1. Introduction
The interannual variability of top-of-atmosphere (TOA) irradiances observed by Clouds and the Earth’s Radiant Energy System (CERES; Wielicki et al. 1996) instruments is remarkably small. Four years of CERES data from March 2000 through February 2004 indicate that the annual and global mean TOA reflected shortwave irradiance is 97.0 W m−2, with maximum and minimum values of 97.2 and 96.8 W m−2, respectively. The difference between the maximum and minimum values is 0.4% of the mean value. Similarly, the annual mean TOA longwave irradiance is 239 W m−2 and the difference between the maximum and minimum values is 0.3 W m−2, which is only 0.1% of the mean value. Somewhat larger variability of TOA reflected shortwave, longwave, and net irradiance is also reported by Duvel et al. (2001), who used Earth Radiation Budget Experiment (ERBE), Scanner for Radiation Budget (ScaRaB)-Meteor Satellite, and ScaRaB data, but it is still small compared with the mean values. In addition, according to Loeb et al. (2007b), shortwave variability from the International Satellite Cloud Climatology Project (ISCCP; Schiffer and Rossow 1983) is consistent to 40% with that from CERES. To understand possible reasons for the small interannual variability of global and monthly mean TOA shortwave and longwave irradiances at TOA, we need to understand which regions contribute and the ways in which the variation is correlated with the variation of atmospheric and surface properties. Smith et al. (1990) and Bess et al. (1992) analyzed the interannual variability of absorbed shortwave and longwave irradiances at TOA, respectively, observed by Nimbus-6 and -7 Earth Radiation Budget Instruments. They found that El Niño–Southern Oscillation (ENSO) causes the largest interannual variability when seasonal cycles are removed. Work by Loeb et al. (2007a) also suggests that most albedo variations are in the tropics and they are highly correlated with cloud cover.
In this paper, the interannual variability of global radiation budget is further investigated using CERES data taken from the Terra platform. Specifically, the magnitude of the variation, where larger variations happen, and what limits the variability are investigated. Section 2 describes data used in this study. Section 3 discusses the standard deviation of anomalies computed in different ways, quantifies the variability, and identifies processes cause large variability. In section 4, a simple model based on zonal mean thermodynamic equation is used to qualitatively show that temperature anomalies decay exponentially with time.
2. Method

3. Result
a. Global TOA irradiance variability
To demonstrate that monthly anomalies from 1° × 1° grid boxes partially cancel when they are averaged over a larger region, we computed the global mean standard deviation of TOA shortwave, longwave, and net irradiances at TOA in several different ways. When anomalies are averaged over a 1° latitude zone and the area-weighted mean standard deviation is then computed from 48 × 180 zonal monthly anomalies, the standard deviations are reduced, respectively, to 2.4, 2.1, and 2.0 W m−2. When anomalies are averaged over the globe and the standard deviation is then computed from 48 global monthly anomalies, the standard deviations of TOA reflected shortwave, longwave, and net irradiance anomalies are further reduced, respectively, to 0.5, 0.4, and 0.4 W m−2.
b. Regional shortwave and longwave variations
The standard deviation of TOA longwave irradiance anomalies shows a similar pattern as the TOA reflected shortwave irradiance, but the contrast between the tropics and midlatitudes is more pronounced (Fig. 3, middle plot). This is probably because the frequency of occurrence of thick convective clouds and their cloud-top height decrease with increasing latitude, which reduces the longwave anomaly standard deviation. When the TOA reflected shortwave and longwave irradiances are combined for the TOA net irradiance, regions that have large TOA reflected shortwave and longwave variabilities are no longer prominent (Fig. 3, bottom plot). Because a large positive TOA reflected shortwave anomaly resulting from thick convective clouds also causes a large negative longwave anomaly (Kiehl 1994; Cess et al. 2001), such an anomaly has a smaller impact on the TOA net irradiance. Large standard deviations of the TOA net irradiance are also over the oceans. Regions with a larger standard deviation are eastern Pacific subtropical regions, where low-level clouds are present, and the region off the coast of the Antarctic Peninsula. The top and bottom plots of Fig. 3 suggest that large TOA net irradiance standard deviations over these regions are caused by large TOA reflected shortwave standard deviations. Low-level cloud property changes predominately alter the TOA reflected shortwave irradiance. Similarly, sea ice and snow cover changes predominately affect the TOA reflected shortwave irradiance if clouds are absent.

