Sep 15, 1990 - area upper OGCM that is capable of reaching an equilibrium. 1Now at Institute of Ocean Sciences, Sidney, British Columbia,. Canada. 2Now at ...
JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 95, NO. C9, PAGES 16,149-16,167, SEPTEMBER
15, 1990
Numerical Experiments With a Wind- and Buoyancy-Driven Two-and-a-Half-Layer Upper Ocean Model J. Y. CHERNIAWSKY,1 C. W. YUEN, 2 C. A. LIN, AND L. A. MYSAK Climate Research Group, Department of Meteorology, McGill University, Montreal, Quebec, Canada We describe numerical experiments with a limited domain (15ø-67øN, 65ø west to east) coarseresolutiontwo-and-a-half-layerupper ocean model. The model consistsof two active variable density layers: a Niiler and Kraus (1977) type mixed layer and a pycnocline layer, which overlays a semipassivedeep ocean. The mixed layer is forced with a cosinewind stressand Haney type heat and precipitation-evaporationfluxes, which were derived from zonally averaged climatological (Levitus, 1982) surfacetemperaturesand salinitiesfor the North Atlantic. The secondlayer is forced from below with (1) Newtonian cooling to climatological temperatures and salinities at the lower boundary, (2) convective adjustment,which occurswhenever the density of the secondlayer is unstable with respect to climatology, and (3) massentrainmentin areas of strongupwelling, when the deep ocean ventilates through the bottom surface. The sensitivity of this model to changesin its internal (mixed layer) and external (e.g., a Newtonian coupling coefficient) parameters is investigated and compared to the results from a control experiment. We find that the model is not overly sensitive to changesin most of the parametersthat were tested, albeit these resultsmay dependto someextent on the choice of the control experiment.
1.
INTRODUCTION
Most of the present ocean general circulation models (OGCMs) are based on the multilevel full-depth OGCM formulation of Bryan [ 1969]. The main obstacleto their more extensive use in global climate studiesis probably the large amount of computer time that is required to spin up a full-depth OGCM to an equilibrium solution, before a meaningful sensitivity experiment can be performed. In terms of simulationtime the spin-uptime scaleis approximatelygiven by the time it takes a temperature, salinity, or tracer anomaly to diffuse from the surface all the way to the bottom,
state in 20-30 model years and is therefore quite suitable for a fair number of climate sensitivity experiments. There were several similar upper ocean models [e.g., $chopfand Cane, 1983; McCreary and Kundu, 1988], but these were mostly restricted
to simulations
of low-latitude
oceans and did not
include the effects of salinity. The model presented here spans a subtropical-subpolar domain and has two active layers, namely a mixed layer and a pycnocline layer, which overlay a quiescent semipassive deep ocean (Figure 1). It was designedafter the global upper ocean model of Pollard [1982] (hereafter referred to as DP; namely,tv = H2/Ev,whereH and Evare the depthand see also Yuen et al. [1987]). After some initial experiments vertical eddy diffusivity coefficient, respectively. Substitut- we made several significant changes to its formulation. We ingthecharacteristic values H = 5 kmandev= 2 x 10-4 m2 added a prognostic salt conservation equation, on par with s-• oneobtains tv of theorderof 4000yearsTo overcome the heat equation, and added salt fluxes in the mixed-layer this handicap, Bryan [1984] (see also Bryan and Lewis entrainment formulation. As is customary when testing a ,
ß
[1979]) introduced a distorted physics approach, whereby deep-oceanprocessesare accelerated by slowing down the gravity waves and by decreasingthe local heat capacity. In a different model [Maier-Reimer et al., 1982; Maier-Reimer and Hasselmann, 1987] a considerable saving in computer time was achievedby filtering out all gravity waves, allowing time steps of the order of 1 month.
new model, it is forced from above with an idealized wind
stressfunction and linearized net heat and freshwater (P-E) fluxes. The boundary conditions at the base of the second layer now have three components: (1) Newtonian diffusion (with a time scale of 20-30 years) to zonally averaged climatological temperatures and salinities at a local model depth, (2) a limited mass(and therefore heat and salt) uptake For climate simulations on decadal and shorter time scales from the deep ocean that is mostly due to wind-driven a third approachmay be possible.In this casethe deep ocean upwelling (ventilation) in the subpolar gyre and, to avoid is assumedto be in a quasi-equilibriumstate, so that only the model drift due to this gain in mass, a prescribed small upper ocean, extending down to somewhatbelow a seasonal downwelling elsewhere, and (3) a conditional convective thermocline, needsto be modeledexplicitly. In this paper we adjustment between the second layer and its climatological investigatethis third approach. We describethe formulation lower surface (see component 1 above). Boundary condiand examine the sensitivity of a coarse-resolution limited- tions 2 and 3 were not consideredin DP, in which the second area upper OGCM that is capable of reaching an equilibrium layer temperature was cooled to abyssal0øCwith Newtonian diffusionon a time scale that is about 10 times longer than it 1Nowat Instituteof OceanSciences, Sidney,BritishColumbia, is here. Additional differences from the original DP formuCanada. lation will be pointed out in the next section. 2Nowat CanadianClimateCentre,Downsview,Ontario,CanThe physical basis and one reason for using a variable ada. depth layer type model is that its quasi-Lagrangianbehavior Copyright 1990 by the American GeophysicalUnion. makes it well suited for modeling water mass and property transportsin a stratified ocean. The motivation for using (at Paper number 90JC00921. 0148-0227/90/90J C-0921 $05.00 least, for now) a strictly upper ocean model is the apparent 16,149
16,150
CHERNIAWSKY ET AL.' NUMERICAL EXPERIMENTS WITH AN UPPER OCEAN MODEL
section3 we presentthe resultsfrom the control experiment, while in section 4 we test the sensitivity of the model to changesin its parameter values. The discussionof the results is given in section 5.
ATMOSPHERE
Ti, Si, ui
MIXED LAYER
I
2.
$E SECOND
T2, S2, u2
DEEP
Fig. 1.
$Er QUIESCENT WATER
The two-and-a-half-layer model.
