Climate Variability in a Coupled Atmosphere-Ocean Model:
the Role of Ocean Mixed Layer Processes
Michael A. Alexander*
James D. Scott
NOAA-CIRES/Climate Diagnostics Center
University of Colorado
Clara Deser
National Center for Atmospheric Research(Submitted to the Journal of Geophysical Research: Oceans)
March 1999
*Corresponding author address:
Dr. Michael Alexander
NOAA-CIRES/Climate Diagnostics Center
R/E/CD1
325 Broadway
Boulder, CO 80303-3328

ABSTRACTA 50-year coupled atmosphere-ocean model integration is used to study sea surface temperature (SST) and mixed
layer depth (h), and the processes which influence them. The model consists of an atmospheric general circulation
model coupled to an ocean mixed layer model in ice-free regions. The midlatitude SST variability is simulated fairly
well, although the maximum variance is underestimated and located farther south than observed. The model isclearly deficient in the vicinity of the Gulf Stream and in the eastern tropical Pacific where advective processes areimportant. The model generally reproduces the observed structure of the mean h in both March and September but
underestimates it in the North Atlantic during winter.
The net surface heat flux strongly regulates both the mean ( )and anomalous ( ‘ ) SSTs throughout the year.
The entrainment heat flux, which is proportional to the product of the entrainment rate ( W e ) and the temperature jumpat the base of the mixed layer ( ∆T ) , influences SSTs in summer and fall, especially north of ~35˚N (45˚N) in the
Pacific (Atlantic). W e ∆T′ is more important for the development of ( SST′ ) in fall compared to W e ′∆T , which islarger in summer. Anomalies in h have a significant impact on the heat balance of the mixed layer during spring andsummer. The entrainment rate is dominated by wind-induced mixing in summer and surface buoyancy forcing in winter; the density jump at the base of the mixed layer is of secondary importance.

ALEXANDER ET AL.
1.

Introduction

Both bulk mixed layer models and layered models
have been used to simulate vertical processes in theupper ocean [e.g. Garwood, 1977; Niiler and Kraus,
1977; Price et al,. 1986; Kantha and Clayson, 1994;
Large et al., 1994]. In bulk models, the temperature (andsalinity and currents if included) is predicted for themixed layer as a whole, and the mixed layer depth (h)depends on processes which create turbulence including
mechanical mixing by wind stress and convective mixing by the surface buoyancy flux. Bulk models appear
to be as accurate in their simulation of SST and h as
more sophisticated and computationally intensive layered models [Martin, 1985; Gaspar et al., 1988; Kraus,
1988]. However, both types of models have generally
been developed and tested at a few weather ship locations, and bulk models can not reproduce the detailed
vertical structure of turbulence. Bulk models have beenused to study the mean seasonal cycle of SST and h[Gordon and Bottomly, 1985; Le Treut et al., 1985; Siminot et al., 1988] and the formation of SST anomalies
over the North Pacific [Miyakoda and Roasatti, 1984;
Alexander, 1992] and North Atlantic [Battisti et al.,
1995].
Ocean mixed layer models are also useful forunderstanding the processes which contribute to thevariability of SST and h over the course of the seasonal
cycle. Alexander and Penland [1996] used a statisticalatmospheric model, based on observations from weather
ship P, to drive a mixed layer ocean model. The model
provided a reasonable estimate of the range of the meanand standard deviation of upper ocean temperature andmixed layer depth over the seasonal cycle. An analysisof the temperature tendency indicated that anomalies in
the net heat flux, mixed layer depth and entrainment
heat flux all provided a significant contribution to thegrowth of SST anomalies at different times of the year.
Anomalies in h were highly correlated with the surface
buoyancy flux in winter and the surface wind stress insummer.
In this study, we expand on the work of Alexander
and Penland [1996] by examining SST and h and theprocesses which influence them over the Northern
Hemisphere Oceans in a coupled atmosphere-ocean
model. The model, which consists of an atmosphericgeneral circulation model (AGCM) connected to a gridof one-dimensional mixed layer ocean models, isdescribed in section 2. By using a coupled model weavoid the very difficult task of finding the appropriate
boundary conditions to drive an ocean model. The meanand standard deviation of SST and h during March and
September, the peak of winter and summer in the northern oceans, are discussed in section 3. The factors which
control the mean and anomalous SST tendency are
examined in section 4, while the relationships between

Beginning with the pioneering work of Namias[1959, 1963] and Bjerknes [1964], numerous studies
have sought to understand how midlatitude sea surface
temperature (SST) anomalies form and the extent towhich they influence the atmosphere. SST anomalies
may form through changes in air-sea heat fluxes, horizontal and vertical ocean heat transport, and turbulent
mixing. Many of the early studies [see Frankignoul,
1985], focused on the role of advection: Namias [1959,
1965] found that anomalous Ekman drift played an
important role in generating SST anomalies, while
Jacob(1967), Namias [1972], and Favorite and McClain[1973] suggested that the mean advection of anomalous
temperatures could also be important. More recent
modeling studies confirmed that anomalous Ekman
transport could help to create SST anomalies in regionsof strong SST gradients [Haney, 1980; Luksch and vonStorch, 1992; Miller et al., 1994; Luksch, 1996]. However, on times scales of less than ~10 years, most studies
have found that surface heat fluxes play a dominant rolein forcing midlatitude SST anomalies [Gill and Niiler,
1973; Salmon and Hendershott, 1976; Frankignoul andReynolds, 1983; Battisti et al., 1995; Halliwell andMayer, 1996; plus many more], while Ekman pumping
plays a negligible role [White et al., 1980; Haney et al.,
1983; Schneider et al., 1999].
High resolution measurements of currents, temperature, and salinity indicate that upper ocean processes,
in addition to surface heat fluxes, can have an important
impact on SSTs [e.g. Davis et al., 1981; Large et al.,
1986; Webster and Lukas, 1992]. However, most fieldstudies are of short duration, generally lasting less than a
few months. Longer records, on the order of 20-40
years, are available from a few of the ocean weather
ships stationed in the North Atlantic and Pacific Oceans.
Using weather ship data, Clark [1972], Elsberry andGarwood [1980], and Lanzante and Harnack [1983]
found that the anomalies in the depth of the well mixed
surface layer could significantly influence SSTs in
spring and summer. Camp and Elsberry [1978] showedthat cooling due to entrainment of subsurface water into
the mixed layer could be an order of magnitude larger
than the surface energy fluxes during the passage ofstorms at weather ship P (50˚N, 145˚W). Namias andBorn [1970, 1974] and Alexander and Deser [1995] presented evidence that thermal anomalies created in the
deep ocean mixed layer could remain intact in the seasonal thermocline (30-100 m) during summer and returnto the surface layer in the following fall and winter.
However, many upper ocean processes, such as entrainment, and their impact on SST are very difficult to measure directly.

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ALEXANDER ET AL.
the entrainment rate and the shear and buoyancy forcing
are explored in section 5. The results are summarized
and discussed in section 6.
2.

