Five years of measurements from the Earth Radiation Budget Satellite (ERBS) have been analyzed to define the diurnal cycle of albedo from 55°N to 55°S. The ERBS precesses through all local times every 72 days so as to provide data regarding the diurnal cycles for Earth radiation. Albedo together with insolation at the top of the atmosphere is used to compute the heating of the Earth–atmosphere system; thus its diurnal cycle is important in the energetics of the climate system. A principal component (PC) analysis of the diurnal variation of top-of-atmosphere albedo using these data is presented. The analysis is done separately for ocean and land because of the marked differences of cloud behavior over ocean and over land. For ocean, 90%–92% of the variance in the diurnal cycle is described by a single component; for land, the first PC accounts for 83%–89% of the variance. Some of the variation is due to the increase of albedo with increasing solar zenith angle, which is taken into account in the ERBS data processing by a directional model, and some is due to the diurnal cycle of cloudiness. The second PC describes 2%–4% of the variance for ocean and 5% for land, and it is primarily due to variations of cloudiness throughout the day, which are asymmetric about noon. These terms show the response of the atmosphere to the cycle of solar heating. The third PC for ocean is a two-peaked curve, and the associated map shows high values in cloudy regions.
The weather–climate system of Earth is a dynamic system driven by the absorption of sunlight and emission of outgoing longwave radiation. The diurnal cycle of energy into the Earth–atmosphere system is the driver for other diurnal processes. Defined as the fraction of sunlight reflected by Earth, albedo is a useful parameter for defining the diurnal cycle of energy input to the system. A knowledge of the diurnal cycle of Earth is required to compute accurately the diurnal heating of Earth by the sun. Also, one very useful way to study a dynamical system is to observe its response to a cyclical forcing.
The objective of this paper is to define the diurnal cycle of albedo over the portion of Earth that was observed by the Earth Radiation Budget Satellite, that is, 55°N to 55°S. The approach is to compute the principal components (PCs) that describe the temporal variations of the diurnal cycle and their associated empirical orthogonal functions (EOFs) that describe the corresponding spatial variations of the diurnal cycle of albedo. These PCs and EOFs have the advantage that they resolve the diurnal variations into components that often can be understood in terms of the physical processes that create the variations of albedo.
The Earth Radiation Budget Experiment (ERBE; Barkstrom and Smith 1986) included a set of radiation budget instruments aboard the Earth Radiation Budget Satellite (ERBS) in an orbit with a 57° inclination (Harrison et al. 1983). This orbit precessed through all local hours every 72 days, thereby producing measurements from which to study the diurnal variations of outgoing longwave radiation and albedo. This scanning radiometer operated for 5 years, providing the dataset that is the basis of this study.
2. Diurnal variations of albedo
Diurnal variations of albedo are caused by the change of solar zenith angle with time of day and by changes of the atmosphere and surface through the day, primarily variations in cloudiness due to diurnal or synoptic processes (Rutan and Smith 1997). Minor diurnal variations of surface albedo have also been found (Minnis et al. 1997). The resulting variation of solar radiation that is absorbed by the atmosphere and surface creates a cyclical input of energy into the system. The diurnal cycle of outgoing longwave radiation is concomitant with the diurnal cycle of heating. Harrison et al. (1988) and Smith and Rutan (2003) used the ERBE dataset to investigate the diurnal variations of outgoing longwave radiation.
The variation of albedo with solar zenith angle is modeled by use of a factor called a directional model (Suttles et al. 1988), which depends on scene type. The solar zenith angle can be computed precisely for a given location and time (Sellers 1965). The scene type is cloud for about half the planet and clouds have strong diurnal cycles over much of Earth. In many regions of the globe the clouds have diurnal cycles, such as morning cloudiness that clears by afternoon. Conversely, some regions have clear mornings with afternoon cloudiness. Research into the diurnal cycle of clouds often categorized clouds by their morphology (high or low clouds) (Bergman and Salby 1996; Rozendaal et al. 1995). The top-of-atmosphere (TOA) albedo cannot be similarly divided as it represents the integrated value of irradiance reflected by both the surface and atmosphere including clouds at all levels.
