Estimating hydraulic aquifer parameters from tide-induced groundwater fluctuations

Abstract

In this report, the tidal method is used to estimate hydraulic aquifer parameters. The principle of the tidal method is to use head fluctuations in observation wells, caused by tidal motion in a sea or river, to determine regional hydrological characteristics of an aquifer system. As the wave propagates into the aquifer, the amplitude of the signal decreases and the phase increasingly lags behind the tide at sea. The extent of this is determined by hydrological aquifer characteristics, hence aquifer parameters can be estimated, by calibrating a model that reproduces the measured tidal propagation. Knowledge of hydraulic aquifer parameters is important since these are needed in groundwater models. The case study was performed on Schouwen-Duiveland where use was made of hydraulic head fluctuations from three groundwater observation wells and water-level observations in the Oosterschelde. First, these time series were analyzed to estimate the amplitudes and phases of the constituents present in the data. Noise in the data was reduced with the use of Pastas (a model to analyze hydrological time series; Collenteur et al., 2019) and a Butterworth filter, after which both methods were compared. Pastas was used to decompose the fluctuations observed in the groundwater to different contributions of hydrological stresses (e.g. rain and evaporation) and Butterworth was used to flatten the frequency response for frequencies that are not of interest. The use of the Butterworth filter is preferred, partly because it produces the smallest standard deviations for the amplitude and phase estimates and because it is easier to use. Moreover, especially for the wells with a low signal to noise ratio, the Butterworth filter is better at extracting the tidal signal. In addition, a graphical determination of the amplitude and phase was performed to check if this relatively quick and easy analysis gives accurate estimates of the M2 amplitude and phase as well. It was concluded that with a high signal to noise ratio and a dominantly present constituent (M2 in this case), the amplitude can be reliably estimated. Determining the phase with this method did not give satisfactory results. In the inverse modeling part, the hydraulic aquifer parameters are determined, which is done with a least-squares minimization of the observed and modeled amplitudes and phases. For the optimization, both a one-aquifer and a two-aquifer model were used, both based on the one-dimensional, multi-layer solution presented by Bakker (2019). The optimization was performed with a global optimizer. The obtained fit to the observations was somewhat poor, moreover, unrealistic optimal parameter estimates indicate that the model, to some extent, incorrectly represents the real system. This also implies that some of the model simplifications do significantly impact the results. Simplifications presumed to mostly influence the model results include homogeneity, one-dimensional flow and the use of a straight shoreline. The presence of some model error signifies that the resulting parameter estimates should be treated with care. The hydraulic conductivity and the resistance of the one-layer model were consistently estimated at their upper boundary and the storage in the leaky layer was estimated to be negligible. Therefore, only one parameter group (i.e. the diffusivity) could be estimated with the optimization. The fit of the model was not perfect, a compromise must be sought based on what residual the model minimizes. As a result, all diffusivity estimates within and around the range [1.07E6, 1.31E6] m2/day are all considered to be reasonable estimates. For the resistance of the aquitard (CU) and the storage in both the aquifer (SsU) and the aquitard (σU) it was analyzed which parameter values gave unreasonable results. This resulted in a lower bound for CU (CU=663 days) and an upper bound for σU  (σU =1.22E-4 m-1). For SsU reasonable results are obtained between 2.28E-6 m-1 and 1.87E-5 m-1. The lower bound for the CU estimate seems to comply with estimates based on two models (REGIS-II and GeoTOP). Finally, the two-aquifer model was considered to be useless for parameter estimation. Presumably, this is predominantly caused by a small amount of amplitude and phase data compared to the number of parameters to be optimized.