Temporal uncertainty estimation of discharges from rating curves using a variographic analysis

Abstract

A rating curve provides an estimation of river discharges based on stage (water level). This estimation contains a level of uncertainty. Initial uncertainty occurs at the time of establishment of the rating curve. This may be due, for example, to the randomness of natural processes or to the inaccurate measurement of the stage. Temporal uncertainty is related to the well-known processes of erosion and deposition that modify the geometry of the river bed and, consequently, the relationship between the stage and discharge. As time goes by, temporal uncertainty of the estimated discharge from a rating curve increases. Due to the widespread use of rating curves by scientists and water resource managers, it is important to assess these related uncertainties. Several studies have taken into account initial uncertainties but none, to our knowledge, has considered temporal uncertainties. The aim of this paper is to develop a methodology to estimate the temporal uncertainty of the discharge that is estimated by the rating curve. The proposed approach is based on a variographic analysis. At the beginning of rating curve validity period, the estimated discharge is believed to be distributed as a normal distribution centered on the rating curve's estimation. The initial variance of the normal distribution, according to the initial uncertainty, is fixed so that the relative uncertainty is less than 5%. A temporal variance term, estimated using a variographic analysis, is then added to the initial variance to take into account the temporal uncertainty. This term corresponds to the mean of semi-variance between estimations separated by a given time. The proposed method has been applied to 1803 gaugings from 19 hydrometric stations located in the French Alps. The 95% confidence intervals cover 90% of 1803 gaugings. This result shows that the confidence intervals are too short. However, this may be due to an underestimation of the initial variance. The method is efficient and robust since it can be adapted to various station characteristics, such as trends in discharge series or stability of the river bed.