The diurnal variations of albedo are also important to the measurement of Earth's radiation budget. To determine the radiation budget of Earth, one measures the sunlight reflected by the Earth–atmosphere system (Raschke et al. 1973). For an instrument in a sun-synchronous orbit, this measurement is taken at one time of day. Thus, to compute the total solar radiation reflected by the Earth–atmosphere system, one must account for the variation of albedo with local time of day (Brooks et al. 1986; Doelling et al. 2013).
Hendon and Woodberry (1993) studied the diurnal cycle of convective clouds in the tropics using International Satellite Cloud Climatology (ISCCP) data and found significant diurnal cycles of convection occur primarily over landmasses. When it does occur, oceanic convection has its maximum intensity in early morning. Over equatorial Africa, convection is very strong, with maximum intensity just after noon. Rozendaal et al. (1995) studied the diurnal cycles of marine stratiform clouds. They too used ISCCP data, but also included extensive work in comparing the ISCCP data with cloud observations from dedicated weather ships and ships of opportunity. They found low-cloud-cover maxima occur in early morning over almost all oceanic regions. This timing of the cloud maximum and dissipation has a major effect on the heating of the Earth–atmosphere system since insolation is low when the albedo is maximum and high when the clouds have gone and the ocean is quite dark.
Bergman and Salby (1996) used ISCCP data to investigate the diurnal cycle of clouds between 40°N and 40°S. They used four categories for their study of clouds: marine convective, marine nonconvective, land convective, and land nonconvective clouds and partitioned the globe into regions within which one category dominated. They found that each category was characterized by ranges of amplitude and phases of the diurnal and semidiurnal cycles of high or low clouds. Taylor (2012) used Clouds and the Earth’s Radiant Energy System (CERES) data to study the diurnal cycle of tropical outgoing longwave radiation (OLR) and longwave cloud forcing. Though not a direct measure of albedo, the cycle of OLR is related to that of albedo because decreased OLR in the tropics implies high cloud, which indicates high albedo.
Kondragunta and Gruber (1994) used ISCCP data to study the diurnal cycle of cloudiness over the globe for January. They found a cycle over continents of clear mornings and afternoon cloudiness. This cycle was described by the first PC (PC-1) and accounted for 52% of the variance. PC-2 was a mirror image about noon of PC-1 and explained 26% of the variance. The diurnal cycle of cloudiness over ocean deep convective regions is expressed by PC-2.
Figure 1 shows the 5-yr summer-mean TOA albedo in two regions, similar to those considered by the above noted papers. Comparing the eastern Pacific Ocean marine stratocumulus region (37°N, −130°W) one can see a shape that is similar to that shown in Fig. 8 of Minnis and Harrison (1984), where they find a minimum in cloud fraction between 1300 and 1500 local time. A different effect can be found in a marine convective region (15°N, −170°W) where the minimum albedo is found early in the morning between 0800 and 0900 local time. Thus under the right conditions TOA albedo might serve as a proxy for cloud type, but with the extreme variability of clouds there is no unique relation between the diurnal cycles of cloud fraction and TOA albedo. Thus we do not attempt to separate albedo as a function of cloud morphology, optical depth, etc. Instead, we infer the cloud effects on albedo based on the principal components and associated empirical orthogonal functions resulting from the analysis of the radiance measurements.
3. Data and method
The ERBS dataset is the only dataset covering a complete year from a broadband radiometer that precessed through all local times in a season, until now. The CERES ProtoFlight Model (Wielicki et al. 1996) flew aboard the Tropical Rainfall Measuring Mission (TRMM) in a precessing orbit with inclination of 35°. However, it operated from January to August 1998, which is insufficient to add significantly to the ERBS dataset. The Scanner for Radiation Budget (ScaRaB)-3 instrument was placed in orbit aboard the Megha-Tropiques spacecraft in September 2011 (Trémas et al. 2012) and data products are becoming available. This satellite observes the tropics between 20°N and 20°S.