= 1, 2) are
separation in time scales between the decadal variations in upper ocean thermohaline fields and the slower (centennial to millenial) deep-ocean advection-diffusionprocesses.Our immediate plan here is then to describe the new model's formulation and response to simple forcing fields, while exploring the sensitivity to its parameter values. These
experimentsalso serve as a useful introductionto simula-
•7 . (hiuiui) q- hif X ui =
model
for
climate
studies:
Global
simulation
(hi•7pi- •ilq.) PO
+ AMV' (hiVui) - (-1)iEue+ •i2Erur O(hiTi) • + V' (uihiTi) =
0t
tions with more realistic seasonalforcing in a global ocean domain (C. W. Yuen et al., An upper ocean general circulation
FORMULATION
The presentupper ocean model consistsof two interacting layers (Figure 1): a Niiler and Kraus [1977] type mixed layer over a pycnocline layer. The deep water below the second layer is assumed to be motionless, though it interacts with the second layer through Newtonian cooling and limited mass, heat, and salinity exchange. Depth-integrated momentum, heat, salt, and continuity equationsfor the two layers (i
LAYER
I
T3 S3
MODEL
+ AnY' (hiVTi) poCp
-- (--1)iETe+ •i2Errr
(2)
with
O(hiSi) seasonalcycle, submitted to Climate Dynamics, 1990, here- • + •7. (uihiSi) = + AnV' (hiVSi) inafter referred to as Yuen et al. (submitted)). Ot Po As in other numerical models, we had to choose the -- (--1)iESeq-•i2ErSr (3) parameter values for the current set of experiments. In particular, some care was needed in selecting parameters Ohi that characterize the unresolved mixed-layer entrainment• + V' (uihi)= -(-1)iE + •i2Er (4) detrainment processes. The parameter values of DP were Ot changed because of the inclusion of prognostic salinity and the subsequent decrease in density contrast between the where V is the horizontal gradient operator in spherical layers, especially in the subpolar gyre. Most of the bulk coordinates; •0' is the Kroneckerdelta function;ui is the mixed-layer models, of which ours is one, have their origins horizontalvelocity; Ti is the temperature;Si is the salinity; in the Kraus and Turner [1967] formulation. They are mostly hi isthedepth;P0is thereference density(- 1026kgm-3); one-dimensional (no horizontal advection or diffusion), Cpisthespecific heatofwater(- 3990Jkg-• K-l); f = J•; while in DP and in our model the mixed layer is horizontally f-- 212 sin 0 is the Coriolis parameter; •7pi is the depthadvective and diffusive. The effect of horizontal advection averagedpressuregradient; 'r is the wind stress;and A M (= on the mixed-layer heat and kinetic energy budgets can be 4 x 105rn2 s- •) andAn (= 5 x 103m2 s- •) arehorizontal quite significant [e.g., Paduan and DeSzoeke, 1986]. eddy viscosity and diffusivity coefficients, respectively. The Martin [1985] has compared four mixed-layer models and O(hiui)/Otterm is absent in (1), which filters out inertiafound that all four could be "tuned" to perform reasonably gravity waves and allows long time steps in coarsewell when their mixed-layer depths and temperatures are resolution models [Killworth, 1985]. E is the entrainment comparedto single-stationdata. The parametersthat "tune" rate, given by (8) below, and Ue in (1) is ul for E < 0 and u2 different mixed-layer model performancesrepresent unre- for E > 0, while solvedturbulenceand internal wave generationand dissipa(Te, Se) = (T1, S1) E< 0 tion processes which govern the turbulent structure and (5a) depth of the mixed layer. The valuesof theseparametersare (Te, Se) -(T2T, S2T) E > 0 not well known [e.g., Deardorff, 1983], especially where global OGCM applications are concerned. It is therefore where important to know how sensitive OGCMs are to these parameter values, which of them can be simplified, and (T2r, S2r) = (1 - e)(T•, S•) + e(T2, S2) (5b) which need to be known with greater precision. Following
Martin[1985]weclassified ourparameters intotwogroups: and "internal" parametersthat govern mixed-layer entrainmentdetrainment processes and the other parameters, such as Newtonian coupling coefficients, which were called "external."
The numerical
e- eoh2/h
(5c)
with h = hi + h2 and e0 = 0.50. This parameterizationof model is described
in the next section.
In
temperature and salinity shears in the top part of the second
CHERNIAWSKY ET AL.' NUMERICAL EXPERIMENTS WITH AN UPPER OCEAN MODEL
layer is similar to that of DP, except that his e = max (0.5,
16,151
divergence in the interior of the subpolar gyre and, some-
h2/h)is larger.In a high-latitudemixed-layermodel(coupled times, along the middle of the western boundary. Whenever h2 < h2rnin, we first setE'r = (h2rni n - h2)/At, and we set E'r to a sea ice model), Lemke [1987] used a much smaller e A h/h2, with Ah beingthe thicknessof the shearzone(- 8 m, equal to zero elsewhere. But, in order to keep the model obtained from Arctic climatology). Surface heat and salinity fluxes, •0 and ff0, are parameterized as Haney [1971] type boundary conditions'
•o = Po%Xr(ro- r•) fro = -poS•w
(6a) d-I), exceptat grid pointswhereh2 < h2min, whereit is (6b)
where
•w = -xs(So-
S•)/1000
from gaining mass (and heat and salt) from below, we subtractfrom h2 a mean depth excess 8h gained during a previoustime step, so that the actual value of E r = E'r /At is slightly negative in most of the domain (-4 to -7 mm
(6c)
is the freshwater flux, i.e., the precipitation-evaporation (P-E) rate, S is the mean salinity, and TO and So are the zonally averaged surface temperatures and salinities for the North Atlantic [Levitus, 1982]. The surface coupling
usuallylessthan150mmd-• whichis consistent withthe values attributed to annual mean Ekman pumping velocity in the North Atlantic [Isemer and Hasse, 1987]. The corre-
spondingchangesin the second-layermomentum,heat, and salt are calculated in (1)-(3), where (Tr, Sr) = (T2L, S2L) everywhere, while Ur = 0 for E r > 0 and Ur - u2 if E r < 0 (akin to a bottom friction term). The depth-averagedpressure gradients in (1) are
coefficients areXt = Xs - 5 x 10-5 m s-• andtheratioof 1000 is used to convert practical salinity units (PSU) to actual
Vp2 = #[V(Ap32h)+ (hi + h2/2)Vp2]
(7a)
Vpl = #[V(Ap32h+ Ap21hl)+ (hl/2)Vpl]
(7b)
and
fractions.
The interfacial salt flux is accounted for by the entrainment term in (3); therefore ff• = 0. The penetratingcomponent of the solar heat flux at the base of the mixed layer is •
where # = 9.8m s-2 At9ji = t9j-- Piarecomputed froma
= •e-h•/hs,wherehs- 20misa penetration depthscale for linearized equation of state for seawater, Pi = P(Ti, Si) solarradiation, •} = 0.35• s, assuming65% is absorbedin a very thin surfacelayer, and •s is the solarheat flux at the surface. These are typical values for the relatively clear oceanic water types Ia, lb, and II [Paulson and Simpson, 1977], while the more turbid type III waters have hs of the
[Bryan and Cox, 1972], and the almost constant T3 and S3 are the zonally averagedNorth Atlantic potential
order
density (P3) at the chosen 3000-m reference depth in the
of 10 m or less.
temperatures and salinities at 3000 m depth [Levitus, 1982]. This is quite different from DP, where a constantAp32
- 4.0 kg m-3 wasused.We notethat whilethe potential
Two flux terms are included in each of the •2 and ff2. These are (1) vertical diffusion (Newtonian cooling) to cli-
North Atlantic (15ø-67øN) is approximately constant (P3 •
and•f23N= PoX2(S2-S2L), whereX2= 5 x 10-7 m s-• and
domain.
