Adiabatic, Constrained, Stochastic Eddy Parameterisation

<p>Mesoscale eddy-permitting ocean models will be needed as a component of climate ensemble projections most likely for the next decade or more.&#160;&#160; However, the kinetic energy and other measures of variability are typically an order of magnitude too weak at this nominal 0.25 degree lon-lat resolution.&#160;&#160; &#160;This is predominantly due to excessive gridscale damping of momentum, needed for computational stability, which is believed to kill a large fraction of the energy source of the kinetic energy inverse cascade.&#160;&#160; The KE inverse cascade is associated with the generation of intrinsic chaotic variability and ensemble spread, hence the estimation of potential predictability, but also with slower, larger-scale variability associated with climate.&#160; The familiar Gent and McWilliams (1990) eddy parameterisation is problematic when applied to eddy-permitting models, where eddies are partially resolved, and it also tends to damp variability rather than energise it.&#160;&#160; In response to this problem, several recent studies have focussed on the KE backscatter problem, which each attempt to increase the upscale transfer of KE, either deterministically or stochastically.</p><p>Stochastic parameterisation of sub-gridscale eddies has recently become a popular approach in ocean modelling, having been used in atmospheric modelling for many years, but there is still a diverse range of approaches for constraining either the underlying physics (how the forcing is applied) or the statistics (the spatiotemporal signature of the forcing).&#160;&#160; This study explores some basic recipes for constructing the stochastic model from statistics of either observations or higher-resolution models.&#160; The stochastic forcing, representing the sub-gridscale effects of eddies in our eddy-permitting simulations, is also applied adiabatically &#8211; to mimic the predominant behaviour of mesoscale eddies in the ocean interior and to preserve large-scale watermasses.&#160;&#160; A theoretical challenge, which we explore, is to connect the applied, weakly imbalanced forcing, to a response in kinetic energy and upscale transfer.&#160; This must also be applied without generating numerical instability.&#160;&#160;</p>