Atmosphere-Ocean
ISSN: 0705-5900 (Print) 1480-9214 (Online) Journal homepage: http://www.tandfonline.com/loi/tato20
Isopycnal mixing and convective adjustment in an ocean general circulation model William A. Gough To cite this article: William A. Gough (1997) Isopycnal mixing and convective adjustment in an ocean general circulation model, Atmosphere-Ocean, 35:4, 495-511, DOI: 10.1080/07055900.1997.9649601 To link to this article: http://dx.doi.org/10.1080/07055900.1997.9649601
Published online: 19 Nov 2010.
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Date: 30 January 2016, At: 18:31
Isopycnal Mixing and Convective Adjustment in an Ocean General Circulation Model
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William A. Gough Physical Sciences Division, University of Toronto at Scarborough 1265 Military Trail, Scarborough, Ontario M1C 1A4
[Original rnanuscript receivcd 6 August 1996; in revised form 12 August 1997]
ABSTRACT Convective adjastment is exa,nined in an ocean general circulation model ‘,vhich uses an isopycnal mixing parametrization. It is found that the use of an explicit comective adjustment scheîne is not needed in a varieo’ of equilibria and climate change scenario si,nulations. A numerical unechanisun is proposed ta explain this as well as the localized appearance of ne gatii’e’ diffusion. RÉSUME On étudie un schéma d’ajustement convecai dans un modèle de la circulation
océanique générale qui utilise une J)aralnétrisation d’au mélange isapycne. On a trouvé que l’utilisation d’un sché.’na d’ajustement convectif explicite n ‘est îas nécessaire pour une variété de simulations impliquant (les scénarios d’équilibre et de changement climatique. Ou propose un mécanisme numérique pour expliquer cette observation ainsi que l’aspect localisé de diffusion négative.
i Introduction The coarse resolution of ocean general circulation models dictates the parametrizalion of sub-grid scale processes, in particular, convection and diffusion. Killworîh (1983) identified two types of convection in the ocean, sheif siope and open ocean, neither of which can be properly resolved in current ocean models. In order to model the effect of convection, Bryan (1969) introduced a convective adjusîment scheme in which successive levels are iteratively examined for static stability. When static instability is detecîed, homogenization of temperature and salinity occurs. In some instances many iterations are required 10 completely remove the insîability. This approach has been questioned (Killworth, 1989; Smiîh, 1989; Marotzke, 1991). Cox (1984) suggested the use of an alternative scheme in which convection is calculated implicitly as enhanced vertical diffusion. Yin and Sarachik (1994) suggesîed the use of a complete convective adjusîment scheme, superior 10 the enhanced vertical diffusion method. They found that model behaviour under mixed boundary ATMOSPHERE-OCEAN 35(4)1997,495—511 0705-5900/97/OOOO-0495$ 1.25/O © Canadian Meteorological and Oceanographie Snciety
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conditions (restoring condition on temperature, flux condition on salinity) depended on the convection scheme used. Lenderink and Haarsma (1994) illustrated the importance of convective activity in determining the multiple equilibria behaviour for an ocean model under mixed boundary conditions. Rahmstoîf (1995) suggested that climate drift which occurs in coupled atmosphere-ocean models is a result of the shifting of convective regions leading to new equilibria. These studies indicate the importance of convective adjustment modelling in ocean general circulation models. In this work the impact of a lateral mixing scheme on convective activity is examined. In the next section a review of the mixing scheme is presented along with relevant numerics. a Isopycnal mixing Isopycoal mixing has been traditionally recommended for use in coarse resolution models to more accurately represent physical processes such as mixing by mesoscale ocean eddies (Montgomery, 1940; Veronis. 1975; McDougall and Church, 1986; Redi, 1982; Sarmiento, 1983; Gough, 1991a). Redi (1982) derived the appropriate tensor transformation to enable mixing along and normal to constant density surfaces in an ocean general circulation model cast in the traditional geopotential coordinate systeffi. Cox (1987) provided the numerical coding which will hereafter be referred to as C87. Cox began with the diffusive tracer equation (omitting for this discussion the advective and forcing ternis),
where T is any passive or active tracer. The indices i and j represent the three spatial coordinates. K~ is a second rank tensor of the form, PxPy Pz
