Dropping the rating curve

Calibrating a rainfall-runoff model on stage to reduce discharge uncertainty

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Abstract

Direct measurement of river discharge is time consuming and financially demanding. Continuous river discharge measurements are therefore generally derived from continuous stage measurements, through a stage-discharge relation, also called a rating curve. Rating curves are determined by fitting a curve to a limited number of points (hi, Qi), whereby hi and Qi represent stage and discharge measured in a certain cross-section of a river at a fixed geographical location. Commonly these points (hi, Qi) originate from measurements done under regular flow conditions, due to which a considerable part of the curve is based on interpolation and extrapolation. Therefore the uncertainty in the rating curve particularly during floods can be considerable, which directly translates into uncertainty in the discharge data. Calibrating a model on uncertain discharge observations leads to biased model parameter estimates, which directly lead to biased model predictions. This research shows an approach whereby a conceptual rainfall-runoff model is calibrated on the basis of stage data only. In addition to the existing conceptual model parameters, extra parameters have been added that define the rating curve. A stepwise calibration method has been applied whereby first the rating curve parameters were determined and subsequently the remaining model parameters. Once the rating curve parameters had been fixed, the reanalysed hydrograph was established using the observed stage readings. Subsequently, the model hypotheses on catchment behaviour were tested by conventional methods. In this research these methods have been applied to the scarcely gauged Endau River catchment, located in the South-East of peninsula Malaysia. The initial results are promising. It was found that the rating curve parameters are well defined and optimise to values that correspond to the physical property they represent. When comparing the reanalysed rating curve with the original rating curve it can be seen that the initial part of the rating curve overlaps, corresponding with the most reliable part of the original rating curve. When comparing the reanalysed rating curves with discharge measurements, a high correspondence is observed, while the similarity between the measurements and the original rating curve is very low. Finally, the modelled hydrographs appear to be relatively well able to mimic the reanalysed hydrograph, even though it was impossible to find a proper model for the original hydrograph. To test the sensitivity of the calibrated rating curve to model structure, both a lumped and a topography driven model structure have been tested. Additionally, these models were exposed to two rating curve definitions and a variable model forcing. The results of this sensitivity analysis show that the calibrated rating curve is relatively insensitive to model structure and relatively sensitive to the number of parameters used for the rating curve definition. Concerning the forcing, the rating curve is highly sensitive to precipitation and less sensitive to potential evaporation. The reason for this sensitivity is that the established rating curve is strongly determined by the water balance, which is dominated by the primary driver P. The calibrated models have been validated on independent data by split-sample validation and by transfer to a different catchment. The topography driven models appear to perform best during both forms of validation. An additional way of validating was carried out by coupling the best performing rainfall-runoff model to a steady state salt intrusion model: a novel approach which offers mutual model validation. The results show that the predicted discharge of the rainfall-runoff model corresponds rather well with the discharge determined by the salt model. So, the most important conclusions from this research are: calibration of a rainfall-runoff model on stage reduces discharge uncertainty in scarcely gauged basins; topography driven models are better transferable than lumped models; and linking a salt intrusion model to a rainfall-runoff model offers mutual model improvement.