APRIL 1998 ZHANG ET AL. 589 Sensitivity of the GFDL Modular Ocean Model to Parameterization of Double-Diffusive Processes* JUBAO ZHANG MIT/WHOI Joint Program, Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts RAYMOND W. S CHMITT AND RUI XIN HUANG Department of Physical Oceanography, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts (Manuscript received 24 February 1997, in ®nal form 7 July 1997) ABSTRACT The effect of double-diffusive mixing on the general circulation is explored using the GFDL MOM2 model. The motivation for this comes from the known sensitivity of the thermohaline circulation to the vertical diffusivity and the earlier work of Gargett and Holloway, who studied the effects of a simple nonunity ratio between heat and salt diffusivities in a GCM. In this work, a more realistic, yet conservative, parameterization of the double- diffusive mixing is applied, with the intensity depending on the local density ratio Rr 5 aTz/bSz. A background diffusivity is used to represent non-double-diffusive turbulent mixing in the stably strati®ed environment. The numerical model is forced by relaxation boundary conditions on both temperature and salinity at the sea surface. Three control experiments have been carried out: one with the double-diffusive parameterization (DDP) deter- mined by the local density ratio, one with constant but different diffusivities for heat and salt as previously considered by Gargett and Holloway (GHD), and the other with the same constant diapycnal eddy diffusivity for both heat and salt (CDD). The meridional overturning in run DDP is 22% less than in run CDD, and the maximum poleward heat transport is about 8% less. In comparison, the overturning rate and poleward heat transport in run GHD display reductions that are about half as large. The interior temperature and salinity in run DDP and GHD are higher than in run CDD, with the change in run DDP more than twice that in run GHD. In addition, in DDP and GHD, the density ratio distribution becomes closer to unity than in run CDD, with the change in run DDP being larger than in GHD. Interestingly, the double diffusion is stronger in the western boundary current region than the interior, implying a close relation between vertical shear and the intensity of double diffusion. These results indicate a greater sensitivity of the thermohaline circulation to double diffusion than had previously been suspected due to the tendency of the double-diffusive mixing to generate self-reinforcing ¯ows. This effect appears to be more signi®cant when the double-diffusive mixing is applied only when the strati®cation is favorable rather than uniformly applied. In addition, parameter sensitivity experiments suggest that double diffusion could have stronger effects on the meridional overturning and poleward heat transport than modeled here since the parameterizations chosen are rather conservative. 1. Introduction pycnal) eddy diffusivity (K), which is the mechanism that provides the necessary warming of the rising abys- The thermohaline circulation of the ocean plays an sal waters. F. Bryan (1987) found an approximate K 1/3 important role in the climate system of the earth, es- dependence of the MOC; however, his model runs may pecially in controlling the oceanic part of the poleward not have reached equilibrium; later work has found a heat transport. The large-scale structure of the ther- K 2/3 dependence (Marotzke 1997; Zhang et al. 1997, mohaline circulation and its variability has been studied submitted to J. Phys. Oceanogr.), when the conventional extensively in models (Weaver and Hughes 1992; Huang ``relaxation'' boundary conditions are applied for the 1995). One result of these studies is the ®nding that the surface forcing. Whatever the speci®c power law de- strength of the meridional overturning cell (MOC) is pendence, the continual production of cold deep water strongly dependent on the value of the vertical (or dia- at high latitudes requires vertical mixing to close the circulation (Munk 1966). Observational microstructure work in recent years * WHOI Contribution Number 9239. (Gregg 1989; Polzin et al. 1995) has indicated that tur- bulent mixing in the ocean interior caused by internal Corresponding author address: Mr. Jubao Zhang, Room 54-1419, wave breaking is generally much weaker than has been Massachusetts Institute of Technology, Cambridge, MA 02139. inferred from the large-scale budget approach of Munk E-mail: [email protected] (1966), Hogg et al. (1982), and others. However, evi- q 1998 American Meteorological Society Unauthenticated | Downloaded 09/23/21 07:45 PM UTC 590 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 28 dence is emerging that turbulence near rough topogra- plied in the climate-scale