Observational uncertainty in hydrological modelling using data depth

For any river basin management, one needs tools to predict runoff at different time and spatial resolutions. Hydrological models are tools which account for the storage, flow of water and water balance in a watershed, which include exchanges of water and energy within the earth, atmosphere and oceans and utilise metrological data to generate flow. There are several sources of error in meteorological data, namely, through measurement at point level, interpolation, etc. When an erroneous input is passed to a model, one cannot expect an error free output from the prediction. Every prediction is associated with uncertainty. Quantification of these uncertainties is of prime importance in real world forecasting. In this study, an attempt has been made to study uncertainty associated with hydrological modelling, using the idea of data depth. To see the effect of uncertainty in rainfall on flow generation through a model, the input to a model was altered by adding an error and a different realisation was made. A Monte Carlo simulation generated a large number of hydrological model parameter sets drawn from the uniform distribution. The model was run using these parameters for each realisation of the rainfall. The parameters which are good for different realisations are more likely to be good parameters sets. For each parameter set, data depth was calculated and a likelihood was assigned to each parameter set based on the depth values. Based on this, the frequency distribution of the likelihood was analysed as well. The results show that uncertainty in hydrological modelling are multiplicative. The proposed methodology to assign prediction uncertainty is demonstrated using the 'TopNet' model for the Waipara river catchment located in the central east of the South Island, New Zealand. The results of this study will be helpful in calibration of hydrological model and in quantifying uncertainty in the prediction.