Abstract
This work presents an efficient method for calculating the sensitivity of a mathematical model's result to feedback. Feedback is defined in terms of an operator acting on the model's dependent variables. The sensitivity to feedback is defined as a functional derivative, and a method is presented to evaluate this derivative using adjoint functions. Typically, this method allows the individual effect of many different feedbacks to be estimated with a total additional computing time comparable to only one recalculation. The effects on a C02-doubling experiment of actually incorporating surface albedo and water vapor feedbacks in a radiative-convective model are compared with sensitivities calculated using adjoint functions. These sensitivities predict the actual effects of feedback with at least the correct sign and order of magnitude. It is anticipated that this method of estimating the effect of feedback will be useful for more complex models where extensive recalculations for each of a variety of different feedbacks is impractical.