-
K=A1
-
PxPy 2 pz Px
~ ~
Pz
Pz
Px Pz
p
-
(2)
E+82
where two assumptions are made, eQ= AD/AI) < i04 i06 O î0~ O
KE (ergs/cm3)
MMT (Sv)
NHT (PW)
CONV
0.431 0.431 0.435 0.429 0.429 0.412 0.245 0.136
8.43 8.56 8.63 8.52 8.46 6.81 9.90
0.247 0.244 0.251 0.241 0.242 0.242 0.253 0.174
5 S 5 5 5 3 933 744
—
The explicit convection paranietrization is the one suggested by Cox (1984) where convection is treated as intense vertical diffusion. Note that this method is often referred to as an ‘implicît’ scheme due to the numerical method used. The standard value used for the convective diffusivîty is 2.5 x îo~ cm2ls. In these experiments the C87 isopycnal formulation is used for mixing in the tracer equations. A few model runs, for comparison purposes, are done using traditional horizontal and vertical mixing. Values for At, AD, AB and bm, the isopycnal, diapycnal and background horizontal diffusivities and maximum allowable isopycoal slope, respectively, are selected to satisfy an empirically derived criterion to avoid negative diffusion (Gough and Lin, 1995). These are A 2/s, 2.0 x i0~ cm AD = 1.0 cni2ls and AR = 0.5 x î0~ cm2ls. The maximum1 allowable isopycnal slope is set at 0.03535 in order that the maximum vertical diffusivity due 10 sloping isopycnals matches the convective diffusivity of 2.5 x i04 cm2ls. Isopycnal mixing as a convective adjustment parametrization is tested in two ways. First a series of equilibrium simulations are performed (listed in Table 1). Isopycnal mixing is used for the first six experiments while the last two experiments of this series are run using the standard horizontal mixing parametrization. For cases one, six and eight explicit convective adjustment is suppressed. This is equivalent to setting the convective diffusivity to zero. Diapycnal diffusivity, though, does occur with a diffusivity coefficient of 1.0 cm2/s. For the other four isopycnal cases explicit convective adjustment is used with a range of values for the convective diffusivity. In the last isopycnal case (6), the vertical resolution is increased, i.e., ten irregularly spaced layers are replaced by eighty uniforni levels of 50 ni depth. The process of reaching equilibnuni, due to the initial low salinity, is dominated
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TABLE
2.
List of cooiing experiments. Ail experiments use isopycnai mixing. Sudden refers to the instantaneous imposition of a cooiing. Graduai refers ta a rami)ed cuniing over 100 years.
Experiment
Type
Diffusivity 2/s cm
S S S S S 1 1 1 1 10 Il 12 13 14
Sudden Sudden Sudden Sudden Sudden Graduai Graduai Graduai Graduai Graduai Sudden Sudden Sudden Sudden
i iO~ 2.5 x i04 id5 106 i i04 2.5 x i0~ i05 i0~ 2.5 x i04 2.5 x iO~ 2.5 x i0~ 2.5 x i0~
Restoring Timescale 50 50 50 50 50 50 50 50 50 50 25 100 50 50
days days days days days days days days days days days days days days
Temperature Anomaiy 20 20 20 20 20 20 20 20 20 20 20 20 10 30
by convection. For comparison purposes, two final expennients are run. The first of these uses a standard value for convective diffusivity while the last case has convective diffusivity set to zero. The second way of testing the convective paranietrization is in a series of surface cooling experiments (Table 2). These experiments are performed as extensions of the equilibrium simulations. Surface cooling induces convection and enables the evaluation of the model during a convectively dominated period of change. Paranieters that are varied include the use of explicit convection, the magnitude of the convective diffusivity, the resîoring timescale on temperature and salinity forcing and the magnitude of the cooling anomaly. For siniplicity and with no particular physical basis, the surface cooling is uniforni in the domain. The cooling is performed in two ways. The first is a sudden change of the surface restoring temperature and the second is a graduai change of the sanie quantity over 100 years (as in Gough and Lin, 1992). 3 Resuits and Discussion
a Equilibrium results The results of the six isopycnal and two horizontal mixing equilibrium simulations are presented in Table 1. Each case is integrated for 2000 years beginning at rest. For an idealized basin configuration this is sufficient to reach equilibrium. Ah cases use a 50-day surface restoring timescale for temperature and salinity. The results include equilibrium values of kinetic energy density (KE), number of statically unstable points (CONV), peak values of the overturning streanifunction (MMT) and northward heat transport (NHT).
