1. Introduction
Coupled variability in the equatorial Atlantic is dominated by a meridionally antisymmetric mode sometimes known as the Atlantic meridional mode (AMM; Chiang and Vimont 2004). Anomalous climate conditions associated with the AMM include a meridional sea surface temperature (SST) gradient in equatorial region, meridional winds that blow toward the anomalously warm hemisphere, and a shift of the intertropical convergence zone toward the warmer hemisphere (Chiang and Vimont 2004). Phenomena ranging from drought in northeastern Brazil (Hastenrath 1978) and the Sahel (Folland et al. 1986) to seasonal changes in Atlantic hurricane frequency and intensity (Vimont and Kossin 2007) are thought to be dependent on the meridional gradient of tropical Atlantic SST. As such, understanding the physical mechanisms governing such coupled variability and identifying the forcing agents is of societal importance.
The AMM emerges as a dominant mode of coupled ocean–atmosphere variability in the observed record and in simple theoretical models. The spatial and temporal structure of the AMM in nature can be quantified via a maximum covariance analysis of SST and surface winds (Chiang and Vimont 2004) (Fig. 1). The AMM spatial structure shows SST anomalies with maximum amplitude at approximately 15°N and S latitude, and the surface wind anomalies blow from the cool to the warm hemisphere and are westerly (easterly) in the warm (cool) hemisphere, therefore decreasing (increasing) the climatological easterly flow. The decrease (increase) of wind speed over anomalously warm (cold) water decreases (increases) evaporation, leading to a positive wind–evaporation–SST (WES) feedback that destabilizes the meridional mode (Xie and Philander 1994; Chang et al. 1997). When the WES feedback is included in a simple idealized model of the tropical atmosphere coupled with a slab ocean (Vimont 2010), the meridional mode emerges as the structure that experiences the most transient growth over seasonal time scales. Although ocean dynamics can play a role in defining characteristics of the AMM (Chang et al. 1997; Xie 1999), the existence of the meridional mode in idealized models that do not include ocean dynamics (Xie 1997; Vimont 2010) indicates that the AMM can be considered to be a thermodynamic mode of coupled variability.
Spatial structure of the Atlantic meridional mode. Regressions of SST (shaded) and 10-m horizontal wind speed (vectors) onto the SST-normalized expansion coefficient from maximum covariance analysis of the two fields (taken from Chiang and Vimont 2004; Fig. 1b).
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
Although the WES feedback is a positive feedback in the tropical Atlantic, it does not appear strong enough to overcome realistic damping time scales for the ocean (Xie 1999; Vimont 2010). Therefore, the AMM is thought to exist as a transient response to some finite external forcing, such as the North Atlantic Oscillation (Czaja et al. 2002), the Atlantic multidecadal oscillation (Vimont and Kossin 2007; Smirnov and Vimont 2012), African dust storms (Evan et al. 2011), or stochastic processes (Chang et al. 1997).
At the same time stratocumulus (Sc) cloud cover is typically found in tropical–subtropical regions exhibiting a persistent trade wind inversion and coastal upwelling, where cloudiness is inversely proportional to the underlying SST because of the influence of SST on lower-tropospheric stability and boundary layer saturation vapor pressure (Klein and Hartmann 1993). As these low clouds are optically thick and emit longwave radiation near the surface temperature, they exhibit a net negative surface and top-of-the-atmosphere forcing.
Although elucidating processes that externally force the AMM is critical to understanding the temporal evolution of the AMM, particularly on long time scales, there exist several questions related to the mechanics of the AMM itself. Of interest here is that the spatial structure of SST anomalies associated with the AMM (Fig. 1) maximizes in the same regions where climatological stratocumulus (Sc) clouds exist (Klein and Hartmann 1993). Tanimoto and Xie (2002, hereafter TX02) noted the spatial correlation of SST anomalies associated with the AMM and Sc cloud cover and used surface observations of cloud amount to suggest that the presence of Sc clouds can increase the time scales of Newtonian cooling (i.e., linear damping of temperature anomalies) by 30%. Such a relationship between SST and Sc clouds was termed a Sc feedback since Sc clouds have a net negative radiative forcing and Sc cloud cover varies inversely with underlying SST (Klein and Hartmann 1993). More recently, based on output from an atmospheric general circulaion model coupled to a slab ocean, Smirnov and Vimont (2012) speculated that Sc clouds in the tropical North Atlantic may alter the local surface shortwave fluxes sufficiently to assist in the propagation of midlatitude SST anomalies into the tropical Atlantic, thus exciting the AMM remotely.
