22 Apr 2024
 | 22 Apr 2024
Status: this preprint is currently under review for the journal HESS.

Characterizing nonlinear, nonstationary, and heterogeneous hydrologic behavior using Ensemble Rainfall-Runoff Analysis (ERRA): proof of concept

James W. Kirchner

Abstract. A classical approach to understanding hydrological behavior is the unit hydrograph and its many variants, but these often assume linearity (runoff response is proportional to effective precipitation), stationarity (runoff response to a given unit of rainfall is identical, regardless of when it falls), and spatial homogeneity (runoff response depends only on spatially averaged precipitation). In the real world, by contrast, runoff response is typically nonlinear, nonstationary, and spatially heterogeneous. Quantifying this nonlinearity, nonstationarity, and spatial heterogeneity is essential to unraveling the mechanisms and subsurface properties controlling hydrological behavior.

Here I present proof-of-concept demonstrations illustrating how nonlinear, nonstationary, and spatially heterogeneous rainfall-runoff behavior can be quantified, directly from data, using Ensemble Rainfall-Runoff Analysis (ERRA), a data-driven, nonparametric, model-independent method for quantifying rainfall-runoff relationships across a spectrum of time lags. I show how ERRA uses nonlinear deconvolution to quantify how catchments' runoff response varies with precipitation intensity, and also to estimate their precipitation-weighted runoff response distributions. I further illustrate how ERRA combines nonlinear deconvolution with demixing techniques to reveal how runoff response depends jointly on precipitation intensity and nonstationary ambient conditions, including antecedent wetness and vapor pressure deficit. I demonstrate how ERRA's demixing techniques can be used to quantify spatially heterogeneous runoff response in different parts of a catchment, even if those subcatchments are not separately gauged. I also illustrate how ERRA's broken-stick deconvolution capabilities can be used to quantify multiscale runoff responses that combine hydrograph peaks lasting for hours and recessions lasting for weeks, well beyond the average spacing between storms.

ERRA can unscramble these multiple effects on runoff response even if they are overprinted on each other through time, and even if they are corrupted by autoregressive moving average (ARMA) noise. Results from this approach may be informative for catchment characterization, process understanding, and model-data comparisons; they may also lead to a better understanding of storage dynamics and landscape-scale connectivity. An R script is provided to perform the necessary calculations, including uncertainty analysis.

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James W. Kirchner

Status: open (until 17 Jun 2024)

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James W. Kirchner
James W. Kirchner


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Short summary
Here I present a new way of quantifying how streamflow responds to rainfall across a range of timescales. This approach can estimate how different rainfall intensities affect streamflow, and how that may vary, depending on how wet the landscape already is when the rain falls. This may help us to understand processes that regulate streamflow, as well as the susceptibility of different landscapes to flooding.