JOURNAL OF GEOPHYSICAL RESEARCH, YOLo 89, NO. C4, PAGES 6533-6542, JULY 20, 1984

The Variation of Sea Surface Temperature in 1976 and 19772. The Simulation With Mixed Layer Models

K. MIYAKODA AND A. ROSATI

Geophysical Fluid Dynamics Laboratory/National Oceanic and Atmospheric Administration.Princeton University

In connection with a study of the extreme weather events over the North American continent in'" January, 1977, analyses were performed to investigate characteristic properties of spatial and temporal

variation of sea surface temperature for the years of 1976 and 1977, using world distribution of seasurface temperature described in the accompanying paper, part 1. The time evolution of ocean temper-ature patterns for these years are displayed by latitudinal distribution diagrams of sea surface temper-ature, and longitude-time (Hovmoller) diagrams. Gill-Turner's integral model and Mellor-Durbin's tur-bulence closure model of the mixed layer were applied to calculate the sea surface temperature anomalyin the northern hemisphere, using realisitic atmospheric forcing. Increase of time variability of theexternal forcing leads to an appreciably improved simulation of the sea surface temperature anomalyfields. Both models gave reasonable predictions for about 5 months in winter time, if the realistic externalforcings were specified.

1. INTRODUCTION appropriate. Some possible causes of small-scale anomalyIt is perhaps the current understanding that the air-to-sea variability will be suggested. Other authors, such as Haney

influence is direct and in situ, whereas the sea-to-air influence [1980] and Denman and Miyake [1973], have investigatedis complex and often of a teleconnection nature, except within ocean behavior in small regions or at selected ocean stations.the tropics. This teleconnection process has been pointed out In this study, some explanations for SST anomaly behaviorin various ways by a number of authors. For example, the over ~arger areas o~ the norther~ hemisphere will be atte~p-tropics-midlatitude connection was mentioned by Bjerknes ted, since these regIons may be Important for understanding[1966], the connection between the North Pacific and North the abnormal atmospheric events.

America was mentioned by Namias and Born [1972], and thelag association between the North Atlantic sea temperature 2. LATITUDINAL DISTRIBUTION

near Newfoundland and atmospheric pressure at the British In general, the 1976 and 1977 SST's as produced by theIsles was mentioned by Ratcliffe and Murray [1970]. analysis described in Miyakoda and Rosati [1982], exhibit

The impact of the sea surface temperature (SST) may be changes in both latitudinal and longitudinal directions. Torepresented by an integral effect from various regions of the obtain insight into the north-south variability, zonal averagesocean. In particular, anomalous behavior of the SST over were taken for the SST analysis, for the Rand climatologicallarge regions has been connected with abnormal atmospheric SST [Alexander and Mobley, 1976], and for the climatologicaldevelopment, and, concurrently, unusual weather phenomena. SST from Levitus and Oort [19.77]. By using monthly meansFor this reason, to study a large-scale weather phenomenon for the Pacific Ocean for each latitude, Figures 1a and 1b wereover the United States it may be useful to know the SST not produced. For comparison, an annual average of the zonalonly over the North Pacific but over the Equatorial Pacific mean Rand values was subtracted from the above mentionedand even over the Atlantic Ocean. quantities.

Given the SST anomaly analysis as described by Miyakoda One can observe in Figures 1a and 1b that the magnitudesand Rosati [1982], the large-scale SST temporal and spatial of the anomalous SST for the Pacific Ocean are of the order ofvariation, during 1976 and 1977 will be examined. Some de- :t3°C. The two climatologies are generally the same, i.e., notails of the SST structure will be discussed in relation to readi- systematic bias was detected. Nevertheless, it is interesting toly observable phenomena. Possible explanations for the devel- note that differences between the two climatologies in someopment and evolution of particular SST anomaly patterns will instances are as large or larger than the difference between thebe suggested by means of comparative studies using two dif- SST analysis and a climatology (see the recent article by Reyn-ferent types of ocean mixed layer models. As a sidelight, a olds [1983]). This illustrates the delicate nature of SST anoma-.comparison of the two types of models suggests further infor- ly prediction. The persistence of the SST anomaly patterns ismation concerning the SST evolution during 1976 and 1977. noted, with gradual changes from one month to the next.

