IV: GEODESY: Remarks on the Role of Height Datum in Altimetry-Gravimetry Boundary-Value Problems

The problem of global geoid determination is usually solved using satellite altimetry data on the oceans, together with an oceanographic model of sea surface topography, and gravity anomaly data on the continents. Such data, however, enable to obtain only potential differences with respect to a reference surface whose absolute potential is unknown. This situation suggests to modify the classical mixed boundary-value problem of physical geodesy by inserting into the boundary conditions an unknown additive constant, that must be determined by imposing a suitable additional constraint. Yet, such formulation of the boundary-value problem, from the point of view of its mathematical properties, is not unconditionally well-posed, and, furthermore, does not reflect faithfully the available physical model, as the present knowledge of ocean circulation does not allow to connect along coastlines the reference surfaces defined on the oceans and on the continents. The introduction of two different unknown additive constants, one for the oceans and one for the earth, to be determined by imposing two additional constraints, gives rise to a more faithful picture of the present physical knowledge, and, at the same time, to a new well-posed formulation of the boundary-value problem. This revised version was published online in August 2006 with corrections to the Cover Date.     

Viscous-type processes in the solar wind-magnetosphere interaction

A debate of long standing concerns the role viscous interactions play in magnetospheric dynamics. Is it minor or is it central to, e.g., drive the low latitude boundary layer on closed field lines and account for the substantial level of wave activity seen on the flanks? Newer data and theoretical considerations leave little doubt that viscous coupling is important. The Kelvin-Helmholtz instability is a major protagonist in fostering momentum transfer. Closer studies of the state of the flank magnetosphere will help to resolve the issue.