ERBE data are processed (Barkstrom et al. 1989) for 2.5° × 2.5° regions for a number of variables, including albedo, in terms of local hour box and day of the year in the S-9 data product. They are available at the Langley Atmospheric Sciences Data Center. Five years of ERBS data were used for this investigation. Diurnal variations of albedo may be expected to change with season. The spacecraft orbit precessed through all local times of the day every 72 days so that the data are well suited for partitioning into seasons, which were defined as northern winter [December, January, and February (DJF)], northern spring [March, April, and May (MAM)], northern summer [June, July, and August (JJA)], and northern autumn [September, October, and November (SON)]. Data were analyzed within the domain between 55°N and 55°S for a total of 6336 2.5° × 2.5° regions. Sampling patterns for two regions (40°N, 100°E and 35°S, 60°W) are shown in Fig. 2 for the 5-yr, 3-month spring sampling. The top panels of Fig. 2 show individual TOA albedo observations and the precession of the orbit across local time. The middle panels show the cumulative distribution within each hour box, and the bottom panels show the resultant TOA albedo curves. Sampling is sparsest near sunrise and sunset.
Two basic problems arise when attempting to use an EOF analysis on TOA albedo; namely, the albedo is undefined at night and the length of the day varies as a function of latitude. Initially, for each region, the mean of the albedo observations was computed for each local hour box of each season to average out the synoptic variations (see Fig. 2). The daily-mean albedo was computed for each region and season and subtracted from the hour-box albedo to give a vector with 24 components giving the diurnal variations for each hour box so that the albedo variation vector for each region was a single realization. The covariance matrix of diurnal variations was then computed. Because of the decrease of regional area with increasing latitude, the contribution of each region to the covariance was area weighted (Buell 1978; Smith et al. 1990). The results of this initial computation were unsatisfactory because many PCs were required to describe the albedo variation due to the variation of length of day with latitude. The results were primarily an artifact of the time-coordinate system (the hour boxes). Pictorially this is seen in Fig. 3, which shows the solar terminator for a typical Northern Hemisphere winter day. The solid horizontal lines indicate the limits of the ERBS data, between 55°N and 55°S; thus there are no latitudinal zones that are either completely day or completely night. However, length of day still varies significantly by latitude, retaining the previously mentioned problems. To account for this effect we reproject the observations to a new time-coordinate system that is uniform regardless of latitude. To do this, first the time t of each observation is measured from noon and normalized as
where TD is the length of daylight. Thus, u is between −1 at sunrise and 1 at sunset. The middle portion of Fig. 3 shows this renormalization. The second step is to regrid the data. Though the number of new time boxes is arbitrary, 12 was a reasonable choice in that it allowed for those latitude bands with 12-h days (near the equator) to maintain the same sample pattern across time. The final placement of the hypothetical measurement (M) is shown in the final plot of Fig. 3.
The diurnal covariance matrix was computed as
where yi(u) is the 12-component diurnal albedo variation vector for the ith region, Ai is the area of the ith region of the domain D, and Ti is the weight associated with variation in the length of day for that grid box. The u is the normalized time and has 12 values. The eigenvectors of the diurnal covariance matrix are the principal components that describe the variation of albedo with local time. These PCs are used to compute the EOFs, each of which is a map of the domain. The procedure is the same as used by Smith and Rutan (2003). All results in this paper are based on this formulation of the problem.
The mean albedo for region x at normalized time u can thus be expressed as
where is the diurnal-mean map of albedo; EOFp(x) is the pth EOF, describing the spatial distribution of the contribution; and PCp(u) is the corresponding pth principal component, describing the variation of the albedo with normalized time.
More than 50% of Earth is covered at any time by cloud. When a seasonal average of albedo is computed, the effects of clouds will be present in nearly every region. The principal component analysis of the diurnal cycle of Earth's albedo shows that the first PC describes a very large part of the diurnal cycle. To understand this result, we will consider the diurnal variation of albedo over a planet with an albedo that is constant over its surface but varies with solar zenith angle (SZA). This planet we will refer to as the cue ball. Earth will then be considered.
a. Cue ball
We will assume that the albedo of the cue ball varies with solar zenith angle as the mostly cloudy over ocean case given by Suttles et al. (1988), shown by Fig. 4. The mostly cloudy over ocean directional model of albedo was chosen because ocean covers most of Earth and much of the ocean is mostly cloudy. Also, the radiation reflected by clouds greatly exceeds that reflected by clear sky over ocean (albedo about 0.1) so that the mostly cloudy over ocean directional pattern of radiance dominates. By understanding the effects of SZA variations on albedo for this case, it will be easier to distinguish between the SZA effects and those due to cyclical variations of the scene for Earth as measured. Figure 4 shows that albedo increases with solar zenith angle. This increase is due to the apparent increase of cloud fraction with zenith angle and the increasing Rayleigh scattering of radiation with increasing zenith angle (Liou 2002).
