<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><div><br class=""><blockquote type="cite" class=""><div class="">On Jul 7, 2020, at 6:42 PM, Fukumori, Ichiro (US 329B) <<a href="mailto:ichiro.fukumori@jpl.nasa.gov" class="">ichiro.fukumori@jpl.nasa.gov</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div class="WordSection1" style="page: WordSection1; caret-color: rgb(0, 0, 0); font-family: Helvetica; font-size: 16px; font-style: normal; font-variant-caps: normal; font-weight: normal; 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;"><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">Hi Christopher,<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">I don't think the sensitivity to wind stress curl can be derived from<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">sensitivity to wind stress alone. The problem stems from the<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">indeterminate nature of deriving wind stress from its curl.<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">For instance, consider two wind stress perturbations that have<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">identical curls but different irrotational components. A<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">wind-stress-forced model's sensitivity to the perturbations would in<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">general be different between the two; i.e., the sensitivity to wind<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">stress curl is indeterminate. Expressing this sensitivity from<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">sensitivity to wind stress alone amounts to implicitly specifying<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class="">allowable irrotational perturbations to the wind.<o:p class=""></o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><o:p class=""> </o:p></div><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""></div><div class=""><div class=""><div style="margin: 0in 0in 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""></div></div></div></div></div></blockquote><div><br class=""></div><div><br class=""></div><div><div class=""></div><blockquote type="cite" class=""><div class="">On Jul 6, 2020, at 9:16 PM, Paola Cessi <<a href="mailto:pcessi@ucsd.edu" class="">pcessi@ucsd.edu</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 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></div></blockquote><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></div></body></html>