(1)
where Tm is the mixed layer temperature, ∆T = Tb-Tm,
Tb is the temperature of the remainder of the layer belowh, Qnet the net surface energy flux into the ocean, Qcor
the surface heat flux correction, Qswh the penetrating
solar radiation at h, We the entrainment rate, ρ and c thereference density and specific heat of sea water, κ thediffusion coefficient for small scale motion, and z thevertical coordinate. Convective adjustment, CA, occurs
when the mixed layer is more dense than the layer
below, at that time heat within the remainder of the layer
below h is incorporated into the mixed layer and h isthen set to the top of the next layer. The model has asimilar predictive equation for mixed layer salinity,
where the fresh water flux is due to precipitation - evaporation (P-E).
The mixed layer depth primarily increases via
entrainment, except in high latitudes where h can significantly deepen via CA. By vertically integrating the turbulent kinetic energy equation over h and then theapplying a fairly standard set of assumptions [see Niiler
and Krauss, 1977], We can be expressed as:

Coupled model

A 50-year simulation with a global coupled atmosphere-ocean model is used to study upper ocean variability in the northern midlatitude oceans. The model
consists of a Geophysical Fluid Dynamics Lab (GFDL)
AGCM connected to an upper ocean mixed layer model(MLM). Alexander and Deser [1995], Battisti et al.
[1995], Alexander and Penland [1996], and Bhatt et al.
[1998] have used a slightly different version of theMLM to study upper ocean processes and midlatitude
air-sea interaction. The ocean model consists of a gridof independent column models which include local
atmosphere-ocean fluxes and the turbulent entrainmentof water into the surface mixed layer, but not mean vertical motions or horizontal processes. The ocean column
models are aligned with the AGCM grid over ice free
regions of the global oceans. In regions with sea ice, theice fraction, ice thickness and SST are specified.
a.

atmospheric model
mu*3 – 0.5hB ( h ) – hε
W e = ---------------------------------------------------2h∆b + qThe GFDL AGCM is a global spectral model withrhomboidal truncation at wave number 30, which isapproximately 2.25º latitude by 3.75º longitude. The
model has 14 unequally spaced sigma levels in the vertical, with the lowest level at ~30 m above the surface.
The model includes smoothed topography, gravity wave
drag, and predicted clouds and soil moisture. Stratiform
clouds form and precipitation occurs when the relative
humidity exceeds 100%, while subgrid scale precipitation is parameterized by moist convective adjustment.
Many features of the model's climate are presented on
the World Wide Web [Collins et al., 1999], while a more
complete description of an earlier version of the GCM isgiven by Gordon and Stern [1982] and Manabe andHahn [1981].
b.

(2)

where m is a constant, the surface friction velocity
u* = τ ⁄ ρ , where τ is the surface wind stress, and ∆bis the buoyancy jump at the base of the mixed layer; following Gaspar [1988], Eq. (2) neglects mixing due tocurrent shear across the base of the mixed layer. The
buoyancy flux integrated over the mixed layer, B(h),depends on Qnet, P-E, and the absorption of solar radiation in the water column. The mean turbulent kinetic
energy, q2, which is usually small but can be importantfor near neutral conditions, is parameterized following
Kim [1976]. Mixed layer models generally differ intheir parameterization of ε, the turbulent dissipation
rate; here we use the formulation and parameter values
given by Gaspar [1988]. When deepening by entrain-

mixed layer ocean model

ment, h is computed as a prognostic variable  ∂h = W e .

The individual column models consist of a uniform
mixed layer atop a layered model that represents conditions in the pycnocline. Here we use the model developed by Gaspar [1988], which has been formulated withclimate simulations in mind. The temperature tendencyof the mixed layer is given by:∂t

When shoaling, the mixed layer reforms closer to thesurface, We is set to zero, and h is computed as a diagnostic quantity by assuming a balance between windstirring, buoyancy forcing and dissipation. When themixed layer shoals, the temperature (salinity) profile isadjusted to conserve heat (salt) and the temperature(salinity) jump at the base of the mixed layer. The prognostic equations for Tm, Sm and h are integrated using a

Q net + Q cor Q swh W e ∆T
∂T m
κ ∂T
- – ------------ + --------------- + CA – --= ---------------------------h ∂ z z = –h
ρch
h
∂t
ρch

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ALEXANDER ET AL.
first order forward in time scheme.
The region beneath the mixed layer is represented
by a multi-layer system, where the temperature andsalinity of the layers change by convective adjustment,
vertical diffusion, and linear damping. The temperatureof the upper 300 m can also change due to penetrating
solar radiation. The vertical diffusion is calculatedusing the Crank-Nicholson scheme with a constant diffusion coefficient of 1.0x10-5 m s-2, a value suggestedby the tracer experiments of Ledwell et al. [1993]. The
temperature and salinity in all model layers are damped
towards their monthly mean climatological values on a
10-year time scale. This weak Newtonian damping,which crudely represents processes that vary with depth
such as the mean heat transport, was necessary for themodel to retain a stable density profile in regions ofstrong current shear. The absorption of solar radiation isparameterized following Paulson and Simpson [1977].
The bottom of the MLM is 1000 m or the actual
ocean depth, which ever is smaller. For open ocean
points the MLM contains 31 unequally spaced layers
between the surface and 1000 m, where 15 of the layers
are within the first 100 m, and the temperature and salinity of the final layer is set to the observed climatologicalvalue. The mixed layer depth is not forced to coincidewith the levels of the layered model; the temperature oflayers that are entirely above h are set to Tm, while Tb isfrom the remainder of the layer which is beneath h.
However, h is constrained to be greater than 10 m andless than 850 m or the bottom of the ocean, which everis smaller.
c.

heat flux. The radiative fluxes in the AGCM depend on
temperature, water vapor, clouds, and specified trace
constituents. The sensible and latent heat flux are computed using standard bulk aerodynamic formulas where
the exchange coefficients have a constant value of
1.0x10-3. The surface wind stress is computed in a similar fashion. The wind speed, air temperature and specific humidity used in the bulk formulas are taken
directly from the lowest model level, while the SST isgiven by Tm obtained from the ocean model. The atmosphere and ocean models exchange information once perday, the time step of the MLM. The atmosphere-toocean fluxes are averaged over the 96 time steps in one
AGCM day, while the ocean-to-atmosphere fluxes arecomputed every AGCM time step using the daily SST
values.
Due to errors in the surface fluxes and processes
absent from the ocean model it is necessary to correct
the surface fluxes in order for the simulated climate toremain close to observations [Sausen et. al., 1998;
Manabe and Stouffer, 1988; Battisti et al., 1995]. Herethe surface heat and salt flux corrections are obtained
from a 20-year MLM simulation using surface fluxes
from a separate GFDL AGCM run, where the AGCM
had observed climatological SSTs as boundary conditions. Prior to each time step, the SST is set to theobserved climatological value on that day.
The
observed daily SSTs were obtained by interpolating themonthly values of Smith et al. [1996] onto the R30 grid.
The MLM is then run for one time step where Tm and h
are free to evolve. The difference between the predicted
Tm and observed SST is used to compute the heat flux
correction necessary for the model to match observations. A similar method is used to obtain the salt flux
correction. This procedure is repeated to obtain 20
years of daily flux correction values. Long termmonthly mean corrections are computed and then linearly interpolated to daily values which are then added
to the temperature and salinity tendency equations but
not the entrainment equation.
The flux corrections vary with location and time ofyear but do not vary from one year to the next. The
annual mean surface heat flux correction, Qcor, is shownin Fig. 1 for the North Atlantic and Pacific Oceans.
Heat is added to the oceans in the western ~1/2 of bothbasins, with maxima of ~150 W m-2 to the east of Japanand the east coast of the United States. The magnitude
and pattern of -Qcor resembles the observed annual
mean Qnet and equivalently the mean oceanic heat flux
convergence [Hsuing, 1985; Moisan and Niiler, 1998],
indicating that the correction is primarily accounting forthe absence of advection in the ocean model. Qcor

sea ice

For points where sea ice occurs during any part ofthe mean seasonal cycle, the MLM is not active; insteadthe daily ice thickness and ice fraction (or SST during
ice-free periods) are specified based on the interpolatedmonthly mean climatology for the period 1950-95. Heat
fluxes in these areas are weighted for the appropriate
proportions of open water and ice. Sea ice can also form
over the active MLM points, which are beyond the maximum extent of climatological ice when Tm drops to thefreezing point for sea water, 271.16 K. A simple heatbalance model is used for the ice, which is assumed tocover 100% of the grid box.
d.

air-sea coupling and the surface heat flux correction

Heat, momentum, and fresh water are exchanged
across the models air-sea interface. The net heat flux
consists of the shortwave, longwave, sensible and latent

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ALEXANDER ET AL.