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ISopycnal Mixing and Convective Adjustment in an Ocean GCM I 501 The first five isopycnal mixing cases have five statically unstable points at equilibrium and the sixth case with finer vertical resolution has three statically unstable points. The first horizontal niixing case in contrast has 933 unstable points. The second horizontal mixing case, which suppressed explicit convection through enhanced vertical diffusivity, produced an unrealistic circulation with evidence of second law of thermodynamics violations. In the case of isopycnal niixing, excluding the explicit convection adjustment scheme (case 1) makes no difference in the number of unstable points nor does using a very large (106 cni2/s) convective diffusivity (case 5). These results are consistent with Gough (199 la) and Gough and Welch (1994) which showed that the isopycnal cases had a much lower number of statically unstable points. The isopycnal niixing cases show only small variations of kinetic energy density, peak value of the overturning streanifunction and northward heat transport. The horizontal mixing case, though, has a much snialler kinetic energy density than the isopycnal cases in spite of the more intense meridional overturning. This is consistent with the earlier results of Gough and Lin (1992) in which the isopycnal mixing case had a larger gyre kinetic energy component due to reduced damping of smaller scale features. The meridional overturning streamfunction for cases 7 (horizontal mixing), i (isopycnal mixing with no explicit convective adjustment schenie) and 5 (isopycnal niixing with a convective diffusivity of 106 cm2/s) are shown in Fig. 1. All three exhibit the sanie overaîl structure. A wind driven Ekman circulation is present near the surface and the therniohaline overturning cell is found in the deeper ocean. The two isopycnal cases are essentially identical. The horizontal case has a more intense and deeper thermohaline circulation as evidenced by the value and location of the peak value of the overturning streanifunction. The temperature distributions for the same cases are shown in Fig. 2. Once again the two isopycnal cases are virtually identical. The abyssal waters are cooler in the isopycnal cases, a resuit consistent wtth Danabasoglu et al. (1994) and Danabasoglu and McWillianis (1995). b Cooling experiments i KINETIC ENERGY DENSITY ANO MERIDIONAL OVERTURNINO STREAMFUNCTION Figure 3 depicts the tue evolution of the kinetic energy density for the three isopycnal cases (1, 3 and 5 of Table 2) with sudden cooling. All cases exhibit an initial surge in kinetic energy followed by gradual reduction to the new equilibrium value. The approach to equilibrium tends to be a little more rapid for cases of larger convective diffusivity; case 1 taking about 300 years to reach the new state, and case 5 taking about 200 years. In Fig. 4, the corresponding results for the gradual cooling cases (6, 8 and 10) are shown. In these cases the initial surge is much less pronounced than in the sudden cooling cases. The initial peak occurs at or slightly after 100 years, the end of the gradual cooling. The peak value is marginally larger for case 10. All three cases approach the new equilibrium value by year 400, although the path taken varies.
502 I William A. Gough O
a)
500
ow
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i 000
20N
45N TO
CONTOIJO FR00
10.089
CONTOUR INTERVAL ~
4000
70N 1.0000
PTI~.3I~ 1.1023
—lINON
o b)
500 IZ T
ow i 000
4000 45N
20N
c00rouR Fig. i
TO FaON
—1.00e
10.000
CORTOJ8 IRTERRM. 0F
70N 1.0080 PT(3.31.
.56607
Meridionai overturning streamfunction (Sv) for a) horizontal mixing case, b) the isopycnai mixing case with no explicit convection 2fs). and, c) the isopycoal mixing case with explicit convection (convective diffusivity of 106 cm
Isopycnal Mixing and Convective Adjustment in an Ocean GCM I 503
o c) 500
oL~J
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o
1000
4000 45N
20N CONTOUR PROM
—19.918
TO
19.999
Fig. i
CONTOUR INTERRAL IF
70N 1.0990
PTI3.21.
.62667
Concluded.
The time evolution of the peak value of meridional overturning streanifunction for the sudden and gradual cases (not shown) closely mimics the trend of the kinetic energy density. The initial surge of the kinetic energy density coincides with a sudden intensification of the thermohaline circulation. After the initial surge the overturning streanifunction gradually approaches the new equilibrium value. 2 STATIC INSTABILITY ANO TEMPERATURE ANOMALIES The tue evolution of the number of statically unstable points is depicted in Fig. 5 for the three sudden cooling cases (1, 3, 5). After an initial surge of unstable points there is a rapid drop-off to nearly zero by year 100. This minimum is followed by a secondary peak near year 200. The three cases, although the sanie in these gross features, do exhibit some smaller scale variability, particularly case 5. Figure 6 shows the corresponding plots for the gradual cases (6, 8, 10). The initial surge in unstable points is considerably muted for these three cases compared to the sudden cooling cases. The secondary peak is present but is delayed by about 100 years. Once again case 10 exhibits more variability and has a slightly larger number of unstable points during the secondary peak. To further examine the nature of the secondary peak several more experiments are run (experiments 11—14 of Table 2) in which the size of the temperature anomaly and the restoring timescale are varied. It is found that the tue of the secondary peak
504/ William A. Gough
o a)
500
z z o-
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w
1000
4000 20N CONTOUR FRON
—2.9019
45N TO
30.801
CONTOUR INTERVAL 0F
70N 1.0089
PT