The years 1976 and 1977, for which extensive oceanic and Notable features are negative anomalies at 00-200N from Jan-atmospheric data were available, were characterized by rela- uary to May of 1976 and 1977 and negative anomalies attively rapid development of localized anomaly extrema, inter- 500-600N from July to October of 1976 and 1977. A consistentspersed with relatively persistent anomaly patterns. Concomi- feature during all months is a warm anomaly between 20°-tantly, extreme weather patterns were experienced over North 400S and a cold anomaly farther south.America, which makes investig~tion of these years particularly A possible pattern recurrence is indicated in the winter

months of both years in the North Pacific anomaly compo-This paper is not subject to U.S. copyright. Published in 1984 by nent. Namias and Born [1970 1974] ascribed the pattern re-

the American Geophysical Union. currence to storage of anomal~usly cold or warm water that is

Paper number 4C0458. shielded by a shallow layer in summer but is stirred up to the

6533

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6534 MIYAKODA AND ROSATI: VARIAllON OF SEA SURFACE TEMPERATURE

orN 9O'N ...80'S

,

2

0 0

.1 ,

-2 2

.2 2., 1 .

0

, -I

-2

-4 1 -, 1

0

, -I , -I

2 -2 3 -2

2 -2 2 -2

1 -,

-32

-2 2 2-4 1

1

0

, -I -I3 -2

, 2

-,-, 3

-, 3

-3 ,-,

-4 1

0, -

, -1-,

, -,

, -

0, -

, -I3 -,

3 -,, -3

2 -3

1 -,

0

-I ,

-3 3

.3 2-, 1 '

0 K:E

-I

-3

-,orN ...,..

to"N EO ,.. ...80'S

Fig. la. Monthly variati?n of. S~T in 1976 over the Pacific Fig. lb. The same as in Figure la but for 1977.

Ocean. All the curves and CIrcles indicate departures rC) from the

cli~at?logical annual mean o~. SST at the respective latitude. .The surface by the increased wind stress during cold months. This

SOlId lines are 1976 values obtained from the amalgamated analysIs of ship and satellite data. The dashed lines are the RAND climatological possible recurrence feature, especIally indIcated In J~nuary

normals and the normals of Levitus and Oort are shown by small through March of 1976 and 1977, may be present In the

circles. Negative anomalies area are shaded. anomalies as well as in the seasonal cycle. Other similarities

MIYAKODA AND ROSATI: VARIAnON OF SEA SURFACE TEMPERATURE 6535

1400E 1600 1800 1600 1400W 1400E 1600 1800 1600 1400W

Jan 76 Jan 76

Mar Mar

Jun Jun

.Sep Sep

~ Dec Dec

77 77

Mar Mar

Jun Jun

Sep Sep

Dec Dec

1400E 1600 1800 1600 1400W 1400E 1600 1800 1600 1400W

TOTAL ANOMALY

Fig. 2. Longitude-time chart of SST rC) total (left) and anomalies (right) for 4Oo-50oN belt in the North Pacific. Theordinate is time, directed downward from January 1976 to December 1977. Negative values are shaded.

from year to year could reveal similarities in seasonal atmo- variance where the intense negative SST anomalies are locatedspheric forcing patterns on interannual time scales. This may in Figure 2, possibly indicating a cause-effect relationship. Abe particularly true on the regions of the subtropical and sub- maximum in cyclonic activity also reported by Petterssenarctic oceanic gyres. Evidence for such coherence of SST [1956] seems to coincide with the centers of largest anomalies.anomalies was given by Middleton [1980]. The detailed structure near the western boundary of Figure 2

The point to be emphasized here is the capricious nature of could represent meanders in the Kuroshio-Oyashio confluenceSST anomalies, and the delicate task of predicting them on a zone. A positive anomaly persisted from October 1976 tolarge scale. While the seasonal cycle of SST may be repro- March 1977, which corresponds to the warm water observedduced with fair accuracy, a different degree of difficulty resides off the west coast of the United States during this period.in predicting anomalies, which are relatively small compared Little large-scale movement seems to be observed in the Paci-to the total field. fic SST anomaly, again reinforcing the suggestion by Ciesielski

..[1980] that in mid-oceanic regions in situ surface processes,3. HOVMOLLER DIAGRAMS rather than advection, etc., account for observed SST anoma-