Fig. 1. Annual average surface heat flux correction (Wm-2). Positive values indicate heat is added to theocean. The contour interval is 25 and values greater than 50 are shaded. This figure and all subsequent
planar plots have been smoothed using a 9-point filter.

are due to nonlinearities in the MLM, computing theflux corrections from a 20-year ocean only integration,and the method used to interpolate the flux corrections
in time did not preserve the monthly means from which
they were computed.
The observed and simulated interannual standard
deviations (σ) of SST in March over the Northern Hemisphere Oceans are shown in Fig. 2. The standard deviations are computed from the departures of the individual
monthly means from the long term monthly means. The
observed σ values are derived from the Smith et al.
[1996] data set for the period 1950-95, while the simulated values are from the 50-year model integration.
Both the simulated and observed σ range from 0.3º to
1.2ºC over the open ocean. In the Atlantic, σ is maximized along the east coast of North America, in part due
to the variability in wind speed and air temperature associated with continental air masses moving over theocean. However, only the observations exhibit a band ofenhanced σ that extends from the mid-Atlantic states toeast of Newfoundland, which likely arise due to variability in Ekman transport across strong SST gradients[Luksch, 1996] and in heat transport by the Gulf Stream
and North Atlantic Current. The March σ exceeds
0.6ºC in the central North Pacific in both the model andobservations, but the maximum variability of ~0.8ºC
occurs 10º-15º farther south in the model. The simulated SST variability is also greater (less) than observedin the South China Sea (Gulf of Alaska). Since the coupled model does not contain horizontal processes suchas currents and wave dynamics, there is no El Niño/
Southern Oscillation (ENSO), and σ is significantly
underestimated in the eastern tropical Pacific (Fig. 2).
Fluctuations in the strength and position of the
Aleutian low associated with ENSO have been shown tocause SST anomalies to form in the North Pacific primarily through changes in Qnet [Alexander, 1992; Luksch

exceeds 300 W m-2 in the vicinity of the Kuroshio Current and Gulf Stream in March, but is negligible in September (not shown), due to the large seasonal cycle inheat transported by these current systems [Wilkin et al.,
1995; Yu and Malanotte-Rizzoli, 1998]. The GFDL
AGCM, like many current climate models, overestimates the shortwave radiation reaching the surface, primarily due to errors in simulating clouds [Garratt et al.,1998]. As a result, Qcor values between -50 and -100
Wm-2 are applied to the MLM during summer from
40ºN-60ºN.
e.

initial conditions

The initial ocean conditions for the coupled model
integration were derived by averaging the MLM variables on January 1st for 20 years of an MLM simulation
driven by surface fluxes from a previous AGCM simulation. The atmospheric conditions were obtained for January 1st by integrating the GFDL AGCM for five years
beginning from a state of rest. Since the AGCM and
MLM initial conditions were obtained independently,
there is an adjustment period of a few months once thetwo models are coupled.
3.

SST and h

Here we examine sea surface temperature andmixed layer depth fields from the 50-year coupled atmosphere-ocean integration and compare them to observations. The simulated and observed long-term monthly
mean SST differ by less than 1ºC at nearly all of theMLM grid points (not shown), a result of imposing asurface flux correction. However, these small differences are systematic: the simulated SSTs tend to be too
warm (cold) in summer (winter). These model biases

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ALEXANDER ET AL.

Fig. 2. The standard deviation ( )of March SSTs (˚C) from (a) observations and (b) the 50-year coupled model simulation. The
observed SSTs, which extend from 1950-95, are originally from the data set of Smith et al. (1996) which have then been interpolated from a 2˚x2˚ grid to the R30 Gaussian grid. The contour interval is 0.1˚C, and 0.6˚C<SST <0.8˚C is shaded light while
those greater than 0.7˚C are shaded dark.

exceeds 0.6ºC over both oceans between 30ºN-50ºN andreaches a maximum of 1ºC along 40ºN in the Pacific.
The simulated σ also exceeds 0.6ºC in both basins but
the region of enhanced variability is located about 15º
farther south in the Atlantic compared to observations.
While the region of SST σ > 0.6ºC is close to thatobserved in the North Pacific, it extends too far south in
the central Pacific and does not cover the eastern Pacificfrom 20ºN-35ºN. The model simulates regions where σ> 0.7ºC in the North Pacific but it is too broad comparedto observations.
Studies by Norris and Leovy [1994] and Norris etal. [1998] indicate that variability in stratus clouds contributes to SST anomalies in the central North Pacificduring summer. As discussed in section 2, the GFDL
model like most AGCMs have difficulty simulating
clouds, especially low-level stratus decks. Thus, some ofthe differences between the observed and simulated SST
σ in September may result from errors in the in simu-

and von Storch, 1992; and Lau and Nath, 1996). We
have examined the influence of ENSO on midlatitude
SSTs using an additional GFDL AGCM-MLM experiment where observed SSTs are specified between
approximately 25˚N-25˚S in the Pacific for the period
1950-1995 and SSTs are provided by the MLM elsewhere over the global oceans. Including the observed
ENSO signal generally improves the simulation of SST
variability in the North Pacific, including: a ~15º northward shift in the maximum SST σ to 30ºN-40ºN in thecentral Pacific; a decrease in σ in the Sea of Japan; and aslight increase in σ in the northeast portion of the basin(not shown).
The SST σ from observations and the model simulation during September are shown in Fig. 3. Both theobserved and simulated variability are greater in September than in March, primarily due to the relatively
small thermal inertia of the shallow mixed layer in summer (see section 4). The observed SST σ in September

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ALEXANDER ET AL.

Fig. 3. The (a) observed and (b) simulated standard deviation of September SSTs (˚C). Contour interval and shading as in Fig. 2.

lated stratus clouds and the attendant surface shortwave
radiation.
As expected, the model strongly underestimates
the SST variability associated with ENSO in the tropical
Pacific during September. Unlike March, there is noclear change in the pattern or strength of the variability
outside of the tropical Pacific in the model simulation
which included the specified ENSO signal. This is consistent with Horel and Wallace [1981], Mitchell andWallace [1996] and Kumar and Hoerling [1998] who
found that the extratropical atmospheric changes associated with ENSO are much greater in winter than summer.
The observed and simulated mean mixed layer
depth, h, are shown in Fig. 4 for March. The observed h
is obtained from Monterey and Levitus [1997] based on
the depth where the density is 0.0125 kg m-3 less than
the surface density. The observed h values, which wereoriginally on a 1ºx1º grid, have been interpolated onto to
the models Gaussian grid.
The observed mixed layer reaches its greatest

depth in the North Atlantic where it exceeds 500 m fromthe Labrador Sea to east of Scotland. In nature, the formation of deep water through complex convective processes can lead to instantaneous mixed layer values ofgreater than 1500 m in the Labrador and Greenland Seas
[Gascard and Clarke, 1983; Dickson et al., 1996]. A
secondary maximum in the observed h extends northeastward across the central Atlantic. The MLM simulates the observed structure of h but underestimates its
magnitude especially north of ~45ºN.
The observed March mixed layer depths are muchsmaller in the Pacific where there is no deep water formation. The observed h reaches a maximum value of~200 m, slightly greater than h in the coupled model
integration. The observed and simulated h maxima arelocated in the western Pacific between 30ºN-45ºN, but
the center of this maximum is located 5º to the south andcloser to the coast in the model. The elongated regionsof enhanced h between 30ºN-50ºN in both oceans arecoincident with the surface forcing associated with themain storm tracks [Alexander and Scott, 1997]. Unlike

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ALEXANDER ET AL.

