Abstract

The contribution to time-mean energetics from cloud diurnal variations is investigated. Cloud diurnal contributions to radiative fluxes follow as the differences between time-mean radiative fluxes based on diurnally varying cloud properties and those based on fixed cloud properties. Time-mean energetics under both conditions are derived from an observationally driven radiative transfer calculation in which cloud cover, temperature, and moisture are prescribed from satellite observations.

Cloud diurnal contributions to time-mean energetics arise from the nonlinear dependence of radiative fluxes on diurnally varying properties. Diurnal variations of cloud fractional coverage and solar flux are the main factors of the cloud diurnal contributions to shortwave (SW) flux, although the diurnal variation of cloud type is also important. The cloud diurnal contribution to longwave (LW) flux at the top of the atmosphere (TOA) is produced by diurnal variations of cloud fractional coverage, cloud-top height, and surface temperature. The cloud diurnal contribution to LW flux at the surface is produced by diurnal variations of cloud fractional coverage and cloud-base height. Cloud diurnal contributions to SW fluxes at the surface and TOA are much larger than the contribution to SW atmospheric absorption. The contribution to radiative heating in the atmosphere is concentrated inside the cloud layer. Its vertical profile changes sign, so the cloud diurnal contribution to atmospheric energetics is significantly larger than is implied by the column average.

Cloud diurnal contributions to SW flux at the surface and TOA are 5–15 W m−2 over continental and maritime subsidence regions, where the diurnal variation of cloud fractional coverage is large. The contributions to LW fluxes are 1–5 W m−2 over continental regions, where diurnal variations of cloud fractional coverage and surface temperature are large. A cancellation between contributions of opposite sign makes the cloud diurnal contributions to globally averaged energetics much smaller than regional contributions. However, a shift in regional climate from one dominated by high clouds to one dominated by low clouds can alter time-mean surface energetics by as much as 20 W m−2.

1. Introduction

Clouds are an integral component of the atmosphere and exist on a wide range of time and space scales. Their strong interactions with shortwave (SW) and longwave (LW) radiation alter the distribution of surface and atmospheric heating, which in turn drives atmospheric motion. Of the timescales exhibited by clouds, diurnal variations are particularly important. Most of the solar energy variance is contained in diurnal harmonics. In the Tropics, where half of that energy is absorbed, nearly all of the solar variance is diurnal.

The diurnal variation of cloud fractional coverage is large over continental convective regions and over regions of maritime subsidence (Minnis and Harrison 1984; Warren et al. 1986; Warren et al. 1988: Rozendaal et al. 1995; Bergman and Salby 1996). Furthermore, “cloud diurnal variations” (i.e., diurnal variations of cloud properties such as fractional coverage, height, and thickness) are coherent over large horizontal dimensions, which are typical of the low-frequency atmospheric variability that figures in climate (e.g., Salby et al. 1991; Bergman and Salby 1996). Thus, cloud diurnal contributions to atmospheric and surface energetics are also coherent over large horizontal dimensions and so are not eliminated by spatial averaging.

The impact of cloud diurnal variations on atmospheric energetics is observed in diurnal variations of both SW and LW flux at the “top of the atmosphere” (TOA, Harrison et al. 1988; Hartmann et al. 1991). Because of the nonlinear dependence of radiative flux on diurnally varying properties such as cloud cover, insolation, and surface temperature, cloud diurnal variations also affect the time-mean radiative energy budget. The contributions to time-mean radiative fluxes by cloud diurnal variations can affect satellite observations (Dhuria and Kyle 1990) and GCM simulations (Randall et al. 1985, 1991).

The “cloud diurnal contributions” to time-mean radiative fluxes is relevant to climate modeling studies, which focus on large spatial and temporal scales. Climate models do not resolve the small spatial scales important to cloud formation. As a result, the misrepresentation of cloud variability is a major weakness of these models (e.g., Cess et al. 1990, 1996; Cubasch et al. 1990). Furthermore, explicitly resolving diurnal variability is computationally expensive. In this context, the cloud diurnal contributions to radiative fluxes reflect an error that is introduced to the time-mean energy budget by neglecting or misrepresenting cloud diurnal variations. Rozendaal et al. (1995) estimate the error introduced to a radiative flux calculation by neglecting the diurnal variation of cloud fraction to be 3 W m−2 at the surface and TOA for a maritime subsidence location in the northeast Pacific. That error can be much larger over continental locations, where diurnal variations of cloud cover are strong.

