Premium
Spatiotemporal averaging of in‐stream solute removal dynamics
Author(s) -
Basu Nandita B.,
Rao P. Suresh C.,
Thompson Sally E.,
Loukinova Natalia V.,
Donner Simon D.,
Ye Sheng,
Sivapalan Murugesu
Publication year - 2011
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2010wr010196
Subject(s) - biogeochemical cycle , scaling , inverse , exponent , environmental science , soil science , hydrology (agriculture) , statistical physics , mathematics , physics , ecology , geology , geometry , linguistics , philosophy , geotechnical engineering , biology
The scale dependence of nutrient loads exported from a catchment is a function of complex interactions between hydrologic and biogeochemical processes that modulate the input signals from the hillslope by aggregation and attenuation in a converging river network. Observational data support an empirical inverse relation between the biogeochemical cycling rate constant for nitrate k (T −1 ) and the stream stage h (L), k = v f / h , with v f , the uptake velocity ( LT −1 ), being constant in space under steady flow conditions. Here we offer a physical explanation for the persistence of this pattern across scales and then extend the analysis to spatiotemporal scaling of k under transient‐flow conditions. Inverse k ‐ h dependence arose as an emergent pattern by coupling the mechanistic Transient Storage Model with a network model. Analytical modeling indicated that (1) nitrate processing efficiency increases with increasing variability in the discharge Q and (2) temporal averaging had no effect on the exponent a of the k ‐ h relationship ( k = v f / h a ) in catchments with low Q variability, but strong dependence arose in catchments with high variability in Q . Network modeling in domains with low Q variability confirmed that the exponent a was independent of temporal averaging, but v f was a function of the averaging timescale. The probability distribution functions for k could be adequately predicted using analytical approaches. Understanding the k ‐ h scaling relationships enables the direct estimation of the variability in nutrient losses due to in‐stream reactions without requiring explicit information for spatially distributed network modeling.