An adjoint based method for the inversion of the Juno and Cassini   gravity measurements into wind fields
  During 2016-17 the Juno and Cassini spacecraft will both perform close eccentric orbits of Jupiter and Saturn, respectively, obtaining high-precision gravity measurements for these planets. This data will be used to estimate the depth of the observed surface flows on these planets. All models to date, relating the winds to the gravity field, have been in the forward direction, thus allowing only calculation of the gravity field from given wind models. However, there is a need to do the inverse problem since the new observations will be of the gravity field. Here, an inverse dynamical model, is developed to relate the expected measurable gravity field, to perturbations of the density and wind fields, and therefore to the observed cloud-level winds. In order to invert the gravity field into the 3D circulation, an adjoint model is constructed for the dynamical model, thus allowing backward integration. This tool is used for examination of various scenarios, simulating cases in which the depth of the wind depends on latitude. We show that it is possible to use the gravity measurements to derive the depth of the winds, both on Jupiter and Saturn, taking into account also measurement errors. Calculating the solution uncertainties, we show that the wind depth can be determined more precisely in the low-to-midlatitudes. In addition, the gravitational moments are found to be particularly sensitive to flows at the equatorial intermediate depths, therefore we expect that if deep winds exist on these planets they will have a measurable signature by Juno and Cassini. 
Eli Galanti and Yohai Kaspi
astro-ph.EP