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Understanding the Persistence of Sea Surface Temperature Anomalies in Midlatitudes
CLARA DESER
National Center for Atmospheric Research, Boulder, Colorado

MICHAEL A. ALEXANDER AND MICHAEL S. TIMLIN
Climate Diagnostics Center, Boulder, Colorado(Manuscript received 21 December 2001, in final form 16 July 2002)
ABSTRACTAn extension of the simple stochastic climate model of Frankignoul and Hasselman that includes the effects
of seasonal variations in upper-ocean mixed layer depth upon the persistence of winter sea surface temperature(SST) anomalies is proposed. Seasonal variations in mixed layer depth allow for the ‘‘reemergence mechanism,’’
whereby thermal anomalies stored in the deep winter mixed layer persist at depth through summer and become
partially reentrained into the mixed layer during the following winter. In this way, SST anomalies can recur
from winter to winter without persisting through the intervening summer. Reformulating the simple stochastic
climate model in terms of an effective ocean thermal capacity given by the depth of the winter mixed layer,
thereby implicitly taking into account reemergence, is shown to provide a favorable fit to the observed winterto-winter SST autocorrelations in the North Atlantic and Pacific, and represents a considerable improvement
over the original model. The extended model also compares favorably with results from an entraining bulk ocean
mixed layer model coupled to an atmospheric general circulation model. The authors propose that the extended
model be adopted as the new ‘‘null hypothesis’’ for interannual SST variability in middle and high latitudes.

1. Introduction
The oceans are generally regarded as the ‘‘flywheel’’of the climate system, providing a vast source of thermal
inertia to the overlying atmosphere. The large thermal
inertia of the oceans derives from their heat storage
capacity: ;2.5 m of water contains as much energy as
an entire atmospheric column. The ocean communicates
its thermal inertia to the atmosphere largely via the surface turbulent fluxes of sensible and latent energy. These
turbulent fluxes, in turn, depend upon a single oceanic
variable, the sea surface temperature (SST), and several
atmospheric parameters including the near-surface windspeed, air temperature, and relative humidity. Given the
primary importance of SST in the thermal communication between the ocean and atmosphere, and the potential for SST variations to induce slow climatic fluctuations, it is of interest to investigate the nature of
temporal persistence of large-scale SST anomalies. In
the present study, we focus on understanding the behavior of SST anomaly persistence in middle and highlatitudes.
Large-scale SST anomaly persistence in the North
Atlantic and Pacific has been examined in numerous
Corresponding author address: Dr. Clara Deser, Climate and Global Dynamics Division, NCAR, P.O. Box 3000, Boulder, CO 80307.
E-mail: cdeser@ucar.edu

q 2003 American Meteorological Society

studies, including Namias and Born (1970, 1974), Reynolds (1978), Frankignoul and Reynolds (1983), Namias
et al. (1988), Bhatt et al. (1998), Watanabe and Kimoto(2000), Kushnir et al. (2002), and Timlin et al. (2002).
Collectively these studies indicate typical SST e-folding
timescales on the order of 3–6 months based on datafrom all calendar months. However, as recognized by
Namias and Born, the duration of large-scale SST anomalies is seasonally dependent. Specifically, Namias andBorn noted a tendency for SST anomalies at selected
locations in the North Atlantic and Pacific to recur fromone winter to the next without persisting through theintervening summer, effectively extending the memoryof winter SST anomalies to longer than 1 yr. In contrast,
summer SST anomalies decay rapidly, within a coupleof months, at the locations examined by Namias andBorn. Subsequent studies, including Namias et al.
(1988), Bhatt et al. 1998, Watanabe and Kimoto (2000),
Kushnir et al. (2002), and Timlin et al. (2002), haveconfirmed the strong seasonal dependence of the persistence characteristics of large-scale SST anomaly patterns in both the North Atlantic and North Pacific.
What physical processes contribute to the seasonal
differences in persistence of extratropical SST anomalies? Namias and Born speculated that the seasonal evolution of upper-ocean mixed layer depth was a crucial
factor. They hypothesized that vigorous air–sea energy

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exchange during winter creates temperature perturbations that extend down to the base of the deep wintermixed layer, typically 100–200 m in the North Pacificand considerably deeper in portions of the North Atlantic. When the mixed layer shoals (or more accurately,reforms) in late spring, the winter thermal anomalies
become sequestered beneath the shallow (;20–30 m)
summer mixed layer in a highly stratified environment(the seasonal thermocline) and become effectively insulated from further air–sea heat exchange. As themixed layer deepens again in late fall and early winter,a portion of the subsurface thermal anomalies may become reentrained into the mixed layer, thus influencing
the mixed layer heat budget and SST in the following
winter. In this way, an SST anomaly would recur fromone winter to the next without persisting through theintervening summer. Alexander and Deser (1995)
termed this process the reemergence mechanism.
This scenario was tested in a series of studies examining the vertical structure of upper-ocean temperature anomalies that accompany reemerging winter SST
anomalies. Alexander and Deser (1995) used upperocean temperature profiles from ocean weather ships in
the North Atlantic and Pacific to document that wintermixed layer temperature anomalies persist beneath theshallow summer mixed layer, and that a portion of theanomalous heat storage is reentrained into the mixed
layer during the following early winter, imparting a signal to the following winter’s SST anomaly. In a followup study, Alexander et al. (1999) used gridded subsurface temperature profiles over the North Pacific to document the spatial extent of the reemergence process,and to investigate the seasonal dependence of the signal.
It was clear from that study that reemergence occurs
basinwide, but that the timing can differ considerablyfrom one region to the next due to differences in thedepth of the winter mixed layer. Also, an SST anomaly
formed in late winter (March) when the mixed layer isdeepest will reemerge later than one formed in earlysummer (June) when the mixed layer is shallower. Thus,
SST anomalies from January through June all exhibit
reemergence during the following winter, but the timingof when they are reentrained into the mixed layer isdependent upon the depth of the mixed layer when they
were originally formed. Recently, Watanabe and Kimoto(2000) and Timlin et al. (2002) have analyzed gridded
subsurface temperature profiles in the North Atlantic to
document the reemergence process there, and showedthat the larger the difference between the depth of themixed layer in summer and winter, the stronger the influence of the reemergence process upon winter SST
anomalies.
In this study, we shall make extensive use of theconcept of the reemergence mechanism to understandthe nature of SST anomaly persistence over the North
Atlantic and Pacific. We focus on the following question: to what extent can ocean mixed layer processes
account for the observed seasonal and geographical de-