The above results indicate that clouds increase the variability of the reflected shortwave, longwave, and net irradiances at TOA, as well as the variability of the atmospheric net irradiance. To understand the contribution of cloud cover change to the variation of these irradiances, the regional correlation coefficients between TOA reflected shortwave and cloud cover anomalies and between TOA longwave and cloud cover anomalies are shown in Fig. 6. Over most of the tropics and a part of the midlatitudes, the correlation coefficient between TOA reflected shortwave irradiance and cloud cover anomalies is greater than 0.8. The correlation coefficient between TOA longwave irradiance and cloud cover is less than −0.8 over most of the tropics and the Northern Hemisphere midlatitudes, except for regions where predominately low-level clouds are present.
When the TOA reflected shortwave and longwave irradiance anomalies are combined with surface irradiance anomalies for the atmospheric net irradiance anomalies, tropical regions where both TOA reflected shortwave and longwave correlations are large maintain a large correlation with cloud cover (Fig. 6, bottom plot). However, the correlation in the midlatitudes is smaller even though the correlation both between TOA reflected shortwave irradiance and cloud cover anomalies and between TOA longwave irradiance and cloud cover anomalies is large. The correlation between the atmospheric net irradiance and cloud cover decreases with latitude and it is negative at high latitudes. The reason for the weak correlation in the midlatitudes is that the atmospheric net irradiance depends not only on cloud cover, but it also depends on either cloud height or cloud effective temperature. The net atmospheric radiative effect of low-level clouds is negative while the net atmospheric radiative effect of high-level clouds is positive. The sign changes around the 500-hPa pressure level (Fig. 7). Because high- and low-level clouds are both frequently present in midlatitudes and the sign of the atmospheric cloud radiative effect depends on the height, the correlation coefficient is reduced in the midlatitudes. In polar regions, where low-level clouds are dominant, the correlation between the net atmospheric irradiance and cloud cover is negative.
4. Discussion
The interannual variation of global mean reflected shortwave and longwave irradiances at TOA are less than 0.5% of the respective mean value during the 4-yr period from March 2000 through February 2004. Larger variabilities apprear in the tropics, and are caused by clouds responding to ENSO, that is, the atmospheric response to regional variations of the sea surface temperature. Atmospheric processes are volatile compared with oceanic processes, but oceanic processes alone do not affect TOA reflected shortwave irradiance very much. Interactions between the ocean and the atmosphere provide persisting anomalies of both TOA reflected shortwave and longwave irradiance. For example, Norris and Klein (2000) investigated the variability of upward velocity at the 500-hPa level over the North Pacific and found that it is correlated with sea surface temperature variability. A large part of the energy input to the atmosphere in the tropical western Pacific comes from the ocean as the surface enthalpy flux (Trenberth et al. 2002). According to a bulk formula, increasing the temperature gradient between the sea surface and lower atmosphere increases the energy inputs to the atmosphere (Fairall et al. 1996).
The variation of the surface flux to the atmosphere in tropics is, therefore, predominantly due to anomalous ocean processes that cause the anomalous regional sea surface temperature. A significant part of El Niño can be modeled just shifting around a warm pool of seawater in the tropical Pacific (Enfield 1989). During El Niño, anomalous convection migrates eastward with the 29°C sea surface temperature isotherm (Enfield 1989). These suggest that most of variations in the TOA reflected shortwave and longwave irradiances over the tropics come from a shifting warm pool of seawater instead of local variations of either heating or cooling of the seawater by radiation. A smaller σt
There are few disturbances that persist in a large area, as demonstrated in Figs. 4 and 5, and for a long time (e.g., more than a year). This might be because large-scale dynamics is driven by the meridional temperature gradient that is determined by solar energy inputs and poleward energy transport. Stone (1978), using a simple model, concluded that the energy transport by dynamics are primarily controlled by the solar constant, size of the earth, the tilt of the earth’s axis, and hemispheric mean albedo. In other words, the solar energy input to the earth as a function of latitude controls poleward energy transport and the meridional temperature gradient. As long as the meridional temperature gradient is nearly constant, large-scale dynamics that transport energy poleward and the TOA longwave irradiance may be stable. Because clouds are generated by dynamical processes and the albedo of the earth or energy input to the earth largely depend on the cloud cover (Fig. 6), this implies that the interannual variability of cloud cover is also small. According to cloud cover retrieved from Moderate Resolution Imaging Spectroradiometer by the CERES cloud algorithm (Minnis et al. 2008), the interannual variability of cloud cover is indeed less than 1% of the mean cloud cover. However, why is the variability of cloud cover, which affects absorption of the shortwave irradiance by the earth system, so small compared with the mean cloud cover? In other words, what prevents the albedo perturbation by clouds to intensify with time? The compensation of shortwave anomalies by longwave anomalies in the tropics reduces the effect on the large-scale dynamics, but Fig. 5 shows that there is significant variability of the net atmospheric irradiance in the tropics.





