Improving the spectral analysis of hydrological signals to efficiently constrain watershed properties

The footprint of catchment properties on water flow is reflected into hydrological signals, such as stream discharge. Here we demonstrate that it is possible to constrain catchment properties from the spectral analysis of hydrological signals but only when an appropriate transfer function (TF) is used for interpretation. We show that the appropriate theoretical TF, newly derived, is the only one to robustly describe a large diversity of experimental TFs that could be encountered in nature, because it entails the role of diffuse overflow and flow through the vadose zone, which have never been considered in spectral approaches before. The properties that may be estimated are the characteristic time scales of transfer in each compartment (surface, vadose zone, and aquifer) and the flow partitioning between surface and subsurface. We validate our approach by comparing the new and previous theoretical TFs to experimental TFs generated by a physically based distributed hydrological model, for a wide range of properties. The results confirm that without the use of the new TF, the interpretation of observed spectra may often lead to severe misestimations of catchment properties. The potential of the new TF to constrain catchment characteristics is exemplified by analyzing real hydrological signals from two watersheds with distinct behaviors. We finally discuss the broad implications of our findings and how they may contribute to a variety of topics in hydrology, thereby opening the way to a more widespread and robust use of spectral analysis to describe hydrosystems from effective rainfall, river discharge, and piezometric data. Plain Language Summary Time series of hydrological variables, such as river discharge rates or groundwater levels, are very different from the rainfall signal that feeds continental hydrosystems. In addition, different watersheds undergoing similar climatic conditions do not produce similar hydrological responses. Therefore, deciphering how a climatic signal is altered and retranscribed into hydrological signals is a difficult task. Nevertheless, understanding how hydrosystems react to different time scales of climatic forcing remains an important challenge for water management, as it is key to predicting extreme hydrological events (severe droughts and floods). Here we develop and validate a new approach to study the impact of various hydrological compartments (such as surface waters or subsurface waters) on climatic signal transformation. We use a spectral domain approach, meaning that river discharge, for instance, is not seen as function of time but rather as a function of the various elementary frenquencies that compose the signal. We demonstrate that our new approach favors the interpretation of data in the spectral domain and thereby enhances comprehension of flow processes in response to different time scales of climatic inputs.