Another way of looking at temporal and spatial variation of lies. In sections 5 and 6, the results of the simulation withSST anomalies over selected regions is by constructing a mixed layer models, we will attempt to evaluate this point.longitude-time chart, or Hovmoller diagram. In this manner, In summary, inspection of SST's on a large scale in 1976differences across a latitude line may be quantified, as well as and 1977 seems to reveal the suggested importance of surfacemeasured against Rand climatology. The region between 400 processes and atmospheric forcing in large portions of theand 500N of the North Pacific is of considerable interest in ocean basins.connection with the extraordinary weather event of January1977. 4. MIXED LAYER MODELS USED FOR SIMULAllON

Figure 2 is a diagram of the SST and corresponding anoma- To gain some insight into the causes of the SST anomaly.lies for the North Pacific (400-500N) where the latitudes in patterns during 1976 and 1977, an attempt was made to simu-

parenthesis indicate the domain of the average. In these dia- late anomaly patterns using observed atmospheric forcing.grams the monthly mean SST values are based on the amalga- Evaluation of model performance could yield informationmated analysis of ship-of-opportunity reports and of satellite concerning the importance of surface mixingfheating versussoundings as described in part 1. other possible causes in defining the large-scale SST behavior.

One may note a similar type of SST structure across the There are in general two classes of the mixed-layer models,zone in the North Pacific (Figure 2) up to June 1977, with i.e., "the integral model" and "the multilevel model." The firstlocalized intense negative anolpalies interspersed. The general class includes Kraus and Turner [1967], Kitaigorodosky andcharacter of this pattern over 18 months may reflect consistent Miropolsky [1970], Pollard et al. [1973], Denman [1973],atmospheric forcing patterns associated with flow along the Denman and Miyakde [1973], Niiler [1975], and De Szoekesubarctic gyre, as indicated by Middleton [1980]. Ciesielski and Rhines [1976]. The second class includes Mellor and[1980] found maxima of mean wind speed and wind speed Durbin [1975], Marchuk et al. [1977], Madsen [1977], and

--

6536 MIYAKODA AND ROSATI: VARIATION OF SEA SURFACE TEMPERATURE

Z Z where S is the solar heat flux through the surface; /l is an

l l entrainment parameter due to penetrative convection at theR,. base of the mixed layer.

4.1.2. External forcing. The formulation for the rate of10m To mechanical stirring M is based on the laboratory experiments

M Q of Kato and Phillips [1969] as

M = 1.25/[g .IX(T)]U.3 (7)

where U. = (Tw/Pw)1/2 is the ocean friction velocity, g is grav- .ity, and IX(T) is the coefficient of thermal expansion. In this

(!) T"f case, Pw is the ocean density and Tw is the surface ocean stress,ER assumed equal to the atmospheric stress T. at the interface.

T"f From equations (3H6), the mixed layer temperature 1:; anddepth h may be derived.

Surface boundary conditions for the Gill-Turner model maybe determined by a heating term and a momentum flux term.Heat flux Q at the interface is given by

Q = [R. ~(1 -a) + RL -60"1:;4 -H. -LE.] (8)T T"f

V//~ V//a where R. ~ is the portion of insolation absorbed near the sur-Fig. 3. Schematic illustration of the vertical levels and the atmo- face, a is the albedo, RL ~ is the downward longwave flux. R.,

spheric forcings for the Gill-Turner model (left) and the turbulence a, and RL ~ are produced as climatologies from a grid pointclosure model (right). atmospheric model assuming a zonal distribution of cloudi-

nd I ness. The term 60"1:;4 is a longwave upward flux term, where 0"Ko 0 et a. [1979]. The two specific models applied In this is the Stefan-Boltzman constant, and 6 is the emissivity. L ispaper are the Gill and Turner [1976] model and the Mellor the latent heat. Sensible heat flux H is given byand Durbin [1975] model. These mixed-layer models differ in .

their prescription of surface mixing processes occurring in H. = p.CpCHIw.I(1:; -1;,) (9)conjunction with the atmospheric forcing.

where P. is the air density and Cp is the specific heat at con-4.1. Gill-Turner Model stant pressure, CH is the bulk aerodynamic exchange coef-

This model is based on the original work of Kraus and ficient, I w.1 is t~e wind. magnitude at 70 m above the oceanTurner [1967] and falls into the class termed "integral surface, and 1;, IS the ~Ir tem~erature also at 70 m. Values oftheories." By considering the layer to be homogeneous and 1w.1 and 1;, we~e obtained tWIC~ a day from a N~C level IIIeliminating eddy diffusivities, relatively easy solutions based Houg~ analysIs (NMC, NatIona~ Meteorological Center,on energy balance considerations are found. The existence ora Washington, D. C:) of observed winds and tem~er~tures formixed layer is assumed a priori, rather than a consequence of the nort~ern hemls.ph~re for 1976 and 1977. S!mllarly, ~heavailable oceanic boundary conditions. evaporative flux E. IS gIven as a bulk aerodynamic expreSSIon