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FIG. 1. Conceptual ocean–atmosphere systems considered in thisstudy. (left) The original simple stochastic climate model of Frankignoul and Hasselmann (1977) and (right) the proposed extension.
In both systems, temperature anomalies (T 9) in the ocean mixed layer
are assumed to result from atmospheric forcing (F9) only and damp
back to the atmosphere at a rate lT 9. In the original model, the mixed
layer depth (H ) is constant; in the extended model, H undergoes astrong seasonal cycle, with largest extent in winter and smallest insummer. In this configuration, T 9 created in winter can persist beneaththe summer mixed layer and become reentrained into the mixed layer
the following winter, as indicated schematically by the thick blackarrows. The effective thermal capacity of this system depends upon
the depth of the winter mixed layer (Heff ).

pendence of SST anomaly persistence? To address thisquestion, we introduce a conceptual physical framework
based upon the paradigm of the simple stochastic climate model for midlatitude SST variability due to Frankignoul and Hasselmann (1977, hereafter FH77). We
consider first the simplest possible coupled ocean–atmosphere system consisting of a slab ocean mixed layerof fixed depth H coupled to an atmosphere above andan ocean interior below (Fig. 1, left), the original formulation of FH77. Conceptually, this model assumes
that ocean mixed layer temperature anomalies T9 areforced by random atmospheric variability (with a shortdecorrelation time, on the order of a week or two) anddecay by damping back to the atmosphere (modeled asa negative linear feedback term): dynamical processes
in the ocean interior do not impact T9. This model yields
typical e-folding timescales for SST anomalies on theorder of 3–6 months depending upon the value used for
H (the deeper the mixed layer, the larger the associatedthermal inertia, which is manifest as a longer persistencetime). This paradigm has been used successfully to understand the initial rate of decay of SST anomalies in
the North Pacific and Atlantic (cf. FH77; Reynolds
1978; Frankignoul and Reynolds 1983; Herterich andHasselmann 1987; Lau and Nath 1996; Alexander andPenland 1996; Hall and Manabe 1997; Deser and Timlin
1997). However, this framework does not explain thehigh winter-to-winter memory of SST anomalies documented in the studies cited earlier. To account for winter-to-winter persistence, we propose the following extension to the FH77 paradigm.

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As discussed earlier, the reemergence mechanism depends on the existence of a strong seasonal cycle inmixed layer depth, typical of middle and high latitudes.
Extending the mixed layer ocean–atmosphere system toinclude a seasonally varying H (Fig. 1, right) allows forreemergence by incorporating the entrainment/detrainment process. In this new system, thermal anomalies
created by wintertime atmospheric forcing persist at
depth through summer and become reentrained into themixed layer during the following late fall and early winter, as indicated schematically by the arrows in Fig. 1(right). In the absence of additional oceanic processes,
for example, turbulent mixing, diffusion, and subduction through the main thermocline, and advection by
geostrophic and thermohaline currents, this system may
be viewed in a manner analogous to the simple stochastic climate model where the mixed layer depth H
is reinterpreted as an ‘‘effective’’ depth H (hereafter
denoted by Heff given by the maximum mixed layer
depth during the course of the seasonal cycle (typicallyin February or March for the northern oceans). In thisview, the impact of entrainment and the reemergencemechanism upon winter SST anomaly persistence is implicitly accounted for.
We shall make use of the extended simple stochastic
climate model depicted in Fig. 1 (right) to guide ouranalysis and physical interpretation of SST anomaly persistence in the North Pacific and Atlantic. The paper isorganized as follows. The datasets and methods are described in section 2. Observational results and their
physical interpretation within the framework of the extended simple stochastic climate model are presented in
section 3. More sophisticated physical models are considered in section 4, including one in which an entrainment term is explicitly included within the simple stochastic climate framework, and one in which a variabledepth bulk ocean mixed layer model is coupled to an
atmospheric general circulation model. Additional results are presented in section 5. The paper concludes
with a discussion in section 6.

59

yses in section 3c [an updated version of GISST, theHadley Centre Sea Ice and SST (HADISST) dataset, isused in section 5a].
b. Subsurface temperature
Monthly subsurface temperature data are obtained
from the Joint Environmental Data Analysis Center at
the Scripps Institution of Oceanography. This archive
contains temperatures at 11 levels (0, 20, 40, 60, 80,
120, 160, 200, 240, 300, and 400 m) during 1955–95.
The temperature profiles, collected from mechanical andexpendable bathythermographs and Nansen bottle casts,
were subjected to a statistical optimal interpolation
scheme to generate gridded values (28 3 58 lat–lon grid)from sparse data as described in White (1995). We makeuse of data during 1960–92 when the number of observations is greatest. It is worth noting that there areapproximately an order of magnitude fewer upper-ocean
temperature profiles than SST measurements in the surface marine archives.
In the course of this study, we noted a suspicious
jump in the temperature fields at 300- and 400-m depth
in the northern North Atlantic compared to shallower
levels. We have therefore omitted these data from ourempirical orthogonal function analysis of upper-ocean
heat content over the North Atlantic (section 3a). For
the regional analysis of heat content in the northern
North Atlantic (section 3c), we make use of an alternative dataset provided by M. Watanabe (2000, personalcommunication) that extends to 500-m depth without
evidence of spurious jumps (note that we only haveaccess to the regionally averaged temperature profiles,
not the full lat–lon gridded dataset). These data are
based upon objective analysis using a three-dimensionalvariational algorithm (Derber and Rosati 1989) of subsurface temperature data from the World Ocean Atlas
1994 (Levitus and Boyer 1994). Analyses of the gridded
version of these data are presented in Watanabe andKimoto (2000). The region we examine corresponds tothe ‘‘HIGH’’ area in Watanabe and Kimoto’s study.

2. Data and Methodsc. Mixed layer depth
a. SST
Monthly SST data for the period 1948–97 are obtained from the Comprehensive Ocean–Atmosphere
Data Set (COADS; Woodruff et al. 1987) and the Global
Sea Ice Sea Surface Temperature (GISST) dataset (version 2.3b; Raynor et al. 1996). The COADS data, binned
on a 28 3 28 latitude–longitude grid, are quality controlled but not smoothed in space or time, and missing
data have not been filled in. The GISST data, on a 18
3 18 grid, are quality controlled, smoothed in space,and missing grid boxes are filled in using an EOF-based
technique. We use COADS for the regionally averaged
analyses in section 3a (GISST yields virtually identicalresults, not shown), and GISST for the basinwide anal-

We use climatological monthly mean mixed layer
depths (MLD) from Monterey and Levitus (1997) on a
18 3 18 lat–lon grid, where mixed layer depth is definedas the shallowest depth where the density exceeds thesurface density by 0.0125 kg m 23 .
d. Surface fluxes and Ekman currents
Monthly surface turbulent fluxes of sensible and latent energy were obtained from the COADS archive forthe period 1948–97, using a constant exchange coefficient (1.3 3 10 23 ), air density (1.2 kg m 23 ), and specificheat of air (1004 J K 21 kg 21 ). Monthly Ekman currents
were computed using wind stress measurements from