The cloud contributions to time-mean radiative fluxes Fc are defined as the differences between time-mean fluxes with cloud radiative interactions included and those without those interactions. Corresponding to “cloud radiative forcing,” Fc measures the impact of clouds on atmospheric and surface energetics (e.g., Cess and Potter 1987; Ramanathan et al. 1989; Harrison et al. 1990; Kiehl and Ramanathan 1990; Dhuria and Kyle 1990; Randall et al. 1991; Hartmann and Doelling 1991; Ockert-Bell and Hartmann 1992; Hartmann et al. 1992; Gupta et al. 1993).

This investigation explores the contributions made by cloud diurnal variations to the time-mean energy budget in the cloud diurnal contributions to time-mean radiative fluxes Fc. Representing either SW or LW fluxes, Fc is the component of Fc that results solely from the diurnal variation of cloud properties. It follows as the difference between time-mean radiative fluxes with diurnally varying cloud properties and those with fixed cloud properties.

It is important to distinguish the contributions Fc that affect atmospheric heating directly from those that affect surface heating. Therefore, this investigation examines the cloud diurnal contributions Fc to several time-mean radiative properties: 1) The net vertical (upward minus downward) SW flux at TOA: FTOASW; 2) the net vertical SW flux at the surface: FSRFSW; 3) the net SW flux absorbed by the atmosphere:

 
FATMSW = FSRFSWFTOASW;
(1)

4) the net vertical LW flux at TOA or outgoing LW radiation (OLR): FTOALW; 5) the net vertical LW flux at the surface: FSRFLW, and 6) the net LW flux absorbed by the atmosphere:

 
FATMLW = FSRFLWFTOALW.
(2)

Also, FTOASW and FTOALW measure the cloud diurnal contribution to time-mean radiative heating of the surface plus atmospheric column. Similarly, FSRFSW and FSRFLW measure the cloud diurnal contribution to time-mean radiative heating of the surface; whereas, FATMSW and FATMLW measure the cloud diurnal contribution to time-mean radiative heating of the atmospheric column.

A radiative transfer calculation in an idealized atmosphere (section 2) illustrates how the components of Fc arise from the nonlinear dependence of radiative fluxes on diurnally varying properties and explores the cloud diurnal contributions to the vertical distribution of atmospheric heating rates. In section 3, an observationally driven radiative transfer model quantifies Fc for observed atmospheric and surface conditions. The ramifications of those results to climate and climate change are discussed in section 4.

2. Radiative transfer in an idealized atmosphere

a. Conceptual model

Because clouds can be highly reflective to SW radiation and variations in solar flux are dominated by diurnal variability, even a modest diurnal variation of cloud fractional coverage can contribute significantly to the time-mean SW flux. Consider an atmosphere comprised of two states: one cloudy with albedo Acld, and the other clear with albedo Aclr. The diurnal variation of cloud fractional coverage

 
formula

where is the time-mean fractional coverage, C1 is its diurnal amplitude or “cloud diurnal amplitude,” t is local time in hours, and δc is time of maximum cloud cover or “cloud diurnal phase,” introduces a diurnal variation of albedo:

 
formula

With the diurnally varying insolation represented by equinox conditions at the equator,

 
formula

the cloud diurnal contribution to the time-mean TOA SW flux is

 
formula

Here FTOASW is seen to depend on the cloud diurnal amplitude, the reflectivity difference between the cloudy and the clear conditions, and the diurnal phase of cloud fraction relative to that of the sun.

The nonlinear dependence of OLR on diurnally varying cloud-top temperature, cloud fractional coverage, and surface temperature leads to a cloud diurnal contribution to the time-mean TOA LW flux: FTOALW. Consider an atmosphere with diurnal variations of cloud-top temperature,

 
formula

cloud fraction,

 
formula

and surface temperature,

 
formula

Then,

 
formula

where σ is the Stefan–Boltzmann constant. Equation (10) has been expanded in powers of “relative diurnal amplitude,” diurnal amplitude normalized by the time mean. The three leading terms, which are quadratic in diurnal amplitude, are shown explicitly. The first is proportional to the diurnal amplitude of surface temperature, the diurnal amplitude of cloud fractional coverage, and the cosine of the diurnal phase of surface temperature relative to that of cloud cover. The phase dependence indicates that OLR is diminished if the time of maximum cloud cover coincides with the time of maximum surface LW emission. The second term in the expansion involves diurnal variations of cloud-top temperature and cloud fractional coverage. That term indicates that OLR is enhanced if the time of maximum cloud cover coincides with the time of maximum LW emission at cloud top, that is, with the time of lowest cloud top. The third term in the expansion is proportional to the diurnal variance of cloud-top temperature and is a consequence of the T4c dependence of cloud-top LW emission.