Because D > 0, ω > 0, and Dk2 − C − a is likely to be positive (unless k is small and C + a is a large positive number), both cosϕ and sinϕ are positive. Therefore, we expect that
Figure 8 shows the correlation coefficient between the anomalies of the geopotential height difference at 1000- and 300-hPa
We would expect that τ can substantially vary temporally and spatially. The value of D depends on the temperature advection in the atmosphere that transports energy poleward. A study by Held and Hou (1980) suggests that D also depends on the viscosity of the air. We would also expect that variations in a and C affect τ significantly.
If a positive
The first two terms on the left-hand side of (21) are the change of the thermal wind relation with time. Clouds perturb the meridional gradient of diabatic heating in the atmosphere by warming in the tropics and cooling in polar regions (Stuhlmann and Smith 1988; Zhang and Rossow 1997; Kato et al. 2008). Therefore, the cloud radiative effect on the term R/(Hcp)∂
Figures 9a,b show
In summary, the interannual variability of global and annual albedo is small for the following two reasons: 1) For most of the globe, the variability of atmospheric temperature is caused by the variability of dynamics that transport energy poleward and atmospheric longwave irradiance, which reduce the temperature anomaly in the atmosphere. 2) Albedo variability, which regulates the variability of solar irradiance input to the earth system, does not increase with time. To augment the albedo anomalies, temperature anomalies need to alter dynamical processes, which in turn can alter albedo by altering clouds. Temperature anomalies are, however, damped by dynamical processes that transport energy poleward and by longwave emission. As a result, the mean meridional temperature gradient is maintained and the mean meridional circulation is not altered by albedo anomalies on an annual time scale. If large-scale dynamics determines the global mean cloud cover, therefore, the interannual variability of the global and annual mean albedo is small.
While these results do not answer why the global and annual mean albedo is at the current value, they offer a qualitative explanation toward understanding why the interannual variation of global albedo is so small. The results also indicate that albedo variability affects atmospheric temperature variability indirectly and that the interannual variability of temperature is predominately caused by the variability of the atmospheric response of meridional and vertical energy transport to the solar forcing. These results, however, do not mean that the albedo has no trend over a long time period. As anthropogenic forcing increases, and if τ depends on forcing, the time constant τ might be altered significantly over time. When τ becomes larger and temperature anomalies persist over a long time, temperature anomalies from different anomalous processes in the atmosphere can accumulate and consequently can alter the mean temperature.
5. Conclusions
Four years of CERES data from March 2000 through February 2004 show that the difference between the maximum and minimum annual mean TOA reflected shortwave and longwave irradiances is 0.4% and 0.1% of the respective annual mean value. Clouds are mostly responsible for these variations at TOA. The largest variation in the monthly mean 1° × 1° TOA reflected shortwave and longwave irradiance occurs in the western and central tropical Pacific due to a shift from La Niña to El Niño during the period. Small global and interannual variability is a result of cancellation of larger regional anomalies when they are spatially and temporally averaged. Anomalies of 300–1000-hPa thicknesses are positively correlated with atmospheric shortwave irradiance anomalies and negatively correlated with atmospheric longwave irradiance anomalies. The 300- and 1000-hPa thickness anomalies are negatively correlated with atmospheric net irradiance anomalies, which indicate that temperature anomalies are not directly driven by shortwave irradiance anomalies. In addition, the standard deviation of 300- and 1000-hPa thickness anomalies increases with latitude. Therefore, it is postulated that 300- and 1000-hPa thickness anomalies are caused by the variability of dynamical process that transport energy poleward and by longwave emission. Because of these processes, temperature anomalies in the atmosphere decay exponentially with time and the mean meridional temperature gradient is maintained on an annual time scale. With an assumption that the global mean cloud cover depends predominately on large-scale dynamics, the exponential decay of temperature anomalies leads to a small interannual variability of global mean cloud cover and albedo.