The solar declination was computed from the date, then for a given latitude and time of day, the solar zenith angle was computed and the albedo was determined from Fig. 4. The albedo computed in this way was averaged over the Northern Hemisphere spring (MAM) for each region in the ERBS domain, as was done with the ERBS data. The results are independent of longitude. Figure 5 shows the diurnal average albedo as a function of latitude. The minimum albedo is near 20°N, as the sun is near overhead at noon and the SZA and albedo are smaller at all times of day than for other latitudes. The maximum albedo is at the southern edge of the domain, where the SZA is larger at all times of day than at other latitudes.
A database of the albedo was made by sampling the albedo as would the ERBE in its precessing orbit. The principal components were computed in terms of the normalized time u, as indicated by Eq. (3). The first PC accounts for 99.3% of the variance and PC-2 accounts for 0.6%. Figure 6 shows the variation of PC-1 with u. Near noon, the solar zenith angle is small and PC-1 is negative, decreasing the instantaneous albedo from its average value . PC-1 is symmetric about noon, as the cue ball does not change during the day.
The empirical orthogonal function EOF-1 associated with the principal component PC-1 is shown in Fig. 7. Some deviation from a smooth curve is evident; this is attributed to the sampling simulated as being from the ERBE orbit. The solar declination is positive in April and May. EOF-1 has small variation over the latitude range from 55°N to 55°S, with a broad maximum just north of the equator, where the sun will pass overhead during April and May. At this latitude SZA varies from near 0°–90° and the albedo range is largest. With increasing distance from this latitude, the minimum SZA increases and the range of the variation of sunlight during the day decreases, so that EOF-1 decreases.
The results of this cue-ball case demonstrate the variations of the diurnal cycles that only vary because of the dependence of albedo on SZA. The results for the observed Earth will now be considered.
b. Results for Earth observations
The albedo of each region was computed from the measurements as the spacecraft overpassed that region. This information is in the S-9 data product of ERBE (Barkstrom et al. 1989). The albedo of a region may change because of synoptic effects as various weather systems move through the region or because of interannual variations. The albedo data for each season, each region, and each hour box were averaged over the 5-yr period to average out these effects and to give an average albedo for each region and hour box. The diurnal-mean albedo for a month is the average of the hour-box values weighted by the insolation.
The diurnal-mean map of monthly-mean albedo for DJF is shown by Fig. 8a. The albedo over high-latitude North America and Eurasia is high because of snow, ice cover, and cloudiness. Over the oceans the TOA albedo is governed by clouds. Over the high-latitude Southern Ocean, extensive cloudiness and large solar zenith angle result in a high albedo. The oceanic high pressure regions are marked by the low albedo, because subsidence in these regions suppresses formation of clouds. The intertropical convergence zone (ITCZ) is clearly defined as a high-albedo belt. Sub-Saharan North Africa and the Indian subcontinent have low albedo because of the absence of clouds during this season, but the North African deserts have high albedos because of their highly reflective surfaces with little vegetation. These features are discussed by Mlynczak et al. (2011).
The monthly-mean albedo for JJA is shown by Fig. 8b. Over North America and Eurasia the snow has thawed, so the albedo over the northern continents is low. There is a movement of major cloud systems from land to ocean as the high pressure regions move from ocean to land (Haurwitz and Austin 1944). The deep convection over the Congo basin in DJF has moved northward to sub-Saharan North Africa, associated with the African monsoon and a high albedo.
