## Abstract

Interannual variability of the global radiation budget, regions that contribute to its variability, and what limits albedo variability are investigated using Clouds and the Earth’s Radiant Energy System (CERES) data taken from March 2000 through February 2004. Area-weighted mean top-of-atmosphere (TOA) reflected shortwave, longwave, and net irradiance standard deviations computed from monthly anomalies over a 1° × 1° region are 9.6, 7.6, and 7.6 W m^{−2}, respectively. When standard deviations are computed from global monthly anomalies, they drop to 0.5, 0.4, and 0.4 W m^{−2}, respectively. Clouds are mostly responsible for the variation. Regions with a large standard deviation of TOA shortwave and longwave irradiance at TOA are the tropical western and central Pacific, which is caused by shifting from La Niña to El Niño during this period. However, a larger standard deviation of 300–1000-hPa thickness anomalies occurs in the polar region instead of the tropics. The correlation coefficient between atmospheric net irradiance anomalies and 300–1000-hPa thickness anomalies is negative. These indicate that temperature anomalies in the atmosphere are mostly a result of anomalies in longwave and dynamical processes that transport energy poleward, instead of albedo anomalies by clouds directly affecting temperature anomalies in the atmosphere. With simple zonal-mean thermodynamic energy equations it is demonstrated that temperature anomalies decay exponentially with time by longwave emission and by dynamical processes. As a result, the mean meridional temperature gradient is maintained. Therefore, mean meridional circulations are not greatly altered by albedo anomalies on an annual time scale, which in turn provides small interannual variability of the global mean albedo.

## 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

The 48 months of reflected shortwave and longwave irradiances at TOA estimated from observed CERES broadband radiances from March 2000 through February 2004 were used in this study. TOA reflected shortwave and longwave irradiances were from a CERES data product, the Single Scanner Footprint (SSF) edition 2B (Ed2B). The rev1 correction (Matthews et al. 2005) was applied to account for a small drift of shortwave CERES instrument calibrations. Surface shortwave and longwave irradiances used in this study to estimate atmospheric irradiances were from a CERES data product, Clouds and Radiative Swath (CRS) Ed2B. Forty-eight months of surface irradiances starting from March 2000 were also used. The instantaneous TOA and surface shortwave irradiances were converted to a daily value with the assumption that meteorology does not change over the course of a day. The conversion process is described in Kato et al. (2008). The daily value of the longwave irradiance is simply the mean of daytime and nighttime values weighted by the day–night fraction of a given day. Daily mean shortwave and longwave irradiances were averaged over a 1° × 1° grid box and over 1 month. The monthly mean value computed from 4 months of was then subtracted from each month value *F*(*t*, *x*) to obtain a deseasonalized anomaly (hereafter anomaly) Δ*F*,

where *t* and *x* indicate that the irradiance is a function of time (month) and location (1° × 1° grid), respectively. The standard deviation of Δ*F*(*t*) for given *x* was computed as the measure of the interannual variability of the shortwave or longwave irradiances for the region. In the following section, we investigate the standard deviation of these deseasonalized anomalies. Note that the uncertainty in the absolute calibration of CERES instruments (Loeb et al. 2009) does not affect the variability estimate unless the calibration shifts with time. A study by Loeb et al. (2007b) indicates that the stability of CERES shortwave instruments on *Terra* is approximately within 0.3 W m^{−2} decade^{−1}. The uncertainty associated with the conversion of instantaneous irradiance to daily mean with a constant meteorology assumption is discussed in Kato et al. (2008). Briefly, if the uncertainty in the accuracy is defined as the difference between modeled and observed irradiances, the uncertainty in the daily mean downward shortwave irradiance at the surface is 7.8% and the downward longwave irradiance at the surface is 1.1%. The uncertainty in the net atmospheric shortwave irradiance is 16.1%, the net atmospheric longwave irradiance is 4.4%, and the net atmospheric irradiance is 10.8%. Similar to TOA irradiances, however, the stability of the surface and atmospheric irradiances is expected to be better than these uncertainties.

