A Physically‐Based Reverse‐Stage Routing Model Considering Lateral Flow for Establishing Normal Rating Curves at Ungauged Upstream River Sections

Abstract

AbstractMany of the world‐rivers are often ungauged or poorly gauged due to inadequate streamflow monitoring networks. Even with the limited available monitoring stations, only a few of them monitor both stage and discharge data. But when there is a need for estimation of discharges at a gauging station, where only stage data is monitored, one may employ a reverse routing technique using the stage data monitored at a nearby downstream gauging station. This study develops a novel single‐parameter reverse‐stage routing (RSR) model based on the second‐order approximate water surface gradient governing equation to estimate stage and discharge at any scantily‐gauged upstream river section using the known stage information available at the downstream section. A novel criterion is also developed for checking the applicability of the RSR model. Reverse routing experiments, carried out by the RSR model using different hypothetical downstream stage hydrographs in a number of hypothetical trapezoidal and rectangular channel reaches to reproduce the benchmark upstream stage and discharge hydrographs, demonstrate the good performance of the RSR model with the Nash–Sutcliffe Efficiency >98%, absolute volume conservation error <1.5%, and an absolute error in peak ≤1%. Subsequently, the RSR model was tested for three real‐river case studies in India and Italy with good reproduction performances, and along with the development of the corresponding normal rating curves at the upstream river sections. The study results reveal that the parsimonious RSR model has good potential for solving reverse routing problems with stable numerical solutions for rivers under ungauged and scantily‐gauged scenarios.