Regionalisation of hydrological model parameters under parameter uncertainty: A case study involving TOPMODEL and basins across the globe

Abstract

In this paper, we present a method to account for modeling uncertainties while regionalising model parameters. Linking model parameters to physical catchment attributes is a popular approach that enables the application of a conceptual model to an ungauged site. The functional relationship can be derived either from the calibrated model parameters (direct calibration method) or by calibrating the functional function (regional calibration method). Both of these approaches are explored through a case study involving TOPMODEL and a number of small- to medium-sized humid basins located in various geographic and climatic regions around the globe. The predictive performance of the functional relationship derived using the direct calibration method (e.g., multiple regression, artificial neural network and partial least square regression) varied among the different schemes. However, the average of the model parameters estimated from regionalisation schemes based on direct calibration is found to be a better surrogate. Even with the use of a parsimonious hydrological model and with posing model calibration as a multi-objective problem, the model parameter uncertainty and its effect on model prediction were observed to be high and varied among the basins. Therefore, to avoid the effect of model parameter uncertainty on regionalization results, a regional calibration method that skips direct calibration of the hydrological model was implemented. This method was improved in order to take into account multiple objective criteria while calibrating regional parameters. The predictive performance of the improved regional calibration method was found to be superior to the direct calibration method, indicating that the identifiability of model parameters has an apparent effect on deriving predictive models for regionalisation. However, the regional calibration method was unable to uniquely identify the regional relationship, and the modeling uncertainties quantified using Pareto optimal regional relationships were considerable. Regionalisation schemes that are based on direct calibration do not explicitly account for the modeling uncertainties. Therefore, to account for these uncertainties in model parameters and regionalisation schemes, methods based on regionalisation of vectors of model parameters (i.e. regionalizing the vectors of equally likely values of model parameters) and posterior probability distribution of model parameters (i.e. estimating the posterior probability distribution of model parameters at ungauged sites by linking the entries of model parameters’ covariance matrix and the posterior mean of model parameter to the catchment attributes) are introduced. The uncertainties in model prediction as quantified from both methods closely followed the prediction uncertainties quantified from calibrated posterior probability distributions of model parameters. Moreover, though the prediction uncertainties associated with the regional calibration method as quantified from the Pareto optimal regional relationship were comparatively higher than those obtained from the direct calibration schemes, they were in close agreement with the prediction uncertainties quantified from the calibrated posterior probability distribution. The ensemble of simulated flows realized from the model parameters sampled from regionalized posterior probability distributions for five ungauged basins are also presented as validation of the proposed methodology.