Acknowledgments
NOAA OISST V2 data and NCEP–NCAR reanalysis-derived data were provided by the NOAA/OAR/ESRL PSD, Boulder, Colorado, from their Web site (http://www.cdc.noaa.gov/). I thank Drs. Thomas Ackerman, Alan Betts, Norman Loeb, Ehrhard Raschke, Fred Rose, Graeme Stephens, Bruce Wielicki, Takmeng Wong, Robert Woods, and Kuan-man Xu, and one anonymous reviewer for useful comments and constructive discussions. I also thank Dr. Graeme Stephens for encouraging me to work on this subject. The work was supported by the NASA Science Mission Directorate through the CERES and NASA Energy Water Cycle Study (NEWS) projects.
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Global mean TOA albedo as a function of month derived from 4 yr of CERES data taken from March 2000 through February 2004 for (a) all sky and (b) clear sky. (c) TOA longwave all-sky and (d) TOA longwave clear-sky irradiances. Vertical bars indicate the range of maximum and minimum values for the month. Horizontal dotted lines indicate the annual mean value.
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Standard deviation of the TOA (a) shortwave, (b) longwave, and (c) net (net shortwave minus longwave) irradiances as a function of month. All sky (closed circles) and clear sky (open circles). The standard deviation σtx given by (2) is computed from global 1° × 1° monthly deseasonalized anomalies over the period from March 2000 through February 2004 and averaged over the globe weighting by the area.
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Standard deviation of the TOA reflected (top) shortwave, (middle) longwave, and (bottom) net irradiances. The standard deviation σt given by (3) is computed over 1° × 1° regions based on monthly deseasonalized anomalies over 4 yr and averaged over 5° × 5° regions for plotting purposes. The TOA net irradiance is defined as the TOA net shortwave irradiance minus TOA longwave irradiance.
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Standard deviation of TOA reflected shortwave, longwave, and net irradiance anomalies as a function of latitude computed from data taken from March 2000 through February 2004 for all sky. Indicated are
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Zonal mean standard deviation of net atmospheric irradiance anomalies for March–May (MAM), June–August (JJA), September–November (SON), and December–February (DJF) computed from 1° × 1° gridded values. Indicated are
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Correlation coefficient of TOA (top) reflected shortwave, (middle) longwave, and (bottom) net atmospheric irradiance with cloud cover. Monthly values averaged over a 5° × 5° grid box are used to compute the correlation coefficient. The contour line increment is 0.2. Areas with a value greater than 0.8 for shortwave, less than −0.8 for longwave, and greater than 0.8 and less than −0.8 for the atmospheric net are shaded with a contour increment of 0.1.
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Contour of the (first row) daily mean cloud shortwave radiative effect, (second row) longwave radiative effect, and (third row) shortwave plus longwave radiative effect (net) to the atmosphere for Antarctic latitudes (60°–90°S), Southern Hemisphere midlatitudes (30°S–60°N), the tropics (30°N–30°S), Northern Hemisphere midlatitudes (30°–60°N), and Arctic latitudes (60°–90°N) as a function of the cloud optical thickness (τ) and cloud-top height in the pressure coordinate estimated from July 2002 data. Only single-layer clouds are used. (fourth row) The logarithm (base 10) of the 2D normalized histogram of cloud occurrence. Shortwave effects are converted to daily values and daily mean longwave effects are computed by weighting daytime and nighttime longwave irradiances by the number of samples.
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
Correlation coefficients between 300- and 1000-hPa thickness anomalies and atmospheric shortwave (SW), atmospheric longwave (LW), and atmospheric net [shortwave + longwave (NET)] irradiance anomalies. The coefficients are computed with 1° × 1° anomalies averaged over 1° latitudinal zone; 48 months of data from March 2000 through February 2004 are used.
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1
(a) Standard deviation σt
Citation: Journal of Climate 22, 18; 10.1175/2009JCLI2795.1