The traditional calibration objective of hydrological models is to optimize streamflow simulations. To identify the value of satellite soil moisture data in calibrating hydrological models, a new objective of optimizing soil moisture simulations has been added to bring in satellite data. However, it leads to problems: (i) how to consider the trade-off between various objectives; (ii) how to consider the uncertainty these satellite data bring in. Among existing methods, the multi-objective Bayesian calibration framework has the potential to solve both problems but is more suitable for lumped models since it can only deal with constant variances (in time and space) of model residuals. In this study, to investigate the utilization of a soil moisture product from the Soil Moisture Active Passive (SMAP) satellite in calibrating a distributed hydrological model, the DEM (Digital Elevation Model) -based Distributed Rainfall-Runoff Model (DDRM), a multi-objective Bayesian hierarchical framework is employed in two humid catchments of southwestern China. This hierarchical framework is superior to the non-hierarchical framework when applied to distributed models since it considers the spatial and temporal residual heteroscedasticity of distributed model simulations. Taking the streamflow-based single objective calibration as the benchmark, results of adding satellite soil moisture data in calibration show that (i) there is less uncertainty in streamflow simulations and better performance of soil moisture simulations either in time and space; (ii) streamflow simulations are largely affected, while soil moisture simulations are slightly affected by weights of objectives. Overall, the introduction of satellite soil moisture data in addition to observed streamflow in calibration and putting more weights on the streamflow calibration objective lead to better hydrological performance. The multi-objective Bayesian hierarchical framework implemented here successfully provides insights into the value of satellite soil moisture data in distributed model calibration.
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