Leveraging multi-variable observations to reduce and quantify the output uncertainty of a global hydrological model: evaluation of three ensemble-based approaches for the Mississippi River basin
Authors: Döll Petra , Hasan Howlader Mohammad Mehedi , Schulze Kerstin , Gerdener Helena , Börger Lara , Shadkam Somayeh , Ackermann Sebastian , Hosseini-Moghari Seyed-Mohammad , Müller Schmied Hannes , Güntner Andreas , Kusche Jürgen 
Published: May 2024

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, soil properties, and the location and extent of surface waterbodies) to describe the state of the Earth. However, they do not fully utilize observations of model output variables (e.g., streamflow and water storage) to reduce and quantify model output uncertainty through processes like parameter estimation. For a pilot region, the Mississippi River basin, we assessed the suitability of three ensemble-based multi-variable approaches to amend this: Pareto-optimal calibration (POC); the generalized likelihood uncertainty estimation (GLUE); and the ensemble Kalman filter, here modified for joint calibration and data assimilation (EnCDA). The paper shows how observations of streamflow (Q) and terrestrial water storage anomaly (TWSA) can be utilized to reduce and quantify the uncertainty of model output by identifying optimal and behavioral parameter sets for individual drainage basins. The common first steps in all approaches are (1) the definition of drainage basins for which calibration parameters are uniformly adjusted (CDA units), combined with the selection of observational 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. Data assimilation with the ensemble Kalman filter was modified, to our knowledge, for the first time for a global hydrological model to assimilate both TWSA and Q with simultaneous parameter adjustment. In the estimation of model output uncertainty, we considered the uncertainties of the Q and TWSA observations. Applying the global hydrological model WaterGAP, we found that the POC approach 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 GLUE approach is almost as successful as POC in increasing WaterGAP performance and also allows, with a comparable computational effort, the estimation of model output uncertainties that are due to the equifinality of parameter sets given the observation uncertainties. Our experiment reveals that the EnCDA approach performs similarly to POC and GLUE in most CDA units during the assimilation phase but is not yet competitive for calibrating global hydrological models; its potential advantages remain unrealized, likely due to its high computational burden, which severely limits the ensemble size, and the intrinsic nonlinearity in simulating Q. Partitioning the whole Mississippi River basin into five CDA units (sub-basins) instead of only one improved model performance in terms of the Nash–Sutcliffe efficiency during the calibration and validation periods. Diverse parameter sets achieved comparable fits to observations, narrowing the range for at least three parameters. Low coverage of observation uncertainty bands by GLUE-derived model output bands is attributed to model structure uncertainties, especially regarding artificial reservoir operations, the location and extent of small wetlands, and the lack of representation of rivers that may lose water to the subsurface. These uncertainties are also likely to be responsible for significant trade-offs between optimal fits to Q and TWSA. Calibration performed exclusively against TWSA in regions without Q observations may worsen the Q simulation as compared to the uncalibrated model variant. We recommend that modelers improve the realism of the output of global hydrological models by calibrating them against observations of multiple output variables, including at least Q and TWSA. Further work on improving the numerical efficiency of the EnCDA approach is necessary.