Time series analysis is applied to identify and analyze a transition in the groundwater regime in the aquifer below the sand ridge of Salland in the Netherlands, where groundwater regime refers to the range of head variations throughout the seasons. Standard time series analysis revealed a discrepancy between modeled and observed heads in several piezometers indicating a possible change in the groundwater regime. A new time series modeling approach is developed to simulate the transition from the initial regime to the altered regime. The transition is modeled as a weighted sum of two responses, one representing the initial state of the system, the other representing the altered state. The inferred timing and magnitude of the change provided strong evidence that the transition was the result of significant dredging works that increased the river bed conductance of the main river draining the aquifer. The plausibility of this explanation is corroborated by an analytical model. This case study and the developed approach to identify a change in the groundwater regime are meant to stimulate a more systematic application of time series analysis to detect and understand changes in groundwater systems which may easily go unnoticed in groundwater flow modeling.@en

A new method is presented to estimate average diffuse aquifer recharge of water table aquifers in temperate climates using time series analysis of water table level fluctuations. An accurate estimate of the recharge caused by rainfall requires an accurate estimate of the influence of evaporation. In temperate climates, evaporation imprints a seasonal component in the water table fluctuations. As such, recharge is estimated from time series models fitted to observed heads under the additional constraint that the seasonal harmonic of the observed head is reproduced as the sum of the transformed seasonal harmonics present in precipitation, evaporation, and pumping. An explicit equation is presented, in terms of the model parameters, for the damping and phase shift of the response to the seasonal harmonic of the stresses. Taking into account the seasonal harmonic of the observed heads results in more reliable recharge estimates compared to standard time series analysis. The method is limited to systems that are sufficiently linear and that remain unaltered over the analysis period. Head fluctuations and stresses should contain a seasonal harmonic that can be estimated with accurately. Runoff must be negligible or quantifiable. The method is applied to measured heads obtained from piezometers situated on and around the ice-pushed sand ridge of Salland in the Netherlands and compares well with recharge estimates based on the saturated zone chloride mass balance.@en

The methods behind the predefined impulse response function in continuous time (PIRFICT) time series model are extended to cover more complex situations where multiple stresses influence ground water head fluctuations simultaneously. In comparison to autoregressive moving average (ARMA) time series models, the PIRFICT model is optimized for use on hydrologic problems. The objective of the paper is twofold. First, an approach is presented for handling multiple stresses in the model. Each stress has a specific parametric impulse response function. Appropriate impulse response functions for other stresses than precipitation are derived from analytical solutions of elementary hydrogeological problems. Furthermore, different stresses do not need to be connected in parallel in the model, as is the standard procedure in ARMA models. Second, general procedures are presented for modeling and interpretation of the results. The multiple-input PIRFICT model is applied to two real cases. In the first one, it is shown that this model can effectively decompose series of ground water head fluctuations into partial series, each representing the influence of an individual stress. The second application handles multiple observation wells. It is shown that elementary physical knowledge and the spatial coherence in the results of multiple wells in an area may be used to interpret and check the plausibility of the results. The methods presented can be used regardless of the hydrogeological setting. They are implemented in a computer package named Menyanthes (www.menyanthes.nl).

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A comprehensive and efficient approach is presented for the calibration of transient groundwater models. The approach starts with the time series analysis of the measured heads in observation wells using all active stresses as input series, which may include rainfall, evaporation, surface water levels, and pumping. The time series analysis results in the impulse response function of each stress at the observation well. For each impulse response function, the temporal moments M0 and M1 may be computed. Both moments fulfill differential equations that are equivalent to the differential equation for steady groundwater flow, with known values along physical boundaries. The model of M0 may be calibrated for the transmissivity, as it does not depend on the storage coefficient; the computed values of M0 at the observation wells are used for calibration. The model of M1 may be calibrated for the storage coefficient, once the transmissivity is known from the M0 model; the computed values of M1 at the observation wells are used for calibration. The approach is intended for systems that may be approximated as linear. In summary, our proposed calibration process for transient models reduces to the calibration of only two steady models. Several examples are given to demonstrate the accuracy and efficiency of the proposed approach.@en

An analytic approach is presented for the simulation of variations in the groundwater level due to temporal variations of recharge in surficial aquifers. Such variations, called groundwater dynamics, are computed through convolution of the response function due to an impulse of recharge with a measured time series of recharge. It is proposed to approximate the impulse response function with an exponential function of time which has two parameters that are functions of space only. These parameters are computed by setting the zeroth and first temporal moments of the approximate impulse response function equal to the corresponding moments of the true impulse response function. The zeroth and first moments are modeled with the analytic element method. The zeroth moment may be modeled with existing analytic elements, while new analytic elements are derived for the modeling of the first moment. Moment matching may be applied in the same fashion with other approximate impulse response functions. It is shown that the proposed approach gives accurate results for a circular island through comparison with an exact solution; both a step recharge function and a measured series of 10 years of recharge were used. The presented approach is specifically useful for modeling groundwater dynamics in aquifers with shallow groundwater tables as is demonstrated in a practical application. The analytic element method is a gridless method that allows for the precise placement of ditches and streams that regulate groundwater levels in such aquifers; heads may be computed analytically at any point and at any time. The presented approach may be extended to simulate the effect of other transient stresses (such as fluctuating surface water levels or pumping rates), and to simulate transient effects in multi-aquifer systems.

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