Dynamically consistent parameterization of mesoscale eddies. Part I: Simple model

• Published in: Ocean modelling (Oxford) 2015-03, Vol.87, p.1-19
• Main Author: Berloff, Pavel
• Format: Article
• Language: English
• Subjects: Algorithms; Eddies; Footprints; Geophysical fluid dynamics; Marine; Mathematical models; Mesoscale phenomena; Nonlinearity; Ocean models; Parameterization of mesoscale eddies; Parametrization
• ISSN: 1463-5003; 1463-5011
• DOI: 10.1016/j.ocemod.2014.12.008

•Novel framework for parameterizing oceanic mesoscale eddies.•It is based on the explicit use of the dynamics of localized impulses that model transient eddy forcing.•The parameterization is tested with the double-gyre ocean circulation model. This work aims at developing a framework for dynamically consistent parameterization of mesoscale eddy effects for use in non-eddy-resolving ocean circulation models. The proposed eddy parameterization framework is successfully tested on the classical, wind-driven double-gyre model, which is solved both with explicitly resolved vigorous eddy field and in the non-eddy-resolving configuration with the eddy parameterization replacing the eddy effects. The parameterization locally approximates transient eddy flux divergence by spatially localized and temporally periodic forcing, referred to as the plunger, and focuses on the linear-dynamics flow solution induced by it. The nonlinear self-interaction of this solution, referred to as the footprint, characterizes and quantifies the induced cumulative eddy forcing exerted on the large-scale flow. We find that spatial pattern and amplitude of the footprint strongly depend on the underlying large-scale and the corresponding relationships provide the basis for the eddy parameterization and its closure on the large-scale flow properties. Dependencies of the footprints on other important parameters of the problem are also systematically analyzed. The parameterization utilizes the local large-scale flow information, constructs and scales the corresponding footprints, and then sums them up over the gyres to produce the resulting eddy forcing field, which is interactively added to the model as an extra forcing. The parameterization framework is implemented in the simplest way, but it provides a systematic strategy for improving the implementation algorithm.