Fig. 4. The (a) observed and (b) simulated mixed layer depth (m) in March. The observed h values are from Monterey andLevitus (1997) which have then been interpolated from a 1˚x1˚ grid to the R30 grid.. Note that the contour interval changes:
it is 25 for h < 200 and 100 for h >200; values greater than 200 are shaded.

observations, the model does not contain a narrow
region of shallow h along the west coast of North America perhaps due to the absence of coastal upwelling in
the MLM. The observed and simulated h range between
25-75 m throughout the tropics.
Several factors may contribute to the underestimation of h during winter in the coupled model simulation:(i) The MLM tends to shoal too rapidly under stableconditions and thus may be unable to maintain deep
mixed layers through late winter. (ii) Many ocean processes which generate turbulence are not included in theMLM, such as surface wave breaking, Langmuir cells,
inertial current shears, etc. (iii) The surface mechanicalforcing is proportional to the cube of the wind speed andthe buoyancy forcing depends on the square of the windspeed; thus h deepens significantly during short periodsof high wind speed. The surface boundary conditions
are averaged over one day, which suppresses extreme

short-duration forcing. (iv) The mixed layer is constrained to be less than 850 m in the MLM, thereby limiting h when deep convection occurs. (v) The MLM
does not include currents, which limits h due to theabsence of mixing due to vertical shear and the advection of heat and salt which can change the vertical stability of the water column. Both of these processes arelikely to be important in the western boundary currents
and the subpolar gyre of the North Atlantic, where theMLM greatly underestimates h. (vi) The observed
mixed layer depth is estimated from the mean temperature and salinity profiles, while in the MLM h is thelayer over which surface generated turbulence is active.
The observed and simulated mixed layer depths
are at a minimum in June-August (not shown) but are
still quite shallow in September (Fig. 5). The model
closely approximates observations with h on the order of
20 m in the central North Atlantic and much of the8

ALEXANDER ET AL.

Fig. 5. The (a) observed and (b) simulated mixed layer depth (m) in September. The contour interval is 10, where 20<
h<30 is shaded light and h> 30 is shaded dark

4.

North Pacific, and somewhat deeper mixed layers northof 50ºN in the Atlantic and in the subtropics of bothocean basins. The MLM also reproduces the observed
minimum in h between 0º-10ºN and the deepening of
the mixed layer from 0º to10ºS.
Basin-wide estimates of the interannual standard
deviation of mixed layer depth are not available fromobservations; the simulated σ of h are shown in Fig. 6
for March and September. The regions of greatest variability coincide with the maximum mean h values bothin winter and summer (c.f. Figs. 4 and 5). The σ of h isgreatest in the north Atlantic in March where it exceeds
30 m north of ~30ºN and 60 m from about 45ºN-65ºN.
While h σ in March exceeds 30 m over much of thenorthwest Pacific and in the vicinity of Hawaii, it is lessthan 60 m over the entire Pacific. The variability isgreatly reduced in September when the σ of h < 5 mover much of the ocean between 30ºN-60ºN and has amaximum of 15-20 m at 15ºN and 10ºS in the central
Pacific and western Atlantic.

Components of the SST tendency equation

The factors which control the SST tendency in theMLM, shown on the right hand side of Eq. 1, are associated with fluxes through the surface and the base of themixed layer. Multiplying Eq. 1 by ρch gives the terms
in flux form: the net surface heat flux (Qnet); surface flux
correction (Qcor); penetrating solar radiation (Qswh),
entrainment heat flux (Qwe = ρcWe∆T); convective
adjustment (CA); and temperature diffusion at h (Tdif).
The seasonal cycle of the zonal average of these 6 terms,
obtained from the long term monthly means of the simulated fluxes, are shown in Fig. 7.
As expected, Qnet is the dominant term over muchof the Northern Hemisphere, with magnitudes exceeding 80 Wm-2 north of 20ºN in summer and winter.
Heating due to solar radiation in summer and cooling by
the sensible and latent heat fluxes in winter results in astrong seasonal cycle of Qnet with a maximum ampli-

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ALEXANDER ET AL.

Fig 6. The simulated standard deviation of mixed layer depth (m) in (a) March and (b) September. In (a) values of hσ<30 mhave a contour interval of 10 and are shaded light, while hσ > 30 m have a contour interval of 30 and are shaded dark. The
contour interval in (b) is 2.5 where 5< hσ<10 is shaded light and hσ >10 is shaded dark.

The σ values for Qnet and Qwe+CA over the courseof the seasonal cycle, shown in Fig. 8, are computedfrom the departure of monthly means from the 50-year
mean at each model grid point which are then zonallyaveraged. Recall that the seasonal cycle of the flux correction is the same each year (Qcor σ = 0). We havecombined CA with Qwe since the former represents convective plumes, an extreme form of entrainment. The
Qnet σ has a maximum in winter opposite to the mean
Qnet. However, the simulated variability of Qnet may beunderestimated due to the lack of low cloud variability.
The seasonal cycle of the σ of Qnet tends to lag the mean
by about one month, e.g. the magnitude of the mean (σ)
Qnet is maximized in January (February). The Qwe+CA

tude of 200 Wm-2 at ~40ºN. However, the total flux
through the surface is reduced by Qcor which is roughly
half as large as Qnet but of opposite sign. Qwe acts tocool SSTs over most of the Northern Hemisphere, since
We is always positive and ∆T (=Tb-Tm) is negative overmost of the worlds oceans. When |∆T| reaches a maximum in fall, Qwe is similar in magnitude to Qnet,
exceeding |80| Wm-2 between 35ºN-60ºN. The otherthree components, CA, Qswh and Tdif, are substantiallysmaller (note that the contour interval is 1/4 as large
compared with the other 3 components) over most of the
globe. CA is negligible except at high latitudes in winterwhen episodic deep convection brings warm salty water
into the mixed layer. Qswh cools the mixed layer, primarily in the subtropics in summer when the surface solar
radiation is a maximum and h is a minimum. Like
entrainment, Tdif acts to cool the mixed layer primarily
at mid latitudes in fall when |∆T| is a maximum.

σ has two maxima exceeding 25 Wm-2, one at high latitudes in winter and the second in midlatitudes in fall; theformer (latter) is due to variability in CA (Qwe). The
general zonal structure of the σ of Qswh and Tdif resem-

10

ALEXANDER ET AL.

Fig. 7. Zoally averaged (a) net surface heat flux, (b) entrainment heat flux, (c) surface heat flux correction, (d) convective
adjustment (e) penetrating solar radiation, and (f) temperature diffusion (Wm-2) in the MLM as a function of calendar
month. The contour interval is 20 in (a)-(c) and 5 in (d)-(f). Negative contours are dashed and values <-80 (>80) areshaded light (dark).

Pacific, and at 50˚N in the central Atlantic. CA leads towarming (> 30 Wm-2) south of Greenland (not shown).
In September, when CA is negligible, Qwe is fairly zonal
in structure and decreases poleward. The maximum
cooling occurs in the northwestern Pacific, where themagnitude of Qwe exceeds 100 W m-2, roughly twicethat in the Atlantic at the same latitude. Qwe+CA weakly
warms the tropical Pacific as ∆T > 0. In this region, P-E> 0 increases the surface buoyancy creating a shallow

ble their means, with maximum values of 8 and 4 Wm-2,
respectively (not shown).
The spatial structure of Qnet in the R30 version of
the GFDL is in general agreement with observations[Alexander and Scott, 1997]. The mean Qwe+CA fromthe coupled model simulation in March and September
are shown in Fig. 9. During March Qwe+CA is relatively
weak over both ocean basins with the strongest cooling(< -30 Wm-2), south of Japan, at 10˚N in the central

11

ALEXANDER ET AL.

