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JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C11, 3345, doi:10.1029/2002JC001704, 2003
Impact of isopycnal mixing on the tropical ocean circulation M. Lengaigne, G. Madec, and C. Menkes Laboratoire d’Oce´anographie Dynamique et de Climatologie (CNRS/UPMC/IRD), Universite´ Pierre et Marie Curie, Paris, France
G. Alory Laboratoire d’Etudes en Ge´ophysique et Oce´anographie Spaciales (CNRS/CNES/UPS/IRD), Observatoire Midi Pyre´nne´es, Toulouse, France Received 6 November 2002; revised 26 April 2003; accepted 26 June 2003; published 8 November 2003.
[1] The sensitivity of tropical ocean dynamics to the ocean lateral mixing orientation is
explored using a z-coordinate climate-type ocean general circulation model. Compared to a simulation using horizontal mixing on both tracers and dynamics (HOR), a rotation of the tracer tensor in which mixing occurs along isopycnals (ISOT) improves the structure of the off-equatorial density field, which consequently enhances the offequatorial circulation through geostrophy. However, the dynamics at the equator in ISOT are degraded compared to observations, as the upper part of the Equatorial Undercurrent (EUC) is too deep and the South Equatorial Current (SEC) is too intense. Next, isopycnal diffusion on momentum is implemented (ISOMT). An examination of the momentum balance at the equator shows that this change in lateral diffusion direction significantly reduces the meridional diffusive flux of momentum at the top of the EUC. This intensifies the EUC, which, in turn, weakens the SEC along the equator through vertical diffusion. The equatorial degradations observed in ISOT disappear. Compared to ISOT and HOR, the separation of the two SEC branches and the equatorial current magnitude in the surface layers are much better reproduced. Moreover, in contrast to the results from ISOT and HOR, isopycnal momentum mixing allows the existence of both horizontal up-gradient and down-gradient eddy momentum fluxes, notably improving the vertical profile of the lateral viscosity term. The ISOMT experiment is therefore shown to be the closest to observations. These results suggest that isopycnal mixing should be used on both tracers and momentum to better simulate the observed eddy effects and the INDEX TERMS: 4568 Oceanography: Physical: Turbulence, tropical circulation in climate models. diffusion, and mixing processes; 4231 Oceanography: General: Equatorial oceanography; 4512 Oceanography: Physical: Currents; 4572 Oceanography: Physical: Upper ocean processes; KEYWORDS: tropical Pacific, mixing parameterization, equatorial currents Citation: Lengaigne, M., G. Madec, C. Menkes, and G. Alory, Impact of isopycnal mixing on the tropical ocean circulation, J. Geophys. Res., 108(C11), 3345, doi:10.1029/2002JC001704, 2003.
1. Introduction [2] The tropical region plays a fundamental role in the Earth’s climate. A precise knowledge of the upper tropical ocean structure and its physical processes is of paramount importance in understanding coupled air-sea mechanisms, and in better explaining the global climate. In fact, the development of large-scale climatic events such as the El Nin˜o-Southern Oscillation (ENSO) is intimately tied to the structure of the equatorial currents and temperature in the surface layers of the Pacific Ocean [Zebiak and Cane, 1987]. Many investigations of these phenomena rely on ocean general circulation models (OGCMs), which have the goal of simulating an oceanic circulation comparable to observations. Tremendous efforts have therefore been Copyright 2003 by the American Geophysical Union. 0148-0227/03/2002JC001704
invested in their development and improvement. However, when coupled to atmospheric GCMs (AGCMs), OGCMs still have limited success in producing ENSO-like oscillations. Part of the problem lies with the inaccuracy in the representation of oceanic subgrid-scale physics, which is known to significantly contribute to the heat and momentum budget in the tropical region [Bryden and Brady, 1989; Wacongne, 1989; Johnson and Luther, 1994; Qiao and Weisberg, 1997]. One challenge for climate modeling is thus to reliably parameterize subgrid-scale processes and to understand the climate sensitivity to these processes. In this paper we address the lateral mixing parameterization in a z-coordinate climate OGCM framework for tropical oceans. [3] For active tracers (temperature and salinity), lateral mixing was first implemented along horizontal surfaces, which is inconsistent with the fact that tracer mixing occurs predominantly along isopycnal/neutral surfaces [Iselin, 1939; Montgomery, 1940; McDougall and Church, 1986].
