S U M M A R YMost applications of the publicly released Gravity Recovery and Climate Experiment monthly gravity field models require the application of a spatial filter to help suppressing noise and other systematic errors present in the data. The most common approach makes use of a simple Gaussian averaging process, which is often combined with a 'destriping' technique in which coefficient correlations within a given degree are removed. As brute force methods, neither of these techniques takes into consideration the statistical information from the gravity solution itself and, while they perform well overall, they can often end up removing more signal than necessary. Other optimal filters have been proposed in the literature; however, none have attempted to make full use of all information available from the monthly solutions. By examining the underlying principles of filter design, a filter has been developed that incorporates the noise and full signal variance-covariance matrix to tailor the filter to the error characteristics of a particular monthly solution. The filter is both anisotropic and nonsymmetric, meaning it can accommodate noise of an arbitrary shape, such as the characteristic stripes. The filter minimizes the mean-square error and, in this sense, can be considered as the most optimal filter possible. Through both simulated and real data scenarios, this improved filter will be shown to preserve the highest amount of gravity signal when compared to other standard techniques, while simultaneously minimizing leakage effects and producing smooth solutions in areas of low signal.

Abstract. The estimation of terrestrial water storage variations at river basin scale is among the best documented applications of the GRACE (Gravity and Climate Experiment) satellite gravity mission. In particular, it is expected that GRACE closes the water balance at river basin scale and allows the verification, improvement and modeling of the related hydrological processes by combining GRACE amplitude estimates with hydrological models' output and in-situ data. When computing monthly mean storage variations from GRACE gravity field models, spatial filtering is mandatory to reduce GRACE errors, but at the same time yields biased amplitude estimates. The objective of this paper is three-fold. Firstly, we want to compute and analyze amplitude and time behaviour of the bias in GRACE estimates of monthly mean water storage variations for several target areas in Southern Africa. In particular, we want to know the relation between bias and the choice of the filter correlation length, the size of the target area, and the amplitude of mass variations inside and outside the target area. Secondly, we want to know to what extent the bias can be corrected for using a priori information about mass variations. Thirdly, we want to quantify errors in the estimated bias due to uncertainties in the a priori information about mass variations that are used to compute the bias. The target areas are located in Southern Africa around the Zambezi river basin. The latest release of monthly GRACE gravity field models have been used for the period from January 2003 until March 2006. An accurate and properly calibrated regional hydrological model has been developed for this area and its surroundings and provides the necessary a priori information about mass variations inside and outside the target areas. The main conclusion of the study is that spatial smoothing significantly biases GRACE estimates of the amplitude of annual and monthly mean water storage variations. For most of the practical applications, the bias will be positive, which implies that GRACE underestimates the amplitudes. The bias is mainly determined by the filter correlation length; in the case of 1000 km smoothing, which is shown to be an appropriate choice for the target areas, the annual bias attains values up to 50% of the annual storage; the monthly bias is even larger with a maximum value of 75% of the monthly storage. A priori information about mass variations can provide reasonably accurate estimates of the bias, which significantly improves the quality of GRACE water storage amplitudes. For the target areas in Southern Africa, we show that after bias correction, GRACE annual amplitudes differ between 0 and 30 mm from the output of a regional hydrological model, which is between 0% and 25% of the storage. Annual phase shifts are small, not exceeding 0.25 months, i.e. 7.5 deg. Our analysis suggests that bias correction of GRACE water storage amplitudes is indispensable if GRACE is used to calibrate hydrological models.

Abstract. The estimation of terrestrial water storage variations at river basin scale is among the best documented applications of the GRACE (Gravity and Climate Experiment) satellite gravity mission. In particular, it is expected that GRACE closes the water balance at river basin scale and allows the verification, improvement and modeling of the related hydrological processes by combining GRACE amplitude estimates with hydrological models' output and in-situ data.When computing monthly mean storage variations from GRACE gravity field models, spatial filtering is mandatory to reduce GRACE errors, but at the same time yields biased amplitude estimates.The objective of this paper is three-fold. Firstly, we want to compute and analyze amplitude and time behaviour of the bias in GRACE estimates of monthly mean water storage variations for several target areas in Southern Africa. In particular, we want to know the relation between bias and the choice of the filter correlation length, the size of the target area, and the amplitude of mass variations inside and outside the target area. Secondly, we want to know to what extent the bias can be corrected for using a priori information about mass variations. Thirdly, we want to quantify errors in the estimated bias due to uncertainties in the a priori information about mass variations that are used to compute the bias.The target areas are located in Southern Africa around the Zambezi river basin. The latest release of monthly GRACE gravity field models have been used for the period from January 2003 until March 2006. An accurate and properly calibrated regional hydrological model has been developed for this area and its surroundings and provides the necessary a priori information about mass variations inside and outside the target areas.Correspondence to: R. Klees (r.klees@tudelft.nl)The main conclusion of the study is that spatial smoothing significantly biases GRACE estimates of the amplitude of annual and monthly mean water storage variations and that bias correction using existing hydrological models significantly improves the quality of GRACE estimates. For most of the practical applications, the bias will be positive, which implies that GRACE underestimates the amplitudes. The bias is mainly determined by the filter correlation length; in the case of 1000 km smoothing, which is shown to be an appropriate choice for the target areas, the annual bias attains values up to 50% of the annual storage; the monthly bias is even larger with a maximum value of 75% of the monthly storage. A priori information about mass variations can provide reasonably accurate estimates of the bias, which significantly improves the quality of GRACE water storage amplitudes. For the target areas in Southern Africa, we show that after bias correction, GRACE annual amplitudes differ between 0 and 30 mm from the output of a regional hydrological model, which is between 0% and 25% of the storage. Annual phase shifts are small, not exceeding 0.25 months, i.e. 7.5 deg. It is shown that after bias co...

