Temporal variability in stage–discharge relationships

SummaryAlthough discharge estimations are central for water management and hydropower, there are few studies on the variability and uncertainty of their basis; deriving discharge from stage heights through the use of a rating curve that depends on riverbed geometry. A large fraction of the world’s river-discharge stations are presumably located in alluvial channels where riverbed characteristics may change over time because of erosion and sedimentation. This study was conducted to analyse and quantify the dynamic relationship between stage and discharge and to determine to what degree currently used methods are able to account for such variability. The study was carried out for six hydrometric stations in the upper Choluteca River basin, Honduras, where a set of unusually frequent stage–discharge data are available. The temporal variability and the uncertainty of the rating curve and its parameters were analysed through a Monte Carlo (MC) analysis on a moving window of data using the Generalised Likelihood Uncertainty Estimation (GLUE) methodology. Acceptable ranges for the values of the rating-curve parameters were determined from riverbed surveys at the six stations, and the sampling space was constrained according to those ranges, using three-dimensional alpha shapes. Temporal variability was analysed in three ways: (i) with annually updated rating curves (simulating Honduran practices), (ii) a rating curve for each time window, and (iii) a smoothed, continuous dynamic rating curve derived from the MC analysis. The temporal variability of the rating parameters translated into a high rating-curve variability. The variability could turn out as increasing or decreasing trends and/or cyclic behaviour. There was a tendency at all stations to a seasonal variability. The discharge at a given stage could vary by a factor of two or more. The quotient in discharge volumes estimated from dynamic and static rating curves varied between 0.5 and 1.5. The difference between discharge volumes derived from static and dynamic curves was largest for sub-daily ratings but stayed large also for monthly and yearly totals. The relative uncertainty was largest for low flows but it was considerable also for intermediate and large flows. The standard procedure of adjusting rating curves when calculated and observed discharge differ by more than 5% would have required continuously updated rating curves at the studied locations. We believe that these findings can be applicable to many other discharge stations around the globe.

► Traditional rating curves cannot cope with a variable stage-discharge relationship.
► The rating parameters can be constrained using topography and Manning´s equation.
► Static rating curves can yield large errors in discharge estimation.
► Different objective functions and models yield different discharge quantifications.
► A time-dependent parameter can account for the temporal variability of ratings.