Including Momentum Advection in Scatterometer Sea-Level Pressure Retrievals

Direct measurements of surface pressure over the ocean are relatively scarce. However, it was long ago demonstrated that an "inverse" PBL model that took as input scatterometer wind vectors could produce accurate and detailed sea-level pressure fields. The standard method uses an inverted two-layer similarity PBL model, which implies linear dynamics. Two methods have been previously implemented to partially correct for this deficiency. The first technique applied the geostrophic momentum approximation. The second technique applied an ad hoc gradient wind correction a posteriori. The limitations of these two techniques are well known. We present a new formulation of the pressure retrieval methodology that formally incorporates the momentum advection in terms of a perturbation expansion around the linear solution in a direct PBL model. We show that the linear dynamics pressure gradient retrieval reduces to the solution of a simple quadratic equation, which places the surface wind/sea-level pressure relationship into a simple-to-understand framework. The perturbation expansion has two clear advantages over the standard methodologies. First, it takes advantage of the fact that the satellites measure swaths of surface stress vectors. Secondly, it generalizes simply to include stratification, thermal wind, heat and moisture advection and the effects of coherent structures. Two potential limitations have also been identified. First, a linear, inhomogeneous ODE must be solved at each order of the solution, which will require an efficient implementation. Second, the expansion parameter, which is the product of the aspect ratio and the Reynolds number, may not be small in the cores of strong storms or at strong fronts. The model formation and preliminary tests will be presented.