Fig. 8. Zonally averaged standard deviations of (a) the net surface heat flux and (b) the heat flux due to entrainment plus
convective adjustment (Wm-2) as a function of calendar month. Qnet and Qwe + CA σ are computed using monthly
anomalies at each MLM grid point and then zonally averaged. The contour interval is 5, values greater than 25 areshaded.

mixed layer (Figs. 4 & 5) that is often maintained by ajump in salinity. Observational studies by Lukas andLindstrom [1991] and Anderson et al. [1996] also indicate that entrainment acts to slightly warm the mixed
layer and helps to maintain high SSTs in the tropicalWest Pacific. The warming due to Qwe+CA in the eastern equatorial Pacific during September in the model isunrealistic.
Previous studies [e.g. Cayan, 1992; Iwasaka andWallace, 1995; Delworth, 1996; Deser and Timlin,
1997] along with Fig. 8 indicate that variability in Qnetplays an important role in the development of SST
anomalies. Here, we assess the relative importance ofentrainment in generating SST variability by taking theratio of (Qwe+CA)σ to Qnetσ during March and September (Fig. 10). During March (Qwe+CA)σ/Qnetσ issmall, between 0.2-0.4, over most of the ocean north of
10˚S, except for the tropical West Pacific and in the
Atlantic north of 30˚N. Ratios which exceed unity in
the North Atlantic are due to CA rather than Qwe. The(Qwe+CA)σ also exceeds that of Qnetσ in the vicinity ofthe equator near 160˚E, which may be related to interannual variability in the strength of the Madden-Julian
Oscillation [Shinoda and Hendon, 1998].
Variability in the entrainment heat flux clearlyplays an important role in generating SST anomalies
during September over much of the Atlantic (Pacific)
north of 45˚N (35˚N) where (Qwe+CA)σ/Qnetσ > 1.0.
During summer most of the heat flux across the base of
the mixed layer is associated with mixing in a convectively stable environment , and thus Qwe σ >> CA σ.
The development of the simulated SST anomalies,
due to surface heat fluxes and entrainment, the dominant
processes in the MLM, is examined further by decom-

posing the variables in Eq. 1 into daily mean ( ) anddepartures ( ‘ ) from the mean. Clark [1972] and Alexander and Penland [1996] have performed a similar
analysis,using
theapproximation
1 ⁄ ( h + h′ ) ≈ 1 – ( h′ ⁄ h ), which is valid only whenh′ ⁄ h < 1 , a condition that is violated over parts of theocean especially in spring and summer. Here, h ≡ 1 ⁄ η ,then using Eq. 1 the anomalous Tm tendency can be
written as :Q′ net η ( Q net + Q cor )η′ Q′ net η′ – Q′ net η′∂T′ m ---------------- ------------------------------------------= ρc + -------------------------------------+
ρc
ρc
∂t
I
II
III

+

W ′ e ∆Tη W e ∆T′η W e ∆T η′

+

IV

+

V

VI

+ ( W ′ e ∆T′ – W ′ e ∆T′ )η + ( W ′ e η′ – W ′ e η′ )∆T+ ( ∆T′η′ – ∆T′η′ )W e + W ′ e ∆T′η′ – W ′ e ∆T′η′ + CA′ (3)Composites of the individual terms in (3) are constructed at each model grid point based on when thelocal monthly value of∂
T ′ > 1σ Composites are com∂t mputed for each calendar month by summing daily valuesof each term during the months when the σ criteria is
exceeded. Approximately 10 months of data went into
each composite.
Analyses of zonal means of the terms in Eq. 3 indicates that only the first six make a significant contribution to Tm anomaly development and that thecontribution of the individual terms is distinctly differ-

12

ALEXANDER ET AL.
ent in the tropics and midlatitudes but relatively uniform
north of ~20ºN (not shown). Fig. 11 shows the seasonal
cycle of the first six terms on the right hand side of (3)averaged between 20ºN-70ºN. Term I is dominant
through out the year, indicating that Q’net strongly contributes to the fastest growing SST anomalies. Even
though Q’net is 2-3 times larger in winter than summer

During early spring the distribution of η’ is highly
skewed, since the mixed layer tends to shoal abruptly
but only gets marginally deeper than the mean. As a

(Fig. 8), η (= 1 ⁄ h ) is an order of magnitude smaller inwinter than summer (Figs. 4&5), as a result term I
ranges from about 0.4ºC mon-1 in January to 1.0ºC
mon-1 in July. Term II plays an important role in generating SST during spring and summer, in general agreement with Clark [1972] and Alexander and Penland[1996], although they estimated its impact to equal or
exceed Term I. Term III depends on how the instantaneous relationship between Qnet and η differs from theirlong term correlation. The net surface heating causes amore buoyant and thus shallower mixed layer, which
results in a positive correlation between Q’net and η’.

posite (not shown). Term IV, associated with the anomalous entrainment rate, is maximized in July when it
contributes ~ 0.4˚C mon-1 to SST anomaly growth.
Positive values of term IV result from weaker entrainment of colder water from below (W’e<0), since

result, Q' net η' > Q' net η' and thus term III makes a significant contribution in February-April to the positive∂T ′ composite, but is negligible for the negative com∂t m∆T = T b – T m < 0 and η > 0 . Term V, which represents

the mean entrainment of the anomalous temperature
jump at the base of the mixed layer, reaches a maximumin September, when ∆T′ and η are large. Term VI
always acts to damp SST anomaly growth, as W e is positive, ∆T is almost always negative, and the mixed layer

Fig. 9. The heat flux due to entrainment plus convective adjustment (Wm-2) in (a) March and (b) September. The contour interval is 10, values less than 30 are shaded.

13

ALEXANDER ET AL.

Fig 10. The standard deviation of entrainment heat flux plus convective adjustment divided by the standard deviation of the net surface heat flux (Qwe+CA)σ/Qnetσ in (a) March and (b) September. The contour interval is 0.2, values greater than 1.0 are shaded.

tends to be shallower ( η’>0) when it is warming rapidly.
5.

We and -B(h) peak near ~0.6 in winter and decrease to~0.3 in summer. Correlations between We and -∆b,while generally small, approach ~0.3 in fall.
The analysis above examines the linear relationship between We and the anomalous forcing terms. In
some mixed layer models, including the one describedby Niiler and Krauss [1977], dissipation is a constantfraction of the individual forcing terms, so their contribution to We can be determined independently [Hanson,
1992]. In the MLM dissipation is non-linear: ε in Eq. 2
is a complex function of B(h), u*3 and u*/f, where f is
the coriolis parameter. However, a non-dimensional
mixing efficiency can be defined:

Components of the entrainment equation

The entrainment rate in the MLM, given by Eq. 2,
is governed by u*3, B(h) and ∆b which represent windstirring, buoyancy forcing integrated over the mixed
layer, and the buoyancy jump at the base of the mixed
layer, respectively. Correlations between these threeterms and We, are computed for each calendar monthusing daily anomalies of u*3, -B(h) and -∆b only on days
when entrainment has occurred. Negative values of
B(h) and ∆b anomalies should enhance entrainment allother factors being equal. Averages of the correlations
for all of the ocean model grid points between 20ºN and
70ºN are shown in Fig. 12. The correlation between We

P∗ = h∆bW e ⁄ u∗ 3(4)which is solely a function of h/L and h/λ [Gaspar, 1988],
where L(=u*3/B(h)) is a bulk Monin-Obukov lengthand u*3 anomalies ranges between about 0.35 in February to 0.6 in June. In contrast, the correlations between

14

ALEXANDER ET AL.
scale and λ(=u*/f) is the Ekman or Rossby rotation
scale. Contoured values of P*(h/L, h/λ) are shown in
Fig. 13. P* increases as h/L decreases since more surface cooling (B(h) < 0) leads to enhanced mixing. P*
decreases as h/λ increases since rotation limits the vertical size of eddies. However, h/λ has a negligible impact
on P* for values of h/L< ~5.
A scatter plot of 50 years of monthly mean valuesof h/L verses h/λ averaged between 20˚N-70˚N obtained
from the coupled model simulation are also shown in
Fig. 13. From September through April the seasonal
cycle dominates the interannual variability, as all 50 values within a given month reside in a distinct area of theh/L, h/λ phase space. The spread in the individual
monthly values of h/L and thus P* is largest in January
and February. The maximum values of h/L (h/λ) occur
in December-February (January-March), while the minimum of both length scales occurs in June-July. Fig. 13
suggests that entrainment occurs much more often than
shoaling, since P* is almost always greater than zero.
While P* appears to depend much more strongly on L
than λ, at a given time and location variations in λ caninfluence entrainment, especially from March throughSeptember.

