<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">Hi Christopher,<div class=""><br class=""></div><div class="">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.</div><div class=""><br class=""></div><div class="">Sorry,</div><div class=""><br class=""><div class="">
<div style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 20px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px;">Paola<br class=""><br class=""><span style="font-size: 12px;" class="">--------------------------------------------------------------------------------------------<br class="">Paola Cessi </span><span style="font-size: 12px;" class="">Tel: +1 858 534 0622 </span><span style="font-size: 12px;" class=""><br class="">Scripps Institution of Oceanography </span><span style="font-size: 12px;" class=""> Fax: +1 858 534 8045</span><span style="font-size: 12px;" class=""><br class="">9500 Gilman Drive #0213 </span><span style="font-size: 12px;" class="">e-mail: <a href="mailto:pcessi@ucsd.edu" class="">pcessi@ucsd.edu</a> </span><span style="font-size: 12px;" class=""><br class="">La Jolla, CA 92093-0213 </span><span style="font-size: 12px;" class="">Web: <a href="http://pordlabs.ucsd.edu/~pcessi" class="">http://pordlabs.ucsd.edu/~pcessi</a></span><span style="font-size: 12px;" class=""><br class="">USA <br class=""><br class=""></span><span style="font-size: 12px;" class="">Delivery address (Fed-Ex, DHL, UPS, etc.):</span><br style="font-size: 12px;" class=""><span style="font-size: 12px;" class="">University of California San Diego</span><br style="font-size: 12px;" class=""><span style="font-size: 12px;" class="">Keck Center - Room 366</span><br style="font-size: 12px;" class=""><span style="font-size: 12px;" class="">8851 Shellback Way</span><br style="font-size: 12px;" class=""><span style="font-size: 12px;" class="">La Jolla, CA 92093-0213, USA</span></div>
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<br class=""><div><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="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;" class=""><div dir="auto" style="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;" 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;" 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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