<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="">Hi Matt and Hong:</div><div class=""><br class=""></div><div class="">Thanks for the pointers. I had initially thought something similar: the sensitivities are linear, so you should just be able to do calculus operations on them. On further reflection, though, the units don’t work out. Going back to the wind stress curl example, if the cost function has units C, the sensitivities to wind stress are ∂J/∂τ and have units of C per N m^–2 = C m^2 N^–1. The sensitivities to wind stress curl, w, are <span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class="">∂J/∂w</span><span style="caret-color: rgb(0, 0, 0); color: rgb(0, 0, 0);" class=""> and </span>should have units of C per N m^–3 = C m^3 N^–1. However, if you just take the curl of the sensitivities, you get units of C m N^–1, which are off by a factor of m^2. </div><div class=""><br class=""></div><div class="">It’s straightforward to work out the transformation rule for the derivative of τ in 1D using finite differences. The sensitivity of J to τ at the ith grid point is</div><div class=""><br class=""></div><div class=""><span class="Apple-tab-span" style="white-space:pre"> </span></div></body></html>