1027.9kgm-3 [seeLevitus,1982]),Ap32in ourmodelspans matologyat the bottomsurface,•23N=PoCpX2(T2 - T2L) a rangeof 0.4-2.0kg m-3. Thisrangeis largerfor a global The last terms in (7a) and (7b) owe their existence to the T2Land S2Lare obtainedby interpolatingto the local model depth the zonally averagedLevitus [1982]data for the North horizontal density variations in each layer [e.g., Schopf and
and ff23c,which are explainedbelow. The abovechoiceof X2 yields a vertical diffusiontime scaleof t2 = h2/x2 • 22
Cane, 1983; McCreary and Kundu, 1988]. They do not appear in DP or in isopycnal models. More often than not, they opposeother pressuregradient terms and thus tend to
years for h2 • 335 m. In a multilevel GCM [e.g., Bryan, 1969] an equivalent adjustment time scale would be tv =
weaken the horizontal transports. We should mention that it is numerically advantageous to
Atlantic; and (2) "deep" convective adjustmentfluxes •23c
h--•2/ev, whereevis a verticaldiffusivity coefficient. In order have, as in DP, a larger Ap32,especiallyat high latitudes.It
fortv - t2 - 22years,onewouldneedev• 1.6x 10-4 m2
results in faster internal Kelvin waves, somewhat compen-
s-•. Similarly,for ff• • 70m thetimescales formixed-layer satingfor the effectsthat coarse spatial resolutionand large adjustmentto the surface forcing of (5a) and (5b) are tr =
eddy viscosity have on the geostrophicadjustment process
•/Xr • 16 daysand ts - (1000/S•)tr = 460 days,respec- [Hsieh et al., 1983; Wajsowiczand Gill, 1986; Cherniawsky tively. The longerts simplyreflectsthe weak dependenceof and Mysak, 1989]. It facilitates a faster model spin-upand •w(ff0) on the surfacesalinity So. As in DP, instantaneous "shallow" convection occurs between the two layers when p• > P2. Temperatures and salinitiesare then set to (T, S) = [(T•, S•)h• + (T2, S2)h2]/h. We also added a deep convective adjustment' when P2 > P2L (where P2L= P(T2L,S2L)is the climatologicaldensityon the lower surface), we set (T2, S2) = (T2L, S2L). This is equivalent to mixing the second layer with an equal depth "under" layer, assuming(T2L, S2L) to be at midpoints of linear temperature and salinity profiles. The last term in each of (1)-(4) contains what we have called the "residual entrainment" rate E r. It is nonzero only if the secondlayer depth upwells to the prescribed minimum depth h2min(= 20 m here), which is usually due to Ekman
reducesthe total depth variations. On the other hand, while weak stratification at high latitudes makes the layer structure
less certain there, computed Ap32are in better agreement with ocean climatology. Also, an upper ocean model that is sufficientlydeep at high latitudes (becauseof the small Ap32 there) shouldbe more capableof simulatingvery deep (--•500 m) mixed layers that, for example, occur in winter in the northeast Atlantic [Robinson et al., 1979].
The entrainment rate E is determined by an excess of available turbulent kinetic energy in the mixed layer, which comes from wind mixing and from buoyancy-generated (negative buoyancy flux) or buoyancy-dissipated(positive buoyancyflux) turbulence[e.g., Niiler and Kraus, 1977]. It is given by
16,152
CHERNIAWSKY ET AL.' NUMERICAL EXPERIMENTSWITH AN UPPER OCEAN MODEL
E•
2mpou3,e -h'/ha -t7hl{(a/cp•rr(hl/hs) + n[(a/cp(•o-•;)-
(8)
poC2, + t7hlAp2t
ensure a relatively smooth spin-up subject to the prescribed forcingfields. In retrospect,it would have been sufficient(and potential energy in the mixed layer, (#h•Ap2r/Po)(Oh•/Ot)/2, simpleD to start with constantlayer depths and zonally averand turbulentenergyproduction at its base,rnu,3e -h'/hd aged climatologicaltemperaturesand salinities.) The wind stress was given the simple form 'r = (r •, 0), [Kraus and Turner, 1967]. Similarly, the second term is the contribution to this balance from the net buoyancy flux, where which is due to the penetratingcomponent•;r(h•/hs) of the (9) •x(o) = -3-0 cos [rr(0 - 00)/30ø] solar radiation •s [Kirn, 1976] (also DP) and the remaining The first term in the numerator in (8) is the contribution to
E from
the balance
between
a time
rate
of increase
in
heatandsalinityfluxes,n[a(•0 - •)/c v -/3Sø0].A "mixing (00 = 15øN, 3-0 = 0.1 Pa), and was somewhat tapered near
efficiency" coefficient is rn(= 3), u, = ('r/P0)•/2isfriction the boundaries.The surfaceforcingfieldsr •, To, So, and •s velocity, and hd (= 30 m) is the penetration depth scale against wind-driven turbulent dissipation. The heat and salt expansion coefficients are a = -(1/po)(Op/OT) and /3 = (1/po)(Op/OS), respectively,while Ap2r = P(T2r, S2r) -- Pl is the density jump under the mixed layer, with T2T and S2T
are shown in Figures 2 a-2d. 3.
THE CONTROL
EXPERIMENT
We have run two groupsof numerical experiments. In the first group we tested the sensitivity of the model to changes The function•hl/hs) is given by st(x) = 1 - 2/x + e-X(1 in the internal (mixed layer) parameters (Table 1), while in + 2/x) [Kim, 1976] (see also DP), prescribing the buoyancy the secondgroup the samewas done with the externalparamflux at the base of the mixed layer due to penetrating solar eters. In each experiment the model was spun up to a steady radiation. When the terms in square brackets in (8) are stateand beyondby integratingit for 60 model years (--•10 min of CPU on an IBM 3090).It would usuallyreach an equilibrium positive,[ ]>0, wesetn = 1. When[ ] 1/e. On 1). Table 1 lists the internal and the external parameter values chosen for this experiment. Figures 3a-3e show the the other hand, DP simply set n = 0.5 when [ ] < 0. C, = 3 max(1, u,) cm s-• is a typicalturbulentvelocity,sothat time history of area-averaged depth-integrated kinetic endefined in (5b).
2 + v/2)/2) (Figure3a),area-averaged depth poC, 2limitstheentrainment ratewhenh•Ap2 r issmall[Kim, ergyKEg= {hi(ui 1976] (DP).
