## 1. Introduction

[2] The Gravity Recovery and Climate Experiment (GRACE) mission, a joint project of the US National Aeronautics and Space Administration (NASA) and German Aerospace Center (DLR), has been providing the scientific community with global gravity observations since early 2002 [*Tapley et al.*, 2004]. One of the major problems one has to deal with when working with GRACE data is the increasing error spectrum at higher degrees in the provided Stokes coefficients *C*_{lm} and *S*_{lm}. As demonstrated by *Swenson and Wahr* [2006], these errors are not purely random, but also exhibit a strong correlation between even and odd degree coefficients respectively. When no post-priori filtering is applied, the errors show up as unphysical longitudinal striping patterns in the maps of equivalent water height (EWH). Commonly, these are suppressed by weighting the Stokes coefficients by means of a Gaussian smoothing function *W*_{l} which decreases in value with increasing degree *l* and thus attenuates the contribution of the ill-determined higher degree coefficients [*Wahr et al.*, 1998]. The value of the Gaussian smoothing function *W*_{l} depends on the degree *l* only and thus is isotropic [*Jekeli*, 1981]. However, as indicated by the correlation between the even and odd degree coefficients, the error has a non-isotropic character and consequently a large smoothing radius is required to remove all stripes in the GRACE maps, which implies a non-negligible loss of the information contained in the GRACE solutions [*Chen et al.*, 2007]. Moreover, with an increasing smoothing radius leakage between basins (e.g. land/ocean) will increase, making the separation of signals more cumbersome.

[3] This is illustrated in Figure 1, where we plotted a map of equivalent water height anomaly for March 2007 for several Gaussian smoothing radii. Without any smoothing (Figure 1a) the map is dominated by the meridional stripes and little geophysical signal can be discerned. At a smoothing radius of 350 km (Figure 1b), the larger hydrological basins (e.g. Amazon, Zambezi) start to stand out, but are still corrupted by the stripes. Increasing the smoothing radius to 500 km removes most of the striping over land, only at smoothing radii of 750 km and larger the oceans appear mostly stripe free.

[4] Various procedures have been proposed to remove the correlated errors in the Stokes coefficients and increase the resolution of EWH maps. Most of these make use of the calibrated error spectrum, the error covariance matrix or an a-priori signal covariance matrix, [see, e.g., *Swenson and Wahr*, 2002; *Chen et al.*, 2006; *Kusche*, 2007]. *Swenson and Wahr* [2006] propose to fit a quadratic polynomial in a moving window to the Stokes coefficients of even and odd degrees for a particular order *m* and remove this from the original Stokes coefficients. Using a slightly modified version, *Chambers* [2006b] showed that this reduces the uncertainty of the GRACE solutions by more than 51% over the oceans.

[5] In this paper we use an alternative approach to remove the North-South striping in the GRACE solutions and use empirical orthogonal functions (EOFs) to isolate significant geophysical signal. The effectiveness of this procedure was demonstrated by *Schrama et al.* [2007], in which EOF analysis of the Gaussian smoothed EWH maps was used to suppress noise. We apply the EOF procedure directly to the Stokes coefficients and use the temporal (un)correlatedness of the degree dependent correlation in the coefficients, which allows a significantly better separation of noise and ‘real’ signal. Moreover, we will show that this method retains most of expected geophysical signals, by applying the filter to modelled maps of EWH variations.