## 3. Result

### a. Global TOA irradiance variability

The area-weighted global annual mean TOA all-sky albedo (the global annual mean TOA upward shortwave irradiance divided by the global annual mean downward shortwave irradiance) is 0.283, while the clear-sky albedo counterpart is 0.171 (Fig. 1). These correspond to the TOA reflected shortwave irradiance of 96.8 W m^{−2} for all-sky conditions and 58.5 W m^{−2} for clear-sky conditions, respectively. Similarly, the area-weighted global annual mean TOA all-sky longwave irradiance is 239 W m^{−2} and the clear-sky value is 267 W m^{−2}. The all-sky TOA reflected shortwave (longwave) irradiance is significantly larger (smaller) than the clear-sky value, and it is 36 W m^{−2} larger (23 W m^{−2} smaller) than the clear-sky maximum TOA reflected shortwave (minimum longwave) irradiance of 60.8 (262) W m^{−2} during the period. To show the variability difference under all-sky and clear-sky conditions, the area-weighted mean standard deviations from global 1° × 1° TOA reflected shortwave, longwave, and net (TOA net shortwave minus TOA longwave) irradiance anomalies are plotted as a function of month (Fig. 2). The standard deviation for a given month is computed by

where *w _{i}* is the area weight,

*n*is the number of months used in the study for a given month of a year, and

_{m}*m*is the number of 1° × 1° regions over the globe. Figure 2 shows, therefore, a typical 1° × 1° variation of the TOA reflected shortwave, longwave, and net monthly anomalies as a function of month. Note that the TOA net irradiances are defined as the TOA downward shortwave irradiance minus the TOA reflected shortwave minus the TOA longwave irradiance. Note also that computed clear-sky irradiances with all-sky atmospheric conditions were used in Fig. 2 to minimize the effect of atmospheric properties other than clouds and make the number of clear-sky samples equals to the number of all-sky samples. When the TOA reflected shortwave, longwave, and net irradiance standard deviations from 1° × 1° regions are averaged over a year, they are 9.6, 7.6, and 7.6 W m

^{−2}, respectively. The standard deviation of the TOA reflected shortwave, longwave, and net irradiance under clear-sky conditions is 3.4, 3.2, and 4.6 W m

^{−2}, respectively. Clouds, therefore, increase the standard deviation of TOA reflected shortwave and longwave anomalies by more than a factor of 2. Because there is a significant anticorrelation between TOA reflected shortwave and longwave cloud radiative effects (Kiehl 1994), an increase of the TOA net irradiance standard deviation by clouds from the clear-sky value is smaller, ≈65%, when it is averaged over a year.

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 48 anomalies over a 1° × 1° region *x* was computed by

where *n* (=48) is the number of months. The map of *σ _{t}* is shown in Fig. 3. Larger standard deviations of 1° × 1° TOA monthly reflected shortwave irradiance anomalies occur over the tropical western and central Pacific, the eastern Pacific, the tropical Indian Ocean, Europe, eastern Asia, and parts of North and South America regions (Fig. 3a). While standard deviations over storm-track regions—the northwest Pacific and the northwest Atlantic Ocean—are smaller than that in the tropical western Pacific, the mean TOA reflected shortwave irradiance over the northern Pacific storm-track region is larger than that over the tropical western Pacific; the annual mean TOA reflected shortwave irradiance over the northern Pacific is approximately 140 W m

^{−2}compared to the approximately 100 W m

^{−2}over the tropical western Pacific. Significant standard deviations of TOA reflected shortwave anomalies are caused by disturbances that last more than 1 month and occupy a larger part of a 1° × 1° grid box. Such anomalies involve an ocean system because a typical midlatitude frontal system moves of the order of 10 m s

^{−1}, which takes a few days to move 1000 km. The variability resulting from the synoptic system, therefore, mostly cancels when the TOA reflected shortwave irradiance is averaged both over 1 month and a 1° × 1° region. This is apparent in Fig. 3; large standard deviations occur predominantly over the oceans. Anomalies resulting from ENSO persist for more than 6 month or longer (Trenberth 1997). The Multivariate ENSO Index (Wolter and Timlin 1998) changed from negative to positive during the period from March 2000 through February 2004, indicating that the tropical Pacific Ocean was changed from La Niña to El Niño. Therefore, ENSO is responsible for large standard deviations over the tropical western Pacific during this period.

