| For regional gravity-field improvement short-arc SST in the low-low mode is frequently
applied. Usually, the regional correction to the gravity-field is expressed as a superposition of
localizing base functions:
∑N
δV (x) = φi(x,ηi).
i=1
The base functions φi depend on parameter vectors ηi, which describe the locations and the
shapes of the base functions. These parameter have to be chosen so, that the field correction
δV optimally matches the residual SST observations.
In general, the base functions φi depend nonlinearly from their parameter vectors ηi.
Therefore, the partial derivatives ∂φi∕∂ηi are needed for the least-squares approximation of
the residual observations by the gravity-field correction model. In most cases, these partial
derivatives are obtained by the integration of the variational equations |