The mean seasonal cycle of h/L versus h/λ in Fig.
13 displays a "hysteresis loop": with a different paththrough the h/L, h/λ phase space in the first and second
half of the year. The hysteresis loop results from lags in
the seasonal cycle between B(h), u*, and h; zonal averages of the quantities reach a maximum in November,
January, and March, respectively. Hysteresis loops inthe seasonal cycles of heat content and SST or potential
energy have been discussed by Gill and Turner [1976].
Fig. 13 along with previous studies indicate that the hysteresis effect in the upper ocean depends on lags
between the surface heating and mechanical forcing andon the physics of the mixed layer, which deepens byentrainment but shoals by reforming closer to the surface.
6. Summary
A coupled model consisting of an R30 atmospheric GCM connected to an ocean mixed layer model,
is used to study variability of the upper ocean in the
Northern Hemisphere. The ocean model consists of agrid of independent column models which allow for
local air-sea energy exchange and the turbulent entrain-∂T ′ m+Composite of 6 components on ------------ [ ( °C ) ⁄ ( mon ) ]∂tQ′η ⁄ ρ ( I )cQη′ ⁄ ρ ( II )c

[ Q′η′ – Q′η′ ] ⁄ ρ ( III )c
W ′∆T η ( IV )e

20° – 70°N

W ∆T′η ( V )e
W ∆T η′ ( VI )e

Fig. 11. Composite of the six leading components (˚C mon-1) of the SST tendency equation (3) as a function of calendar month. The composites are constructed at each MLM grid point based on when the local monthly SST tendency exceeds one standard deviation, the resulting values are then averaged between 20˚N-70˚N.

15

ALEXANDER ET AL.
ment of water into the surface mixed layer, but excludes
currents and vertical motion. With the application of aseasonally varying surface flux correction, the long termmonthly mean SSTs in a 50-year integration of the coupled model remain close observations.
The model does a reasonable job of simulating
SST variability in midlatitudes. Like observations, theinterannual standard deviation (σ) of SST in the model
is slightly higher in September than in March and varies
between 0.4-1.2˚C over most of the northern oceans inboth months. However, the model is clearly deficient in
the Gulf Stream region and the eastern tropical Pacificwhere currents and vertical motion strongly influence
SSTs, and in the eastern portion of the subtropics where
the AGCM does not properly simulate stratiform clouds.
The model slightly underestimates SST σ, and theregions of maximum variability are located at about
20˚N-30˚N, 10˚-15˚ south of their observed position. In
an additional coupled model integration with observed
SSTs specified in the tropical Pacific, the simulated SST
σ maximum in the Pacific during March is located at~35˚N in agreement with observations, suggesting that
SST variability in the central and eastern North Pacificduring winter is dependent on ENSO.
The model simulates the general structure of themean mixed layer depth ( h ) north of 10˚S in both
March and September well, but underestimates its magnitude in the North Atlantic during winter. As discussed
in section 3, there are many reasons why h might be too
small in the subpolar gyre of the North Atlantic in winter; analyses of ocean GCMs could help to elucidate theinfluence of currents on vertical shear and stratificationand thus h. The regions of greatest mixed layer depth
variability coincide with the maximum h in both winterand summer.
The surface and entrainment heat fluxes are thedominant terms in the SST tendency equation. The net
surface heat flux strongly influences the mean seasonal
cycle of SSTs and the development of SST anomalies
throughout the year, but is especially dominant in winter. Entrainment of subsurface water into the mixed
layer acts to cool SSTs over most of the Northern Hemisphere, except at high latitudes in the North Atlantic in
winter and in portions of the tropical Pacific where thewater is warmer at depth and salinity controls the density profile. Entrainment strongly influences SSTs
anomalies in fall, especially north of ~35˚N (45˚N) in
the Pacific (Atlantic). The impact of entrainment on SST
tendencies depends mainly on the anomalous entrainment ( W ′ e ∆Th ) in summer and the anomalous temperature jump at the base of the mixed layer W e ∆T′h in fall.
Anomalous entrainment also influences SSTs indirectly
through the mixed layer depth, and h’ has a significant
impact on the SST’ tendency during spring and summer.
In agreement with Alexander and Penland [1996], theresults of the present study suggest that while a fixedslab representation of the upper ocean may be reasonable in winter, changes in h and the heat flux through thebase of the mixed layer play an important role in thedevelopment of SST anomalies during the remainder ofthe year.

Fig. 12. Correlations of the entrainment rate (We ) with the friction velocity (u*3 ), and the negative buoyancy forcing
integrated over the mixed layer (-B(h)), and buoyancy jump at the base of the mixed layer (-∆b) computed using daily
anomalies within a given calendar month.

16

ALEXANDER ET AL.

Fig 13. Non-dimensional mixing efficiency (P*) as a function of the non-dimensional stability (h/L) and rotational(h/λ) parameters, which uniquely govern P* in the MLM. The contour interval is 0.5 for 0.0 P* 3.0 and 1.0 for
P*>3.0. Overlaid on the P* contours is a scatter plot of h/L , h/λ obtained from the coupled model simulation, whereh/L and h/λ are monthly means that have been averaged between 20˚N-70˚N.

Correlations between monthly anomalies of We

to a 50 m slab ocean to an atmospheric simulation withspecified SSTs assuming perpetual January conditions.
These studies along with the idealized modeling studyof Barsugli and Battisti [1997] found that midlatitude
air-sea coupling leads to a reduction in thermal damping
which results in an increase in the variance of the nearsurface air temperature and a slight enhancement of thepersistence of certain atmospheric structures. Bhatt etal. [1998] confirmed the reduction of thermal damping
in a coupled model which included the seasonal cycle
and a variable depth mixed layer ocean model, but foundthat the subsurface storage of thermal anomalies andtheir re-entrainment into the mixed layer had an evengreater impact on near surface air temperature variability on interannual time scales. In the future, we plan tocompare the coupled model described here to an atmospheric GCM simulation in which the SSTs are specified to follow the long term mean seasonal cycle of thecoupled run to study how midlatitude air-sea interaction

and u*3, B(h) and ∆b indicate that wind mixing is thedominant term driving anomalous entrainment in summer, buoyancy forcing is most important in winter,
while the density jump at the base of the mixed layer isof secondary importance throughout the year. However,
the mechanical and buoyancy forcings are linked
through their mutual dependence on the wind speed.
Entrainment in the mixed layer model used here is governed by the Monin-Obukov (u*3/B(h)) and Rossby rotation (u*/f) length scales. The former is dominant in the
coupled model simulation especially in winter, althoughrotation can be important for determining whether
shoaling occurs at any given time.
In this paper, we have focused on how surface
fluxes and entrainment influences SST and mixed layer
depth. Barsugli [1995] and Blade [1997] compared the
behavior of a low resolution atmospheric model coupled

17

ALEXANDER ET AL.
and mixed layer physics influence atmospheric variability.