b. Detailed radiative transfer calculation

A detailed radiative transfer calculation in an idealized atmosphere quantifies the cloud diurnal contributions to radiative fluxes under idealized conditions. It also illustrates their role in the vertical distribution of time-mean atmospheric heating. This calculation is performed with the radiative transfer model developed for the National Center for Atmospheric Research (NCAR) community climate model (CCM2; Hack et al. 1993). That model utilizes sophisticated parameterizations for the scattering and absorption of SW radiation by ozone, water vapor, CO2, clouds, and a variety of surface types (Briegleb 1992). The calculation also utilizes parameterizations for the LW emissivity of water vapor (Ramanathan and Downey 1986), CO2 (Kiehl and Briegleb 1991), and clouds.

The idealized atmosphere involves 38 tropospheric levels between 1000 and 100 mb and five upper atmospheric levels. Tropospheric pressure increments are uniform except when clouds are present, in which case a finer pressure increment is used. Upper-atmospheric levels are positioned at 60, 30, 15, 5, and 2 mb. The near-surface air temperature is fixed at 298 K. The troposphere has a constant lapse rate of 6.5 K km−1, and the upper atmosphere is isothermal. Surface temperature is prescribed, in kelvins, to vary diurnally as

 
formula

where t is local time in hours. Relative humidity is fixed at 0.65 throughout the atmosphere. A single cloud layer is specified with constant cloud-top temperature Tc = 250 K, constant liquid water path LWP = 100 kg m−2, and diurnally varying fractional coverage

 
formula

where δc is the diurnal phase. The specified diurnal amplitudes are representative of strong diurnal variations over some continental locations.

Time-mean radiative fluxes are calculated from 24 radiative transfer calculations, one for each hour of the day, with corresponding diurnal variations of surface temperature, cloud fraction, and solar zenith angle. Time-mean fluxes are also calculated with fixed cloud properties. The cloud diurnal contributions Fc then follow as the differences between the time-mean fluxes obtained by these two calculations.

Figure 1 displays the cloud diurnal contributions to time-mean fluxes in the idealized atmosphere in terms of (a) FTOASW, (b) FATMSW, (c) FSRFSW, (d) FTOALW, (e) FATMLW, and (f) FSRFLW as functions of cloud diurnal phase δc. The cloud diurnal contribution to time-mean TOA SW flux (Fig. 1a) is as large as 17 W m−2, which is approximately 10% of the SW cloud radiative forcing at TOA in the idealized atmosphere. The sinusoidal dependence of that contribution on the phase of the diurnal variation of cloud fraction is consistent with the conceptual model (6). Here, FTOASW attains its maximum positive value (i.e., the cloud diurnal contribution cools the time-mean atmosphere–surface system) if cloud fraction maximizes at noon (δc = 12); FTOASW attains its maximum negative value if cloud fraction minimizes at noon (δc = 0); and FTOASW is 0 if cloud fraction maximizes near sunrise (δc = 6) or sunset (δc = 18). However, for those phases of cloud fraction, FTOASW is very sensitive to a change of δc. In fact, a change of diurnal phase of cloud fraction of one hour changes FTOASW by 4 W m−2. The cloud diurnal contribution to the time-mean SW flux at the surface (Fig. 1c) is comparable to that at TOA and is much larger than the contribution to the time-mean column-integrated SW absorption in the atmosphere (Fig. 1b).

Fig. 1.

The cloud diurnal contributions to time-mean (a) SW flux at TOA, (b) SW flux absorbed into the atmosphere, (c) SW flux at the surface, (d) LW flux at TOA, (e) LW flux absorbed into the atmosphere, and (f) LW flux at the surface as functions of the diurnal phase of cloud fraction in the idealized atmosphere.

Fig. 1.

The cloud diurnal contributions to time-mean (a) SW flux at TOA, (b) SW flux absorbed into the atmosphere, (c) SW flux at the surface, (d) LW flux at TOA, (e) LW flux absorbed into the atmosphere, and (f) LW flux at the surface as functions of the diurnal phase of cloud fraction in the idealized atmosphere.

