A Stochastic Model of the Isopycnal Slope for Use in the Gent-McWilliams Parameterization

Zofia Stanley1, Alistair Adcroft2, Scott Bachman3, Frederic S Castruccio4, Ian Grooms5 and William Kleiber5, (1)University of Colorado at Boulder, Applied Mathematics, Boulder, United States, (2)Princeton University, Princeton, United States, (3)National Center for Atmospheric Research, Climate and Global Dynamics, Boulder, CO, United States, (4)NSF National Center for Atmospheric Research, Boulder, United States, (5)University of Colorado at Boulder, Applied Mathematics, Boulder, CO, United States
Abstract:
The seawater equation of state is a nonlinear function of temperature, salinity, and pressure. Averaging nonlinear functions leads to errors. Thus, the density calculated by ocean models is not the same as the true grid-cell-average density. Jean-Michel Brankart proposed a stochastic correction to this error, which he used in the hydrostatic equation to compute the pressure gradient force [1]. His correction samples the nonlinear equation of state several times, and thus is computationally expensive.

This work proposes a novel way to correct the density errors incurred by averaging a nonlinear function and a new application of the correction. We found an analytic expression for a correction to the error. Our method requires only one evaluation of a nonlinear function and thus provides great computational savings over previous methods. We propose to use our correction to compute the isopycnal slope in the Gent-McWilliams parameterization of eddy-induced transport. Free parameters in our correction were assessed using model output from a high resolution (0.1 degree) eddy resolving Community Earth Systems Model 2 (CESM2) ocean model run [2]. These data constitute a 33-year time series of over 70 three-dimensional fields, saved every five days for a total of 2,400 files.

[1] Brankart, Ocean Modelling, (2013). [2] Bryan and Bachman, J. Phys. Ocean., 45 (2015).

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