A new approach to tackling stripes in gravity field solutions using directional gradient regularization

The spurious North-South stripes in gravity field solutions of satellite gravimetry mission such as GRACE and its follow-on (GRACE-FO), are a well known issue. They are thought to be the result of residual non-Gaussian errors, most notably stemming from residual sub-monthly dealiasing model errors, which propagate into the gravity field solutions. The typical pattern is known to be linked to the orbit geometry (e.g. Peidou and Pagiatakis 2020) in combination with the directional sensitivity of the raw observations.

 

Over the years, various approaches have been developed to reduce these striping patterns as a trade-off against signal attenuation, resulting in varying filtered solutions. One particular type of these approaches stems from using diagonal regularization matrices using approximate or real error-covariance matrices (e.g. Kusche et al 2009, Klees et al 2008, Horvath et al. 2018). These can be done either at the normal equation system level or be formulated as a post-processing filter operator.

 

In this work, we revisit this regularization principle and explore ways of constraining the East-West and North-South gravity field gradients at given satellite heights.

We show that, in the spherical harmonic domain, the associated regularization matrices resolve to order-block-diagonal matrices with a typical checkerboard pattern separating even and odd degrees.

Furthermore, we compute an empirical degree varying power law for the gradients based on the ESA earth system model (Dobslaw et al 2015). We present the result of testing various regularization strengths and weighing schemes, which are applied to the publicly available normal equation system from ITSG and GFZ. The regularized solutions are compared against conventional filter approaches (DDK filters, Gauss,) in the spatial and spectral domain.