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An optimisation scheme is developed to accurately represent the sub-gridscale forcing of a high dimensional chaotic ocean system. Using a simpleparameterisation scheme, the velocity components of a 30km resolution shallowwater ocean model are optimised to have the same climatological mean andvariance as that of a less viscous 7.5km resolution model. The 5 daylag-covariance is also optimised, leading to a more accurate estimate of thehigh resolution response to forcing using the low resolution model.  The system considered is an idealised barotropic double gyre that is chaoticat both resolutions. Using the optimisation scheme, we find and apply theconstant in time, but spatially varying, forcing term that is equal to the timeintegrated forcing of the sub-mesoscale eddies. A linear stochastic term,independent of the large-scale flow, with no spatial correlation but aspatially varying amplitude and time scale is used to represent the transienteddies. The climatological mean, variance and 5 day lag-covariance of thevelocity from a single high resolution integration is used to provide anoptimisation target. No other high resolution statistics are required.Additional programming effort, for example to build a tangent linear or adjointmodel, is not required either.  The focus of this paper is on the optimisation scheme and the accuracy of theoptimised flow. The method can be applied in future investigations into thephysical processes that govern barotropic turbulence and it can perhaps beapplied to help understand and correct biases in the mean and variance of amore realistic coarse or eddy-permitting ocean model. The method iscomplementary to current parameterisations and can be applied at the same timewithout modification.

Optimisation of an idealised ocean model, stochastic parameterisation of sub-grid eddies