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COADS, and a constant drag coefficient (1.3 3 10 23 ),water density (1000 kg m 23 ) and specific heat of water(4218 J K 21 kg 21 ).
e. Methods
Monthly anomalies were formed by subtracting thelong-term monthly means from the appropriate monthfor each year. EOF analysis is based upon the areaweighted covariance matrix of monthly anomalies.
3. Resultsa. Basinwide analyses of monthly heat content andSST anomalies
Guided by the physical framework of the extended
simple stochastic climate model (Fig. 1, right), we examine the persistence characteristics of heat content(HC) anomalies, where HC is defined as the verticallyintegrated temperature anomaly from the sea surface toHeff in all months. Thus, we do not restrict the heat
content to the base of the seasonally varying mixed
layer, but to the base of the deepest winter mixed layer,
thus incorporating the subsurface thermal pathway indicated schematically in Fig. 1 (right). The value Heff
is obtained from the climatological distribution of February/March average mixed layer depths from Monterey
and Levitus (1997) as shown in Fig. 2 (top). The leading
EOF of monthly HC anomalies over the North Atlantic,
shown in Fig. 2 (bottom), accounts for 23% of the total
variance over the domain. It exhibits a primary centerof action between 458 and 608N with maximum amplitude south of Greenland, and another center of opposite
polarity to the southwest near 308N. This pattern describes an out-of-phase fluctuation between HC anomalies in the two regions, and is similar to the leading
EOF of monthly SST anomalies (not shown, but see
Kushnir et al. 2002 and Timlin et al. 2002) but withmore weight in the northern center of action comparedto the southern one. This change in spatial emphasis
between the SST and HC EOF patterns is consistent
with the fact that Heff increases to the north (Fig. 2, top).
To quantify the temporal persistence of the HC EOF
pattern, we have computed the monthly lag autocorrelation curve of the associated principal component (PC)time series based on a starting month of March [e.g.,correlating the PC time series in March with the PC
time series in April of the same year (year 0), May ofthe same year . . . January of the next year (year 1) . . .
December of the year following year 1 (year 2)]. The
PC time series is obtained by projecting the individual
monthly HC anomaly maps upon the EOF pattern using
linear regression. The HC autocorrelation curve (Fig. 3,top) decays in a relatively monotonic fashion, with values ;0.6 in year 1 and ;0.4 in year 2. The most rapid
decline occurs in early winter (November–January)
when the rate of mixed layer deepening is greatest, con-

FIG. 2. (top) Observed long-term mean winter mixed layer depths
in the North Atlantic (values . 200 m shaded). (bottom) Leading
EOF of monthly heat content anomalies in the North Atlantic during
1960–92. Thick solid (dashed) contours indicate positive (negative)
values; the contour interval is arbitrary.

sistent with the effect of entrainment, which mixes theexisting heat content anomaly with thermal anomalies
newly created by the atmosphere. In contrast, the autocorrelation curve for the associated SST time series(Fig. 3, top), formed by projecting individual monthly
SST anomaly maps upon the HC EOF pattern using
linear regression, exhibits a pronounced seasonal cycle,
with relative minima in the summers (;0.2 in year 0
and year 1, and ;0.1 in year 2) and relative maxima
in the winters (;0.6 in year 1 and ;0.4 in year 2). Notethat HC autocorrelations are similar to those for winter
SST, consistent with the fact that winter SST anomalies
extend to Heff . Note also that the summer minima in the
SST autocorrelation curve are entirely absent from theHC curve. These characteristics of the HC and SST
autocorrelation functions are qualitatively consistent
with our simple conceptual model of a seasonally varying mixed layer that includes entrainment and the subsurface thermal pathway from winter to winter. The corresponding e-folding timescale for HC anomalies or,equivalently, winter SST anomalies is ;2–3 yr. Noneof the autocorrelation curves change appreciably when
the data are first linearly detrended (not shown).
When all months of the year are used to construct
the SST autocorrelation curve (e.g., by lagging the1 JANUARY 2003

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DESER ET AL.

FIG. 4. As in Fig. 2 but for the North Pacific.

center of opposite polarity along the west coast of North
America. As in the Atlantic, this pattern is similar tothe leading EOF of monthly SST anomalies (not shown),
but with a different spatial emphasis: more weight forthe primary center of action where the winter mixed
layers are deepest, and relatively less weight along theAmerican coast where they are shallower. The lag autocorrelation curves for the HC PC and the associated
SST projection time series starting from March are
shown in Fig. 5. As in the Atlantic, the decay of theHC autocorrelations is nearly monotonic and resembles
the attenuation rate for winter SST. Also as in the Atlantic, the summer (August–September) minima in the
SST autocorrelation curve are absent from the HC
curve, and the HC autocorrelations decay most rapidly
in late fall and early winter, and least rapidly in late
FIG. 3. (top) Monthly lag autocorrelation curves from Mar for theleading principal component time series of North Atlantic heat content
anomalies (thick) and associated SST anomalies (thin). (bottom)
Monthly lag autocorrelation curve for the SST record based upon all
months.

monthly SST anomaly time series by 1 month, 2 months,. . . 36 months), the seasonal cycle virtually disappears,
with a rapid decay to ;0.3 within first 3 months followed by a more gradual decline (Fig. 3, bottom). Thus,
the SST e-folding timescale based upon all months ofthe year (;3 months) is considerably shorter than thatobtained by considering only winter SST anomalies(;2–3 yr).
The leading EOF of monthly HC anomalies over the
North Pacific is shown in Fig. 4 together with the climatological distribution of February mixed layer depths.
The EOF, which accounts for 30% of the variance, exhibits a primary center of action along ;408N that extends across the western two-thirds of the basin, and a

FIG. 5. As in Fig. 3 (top) but for the North Pacific.

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spring and summer. The overall rate of decay of the HC
autocorrelations is faster for the Pacific than the Atlantic, qualitatively consistent with the fact that the wintermixed layers depths are smaller in the Pacific than the
Atlantic.
b. An extension of the simple stochastic climate
model: Implicitly incorporating the effect ofentrainment
To understand quantitatively the rate of attenuationof the lag autocorrelation curve of monthly HC anomalies (or equivalently, the rate of decay of winter SST
autocorrelations), it is helpful to consider the formulation of FH77 in terms of Heff . The governing equation
for the simple stochastic climate model is

VOLUME 16

the autocorrelation function (r) of T9 as a function oftime lag t is simply
r (t) 5 exp{2[l/(rC p Heff )]t }(2)

According to (2) with constant l, T9 decays exponentially at a rate proportional to the inverse of Heff : thedeeper the mixed layer, the slower the rate of attenuation
due to the larger thermal inertia. In the following analysis, we shall compare the theoretical autocorrelation
function given by (2) with observed autocorrelation
curves for HC and winter SST for selected regions,using observed long-term mean values for Heff fromMonterey and Levitus (1997). We shall refer to Eq. (2)as the extended simple stochastic climate model.