The Gill-Turner model includes equations for the heat con- as

tent H and for potential energy P, E. = P.CE 1w.1 (q.(1:;) -q.) (10)

H = (OT dz (1) where.cE is ~~ evap~rative exchange coefficient, q.(1:;) is t~eJD saturatIon mixing ratio at the ocean surface for 1:;, and q. IS

Lo the atmospheric mixing ratio, which was taken to be theP = ZT dz (2) monthly mean climatology of Dort [1977].

D The momentum boundary condition is given by a windh ..stress, T., defined as

were T IS temperature, Z IS depth, and D is the bottom depthof the model. The model is based on the principle that me- T. = p.CDIw.12 (11)chanical turbulence generated by the surface wind changes the h C . h d ffi . d . IWI . k f...were D IS t e rag coe ICient an again IS ta en rompotential energy of the temperature profile by mixing buoyant b d . d U f' h.' .

f b lk dt d d " th ..0 serve Win measurements. se 0 t IS type 0 u aero y-wa er ownwar ,rom e sur,ace. ...411 B . t. D t. th ... f h namlcs method was indIcated by Esbensen and Reynolds...aslc equa Ions. eno Ing e sur,ace Input 0 eat [1981] ..

by Q, and the surface input of mechanical energy due to wind V 1. f C d C h Id 11 10-3 d..b M ( F. 3) h . f h G.l a ues 0 H an E were e constant at .x , anmIxing y see Igure ,t e equatIons 0 tell-Turner C t t 15 10-3 Th 1 1.. h .ddld 1 b . tt D was se 0 .x .ese va ues Ie In t e ml e range

mo e may e wn en as ..of values as determined by Bunker [1976] from experImental

for Q ~ 0 (heating) data.4.1.3. Boundary conditions. A bottom boundary con-

dH/dt = Q (3) dition for this one-dimensional model is that heat flow is zero,

dP/dp= M + S (4) i.e., no heat is allowed to escape.4.1.4. Levels and grids. Figure 3 illustrates schematically,

and for Q < 0 (cooling) on the left, the form the temperature profile of the upper layersdH/dt = Q (5) of the ocean is assumed to have. The number of levels is eight

extending from the surface to a depth of 248 m. It is assumeddP/dt = th(1 -/l) dH/dt + M + S (6) that a surface mixed layer exists with a temperature 1:;, and a

r_- -

MIYAKODA AND ROSATI: VARIAnON OF SEA SURFACE TEMPERATURE 6537

discontinuity in temperature 7;, at the base of the mixed layer. a cm2fsecThe depth h is carried as an extra variable so that changes in 56789103 2 3 4 56789104 2 3 4the mixed layer depth are not restricted by the vertical resolu-tion of the model. Dec-Jan-feb

The horizontal domain covers the Northern Hemisphere. IThe grid [Bryan and Lewis, 1979] is a latitude-longitude grid.The east-west grid spacing is 5.6°, and the north-south gridspacing is 4.5°.

.4.2. Mellor-Durbin Model

The second class of mixed layer models is based on theturbulence closure method. In this approach, the vertical pro H+tT E

., files of the turbulent variables are obtained as a solution of a ~closure system of turbulence and thermodynamic equations. ...

Thus the vertical structure within the upper layers, which neednot be well mixed, can be predicted in mOre detail by thismethod than by the former method. Only one-dimensionaldiffusive processes are considered here; advective, horizontal,etc., processes are neglected. , 8

4.2.1. Basic equations. The model equations are

au a [ au] '1 at = fv + & (v + KM) & (12) 10

av a [ av]at = -fu + & (v + KM) & (13) b cm2fse(aT a [ aT]at = & (K + KH) fu (14)

wherefis the Coriolis parameter, KM is the eddy viscosity, KHis thermal diffusivity, and v and K are molecular viscosity, andconductivities of heat, set at 1 cm2 S-I and 0.1 cm2 S-I,respectively.