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.

We further separate the atmosphere from the surface and analyze the contribution of clouds to the variability of the net atmospheric irradiance to understand the cloud radiative effect on the variability of atmospheric energy deposition. The atmospheric net irradiance *F*_{atm,net} is the TOA net irradiance minus surface net irradiance,

where subscripts toa, sfc, sw, and lw indicate, respectively, the top of atmosphere, surface, shortwave irradiance, and longwave irradiance, and superscripts up and dn indicate, respectively, upward and downward. The atmospheric net irradiance *F*_{atm,net} is also the sum of the atmospheric shortwave irradiance *F*_{atm,sw} and atmospheric longwave irradiance *F*_{atm,lw}, where

and

Figure 4 shows the standard deviation of TOA irradiances as a function of latitude, and Fig. 5 shows the standard deviation of atmospheric net irradiances as a function of latitude for all-sky and clear-sky conditions. The standard deviation is computed in two different ways. The first value, which is shown by solid lines in Figs. 4 and 5, was computed from 1° × 1° anomalies for a given latitudinal zone and averaged over *n* months, such that

where *m _{z}* is the number of 1° × 1° regions for a given 1° zone. This standard deviation provides a mean standard deviation of 1° × 1° region within a latitudinal zone. The second value, which is shown by dashed lines in Figs. 4 and 5, was computed from 4 yr of monthly zonal anomalies such that,

which provides the temporal variation of zonal anomalies. A smaller *σ*_{tx} than indicates that 1° × 1° anomalies move along the longitude or 1° × 1° anomalies are partially canceled when anomalies are averaged along the longitude. Figure 5 also indicates that clouds increase the standard deviation of the atmospheric net irradiance in a latitudinal zone at all latitudes for all seasons. The implication of this increasing variability to atmospheric energy transport is following. Because eddy potential energy is generated by increasing the standard deviation of atmospheric temperature for a given latitudinal zone (Lorenz 1955; Peixoto and Oort 1992), a larger standard deviation of 1° × 1° anomalies in a given latitudinal zone under all-sky conditions than that under clear-sky conditions suggests that clouds increase the generation of eddy potential energy.

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 *σ*_{tx} than over the tropics, shown in Figs. 4 and 5, agrees that warm water predominantly moves longitudinally in the tropics. In addition, according to National Oceanic and Atmospheric Administration (NOAA) Optimum Interpolation SST version 2 (Reynolds et al. 2002), the mean sea surface temperature of tropical Pacific Ocean (30°N–30°S, 120°E–105°W) averaged over the 4-yr period (March 2000–February 2004) is 25.6°C and the standard deviation of monthly mean values is 0.16°C. Therefore, the standard deviation of TOA reflected shortwave and longwave irradiances over tropical Pacific is predominately due to shifts of warm seawater along the longitude.

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.

In the remaining part of this section, using zonal mean momentum and thermodynamic energy equations, we investigate whether or not the energy of the atmosphere explains a small interannual variability of the cloud cover. In the following, albedo variability is treated as variability in forcing to the system. In addition, a basic assumption is that large-scale dynamics that transports energy poleward as a response to the forcing depends on the meridional temperature gradient, which in turn controls the global mean cloud cover and albedo. The zonal mean momentum and thermodynamic energy equations for quasigeostrophic motions on the midlatitude *β* plane are (Holton 1992, 369–371)

where *u*, *υ*, and *w* are the zonal, meridional, and vertical components of wind, *f*_{0} is the Coriolis parameter, *T* is the temperature, *N* is the buoyancy frequency, *H* is the depth of the atmosphere, *R* is the gas constant, *X* is the drag force, *J*/*c _{p}* is the diabatic heating, and

*y*increases toward the north. The overbar indicates the zonal mean and the prime indicates the deviation from the mean along the longitude. The diabatic heating term is composed of

where *F*_{atm,sw} and *F*_{atm,lw} are atmospheric shortwave and longwave irradiance, *F*_{sh} is the sensible heat flux from the surface, and *F*_{precip} is the latent heat of vaporization multiplied by the mean precipitation rate.