(1)c. Regional analyses and application of the extended
simple stochastic climate model

where r is the density of seawater (taken here as 1000kg m 23 ), C p is the heat capacity of seawater (4128 J
kg 21 K 21 ), Heff is the mean maximum mixed layer depth,
T9 is the mixed layer temperature anomaly, t is time,
F9 represents the atmospheric forcing of T9, and l is alinear damping coefficient. The linear damping term lT9
is a highly idealized representation of the turbulent fluxes of latent and sensible heat flux from the ocean to theatmosphere associated with T9. Note that without damping, Eq. (1) would result in unbounded growth of T9.
The damping parameter l may be derived by linearizing the bulk formulas for the sensible and latentenergy fluxes about T9, as shown in Haney (1985), Frankignoul (1985), Barsugli (1995), Barsugli and Battisti(1998), and Frankignoul et al. (1998). The magnitudeof l depends upon the strength of the near-surface windspeed and the degree to which the near-surface air temperature and relative humidity adjust to the underlying
SST perturbation (see also Seager et al. 1995). For the
North Atlantic and Pacific, l is estimated to be in therange 15–20 W m 22 K 21 . These estimates may be compared with values obtained directly from atmospheric
GCM experiments with an imposed SST anomaly anddiagnosing the resulting change in the local surface turbulent energy flux. As reviewed by Frankignoul et al.,these experiments yield annually averaged values ;10–
20 W m 22 K 21 depending on location. A recent GCM
study by G. Magnusdottir, C. Deser, and R. Saravanan(2002, unpublished manuscript) for a prescribed SST
anomaly in the North Atlantic confirms this result, withl ;15 W m 22 K 21 . Although difficult to obtain accurately from data, l has been estimated on the basis ofobserved lagged covariances between turbulent heat flux
and SST anomalies over the eastern North Atlantic by
Frankignoul et al. (1998), with a range similar to thatfound in the atmospheric GCM experiments.
If F9 in Eq. (1) is specified to be ‘‘white’’ in time,that is, the decorrelation timescale for atmosphericweather variations (on the order of a week) is much
shorter than that for SST fluctuations (see FH77), thenWe have selected two regions for analysis, each thedominant center of action of the leading EOF of monthly
HC anomalies in their respective basins: the northern
North Atlantic (458–608N, 458–208W; hereafter referred
to as NATL) and the western central North Pacific (358–
458N, 1558E–1708W; hereafter referred to as NPAC).
Monthly lag autocorrelation curves based upon March
SST and HC anomaly time series for NATL and NPAC
are shown in Figs. 6a and 6b, respectively [results based
upon linearly detrended data are similar, with a small(;0.05–0.10) reduction in the autocorrelation values,
which is approximately uniform with lag; not shown.]
Also shown are the theoretical autocorrelation curves
from Eq. (2) with Heff given by the observed February
climatological mixed layer depth (367 m for NATL and
178 m for NPAC) and l in the range 15–20 W m 22
K 21 . The observed HC and SST autocorrelation curves
exhibit many of the same features as found in the EOFbased results: a nearly monotonic decay for HC and apronounced seasonal cycle for SST, with minima insummer and maxima in winter. The winter SST autocorrelation magnitudes are similar to the concurrent HC
values. The theoretical decay based upon Heff (shaded
region in Fig. 6) exhibits good agreement with the observed decay of HC and winter SST autocorrelations inboth regions. Given the simplicity of the model and thelack of ‘‘tuning’’ of parameters (l, Heff ), the fit between
observations and theory is highly encouraging. One notable difference between the two regions is the stronger
seasonal variation in the SST autocorrelation curve, due
principally to the lower values in summer, in NPAC
than in NATL.
The SST autocorrelation curves exhibit a rapid decline within the first 6 months, reaching a minimum in
September in both regions. What controls the rate ofattenuation of SST anomalies from March to September? The original formulation of FH77 is applicablehere, given that entrainment is weak during this half ofthe year when the mixed layer is either shoaling (inspring) or steady (in summer). Accordingly, we have(rC p Heff )dT9/dt 5 F9 2 lT9,

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initial rate of decay of the observed SST autocorrelation
curve within the first 2–3 months, but then strongly
underestimates the values from July to September.
In Eq. (1), we have treated the mixed layer as a fixeddepth slab (H 5 Heff ) whose temperature anomaly T9damps to the atmosphere at a constant rate l. However,in summer, the fossil winter mixed layer becomes effectively isolated from the atmosphere due to the formation of a warm thin surface layer and thus temperature anomalies within this layer do not damp to theatmosphere. Therefore, the damping parameter for HC9
should be nearly zero in the summer months, unlike thatfor SST9. To illustrate the impact of a seasonally varying
damping rate, we use a simple binary specification ofl in Eq. (2): zero in the summer months (July–September) and 20 W m 22 K 21 in the remaining months (notethat l in this context should be interpreted as the effective damping rate for HC9 and not for SST anomalies
per se). As expected, the theoretical autocorrelation
function with zero damping in summer (thin solid curvein Figs. 6a,b) decays less rapidly than that with constant
year-round damping, but the differences are relatively
small (;0.1). Given the empirical nature of l to begin
with, we do not consider it useful at this stage to pursue
a more complicated formulation for the seasonal dependence of l.
d. Atmospheric forcing

FIG. 6. Observed monthly lag autocorrelation curves from Mar forheat content (thick black) and SST (dashed) anomalies in the (a)NATL and (b) NPAC regions. The broad band of shading denotes
the theoretical autocorrelation function from the extended simple stochastic climate model. The thin gray curve that ends in Sep of year
0 denotes the theoretical autocorrelation function from the originalmodel. The thin black curve denotes the theoretical autocorrelation
function from the extended simple stochastic climate model with zero
damping in summer (see text for details).

calculated the theoretical autocorrelation curve from Eq.
(2) using observed long-term mean monthly values of
mixed layer depth from March through September foreach region and l 5 17.5 W m 22 K 21 based on a simple
forward time stepping technique. The resulting theoretical autocorrelation function (gray curve in Fig. 6b)
approximates well the observed SST autocorrelation
curve in the NPAC region. Thus, winter SST anomalies
in the NPAC region decay through summer at a rateconsistent with the simple (nonentraining) stochastic climate model. In the NATL region, the theory fits the