9-1
9-2
LENGAIGNE ET AL.: IMPACT OF ISOPYCNAL MIXING
Table 1. Model Experiments
HOR ISOT ISOMT
Orientation of Tracers Mixing in the Ocean
Orientation of Momentum Mixing in the Ocean
horizontal isopycnal isopycnal
horizontal horizontal isopycnal
Isopycnal mixing parameterizations have therefore been introduced in level models [Redi, 1982; Cox, 1987; Griffies et al., 1998]. Another major improvement (mainly for middle and high latitudes) has been the introduction of the Gent and McWilliams [1990] eddy induced velocity parameterization, which mimics the effect of baroclinic instabilities on the large-scale thermohaline structure of the ocean. Numerical studies in both forced OGCMs [Hirst and Cai, 1994; Duffy et al., 1995; Robitaille and Weaver, 1995] and coupled GCMs [Hirst et al., 2000; Speer et al., 2000; Guilyardi et al., 2001] have emphasized that a change in the orientation of the mixing tensor on tracers from horizontal to isopycnal greatly improves the tropical thermohaline structure and modifies ENSO characteristics [Raynaud et al., 2000]. [4] Less attention has been devoted to the problem of lateral mixing for momentum. This mixing is usually parameterized by assuming that eddy fluxes act against horizontal gradients and are proportional to these gradients. The coefficient of proportionality (the eddy viscosity coefficient) is commonly taken as constant, at least in the vertical, and its magnitude is adjusted to ensure numerical stability. This often compromises the realism of the simulated tropical ocean dynamics, as a large lateral viscosity coefficient significantly reduces the Equatorial Undercurrent (EUC) magnitude, resulting in a South Equatorial Current which is too intense and strongest right at the equator [Maes et al., 1997; Delecluse and Madec, 1999]. Recent studies have partly avoided this problem by reducing the viscosity coefficient in the tropics to a value O(103 m2 s1) comparable to the one derived from observations [Bryden and Brady, 1989] (hereinafter referred to as BB89). The choice of reasonable and identical values for both the diffusivity and viscosity coefficients around the equator in the OPA OGCM [Madec et al., 1998] explains the quality of the simulated equatorial dynamics [Aumont et al., 1999; Vialard et al., 2001; Radenac et al., 2001; Lengaigne et al., 2002]. The use in the NCAR OGCM of an anisotropic coefficient with a low value in the meridional direction results in similar improvements [Large et al., 2001]. However, the use of these latest parameterizations which consider the viscosity coefficient as vertically uniform still does not allow a reproduction of the vertical structure of the observed eddy effects [Lukas, 1987; BB89]. Indeed, BB89 have shown that the magnitude of the horizontal eddy viscosity coefficient deduced from the observations varies strongly with depth at the equator: This coefficient is at a minimum and even negative in the upper and lower part of the EUC, and reaches a maximum O(103m2 s1) in the EUC core and at the surface (see Table 1 of BB89). [5] In this paper, we investigate the effect of orienting the lateral eddy momentum mixing along the isopycnal surfaces in a z-coordinate climate OGCM framework. This isopycnal lateral mixing parameterization has never been tested in this
type of model, since the choice of the lateral diffusive operator has mostly been motivated by numerical constraints and is therefore not physically based [Griffies et al., 2000]. However, isopycnal momentum mixing is naturally incorporated in isopycnal coordinate models [Bleck and Smith, 1990; Oberhuber, 1993; Schopf and Loughe, 1995] as the prognostic variables are carried in layers of constant potential density, and thus both lateral tracers and momentum mixing occur strictly along isopycnal surfaces. Recent studies [Chassignet et al., 1996; Megann and New, 2001] have demonstrated that an isopycnal model is able to realistically reproduce equatorial dynamics in the presence of a pure isopycnal diffusion on momentum. This study will allow us to highlight, at least partially, the consequence of such a parameterization on the ocean dynamics. It will also provide evidence that this new parameterization more accurately simulates the effects of the observed eddies and the equatorial dynamics. [6] The paper is organized as follows. Section 2 describes the model and the sensitivity experiments. Section 3 compares the responses of the sensitivity experiments and addresses the physical mechanisms involved in their differences, with special attention devoted to the Pacific sector where the sensitivity is greatest. In section 4, the results are compared with observations in the equatorial Pacific Ocean, the region with the longest and the most complete set of measurements [McPhaden et al., 1998]. Section 5 contains a general discussion and the overall conclusions.
2. Model Formulation and Experiments [7] The OGCM used in this study is the OPA model [Madec et al., 1998; Delecluse and Madec, 1999] in its global configuration ORCA2. The horizontal mesh is based on a 2 by 2 Mercator grid (i.e., the same zonal and meridional grid spacing). Following Murray [1996], two numerical inland poles have been introduced in order to remove the North Pole singularity from the computational domain. The departure from the Mercator grid starts at 20N, and is constructed using a series of embedded ellipses following the semi-analytical method of Madec and Imbard [1996]. In addition, a local transformation is applied in the tropics to refine the meridional resolution, to up to 0.5 at the equator. The model has 31 levels with a 10-m spacing in the upper 150 m, increasing to 500 m in the deep ocean. [8] The model uses a free surface formulation [Roullet and Madec, 2000] and computes the density from potential temperature, salinity, and pressure using the Jackett and McDougall’s [1995] equation of state. Vertical eddy viscosity and diffusivity coefficients are computed from a turbulence closure scheme [Blanke and Delecluse, 1993] allowing high values in the surface boundary layer as well as a minimum value of 105 m2 s1 in the thermocline. Convective mixing is simulated by setting the vertical viscosity and diffusivity coefficients to 100 m2 s1 in statically unstable regions. The model uses Gent and McWilliams’ [1990] eddy induced velocity parameterization with a varying coefficient, depending on the growth rate of the baroclinic instability [Tre´guier et al., 1997]. Nevertheless, this parameterization has a negligible impact on the simulated equatorial dynamics as the coefficient is decreased equatorward of 20 to cancel out at the equator.
LENGAIGNE ET AL.: IMPACT OF ISOPYCNAL MIXING
[9] The lateral viscosity and diffusivity operator is defined as Dl ðÞ ¼ r ½Al < rðÞ ;
ð1Þ
where the bold center dot is either a horizontal velocity component or temperature or salinity, r is the threedimensional gradient operator and < is the rotation matrix, 0 B B
