an existing transfer function noise model. The soil moisture module has a highly flexible structure that allowed 84 different forms to be built. Application of the time-series model requires numerical calibration of parameters for the transfer functions, noise model and, for the nonlinear models, the soil moisture module. This was undertaken using the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) global calibration scheme. However, reproducible calibration to the global optima was challenging and a number of modifications were required to the transfer function noise model. In trialing the 84 nonlinear models and 2 linear models, each was applied to eleven observation bores within a paired catchment study area in Great Western, Victoria, Australia. In comparison with existing groundwater hydrograph time-series models, the proposed nonlinear time-series model performed significantly better at all observation bores during calibration and evaluation periods. Both the linear and nonlinear models were also used to quantify the impact of revegetation within the paired catchment; however, results were inconclusive, which is likely due to time-series data for the state of the revegetation being unavailable. By analyzing the application of 84 nonlinear models to each bore, an optimal structure for the soil moisture module was identified. It is unlikely, however, that this model structure would be appropriate for all climates and geologies. To encourage further investigations, open-source code for the highly flexible groundwater time-series modeling framework is available and we invite others to develop new models. Key Points Groundwater hydrograph models cannot simulate episodic recharge and droughts Nonlinear transformation of climate forcing overcame these weaknesses Robust calibration required reformulation of existing time-series equations