Skills and Limitations of the Adiabatic Omega Equation: How Effective Is It to Retrieve Oceanic Vertical Circulation at Mesoscale and Submesoscale?

Abstract

The quasi-geostrophic and the generalized omega equations are the most widely used methods to reconstruct vertical velocity (w) from in-situ data. As observational networks with much higher spatial and temporal resolutions are being designed, the question rises of identifying the approximations and scales at which an accurate estimation of w through the omega equation can be achieved and what are the critical scales and observables needed. In this paper we test different adiabatic omega reconstructions of w over several regions representative of main oceanic regimes of the global ocean in a fully eddy-resolving numerical simulation with a 1=60^o horizontal resolution. We find that the best reconstructions are observed in conditions characterized by energetic turbulence and/or weak stratification where near-surface frontal processes are felt deep into the ocean interior. The quasi-geostrophic omega equation gives satisfactory results for scales larger than ~ 10 km horizontally while the improvements using a generalized formulation are substantial only in conditions where frontal turbulent processes are important (providing improvements with satisfactory reconstruction skill down to ~ 5 km in scale). The main sources of uncertainties that could be identified are related to processes responsible for ocean thermal wind imbalance (TWI), which is particularly difficult to account for (especially in observation-based studies) and to the deep flow which is generally improperly accounted for in omega reconstructions through the bottom boundary condition. Nevertheless, the reconstruction of mesoscale vertical velocities may be sufficient to estimate vertical fluxes of oceanic properties in many cases of practical interest. The quasi-geostrophic and the generalized omega equations are the most widely used methods to reconstruct vertical velocity (w) from in-situ data. As observational networks with much higher spatial and temporal resolutions are being designed, the question rises of identifying the approximations and scales at which an accurate estimation of w through the omega equation can be achieved and what are the critical scales and observables needed. In this paper we test different adiabatic omega reconstructions of w over several regions representative of main oceanic regimes of the global ocean in a fully eddy-resolving numerical simulation with a 1=60^o horizontal resolution. We find that the best reconstructions are observed in conditions characterized by energetic turbulence and/or weak stratification where near-surface frontal processes are felt deep into the ocean interior. The quasi-geostrophic omega equation gives satisfactory results for scales larger than ~ 10 km horizontally while the improvements using a generalized formulation are substantial only in conditions where frontal turbulent processes are important (providing improvements with satisfactory reconstruction skill down to ~ 5 km in scale). The main sources of uncertainties that could be identified are related to processes responsible for ocean thermal wind imbalance (TWI), which is particularly difficult to account for (especially in observation-based studies) and to the deep flow which is generally improperly accounted for in omega reconstructions through the bottom boundary condition. Nevertheless, the reconstruction of mesoscale vertical velocities may be sufficient to estimate vertical fluxes of oceanic properties in many cases of practical interest.