The process of finding a set of model parameters that “best” describes the behaviour of a model or a system is called parameter calibration. Calibration is a crucial issue in the context of Earth System (e.g., hydrology and atmosphere) modelling to simulate the underlying physical processes as realistic as possible. To obtain the optimal parameter set, the so-called cost function is defined. Then a statistical measure such as the Root Mean Squared Error (RMSE) between the model simulation outputs and measurements or the Nash-Sutcliffe coefficient (NSC) are applied to describe how well the model is tuned to the reality. To gain a feeling of the model uncertainties, often, a large ensemble of parameter sets is generated based on predefined statistical assumptions. By running the model with the different parameter sets and comparing the simulation outputs with the observations, the smallest RMSE or highest NSC identifies the “best” parameter sets and therefore the calibrated parameter values.
Traditionally, hydrological models have been calibrated against river discharge measurements. The availability of global maps of Terrestrial Water Storage Changes (TWSC) from the Gravity Recovery And Climate Experiment (GRACE) and its Follow-On mission GRACE-(FO) made it for the first time possible to globally calibrate parameters with respect to water states. Werth and Güntner (2010) presented the first investigation to use GRACE-derived TWSC to calibrate the six most sensitive parameters of a global water balance model over the 33 largest river basins worldwide. Since the GRACE-calibrated model version provided improved water storage simulations, the simultaneous calibration of model parameters had been introduced into the so-called Calibration and Data Assimilation (C/DA) system (Schumacher, 2016; GRACE(-FO) C/DA Systems).
An application of daily GRACE-derived TWS along with daily runoff measurements to calibrate a hydrological model was proposed for the first time by our group (for example see Mostafaie et al., 2018). This study compared the performance of five different calibration techniques to achieve reliable sets of parameters for tuning the GR4J hydrological models within the Danube River Basin. These techniques, from which four of them are widely used as multi-objective evolutionary algorithms for model calibration, include the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the Multi-objective Particle Swarm Optimization (MPSO), the Pareto Envelope-Based Selection Algorithm II (PESA-II), and the Strength Pareto Evolutionary Algorithm II (SPEAII). After calibration, the GR4J model we could find satisfactory performance of the model to describe the mean runoff behavior. But runoff extremes flow periods were not properly estimated. Our conclusion was that this behaviour might likely be related to the limitation of the GR4J model in representing hydro-meteorological processes like snow accumulation and snowmelt. Therefore, this research continues to assess alternative methods and extensions to improve hydrological predictions in medium and large river basins.
A comparison between simulated TWSCs and GRACE before and after calibration within the Danube River Basin during calibration (2003–2010) and validation periods. The Y axes represent TWSC while the X axes indicate time (see the details in Mostafaie et al., 2018)
Related Publications:
Werth, S., Güntner, A. (2010), Calibration analysis for water storage variability of the global hydrological model WGHM. Hydrol Earth Syst Science, 14:59–78. doi:10.5194/hess-14-59-2010
Schumacher, M. (2016), Methods for assimilating remotely-sensed water storage changes into hydrological models. PhD dissertation. University of Bonn, Germany. http://hss.ulb.uni-bonn.de/2016/4508/4508.pdf
Mostafaie, A., Forootan, E., Safari, A., Schumacher, M. (2018), Comparing multi-objective optimization techniques to calibrate a conceptual hydrological model using in situ runoff and daily GRACE data. Comput Geosci 22, 789–814, doi:10.1007/s10596-018-9726-8