Our analyses and interpretation of the results within
the framework of the simple stochastic climate model
are predicated on the assumptions that 1) the atmosphereis forcing the winter SST anomalies, and 2) the atmospheric forcing has a short decorrelation timescale (aweek or two) with a white-noise power spectrum atlower frequencies (see FH77). In this section, we investigate to what extent these assumptions are valid for
the NATL and NPAC regions. Previous studies indicatethat the primary forcing terms in winter are the turbulent
fluxes of sensible and latent heat, and horizontal temperature advection by Ekman currents (cf. Cayan 1992;
Frankignoul and Reynolds 1983; Deser and Timlin
1997; Frankignoul et al. 1998; Seager et al. 2000, 2001).
Note that Ekman currents are set up nearly instantaneously in the ocean mixed layer as a response to the
local wind stress, and produce SST variations by advecting the background SST gradient. We shall refer tothe sum of the fluxes of sensible and latent heat andEkman advection as F9. Figure 7 (top) shows the monthly lag cross correlations between F9 and the anomalous
SST in March (the base month used for the SST autocorrelation curves shown previously) for both NATL
and NPAC. The cross correlations are shown for F9 fromthe previous October through the following September
relative to the SST anomaly in March. Positive (negative) values denote the atmosphere is forcing (damping)
SST. A correlation coefficient exceeding 0.21 in absolute value is significantly different from zero at the 5%

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JOURNAL OF CLIMATEVOLUME 16role for the reemergence mechanism? Figure 7 (bottom)
shows the lag autocorrelation curves for F9 starting fromFebruary (other winter months give similar results). The
value F9 exhibits a rapid decorrelation timescale (;1month), with weak (generally less than 0.2 in absolutevalue) autocorrelations at longer lags, consistent withmore comprehensive analyses of atmospheric decorrelation timescales (cf. FH77; Alexander and Penland
1996). The autocorrelation of F9 from one winter to thenext is also small (;0.1–0.2). Whether this small positive winter-to-winter autocorrelation has any appreciable influence upon winter SST anomaly persistence remains to be seen.
4. Further modeling results
Next we employ two additional models to investigate
the role of entrainment in accounting for the seasonal
dependence of winter SST anomaly persistence. The
first is an explicit treatment of entrainment within theframework of the simple stochastic climate model of
FH77; the second is an atmospheric general circulation
model coupled to a ‘‘full-physics’’ entraining ocean
mixed layer model.
a. The explicit ‘‘entraining’’ simple stochastic climate
model

FIG. 7. (top) Lag cross correlations between Mar SST and monthly
atmospheric forcing (F9) from the previous Oct through the following
Sep for NPAC (solid) and NATL (dashed). (bottom) Monthly lag
autocorrelations for F9 starting from Feb for NPAC (solid) and NATL
(dashed).

confidence level. The results show that the strongest
positive correlations (;0.5) occur when the atmosphereleads SST by 1–2 months, consistent with our assumption of atmosphere forcing and with the results of numerous previous studies (cf. Davis 1976; Cayan 1992;
Deser and Timlin 1997; FH77). The magnitude of the
maximum cross correlation is in excellent quantitative
agreement with simple stochastic climate model theory(see appendix in FH77). Negative correlations, indicative of SST anomalies dampling to the atmosphere, occur when SST lags the atmosphere by 1–6 months, also
consistent with previous studies (e.g., Frankignoul et al.
1998; Kushnir et al. 2002).
Does F9 exhibit any substantial winter-to-winter autocorrelation that might contribute to the observed winter-to-winter persistence in SST, thereby diminishing theHere we propose an extension of the simple stochastic
climate model that explicitly incorporates entrainmentand hence allows for the reemergence mechanism; weshall refer to this system as the entraining stochastic
climate model. We modify Eq. (1) to include a variabledepth mixed layer H(t) that undergoes an identical seasonal cycle each year and an entrainment velocity W e
5 dH/dt if the mixed layer is deepening and zero if themixed layer is steady or shoaling. With the addition ofthis term, the entraining simple stochastic climate model
may be written as(rC p )d(HT )9/dt 5 F9 2 lT9 1 (rC p We )(T9 2 T9),b(3)where T9b is the temperature anomaly below the mixed
layer, formed at an earlier time t e . Note that t e is afunction of the seasonal cycle of mixed layer depth: that
is, a temperature anomaly existing at a depth k in aparticular year will persist beneath the summer mixed
layer at that depth and be recaptured into the mixed
layer during the following winter when it deepens again
to depth k. Equation (3) was numerically solved for T9(z)using a time step of 3 days, a vertical resolution of 40
levels between the surface and the maximum mixed
layer depth, and integrated for 5000 yr. For the integrations, a maximum and minimum value for H(t) isprescribed, with the added specification that the mixed
layer shoals for 4 months, remains steady for 4 months,
and deepens for 4 months. The damping parameter l isprescribed to vary sinusoidally over the annual cycle,
with a maximum value of 25 W m 22 K 21 in February1 JANUARY 2003

65

DESER ET AL.

FIG. 8. (top) Mean seasonal cycle of mixed layer depth (m) for
NPAC from observations (dashed) and that used in the entraining
stochastic climate model (solid). (bottom) Monthly lag autocorrelation curves from Mar for heat content (solid step functionlike curve)
and SST (solid) from the entraining model. The observed SST autocorrelation curve is dashed. The theoretical autocorrelation function
for heat content based upon the extended simple stochastic climate
model is shaded.

and a minimum value of 5 W m 22 K 21 in August according to the atmospheric GCM results of G. Magnusdottir, C. Deser, and R. Saravanan (2002, unpublished manuscript). We note that the location of the imposed SST anomaly in their experiments corresponds
closely to our NATL region. We note further that theatmospheric GCM experiments of Peng et al. (1997) for
an imposed SST anomaly in the North Pacific that corresponds closely to our NPAC region yields wintertime
values for l of 25–30 W m 22 K 21 (other months were
not examined in their study).
Figure 8 (top) shows the seasonal cycle of the observed long-term monthly mean mixed layer depth for
NPAC and the one we specify for the model integration.
The idealized seasonal cycle approximates the observed
seasonal evolution of mixed layer depth. The resulting
lag autocorrelation curves for SST and HC from thesimple model, and the observed SST, based upon a starting month of March are shown in the bottom portionof Fig. 8. The entraining model agrees well with theobservations in terms of the timing and magnitudes of

FIG. 9. As in Fig. 8 but for the NATL region.

the summer minima and winter maxima. The main shortcomings of the model are the underestimation of the
autocorrelations in June–August of the first year andslight overestimation of the winter values. Given thesimplicity of the model, the agreement is encouraging.
To benchmark this model against the extended or ‘‘implicit-entraining’’ stochastic climate model [Eq. (2)], theexponentially decaying autocorrelation curves based
upon Heff and l in the range 15–20 W m 22 K 21 are also
shown in Fig. 8. The implicit-entraining model provides
a good approximation to the ‘‘explicit-entraining’’ model in terms of the winter-to-winter autocorrelations in
SST and HC. Figure 9 shows the results for the NATL
region. Although the timing of the summer minima andwinter maxima in the observed SST autocorrelations iswell simulated, the model overestimates the values in
winter and strongly underestimates the values in the firstand second summers.
b. A full-physics ocean mixed layer model coupled to
an atmospheric GCM
The most complex ocean–atmosphere configurationin our model hierarchy is a full-physics ocean mixed
layer model coupled to an atmospheric GCM. Comparedto the simple stochastic climate models, this configuration is a more realistic representation of the relevant

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FIG. 11. As in Fig. 10 but for the North Pacific.

