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.

Spaceborne radar interferometric delay measurements were used to infer high-resolution maps of integrated atmospheric water vapor, which can be readily related to meteorological phenomena. Maps of the water vapor distribution associated with a precipitating cloud, a partly precipitating cold front, and horizontal convective rolls reveal quantitative measures that are not observed with conventional methods, and suggest that such radar observations can be used for forecasting and to study atmospheric dynamics.

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.

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 ).

We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35-69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with detrended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24-47%.B J. Ran