When using GRACE as a tool for hydrology, many different gravity field model products are now available to the end user. The traditional spherical harmonics solutions produced from GRACE are typically obtained through an optimization of the gravity field data at the global scale, and are generated by a number of processing centers around the world. Alternatives to this global approach include so-called regional techniques, for which many variants exist, but whose common trait is that they only use the gravity data collected over the area of interest to generate the solution. To determine whether these regional solutions hold any advantage over the global techniques in terms of overall accuracy, a range of comparisons were made using some of the more widely used regional and global methods currently available. The regional techniques tested made use of either spherical radial basis functions or single layer densities (i.e., mascons), with the global solutions having been obtained from the various major processing centers. The solutions were evaluated using a range of computed statistics over a selection of major river basins, which were globally distributed and ranged in size from 1 to 6 million km 2 .For one of the basins tested, the Zambezi, additional validation tests were conducted through comparisons against a custom designed regional hydrology model of the region. We could not prove that current regional models perform better than global ones. Monthly mean water storage variations agree at the level of 0.02 m equivalent water height. The differences in terms of monthly mean water storage variations between regional and global solutions are comparable with the differences among only global or regional solutions. Typically they reach values of 0.02 m equivalent water heights, which seems to be the level of accuracy of current GRACE solutions for river basins above 1 million km 123Surv Geophys (2008) 29:335-359 DOI 10.1007 The amplitudes of the seasonal mass variations agree at the sub-centimetre level. Evident from all of the comparisons shown is the importance that the choice of regularization, or spatial filtering, can have on the solution quality. This was found to be true for global as well as regional techniques.

Abstract. Variations of water stocks in the upper Zambezi river basin have been determined by 2 different hydrological modelling approaches. The purpose was to provide preliminary terrestrial storage estimates in the upper Zambezi for comparison with estimates derived from the Gravity Recovery And Climate Experiment (GRACE). The first modelling approach is GIS-based, distributed and conceptual (STREAM). The second approach uses lumped elementary watersheds identified and modelled conceptually (LEW). The STREAM model structure has been assessed using GLUE (Generalized Likelihood Uncertainty Estimation) a posteriori to determine parameter identifiability. The LEW approach could, in addition, be tested for model structure, because computational efforts of LEW are low. Both models are threshold models, where the non-linear behaviour of the Zambezi river basin is explained by a combination of thresholds and linear reservoirs. The models were forced by time series of gauged and interpolated rainfall. Where available, runoff station data was used to calibrate the models. Ungauged watersheds were generally given the same parameter sets as their neighbouring calibrated watersheds. It appeared that the LEW model structure could be improved by applying GLUE iteratively. Eventually, it led to better identifiability of parameters and consequently a better model structure than the STREAM model. Hence, the final model structure obtained, better represents the true hydrology. After calibration, both models show a comparable efficiency in representing discharge. However the LEW model shows a far greater storage amplitude than the STREAM model. This emphasizes the storage uncertainty related to hydrological modelling in data-scarce environments such as the Zambezi river basin. It underlines the need and potential for independent observations of terrestrial storage to enhance our understanding and modelling capacity of the hydrological processes. GRACE could provide orthogonal information that can help to constrain and further enhance our models. In the near future, other remotely sensed data sources will be used to force modelling efforts of the Zambezi (e.g. satellite rainfall estimates) and to identify individual storage components in the GRACE observations (e.g. altimeter lake levels and microwave soil moisture). Ultimately, this will create possibilities for state updating of regional hydrological models using GRACE.