The cloud diurnal contributions to time-mean LW fluxes (Figs. 1d–f) are smaller than the corresponding SW contributions, with values less than 1 W m−2. As with its SW counterpart, the dependence of FTOALW (Fig. 1d) on the diurnal phase of cloud fraction relative to that of surface temperature is consistent with the conceptual model (10). Clouds are colder than the surface and therefore emit less LW flux. So, OLR is diminished if the time of maximum cloud fraction coincides with the time of maximum surface temperature. There is no cloud diurnal contribution to time-mean LW flux at the surface (Fig. 1f) in this idealized calculation, principally because there is no diurnal variation of cloud base temperature in this calculation. However, time-mean LW surface flux can be diminished if the time of maximum cloud fraction coincides with the maximum cloud base temperature. Here FATMLW (Fig. 1e) is the difference between FSRFLW and FTOALW and is, therefore, a function of the diurnal variations of cloud fraction, cloud-top temperature, cloud-base temperature, and surface temperature.

Cloud fraction in the idealized atmosphere contains only the fundamental diurnal harmonic, but higher harmonics can also be important. Near the equator, the amplitude of the semidiurnal component of insolation is 40% of the diurnal amplitude. If the cloud diurnal variation also includes a semidiurnal amplitude that is 40% of its diurnal amplitude, the cloud semidiurnal variation contributes as much as 2.5 W m−2 to the time-mean TOA SW flux, depending on the semidiurnal phase.

Figure 2 displays the vertical distributions of cloud diurnal contributions to the time-mean atmospheric heating rates. Their vertical integrals are the column properties FATMSW and FATMLW. For clarity, the vertical extent of the cloud layer (stippled) is exaggerated. When cloud fraction maximizes at noon, SW absorption (Fig. 2a) is enhanced throughout the cloud layer, where the cloud diurnal contribution represents about 10% of the time-mean radiative heating rate (Fig. 3a) and SW absorption is reduced below the cloud. Those effects reinforce the radiative effect of a steady cloud layer (e.g., Stephens 1978; Liou 1992). Even though the cloud diurnal contribution to SW radiative heating below the cloud is only 0.1 K day−1, it represents a significant portion of FATMSW because nearly 65% of the atmosphere’s mass lies beneath the cloud layer. In fact, locating the cloud layer above 225 K makes this contribution to SW column heating larger than the contribution inside the cloud layer, which drives FATMSW negative. The change of sign of the contribution that occurs near cloud base also implies that the impact on atmospheric heating by cloud diurnal variations is greater than is suggested by the column-integrated value FATMSW alone, which is reduced by a cancellation between positive and negative contributions.

Fig. 2.

The cloud diurnal contributions to time-mean (a) shortwave and (b) longwave radiative heating rates as functions of atmospheric pressure in the idealized atmosphere. The pressure range of the cloud layer is stippled.

Fig. 2.

The cloud diurnal contributions to time-mean (a) shortwave and (b) longwave radiative heating rates as functions of atmospheric pressure in the idealized atmosphere. The pressure range of the cloud layer is stippled.

Fig. 3.

The time-mean (a) shortwave and (b) longwave radiative heating rates as functions of atmospheric pressure in the idealized atmosphere. The pressure range of the cloud layer is stippled.

Fig. 3.

The time-mean (a) shortwave and (b) longwave radiative heating rates as functions of atmospheric pressure in the idealized atmosphere. The pressure range of the cloud layer is stippled.

The cloud diurnal contribution to time-mean LW atmospheric heating rate (Fig. 2b) is confined to lower portions of the cloud layer, where cloud water strongly interacts with the diurnally varying upward LW emissions from the surface. That contribution is smaller than the cloud diurnal contribution to SW heating rate and represents only a very small fraction of the time-mean LW heating rate (Fig. 3b).

3. Observationally driven calculation

a. Input

Input to the radiative transfer calculation is now drawn from diurnal variations of cloud cover, monthly mean temperature, and monthly mean humidity statistics from the International Satellite Cloud Climatology Project (ISCCP) C2 data archive (Rossow and Schiffer 1991; Rossow and Garder 1993); C2 provides 7 years (1984–90) of monthly compiled data, binned eight times daily, with 2.5° horizontal resolution at the equator. To further improve the statistics and preserve the seasonal cycle, the C2 data is consolidated here into composite daily variations, one for each location and month of the year averaged over the time span 1985–88. This record coincides with the operational period of the Earth Radiation Budget Experiment (ERBE).

