1 National Space Institute, Technical University of Denmark2 Geodesy, National Space Institute, Technical University of Denmark3 Water Resources Engineering, Department of Environmental Engineering, Technical University of Denmark4 Department of Environmental Engineering, Technical University of Denmark
Calibration of large scale hydrological models have traditionally been performed using point observations, which are often sparsely distributed. The Gravity Recovery And Climate Experiment (GRACE) mission provides global remote sensing information about mass fluxes with unprecedented accuracy, which can be used for calibration of such models. Mass concentration (mascon) parameters used at the Goddard Space Flight Center are spatial and temporal step functions of equivalent water height in predefined regions, estimated directly from the level-1B K-band Range-Rate (KBRR) data from GRACE. The mascon parameters are recovered through least squares inversion of a normal equation system, which is based on partial derivatives of the KBRR data residuals with respect to the mascon parameters. Spatial and temporal constraints are added for stability reasons, and the recovered mascon parameters represent mass redistributions on/near the surface of the Earth. A grid of 1.251.5 and 1.51.5 blocks1 (latitudelongitude) is used. A simple water balance model of the Okavango River Basin covering parts of Angola, Namibia, and Botswana, is build using a modified Budyko type framework on each of seven sub-catchments, derived for the river basin from a digital elevation model. The hydrological model is initially calibrated to discharge and mass variations in a 1.251.5 grid every ten days from five years of GRACE mascon only solutions, using a joint sequential calibration function. Coupling of the mascon method with the hydrological model is done by chaining of partial derivatives, so that the normal equation system is solved for model parameters instead of mascon parameters. The mass variations from GRACE are relative, meaning that the origin is arbitrary, while the terrestrial water storage variations from model, are absolute. Thus, a bias exists between the model output and the GRACE derived mass variations, which must be accounted for by the use of bias parameters. One bias parameter is introduced for every mascon block, in order to account for the difference in level between the GRACE derived mass variations and the hydrological model, and spatial constraints on the bias parameters are used. The coupling method is tested with different correlation distances on the bias constraint equations, and different scaling of the bias parameter constraints as well as the mascon parameter constraint equations. The results are evaluated by comparing the observed and simulated data with respect to the KBRR data, the discharge data, and the terrestrial water storage from the GRACE mascon only solutions used for the initial calibration of the model. The discharge and terrestrial water storage data were also used for the initial joint model calibration. In the coupled inversion, the adjustment of the hydrology parameter in the model is in general very small, since the model was already pre-calibrated. The terrestrial water storage output from the model, using the adjusted parameter value, shows a higher annual amplitude (14.79 cm) than the mascon only solution (12.09 cm), the 10-day spherical harmonic solutions from CNES/GRGS (8.85 cm), and the terrestrial water storage from GLDAS/Noah (11.39 cm), for the same area. The annual signal peaks around March to April. The timing of signal peaks for the model output is earlier than for the mascon only solution, but later than the GLDAS/Noah TWS and the CNES/GRGS SH solutions. The deviations are 10–20 days. From this point of view, the tuning of hydrological models with KBRR data is certainly feasible, though highly time consuming and complicated at the moment. The method definitely has potential and should be tested with more model parameters and for larger models.