<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="">I see - this makes sense.<div class=""><br class=""></div><div class="">Though I agree with Dimitris. The adjoint only gives sensitivities in a perturbation sense. I do see the value of removing the strong nonlinearities in the bulk formulae, but the entire system is nonlinear (e.g. the transmission of those fluxes through the mixed layer) so you are never decoupling the flux components beyond that perturbation scale.</div><div class=""><br class=""></div><div class="">Matt</div><div class=""><br class=""><div class=""><br class=""></div><div class=""><br class=""><div><blockquote type="cite" class=""><div class="">On Apr 6, 2020, at 8:10 AM, Dimitris Menemenlis <<a href="mailto:menemenlis@jpl.nasa.gov" class="">menemenlis@jpl.nasa.gov</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="">I agree but maybe call it “linear dependence” instead of “double counting”. Although this linear dependence may be stronger between atmospheric variables that are used as input for bulk formulae, there is also non-zero linear dependence between surface fluxes.<div class=""><div class=""><div class=""><br class=""><div class=""><div class=""><div class=""><blockquote type="cite" class=""><div class="">On Apr 3, 2020, at 6:53 AM, Dan Jones <<a href="mailto:dcjones.work@gmail.com" class="">dcjones.work@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><meta http-equiv="Content-Type" content="text/html; charset=utf-8" class=""><div dir="ltr" class=""><div class="">Hi Dimitris,</div><div class=""><br class="">Although I could be wrong, I do not think that the potential double counting issue matters much for the adjoint optimization process. As long as the control adjustments reduce the cost function, then I suppose that the optimization process will still work. Do you agree?<br class=""><br class="">However, if we are attempting to reconstruct an objective function using adjoint sensitivities and anomalies (e.g. Helen Pillar's work on RAPID time series reconstructions, see her 2016 J. Climate paper), then the potential double-counting could be an issue. I'm hoping that by avoiding the bulk formulae I can more cleanly separate the effects of wind stress anomalies from those of heat flux anomalies. </div><div class=""></div><div class=""><br class=""></div>Best,<br class="">Dan<br class=""><br clear="all" class=""><div class=""><div dir="ltr" class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div dir="ltr" class=""><div style="font-family: Calibri, Arial, Helvetica, sans-serif; font-size: small;" class=""><div class="">--------------------------------------------------------------<br class="">Dr Dan Jones / British Antarctic Survey</div><div class=""><a href="http://www.danjonesocean.com/" target="_blank" class="">danjonesocean.com</a> / @DanJonesOcean</div><div class="">--------------------------------------------------------------</div></div></div></div></div></div></div></div></div></div></div></div></div></div></div>
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