in the paper below we studied the dynamics of water parameter change in wells that demonstrated the change of aquifer. We used VMD-Petro software developed in my project for visualization of such dynamics.
Sheremetov L., Cosultchi A., Batyrshin A., Velasco-Hernandez J. Application of pattern recognition techniques to hydrogeological modeling of mature oil fields. - Lecture Notes on Computer Science, vol. 6718, 2011, pp.85-94. Springer-Verlag
Berlin Heidelberg. 3rd Mexican Conference on Pattern Recognition, June 29 - July 2, 2011. J.-F. Martínez-Trinidad et al. (Eds.): MCPR 2011.
I used time series analyses (autocorrelation and crosscorrelation) for investigating the bahaviour of karst springs in Classical karst in Slovenia (Europe). Thise is a statistical approach, which is suitable for regional chracterization of karst aquifers. Here you can follow the link to one of my articles regarding this subject (see references in this paper for others). http://carsologica.zrc-sazu.si/downloads/392/Kovacic.pdf
The difficulty in modeling the karst hydrodynamics is that karsts have a heterogeneous structure. This heterogeneousness implies that physical properties are very different considering the scale of observation, or the place of observation (implying non linearity). Consequently, measurements are not representative of the whole karst. For these reasons the systemic paradigm introduced for karst systems by Alain Mangin is a good approach.
Linear correlations and cross correlation developed in this framework are useful but can't take into account the non-linearity. Others methods must be developed, for example AMI (Average Mutual Information), or machine learning (neural networks, ...). My preference is for neural networks because they can identify nonlinear and dynamic models. They can perform forecasting. Moreover we have shown that they can help to better understand the considered aquifer. See for instance several paper of our tem on this subject :
1) KnoX method, or Knowledge eXtraction from Neural Network model. Case study on the Lez karst aquifer (southern France)
Line Kong A Siou, Kévin Cros, Anne Johannet, Valérie Borrell-Estupina, Séverin Pistre
Journal of Hydrology (Impact Factor: 2.66). 10/2013; In press.
2) Complexity selection of a neural network model for karst flood forecasting: The case of the Lez Basin (southern France)
Line Kong A Siou, Anne Johannet, Valérie Borrell, Séverin Pistre
Journal of Hydrology. 01/2011; 403:367-380.
3) Prediction of Spring Discharge by Neural Networks using Orthogonal Wavelet Decomposition
anne johannet, Line Kong-A-Siou, Alain Mangin, Valérie Borrell, Séverin Pistre, Dominique Bertin
2012 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN); 01/2012
Karst is very difficult to study if you don't have a good knowledge of the aquifer structure. The discharge chronicles are often uncomplete as low discharges and floods are usually not measured. It is also very difficult to know all the water outlets
Some karst systems have several perennial or temporary springs. Another problem is the existence of deep leaks and the possibility to have communications with other aquifers (karst or alluvial ones). The behavior may be very different between high and low water periods.
Thus discharge time series from a spring only give data on part of the aquifer.
For modelling, in addition to the previously described softwares, you may also try VENSIM. You create different reservoirs (rain fall, epikarst, drains, ...) and affect filling and emptying formulas to each of them. It is not the worse one. Good luck...