Sensitivity analysis of the climate of a chaotic ocean circulation model

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Abstract
We explore sensitivity analyses of ocean circulation models by comparing the adjoint and direct‐perturbation methods. We study the sensitivity of time‐averaged inter‐gyre vorticity transport to the imposed wind‐stress curl in an eddy‐permitting reduced‐gravity ocean model of a double gyre. Two regimes exist: a non‐chaotic regime for low wind‐stress curl, and a chaotic regime for stronger wind forcing. Direct‐perturbation methods are found to converge, with increasing integration time, to a stable ‘climate’ sensitivity in both the chaotic and non‐chaotic regimes. The adjoint method converges in the non‐chaotic regime but diverges in the chaotic regime. The divergence of adjoint sensitivity in the chaotic regime is directly related to the chaotic divergence of solution trajectories through phase‐space. Thus, standard adjoint sensitivity methods cannot be used to estimate climate sensitivity in chaotic ocean circulation models. An alternative method using an ensemble of adjoint calculations is explored. This is found to give estimates of the climate sensitivity of the time‐mean vorticity transport with O(25%) error or less for integration times ranging from one month to one year. The ensemble‐adjoint method is particularly useful when one wishes to produce a map of sensitivities (for example, the sensitivity of the advective vorticity transport to wind stress at every point in the domain) as direct sensitivity calculations for each point in the map are avoided. However, an ensemble‐adjoint of the variance of the vorticity transport to wind‐stress curl fails to estimate the climate sensitivity. We conclude that the most reliable method of determining the climate sensitivity is the direct‐perturbation method, but ensemble‐adjoint techniques may be of use in some problems. Copyright © 2002 Royal Meteorological Society.

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