A spectral approach to evaluate the groundwater response time at regional scale

Abstract:

Streamflow is the integrated response of a catchment to precipitation. Following a conceptual approach, we can model this integrated response as outflows from a series of three compartments representing the direct runoff, the interflow and the baseflow. The latter, which predominately sustains the discharge during dry periods, generates mainly from groundwater. The aquifer's response time to external perturbations (e.g., recharge) plays a central role in stream flow propagation during dry periods (or droughts) and depends on the underlying catchment hydro-geological characteristics. The traditional method to infer the response time is through a recession analysis, under the assumption of zero recharge. However, such an assumption might lead to a misleading evaluation of response time, when it is not met in reality.

Here, we propose an alternative method to evaluate the aquifer response time based on the spectral analysis approach. The underlying reasoning is based on the assumption that the aquifer acts as a low-pass filter, transforming the input signal (e.g., the recharge) in the output signal (e.g., the baseflow). An equation for a linear reservoir – a common approach used for representing groundwater outflows at regional or large scale models - is solved in the Fourier domain, thereby leading to an analytical solution of the transfer function. For lower frequencies the transfer function remains constant, while it scales for higher frequencies due to the low-pass filter characteristic of the aquifer. This introduces a breaking point which corresponds to the characteristic time of the diffusive system.

We tested our approach across a wide range of European catchments using stream flow datasets. The spectral analysis leads to a response time shorter than the one evaluated by recession analysis. Our results also show that the linear reservoir is a good approximation for natural aquifer at a regional scale. Our approach can help to evaluate the response time in humid regions, where the recharge during recession periods cannot be neglected. Moreover, response time can serve as a valuable indicator for analyzing the effect of possible external perturbation (climate or land management changes) on aquifer resilience.