Values of KM and KH are obtained by a turbulence closuremodel presented by Mellor and Durbin [1975] and are givenby ]

J:KH = IbSH (15) :~

KM = IbSM (16)

where b is the square root of twice the turbulent kineticenergy, I is a turbulence length scale, and SM and SH are fluxRichardson number R; dependent stability factors [Mellor andYamada, 1974], where 8

aT/[( au)2 (av)2] 9 Ri=P.gfu & + & (17)10

Here, 9 is the acceleration of gravity and p is the coefficient of Fig. 4. An example of vertical distribution of turbulent eddy cqef-thermal expansion. SM and SH are determined in such a way ficients, KM and KJi, at a point of 42.75°N and 172°W for two differ-that turbulence disapppears at R. = 0.23. Given newly com- en.t seasons. The ran~e .between KH + (J and KH -(J is shaded, where

, (J IS the standard deviation.puted values of KM and KH, values of u, v, T are computed at

.every time step. ....where (XI = 0.20. ThIs equatIon, plus (15)--{18), closes the tur-

.Th~ quantIty b IS. calculated fr.om a form of the turbulent bulence parameterization.kinetic ~nergy equatton repres~ntIng a ?a~anc~ between shear Perhaps it is necessary to mention that this approach uses

, productIon, buoyancy productIon and dISSIpatIon: empirical constants, determined by laboratory experiments,

[( au)2 (av)2] ( aT) b3 for the subgrid scale parameters, and they can be applied asIbSM & + & -lbSH pg fu -"i5l = 0 (18) uni~ersal co~st~nts to the oce~n as .wel! as .to the atmosphere.

FIgure 4 indIcates the vertIcal dlstnbutIons of KM and KHFollowing Mellor and Durbi~ [1975] we calculate the turbu- at 4rN, 172°W for the warm and cold seasons. The KM

lence length scale from the ratio of the first to the zero-th values are generally smaller than for KH. This is also the casemoment of the turbulence field: for the atmosphere [see Miyakodaand Sirutis, 1977]. In the

0 0 warm season, KM and KH are small because the thermal

1= (Xlf Izi bdz/f bdz (19) stratification tends to be stable and the wind stress is weak;-00 -00 and in the cold season, KM and KH become very large.

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6538 MIYAKODA AND ROSATI: VARIATION OF SEA SURFACE TEMPERATURE

111 CORRELATiON COEFFK:IENT FOR SST ANOMALIES NORTHERN HEMISPHERE CORRELATlON COEFFK:IENT FOR SST ANOMALIES NORTHERN HEMISPHERE

p"""""09... -lid 1 p",;"""OJ lad ~ Clos

-300 o. -1m,.III

1l6~ .-"-' ::.~ /:; ~.Il3 " \ Q

1l2nI

0 O.~I

JFMAMJ JFMAMJJASONO

'976 '9" '976 1977

Fig. 5. Correlation coefficients of the SST anomalies between the F. 7 C I t. ffi . t f th SST I. b t thIg.. orre a Ion coe Iclen s 0 e anoma les e ween esimulation and the observation over the northern hemisphere for the. It . d th b t. th th h . h .. th..slmu a Ion an e 0 serva Ion over e nor em emlsp ere lor ecases of 30-day, 10-day mean and half day atmospheric forcmgs. f 1976 d 1977 .th th I d I Th It f thcase 0 an WI e c osure mo e. e resu 0 e

4 2 2 R d ,. Th " integral model with twice daily atmospheric forcing is also shown for...alatIon. e same treatment as In the GIll. reference.

Turner model is used.4.2.3. ; Nume:ical. .calcula~ion. Diffusion ~quatio~s were a

solved wIth an ImplicIt algorithm, where the Z integratIon pro. -(u, v) = 0 (22)ceeds with the standard tridiagonal matrix reduction tech- az

nique [see Richtmyer and Morton, 1967]. aT4.2.4. Levels and grids. The horizontal grid spacing and a = 0 (23)

type of grid are the same as previously discussed for the Gill- Z

Turner model. In this case there are eight vertical levels (see Simulations using these two types of one-dimensional mixedFigure 3) down to 248 m, with increased resolution near the layer models will be made to attempt to predict SST anomalysurface, where the first level is 2.5 m below the surface as patterns.shown on the right-hand side of Figure 3. Values of T and Ware located at the midpoints of each layer. 5. RESULTS OF THE SIMULATIONS

