S. Polavarapu et al., THE TANGENT LINEAR-MODEL FOR SEMI-LAGRANGIAN SCHEMES - LINEARIZING THE PROCESS OF INTERPOLATION, Tellus. Series A, Dynamic meteorology and oceanography, 48(1), 1996, pp. 74-95
The tangent linear model may be used in diverse applications such as K
alman filtering, variational assimilation using the adjoint method, se
nsitivity studies or predictability studies. A ''correct'' tangent lin
ear variation contains all of the linear part of the nonlinear variati
on. This concept is used to show that simply differentiating a nonline
ar model's code does not necessarily lead to a tangent linear model wh
ich is correct in all circumstances. The example of linearizing interp
olation schemes is used. For infinitesimal variations, the linear vari
ation is correct if and only if the first derivative of an interpolato
r is continuous. Even if the tangent linear variation is occasionally
incorrect, the size of the error can be determined and may in fact be
quite tolerable. Therefore, there should be no Fundamental difficulty
in linearizing semi-Lagrangian schemes if care is taken in choosing an
appropriate interpolation scheme.