Multiple regression and inverse moments improve the characterization of the spatial scaling behavior of daily streamflows in the Southeast United States

Abstract

Understanding the spatial structure of daily streamflow is essential for managing freshwater resources, especially in poorly gaged regions. Spatial scaling assumptions are common in flood frequency prediction (e.g., index-flood method) and the prediction of continuous streamflow at ungaged sites (e.g. drainage-area ratio), with simple scaling by drainage area being the most common assumption. In this study, scaling analyses of daily streamflow from 173 streamgages in the southeastern United States resulted in three important findings. First, the use of only positive integer moment orders, as has been done in most previous studies, captures only the probabilistic and spatial scaling behavior of flows above an exceedance probability near the median; negative moment orders (inverse moments) are needed for lower streamflows. Second, assessing scaling by using drainage area alone is shown to result in a high degree of omitted-variable bias, masking the true spatial scaling behavior. Multiple regression is shown to mitigate this bias, controlling for regional heterogeneity of basin attributes, especially those correlated with drainage area. Previous univariate scaling analyses have neglected the scaling of low-flow events and may have produced biased estimates of the spatial scaling exponent. Third, the multiple regression results show that mean flows scale with an exponent of one, low flows scale with spatial scaling exponents greater than one, and high flows scale with exponents less than one. The relationship between scaling exponents and exceedance probabilities may be a fundamental signature of regional streamflow. This signature may improve our understanding of the physical processes generating streamflow at different exceedance probabilities.

Developing and testing a global-scale regression model to quantify mean annual streamflow

“…Nevertheless, additional predictors considerably increased the explained variance (Table S1). This suggests that multiple regression improves the interpretation of the spatial scaling of MAF at a global level, in agreement with recent findings that point toward multiple regression (called "multiscaling") to improve the interpretation of scaling behavior for daily streamflow of the Southeast United States (Farmer et al, 2015).…”

“…Moreover, regression equations relating streamflow to explanatory catchment characteristics like upstream drainage area, precipitation and temperature may help to better understand general hydrological patterns and processes across different scales (Burgers et al, 2013;Farmer et al, 2015). However, to date, regression-based approaches relating mean annual streamflow to catchment characteristics have been mainly applied at a regional scale (Hortness and Berenbrock, 2001;Stuckey, 2006;Tran et al, 2015;Verdin and Worstell, 2008;Vogel et al, 1999) or to specific climate zones (Syvitski et al, 2003), and the extent to which these models can be extrapolated to other regions is not known.…”

Classical and generalized Horton laws for peak flows in rainfall-runoff events

“…Both annual maximum flood series and monthly streamflow time series were considered. We close this section with a new paper on scaling in low flows (Farmer et al, 2015). Both of the above papers directly relate to prediction in poorly gauged and ungauged basins.…”

Climate Sensitivity of Phosphorus Loadings to an Urban Stream

“…Further information on the impact of OVB on multivariate models in water resources is provided by Farmer et al. ().…”

“…However, the estimates of climate elasticity of water quality introduced by Jiang et al (2014) did not account for OVB since they only considered estimation of the sensitivity of water quality variables to changes in precipitation and temperature, separately. Further information on the impact of OVB on multivariate models in water resources is provided by Farmer et al (2015).…”