Ki (Figure3b), area-averaged temperatureT• (Figure3c),
When E is negative, we set Ap2Tto zero, giving a faster detrainment rate. The choice of a mixed-layer model formulation and a suitableparameter set is not unique [Niiler and
area-averaged salinity Si (Figure 3d), and area-averaged maximumdepth h/max(Figure 3e) in each layer (i = 1, 2), as
Kraus, 1977; Zilitinkevich et al., 1979; Martin, 1985]. Our formulation does not depart far from that of DP, and the parameter values listed here are for the control experiment. The model was set in a subtropical-subpolar domain, centered at 41øN and spanning 52ø in latitude and 65ø in longitude. The numerical grid is the Arakawa B grid. The resolution is the same as in DP and in our global model [Yuen et al., 1987, submitted], namely, 4ø latitude by 5ø longitude. The use of the diagnostic momentum equation (1) and the coarse resolution allow time steps of up to 4 days [see Killworth, 1985]. But, to cut down on noise and time truncation errors, we chose At = 1 day. Time stepping is
with the leapfrog scheme. Nonslip and no-flux boundary conditionsare imposed on all lateral boundaries. The initial layer depths, temperatures, and salinitieswere derived from the zonally averagedLevitus [ 1982]data for the North Atlantic, interpolated to the model grid. The initial depths were computed as follows. The total depth in the south was based on the climatological crt = 27.1 contour, while north of 45øN it was smoothlyjoined with a depth that
isbasedonthe -Op/Oz= 1.0g m-4 stability contour, giving a mean depth of 402 m (an external parameter). The initial h• was set to a constant 75 m. The initial temperature and salinitieswere then obtained by integratingthe zonally averagedLevitus [ 1982]data over each layer. (Our intentionwas to
well as their sum or mean. The numbers
over each curve are
the values averaged over the last 20 days. Figure 3f shows Ns, the number of shallow convective overturning grids between the mixed and the second layers, and Nd, the number of deep overturning grids between the secondlayer and its lower surface. There are Ns = 7 and Nd = 9 convective overturninggrids toward the end of the run, but, as we shall see below, they occur in different areas. We note that the thermodynamic adjustment time scale (see Figures 3c, 3d, and 3f) is at least twice as long as the dynamic time scale (Figures 3a and 3e). The latter is governed by the propagation of the slowest waves (namely, baroclinic Rossby waves in the subpolargyre) in the numerical model [e.g., Cherniawsky and Mysak, 1989], while the former is limited by vertical diffusion, parameterized here as Newtonian cooling to climatology at the bottom surface. Figures 4-7 show the output fields (interpolated to the velocity grid before plotting) on day 21,600 (= 60 x 360 days). Figures 4a-4f show the temperature, salinity, and depth fields. Becauseof different relaxation time scales,tT = 16 days and ts • 460 days, T• (Figure 4a) is much closerin appearanceto To (Figure 2b) than S• (Figure 4c) is to So (Figure 2c). The secondlayer depth outcrops in the middle of the subpolargyre (Figure 4f), albeit thick boundarylayers
('-•103 km) in thiscoarse-resolution model(and,to a lesser degree, the interpolation to the velocity grid) have shrunk
CHERNIAWSKY ET AL ' NUMERICAL EXPERIMENTSWITH AN UPPER OCEAN MODEL
16,153
(c)
(a) t=O
WIND $TRESS-x (cgs)
SURFRCE SRLINITY
d
(PSU)
t:O
d
33.8 3q.O 3q.•
65 61
57
53 3q.6 3q.8
37 36.L•
33
36.6
29 25 36.6 36.L• 36.2
....
MRX:O.98(13,9)
MIN:-0.91
(13,2) CI:0.20
SURFACETEMPEFl.(deg C) 65 61
5 B 7
57
õ
53
[: 0 d
17 ....
M[N=33.6(1LI,lq)
SOLAR FLUX
(N/m2)
90
80
CI=0.2 t= 0 d 65 61
57 53
10 11
q9
•R n
MRX=36.7(lq,q)
21
8O 90 lOO
•5
u,9 65
ql 37
37
33
33
22 23
29
19o 2o0
2•
25
25
21
29
25 21
17
17
MRX=25.9(1LI,1)
MIN=q.25(lq,lq)
CI=
kI--'•o
(d)
(b) Fig. 2.
MJ:J'X=•O8'(11.jI,3) ' MiN=•I.'2 {iq.il)'
Surfaceforcing fields' (a) v•, (b) To, (c) So, and (d) •s.
Some prominent features are the relatively large second the apparent area of this outcropping. Figures 5a and 5b showh = hi + h2 and entrainmentrate E. We note that in layer (Figure 4f) and total (Figure 5a) depths along the purely one-dimensionalmixed-layer models under steady northernboundary(due to small Ap32there; Figure 5c), the forcing, the entrainment rate should vanish as the mixed two maxima in the mixed-layer depth (Figure 4e) in the layer approaches its equilibrium depth. Here nonzero E northeast (--•170 and 190 m), and one maximum along the values (Figure 5b) mark the areas of divergenceand conver- westernboundary(•-120 m), where Ap21(Figure 5d) is small gence, reflectingEkman and buoyancypumpingvelocitiesat andsurface heatlosses (Figure7a)reach-200 W m-2. The the base of the mixed layer. shallow convection takes place in the northeast, effectively extending the depth of the mixed layer to be equal to the total depth and making it comparable to the observed TABLE 1. Internal (Mixed Layer) and External Model mixed-layer depths in the northeast Atlantic [Robinson et Parameters al., 1979]. On the other hand, deep convectionoccursin this model in the western part of the subpolar gyre, where Ap32 Symbol Value Units (Figure 5c) is smalland AP2L(not shown)vanishes.The deep Internal Parameters convection is strongestjust east of the southwardbranch of m 3 the western boundary current, where cold water overflows hd 30 warmer deep water. H•/Hs 0.35 hs 20 Dynamic pressurefieldsP2 andp I are shownin Figures5e hb eo
100 0.50 External
h
dependent terms (see equations (7a) and (7b)). Note that
Parameters 402.3
A0, AA
(4, 5)
At
24
AM AH
and 5f (in decibars,1 dbar = 104 Pa) withoutthe depth
4 x 105 5 x 103
•'0
0.1
Xr, Xs X2
5 x 10-5 5 X 10-7
Op2/Oy • -O(Ap32)/Oy(Figure 5c) has an oppositesignto the m
deg hours
m 2 s-I m 2 s-1 Pa ms ms
The numerical values shown are for the control experiment.
-1 -1
first O/Oyterm in (7a) (Figure 5e), thus weakening the zonal transports. The meridional velocity component vl (Figure 6b) shows ageostrophiccontributions from Ekman drift in the interior and upwelling along the southernboundary. The
latteris fedby entrainment (E ---0.1-0.2m d-l; Figure5b), negativev2 (Figure 6d), and a strongerul (Figure 6a); u2 (Figures 6c and 6d) is closer to geostrophy, following the pressurecontours(Figure 5e). As in other coarse-resolution
16,154
CHERNIAWSKYET AL.' NUMERICAL EXPERIMENTSWITH AN UPPEROCEAN MODEL
I
I
I
I
(b) u,02.3
329.5
0.11tl
O. 079
0.035 I
I
[',..-
72.7
i
i
I
I
(c)
(d)
16.99
15.03 lq. 60
35.•92
I
I
I
I
•) (:3 I
I
I
I
(e)
9
I
0
20
I
L[O
60
TIME FROMSTRRT (years)
0
I
I
20
q0
o
60
TIME FROM$TRRT (years)
Fig. 3. Controlexperiment: 60-yeartime seriesof area mean(a) KEi, (b) •-i, (c) Ti, (d) •i, and (e) h/max (short-dashedcurve, mixed layer; long-dashedcurve, secondlayer; solid curve, total). (f) The number of shallow (short-dashedcurve) and deep(long-dashedcurve) convectiveoverturninggridsis also shown.The numbersover each curve on the right are mean values averagedover the last 20 days.