Here we continue the investigation of the role that Sc clouds play in the fundamental mechanics of the AMM via Sc modification of Newtonian cooling time scales. To do so we will employ observations of cloud cover and SST, an idealized linear model, and output from phase 3 of the Coupled Model Intercomparison Project (CMIP3) models. The remainder of our paper is organized as follows: in section 2 we describe the datasets and models used in this study; in section 3 we quantify the Sc cloud feedback, evaluate the influence of the Sc feedback on thermodynamically coupled modes of variability, and examine such behavior in CMIP3 models; and in section 4 we conclude by summarizing our findings and placing them in the context of understanding coupled variability in the tropical Atlantic.
2. Data and models
Here we describe the source of the satellite cloud climatologies used in this paper and then discuss the radiative transfer model employed to calculate the cloud surface forcing as well as the assumptions made about typical stratocumulus cloud properties. We then detail the idealized linear model used to evaluate the influence of the Sc feedback on thermodynamically coupled variability of the tropical Atlantic. We end with a description of the model output used to examine the Sc feedback in CMIP3 models. The monthly mean SST data used in this paper are from version 2 of the Hadley Centre Sea Ice and Sea Surface Temperature dataset (HADISST v2) (Rayner et al. 2006).
a. Cloud climatologies
We evaluate two climatologies of cloud cover retrieved from multidecadal satellite measurements of longwave and shortwave radiation. One cloud climatology, the Pathfinder Atmospheres Extended (PATMOSx) record, is from satellite measurements made exclusively from polar-orbiting platforms (Heidinger et al. 2012). The other cloud climatology, the International Satellite Cloud Climatology Project (ISCCP), is from satellite measurements made mostly from geostationary platforms, although some polar-orbiting satellite data are incorporated into this climatology near the poles (Rossow and Schiffer 1999).
Both of these cloud climatologies have been corrected, post hoc, for temporal inhomogeneities related to artifacts in the data. These artifacts stem, in large part, from coherent changes in the average satellite or solar zenith angle at any one location on Earth’s surface, over the lifetime of the climatology. However, it is possible that the artifacts are also related to sensor degradation over the lifetime of any one instrument. In PATMOSx these artifacts are mostly related to the satellite drift (Ignatov et al. 2004) and are corrected in a manner consistent with Rausch et al. (2010). In ISCCP these errors are mostly related to the numbers and physical location of the geostationary satellites. Qualitatively the ISCCP corrections are similar in nature to those for PATMOSx and involve regressing out variability in the cloud climatology that is correlated with the solar or satellite zenith angle. We note that these corrections are more relevant for evaluating long-term trends in the satellite data. In this paper we are interested in variability on subannual time scales, thus the corrections are less relevant to this study and are not discussed further.
From both cloud climatologies we use monthly mean values of low and mid cloud amount, which is defined as all clouds with cloud-top heights at or below 440 hPa, for July 1983–June 2008. Although retrieved low cloud amounts (cloud tops below 680 hPa) should better reflect Sc cloud cover, biases in the ISCCP cloud height climatology likely overestimate the height of low clouds. We use this same 440-mb threshold for the PATMOSx cloud data for consistency. The PATMOSx cloud climatology is resampled from the native 1° horizontal resolution to 2.5° to be consistent with the ISCCP climatology.
b. Radiative transfer model
All surface radiative flux calculations are done using the Streamer radiative transfer model (Key and Schweiger 1998). Streamer is a radiative transfer model that can be used for computing either intensities or fluxes for a wide variety of atmospheric and surface conditions. Here fluxes are calculated for four streams and 24 Legendre coefficients using a discrete ordinate solver. A standard (Jordan mean) tropical moisture and humidity profile are used in the flux calculations.