The albedo will vary during the day because of the solar zenith angle variation during the day and because of cyclical variations of the scene during the day, for example, the formation of maritime stratus during the night and dissipation during the morning or afternoon thunderstorms in subtropical regions. Because of the immense heat storage capacity of the ocean, the responses differ between ocean and land, so ocean and land were treated as two separate domains to study their diurnal cycles. The ocean surface absorbs most incoming solar radiation, so that most reflected sunlight is from clouds. The land surface has greater albedo than ocean, so the clouds produce less contrast. Also, the diurnal temperature cycles in the atmosphere above the land and ocean surfaces are very different (Bergman and Salby 1996), leading to different patterns of diurnal cloud variabilities. Regions with approximately 33%–66% land/ocean mix are classified as “coastal” by the ERBE data processing system and are not considered.
The average variance for the domain is the trace of the covariance matrix when expressed as in Eq. (2). The resulting standard deviation for the ocean albedo is between 0.064 and 0.068 for each season and for land is between 0.027 and 0.029. The fraction of variance explained by the first five PCs are listed for ocean and land for each season in Table 1.
PC-1 accounts for 90%–92% of the variance for the diurnal cycle over ocean and 84%–89% of the variance for land. PC-1 for each season is shown in Fig. 9 for ocean and in Fig. 10 for land. The PC-1 for each case is symmetric about noon and is caused primarily by the variation of albedo with solar zenith angle. Both cases are very similar to PC-1 for the cue ball. There is a large difference in the magnitudes of PC-1 between ocean and land. For ocean PC-1 is ~12 at sunrise and sunset and ~−7 at noon, but for land it is ~10 at sunrise and sunset and ~−5 at noon.
The EOFs are likewise computed separately for ocean and land but are shown in the same figure to conserve space. PC-1 describes the variation of albedo with time, which we relate to solar zenith angle. EOF-1 describes the part of the albedo of the scene that is varying with PC-1, so that the cloud patterns appear prominently. EOF-1 for northern winter (DJF) is shown by Fig. 11a and for northern summer (JJA) in Fig. 11b. EOF-1s for ocean are largest in a band at about 30° latitude in the summer hemisphere and a band between the equator and 20° latitude in the winter hemisphere, where the solar elevation goes through a large range and the directional model for albedo goes through a large variation through the day. Over the oceans EOF-1 is near 1 except at high latitudes in the winter hemisphere, where EOF-1 decreases to about 0.5. In boreal summer there are three regions over the ocean near 20°S where the EOF-1 increases to 1.9. At near 20°N west of Central America and east of the Philippines there are regions where EOF-1 decreases to 0.9. Over much of the ocean there appears to be an artificial cutoff of clouds at 20°S. The reason for this feature is unknown. Over the summer continents EOF-1 is between 1.9 and 2.5.
The horizontal band that traces along the Tropic of Capricorn is a result of the discretization of local time into normalized time combined with poor sampling of the diurnal cycle near sunrise and sunset as shown in Fig. 2b. This effect is most evident in the winter hemisphere for each season EOF map near ±23° as that is where the cosine of the solar zenith angle is changing most rapidly as a function of latitude.
PC-1 and EOF-1 describe statistically the variation of the albedo with solar zenith angle for each region. This variation is the average over the season of the variation of the albedo, with solar zenith angle and day-to-day scene type. It is remarkable that so much of the variation of albedo is described by a single function of local time.
The second principal component accounts for 2%–4% of the variance of albedo over ocean and approximately 5% over land. Figures 12 and 13 show PC-2 for ocean and land. For both cases, PC-2 is an asymmetric function that describes high (low) morning albedo and low (high) afternoon albedo for regions with positive (negative) EOF-2 values. To a large degree, high albedo corresponds to increased cloudiness. PC-2 and EOF-2 reveal much about the diurnal response of the atmosphere to solar heating. Figure 14 shows EOF-2 for northern winter and summer. EOF-2 for ocean is largest for eastern sections of the oceans, where there is a strong pattern of marine stratus clouds in the morning. EOF-2 has the greatest negative values near the tropical convergence zone, the South Pacific convergence zone, and the outflow regions over the South Atlantic Ocean from the deep convective region of Amazonia, indicating a large increase of cloudiness in the afternoon. This response to solar heating is related to cyclogenesis in these regions. The equatorial Indian Ocean shows high afternoon albedo in northern winter, but in northern summer, when the Indian monsoon occurs, the most active afternoon cloudiness moves to India and the Bay of Bengal.
