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.

The focus of the study is optimizing the technique for estimating geocenter motion and variations in J2 by combining data from the Gravity Recovery and Climate Experiment (GRACE) satellite mission with output from an Ocean Bottom Pressure model and a Glacial Isostatic Adjustment (GIA) model. First, we conduct an end‐to‐end numerical simulation study. We generate input time‐variable gravity field observations by perturbing a synthetic Earth model with realistically simulated errors. We show that it is important to avoid large errors at short wavelengths and signal leakage from land to ocean, as well as to account for self‐attraction and loading effects. Second, the optimal implementation strategy is applied to real GRACE data. We show that the estimates of annual amplitude in geocenter motion are in line with estimates from other techniques, such as satellite laser ranging (SLR) and global GPS inversion. At the same time, annual amplitudes of C10 and C11 are increased by about 50% and 20%, respectively, compared to estimates based on Swenson et al. (2008). Estimates of J2 variations are by about 15% larger than SLR results in terms of annual amplitude. Linear trend estimates are dependent on the adopted GIA model but still comparable to some SLR results.

We discuss and develop further the methods of surface wave tomography in the frame of the geometric ray approximation. The general approach for determining the lateral phase or group velocity distribution, which is a standard 2-D tomography problem, involves linearization, representation of the unknown function as a series in some basis functions, and evaluation of the coefficients by the methods of linear algebra. If the wave paths cover the area under investigation non-uniformly, the basis functions should not be chosen a priori, but constructed proceeding from the pattern of paths. Different criteria for constructing the basis functions are compared, and a relation between them is considered.A more preferable approach is joint interpretation of phase and group velocity data for different periods, because it allows the information about phase velocity variations to be enlarged due to the use of the group velocity data. Both the phase and group traveltimes are represented as linear functionals of the unknown phase slowness corrections. A specific form of the data kernels allows the basis functions to be represented as a product of two functions, one depending on the horizontal coordinates, and the other on frequency.

S U M M A R YThe DEOS Mass Transport release 1 (DMT-1) model has been produced on the basis of intersatellite K-band ranging data acquired by the GRACE satellite mission. The functional model exploited in the data processing can be considered as a variant of the acceleration approach. Each element of the data vector is defined as a linear combination of three successive range measurements and can be interpreted as the line-of-sight projection of a weighted average of intersatellite accelerations. As such, the data vector can be directly linked to parameters of the gravitational field. In this way, a series of unconstrained monthly gravity field solutions is produced, each of which is defined as a set of spherical harmonic coefficients complete to degree 120. At the post-processing stage, the unconstrained solutions are filtered with a statistically optimal Wiener-type filter based on full covariance matrices of noise and signal. As such, the DMT-1 model is free from along-track artefacts, which are typical for many other GRACE gravity models. The accuracy of the DMT-1 model has been analysed in different ways. First, the signals observed in areas with minimal mass variations (Sahara, East Antarctica and the middle of the Pacific Ocean) are analysed and interpreted as an upper bound of the noise in the DMT-1 model. It is concluded that the pointwise errors after filtering are of the order of 2-3 cm in terms of equivalent water heights. For the mean mass variations in an area of 10 6 km 2 , the corresponding error reduces to 1.5-2 cm. Second, a time-series of mass variations in the Marie Byrd Land (Antarctica) has been analysed, where the true signal (mostly caused by postglacial rebound) is expected to be close to a linear trend. The rms of the post-fit residuals is found to be 3.3 cm, which is consistent with the error analysis in areas with minimal mass variations. Thirdly, the DMT-1 model has been applied to estimate mass variations in [2003][2004][2005][2006] in Lake Victoria (Africa), where a large drop of water level is observed in recent years. The obtained linear trend (−31 ± 3 cm yr −1 ) is in good agreement with that derived from the satellite altimetry data (−35 ± 1 cm yr −1 ).

Abstract. The ability to estimate terrestrial water storage (TWS) realistically is essential for understanding past hydrological events and predicting future changes in the hydrological cycle. Inadequacies in model physics, uncertainty in model land parameters, and uncertainties in meteorological data commonly limit the accuracy of hydrological models in simulating TWS. In an effort to improve model performance, this study investigated the benefits of assimilating TWS estimates derived from the Gravity Recovery and Climate Experiment (GRACE) data into the OpenStreams wflow_hbv model using an ensemble Kalman filter (EnKF) approach. The study area chosen was the Rhine River basin, which has both well-calibrated model parameters and high-quality forcing data that were used for experimentation and comparison. Four different case studies were examined which were designed to evaluate different levels of forcing data quality and resolution including those typical of other less wellmonitored river basins. The results were validated using in situ groundwater (GW) and stream gauge data. The analysis showed a noticeable improvement in GW estimates when GRACE data were assimilated, with a best-case improvement of correlation coefficient from 0.31 to 0.53 and root mean square error (RMSE) from 8.4 to 5.4 cm compared to the reference (ensemble open-loop) case. For the data-sparse case, the best-case GW estimates increased the correlation coefficient from 0.46 to 0.61 and decreased the RMSE by 35 %. For the average improvement of GW estimates (for all four cases), the correlation coefficient increases from 0.6 to 0.7 and the RMSE was reduced by 15 %. Only a slight overall improvement was observed in streamflow estimates when GRACE data were assimilated. Further analysis suggested that this is likely due to sporadic short-term, but sizeable, errors in the forcing data and the lack of sufficient constraints on the soil moisture component. Overall, the results highlight the benefit of assimilating GRACE data into hydrological models, particularly in data-sparse regions, while also providing insight on future refinements of the methodology.