A new data-driven method to diagnose ocean eddy transport coefficients

Abstract:

Tracer transport by mesoscale eddies (e.g., heat, salt, dissolved chemicals, etc.) is essential in climate models. However, the scales of the mesoscale eddy are about 10~100 km, barely resolved by a global climate model (GCM). The dominant method to parameterize the unresolved transport is the Gent-McWilliams (GM) scheme. The choice of GM parameters strongly influences the accuracy of the GCM. Eddy resolving simulations should, in principle, be able to inform the choice of GM parameters; however, using such simulations to quantitatively infer GM parameters is a difficult problem. Existing methods require a large number of numerical tracer or Langrangian particles and are possibly corrupted by the presence of rotational components in the eddy flux vector. We introduce a new method which is able to infer GM parameters from the divergence of the eddy flux of a single tracer (e.g., temperature). This method relies on an offline implementation of the GM parameterization coded using the Jax differentiable programming framework. We employ a gradient-descent-based approach from the machine learning community to iteratively diagnose the globally-dependent GM parameter based on data from eddy-resolving simulations. The simulations are a channel model meant to resemble the ACC with a topographic ridge, run at 5km resolution. The space and time structure of the inferred GM parameter sheds light on the underlying physics of mesoscale transport, highlighting, for example, the importance of topography in modulating the efficiency of eddy transfer. This method also reveals the structural limitations of the GM scheme, which are reflected in the upper bound of the parameterization skill after optimization. Also, we explore the accuracy of the GM scheme based on the anisotropic GM parameter.