We start with the zonal mean thermodynamic energy Eq. (10), and apply the equation to monthly mean values. We then separate each term into the climatological monthly mean and anomaly. We assume that climatological means and anomalies both satisfy (10) separately. We also assume that the vertical motion anomaly is proportional to the temperature anomaly,

and the advection anomaly is proportional to the second derivative of temperature anomaly with respect to *y*,

The sign of *D* is positive but *C* can be positive or negative depending on the correlation between and . In addition, we separate the diabatic term into two parts—the portion that is linearly related to the temperature anomaly and the residual that is treated as a forcing. The longwave anomaly is related linearly to the temperature anomaly,

where the negative sign indicates that the atmospheric longwave irradiance has a cooling effect. Atmospheric shortwave irradiance, latent heat, and sensible heat anomalies are treated as forcing so that the diabatic anomalies are expressed as

where is the forcing term. The forcing term can also include diabatic heating that is not related to the temperature anomaly directly, such as the direct aerosol radiative forcing. The coefficient *a* is negative because the atmospheric longwave irradiance dominates in the first term on the right-hand side. The anomalies equation of (10) then becomes

If we assume that the system is forced by

then that satisfies (16) is

where

here, is the temperature anomaly at *t* = 0, and *λ*^{2} is a positive constant determined by boundary conditions. The forcing term can have more terms, composed with a Fourier series, but the result discussed below does not change by this simplification.

Because *D* > 0, *ω* > 0, and *Dk*^{2} − *C* − *a* is likely to be positive (unless *k* is small and *C* + *a* is a large positive number), both cos*ϕ* and sin*ϕ* are positive. Therefore, we expect that is positively correlated with the forcing term . The phase shift increases and the correlation decreases as the ratio of *ω* to *Dk*^{2} − *C* − *a* increases. We also expect that the correlation between the temperature and longwave anomalies is negative because of (14).

Figure 8 shows the correlation coefficient between the anomalies of the geopotential height difference at 1000- and 300-hPa , and , , and as a function of latitude. The geopotential height is derived from the National Centers for Environmental Prediction–National Center for Atmospheric Research (NCEP–NCAR) reanalysis (Kalnay et al. 1996). Geopotential height anomalies represent temperature anomalies in the atmospheric column. The correlation is computed with monthly 1° × 1° anomalies. The correlation coefficient between and is mostly negative and the correlation coefficient between and is mostly positive. The correlation coefficient between and is negative and the shape resembles the correlation coefficient between and . Negative correlations between and Δ*F*_{net} indicate that the first term in (18) dominates, and decays exponentially with time. Because the variation of the diabatic heating is predominately associated with the variation of clouds, this implies that the effect of cloud variation on the temperature anomaly decays exponentially with time. The time constant *τ* for the exponential decay is −1/(*a* + *C* − *Dλ*^{2}). If *τ* is small, anomalies are damped quickly so that monthly anomalies might be small. If *τ* is much longer and variable, the interannual variability of the albedo would be larger. Apparently, the actual value of the time constant *τ* is to give significant monthly anomalies but small global interannual variability.