FIG. 10. As in Fig. 2 but for the 16-member ensemble of coupled
ocean mixed layer–atmospheric GCM integrations.

physical processes of atmosphere–ocean mixed layer interaction including the reemergence mechanism. For example, atmospheric forcing of the ocean mixed layer is
no longer assumed to be white noise, the rate of dampingof SST anomalies back to the atmosphere is not assumed
to be constant, and the entrainment rate in the ocean
model is derived from the turbulent kinetic energy equation. We make use of an ensemble of 16 integrations of
this coupled model as described in Alexander et al.
(2002). Each integration spans the period 1950–99 andconsists of prescribed monthly SST anomalies in theeastern tropical Pacific (158N–158S, 1728E–SouthAmerican coast) taken from observations and the ocean
mixed layer model elsewhere. This configuration is designed to incorporate boundary forcing due to variability
associated with the El Niño–Southern Oscillation(ENSO) phenomenon whose governing dynamics are
not described by mixed layer processes. The ocean model consists of a grid of one-dimensional bulk mixed layer
models atop a simple layered model representative ofthe thermocline; each ocean column is coupled to theatmospheric column above it, but there is no communication between adjacent grid cells in the ocean model.
The bulk mixed layer model, based on Gaspar (1988),
contains a prognostic formulation for mixed layer depth
and entrainment. Beneath the mixed layer, heat is redistributed via convective overturning, vertical diffu-

sion, and penetrating solar radiation. The atmosphericmodel is the Geophysical Fluid Dynamics Laboratory(GFDL) R30 GCM which has an equivalent horizontal
resolution of ;2.258 in latitude and 3.758 in longitude
and 14 sigma levels in the vertical.
The model output was analyzed in the same manneras the observations, including EOF analysis of monthly
SST and HC anomalies in the North Atlantic and Pacificbasins, and regional analyses based upon the main centers of action of the leading EOF in each basin. For all
analyses, the 16 integrations were appended to form one
long record to provide a more robust representation of
the model’s variability.
Figure 10 shows the leading EOF of monthly heat
content anomalies in the North Atlantic together withthe long-term mean February MLD. The distribution of
MLD in the model is similar to observations (recall Fig.
2), with higher values in the northern portion of thebasin extending in a narrow tongue toward the southwest. However, the model strongly underestimates the
MLD in the north (maximum values ;200–300 m compared to 300–800 m in observations). The leading EOF,
which accounts for 34% of the variance, exhibits anorth–south dipole pattern, similar to observations. Unlike observations, the two centers of action are comparable in strength, in line with their similar February
MLDs.
The leading EOF of monthly heat content anomalies
in the North Pacific together with the long-term mean
February MLD is shown in Fig. 11. The model simulates
well the distribution of MLD, with higher values along;408N in the western portion of the basin and in the
Bering Sea. The leading EOF, which accounts for 35%of the variance, closely resembles observations, with a
primary center of action along 408N extending acrossthe western two-thirds of the basin and a second centerof opposite polarity in the Gulf of Alaska. Unlike ob-

1 JANUARY 2003

DESER ET AL.

FIG. 12. (top) Mean seasonal cycle of mixed layer depth (m) in
the NPAC region from observations (dashed) and the coupled model(solid). (bottom) Monthly lag autocorrelation curves from Mar forheat content (solid steplike curve) and SST (solid) from the coupledmodel. The observed SST autocorrelation curve is dashed. The theoretical autocorrelation function for heat content based upon the extended simple stochastic climate model is the thin gray exponential
curve.

servations, the two centers are of comparable strength,
in line with their similar February MLDs.
Figure 12 (top) shows the seasonal cycle of the observed long-term monthly mean mixed layer depth formodel’s equivalent of the NPAC region defined as thecenter of action of the leading EOF in the Pacific (338–
468N, 1548–1918E). The model approximates well theobserved seasonal evolution of mixed layer depth, although it is somewhat too shallow at the time of maximum extent in February (143 m compared to 178 m
in observations) and shoals most rapidly from March
to April, about 1 month ahead of nature. Figure 12 (bottom) shows the monthly lag autocorrelations of the model’s NPAC SST and HC anomalies starting from March;
the observed SST autocorrelations are also shown forcomparison. The model’s HC autocorrelation curve exhibits a rapid decay during the months of mixed layer
deepening (November–February), consistent with theeffect of entrainment, which mixes or dilutes the existing heat content anomaly with thermal anomalies newly
formed by wintertime atmospheric forcing, and little

67

FIG. 13. As in Fig. 12 but for the coupled model’s NATL region.

attenuation during the months when the mixed layer
shoals or remains steady (April–October). The SST autocorrelation curve from the model is very similar toobservations, including the magnitude and timing of thesummer minima and winter maxima. The theoretical
autocorrelation curve based on the extended simple stochastic climate model [Eq. (2)] with Heff given by themodel’s long-term mean February mixed layer depth
and l 5 12 W m 22 K 21 provides an excellent fit to themodel’s SST correlations from winter to winter [notethat the annually averaged damping parameter that fits
the model the best is somewhat smaller than the rangeof values used to benchmark the observations against(15–20 W m 22 K 21 ), possibly because vertical diffusion
through the main thermocline also acts to damp mixed
layer temperature anomalies in the model].
The results for the model’s equivalent of the NATL
region, given by the center of action of the leading EOF
in the Atlantic (528–598N, 498–268W), are shown in Fig.
13. The seasonal cycle of mixed layer depth is not wellsimulated due to the lack of deep winter mixing (themodel’s maximum value is 149 m in February, compared to an observed value of 390 m). Consistent withthe shallower winter mixed layer, the model exhibits astronger attenuation of the SST autocorrelation curve
compared to observations. As for NPAC, the theoretical
autocorrelation curve based on the extended simple sto-

