Nonlinear time‐series modeling of unconfined groundwater head

Abstract

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.

Automated Time Series Modeling for Piezometers in the National Database of the Netherlands

“…The basis of the approach is modeling of head time series using transfer function‐noise modeling with precipitation and evaporation as independent variables (Figure ). We use a setup that has proven itself in many practical applications (see e.g., Bakker et al ; Manzione et al ; Peterson and Western ; Shapoori et al ), consisting of: An impulse response function for precipitation which is used for convolution with the precipitation to give the transfer of the precipitation to its contribution to the piezometric head; An impulse response function for evaporation which is either a separately estimated function, or a factor times the function used for precipitation; A noise model with exponential decay. …”

Physical-based time series model applied on water table depths dynamics characteristics simulation

“…Since the monitoring period of the simulated wells comprised two periods of climatic anomalies (end of the drought -2014and ENSO 2015, we compared the values of MGL only calculated for the period of the series with the simulated values, denoting a good relationship as can be seen in Figure 7.…”

“…More complex time series models can estimate groundwater recharge (YIHDEGO; WEBB, 2011), capture nonlinear soil drainage behavior (PETERSON; WESTERN, 2014) or even define recharge response time from precipitation (HOCKING; KELLY, 2016;MANZIONE et al, 2017).…”

A time-series analysis framework for the flood-wave method to estimate groundwater model parameters

“…A first approximation for the response function of evaporation is the response function of precipitation multiplied by a negative scale factor. Alternatively, evaporation can be attributed its own response function describing; for example, how the root zone reacts to a drought period (Peterson and Western 2014). The response functions for river stage variations and pumping represent the propagation of the head change from the river or the pumping well to a point in the aquifer.…”

“…Convolution of each response function with the corresponding stress time series results in the separate fluctuations caused by each stress, where it is assumed that the system's response is linear. The method of predefined response functions has recently been extended to simulate nonlinear reactions of the phreatic water table in Australia (Peterson and Western 2014;Shapoori et al 2015a, b, c). An evaluation of the method using synthetic data was presented by Shapoori et al (2015a, b, c).…”