Assessing the Nonlinearity of Karst Response Function under Variable Boundary Conditions

The hydraulic and transfer response of karst aquifers is complex and often highly nonlinear: due to their high transmissivity and connection with the surface, such systems are very sensitive to modifications of their boundary conditions. The aim of this study was to assess the variation of the response depending on both upstream and downstream parameters, and propose a methodology to simulate the response of the karst system depending on those parameters. The impact of the variations of multiple environmental parameters on the response of a karstic system submitted to tidal variations (Normandy, France) was investigated after a campaign of artificial tracer tests acquired in very different hydrologic conditions (rainfall events, low tide, high tide, low/high piezometric level, and low/high waters). Principal components analysis and hierarchical clustering were applied on both environmental variables and karstic system response variables (parameters of the residence time distribution [RTD] curves). Equations between the RTD parameters and the most relevant variables were established using a symbolic regression algorithm. It appeared that the variations of the RTD parameters depend mainly on the cumulated rainfall preceding the injection, the piezometric level of the aquifer, and on the tide parameters. The hydraulic conditions downstream of the aquifer have a strong influence on the hydraulic and transfer response of the aquifer. The response of the aquifer in various and extreme conditions has been simulated using the equations resulting from the symbolic regression algorithm. Such relationships can be useful for management of water resources in karst media, and support decision making.