|
|
|
Next: 5.1.2 Reverse or adjoint
Up: 5.1 Some basic algebra
Previous: 5.1 Some basic algebra
Contents
Consider a perturbation to the input variables
(typically a single component
).
Their effect on the output may be obtained via the linear
approximation of the model
in terms of its Jacobian matrix
, evaluated in the point
according to
![$\displaystyle \delta \vec{v} \, = \, M \vert _{\vec{u}^{(0)}} \, \delta \vec{u}$](img1789.png) |
(5.2) |
with resulting output perturbation
.
In components
,
it reads
![$\displaystyle \delta v_{j} \, = \, \sum_{i} \left. \frac{\partial {\cal M}_{j}}{\partial u_{i}} \right\vert _{u^{(0)}} \, \delta u_{i}$](img1792.png) |
(5.3) |
Eq. (5.2) is the tangent linear model (TLM).
In contrast to the full nonlinear model
, the operator
is just a matrix
which can readily be used to find the forward sensitivity of
to
perturbations in
,
but if there are very many input variables
for
large-scale oceanographic application), it quickly becomes
prohibitive to proceed directly as in (5.2),
if the impact of each component
is to be assessed.
Next: 5.1.2 Reverse or adjoint
Up: 5.1 Some basic algebra
Previous: 5.1 Some basic algebra
Contents
mitgcm-support@mitgcm.org
Copyright © 2006
Massachusetts Institute of Technology |
Last update 2018-01-23 |
![](../images/designedbyscs.gif) |
|