EVALUATION OF TRANSFER FUNCTION NOISE MODELLING AND DIMENSIONALITY REDUCTION TECHNIQUES FOR KARST SYSTEMS

Though karst aquifers are important sources of drinking water on a global scale, these systems are still insufficiently understood regarding adequate model representation. Time Series Analysis (TSA), as a data-driven approach, has been demonstrated to be useful for the characterization of karst system hydrodynamics with sparse data. Recently, transfer function noise (TFN) modelling with predefined impulse response functions, as a linear TSA-method, has been applied to analyze and manage groundwater systems. In this approach, impulse response functions in continuous time are used to describe the system response (e.g., spring discharge) to independent stress input time series (e.g., precipitation).

The goal of this study is to evaluate the suitability of TFN models and dimensionality reduction (DR) techniques to simulate and study karst systems. To reach this objective, the following steps are carried out. First, we develop synthetic karst systems using the distributed numerical flow code MODFLOW-CFP. With these models we generate data to be in turn modeled by the TFN approach. After fitting the TFN models to the synthetic data, the corresponding parameter spaces are explored and studied using DR methods. In combination with statistical model diagnostics, all results are used to evaluate the applicability of TFN models for karst systems. Lastly, we study a real karst system with the proposed framework.

The TFN model may have a large number of parameters of which not all may be physically interpretable. DR techniques can be used to study the model parameter space, identify most important parameters, and potentially lower the total number of model dimensions. Because the technique has been used before in karst hydrology, we employ active subspaces as a linear DR method.

Preliminary results show that the TFN approach may be used to model karst spring discharge, as evaluated according to fit metrics. When using complex TFN models, though, the initial solutions were found not to be unique. Lower dimensional structures could be identified independently of general TFN model structure or defined response function. Preliminarily, linear DR may be insufficient in capturing the lower dimensional structures, however giving the most useful results for further applications.