Generalizable insights for nonlinear, nonstationary hydrological behavior using Ensemble Rainfall-Runoff Analysis (ERRA)

The quest for generalizable insights in hydrology begins with quantifying hydrological behavior in ways that are widely applicable (and thus potentially generalizable) and that also reflect key characteristics of hydrological processes.  Rainfall-runoff data sets are widely available, but runoff responses to individual precipitation events are rarely generalizable, because each mm of rain may affect streamflow differently, depending on how it fits into the sequence of past and future precipitation.  A longstanding approach to this problem is the unit hydrograph and its many variants, but these typically 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).  By contrast, landscape responses to precipitation are typically nonlinear and nonstationary, and quantifying this nonlinearity and nonstationarity is essential to unraveling the mechanisms and subsurface properties controlling hydrological behavior.

 

Here I show how the nonlinearity and nonstationarity of rainfall-runoff behavior can be quantified, directly from data, using Ensemble Rainfall-Runoff Analysis (ERRA), a data-driven, model-independent method for quantifying rainfall-runoff relationships across a spectrum of time lags.  ERRA 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).

 

Applications of ERRA to experimental catchments and large multi-catchment data sets reveal that some catchments exhibit substantially greater nonstationarity and nonlinearity than others do.  ERRA also reveals that some catchments exhibit strong spatial heterogeneity in their response to precipitation, resulting from spatial heterogeneity in land use and subsurface characteristics. 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.