Multivariate calibration of large scale hydrologic models: The necessity and value of a Pareto optimal approach

Multivariate calibration using measurements of multiple water balance components has emerged as a potential solution for improving the performance and realism of large scale hydrologic models. In this study we develop a novel multivariate calibration framework to rigorously test whether incorporation of multiple water balance components into calibration can result in sufficiently accurate (behavioral) solutions for all model responses. Unlike previous studies, we use Bayesian calibration to formally define limits of acceptability or error thresholds in order to distinguish behavioral solutions for each of the incorporated fluxes. We apply the framework in the Mississippi river basin for the calibration of a large scale distributed hydrologic model (Noah-MP) with different combinations of model responses - evapotranspiration (ET), soil moisture (SM), and streamflow (SF). The results of the study show that incorporation of additional fluxes and soil moisture (a storage variable) is not always valuable due to significant trade-offs in accuracy among the model responses. In our experiments, only ET and SF could be simulated simultaneously to a reasonable degree of accuracy. In addition, we quantify the trade-offs in accuracy between the model responses using the concept of Pareto optimality. We find that combining ET with other fluxes entails higher trade-offs in accuracy compared to either SM or SF. Unlike deterministic calibration, with the developed framework we are able to identify deficiencies in model parameterization that lead to significant trade-offs in accuracy, especially between ET and SM. We find that the parameters which are insensitive to individual model responses can influence the trade-off relationship between them.