We estimate the Sc cloud forcing as a function of fractional Sc cloud cover by subtracting the net flux at the surface for cloudy conditions minus the flux for clear sky conditions. Sc cloud forcing was calculated at every 1% change in cloudiness for a clear sky to a 100% cloudy scene. We assume single phase liquid water clouds and one set of physical cloud properties for all flux calculations (Table 1) from Bennartz (2007). Sc cloud forcing is assumed to be the averaged forcing from calculations made every three hours on the 15th of every month a calendar year as shortwave forcing is dependent on the diurnal cycle of the solar zenith angle. We note that cloud longwave surface forcing is invariant with season since in our calculations cloud-base height is fixed.
Typical Sc cloud properties. Physical cloud properties assumed for calculations of Sc cloud surface radiative forcing.
c. Idealized linear model
d. CMIP3 output
We also examine output from CMIP3 models to determine if there exists a relationship between Sc clouds and coupled variability of the equatorial Atlantic in fully coupled general circulation models. More specifically we evaluate model output SST and low cloud cover from the twentieth-century historical forcing runs and for the model years of 1950–2000. Since model cloud cover from the ISCCP simulator (Klein and Jakob 1999; Webb et al. 2001) is not available for all models for these runs we use model cloud fraction (on each model’s hybrid-sigma pressure coordinate) and estimated low cloud fraction by taking the maximum cloud cover below 680 hPa. Since we are only considering the relationship between SST and low cloud cover in these models we utilize output from one realization of the model ensembles within this experiment. A list of the models used can be found in Table 2.
CMIP3 models used in this study. The models listed are examined to estimate the degree to which coupled models reproduce the relationship between Sc cover and SST changes.
3. Results
Climatological annual mean values of low cloud cover from ISCCP and PATMOSx exhibit maxima in cloud cover in the Sc cloud decks of the eastern and subtropical sectors of each hemisphere (Fig. 2). The maximum in cloud cover is most pronounced in the Southern Hemisphere in both datasets, with cloud cover peaking at greater than 60% in the area of 0° and 15°S in each. The Northern Hemisphere Sc cloud decks are not as well defined, although both climatologies do show a region of low clouds contouring the coast of West Africa and the Iberian Penninsula where there is greater than 30% low cloud cover. We are encouraged by the agreement between these two independent climatologies of cloud cover and next quantify the relationship between low cloud cover and changes in the underlying SST.
Satellite-retrieved long-term mean low cloud cover. Overwater cloud amounts are from the (a) ISCCP and (b) PATMOSx climatologies. Averages are for the 25-yr period of June 1983–May 2008.
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
a. Changes in Sc clouds and underlying SST
We estimate ∂Sc/∂T via linear regression of monthly mean low cloud cover from ISCCP and PATMOSx onto monthly mean observed SST. We calculate the regression using data over the period July 1983–June 2008, and prior to calculating the regression coefficients the annual cycle and linear trends are removed from the SST and both cloud datasets. Assuming that the PATMOSx and ISCCP cloud climatologies have an equal likelihood of being accurate, we average the regression coefficients from ISCCP and PATMOSx as the spatial structure of the PATMOSx and ISCCP regression coefficients are similar. We note that we also calculated λSc in a manner consistent with Deser (1993), obtaining nearly identical results.
In the Southern Hemisphere ∂Sc/∂T is a maximum in the region of 5°–15°S and −20°–10°E, exhibiting values of −6% to −8% K−1, (Fig. 3a). In the Northern Hemisphere the maximum Sc sensitivity to the underlying SST is also −6% to −8% K−1 but is spread over a larger region, approximately 5° to 20°N and −50° to −20°E. We note that these regression coefficients have smaller magnitudes than those from TX02, who report an average Southern Hemisphere dependency of cloudiness on underlying SST in the range of −10% K−1.
