Rainfall-runoff modelling using river-stage time series in the absence of reliable discharge information: a case study in the semi-arid Mara River basin

Hydrological models play an important role in water resources management. These models generally rely on discharge data for calibration. Discharge time series are normally derived from observed water levels by using a rating curve. However, this method suffers from many uncertainties due to insufficient observations, inadequate rating curve fitting procedures, rating curve extrapolation, and temporal changes in the river geometry. Unfortunately, this problem is prominent in many African river basins. In this study, an alternative calibration method is presented using water-level time series instead of discharge, applied to a semi-distributed rainfall-runoff model for the semi-arid and poorly gauged Mara River basin in Kenya. The modelled discharges were converted into water levels using the Stickler-Manning formula. This method produces an additional model output; this is a "geometric rating curve equation" that relates the modelled discharge to the observed water level using the Stickler-Manning formula and a calibrated slope-roughness parameter. This procedure resulted in good and consistent model results during calibration and validation. The hydrological model was able to reproduce the water levels for the entire basin as well as for the Nyangores sub-catchment in the north. The newly derived geometric rating curves were subsequently compared to the existing rating curves. At the catchment outlet of the Mara, these differed significantly, most likely due to uncertainties in the recorded discharge time series. However, at the "Nyangores" sub-catchment, the geometric and recorded discharge were almost identical. In conclusion, the results obtained for the Mara River basin illustrate that with the proposed calibration method, the water-level time series can be simulated well, and that the discharge-water-level relation can also be derived, even in catchments with uncertain or lacking rating curve information.