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chastic climate model with l 5 12 W m 22 K 21 provides
an excellent fit to the model’s SST correlations fromwinter to winter.
Like observations, the model produces a substantial
difference in the level of the winter-to-summer SST autocorrelations between the NATL and NPAC regions.
In NPAC, the summer SST anomalies are practicallyuncorrelated (r ; 0.2) with those in the previous winterin both the model and observations, while in NATL they
are substantially correlated (r ; 0.4–0.5) in both modeland nature. The fact that the model, with 16 3 50 yrof record, reproduces this aspect of the observations(with only 50 yr of record), suggests that this is a realfeature of both the model and nature. One possible reason for the different behavior in the Atlantic and Pacificis that the static stability within the seasonal thermocline
beneath the summer mixed layer is weaker in NATL
than in NPAC (not shown) such that episodic entrainment events during summer are more effective in bringing temperature anomalies stored within the seasonal
thermocline up into the mixed layer, resulting in higher
SST anomaly persistence from winter to summer.
One of the benefits of the coupled ocean mixed layer–
atmospheric GCM configuration is that the atmosphericforcing of SST anomalies is not assumed to be a white
noise process as was the case for the implicit- and explicit-entraining stochastic climate models. In view ofthis, and given the potential influence of ENSO teleconnections on the characteristics of atmospheric variability over the North Pacific and Atlantic (see Alexander et al. 2002), we examine the model’s atmosphericforcing over the NPAC and NATL regions. Note thatthe primary atmospheric forcing of SST anomalies in
the model is the net surface heat flux, which includes
the turbulent fluxes of latent and sensible heat, andshortwave and longwave radiation: there are no Ekman
currents. Figure 14 (top) shows the lag cross correlations
between the time series of SST anomalies in March (thebase month used for the SST autocorrelation curves
shown above) and the time series of the net surface heat
flux (Q) from the previous October through the following March for NPAC and NATL. The strongest positive
correlations (;0.4 and 0.5 for NPAC and NATL, respectively) are found when the atmosphere leads SST
by 1–2 months, and negative correlations occur when
SST lags the atmosphere by 1–6 months, similar to observations in both timing and magnitude (recall Fig. 7).
The monthly lag autocorrelations of Q9 starting fromFebruary (Fig. 14, bottom) show that the model’s atmospheric forcing decorrelates within ;1 month andexhibits no winter-to-winter autocorrelation, again similar to observations.
5. Additional resultsa. Basinwide patterns of winter-to-winter SST
autocorrelations
Here we examine more generally the relevance of theextended simple stochastic climate model by comparing

VOLUME 16

FIG. 14. As in Fig. 7 but for the coupled model.

the spatial patterns of winter-to-winter SST autocorrelations at each grid point over the northern oceans fromobservations and theory. The observed autocorrelations
are computed between the time series of SST anomaliesin March and those in February of the following year
(this choice is motivated by the monthly lag autocorrelation curves for NATL and NPAC, see Fig. 6). The
theoretical autocorrelations are computed from Eq. (2)with Heff given by the long-term mean February/March
MLDs from observations and l 5 20 W m 22 K 21 .
In the observations (Fig. 15a), the highest winter-towinter autocorrelations occur in the northern North Atlantic, with values in the range 0.5–0.75. A tongue of
relatively high correlations (0.3–0.5) extends from thenorthern North Atlantic southwestward toward theeastern seaboard of the United States. Relatively highcorrelations also occur along the coastal margins of West
Africa and between Cape Hatteras and Nova Scotia. In
the Pacific, a band of high autocorrelations (0.3–0.5) is1 JANUARY 2003

DESER ET AL.

69

FIG. 15. Local SST anomaly autocorrelations from Mar to the following Feb based upon (a)observations and (b) the extended simple stochastic climate model. The contour levels are 0.1
and 0.2 (dashed), 0.3 and 0.4 (thin solid) and 0.5, 0.6 and 0.7, and 0.8 (thick solid); values .
0.3 are shaded. Note that there are no values , 0. (c) Observed minus theoretical autocorrelations[(a) minus (b)]. The contour interval is 0.1, starting at 60.2. Positive (negative) contours are
solid (dashed), and values . 0.2 and ,20.2 are shaded. (d) Observed long-term mean wintermixed layer depths. The contour levels are 100, 150, 200, 300, 500, and 800 m. Shading denotes
locations where the mean annual cycle in mixed layer depth (Feb/Mar minus Aug) is less than
60 m.

found along ;408N in the western half of the basin, in
the Gulf of Alaska, the southeastern Bering Sea, andwest of Baja California. High correlations are also foundin the Sea of Okhotsk, the Sea of Japan and off Kamchatka. Elsewhere, the correlations are ;0.1–0.2.
The broad features of the observed autocorrelation
distribution are evident in the simple theoretical results(Fig. 15b). In particular, the highest values are found in
the northern North Atlantic (0.5–0.8), with a tongue of
relatively high values (0.3–0.6) extending southwestward across the Atlantic, and a band of high values (0.3–0.5) along ;408N in the western Pacific extending
northward along the western margin; elsewhere the cor-

relations are ;0.1–0.2. The main deficiencies in themodel are the lack of high autocorrelations in the Gulf
of Alaska, off Baja California, the Sea of Okhotsk, theSea of Japan, and between Cape Hatteras and Nova
Scotia. These discrepancies between the observed andtheoretical values are highlighted in the difference map(Fig. 15c). This map also indicates that the model overestimates the autocorrelations directly west of Franceand Great Britain, and in a small region directly southeast of Japan.
The theory tends to underestimate the observed autocorrelation values in coastal regions where the seasonal variation in mixed layer depth is small (see Fig.

70

JOURNAL OF CLIMATE15d). Although the impact of reemergence upon winterSST anomaly persistence should be weak in these areas,other processes such as those associated with ocean dynamics may play a role. For example, previous studies
have suggested that anomalous geostrophic thermal advection may be important for winter SST variability
between Cape Hatteras and Nova Scotia (Bhatt et al.
1998; Seager et al. 2000) and in the Gulf of Alaska(Lagerloef 1995). Similarly, anomalous thermal advection by coastal Kelvin waves and reflected Rossby
waves that occur in association with ENSO (Miller etal. 1997) may contribute to SST variability west of Baja
California. The high autocorrelation values in the Sea
of Japan and Sea of Okhotsk may be related to sea ice
variability.
Uncertainties in the observational estimates of Heff
may also contribute to discrepancies between the observed and theoretical autocorrelation values. There areseveral sources of error in Heff , including paucity of dataand inadequate sampling of its temporal variability(within a month and between years), and sensitivity to
the criterion used to define mixed layer depth. While itis difficult to give a quantitative assessment of theseerrors, we note that other datasets yield broadly similar
distributions of Heff . We also note that a given percentage error in Heff yields a smaller corresponding percentage error in the 1-yr lag autocorrelation of winter
SST9 computed from Eq. (2) for Heff . ;130 m.
Given the simplicity of the model (e.g., use of a constant damping parameter and climatological values for
Heff ), the overall agreement between theory and natureis encouraging (the pattern correlation between the observed and predicted autocorrelation distributions is0.61). Recall that without the use of Heff in the simple
stochastic climate model (that is, without the implicit
effects of entrainment and the reemergence process), thewinter-to-winter lag autocorrelations would be zero everywhere. The rms difference between the observed andtheoretical autocorrelation distributions (excluding grid
points where the mean seasonal variation in mixed layer
depth is ,60 m) is 0.15, compared to 0.34 when theobservations are benchmarked against the original FH77
theory. For the Pacific (Atlantic) basin alone, the rms
difference is 0.13 (0.17) compared to 0.31 (0.39) withthe original theory. A comparison between the winterSST autocorrelation distributions from the 16 coupled
ocean mixed layer–atmospheric GCM integrations andtheory (not shown) indicate a similar level of agreement(0.65 pattern correlation) as between observations andtheory. Spatial variations in l and interannual variations
in Heff presumably account for much of the remaining
unexplained covariance.
6. Discussion
The simple stochastic climate model of FH77 has
been widely adopted as the leading paradigm for thenull hypothesis of SST variability in middle and high