Spatial structure of low cloud sensitivity to the underlying SST. (a) Contours represent the mean PATMOSx and ISCCP regression coefficient of low cloud cover onto the underlying SST (λSc). Also shown is the zonal mean λSc (gray), which has been averaged so that the meridional structure is symmetric about the equator, and an estimate of the function form of λSc (black) from (2).
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
b. Sc radiative forcing
We next estimate ∂F/∂Sc to obtain λ(y) in (6). We estimate surface Sc radiative forcing using the Streamer radiative transfer model (Key and Schweiger 1998), which calculates broadband short and longwave fluxes at the surface for all-sky and clear-sky conditions (see data and models). Sc clouds are optically thick water clouds. As such, when compared to clear-sky scenes these clouds increase the local albedo, which reduces the surface solar insolation. Sc clouds are also low in the atmosphere, existing at the top of the marine boundary layer, thus their effective emission temperature is very close to that of the surface, resulting in a positive net longwave surface forcing. However, the shortwave reduction in surface solar insolation is 2 to 3 times larger than the longwave forcing (e.g., de Szoeke et al. 2012), and the net surface radiative forcing is negative.
We calculated the Sc surface forcing per 10% change in cloud cover assuming constant cloud physical properties from Table 1. To provide a representative sample of various solar geometries throughout the calendar year, the calculations were performed at latitudes of 10°, 20°, and 30°N for the 15th day of every third month of the year, and at 3-hourly increments. The Sc cloud forcing per percent change in cloud cover, averaged over latitude and time (Fig. 4), demonstrates that the relationship between cloud cover and surface forcing, for fixed cloud optical properties, is linear, where ∂F/∂Sc is −0.93 W m−2 %−1. We note this value is similar to the −1.0 W m−2 %−1 top of the atmosphere Sc forcing (Borg and Bennartz 2007; Klein and Hartmann 1993) and to surface observations (Cronin et al. 2006; de Szoeke et al. 2012) The value −0.93 W m−2 %−1 is approximately one-half of the Sc radiative forcing value of −1.8 W m−2 %−1 used in TX02, presumably because the TX02 value is based only on the cloud reduction in surface solar insolation from Reed (1977), which does not account for the positive longwave Sc surface forcing.
Sc surface forcing per amount cloud cover. Cloud surface forcing (solid) is based on cloud properties in Table 1, and the slope of the forcing is −0.93 W m−2 %−1. In the idealized model we assume this slope is −1.0 W m−2 %−1 (dashed).
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
c. Sensitivity to SST damping in an idealized linear model
We estimate an observation-based damping time scale of tropical Atlantic SST anomalies as the e-folding decay time of the autocorrelation function of monthly mean observed SST in the tropical Atlantic. This e-folding time is calculated using detrended and deseasonalized SST anomalies for the period 1950–2010. We average the observed e-folding time scales zonally (65°W–15°E) and then at each absolute value of latitude to produce a meridional structure that is symmetric about the equator (Fig. 5a). From 20°S to 20°N the observational damping time scale is an average of 120 days, with maximums in the damping time scale at latitudes of approximately 15°S and 15°N. There is an additional peak in the observed damping time scales at the equator, which is likely associated with dynamical ocean processes (Foltz and McPhaden 2006).
Meridional structure of linear damping coefficients and the WES feedback. (a) Plotted is 
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
The WES feedback, the destabilizing mechanism for meridional modes of coupled variability, is a maximum at latitudes between 15°–20°N and 15°–20°S (Fig. 5b). It is interesting to note that [ɛC + ɛSc(y)]−1 and the WES feedback parameter (α) have a similar meridional structure, suggesting that Sc clouds, through their modification of surface radiative fluxes, may act to amplify the WES feedback and contribute to the growth of thermodynamically coupled modes of variability.
