<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""></div><div class=""><br class=""></div><div class="">This has the correct units, but is effectively an integral of the original sensitivities rather than a derivative. I ran into trouble in 2D because writing the stress in terms of the curl requires solving an elliptic problem and things got a little hairy. </div><div class=""><br class=""></div><div class="">Christopher</div><div class=""><br class=""></div><div class=""><br class=""></div><blockquote type="cite" class=""><div class="">On Jul 6, 2020, at 6:47 PM, Zhang, Hong (US 398K) <<a href="mailto:hong.zhang@jpl.nasa.gov" class="">hong.zhang@jpl.nasa.gov</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;">Hi Chris,<br class=""><div class="">You might check this paper about transformed gradient:</div><div class=""><a href="https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/jgrc.20240" class="">https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/jgrc.20240</a></div>paragraph [26] and figure6, figure7.<div class="">hope it helps</div><div class="">Hong</div></div></div></blockquote><div class=""><div class=""><div class="" style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;"><div class=""><br class=""></div></div></div></div><div><br class=""><blockquote type="cite" class=""><div class="">On Jul 7, 2020, at 12:27 AM, Matthew Mazloff <<a href="mailto:mmazloff@ucsd.edu" class="">mmazloff@ucsd.edu</a>> wrote:</div><div class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div class=""><br class=""></div><div class="">Ariane V, Bruce C, and I worked this out some time ago (~2013), so the details are blurry. But I am fairly certain that it works out fine to just take the curl of the sensitivity of J to the wind stress. That should give you the sensitivity to the curl. The operation is linear - we should be able to work this out.... Happy to discuss, though like I said, last time I thought about this was ~2013.</div><div class=""><br class=""></div><div class="">Matt</div><div class=""> </div><div class=""><br class=""></div><div class=""><div class=""><blockquote type="cite" class=""><div class="">On Jul 6, 2020, at 3:20 PM, Christopher Wolfe <<a href="mailto:christopher.wolfe@stonybrook.edu" class="">christopher.wolfe@stonybrook.edu</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html; charset=utf-8" class=""><div style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Hi all:<div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">Not sure if this is the right forum. If not, I’m happy to ask the wider MITgcm-support list.</div><div class=""><br class=""></div><div class="">Thanks in advance for any pointers!</div><div class=""><br class=""></div><div class="">Cheers,</div><div class="">Christopher</div><div class=""><br class=""></div><div class=""><br class=""></div><div class="">
<div dir="auto" style="caret-color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div dir="auto" style="caret-color: rgb(0, 0, 0); letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; text-decoration: none; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class=""><div style="letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">----------------------------------------------------------------------------<br class="">Christopher L. Pitt Wolfe<br class="">Associate Professor (Physical Oceanography)<br class="">School of Marine and Atmospheric Sciences<br class="">Stony Brook University<br class=""><a href="mailto:christopher.wolfe@stonybrook.edu" class="">christopher.wolfe@stonybrook.edu</a> 631-632-3152<br class="">----------------------------------------------------------------------------<br class=""><br class=""></div></div></div>
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