[ecco-support] Change-of-variable formulas for adjoint sensitivities

[Paola Cessi]

Hi Christopher,

I don’t think it is possible. You need to know the derivative of the cost of function wrt to the derivatives of the wind-stress (or the curl), and it is not possible to get those from the cost function derivatives wrt to wind-stress alone. For example, in the shallow water case, you only need to know the momentum eqns. to get the sensitivity to the wind stress, but for the sensitivity of the curl, you need to massage the mom. eqns. AND add the continuity.

Sorry,

Paola

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Paola Cessi                                                         Tel: +1 858 534 0622 
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> On Jul 6, 2020, at 3:20 PM, Christopher Wolfe <christopher.wolfe at stonybrook.edu> wrote:
> 
> Hi all:
> 
> Does any know of a simple formula (or reference) for a changing the dependent variables of adjoint sensitivities? For example, suppose you have the sensitivities of a cost function, J, to zonal and meridional wind stress. Is there a straightforward way to use these to calculate the sensitivity of J to the wind stress curl? I figured that there ought to be, but I got buried under a mountain of functional analysis and worried I was overthinking it.
> 
> Not sure if this is the right forum. If not, I’m happy to ask the wider MITgcm-support list.
> 
> Thanks in advance for any pointers!
> 
> Cheers,
> Christopher
> 
> 
> ----------------------------------------------------------------------------
> Christopher L. Pitt Wolfe
> Associate Professor (Physical Oceanography)
> School of Marine and Atmospheric Sciences
> Stony Brook University
> christopher.wolfe at stonybrook.edu <mailto:christopher.wolfe at stonybrook.edu>             631-632-3152
> ----------------------------------------------------------------------------
> 
> 
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