The final structure with the largest singular value is referred to as the “optimal,” as it experiences the maximum amount of transient growth over time period τ, defined as the square of the associated singular value. We repeat the calculation of optimal initial structure and associated growth rates by defining the SST linear damping time scale as 
Not surprisingly, the transient growth of the least stable mode for which the SST damping is given by Eq. (10) is nearly identical to that shown in Vimont (2010), for which the damping time scale is everywhere 120 days and the maximum squared amplitude of the mode is realized at approximately 150 days (Fig. 6). If we assume the SST damping time scale to be 
Transient growth of least stable modes. Plotted is the squared singular value of the leading modes resulting from SVD of 
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
The spatial structure of the optimals’ final condition at 150 days [the first column of U(τ = 150d)], corresponding to the time of maximal growth, is given in Fig. 7 for the model with the SST damping given by (10) and ɛC. It is important to note that Sc clouds do not appear to alter the structure of these modes (i.e., the location of the SST anomalies, etc.) but rather the clouds amplify the growth of the modes over time. As such, the spatial structure for each is very similar, and only the magnitude (variance) of the mode at 150 days is changed. We note that these final structures are nearly identical to those shown by Vimont (2010) and are qualitatively similar to that of the Atlantic meridional mode as defined via reanalysis data (Fig. 1).
Spatial structure of final condition at day 150. Shown are the SST (shading), surface winds (vectors), and geopotential heights (dashed contours indicate negative height anomalies and solid contours positive anomalies) for the leading left singular vectors of 
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
d. The stratocumulus feedback in coupled models
Thus far we have defined the contribution of Sc clouds to thermodynamically coupled variability in the equatorial Atlantic using historical observations of clouds and SST in conjunction with an idealized linear model. Our results suggest that Sc clouds significantly increase the transient growth of the coupled modes considered here (Fig. 6). We next evaluate CMIP3 coupled climate models to determine if such a relationship between Sc clouds and the underlying SST is a consistent feature of these models.
There is a wide degree of disparity among CMIP3 models with respect to the long-term mean low cloud amount (Fig. 8). First, nearly all models exhibit less low cloud cover than is seen in satellite observations, with INM-CM3.0 being the exception. Next, many of the models do not exhibit the same pattern of maximums in low cloud cover over Atlantic near 15°N and S latitudes. As such, we conclude that biases in the mean state of Atlantic low cloud cover are a persistent feature of CMIP3 models.
Long-term mean low cloud cover in CMIP3 models. Contours represent the long-term mean low cloud cover (%) for the CMIP3 models in Table 1 and the ISCCP and PATMOSx satellite datasets. In each maps the thick contour is 10% cloud cover and values increase by 10% in each subsequent contour.
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
Regression maps of low cloud cover onto SST ∂Sc/∂T also show disparity among models and between models and observations (Fig. 9), although the agreement is slightly better than is the case for the low cloud mean state (Fig. 8). Most of the models exhibit a maximum of ∂Sc/∂T in the South Atlantic between 10° and 25°S latitude, and several show an additional maxima in the Northern Hemisphere, consistent with observations.
Spatial Structure of low cloud sensitivity to underlying SST in CMIP3 models. Contours represent the mean regression coefficient of low cloud cover onto the underlying SST (λSc) with units of % °C−1, and for the CMIP3 models in Table 1 and the ISCCP and PATMOSx satellite datasets. In each map the thick contour represents a regression coefficient of zero and values increase by an order of 1% °C−1 in each subsequent contour. Negative contours are not shown.
