Multi-variable parameter estimation for a global hydrological model: Comparison and evaluation of three ensemble-based calibration methods for the Mississippi River basin
Authors: Döll Petra , Hasan H. M. Mehedi , Schulze Kerstin , Gerdener Helena , Börger Lara , Shadkam Somayeh , Ackermann Sebastian , Hosseini-Moghari Seyed-Mohammad , Müller Schmied Hannes , Güntner Andreas , Kusche Jürgen 
Published: May 2023

Abstract. Global hydrological models enhance our understanding of the Earth system and support the sustainable management of water, food and energy in a globalized world. They integrate process knowledge with a multitude of model input data (e.g., precipitation, land cover and soil properties and location and extent of surface water bodies) that describe the state of the Earth. However, they do not fully utilize observations of model output variables (e.g., streamflow and water storage) to decrease model output uncertainty by, e.g., parameter estimation. For the pilot region Mississippi River basin, we assessed the suitability of three ensemble-based multi-variable calibration approaches for identifying both optimal and behavioral parameter sets for the global hydrological model WaterGAP, utilizing observations of streamflow (Q) and total water storage anomaly (TWSA). The common first steps in all approaches are 1) the definition of spatial units for which calibration parameters are uniformly adjusted (CDA units), combined with the selection of observation data, 2) the identification of potential calibration parameters and their a-priori probability distributions and 3) sensitivity analyses to select the most influential model parameters per CDA unit that will be adjusted by calibration. In the estimation of model output uncertainty, we considered the uncertainties of the Q and TWSA observations. We found that the Pareto-optimal calibration (POC) approach, which utilizes the Borg multi-objective evolutionary search algorithm to find Pareto-optimal parameter sets, is best suited for identifying a single “optimal” parameter set for each CDA unit. This parameter set leads to an improved fit to the monthly time series of both Q and TWSA as compared to the standard WaterGAP variant, which is only calibrated against mean annual Q, and can be used to compute the best estimate of WaterGAP output. The Generalized Likelihood Uncertainty Estimation (GLUE) approach is less suitable than POC to identify the optimal parameter set but enables the estimation of model output uncertainties that are due to the equifinality of parameter sets and the observation uncertainty. The potential advantages of the ensemble Kalman filter calibration and data assimilation (EnCDA) approach, in which both parameter sets and water storages are updated, could not be realized, likely due to the high computational burden of this approach, This limited the EnCDA ensemble size to 32, while 20,000 ensemble members could be evaluated in the case of POC and GLUE. Partitioning the whole Mississippi River basin into five CDA units (sub-basins) instead of only one improved model performance during the calibration and validation periods. Very diverse parameter sets were found to lead to similarly good fits to observations, but the range of values of three parameters could be narrowed by calibration. Model structure uncertainties, in particular regarding the operation of man-made reservoirs, the location and extent of small wetlands, and the (lacking) representation of losing river conditions in WaterGAP, are suspected to be the main reasons for the low coverage of the observation uncertainty bands by the GLUE-derived model output uncertainty bands. Model structure uncertainties are also the likely reason for major trade-offs between optimal fit to Q and TWSA. Calibration against GRACE TWSA only, in regions without Q observations, may worsen the Q simulation as compared to the uncalibrated model variant. We plan to add additional remotely-sensed observations in the multi-variable calibration of WaterGAP and suggest considering parameter uncertainty in multi-model ensemble studies of the global freshwater system.