models, the western boundary currents are weak (--•10 cm
s-1), whiletheboundary layersaretoowide(--•1000km). We defined a diagnosticpotential vorticity
tion (Figures 7a and 7b). Because of coarse resolution and idealized forcing fields a detailed comparison to potential vorticity maps in the North Atlantic [e.g., McDowell et al.,
(10)
1982]is premature, thoughbasicfeaturesare similar: a fairly uniform pool of potential vorticity in the subtropicalgyre (2
at the base of the second layer (Figure 6e), which is the
< q2L< 4 x 10-12 cm-1 s-l), low potentialvorticityin
q2L = 2f(P2L- P2)/poh2
upwelling areas, and high potential vorticity along the south10-12cm-1 s-1 in thewestern halfof the subpolar gyre east front in the subpolargyre. Figure 6f shows the total horizontal volume transport point to areasof strongmixingfrom below due to upwelling and deep convectionthere and also mark upwellingalongthe streamfunction,* (in sverdrups;1 Sv = 106 m3 s-1), southernboundary. High q2L values occur in frontal areas, defined by hu = hlUl + h2u2= f•xVxI t andcalculated by where warm and salty waters are advected north and toward solving V2 ß = curl(hu),with• = 0 ontheboundaries. The the surface, causinghigher surfaceheat loss and precipita- linear Munk [1950]theory, appliedto our model subtropical
finite-difference form of q = (fipo)(Op/Oz). Low q2L, 0, owing to an unstablesalinity difference,$2 > S2L. HTo and FTo accountfor about 55% and 67% of HT and FT, respectively. The values of HT and FT at the northern boundary yield the area mean heat and freshwater fluxes into the deep ocean: •23 - •0 • 6.8 W
m-2 and•W23-- •W • -0.28 mmd-•. 4.
PARAMETER
SENSITIVITY
EXPERIMENTS
Following Martin [1985] we classifiedthe parameters into internal parameters, governing directly the entrainment rate (equation (8)), and all the other parameters were called external. The sensitivity experiments are listed in Table 2. We first examine the sensitivity of the model to the internal parameters. 4.1.
Internal
Parameters
Experiment 2:h6 = 100 m --• 200 m. The dissipation depth scale for the buoyancy-generatedturbulence is h6. Changing h6 affects mostly the areas of strong negative buoyancy flux in the northeast and along the middle of the western boundary. Figures 9a-9f show the differences between the fields of h•, h, T•, T2, •, and •0 in experiment 2
16,158
CHERNIAWSKYET AL ' NUMERICAL EXPERIMENTSWITH AN UPPER OCEAN MODEL TABLE
2.
Experiment
Symbol
2 3 4 5
hb eo hs hd
6
External h
Internal
7 8 9
stronger along the western boundary (Figure 9f), where a
Parameter Sensitivity Experiments
Change
secondaryminimumis now •0min• = -107 (versus -73) W
Units
m-2. As expected, the changes in Tt and•0 are mirror imagesof each other and are correlated with The total meridional heat transport decreased by about 16%, the changebeing larger for latitudes greater than 40øN. The area mean heat flux into the deep ocean, •0 = •23,
Parameters
100--• 200 0.5 --• 0.25 20 -• 10 30 --> 15
m m m
Parameters 402 --> 332
X2 XT Xs
decreased aswell, from6.8 to 4.0 W m-• mostof whichis dueto weaker •:3N (lower T:) and stronger•3c. The ocean heat transport changed much less (by --•1%), so that its relative contribution to the mean meridional heat transport
m -1
5 -->I 5 --->I 5-->25
10-7 m s-1 10-5 m s-1 10-5 m s
increased, from 55 to 63%.
and their valuesin the controlrun. Doublinghb hasraisedh t in most of the domain (ht increasedfrom 73 to 96 m), at the expense of the second layer, and the maximum in h t was shifted west along the northern boundary (Figure 9a). The numberof deep convectinggridsNd increasedfrom 9 to 17, while the number of shallow convectinggrids Ns remained unchangedat 7. This is consistentwith lower h2 and Ap2L, sinceT2 is now cooler(closerto T2L) in mostof the interior (Figure 9d). The cooling of the model (T changed from 15.03ø to 14.77øC)has lowered the pressuregradientsand the horizon-
Experiment3: eo = 0.50--• 0.25. According to (5b) and (5c) a smaller "shear" parameter e0 brings T2T and S2T closerto Tt and St and away from T2 and S:. This leadsto a smaller densityjump, Ap2T = P:T -- Pt, in (8), increasing entrainment and the depth of the mixed layer. But the entrained
water
is now more
similar
to that of the mixed
layer, effectively diminishing vertical mixing between the two layers. This negative feedback limits the changesin the
entrainmentrate and in ht (Figure 10a)' h t changedfrom 72.7 to 74.6 m. In other words, the fluxes ET e and ESe between the two layers depend on e. A lower e weakens these fluxes, thus shifting T: (Figure 10d) and S2 closer to T2L and S2L'
tal transports(Figure 9e). •0 has weakenedin the northeast,
The changes in T, and•0 (Figures10cand 10f) are, as
where•0min= -177 (versus-195) W m-2 but became above, well correlated with those in hr. A smaller Ap2L
(a) 02-1
65
(c)
DEPTH-1 (m)
t= 21600 d
02-1
(e)
TEMPERATURE-1 (deg C) t= 21600 d
02-1
TRRNSP STRFN-ttl
(5v)
t: 21600 d
.............
6
....
........
65 61 57 53
q9
q
41 •
q
49
--.
37
33
29 25
•2
29
;.-
25
21
2! 17
ß
MAX=225(9,14) D2-I 65 61 57 53
MIN=-48.5(lt•,11)
DEPTH-kotal
(m)
17
1
C[=20. t: 21600 d
MRX=O.5918,1q)
02-1
MIN=-0.45(14,11)CI=O.10
TEMPERRTURE-2 (deg C) t: 21600 d
MR'X=6.5• (9:10iNiN='-I.'94'IB, 6) 'CI2-0.'50 D2-1
HERT FLUX -
not
(W/m2)
t:21600
d
>2 ' ' '-.... •"---' •
_
- -30.'
'-- -lo. --
----..--..'-..
q9 q5
45
41
41
37
37
33
;3 _
29
•5
25
•,,
33
//
,/
29
0 15"
25 21
21 17
71•.... MRX:72.q(1.8)
MtN:-70.6(14.11)
(b)
C1:20.
HRX=•.0611•,11)
'• • .... HIN=-•.8•I1.7)
', •. . _ CI=O.50
/
x"""•
MAX:91.2(14,11)
17
""I0. MIN=-122
(8,1q)
Cl:20.
(o
Fig. 9. Differenceplots betweenexperiment2 (h6 = 200 m) and the controlexperiment(h6 = 100 m)' (a) hi, (b) h, (c) Tl, (d) T2, (e) •, and (f) •0.
CHERNIAWSKYET AL.' NUMERICAL EXPERIMENTSWITH AN UPPEROCEAN MODEL
(a) O3-1 85
DEPTH-I
16,159
(c) (m)
t= 21800 d
03-1 .........
