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. Seasonality is ubiquitous in nature, and it is closely linked to water quality, ecology, hydrological extremes, and water resources management.Hydrological signatures aim at extracting information about certain aspects of hydrological behaviour. Commonly used seasonal hydro-climatological signatures consider climate or streamflow seasonality, but they do not consider how climate seasonality translates into streamflow seasonality. In order to analyse the translation of seasonal climate input (precipitation minus potential evapotranspiration) into seasonal catchment output (streamflow), we represent the two time series by their seasonal (annual) Fourier mode, i.e. by sine waves. A catchment alters the input sine wave by reducing its amplitude and by shifting its phase. We propose to use these quantities, the amplitude ratio and the phase shift, as seasonal hydrological signatures. We present analytical solutions describing the response of linear reservoirs to periodic forcing to interpret the seasonal signatures in terms of configurations of linear reservoirs. Using data from the UK and the US, we show that the seasonal signatures exhibit hydrologically interpretable patterns and that they are a function of both climate and catchment attributes. Wet, rather impermeable catchments hardly attenuate the seasonal climate input. Drier catchments, especially if underlain by a productive aquifer, strongly attenuate the input sine wave leading to phase shifts up to several months. As an example application, we test whether two commonly used hydrological models (Identification of unit Hydrographs and Component flows from Rainfall, Evaporation and Streamflow – IHACRES; modele du Genie Rural a 4 parametres Journalier – GR4J) can reproduce the observed ranges of seasonal signatures in the UK. The results show that the seasonal signatures have the potential to be useful for catchment classification, predictions in ungauged catchments, and model building and evaluation. The use of potential evapotranspiration in the input restricts the applicability of the signatures to energy-limited (humid) catchments.

Hydrological signatures describing the translation of climate seasonality into streamflow seasonality