EOF-2 describes several patterns of the changing albedo across the day. Given the unique shape of PC-2, areas in the EOF that are negative would have slightly increasing albedo from morning until sunset while those with a positive values would have slightly decreasing albedo across the day. The former occurs over most continental areas except regions of deep convective activity around the Congo basin and central Amazon basin. This can be correlated to clouds as found in Kondragunta and Gruber (1994). There they found in Fig. 1a, many land areas showed increasing cloudiness across the day except for the same deep convective regions as found here in Fig. 10. [Note that in Kondragunta and Gruber (1994), one must switch the sign of the PC and EOF and “limit” the time from sunrise until sunset.] The other areas that show a decrease in albedo across the day are the marine stratocumulus regions off the west coasts of North and South America and southern Africa.
Table 1 shows that PC-3 accounts for 1.0%–1.5% of the variance over ocean for the four seasons and PC-4 has 0.8%. Measurement errors propagate through the analysis of principal components and when the eigenvalues of two PCs are close, as is typical of higher-order PCs, the two PCs will mix in the computation and produce an erroneous result for the PCs and the EOFs. There are at least 50 samples in each time box for each of the 4900 ocean regions, so that PC-4 does not significantly contaminate PC-3 (Smith 2006). In this case, for all four seasons, Fig. 15 shows nearly the same curve for PC-3, a further indication that the two-peaked PC-3 seen here are valid and not mixtures of PC-3 and PC-4.
Figure 16 shows the corresponding EOF-3 for boreal summer for ocean. The oceans north of 30°N have an EOF-3 of greater than 0.8. The rest of the global ocean has alternating positive and negative zonal bands. The ITCZ appears as a positive band, and the oceanic subtropical subsidence zones are negative bands.
The first three PCs for ocean account for 95%–96% of the diurnal cycles of albedo and for land account for 91%–95% of the variance. There is little information in the remaining PCs and EOFs.
We consider the relation between the principal components of the diurnal cycle of albedo and the diurnal cycles of clouds, such as shown by Bergman and Salby (1996). Only the diurnal cycle of clouds during day is relevant. The average cloudiness over the day for a region will appear in PC-1 as varying with SZA. The cosine Fourier component of the diurnal cycle of cloudiness will appear as part of that average. PC-1 is the function on which these cycles are projected that will maximize the variance described. The sine component, describing asymmetry about noon, will appear as part of PC-2. PC-3 provides additional shape to the symmetric part of albedo, including that part of the diurnal cycle of clouds. To relate the diurnal cycle of clouds to that of albedo, it is necessary to have not only the cycle of cloud fraction but also the optical depth to get albedo variation. Fortunately, ERBE has made measurements from which the albedo cycle can be determined.
The Earth Radiation Budget Experiment measured shortwave radiances from which albedo was computed between 55°S and 55°N. The spacecraft precessed through all local times every 72 days for 5 years. These data were used to compute the diurnal cycle of albedo over this domain. The data show that the albedo diurnal cycle is primarily driven by the dependence of albedo on solar zenith angle and that any other signals are an order of magnitude smaller. A principal component analysis has been made of the diurnal cycle of albedo. Ocean and land were treated separately. The first PC described about 91% of the variance for ocean and 84%–88% over land, and it is described by the variation of albedo with solar zenith angle through the day. This variation includes the diurnal cycle of cloudiness as well as the variation of albedo of a fixed scene with solar zenith angle. The second and third PCs describe additional responses of the atmosphere to the diurnal cycle of solar heating. PC-2 shows asymmetry of albedo about noon and is due to difference of albedo from morning to afternoon due, for example, to dissipation of morning cloudiness to create a clear afternoon and vice versa. PC-3 is a two-peaked shape and describes more detail of the shape of the diurnal cycle. For ocean the first three components describe 95%–96% of the variance and for land the first three components describe 91%–95%.
The authors gratefully acknowledge support by the CERES program from the NASA Science Mission Directorate through Langley Research Center to Science Systems and Applications, Inc. They also acknowledge the Atmospheric Sciences Data Center of Langley Research Center for access to the ERBE dataset. These data are available at http://eosweb.larc.nasa.gov.