TEMPERATURE-1 (deg C) t= 21600 d •'...L•,'' ' '
65
81
61
57
57
,'
53
53
X
'.:•._'11
Lt5
L[5
37
37
33
33
29
29
25
25
21
21
17
17
HR•(=I-.22 (ttilOJHiN=--I.-25-13,5) CI•,0.'50 03-1
HERT FLUX -
no{
(W/m2)
{= 21600 d
65
65
61
61
57 53
53 •9
1t5
37
37 33
29
29
25
25
21
21
17
17
Fig. 10. As in Figure 9, but for experiment3 (eo = 0.25). In the control run, eo = 0.5.
increasedthe number of deep convection grids from 9 to 19. Tz cooled more in the subtropicalthan in the subpolargyre, reducingnorth-southgradientsin Ap32andin Pi and lowering the transports (Figure 10e), while redistributing the mass from north to south (Figure 10b). The total meridional heat transport decreased by close to 30%, more so at high
increasedthe role of buoyancyfluxesin (8), reducingh 1from 72.7 to 64.6 m, while increasingT1 from 16.99ø to 17.25øC and Tz from 14.60ø to 14.78øC.N d decreasedfrom 9 to 7, reflectingthe more stableAp32,while Ns increasedfrom 7 to 10. The likely causefor the latter is that a larger Ap32in the south increased pressure gradients and horizontal transports (Figure 1l e), bringing more warm water to the northeast, latitudes, lowering •0 = •23 from6.8 to 4.8W m-2. there, at a more southerly Experiment4: hs = 20-• 10 m. This changeaffects•l = raising the heat loss (-•0) •e-n,/nsin(2)andinthebuoyancy budget in(8).Themodel location (see Figure 1lf), and thus increasingNs. fields changed less here than in other experiments, and the Moderate changes occurred in the model fields. $1 incorrespondingfigures are not shown. A smaller hs should creased by about 0.3 PSU near 49øN along the eastern increase the part of the solar flux trapped in the mixed layer boundary (not shown), linked to the increase in shallow at the expenseof the secondlayer, raising T1, lowering Tz, convection there. This is why h l is deeper there (Figure increasing Ap21, and lowering h 1. This was only partially 1la), while almost everywhere else it decreased. Somewhat true: while h l dropped from 73 to 59 m and T2 decreased highertransportsand higher•23N (warmer T2) increasedthe from 14.60øto 14.30øC,T 1 has somewhatdecreased,more so total meridional heat transport (by --•6%). Combined with (by --•0.1øC)near the western boundary at --•40øN. A likely somewhat less deep convection, this led to a moderate reason is that cooling of T2 in the south (by --•0.5øC)has increase in •0 • •23 (from6.8to 7.2W m-Z). We briefly mention here two other experiments. In one cooled T 1 there throughthe ETe term in (2). Lower T2 and Ap2L (and Ap32)increasedNa from 9 to 13 and weakened experiment, instead of using (8) for both entrainment and pressure gradients and horizontal transports. The total me- detrainment,we detrainedh l (when E < 0) within 1 time step ridional heat transport decreased by --•9%, consistent with to a Monin-Obukhov depth, which was calculated by setting lower X0, T2, •, and •23N. •0 • •23 changedfrom 6.8 E = 0 and eliminatinghi. The resultsfrom this experiment down to 6.1 W m -2. were not that different from the control run, except that the Experiment5: ha = 30 -• 15 m. This new value for the noiselevel in time seriesof T1, S l, and h lmax(Figures 3c-3e) dissipation depth scale for wind-generated turbulence is was significantlyhigher, making this alternative formulation within an acceptablerange (e.g., Lemke [1987] used ha = 7 lessattractive. In anotherexperimentwe increasede0 to 1.0 m, while in DP, ha = 50 m). As expected, a smaller ha (from 0.5 in the control run) and compared the results to
16,160
CHERNIAWSKY ET AL..' NUMERICAL EXPERIMENTS WITH AN UPPER OCEAN MODEL
(a) D$-I
DEPTH-1 (m}
(c) t= 2160D d
DS-I
(e) D5-1
TEHPERRTURE-1 (deg C) '1:=21600 d
TRRNSP $TRFN-t'I:I
($v}
'1:=21600 d
.............
65 61 57
57
53
53
\
q9
q5
\
ql
\"x,, ....... 10. -............
37
37
33 29
25
25
21
21
17
17
,RX=0.31 113,101 ,IN=-0.20Ilq,11}C[=O.10 I'IR'X=O'.6• 05-1
DEPTH-•:o•:al (r•)
•:= 21600 d
D5-I
D5-1
TEHPERRTURE-2 (deg C) 'l:=21600d
õ5
HERT FLUX - net
(W/m2)
'1:=21600 d
65
65
61 57
/'
55
"
',
""
x•.
61
5'7
5'7
' 5•
/"'-•"'• 53 :","..) 'qt ,2-::'_AI
q5 ql
37
$?
25
85
89
21 17
It'
2!
17
t
.........
HRX=I.1811Lt.1)
HIN=-l.30(13.10)
(b)
(d)
CI:0.50
,e"•7%, ,
I'laX=ttl,õ (ltt, 111 HIN=-6$,0
[15,10)
,
CI= 20,
(f)
Fig. 11. As in Figure 9, but for experiment5 (hd = 15 m). In the control run, hd = 30 m.
experiment3 (e0 = 0.25). The new value, e0 = 1.0, made our formula for e and that of DP (see (5c)) almost the same,
except in areas where h2 < h 1. As expected, most of the mean, minima, and maxima of field variables have changed in an opposite senseto the changesin experiment 3, though the details and the magnitudes of these changes were far from symmetrical (e.g., the changes in the number of convective adjustmentgrids were AN s = +9 and AN d = -3, comparedto AN s = -1 and AN d = + 10 in experiment3). Also, the salinity fields in this particular experiment were still slowly changing toward the end of the 60-year run, pointing to processeswith time scaleslonger than the simple Newtonian coolingt2 = h2/x2.
--•0.5øC,owing to warming of T2 over a large area in the subtropical gyre. The larger residual entrainment rate has contributed to a decrease in horizontal volume transports in the two gyres (Figure 12e), reducing the cross-gyre flow, while enhancingthe north-south temperature gradients (Figure 12d). As in other experiments,the changesin h l are reflectedin
T1 and •0 (Figures 12a, 12c and 12f). The meridionalheat transportdecreased(by --•10%), thoughnot as much as (say) in experiments 2 and 3. More dramatic was the doubling in the number of deep convective adjustmentsgrid points, from Nd = 9 to Nd = 18, while Ns also increased,from 7 to 9. The changesin •23c (not shown)had a doublenorth-southdipole
structure (about+_5W m-2 near51øN),thuscontributing 4.2.
