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Analytical Propagation of Runoff Uncertainty Into Discharge Uncertainty Through a Large River Network
Author(s) -
David Cédric H.,
Hobbs Jonathan M.,
Turmon Michael J.,
Emery Charlotte M.,
Reager John T.,
Famiglietti James S.
Publication year - 2019
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2019gl083342
Subject(s) - surface runoff , discharge , environmental science , hydrology (agriculture) , propagation of uncertainty , covariance , routing (electronic design automation) , meteorology , statistics , geology , drainage basin , mathematics , computer science , geography , geotechnical engineering , ecology , computer network , cartography , biology
The transport of freshwater from continents to oceans through rivers has traditionally been estimated by routing runoff from land surface models within river models to obtain discharge. This paradigm imposes that errors are transferred from runoff to discharge, yet the analytical propagation of uncertainty from runoff to discharge has never been derived. Here we apply statistics to the continuity equation within a river network to derive two equations that propagate the mean and variance/covariance of runoff errors independently. We validate these equations in a case study of the rivers in the western United States and, for the first time, invert observed discharge errors for spatially distributed runoff errors. Our results suggest that the largest discharge error source is the joint variability of runoff errors across space, not the mean or amplitude of individual errors. Our findings significantly advance the science of error quantification in model‐based estimates of river discharge.