The resolution of diurnal variability by C2 suffers poleward of 40° because of limited coverage by the geostationary satellites. Consequently, this investigation is restricted to latitudes from 40°S to 40°N. As a practical matter, this restriction is not particularly limiting because cloud diurnal amplitudes are typically small in the excluded region, which represents only 36% of the global area; C2 statistics resolve the first four diurnal harmonics, all of which are utilized in the radiative transfer calculation. This is to be contrasted with calculations in section 2, which considered only the fundamental diurnal harmonic. Visible radiances from the ISCCP satellites supply cloud optical thickness.

The diurnal variation of surface temperature is obtained directly from C2, where it was derived from clear-sky IR radiance. Temperatures near the surface, at the tropopause, and at 15 mb are linearly interpolated to derive the vertical temperature profile, which is fixed. The vertical distribution of water vapor is derived from observed precipitable water and the assumption of constant relative humidity in the troposphere and constant water vapor mass mixing ratio in the upper atmosphere. Surface reflectivity is obtained from CCM2 input files (Briegleb 1992).

In the spirit of ISCCP, three cloud layers are used. The fractional coverage is specified according to C2 values for high clouds (cloud-top pressure pc < 440 mb), midlevel clouds (pc = 440–680 mb), and low clouds (pc > 680 mb). A random overlap assumption (Hartmann and Recker 1986; Tian and Curry 1989) accounts for low clouds that are obscured by midlevel and high clouds,

 
formula

and for midlevel clouds that are obscured by high clouds. In addition,

 
formula

where Clo and Cmid are the low and midlevel cloud fractions input to the calculation, and Cobslo, Cobsmid, and Cobshi are the observed fractions of low, midlevel, and high clouds, respectively. To maintain a consistent diurnal cycle, the cloud fractions used for this investigation are determined from IR observations alone. Also, C2 reports cloud fraction based on both IR and visible radiance observations, but visible data are only available during daylight hours, so the diurnal variations of those cloud fractions are biased. The height of each cloud layer is specified from the observed cloud-top temperature. The liquid water path of each cloud layer, along with cloud fraction determines the radiative effect of clouds in the CCM2 radiative transfer model (Hack et al. 1993). It is obtained from the cloud optical depth τ for each layer in ISCCP-C2 by inverting the liquid water path to SW optical depth algorithm used in the radiative transfer model.

b. Consistency with observed TOA fluxes

To validate the observationally driven radiative transfer calculation, monthly mean fluxes from the calculation are compared with those observed by scanning radiometers in ERBE (Barkstrom 1984). ERBE employs observations from a sun-synchronous and a low-inclination satellite to provide monthly mean TOA radiative fluxes at 2.5° horizontal resolution. The standard error of those fluxes is estimated at 5.5 W m−2 for SW and 3.2 W m−2 for LW (Wielicki et al. 1995).

Figure 4 displays the October mean (1985–88) fractional coverage of high clouds from 40°S to 40°N. High cloud fraction is an important climatological property that is used here to differentiate climate regimes: tropical convective regions have the largest high cloud fraction, whereas regions of subtropical subsidence have the smallest.

Fig. 4.

October-mean fractional coverage of high clouds. Contour increments are 0.1. Cloud fraction 0.1–0.3 is lightly stippled, 0.3–0.5 is heavily stippled, and larger cloud fraction is shaded.

Fig. 4.

October-mean fractional coverage of high clouds. Contour increments are 0.1. Cloud fraction 0.1–0.3 is lightly stippled, 0.3–0.5 is heavily stippled, and larger cloud fraction is shaded.

Figure 5 maps the differences between October-mean TOA fluxes produced by the observationally driven calculation and those observed by ERBE. Calculated outgoing longwave radiation (OLR) agrees with that observed by ERBE (Fig. 5a) to within 15 W m−2 at locations not shaded, where the rms difference is 5.8 W m−2. Calculated OLR is anomalously high over isolated regions of deep convection in the west Pacific. OLR observed by ERBE is anomalously high over India and Argentina, regions of continental convection.

Fig. 5.

The difference between TOA fluxes calculated by the observationally driven radiative transfer model and those observed by ERBE. Shown are the October 1985–88 (a) OLR and (b) reflected SW values. Locations where the calculated fluxes exceed ERBE fluxes by more than 15 W m−2 are shaded. Locations where the calculated fluxes are less than ERBE fluxes by more than 15 W m−2 are stippled. The anomalous flux difference at some locations (e.g., near 40°S, 150°W) follows from insufficient C2 data to complete the radiative transfer calculation.

