The use of adjoint models for determining the sensitivity of integral quantities in an eddy resolving Oean General Circulation Model

Abstract

Adjoint models calculate the exact sensitivity of an output function of a model to infinitesimal perturbations in the forcing or initial conditions. In eddy resolving ocean models the presence of chaotic eddies is expected to lead to sensitivities to infinitesimal perturbations that are very different from the sensitivity to large perturbations and that no longer contain useful information. Previous studies disagree as to whether adjoint models can be used with eddy resolving ocean models on timescales longer than a few months.

Here the MIT ocean general circulation model and its adjoint are used to look at the sensitivity of the time mean heat content, kinetic energy, available potential energy and thermocline depth to the sea surface temperature, zonal wind stress, and vertical diffusivity in an eddy resolving model of a zonally reentrant channel. Using the tangent linear model the non linear timescale of the eddy resolving model is estimated at around 200 days. The adjoint model is integrated over 278 days and 690 days to see whether useful information remains in the sensitivities calculated by the adjoint model for longer than the non linear timescale of the system. The usefulness of the information in the sensitivities calculated by the adjoint model is assessed by comparison with integrations of the full non linear forward model with large spatial scale perturbations to the forcing, finite difference gradient checks, and sensitivities calculated by an adjoint model in a non eddy resolving channel where the adjoint method is known to provide useful information.

Finite difference gradients are found to be unsuitable for calculating sensitivities of time averaged climate quantities in an eddy resolving ocean model as they are also affected by chaos. Comparison of the sensitivities calculated by the adjoint model in the eddy and non eddy resolving models shows that information remains in the spatial structure of the adjoint model results in the eddy resolving model on a time scale of 278 days.

In the non eddy resolving case the adjoint model results agree well with the perturbed forward model experiments, and are clearly climatically relevant on a timescale of 690 days. Use of a parameterisation scheme that reduces the eddy kinetic energy gives adjoint sensitivities that agree with well the perturbed forward model experiments after 690 days, although there are areas of extremely high adjoint sensitivity that may not be physically realistic. Without this parameterisation scheme, adjoint sensitivities involving dynamic variables grow exponentially with time as expected in a chaotic system, but at the end of the integration time of 690 days there is some agreement between the adjoint and forward model results for sensitivities involving thermodynamic variables only.

These results show that even in the presence of chaotic eddies some useful information is retained in the adjoint model solution beyond the nonlinear timescale of the system.

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