A spectral analysis to explore connections between idealized watershed properties and signal filtering

Abram Farley1, Laura Condon1
1Department of Hydrology and Atmospheric Sciences, University of Arizona

Watersheds act as low-pass filters, damping and attenuating climatic signals as they propagate through a watershed. This “reddening'' of climatic signals is a well observed phenomenon; however, the ways in which watershed properties control the nature of this filtering are less well understood. This is especially true with respect to groundwater surface water interactions. Groundwater can serve as an important temporal buffer to watersheds, but temporal shifts between precipitation, soil moisture, and groundwater are not well quantified. Here we use a physically based groundwater surface water model to simulate idealized hillslope ensembles with varying properties to quantitatively explore the relationship between watershed properties and temporal filtering. In all cases, multi-decadal simulations (~95 years) were run with a daily timestep using synthetically-generated climatic forcings derived from historical rain gauge data. The simulations capture multiple modes of variability and trends in groundwater storage and streamflow at time scales ranging from daily to seasonal to interannual. Spectral and Fourier methods were used to quantify the temporal dynamics of each simulation as well as the temporal filtering between the precipitation time series that was used to drive the model and the resulting streamflow and watershed storage time series. Hillslope geometry, hydraulic conductivity, and precipitation magnitude were varied across the ensemble to explore the relationship between filtering properties and watershed properties. With this controlled numerical approach, alterations to the input signal could be readily observed and directly quantified. For the ensemble simulated, the temporal scaling factor ( ) for the streamflow ranged from 0.33 and 0.59. This work provides insights into how various watershed configurations alter the temporal scaling of the specified variables as the signal propagates through the system.

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