Fig. 5.

The difference between TOA fluxes calculated by the observationally driven radiative transfer model and those observed by ERBE. Shown are the October 1985–88 (a) OLR and (b) reflected SW values. Locations where the calculated fluxes exceed ERBE fluxes by more than 15 W m−2 are shaded. Locations where the calculated fluxes are less than ERBE fluxes by more than 15 W m−2 are stippled. The anomalous flux difference at some locations (e.g., near 40°S, 150°W) follows from insufficient C2 data to complete the radiative transfer calculation.

The difference between the calculated TOA SW flux and that observed by ERBE (Fig. 5b) is larger and more extensive than that for OLR. This follows, in part, from the strong dependence of reflected SW flux on cloud properties that are difficult to determine from satellite (e.g., ice and liquid water content, effective radius of water particles, small-scale spatial distribution of clouds, etc.). Nevertheless, the calculated and observed TOA flux are within 15 W m−2 of one another over most of the globe between 40°S and 40°N, with an rms difference of 6.2 W m−2 at locations not shaded. Agreement is especially good over maritime regions, where surface optical properties are nearly uniform. Exceptional are regions in the east Atlantic and east Pacific, where cloud cover is dominated by low-level clouds. This particular discrepancy could result, in part, from the underestimation of low-cloud coverage by IR cloud detection (e.g., Rozendaal et al. 1995), which leads to underestimation of the SW reflectivity over regions dominated by low clouds.

The above comparison indicates that the relative error of calculated time-mean fluxes is less than 10%. Sensitivity tests performed with the radiative transfer calculation in the idealized atmosphere indicate that the relative uncertainty of the calculated cloud diurnal contributions to TOA fluxes should then also be less than 10%. However, the cloud diurnal contributions to surface fluxes and atmospheric absorption are somewhat more uncertain, because those contributions depend on aspects of the vertical cloud distribution that are not detected from space.

c. Cloud diurnal contributions to time-mean radiative fluxes

Maps of the diurnal amplitudes of total cloud fraction and surface temperature serve as important references for maps of the cloud diurnal contributions to time-mean radiative fluxes. The diurnal amplitude of total cloud fractional coverage (Fig. 6) is large over the subsidence regions of the eastern oceans and over many continental regions, particularly over elevated terrain. The diurnal amplitude of surface temperature (Fig. 7), which is important to the LW component of Fc, is largest over deserts and elevated terrain and smallest over maritime and continental deep convective locations.

Fig. 6.

October diurnal amplitude of total cloud fractional coverage. Contour increments are 0.02 beginning at 0.04. Diurnal amplitude 0.04–0.08 is lightly stippled, 0.08–0.12 is heavily stippled, and larger amplitude is shaded.

Fig. 6.

October diurnal amplitude of total cloud fractional coverage. Contour increments are 0.02 beginning at 0.04. Diurnal amplitude 0.04–0.08 is lightly stippled, 0.08–0.12 is heavily stippled, and larger amplitude is shaded.

Fig. 7.

October diurnal amplitude of surface temperature. Contour increments are 2 K beginning at 4 K. Diurnal amplitude 4–8 K is lightly stippled, 8–12 K is heavily stippled, and larger amplitude is shaded.

Fig. 7.

October diurnal amplitude of surface temperature. Contour increments are 2 K beginning at 4 K. Diurnal amplitude 4–8 K is lightly stippled, 8–12 K is heavily stippled, and larger amplitude is shaded.