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 is associated with a positive , *C* would be positive, which reduces *τ*. A possible case that gives a positive correlation between Δ*F*_{sw} and Δ*T* is increasing low-level clouds with increasing atmospheric temperature. Low-level clouds increase the atmospheric shortwave irradiance (shortwave absorbed in the atmosphere) by increasing the pathlength of photons (Fig. 7). Low-level clouds, however, give more negative value of atmospheric longwave irradiance (Fig. 7). A more negative atmospheric longwave irradiance over subtropical region is often associated with stronger subsidence because stronger subsidence pushes the low-level cloud top down, which leads to a larger longwave cooling (Fig. 7). A stronger subsidence gives a larger adiabatic warming in the atmospheric column (Betts and Ridgway 1989), which leads to a negative *C*. Depending on the balance of Δ*F*_{atm,sw}, Δ*F*_{atm,lw}, Δ*F*_{sh}, Δ*F*_{precip}, and changes in the adiabatic warming by subsidence, the value of *a* + *C* can, therefore, vary significantly.

The above results indicate that albedo variability does not drive temperature anomalies in the atmosphere directly and that temperature anomalies in the atmosphere decay exponentially with time. To understand the impact of the cloud radiative effect on general circulations, following Holton (1992, 369–371), we multiply (9) by *f*_{0} and take a derivative with respect to *z*, (10) by *R*/*H* and take a derivative with respect to *y*, and add the resulting equations to obtain

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*/(*Hc _{p}*)∂

*J*/∂

*y*is negative. Because of warming in the tropics and cooling in polar regions, clouds increases the meridional energy transport in the midlatitude and polar regions (Zhang and Rossow 1997; Kato et al. 2008). Meridional energy transport by eddies is a convex function of latitude (Peixoto and Oort 1992). If we assume that the cloud radiative effect on the meridional energy transport is also a convex function and has a maximum somewhere in the midlatitude or polar regions, ∂

^{2}()/∂

*y*

^{2}is negative. The atmospheric cloud radiative effect almost linearly decreases with latitude (Kato et al. 2008) so that the cloud radiative effect on

*R*/

*H*∂/∂

*y*() is small. The cloud effect on

*N*

^{2}∂

*w*/∂

*y*is also negative because increasing

*w*by clouds decreases with latitude. Therefore, if we assume clouds predominately affect temperature and upward velocity, (21) suggest that the cloud effect on the diabatic heating

*R*/(

*Hc*)∂

_{p}*J*/∂

*y*is compensated by two terms, ∂

^{2}()/∂

*y*

^{2}and

*N*

^{2}∂

*w*/∂

*y*. Therefore, if we assume that clouds predominantly affect the temperature and vertical velocity, the cloud radiative effect on the atmospheric temperature is partially canceled by meridional and vertical energy transport by dynamics. Recall that clouds increase the standard deviation of net irradiance in a latitudinal zone (Fig. 5), which can consequently increase meridional energy transport in the atmosphere by eddies, and clouds alter radiation field in a way that radiative anomalies can be compensated by energy transport by dynamics. In other words, the coefficient

*D*in (18) increases with the cloud radiative effect and the temperature anomalies generated by clouds decay exponentially. As a result, thermal wind balance is not altered on the annual time scale.

Figures 9a,b show and *σ*_{tx} from Δ*F*_{atm,sw}, Δ*F*_{atm,lw}, and Δ*F*_{atm,net}. While , which is a mean 1° × 1° standard deviation within a latitudinal zone, is large over the tropics (Fig. 9b), *σ*_{tx}, which is a mean zonal standard deviation, is smaller than and is nearly constant with latitude, except for the polar regions (Fig. 9a). We also computed and *σ*_{tx} from 300- to 1000-hPa thickness anomalies for the same period. Unlike irradiances, *σ*_{tx} and computed from 300- to 1000-hPa thickness anomalies are about the same magnitude. In addition, both *σ*_{tx} and increase with latitude, which is different in shape from those computed with irradiance anomalies. Figure 9 indicates that atmospheric irradiance anomalies, especially atmospheric shortwave irradiance anomalies, are not direct driver of atmospheric temperature anomalies in the midlatitude and polar regions. Instead, based on the above results, it is postulated that temperature anomalies in the midlatitude and polar regions are the result of the variability in energy transport from tropics to polar regions.

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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## Footnotes

*Corresponding author address:* Seiji Kato, Mail Stop 420, NASA Langley Research Center, Hampton, VA 23681-2199. Email: seiji.kato@nasa.gov