Signatures of catchment nonlinearity and nonstationarity, quantified using Ensemble Rainfall-Runoff Analysis

It is almost axiomatic that catchment response to precipitation is nonlinear and nonstationary, implying that each drop of rain may affect streamflow differently, depending on how it fits into the sequence of past and future precipitation.  But do most catchments exhibit similar patterns of nonlinearity and nonstationarity, or not?  If not, which ones are more nonstationary (i.e., more sensitive to antecedent precipitation)?  Which ones are more nonlinear?  And why? 

Understanding catchments’ nonlinear and nonstationary behavior requires widely applicable tools for characterizing and quantifying that behavior in the first place. Here show how catchment nonstationarity and nonlinearity can be quantified using Ensemble Rainfall-Runoff Analysis (ERRA), a data-driven, model-independent method for quantifying rainfall-runoff relationships across a spectrum of time lags.  ERRA is superficially similar to classical unit hydrograph methods, but whereas unit hydrographs assume linearity (runoff response is proportional to precipitation) and stationarity (runoff response to a given unit of rainfall is identical, regardless of when it falls), ERRA can explicitly quantify the nonlinearity and nonstationarity in rainfall-runoff relationships, directly from data.  This approach combines least-squares deconvolution (to un-scramble each input's temporally overlapping effects) with demixing techniques (to separate the effects of individual inputs, or inputs occurring under different antecedent conditions) and broken-stick regression (to quantify nonlinear dependencies). 

Not only can this approach quantify the impulse response of streamflow to precipitation, it can also quantify how this impulse response changes with rainfall rates (nonlinearity), how it varies with catchment wetness (nonstationarity), and how it differs for rain falling on different parts of the landscape (heterogeneity), even if these signals are all overprinted on one another at the catchment outlet.  Results from this approach may be informative for catchment characterization and runoff forecasting; they may also lead to a better understanding of short-term storage dynamics and landscape-scale connectivity.  Applications of these methods will be illustrated using large multi-catchment data sets from Switzerland and North America.