Figure 8a maps the cloud diurnal contribution to the time-mean TOA SW flux, which has magnitudes of 5–15 W m−2. Positive values indicate that SW reflection is enhanced, so SW heating of the surface–atmosphere system must be diminished by cloud diurnal variations; FTOASW is positive over locations where cloud cover is more prominent during the day than during the night (e.g., east Africa, China, and coastal regions of South America, North America, and Australia). This situation occurs at locations where cloud cover is dominated by low cumulus clouds. The magnitude of the cloud diurnal contribution over those regions may be exaggerated because the diurnal amplitude of low-cloud fraction over continental locations is exaggerated in C2 by a diurnal variation of low-cloud detectability introduced by a strong diurnal variation of surface temperature (Bergman and Salby 1996). Extensive negative contributions occur over subsidence regions of the east Pacific and southern Indian oceans and over the deep convective areas of Indonesia, tropical South America, and tropical West Africa. All of those locations have more cloud cover at night than during the day. Despite the large diurnal amplitude of total cloud fraction over regions of maritime subsidence, the magnitude of FTOASW is smaller there than over the tropical land masses, even smaller than over regions of continental deep convection, which have small diurnal amplitudes of total cloud fraction (Fig. 6). This discrepancy results from a combination of factors. Although the diurnal amplitude of total cloud fraction over regions of continental deep convection is small, the diurnal amplitude of very reflective high clouds over those regions is large (Minnis and Harrison 1984; Bergman and Salby 1996). Thus, diurnal variations of cloud type can be as important to Fc as the diurnal variation of total cloud cover. The diurnal phase of cloud fractional coverage also plays a role. Cloud fraction maximizes near sunrise over the maritime subsidence regions, so those diurnal variations are nearly in quadrature with the solar diurnal cycle, which makes FTOASW small (cf. Fig. 1a). This is illustrated in the equatorial Atlantic, where FTOASW is less than 4 W m−2 despite diurnal amplitudes of cloud fraction greater than 0.1 (Fig. 6).

Fig. 8.

The cloud diurnal contributions to (a) upward TOA, (b) upward surface, and (c) atmospheric absorbed SW flux calculated for October. In (a) and (b), contributions of −12 to −4 W m−2 are lightly stippled, 4–12 W m−2 are heavily stippled, and greater than 12 W m−2 or less than −12 W m−2 are shaded. In (c), contributions of −3 to −1 W m−2 are lightly stippled, 1–3 W m−2 are heavily stippled, and greater than 3 W m−2 or less than −3 W m−2 are shaded.

Fig. 8.

The cloud diurnal contributions to (a) upward TOA, (b) upward surface, and (c) atmospheric absorbed SW flux calculated for October. In (a) and (b), contributions of −12 to −4 W m−2 are lightly stippled, 4–12 W m−2 are heavily stippled, and greater than 12 W m−2 or less than −12 W m−2 are shaded. In (c), contributions of −3 to −1 W m−2 are lightly stippled, 1–3 W m−2 are heavily stippled, and greater than 3 W m−2 or less than −3 W m−2 are shaded.

The cloud diurnal contributions to time-mean SW fluxes affect surface absorption more than atmospheric absorption; FSRFSW (Fig. 8b) mirrors the TOA contribution (Fig. 8a), with values of 5–15 W m−2. By contrast, FATMSW (Fig. 8c) exceeds 1 W m−2 only over continental locations. Positive values there indicate that cloud diurnal variations act to warm the atmospheric column.

Figure 9a displays the cloud diurnal contribution to TOA LW flux FTOALW, which has magnitudes of 1–3 W m−2. Here FTOALW is largest over semi-arid and elevated continental regions that have large diurnal variations of both cloud cover (cf. Fig. 6) and surface temperature (cf. Fig. 7). It is positive at locations where cloud fraction is dominated by high clouds, whose diurnal minimum coincides with the diurnal maximum of LW surface emission; FTOALW is negative at locations where cloud fraction is dominated by low clouds, whose diurnal maximum coincides with the maximum of LW surface emission (section 2). The cloud diurnal contribution to time-mean LW surface flux FSRFLW (Fig. 9b) and time-mean LW atmospheric absorption FATMLW (Fig. 9c) are largest at the same locations as FTOALW. Values of FSRFLW and FATMLW may be exaggerated at some locations because of the dependence of FSRFLW on cloud-base height, which is not detected from satellite, and the potentially exaggerated diurnal amplitude of low-cloud fraction at locations with large diurnal amplitude of surface temperature. Also, FATMLW is positive everywhere that its magnitude exceeds 1 W m−2. Because the cloud diurnal contribution to SW atmospheric absorption is also positive at these locations (Fig. 8c), the diurnal contribution to total (LW plus SW) atmospheric absorption is positive with values 2–5 W m−2.

Fig. 9.

The cloud diurnal contributions to (a) upward TOA, (b) upward surface, and (c) atmospheric absorbed LW flux calculated for October. Contributions of −3 to −1 W m−2 are lightly stippled, 1–3 W m−2 are heavily stippled, and greater than 3 W m−2 or less than −3 W m−2 are shaded.

Fig. 9.

