Estimation of groundwater recharge from groundwater levels using nonlinear transfer function noise models and comparison to lysimeter data

Abstract

Abstract. The estimation of groundwater recharge is of paramount importance to assess the sustainability of groundwater use in aquifers around the world. Estimation of the recharge flux, however, remains notoriously difficult. In this study the application of nonlinear transfer function noise (TFN) models using impulse response functions is explored to simulate groundwater levels and estimate groundwater recharge. A nonlinear root zone model that simulates recharge is developed and implemented in a TFN model and is compared to a more commonly used linear recharge model. An additional novel aspect of this study is the use of an autoregressive–moving-average noise model so that the remaining noise fulfills the statistical conditions to reliably estimate parameter uncertainties and compute the confidence intervals of the recharge estimates. The models are calibrated on groundwater-level data observed at the Wagna hydrological research station in the southeastern part of Austria. The nonlinear model improves the simulation of groundwater levels compared to the linear model. The annual recharge rates estimated with the nonlinear model are comparable to the average seepage rates observed with two lysimeters. The recharges estimates from the nonlinear model are also in reasonably good agreement with the lysimeter data at the smaller timescale of recharge per 10 d. This is an improvement over previous studies that used comparable methods but only reported annual recharge rates. The presented framework requires limited input data (precipitation, potential evaporation, and groundwater levels) and can easily be extended to support applications in different hydrogeological settings than those presented here.

Application of Time Series Analysis to Estimate Drawdown From Multiple Well Fields

“…There is probably a point, however, where more head observations introduce more problems (e.g., autocorrelation) than they solve (e.g., better models). Different frequencies (daily, weekly, bi-weekly) of head observations were evaluated to calibrate the models (following Collenteur et al, 2021). A time interval of 14 days yielded good models while greatly reducing the number of models with significant autocorrelation in the noise.…”

“…This led to somewhat different drawdown estimates for some models, but most models showed no significant changes in the estimated drawdowns. This analysis can be repeated 14 times to give additional insight into the robustness of the method to the selected sample of head observations (as was done by Collenteur et al, 2021). 3) Goodness-of-fit criterion.…”

“…The noise model (Eq. 3) is rarely adequate for obtaining uncorrelated noise when using daily head observations, but works reasonably well for head data at 14days intervals (e.g., Von Asmuth and Bierkens, 2005;Collenteur et al, 2021). The calibration data is obtained by taking a sample from each head time series on a 14-days interval within the calibration period.…”

Alternative stable states and hydrological regime shifts in a large intermittent river

“…To support our interpretations of these hydrological data, we also developed a time series model using a transfer function noise approach (Von Asmuth et al 2008, Schaars 2019, Collenteur et al 2019). This model estimated the degree to which historic variation in alluvial aquifer water levels could be attributed to three drivers: (a) climate-driven diffuse recharge through the soil column, represented in the model using a simple soil water budget model driven by precipitation and ETo (Collenteur et al 2021); (b) stream-aquifer exchange, represented via a linear response to stream stage variation; and (c) groundwater pumping, represented via the Hantush and Jacob (1955) response to pumping. This model does not simulate the potential existence of multiple stable states because it does not include interactions among these factors, but provides an indication of the relative importance of each of these drivers on water levels in the alluvial aquifer, and the time scale over which each of them influences alluvial aquifer water levels.…”

“…We propose that cross-scale interactions between regional processes (surface water inflows from upstream, groundwater pumping) and local ecohydrological feedbacks (stream-aquifer exchange, diffuse recharge through the soil column) govern streamflow and can trigger regime shifts at this site (figure 9). The two primary ecohydrological feedbacks in the system are the balance between precipitation and plant water use in the riparian corridor, which drives the amount of diffuse recharge through the soil column (Collenteur et al 2021), and groundwater pumping for agricultural use, which is sensitive to precipitation at the regional scale and depletes streamflow by lowering groundwater levels locally and reducing inflows from upstream (Whittemore et al 2016, Zipper et al 2022a). These cross-scale interactions suggest that the alternative stable states we observed here are symptomatic of stressors related to human activity and climate over much of the Arkansas River basin, and this site is a reflection of the broad-scale shift from perennial to non-perennial streams in western Kansas (figure 2(a)), the Great Plains (Perkin et al 2017), and worldwide (Sauquet et al 2021, Tramblay et al 2021, Zipper et al 2021.…”