Houghton, and L.M. Keller, Atmosphere-oceaninteraction in the North Atlantic: near-surface climate variability, J. Climate, 11, 1615-1632, 1998.

Acknowledgements
Bjerknes, J., Atlantic air-sea interaction, Adv. in Geophys, 20, 1-82, 1964.

We thank Gabriel Lau, Isaac Held, John Lanzante
and Mary Jo Nath for providing to us the GFDL AGCM
and model fields from the simulation with observed
SSTs in the tropical Pacific as part of the GFDL-University Consortium project. Steve Worley at NCAR provided the observed mixed layer depth data. We also
thank Joe Barsugli and Matt Newman for their valuablesuggestions. This research was supported by NSF grant
OCE95-31870 and NOAA grant GC98-139.

Blade, I., The influence of midlatitude coupling on the
low frequency variability of a GCM. Part I: No
tropical SST forcing, J. Climate, 10, 2087-2106,
1997.
Camp, N.T., and R.L. Elsberry, Oceanic thermal
response to strong atmospheric forcing, II, the roleof one-dimensional processes, J. Phys. Oceanogr.,
8, 215-224, 1978.

References
Alexander, M.A., Midlatitude atmosphere-ocean interaction during El Niño. Part I: the North Pacific
Ocean, J. Climate, 5, 944-958., 1992.

Cayan, D.R., Latent and sensible heat flux anomalies
over the northern oceans: driving the sea surface
temperature, J. Phys. Oceanogr., 22, 859-881,
1992.

Alexander, M.A., and C. Deser, A mechanism for therecurrence of wintertime midlatitude SST anomalies, J. Phys. Oceanogr., 25, 122-137, 1995.

Clark, N.E., Specification of sea surface temperature
anomaly patterns in the eastern North Pacific, J.
Phys. Oceanogr., 2, 391-404, 1972.

Alexander, M.A., and J. D. Scott, Web-based atlas ofclimatology and variability in the GFDL R30S14
GCM.,[Available
on-linefrom
http://
www.cdc.noaa.gov/gfdl/], 1999.

Davis, R.E., R. Deszoeke, D. Halpern, and P. Niiler,
Variability in the upper ocean during MILE. Part
I: The heat and momentum balances, Deep Sea
Research, 28, 1427-1451, 1981.

Alexander, M.A., and C. Penland, Variability in a mixed
layer model of the upper ocean driven by stochastic atmospheric surface fluxes, J. Climate, 9, 24242442, 1996.

Delworth, T., North Atlantic interannual variability in acoupled ocean-atmosphere model, J. Climate, 9(10), 2356-2375, 1996.

Alexander, M.A., and J.D. Scott, Surface flux variability
over the North Pacific and North Atlantic Oceans,
J. Climate, 10 (11), 2963-2978, 1997.

Deser, C., and M.S. Timlin, Atmosphere-Ocean interaction on weekly time scales in the North Atlantic
and Pacific, J. Climate, 10 (3), 393-408, 1997.

Barsugli, J.J., Idealized models of intrinsic midlatitude
atmosphere-ocean interaction., Ph.D. thesis, University of Washington, [Available on line fromhttp://www.cdc.noaa.gov/~jjb/thesis.html.], 1995.

Dickson, R.R., J.R.N. Lazier, J. Meincke, P.B. Rhines,
and J. Swift, Long-term coordinated changes in theconvective activity of the North Atlantic, Progressin Oceanography, 38, 241-295, 1996.

Barsugli, J.J., and D.S. Battisti, The basic effects ofatmosphere-ocean thermal coupling on midlatitude
variability., J. Atmos. Sci., 55 (4), 477-493, 1998.

Elsberry, R.L., and R.W. Garwood, Numerical ocean
prediction models-goal for the 1980s, Bull. Amer.
Meteor. Soc, 61, 1556-1566, 1980.

Battisti, D.S., U. S. Bhatt, and M.A. Alexander, A modeling study of the interannual variability in thewintertime North Atlantic Ocean, J. Climate, 8(12), 3067-3083., 1995.

Favorite, F., and D.R. McLain, Coherence in transpacificmovements of positive and negative anomalies ofsea surface temperature, 1953-1960, Nature, 244,
139-143, 1973.

Bhatt, U.S., M. A. Alexander, D. S. Battisti, D. D.

Frankignoul, C., Sea surface temperature anomalies,18

ALEXANDER ET AL.
planetary waves, and air-sea feedback in the middle latitudes, Rev. Geophys., 23, 357-390, 1985.

Haney, L.R., B.H. Houtman, and W.H. Little, The relationship between wind and sea surface temperature
anomalies in the mid-latitude North Pacific Ocean,Atmos. Ocean, 21, 168-186, 1983.

Frankignoul, C., and R.W. Reynolds, Testing a dynamical model for mid-latitude sea surface temperature
anomalies, J. Phys. Oceanogr., 13, 1131-1145,
1983.

Haney, R.L., A numerical case study of the developmentof large-scale thermal anomalies in the central
North Pacific Ocean, J. Phys. Oceanogr., 10, 541556, 1980.

Garrat, J.R., A.J. Pratta, L.D. Rotstayn, and S. Cusack,The surface radiation budget over oceans and continents, J. Climate, 11, 1951-1968, 1998.

Hanson, H.P., COADS as a diagnostic modeling tool:
air-sea interaction and the role of the deep ocean
circulation in climate change, in Proceedings ofthe International COADS Workshop, edited by
K.W. Henry Diaz, Scott Woodruff, pp. 315-322,
NOAA, Boulder, CO, 1992.

Garwood, R.W., An oceanic mixed layer model capableof simulating cyclic states, J. Phys. Ocean., 7, 455468, 1977.
Gascard, J.-C., and R.A. Clarke, The Formation ofLabrador Sea Water. Part II: Mesoscale andsmaller processes, J. Phys. Oceanogr., 13, 1779-1797, 1983.

Horel, J.D., and J.M. Wallace, Planetary-scale atmospheric phenomena associated with the interannual
variability of sea surface temperature in the equatorial Pacific, Mon. Wea. Rev., 109, 813-829, 1981.

Gaspar, P., Modeling the seasonal cycle of the upper
ocean, J. Phys. Ocean, 18, 161-180, 1988.

Hsuing, J., Estimates of global oceanic meridional heattransport, J. Phys. Oceanogr., 15, 1405-1413,
1985.

Gaspar, P., Y. Gregoris, R. Stull, and C. Boisser, Longterm simulations of upper ocean vertical mixing
using models of different types., in Small-scale
turbulence and mixing in the ocean, edited by
N.J.C.J.a.B.M. Jamart, pp. 169-184, Elseveir,
Amsterdam, 1988.

Iwasaka, N., and J.M. Wallace, Large scale air sea interaction in the Northern Hemisphere from a view
point of variations of surface heat flux by SVD
analysis., J. Meteor. Soc. Japan, 73 (4), 781-794,
1995.

Gill, A.E., and P.P. Niiler, The theory of the seasonalvariability in the ocean, Deep Sea Res., 20, 141177, 1973.

Jacob, W.J., Numerical semiprediction of monthly meansea surface temperature, J. Geophys. Res., 72,
1681-1689, 1967.

Gill, A.E., and J.S. Turner, A comparison of seasonal
thermocline models with observations, Deep-Sea
Res., 23, 391-401, 1976.

Kantha, L.H., and C.A. Clayson, An improved mixed
layer model for geophysical applications, J. Geophys Res., 99 (c12), 25235-25266, 1994.

Gordon, C., and M. Bottomley, The parameterization of
the upper ocean mixed layer in coupled oceanatmosphere models, in Coupled Ocean-Atmosphere Models, edited by J.C.J. Nihoul, pp. 613635, Elsevier Oceanography series, New York,
1985.

Kim, J., A generalized bulk model of the oceanic mixed
layer, J. Phys.Oceanogr., 6, 686-695, 1976.