The cloud diurnal contributions to (a) upward TOA, (b) upward surface, and (c) atmospheric absorbed LW flux calculated for October. Contributions of −3 to −1 W m−2 are lightly stippled, 1–3 W m−2 are heavily stippled, and greater than 3 W m−2 or less than −3 W m−2 are shaded.

The SW contributions at the surface and TOA, which are as large as 20 W m−2 at particular locations, are ∼1 W m−2 in the global average. The globally averaged cloud diurnal contribution to SW absorption in the atmosphere is even smaller, as are the LW contributions. These small global averages follow, in part, from a cancellation of positive and negative regional contributions that, in turn, result from the different diurnal phases of cloud fraction in different climate regimes.

4. Conclusions

The cloud diurnal contributions to time-mean SW flux at the surface and TOA are as large as 20 W m−2 locally. Those contributions follow from the cloud-induced diurnal variation of atmospheric reflectivity, which arises primarily from the diurnal variation of cloud fractional coverage and, to a lesser degree, from the diurnal variation of cloud type. The dependence of SW contributions on cloud diurnal phase leads to a difference in sign of those contributions for daytime versus nighttime cloud cover. It also leads to small contributions over maritime regions, where the diurnal variation of cloud fractional coverage is nearly in quadrature with the solar diurnal cycle. The same factor makes the SW contributions sensitive to changes of cloud diurnal phase at maritime subsidence locations. Cloud diurnal variations influence time-mean SW absorption at the surface more than in the atmosphere. Most of that influence arises from the first harmonic of cloud diurnal variations, although the contribution from the second diurnal harmonic of cloud fractional coverage can contribute another 1–3 W m−2.

Cloud diurnal contributions to time-mean LW flux at the surface and TOA are smaller than the SW contributions, typically 1–5 W m−2 over locations with strong diurnal amplitudes of both cloud fractional coverage and surface temperature. The contribution to time-mean LW absorption in the atmosphere is also 1–5 W m−2 and, at humid locations, can be larger than the contribution to LW surface absorption.

Cloud diurnal contributions to radiative heating rates change sign in the vertical. Therefore, the column-integrated contributions on which this article focuses underestimate the local contributions to time-mean atmospheric heating. Furthermore, cloud diurnal variations are spatially coherent, so the cloud diurnal contributions to time-mean radiative fluxes are uniform over large horizontal regions. Consequently, those contributions are not eliminated by spatial averaging and are, therefore, important to regional energetics.

Results here have implications for climate modeling studies. In this context, the cloud diurnal contributions to time-mean radiative fluxes reflect an error introduced into the time-mean energy budget by neglecting or misrepresenting cloud diurnal variations. The importance of properly representing cloud diurnal variations depends on what climate regime is being modeled. For example, in maritime subsidence locations, where cloud fraction maximizes near sunrise, miscalculating the diurnal phase by only an hour or two leads to an error in the time-mean energy budget that is larger than neglecting cloud diurnal variations altogether.

Diurnal variations of cloud cover are characteristic of specific climatological conditions (Bergman and Salby 1996), with amplitude and phase determined by time-mean properties such as cloud fractional coverage, cloud height, surface temperature, and surface type. It follows that cloud diurnal contributions to time-mean energetics are also characteristic of specific climatological conditions. Therefore, the cloud diurnal contributions to time-mean energetics can, in principle, be determined from time-mean climatological properties, and then absorbed into the net cloud contributions to time-mean radiative fluxes. This may enable the effect of diurnal variations to be modeled without explicitly resolving those variations.

The cloud diurnal contributions to time-mean energetics varies sharply between regions of different climatological properties. For this reason, a change in climatological properties induced, for example, by a shift in climate can produce a substantial change in the cloud diurnal contributions to regional energetics. For instance, Cutrim et al. (1995) report that deforestation in the Amazon basin leads to a change of cloud cover from predominantly high clouds, for which FSRFSW ∼ −10 W m−2, to predominantly low clouds, for which FSRFSW ∼ 10 W m−2. That change results in a 20 W m−2 change of the local cloud diurnal contribution to the time-mean SW surface flux, which is equivalent to a change in surface albedo of 0.05.

Acknowledgments

This work owes its success, in part, to discussions with and contributing ideas by Bruce Briegleb, Judith Curry, Harry Hendon, Peter Webster, Charles Zender, and anonymous reviewers.

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Footnotes

* Current affiliation: Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado.

Corresponding author address: Dr. John W. Bergman, CIRES/CDC Campus Box 449, University of Colorado, Boulder, CO 80309-0449.