Linear systems analysis in a karst aquifer, 1999,
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Long A. J. , Derickson R. G. ,

A linear systems analysis applied to ground-water flow is presented as an alternative modeling technique to traditional discretized ground-water 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 3 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 H-as 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 thr 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 3 predictive tool in aquifer management. (C) 1999 Elsevier Science B.V. All rights reserved

Composite transfer functions for karst aquifers, 2003,
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Icjukic V. , Jukic D. ,

Linear transfer functions have been extensively used in hydrological studies. Generally, we support this conclusion: rainfall-runoff models based on the convolution between rainfall rates and a nonparametric transfer function (NTF) are not successful at simulating karst spring discharges during long recession periods. The tails of identified transfer functions have irregular shapes and they are not accurate physical representation of the transport through a karst system. Irregularities are the result of unavoidable errors in input and output time series and simplifications made by considering the system as linear and time invariant. This paper deals with a new form of the transfer functions for karst aquifers, the so-called composite transfer function (CTF). The CTF simulates discharges by two transfer functions adapted for the quick flow and the slow flow hydrograph component modeling. NTF is responsible for the quick flow component. The slow flow component is modeled by a parametric transfer function that is an instantaneous unit hydrograph mathematically formulated and defined from a conceptual model. By using the CTF, the irregular shape of the tail of the identified transfer function can be avoided, and the simulation of long recession periods as well as the simulation of a complete hydrograph becomes more successful. The NTF, the Nash model, the Zoch model and other similar conceptual models can be considered separately as simplified forms of the CTF. The rainfall-runoff model based on the convolution between rainfall rates and the CTF was tested on the Jadro Spring in Croatia. The results of the application are compared with the results obtained by applying NTFs independently. (C) 2003 Elsevier Science B.V. All rights reserved

Linear model describing three components of flow in karst aquifers using O-18 data, 2004,
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Long A. J. , Putnam L. D. ,

The stable isotope of oxygen, 180, is used as a naturally occurring ground-water tracer. Time-series data for 5 180 are analyzed to model the distinct responses and relative proportions of the conduit, intermediate, and diffuse flow components in karst aquifers. This analysis also describes mathematically the dynamics of the transient fluid interchange between conduits and diffusive networks. Conduit and intermediate flow are described by linear-systems methods, whereas diffuse flow is described by mass-balance methods. An automated optimization process estimates parameters of lognormal, Pearson type III, and gamma distributions, which are used as transfer functions in linear-systems analysis. Diffuse flow and mixing parameters also are estimated by these optimization methods. Results indicate the relative proximity of a well to a main conduit flowpath and can help to predict the movement and residence times of potential contaminants. The three-component linear model is applied to five wells, which respond to changes in the isotopic composition of point recharge water from a sinking stream in the Madison aquifer in the Black Hills of South Dakota. Flow velocities as much as 540 m/d and system memories of as much as 71 years are estimated by this method. Also, the mean, median, and standard deviation of traveltimes; time to peak response; and the relative fraction of flow for each of the three components are determined for these wells. This analysis infers that flow may branch apart and rejoin as a result of an anastomotic (or channeled) karst network. Published by Elsevier B.V