External
Parameters
Experiment 6: h = 403 --) 332 m. This change has restored h close to its value in DP. According to Levitus
[1984] theseasonal heatstorage (poCpfffoZT dzdxdy)inthe world ocean changes little when the reference depth (Z) is changed from 275 to 550 m. Most of the seasonal heat storageis therefore above h -- 300 m and is certainly above h = 400 m. This may limit the range of plausible h values for our model to between 300 and 400 m. Reducing h has a stronger effect in the subpolar gyre (e.g., Figure 12b), consistent
with weak stratification
there. The area of venti-
lation increased (Figures 4fversus 12b), cooling the subpolar gyre (Figure 12d), though T has actually increased by
less than •23N and •23R to the changesin •23 and in the meridional heat transport. A shallower h (Figure 12b) has increased"climatological" T2L, more than compensatingfor the higher T2 in the south (Figure 12d). This lowered •23N everywhere, in oppositionto the increase in •23R in the north (higher Nd), leaving •0 (• •23) almost unchangedat 6.6 W m -2.
Experiment7:X2 = 5 x 10-5 --) 1 x 10-5 cm s-•. Decreasing X2bya factorof5 hasweakened •23Nand increasedT2 (Figure 13d)and T (by--•0.5øC). The resulting increase in Ap32 in most of the domain has raised the maximum (absolute values of) transports in both gyres by about 1 Sv (Figure 13e). The strongertransportscontributed
CHERNIAWSKY ETAL.' NUMERICAL EXPERIMENTS WITH AN UPPEROCEANMODEL
16,161
(a) 06-1
OEPTH-I (m)
t= 21600 d 65
85
61
8l
57
57
53
53 Lt9
tt5 37
37
33
33
29
29
25
25
21
21
17
17
D6-1
HERT FLUX - net
[W/mn2) (:=21600d 65
85
61
8!
57
57
53
53
it9
Lt9
q5 L[1 37
37
33 29
i/
29
25
25
i
21
2l
!
iI
17
17
ß
•tn•(=-'o. tissjto) MiN----lq2 (:?. 12) C•=20.
HR•(=C•.õ4 12:õ)'HI/q='}.O'5 [9.10)-CI-'o.so
(b)
(d)
HR•(=l'02 ilO'.lLi')hlN2-S6.õ'(1u•.9) '
(f)
Fig. 12. Asin Figure9, butforexperiment 6 (fi-= 332m).In thecontrol run,h = 402m.
totheshiftsouth andintensification (bycloseto 100W m-2)
Experiment 9:Zs= 5 x 10-3---> 2.5x 10-2 cms-• . This
shortens theadjustment timescaleof S• (to So)from of the heat loss maximum(•(•0min) in the northeast(Figure change in h•, h, 13f), thusincreasing Ns from 7 to 16 in that area, while 460to --•90days.Figures15a-15fshowthechanges in T• andT2 (notshown) decreasing Nd from9 to 6. Theextracooling fromaboveand S•, S2,•0, and•w. Thechanges are correlatedwith thosein •0 (Figure 15e)and h (Figure (in ourunits,AT• --•-A•0/200, whileAT2 the lowerT2 there(Figure13d).The changes in h• andT• 15b),respectively (Figures13aand13c)are,asabove,wellcorrelated withthe is about -Ah/40 in the subpolargyre and between0ø and gyre).Here the extra surfacebuoychanges in •0, and,notsurprisingly, thefractionof thetotal 0.2øCin the subtropical ancy flux in the subpolar gyre is of the sameorderof meridional heattransport carried bythetwolayers(HToH/•-T) as in experiment 8. Thusthe changes in ß (not increased by about$0%,from0.55 to 0.82, while•0 = •23 magnitude shown)are quitesimilarto what is shownin Figure 14e. decreased from 6.8 to 2.1 W m-2. the additional shallow convection in the northeast explain
Experiment 8: Zr = 5 x 10-3 -->1 x 10-3 cms-•. We
The more stablemixed layer leadsto lessshallowconvec-
from7 to 3 grids)andweakerentrainment reducedXr by a factorof 5, thereforeincreasing theadjust- tion(Ns changed menttimescaleof T• (to To)from 14to about70 days.This in the northeast. The heat loss maximum was practically changehasaffectedT• directly(Figure14c)andT2 (Figure erasedfrom the northernboundary(Figure 15e),shiftingit to x, increased 14d) indirectly,throughthe entrainmentterm. The changes --•57øN.The freshwaterflux maximum, C•Wrna from 5.4 to 7.1 mmd -• and shifted south from 65øto 57øN, in T2 are smallin the subtropical gyre,wherethe entrainbyabout3.5mmd-• andshiftedsouth ment(detrainment)rate is weakbecauseof largeAp21 . The aswellasincreased
increasein Ap32in the subpolar gyre(higherT2)increased (by -4 ø) alongthe westernboundary(Figure 15f). The in the mixed-layer depthh• (Figure15a)are well Xtrmi ntherefrom-7.8 to -8.7 Sv(Figure14e).Thechange in changes correlated with those in • w, whilethe changes in S• (Figure Xr hasalsoreduced--•(•0min in thenortheast (Figure14f), aboutthe centrallatitude.As was shiftingit west alongthe northernboundaryby about540 15c)arequitesymmetrical the casefor T2 in experiment 8, the smallerchanges in S2 km. The changesin h• (Figure14a)are correlatedwith •0. h in thenorth The numberof shallowconvectiongrids,Ns, increasedfrom (Figure15d)aremorerelatedto theshallower in •w, stressing theroleof 7 to 9, whileNd decreased from 9 to 6. The stronger•23N (Figure15b)thanto thechanges (higherT2)contributed to theincrease in thetotalmeridional thebottomfluxes.A strongerNewtonJancoolingin the north heattransport(HT) andin the net flux into the deepocean: (dueto higherT2) canbe linkedto the increasein the area
•0 • •23 changed from6.8to7.8W m-2.
meanheatloss•0 from6.8to 8.4W m-2.
(a) 07-1
DE?TH-!
(c) (m)
t= 21600 d
07-1
(e)
TEHPERRTURE-1 (deg C) t= 21600 d
07-1
TRRNSP$TRFN-ttl
($v)
t= 21600 d 65
6S 61
S?
61
......',• .......
u.,,;:)'
57 ,, , u,9
0.25 .....
u,5 u,1
41
37
•?
33
2@
29
2S
25
21
21
17
17 MRX=78.6 (12,10) 07-1
MIN=-39.5
DEPTH-to'I:al
MRX=0.51112,10)
(14, 11) CI=20.
(m)
'1:=21600
d
D7-t
MIN=-0.21
IIU,11)C[=O.10
TENPERRTURE-2 (deg C) t= 21600 d
MRX=0.85(3,6) 07-1
MIN=-l.16(11,10)
HERT FLUX - net
(W/m2)
CI=0.50 t=21600
d
.............
65
65
61
61
57
57
53
53 q9 L[5
ii
U,1
iI
i
/
..... '•o.
I
29
37
33 29
'
25
25
21
21
17
17
MRX:55. q (13,10)
MIN:-23.8
(3,5)
MRX=I.7[
CI: 20.