numerical model runs de- phy may be suf®ciently enhanced to provide the re- scribed below. However, the parameterization of mixing quired downward heat ¯ux (Toole et al. 1994; Polzin et processes, both vertical and horizontal, requires careful al. 1997). One problem with near-bottom mixing is that treatment in numerical models. The oceanic circulation the strati®cation is weak in the abyss, so heat ¯uxes involves extremely broad scales in both time and space; tend to be small, even with very large eddy diffusivities. thus, we can never resolve all the temporal and spatial This reduced effectiveness of deep internal-wave-in- scales in numerical models. Consequently, for the fore- duced turbulence (the mixing of already mixed water) seeable future, subgrid-scale phenomena must be par- leads us to examine the other mixing processes occur- ameterized in ocean general circulation models. In fact, ring in the more strongly strati®ed thermocline. determining suitable parameterizations of subgrid-scale The primary processes that must be considered are phenomena is one of the most critical problems in nu- the double-diffusive instabilities of salt ®ngering, which merical modeling of the general circulation. Early ocean occurs when temperature and salinity both decrease with circulation models were mostly based on z coordinates, depth, and diffusive convection, which occurs when and subgrid-scale mixing was parameterized in terms of temperature and salinity both increase with depth. It is constant horizontal and vertical mixing. However, such well known that on the molecular level heat and salt simple horizontal/vertical mixing schemes can introduce have diffusivities that are two orders of magnitude dif- strong arti®cial cross-isopycnal mixing near fronts, such ferent. This difference drives convective motions even as the Gulf Stream, where isopycnals slope sharply. To if the overall density pro®le is stable. Substantial evi- overcome the arti®cial cross-isopycnal mixing in low- resolution z-coordinate models, a numerical technique dence is now available that these processes play a sig- of rotating the mixing tensor has been proposed by Redi ni®cant role in ocean mixing (Schmitt 1994). Their prin- (1982) and has been implemented here. cipal effect is to transport heat and salt at different rates In addition, Gent and McWilliams (1990, hereafter in the vertical and cause a net upgradient ¯ux of buoy- GM90) pointed out that there is an extra advection term ancy. A number of recent modeling studies show that in the tracer balance equation of non-eddy-resolving such differential transports have important effects on models, whose existence is due to the Lagrangian mean the stability and structure of the large-scale thermoha- transport of mesoscale eddies. They introduced a pa- line circulation. rameterization based on a downgradient diffusion of the In particular, Gargett and Holloway (1992, hereafter isopycnal layer thickness in adiabatic ¯ow. The addition GH92) ®rst investigated the effects of a simple double- of this transport term makes the tracer conservation diffusive parameterization in an ocean model. They equations in a non-eddy-resolving model self-consistent showed that the steady-state characteristics of low-res- and eliminates the unphysical background horizontal olution GCMs used in climate studies are very sensitive diffusion require in the earlier version of the isopycnal/ to the ratio of the vertical eddy diffusivities for salinity diapycnal mixing schemes. The dynamic effect and and temperature. Large differences in meridional trans- model sensitivity on the isopycnal/diapycnal mixing ports resulted due to the upgradient buoyancy ¯ux, have been discussed in several recent papers (Gent et which forced different advective±diffusive balances to al. 1995; Danabasoglu and McWilliams 1995). be realized. Ruddick and Zhang (1989) found that the In this study we will focus on the parameterization ``salt oscillator'' mechanism in a box model could be of diapycnal mixing in connection with double-diffusive completely stabilized by incorporating salt ®ngers into processes. Based on results from theory, laboratory ex- the model. Most recently, Gargett and Ferron (1996) periments, and oceanic observations, the intensity of found that multibox models with nonequal heat and salt double diffusion must depend on the local density ratio diffusivities exhibited extended ranges of multiple equi- Rr 5 aTz/bSz. There is strong evidence indicating that libria, a different mode transition near present-day val- double diffusion is important in controlling the diapyc- ues of freshwater forcing magnitude, and the possibility nal mixing process in the ocean only if Rr is suf®ciently of quasiperiodic oscillatory states