Kondo et al. [1979] discussed the treatment of oceanic con- The initial temperature profiles, for both models, were ob-stant flux layer. The depth of this layer is, according to them, tained by using the observed SST at the first layer and extend-about 63 cm, whereas in our study the uppermost layer is 5 m ing it down to the nearest layer corresponding to the climato.deep. Elsberry and Garwood [1980] mentioned that mixed logical mixed layer depth, as given by Levitus [1982]. Clima-layer models typically use vertical increme~ts of 1-3 m, tological values (Levitus, 1982] are used to initialize temper-whereas the oceanic GCM (general circulation model) may ature below the mixed layer. This initialization procedure ishave layers 10--100 m thick. In our case, the decision of the one method of estimating subsurface temperatures when ob-vertical resolution was made in conjunction with the future servations over the entire domain are not readily available.use of a GCM [Philander and Pacanowski, 1981]. Given initial conditions in mid-January 1976, obtained from

4.2.5. Boundary conditions. The heat flux boundary con- the initialization procedure previously described, simulationdition is the same as in the Gill-Turner model, i.e., runs were performed using the turbulence closure model. The

aTI geographical distributions of SST for 1976 and 1977 were ob-

pcpKH -= Q (20) tained for various atmospheric forcings, i.e., the monthly

az .=0 mean, the 10-day mean, and the half day forcing for v. and 1;..

Similarly, for the momentum condition, The SST anomaly patterns were verified against the observedanomalies [Miyakoda and Rosati, 1982].

pK ~ I = T (21) Figures 5 and 6 show correlation coefficients and rIIis errorsM az .=0 a for the turbulence closure simulation. Points considered to

The boundary conditions for the bottom areRMS ERROR OF SST ANOMALIES NORTHERN HEMISPHERE

RMS ERROR OF SST ANOMALIES NORTHERN HEMISPHERE 2P7 2 ers,ste','

Persiste',e -Clos6. -lid -1m,.

lad-3()d

So I.

I4 °c 1. .4. I

°C 1 I.

1 0

o.o.

I O.I.0 1976 1977

Fig. 8. Root-mean-square difference of the SST between the simu-'976 1977 I . d h b . h h h . h f hatlon an t e 0 servatlon over t e nort em emlsp ere or t e case

Fig. 6. Root-mean-square difference of the SST between the simu- of 1976 and 1977 with the closure model. The result of the integrallation and the observation over the northern hemisphere for the cases model with twice daily atmospheric forcing is also shown for com-of 30-day 10-day mean and half day atmospheric forcings. parison.

~

~

MIYAKODA AND ROSATI: VARIATION OF SEA SURFACE TEMPf:RATURE 6541

havior. More persistent observed anomaly behavior may be ity; the turbulence closure model should be more advancedbetter simulated by the integral model. However, these results than that of the hierarchical level 2.0.indicate that both models give quite similar results.

Results presented in this paper have some noticeable defi- Rciencies such as the SST's in the higher latitudes and the east- ..EFERENCESern subtropics during the summer months are excessively Adem, J., On the prediction of mean monthly ocean temperatures,

d 1 h 1. d f h SST 1 . 1 Tel/us, 22, 410--430, 1970.warm an a so t e amp ItU e 0 t e anoma y IS too arge. Alexander, R. C., and R. I. Mobley, Monthly average sea-surfaceSome of the possible reasons for this are temperature and ice-pack limits on a 10 global grid, Mon. Weather

1. This is a one-dimensional model and therefore lacking Rev., 104, 143-148, 1976..the horizontal and vertical processes of a three-dimensional Bjer~nes, J., A possible. response ?f the atmospheric Hadley circu-

d 1 h. h b . t t t d b Ad [1970] latlon to the equatonal anomalies of ocean temperatures, Tel/us,mo e, w IC may e Impor an as sugges e y em , 18,820-829, 1966.Daly [1978], and Haney et al. [1978]. Bryan, K., and L. J. Lewis, A water mass model of the world oceans,

.2. The vertical mixing in these areas is underestimated. J. Geophys. Res., 84,2503-2517,1979.3. This model does not simulate ice and therefore during B~nker, A: F., Computations of surface ~nergy flux and annual air-sea

the heating season energy goes directly into heating the ocean Interaction cycles of the North Atlantic Ocean, Mon. Weather Rev.,d . 1... h b ..104,1122-1140,1976.an not Into me tIng Ice In t e su arctic region. Ciesielski, P. E., Variability within the ocean-atmospheric system over4. Accurate and real-time observed insolation and/or the North Pacific, Environ. Res. Pap., 25, 97 pp., 1980.