114.1)
MIN:-2.50
(b)
(11,10)
CI:0.50
HRX=43.4(14,11)
HIN=-104(12,10)
(d)
CI=20
(o
Fig. 13. Asin Figure9, butforexperiment 7 (X2= 1 x 10-7 m s-l). In thecontrolrun,X2= 5 x 10-7 m s-1
(a) 08-1 65
DEPTH-I
•
t= 21600 d
06-1
'rEMPE•RTU•F-1 [deg 0
•= 21600 d
.•= ......
57
.......• 'x•.' ••.-•" '
53
;3
49
:9
61
(e)
(c) (m)
t t
''0. •S..
:••) •9
29 25
t= 21600 d
t
....,/' .,...-"'"' \
17
61
57 53
_,*""'
I
-
u,5
' •.... O'•S ..............
u,1
37 33
""
29
25
s• .-'-.........o.a5 .......... "' • I1,",-........... o.•s .............
2t
65
''
.......
•7
93
(Su)
49
:5•'"-,
97
TRRNSP STRFN-ttI
'/""'----:--'-'--'-'/.. ............ 0.753 :o.•s-•
_•
41
08-1
21 17
7 •,. ,; ...........
HR•(=6'3.'• (9•14i.iN=--83.7-•14}•1') Ci=20.
MRX=2.U719,1q)
D8-1
D8-!
BEPTH-to'I:aI
(m)
'1:=21600
d
MIN=-l.25(7,1)
CI=0.5D
TEMPERRTURE-2 (deg C) t= 21600 d
MRX=0.1•(I2,1O) "N=-i.15 (Z12)Ci=0.50 08-1
HERT FLUX -
net
(W/m2)
t=21600
d
.........
65
57
65
,,., ,._.,/\•
61
61
61 '- -30ø -
57
57
53
53 •9
q9
41
L•I
41
37
q5.0. 5.
49
45
45
33
37
33 29
a9
29 25 21
25 21 17
17
17
114,11)MIN=-O.34 13.9)CI=0.50 MX=25.• (10.10)HiN=-63.8(1'4.1'1) •i='2o. MRX=2.50
(b)
Mk=gl.• (1•. 1il 'MN=-•9.•(9.1•')Ci=•O.
(d)
-1
Fig. 14. Asin Figure9, butforexperiment 8 (XT= 1 x 10-5 m s-l). In thecontrol run,XT= 5 x.10-5 m s
CHERNIAWSKY ET AL.' NUMERICAL EXPERIMENTS WITH AN UPPER OCEAN MODEL
(a) D9-1
(c)
DEPTH-1
(m)
t= P1800 d
D9-I
16,163
(e)
$FLINITY-1(ppt)
O9-1
t= F'iõD 0d
HERT FLUX - net
(14/m2) t=21600d
$5 $1
•
__. xo. '.'_•
...........
'- -07:•6rcccc_-_-_-
57 53
\
.....
i
.
(")
.•
61
'•k',
,1,;-- s7
\
•9
O.tO-
-------
37
37
33
33
29
•9 •5
•
17
O. lO•
17
lt,m D9-1
X=t"7
S•LINITY-•
(ppk)
k= •18D0 d
D9-1
PBECIP-EV•P (ram/d) t= 21800 d
65
65
61
61
57 53
)
S7
57
ss
53
q9
•5
37
37
J
33
33
•
P9
•9
/
-
'.......
37
33 29
P5
25 21
17
17
17
.•k=0.1•1o• .)N=LO.'1•'(•L•)ci=6.1o;•X=S. os(•.•k) "•N=-•.9•(•.•)'
(b)
(d)
Fig. 15. Difference plotsbetween experiment 9 (Xs= 2.5 x l0 -4 m s-l) andthecontrolexperiment (Xs= 5 x 10-5 m s-l): (a) hi, (b) h, (c) Sl, (d) S2,(e) Xo, and(f) •w.
5.
DISCUSSION
The above sensitivity experiments are partly summarized
in Figures 16a-16f, which show the changesin hi, KE, T, •0, qtmax,and HT0maxas functionsof the relative changesin the model parameters. Solid lines mark the internal and dashed lines mark the external parameters. Among the
former the dependenceon the shear parameter e0 is the strongest,with the depth scalefor buoyant dissipation,hb, being a close second. Among the external parameters the mean model depth h has the strongest effect, albeit the available range of plausible h values is more limited than is the choice of coupling coefficients. One of the more interesting results evident in Figures 16a-16f is the relatively weak dependence of integrated
quantitieson the surface couplingcoefficientsXT and Xs. The strongerinfluenceof X2 may be due to the fact that it has a more direct effect on the model mass, most of which is contained in the second layer, while the effects of the
changesin XT and Xs are bufferedby the mixed layer. Also, the surface fluxes depend not only on the state (depth, temperature, coupling coefficients, etc.) of the mixed layer alone but also, and possiblymore so, on what happensin the layers below. It is worth noting that some changesin total mean values can exceed the changes in mean values for each layer
separately.For example, while T is a weightedmean of T• and T2, namely,
T= clf l + (1 - cl)T2 where cl = h i/h, giving T1 > T > T2, the changeAT in T is a nonlinear function of Ahl, AT l, and AT2. AT can be expanded about (say) values in the control run,
AT= claT• + (1 - cl)aT2 + (T1 - T2)acl +... which allows it to fall outside the range (AT1, AT2), as was the case, for example, in experiments 4 and 5. Similar considerationsapply to changesin other mean values (e.g., S) and to changeswithin a time dependent model with fixed parameter values. The changes in the number of shallow and deep convection grids, N s and N d, are usually consistent with the
changesin Ti, Si, and the resultingapi+l,i (i = 1, 2). The model shallow convection occurs in the northeast, deepening the mixed layer down to the full depth, in analogy to the case in the winter North Atlantic [Robinson et al., 1979]. In contrast to the real ocean, the deep convective adjustment had a minor effect on balancing the meridional heat trans-
ports. The weaknessof •23c is partly due to coarseresolution and, subsequently,weak horizontal transports, as well as to the idealized forcing fields (Figures 2 a-2d) and a lack of cold continental air from the west. If present, the latter would increase deep convection in the northwest, which would be analogous to the deep convection in the winter Labrador
Sea.
16,164
CHERNIAWSKY ETAL..'NUMERICAL EXPERIMENTS WITHANUPPER OCEAN MODEL
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CHERNIAWSKY ET AL.' NUMERICAL EXPERIMENTSWITH AN UPPER OCEAN MODEL APPENDIX:
It is interesting, for a moment, to consider a possible reason for spatial shifts of heat (or P-E) flux extrema in different experiments. For example, reducing XT in experiment 8 has shifted-•{•0minwest alongthe northernboundary by about 540 km (Figure 14f). Dividing this value by the difference in the adjustment time scales (-•56 days), we get
MERIDIONAL
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HEAT
TRANSPORTS
The meridional transports can be obtained by integrating (2) and (3) from zero to L(y) in x, where L(y) is the width of the basin, and from zero to y in y and by summing over the two layers, i - 1, 2. Let us denote ui = (Ui, Vi) = hiui. The integrals of the advection and diffusion terms in (2) are --•11cm s-•. Thisis considerably largerthanthehorizontal (separately)
velocities(
