Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization

Abstract

Abstract. If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal "K profile parameterization" (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both con- INTRODUCTIONA major challenge in the creation of Earth system models is the development of improved submodels of all its components, including the ocean. Recent experiences with coupled atmosphere-ocean models demonstrate that extensive and pervasive difficulties arise because of a mismatch in the equilibrium surface heat flux of each model individually. To avoid the resulting climate drift, flux corrections are often applied [Sausen et al., 1988]. A demanding, but physically more attractive alternative is model improvement. A critical requirement for an ocean submodel is that it simulate the annual cycle of sea surface temperature (SST) globally, since SST is the most important ocean property governing the exchange of energy between the ocean and atmosphere. The SST represents a balance among many processes, including air-sea exchange, oceanic transport, and vertical mixing. The latter must be parameterized because the processes involve small The first objective of this paper is to choose, from a wide assortment of classes, a vertical mixing scheme that can be developed into a suitable OBL model for climate studies. The choices are surveyed in the secplanetary boundary layers then discusses various PBL models. These layers are fundamentally turbulent and extend from near the surface to the boundary layer depth h, which is the limit to which boundary layer eddies can penetrate in the vertical. PBL models...

Field observations and results of a 1-D boundary layer model for developing near-surface temperature maxima in the Western Arctic

“…To estimate the depth of the actively mixing iceocean boundary layer (IOBL) in the LTC model, the bulk Richardson number (Ri bulk ) is calculated by (e.g., Large et al, 1994) ( ) ( ) ( )…”

Inherent sea ice predictability in the rapidly changing Arctic environment of the Community Climate System Model, version 3

“…For the integrations considered here, the atmosphere model (CAM3) (Collins et al 2006b) is run at T85 resolution (approximately 1.4 degrees) with 26 vertical levels. The ocean model (Smith and Gent 2004) includes an isopycnal transport parameterization (Gent and McWilliams 1990) and a surface boundary layer formulation following Large et al (1994). The dynamic-thermodynamic sea ice model (Briegleb et al 2004;Holland et al 2006b) uses the elasticviscous-plastic rheology (Hunke and Dukowicz 1997), a sub-gridscale ice thickness distribution (Thorndike et al 1975;Lipscomb 2001) and the thermodynamics of Bitz and Lipscomb (1999).…”

Simulated Response of the Arctic Freshwater Budget to Extreme NAO Wind Forcing

“…Ocean surface fluxes (in the absence of sea ice) are calculated using the bulk formula of Large and Pond (1981). Boundary layer and convective mixing in the ocean is parameterized according to Large et al (1994). Background vertical diffusivity of temperature and salinity are set to 4 3 10 26 m 2 s 21 , and an enhanced vertical diffusivity of 1 3 10 24 m 2 s 21 is active at depth, motivated by Bryan and Lewis (1979).…”

“…Ocean surface fluxes (in the absence of sea ice) are calculated using the bulk formula of Large and Pond (1981). Boundary layer and convective mixing in the ocean is parameterized according to Large et al (1994).…”