Gordon, C.T., and W. Stern, A description of the GFDL
global spectral model, Mon. Wea. Rev., 110, 625644, 1982.

Kraus, E.B., Merits and deffects of different approaches
to mixed layer modelling, in Small-scale turbulence and mixing in the ocean, edited by
N.J.C.J.a.B.M. Jamart, pp. 37-50, Elsevier,
Amsterdam, 1988.

Halliwell, G.R., and D.A. Mayer, Frequency response
properties of forced climatic SST anomaly variability in the North Atlantic, J. Climate, 9 (12, Part
III), 3575-3587, 1996.

Kumar, A., and M.P. Hoerling, Annual cycle of PacificNorth America seasonal predictability associatedwith different phases of ENSO., J. Climate, 11,3295-3308, 1998.

19

ALEXANDER ET AL.
flux and wind stress anomalies, Climate Dyn., 10,287-302, 1994.

Lanzante, J.R., and R.P. Harnack, An investigation ofsummer sea surface temperature anomalies in theeastern North Pacific Ocean, Tellus, 35A, 256-268,
1983.

Mitchell, T.P., and J.M. Wallace, ENSO seasonality:1950-78 versus 1979-92., J. Climate, 9, 31493161, 1996.

Large, W.C., J.C. McWilliams, and S.C. Doney, Oceanic
vertical mixing: a review and a model with a nonlocal boundary layer parameterization, Rev. Geophys., 32, 363-404, 1994.

Miyakoda, K., and A. Rosatil, The variation of sea surface temperature in 1976 and 1977 2. The simulation with mixed layer models, J. Geophys. Res.,89, 6533-6542, 1984.

Large, W.G., J.C. McWilliams, and P.P. Niiler, Upper
ocean thermal response to strong autumnal forcing
over the Northeast Pacific, J. Phys. Oceanogr., 16,1524-1550, 1986.

Moisan, J.R., and P.P. Niiler, The seasonal heat budgetof the North Pacific: net heat flux and heat storage
rates (1950-1990), J. Phys. Oceanogr., 28 (3), 401421, 1998.

Lau, N.-C., and M.J. Nath, The role of the 'atmosphericbridge' in linking tropical Pacific ENSO events to
extratropical SST anomalies., J. Climate, 9 (9),2036-2057, 1996.

Namais, J., Macroscopic association between mean
monthly sea surface temperature and the overlying
winds, J. Geophys. Res., 70, 2307-2318, 1965.

Le Treut, H., J.Y. Simonot, and M. Crepon, A model forthe sea-surface temperature and heat content in the
North Atlantic Ocean, in Coupled Ocean-Atmosphere Models, edited by J.C.J. Nihoul, pp. 439446, Elsevier, Amsterdam, 1985.

Namias, J., Recent seasonal interactions between North
Pacific waters and the overlying atmospheric circulation, J. Geophys. Res., 64, 631-646, 1959.
Namias, J., Large-scale air-sea interactions over the
North Pacific from summer (1962) through thesubsequent winter, J. Geophys. Res., 68, 61716186, 1963.

Ledwell, J.R., A.J. Wilson, and C.S. Low, Evidence forslow mixing across the pychnocline from an openocean tracer release experiment, Nature, 364, 701703, 1993.

Namias, J., Experiments in objectively predicting some
atmospheric and oceanic variables for the winter of
1971-1972, J. Appl. Meteor., 11, 1164-1174, 1972.

Luksch, U., Simulation of North Atlantic low frequency
variability., J. Climate, 9 (9), 2083-2092, 1996.

Namias, J., and R.M. Born, Temporal coherence inNorth Pacific sea-surface temperature patterns, J.
Geophys. Res., 75, 5952-5955, 1970.

Luksch, U., and H.v. Storch, Modeling the low-frequency sea surface temperature variability in the
North Pacific, J. Climate, 5, 893-906, 1992.

Namias, J., and R.M. Born, Further studies of temporal
coherence in North Pacific sea surface temperatures, J. Geophys. Res., 79, 797-798, 1974.

Manabe, S., and D.G. Hahn, Simulation of atmosphericvariability, Mon. Wea. Rev., 109, 2260-2286.,
1981.
Manabe, S., and R.J. Stouffer, Two stable equilibria of acoupled ocean-atmosphere model, J. Climate, 1,
841-866, 1988.

Niiler, P.P., and E.B. Kraus, One dimension models of
the upper ocean, in Modeling and Prediction ofUpper Layers of the Ocean, edited by E.B. Kraus,
pp. 143-172, Pergamon Press, 1977.

Martin, P.J., Simulation of the mixed layers at OWS
November and Papa with several models, J. Geophys. Res., 90, 903-916, 1985.

Norris, J.R., and C. Leovy, Interannual variability instratiform cloudiness and sea surface temperature.,
J. Climate, 7, 1915-1925., 1994.

Miller, A.J., D.R. Cayan, T.P. Barnett, N.E. Graham, andJ.M. Oberhuber, Interdecadal variability of the
Pacific Ocean: model response to observed heat

Norris, J.R., Y. Zhang, and J.M. Wallace, Role of clouds
in summertime atmosphere-ocean interactions
over the North Pacific, J. Climate, 11, 2482-2490,

20

ALEXANDER ET AL.
1998.

2204-2214.

Paulson, C., A., and J.J. Simpson, Irradience measurements in the upper ocean, J. Phys. Oceanogr., 7,952-956, 1977.

Yu, L., and P. Malanotte-Rizzoli, Inverse modeling of
seasonal variations in the North Atlantic Ocean, J.
Phys. Oceanogr., 28 (5), 902-922, 1998.

Price, J.F., R.A. Weller, and R. Pinkel, Diurnal cycling:observations and models of the upper ocean
response to diurnal heating, cooling, and wind
mixing, J. Geohpys. Res., 91 (c7), 8411-8427,
1986.
Salmon, R., and M.C. Hendershott, Large scale air-sea
interactions with a simple general circulation
model, Tellus, 28, 228-242, 1976.
Sausen, R., K. Barthel, and K. Hasselmann, Coupled
ocean-atmosphere models with flux correction,
Climate Dyn., 2, 145-163, 1988.
Schneider, N., A. J. Miller, M.A. Alexander, and C.
Deser, Subduction of decadal north Pacific temperature anomalies: observations and dynamics, J.
Phys. Oceanogr., 29, in press, 1999.
Shinoda, T., and H.H. Hendon, Mixed layer modeling of
intraseasonal variability in the tropical west
Pacific, J. CLimate, 11 (10), 2668-2685, 1998.
Simonot, J.Y., H.L. Treut, and M. Crepon, A thermodynamic model of the global sea-surface temperatureand mixed layer depth, in Small-Scale Turbulenceand Mixing in the Ocean, edited by J.C.J. Nihoul,and B.M. Jamart, pp. 123-139, Elsevier, New
York, 1988.
Smith, T.M., R.W. Reynolds, R.E. Livezey, and D.C.
Stokes, Reconstruction of historical sea surface
temperatures using empiracal orthogonal functions., J. Climate, 9, 1403-1420, 1996.
Webster, P.J., and R. Lukas, TOGA COARE: the Coupled Ocean-Atmosphere Response Experiment,
Bull. Amer. Met. Soc., 73 (9), 1377-1416, 1992.
White, W., B., R. Bernstein, G. McNally, S. Pazan, and
R. Dickson, The thermocline response to transient
atmospheric forcing in the interior midlatitude
North Pacific 1976-1978, J. Phys. Oceanogr., 10,372-384, 1980.
Wilkin, J.L., J.V. Mansbridge, and J.S. Godfrey, Pacific
Ocean heat transport at 24 degrees N in a high-resolution global model, J. Phys. Oceanogr., 25 (10),21