Hortonian Scaling of Coupled Hydrological and Biogeochemical Responses Across an Intensively Managed River Basin

Structural and functional attributes across fractal river networks have been characterized by well-established and consistent hierarchical, Hortonian scaling patterns. In most of the global river basins, spatial patterns of human settlements also conform to similar hierarchical scaling. However, emergent spatial hierarchical patterns and scaling of heterogeneous anthropogenic nutrient loads over a river basin are less known. As a case study, we examined here a large intensely managed river basin in Germany (Weser River; 46K km2; 8M population). Archived data for point-/diffuse-sources of total Phosphorus (Ptot) input loads were combined with numerical and analytical model simulations of coupled hydrological and biogeochemical processes for in-stream Ptot removal at the network scale. We find that Ptot input loads scale exponentially over stream-orders, with the larger scaling constant for point-source loads from urban agglomerations compared to those for diffuse-source contributions from agricultural and forested areas. These differences in scaling patterns result from hierarchical self-organization of human settlements, and the associated clustering of large-scale, altered land-cover. Fraction of Ptot loads removed through in-stream biogeochemical processes also manifests Hortonian scaling, consistent with predictions of an analytical model. Our analyses show that while smaller streams are more efficient in Ptot removal, in larger streams the magnitude of Ptot loads removed is higher. These trends are consistent with inverse scaling of nutrient removal rate constant with mean discharge, and downstream clustering of larger cumulative input loads. Analyses of six nested sub-basins within the Weser River Basin also reveal similar scaling patterns. Our findings are useful for projecting likely water-quality spatial patterns in similar river basins in Germany, and Central Europe. Extensions and generalizations require further examination of diverse basins with archetype spatial heterogeneities in anthropogenic pressures and hydroclimatic settings.