VOLUME 16

latitudes, whereby the ocean mixed layer integrates
white noise atmospheric forcing to produce a red noise
SST response. In this view, the predictability or persistence of SST anomalies is limited to the timescale associated with the thermal inertia of the mixed layer, atimescale determined by the depth of the mixed layer
and the rate at which the SST anomaly damps to theatmosphere via turbulent heat fluxes. This paradigm has
been used as a benchmark of comparison for diagnosing
the contribution of other processes upon SST variability
such as wind- and buoyancy-driven ocean currents andtwo-way ocean–atmosphere coupling (cf. Manabe andStouffer 1988; Blade 1997; Seager et al. 2000, 2001;
Pierce et al. 2001). The results of this study suggest thata more relevant null hypothesis for interannual SST variability in middle latitudes is the entraining stochastic
climate model, or more simply, a reformulation of FH77
in terms of an effective mixed layer depth given by the
maximum wintertime value. Adopting this paradigm
augments the winter-to-winter persistence of SST anomalies considerably above the original model, whichyields virtually no memory from winter-to-winter due
to the ‘‘resetting’’ of thermal conditions each summer
when the mixed layer shallows and the associated heatstorage is minimal. Figure 16 illustrates the 1-yr lag
autocorrelations and e-folding timescales for winter SST
anomalies from the extended stochastic climate model
as a function of Heff and l in the range 15–20 W m 22
K 21 (shading). Winter mixed layer depths typical of theNorth Pacific (100–200 m) are associated with 1-yr lag
autocorrelations in the range 0.25–0.58 and e-folding
timescales in the range 0.8–1.8 yr. The deeper wintermixed layers of the northern North Atlantic (300–550m) are characterized by autocorrelations and e-folding
times in the range 0.6–0.8 and 2–5 yr, respectively. Notethat the use of a 50-m fixed-depth slab mixed layer
common to many studies (e.g., Manabe and Stouffer
1988; Blade 1997; Pierce et al. 2001) yields a 1-yr autocorrelation of only 0.1 and an e-folding timescale ofonly 5 months, values that could lead to misinterpretation of the potential influence of the thermal inertia
associated with the ocean mixed layer upon atmosphericvariability.
The higher persistence of winter SST anomalies inthe entraining or extended stochastic climate modelmeans that it is more difficult to discern the influenceof other processes such as internal ocean dynamics
against the red noise background of SST variability due
solely to stochastic atmospheric forcing. For example,
SST fluctuations in the far North Atlantic where wintermixed layers are ;500-m deep may be expected to persist for ;5 yr even though they are being forced byrandom (e.g., unpredictable beyond a week or two) atmospheric fluctuations. Note that the reemergencemechanism does not lead to enhanced variance of winterSST anomalies in the interannual band as might be expected intuitively: rather, it acts as a reddening process,enhancing the variability at low frequencies compared1 JANUARY 2003

DESER ET AL.

FIG. 16. Theoretical (top) 1-yr lag winter SST autocorrelations and(bottom) e-folding timescales as a function of winter mixed layer
depth (Heff ) based upon the extended simple stochastic climate model.

to high frequencies. The reddening effect of the reemergence process can be understood in light of thesimple heuristic model presented in Eq. (2). The deeper
the effective mixed layer depth, the greater the associated thermal inertia and integrating effect of the ocean
mixed layer of short timescale weather variations, andhence the longer the persistence of winter SST anomalies.
Although the simple extension we propose to themodel of FH77 yields encouraging results, several of
the simplifying assumptions we have made should be
scrutinized in future work. One such assumption is theuse of a long-term mean winter mixed layer depth for
Heff rather than one that varies year by year. Anomalies
in Heff may impact the strength of the reemergence71

mechanism in at least two ways: first, Heff may be correlated with the amplitude of the concurrent winter SST
anomaly (the deeper the mixed layer, the smaller thetemperature anomaly for the same atmospheric forcing),and second, winter mixed layer temperature anomalies
may impact the stratification the following winter, which
would affect Heff and hence temperature anomalies. It
will be worth examining these effects when reliablegridded datasets of monthly mixed layer depth become
available for a sufficiently long period of record. The
modeling results of Alexander et al. (2000) suggest,
however, that these effects are of secondary importancecompared to the impact of the mean seasonal cycle ofmixed layer depth.
Another obvious simplification in the model is theuse of a constant damping parameter l. While we have
purposely chosen not to tune this parameter in the present study, it would be useful to examine the sensitivityof the results to a more realistic distribution of l in both
space and time. Unfortunately, at the present time, spatial and seasonal variations of l are difficult to estimate
with sufficient accuracy from the available observations(see Frankignoul et al. 1998). In the 16-member ensemble of coupled integrations, l is free to vary in bothtime and space. Investigation of the impact of a variable
damping rate upon SST persistence in the coupled model
configuration will be the subject of future work.
The results of this study do not preclude the potential
importance of oceanic processes such as advection, diffusion, eddy mixing, and subduction upon the persistence of mixed layer temperature anomalies. The recent
studies of Qiu (2002) and Schneider and Miller (2001;
see also Seager et al. 2001) indicate that both the reemergence mechanism and geostrophic advection influence the upper-ocean heat balance and generation of
winter SST anomalies along the Kuroshio Current Extension, with the former dominating SST anomaly persistence at 1–2-yr timescales and the latter becoming
more important at longer timescales. De Coetlogon andFrankignoul (2003) estimate that e-folding timescales
for winter SST anomalies along the Gulf Stream and in
the subpolar North Atlantic increase by 3–7 months
when mean advection is taken into account. Further
quantitative assessment of the effects of dynamical
ocean processes versus mixed layer physics (e.g., thereemergence mechanism) is needed for a more complete
understanding of interannual and longer timescale SST
variability in midlatitudes.
Acknowledgments. We thank Dr. R. Saravanan for
useful discussions and for help with coding the entraining stochastic climate model. We also thank Adam Phillips and Jamie Scott for their technical assistance. Helpful comments and suggestions were provided by ananonymous reviewer and Drs. T. Joyce, B. Qiu, F. Straneo, and M. Visbeck. This work was supported in partby grants from NOAA’s OGP CLIVAR Program. The

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figures were produced with GrADs software courtesyof the University of Maryland.
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