Quantifying nonlinearity and nonstationarity in catchment runoff response using Ensemble Rainfall-Runoff Analysis (ERRA)

Catchment hydrological response is frequently nonlinear (i.e., it varies more-than-proportionally with precipitation intensity) and nonstationary (i.e., it depends on the ambient conditions in the catchment).  This nonlinearity and nonstationarity implies that each drop of rain may affect streamflow differently, depending on how it fits into the sequence of past and future precipitation.  Thus quantifying the nonlinearity and nonstationarity in hydrological response is critical for understanding how flood behavior is shaped by catchment processes.

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 inputs occurring under different antecedent conditions) and broken-stick regression (to quantify nonlinear dependence on precipitation intensity).  I show how this approach yields a linearity exponent that quantifies how peak runoff depends on precipitation intensity, and a nonstationarity exponent that quantifies how peak runoff depends on antecedent wetness.

Here I apply this approach to data from experimental catchments and large-sample data sets, including the hourly versions of CAMELS and CAMELS-GB.  Results reveal that most catchments exhibit substantial nonlinearity and nonstationarity, but with little evidence of dramatic threshold behavior.