mixing ratio, rather than climatology, could be necessary. Daly, A. W., The response of North Atlantic sea surface temperature5. More accurate wind data could improve the vertical to atmospheric processes, Q. J. R. Meteorol. Soc., 104, 363-382,..1978.

mixIng. .Denman, K. L., A time-dependent model of the upper ocean, J. Phys.In order to determine which of these processes is the most Oceanogr.,3, 173-184, 1973.

probable contributor to the poor simulation some experiments Denman, K. L., and M. Miyake, Upper layer modification at Oceanwere run. By using the three-dimensional model of Bryan and Station 'Papa': Observations and simulation, J. Phys. Oceanogr., 3,

Lewis [1979], with the closure model included on the same D 18s5-19k6, 1R973A. d P B Rh. A t t d. h . f . d . h e zoe e, .., an ..mes, symp 0 IC regimes m mlxe -~Id, a~d the same ~tmos~ enc orCIng use I~ t e on~- layer deepening, J. Mar. Res., 34,111-116,1976.

dimensional models, simulatIons were run. AnalyzIng the dlf- Elsberry, R. L., and R. W. Garwood, Jr., Numerical ocean predictionference maps of the three-dimensional to one-dimensional models-Goal for the 1980's, Bul/. Am. Meteorol. Soc., 61, 1556-monthly means it did not appear that the tendency of the 1566, 1980.

, Esbensen, S. K., and R. W. Reynolds, Estimating monthly averagedwarm SST s was corrected. In fact, In the subarct~c region ~t air-sea transfers of heat and momentum using the bulk aerody-was even warmer. It does not appear, at least In the this namicmethod,J.Phys.(}ceanogr.,11,457-465,1981.preliminary study, that the gross deficiencies we se~ are due to Gill, A. E., and J. S. Turner, A comparison of seasonal thermoclinethe lack of the additional processes included in a three- models with observa~ion, Deep Sea Res.~ 23, 391-401: 1976:dimensional model. The next experiment tried to ascertain the H~lpern, D., Observat!ons of the deepemng of the wInd-mixed layer

m the northeast Pacific Ocean, J. Phys. Oceanogr., 4, 454-466,1974.effects of Increased vertical miXIng. This was accomplished Haney, R. L., A numerical case study of the development of large-simply by increasing t4e background mixing in the closure scale thermal anomalies in the central North Pacific Ocean, J.model and rerunning. The results did show a cooling tendency Phys. Oceanogr., 16, 541-556, 1980.and reduction in the excessive warming. This may indicate Haney, R. L., W. S. S?iver, and K. 1:1. Hunt, A dynamical-numerical

..study of the formation and evolution of large-scale ocean anoma-that If we were to use a higher-order closure scheme, where I. J Ph 0 8 952- 969 1978les,. ys. ceanogr., , ,.the miXIng IS better represented, the results could be Improved. Kato, H., and O. M. Phillips, On the penetration of a turbulent layerTests with the atmospheric forcings will await other, perhaps into a stratified fluid, J. Fluid Mech., 37, 643-655, 1969.more accurate, data sources. Kitaigorodsky, A. N., and Y. Z. Miropolsky, On the theory of open-

ocean active layer, Izv. Akad. Nauk. SSSR Atmos. Ocean. Phys., 6,97-102, 1970.

7. CONCLUSIONS Kondo, J., Y. Sasano, and T. Ishii, On wind-driven current and tem-..perature profiles with diurnal period in the oceanic planetary

There are five major conclusions. boundary layer, J. Phys. Oceanogr., 9, 360-372, 1979.1. The mixed layer model of the ol;ean used in this study Kraus, E. B., and J. S. Turner, A one-dimensional model of the sea-

was, to some extent, capable of simulating the SST anomaly sonal thermocline, II, The general theory and its consequences,fields in 1976 and 1977 for 4-5 months ahead in winter with ~el/us, 19, ~8-106, 1?67.

k.1l . h 1 h ." .Levltus, S., Climatological atlas of the world ocean, NOAA Prof Pap.,some s I , USIng t e rea atmosp enc lOrCIngs. 13,173 pp., 1982.

