Contrasting Patterns in the Decrease of Spatial Variability With Increasing Catchment Area Between Stream Discharge and Water Chemistry

Abstract

Understanding how spatial variability in stream discharge and water chemistry decrease with increasing catchment area is required to improve our ability to predict hydrological and biogeochemical processes in ungauged basins. We investigated differences in this decrease of variability with increasing catchment area among catchments and among specific discharge (Qs) and water chemistry parameters. We defined the slope of the decrease in the variability with increasing catchment area as the rate of decrease in the standard deviation and coefficient of variation (δSD and δCV, respectively), both of which are −0.5 for the simple mixing of random variables (random mixing). All δSD and δCV values of Qs were less than −0.5, while those of most water chemistry values were greater than −0.5, indicating that with increased catchment area the spatial variability of Qs decreased more steeply than for random mixing, while for water chemistry they decreased less steeply. δSD and δCV had linear relationships with both the spatial dissimilarity index and relative changes in parameters' mean values with increasing catchment area. It suggested that differences in δSD or δCV for Qs and water chemistry can be explained by the different spatial structures, where dissimilar values of Qs and similar values of water chemistry, respectively, are located close together in space. Differences in δSD and δCV according to Qs and water chemistry should significantly affect the determination of representative elementary area and therefore need to be considered when predicting representative elementary area from spatial variability of low‐order streams.

A multi‐scale study of the dominant catchment characteristics impacting low‐flow metrics

“…These findings highlight the importance of subsurface transport (through the streambed, in the deeper subsurface or even across catchments) and storage in alluvial sediments. Similar spatial variation in low flows was reported for example by Payn et al (2012) for a mountain watershed in the US and by Egusa et al (2016 & 2019) for a steep catchment in Japan and attributed to subsurface water transport.…”

Is the River a Chemostat?: Scale Versus Land Use Controls on Nitrate Concentration‐Discharge Dynamics in the Upper Mississippi River Basin

“…Aggregation of discharge signals results in an area-weighted mean of the tributary basins, and similarly, the concentration of a solute in a river may be considered as the volume-weighted mean of the concentrations of its tributaries. The CV of these signals should thus decrease when aggregating an increasing number of tributaries, analogous to a central limit theorem (Egusa et al, 2019). However, the rate at which the CV of a concentration or discharge signal decreases with an increasing number of tributaries will depend strongly on the correlation of signals among tributaries.…”

“…In contrast, in the case of perfectly correlated variables, the CV of the summed signal will remain constant regardless of the number of variables summed (slope = 0). Translating this to a river network application, the degree of correlation among tributaries for both discharge and concentration signals will determine the rate at which the CV of the signal decreases with increasing levels of aggregation as basins grow larger ( Figure S3a) (Asano & Uchida, 2010;Egusa et al, 2019). Our finding of a higher (i.e., less negative) slope of the CV C -area relationship (−0.07) compared to the slope of the CV Q -area relationship (−0.23) thus suggests that NO 3 − concentrations are more highly correlated between subbasins in the UMRB than discharge.…”

An Increase in Specific Discharge With Catchment Area Implies That Bedrock Infiltration Feeds Large Rather Than Small Mountain Headwater Streams

“…It is often more difficult to understand processes in mesoscale catchments than in smaller catchments, because it is difficult to conduct sufficiently detailed measurements to characterize the internal flow system of a catchment, except at a few intensively studied sites (e.g., Didszun & Uhlenbrook, 2008; Sayama et al, 2011). The relationship between catchment area and the pattern in the runoff response to rainfall can elucidate catchment processes (e.g., Asano et al, 2018; Blöschl & Sivapalan, 1997; Egusa et al, 2019; Soulsby et al, 2009; Temnerud et al, 2007). The main landscape units that contribute to baseflow may shift from hillslope soil to bedrock, riparian areas, or other features as the catchment area increases (e.g., Gomi et al, 2002).…”