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
We estimate the Atlantic zonal mean ∂Sc/∂T [6)] for the models in a manner similar to that done with the observational data except that we do not force the structure to be symmetric about the equator nor taper the values to zero at 35°N and 35°S. The meridional structure of the mean ∂Sc/∂T in the models is similar to that from observations, although the model mean low cloud sensitivity is maximized at 15°N and 15°S, rather than the observationally derived 10°N and 10°S (Fig. 10). In addition, the magnitude of these maxima in ∂Sc/∂T, approximately −5% °C−1 at 10°N and S latitude, are outside the inner quartile range of the models at these latitudes. More broadly, on average the models appear to underestimate the magnitude of ∂Sc/∂T everywhere in the tropics. Therefore, modeled low clouds are not sufficiently sensitive to the underlying SST, the Sc feedback in the models may be too weak, and Sc clouds likely have too little an influence on SST anomaly damping time scales.
Meridional structure of low cloud sensitivity to underlying SST in CMIP3 models. Regression coefficients (λSc) from Fig. 9 are averaged over 60°W–10°E. Solid red line indicates the model mean λc, and the box and whiskers plots indicate the distribution of values among the models.
Citation: Journal of Climate 26, 11; 10.1175/JCLI-D-12-00370.1
4. Conclusions
Here we used an idealized coupled linear model of the tropics, CMIP3 coupled models, a radiative transfer model, and observations of clouds and SST to examine the influence of Sc clouds on thermodynamically coupled variability in the tropical Atlantic. Via observations we estimated a mean meridional Sc feedback, defined as the change in surface Sc cloud radiative forcing per change in local SST and calculated the influence of the feedback on time scales for Newtonian cooling of the SST (Fig. 5a). We demonstrated that in an idealized coupled linear model of the tropics, in the WES region this Sc feedback doubled the transient growth of a meridionally coupled mode similar to the so-called AMM (Fig. 6). Alternatively, our results suggest that in the absence of stratocumulus clouds the magnitude of the WES feedback would not be sufficient to overcome a shortened SST damping time scale, thus prohibiting transient growth of the coupled meridional mode.
We also demonstrated that CMIP3 models exhibit a meridional structure of ∂Sc/∂T that is similar to our observation based approach (Fig. 10). However, nearly all CMIP3 models underestimate the magnitude ∂Sc/∂T. Given that the models reasonably represent the mean surface radiative forcing for a given change in Sc cloud cover (de Szoeke et al. 2012), we speculate that in the tropical Atlantic the Sc feedback is too weak in CMIP3 models because Sc clouds in the models are not sufficiently sensitive to the temperature of the underlying sea surface.
Although Sc cloud cover is sensitive to the temperature of the underlying waters, Sc cloud cover may also change with the strength of the persistent midtropospheric subsidence over the eastern tropical Atlantic (Klein and Hartmann 1993). Therefore, externally forced changes in Sc cloud cover may excite AMM-like responses in the Atlantic, representing a possible new pathway for forcing coupled variability of the tropical Atlantic. For example, a recent study suggested that water droplet effective radius for clouds in the tropical North Atlantic has been modified over time by changes in emissions of pollution from Europe (Booth et al. 2012). It is conceivable that the changes in Sc radiative forcing associated with aerosol cloud albedo effects have amplified the magnitude of the Sc feedback (and AMM variability) in the past.
From these results we conclude that Sc clouds play an important if not vital role shaping observed coupled variability of the tropical Atlantic. Furthermore, we speculate that stratocumulus clouds are similarly relevant to meridional variability in the eastern Pacific (Chiang and Vimont 2004).
Acknowledgments
Funding for this work was provided by a grant from the NOAA Climate Program Office (Grant NA10OAR4310140). We thank Simon de Szoeke and two anonymous reviewers for providing helpful comments on an earlier version of this manuscript. We thank Joel Norris for providing the corrected ISCCP data. PATMOS-x data and the STREAMER model are available from the Cooperative Institute for Meteorological Satellite Studies (at http://cimss.ssec.wisc.edu/patmosx, and http://stratus.ssec.wisc.edu/streamer, respectively). We acknowledge the modeling groups, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) and the WCRP’s Working Group on Coupled Modelling (WGCM), for their roles in making available the WCRP CMIP3 multimodel dataset (http://www-pcmdi.llnl.gov/ipcc). Support of this dataset is provided by the Office of Science, U.S. Department of Energy.
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