2. The turbulence closure model and the integral model Levitus, S., and A. H. Oort, Global analysis of oceanographic data,produced similar simulations of the SST fields. However, the Bul/. Am. Meteorol. Soc., 58,1270-1284, 1977.integral model requires much less computational resources. Madsen, O. S., A realistic model of the wind-induced Ekman bound-

3 N ." " ffi t . th . t t .ary layer, J. Phys. Oceanogr., 1, 248-255,1977...amlas recurrence e ec In e WIn er Ime was no- M h k I G V P K h . V I KI. k d V A S kharcu,..,..ocergm,.. ImO,an ..uoru-

tlced even In the anomaly component of SST. This may Imply kov, On the dynamics of the ocean surface mixed layer, J. Phys.that the initial conditions of sea temperature for the seasonal Oceanogr., 7,868-875,1977.

, thermocline are important for the winter prediction of SST. Mellor, G. L., an~ P. A. Durbin, The structure and dynamics of the4. When the atmospheric forcing is averaged in time the ocean surface mixed layer, J. Phys. O.ceanogr., 5, 718-728,1975.

1 . d ... fi d ' ffi . h 1. d f h Mellor, G. L., and T. Yamada, A hierarchy of turbulence closureresu ts In Icate a slgm cant I erence In t e amp ItU eo t e models for planetary boundary layers J. Atmos. Sci. 31 1791-1806error but not the phase. This does indicate without the proper 1974. " , ,

time resolution for the atmospheric forcing the heat storage of Middleton, J. W., A cross-spectral study of the spatial relationships inthe ocean could have quite a large error. the North Pacific sea-surface temperature anomaly field, Environ.

5 I d t . th ' 1 t ." th Res. Pap., 23, 123 pp., 1980..n or er 0 Improve e slmu a Ion perlormance, e M. k d K d A R t. Th . t. f " t...Iya 0 a, ., an .osa I, e vana Ion 0 sea surlace emper-

external forcIng data, such as the moisture In the atmosphere, ature in 1976 and 1977, I, The data analysis, J. Geophys. Res., 87,the air temperature and the radiation should be of better qual- 5667-5680, 1982.

6542 MIYAKODA AND ROSATI: VARIAllON OF SEA SURFACE TEMpERATURE

Miyakoda, K., and J. Sirutis, Comparative integrations of global cross-equatorial winds (with application to coastal upwelling in lowmodels with various parameterized processes of subgrid-scale verti- latitudes), Tel/us, 33, 201-210, 1981.cal transports: Description of the parameterization, Beitr. Phys. Pollard, R. T., P. B. Rhines, and R. O. R. Y. Thompson, The deep-Atmos., 50, 445-487,1977. ening of the wind-wind layer, Geophys. Fluid Dyn., 3,381-404,1973.

Namias, J., and R. M. Born, Temporal coherence in north Pacific Ratcliffe, R. A. S., and R. Murray, New lag associations betweensea-surface temperature patterns, J. Geophys. Res., 75(30), 5952- North Atlantic sea temperature and European pressure applied to5955, 1970. long-range weather forecasting, Q. J. R. Meteorol. Soc., 96, 226-246,

Namias, J., and R. M. Born, Empirical techniques applied to large- 1970.scale and long-period air-sea interactions: A preliminary report, Reynolds, R. W., A comparison of sea surface temperature climatol-Ref Ser. 72-1, Scripps Inst. of Oceanogr., Univ. of Calif., San Diego, ogies, J. Clim. Appl. Meteorol., 22, 447-459, 1983.1972. Richtmyer, R. D., and K. W. Morton, Difference Methods for 1nitial-

Namias, J., and R. M. Born, Further studies of temporal coherence in Value Problems, 2nd ed., 405 pp., Interscience, New York, 1967.North Pacific sea surface temperature, J. Geophys. Res., 79, 797-798, 1974. K. Miyakoda and A. Rosati, Geophysical Fluid Dynamics Labora-

Niiler, P. P., Deepening of the wind-mixed layer, J. Mar. Res., 33, toryfNational Oceanic and Atmospheric Administration, Princeton405-422, 1975. University, Princeton, NJ 08542.

Oort, A. H., The interannual variability of atmospheric circulationstatistics, NOAA Prof Pap., 8, 76 pp., 1977.

Petterssen, S., Weather Analysis and Forecasting, 428 pp., McGraw- (Received November 15, 1981;Hill, New York, 1956. revised March 19, 1984;

Philander, S. G. H., and R. C. Pacanowski, The oceanic response to accepted March 19, 1984.)

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