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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

(5.2) 
with resulting output perturbation
.
In components
,
it reads

(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
largescale 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
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