Linear systems analysis in a karst aquifer

A linear systems analysis applied to groundwater flow is presented as an alternative modeling technique to traditional discretized groundwater models (i.e. finite-difference and finite-element), which require elaborate parameters and boundary conditions. Linear systems analysis has been used extensively for surface-water modeling and to a lesser extent for groundwater applications. We present a method for the analysis of an aquifer's response in hydraulic head to recharge that comprises two major components. The first component is to predict the drop in hydraulic head over time if recharge is eliminated. By fitting logarithmic curves to selected short-term hydraulic head recession periods, a long-term recession or “base head” can be established. The estimation of base head is necessary for the second component of the method, which is the derivation of an impulse response function or transfer function. The transfer function was derived by deconvolution of two time series data sets—estimated recharge and the measured response in hydraulic head. An aquifer's response to recharge can be characterized and modeled by using the transfer function, which also establishes the time to peak response, the response time distribution, and the total memory length of the system. The method requires fitting smooth curves to the oscillatory transfer function derived by deconvolution in the Fourier transform domain. The smooth curve is considered to be the physically valid transfer function. In this analysis, curve fitting was more effective than other smoothing techniques commonly used. We applied the method to the karstic Madison aquifer and found that the time to peak response is less than one month, the system's total memory is about six years, and a logarithmic curve best fits the system response. This method has potential to be useful as a predictive tool in aquifer management.