1. Introduction
Radiation at the surface of the earth plays a major role in the energetics of weather and climate processes. A part of the incoming solar flux is reflected by the earth and its atmosphere, so that only the net shortwave (NSW) flux is absorbed within the system. The NSW radiation at the top of the atmosphere (TOA) provides the energy for all subsequent atmospheric and oceanic processes, and the NSW radiation at the surface is the portion that is not absorbed within the atmosphere. NSW at the surface provides energy flux for longwave (LW) cooling of the surface as well as sensible heating and latent heat for evaporation at the lower boundary of the atmosphere. The downward and upward LW radiant fluxes at the surface are major mechanisms for interactions between the atmosphere and the ocean (Ramanathan 1986).
In response to the need for surface radiation budget data for climate research (Suttles and Ohring 1986), an 8-yr dataset of surface radiation budget (SRB) components was produced for the period July 1983–June 1991 (Gupta et al. 1999). These components include the downward, upward, NSW, and LW radiant fluxes at the earth's surface. The algorithms for computing the surface radiation budget components use the International Satellite Cloud Climatology Project (ISCCP) data (Rossow and Schiffer 1991) and are described by Darnell et al. (1992) and Gupta et al. (1993). ISCCP data are also used by Zhang et al. (2004) to calculate surface as well as TOA and within the atmosphere fluxes. The SRB database includes not only the basic components [i.e., the downward shortwave (DSW), upward shortwave (USW), downward longwave (DLW) and upward longwave (ULW)] but also the NSW, net longwave (NLW), and total net radiative fluxes. (The SRB data are available online at http://eosweb.larc.nasa.gov/project/srb/table_srb.html.) The dataset is discussed further in section 2.
In the present paper we quantify the annual cycle of space and time variations of the DSW and NSW. The longwave and total fluxes will be treated in another paper. Although the annual cycle of insolation at the TOA is the dominant factor in the variations of DSW and NSW, the effects of clouds play a major role, especially because any shift of climate is expected to affect the cloud distribution or its annual variations and consequently the DSW and NSW. The first question is how does one study the annual cycles of several thousand regions? To describe the space and time variations, the method of principal component analysis will be used. This technique was used to study the annual cycles and interannual variations of outgoing longwave radiation at the TOA (Bess et al. 1992) and absorbed solar radiation (Smith et al. 1990). A major advantage of the method is that it separates the space and time variations into a series in which each term expresses the most possible variance by letting the data define the functions used for each term. Thus, the description is the most economical one to use, and minimizes the number of terms to understand. The principal component analysis is used to quantify the annual cycles of DSW and NSW into a small set of parameters that are used to relate the annual cycles of a region to its climate class.
This small set of parameters is useful for facilitating comparisons with the seasonal cycles as computed by general circulation models. The annual cycle of insolation causes changes of circulation patterns and cloud distributions and types, resulting in changes of the surface energetics that are coupled with these changes. The ability of a GCM to compute the annual cycle of DSW and NSW is important to its performance.
The results from a principal component analysis are statistical relations and physical interpretations are thus limited. Variations of any parameters that are in phase and collocated with each other cannot be separated by principal component analysis. For example, a change of clouds in phase with solar declination will appear inseparably in a single term.
Interannual variations of SRB are not considered here, except to note the relative importance of annual and interannual variations. Another dataset has been developed and is available at the above Internet site that extends the 8-yr dataset to a 12-yr period and that is generated using improved algorithms. The increased length of record will make it a much more useful dataset for interannual variations. Comparison of the 8- and 12-yr datasets shows only small differences for the 8-yr period, so that the annual cycles are accurately expressed by the 8-yr set.
2. Data
The SRB dataset was developed using data from ISCCP. The algorithms for computing the surface radiation budget components are described by Darnell et al. (1992) and Gupta et al. (1993). Surface radiation budget flux components are computed for a grid system that covers the globe with a quasi-equal-area grid that is 2.5° in latitude. ISCCP data is also used by Zhang et al. (2004) to calculate surface as well as TOA and within the atmosphere fluxes.
The estimated accuracy and precision of the model is found in Gupta et al. (1999). The DSW results were compared to ground measurements from Global Energy Budget Archive (GEBA) for validation. Over the 8-yr data period there were 13 356 data points available. A bias of 5.2 W m−2 and a root-mean-square difference of 24.0 W m−2 were found. The largest differences were found in areas that have biomass burning. The aerosols from burning are not accounted for in this model. The model uses climatological values of optical depths and other radiative properties of aerosols based on scene types. Seasonal effects and transient events are not accounted for because they were not available at the time the model was developed. Improvement in the handling of aerosols is part of the continuing Global Energy and Water Cycle Experiment (GEWEX) SRB program.
3. Method of analysis
To examine the seasonal cycles of the surface radiation budget components, a canonical year was formed by averaging the eight Januaries to form a canonical January, etc. The grid system used is 2.5° quasi–equal area, with 6596 regions to cover the globe.
A useful measure of the variability of a function is its variance, or power, defined as the integral of the square of the function over the domain of interest. For the present case, the variance is computed as ΣtΣxw(x)z2(x, t)/(AT), where x denotes latitude and longitude, t is the month of the year, w(x) is the area weighting for the grid box, A is the area of the earth, and T is the number of months used for the analysis. For this purpose, the annual mean spatial distribution Y(x) is subtracted out. The square root of the variance is simply the root-mean-square (rms) value of the variation of the function over the time and space domain.
4. Results
Table 1 lists the variances of DSW and NSW for the 8-yr period. The variance for the 8-yr period can be resolved into average annual variance and the interannual variance. The interannual variations account for 5.0% of the variability of DSW and 6.3% of NSW. The rms for the total variation of DSW over the 8-yr time period is 62.2 W m−2, and its annual cycle has an rms of 60.6 W m−2, quantifying the importance of the annual cycle. Results for the NSW are similar.
a. Annual mean maps
In accordance with Eq. (1), the first step is to examine the annual mean maps of surface shortwave fluxes, and then the EOFs and principal components. The annual mean maps of DSW and NSW at the surface were computed for the 8-yr data period from July 1983–June 1991. Figure 1a shows the annual mean map of DSW. DSW is the insolation at the “top of the atmosphere” as modified by ozone, water vapor, and aerosols. Longitudinal variations are due primarily to variations of clouds. Over the subsidence areas of the tropical Atlantic and Pacific Oceans and the Sahara and Middle Eastern deserts, there are maxima in the DSW, while there is a band of local minima (relative to latitude) marking the position of the intertropical convergence zone (ITCZ). Over the Tibetan Plateau there is a minimum due to persistent deep stratus. The effect of these clouds on the local climate is investigated in Yu et al. (2004). Over Antarctica the DSW is high, but it is extremely difficult to estimate cloud amount over snow and this high value of DSW may be an artifact due to underestimated cloud amounts there.
The NSW is the DSW times (1 − the surface albedo). The annual mean NSW is shown in Fig. 1b and ranges from 300 W m−2 near the equator to 20 W m−2 at the Poles. Figure 2a shows the latitudinal variation of the zonal means of the annual mean DSW and NSW, together with the annual mean insolation at the TOA. The DSW is about half of the TOA insolation within 60° of the equator, with a dip just north of the equator, indicating the zonal annual mean of the ITCZ. From 0° to 20°S, the DSW is lower than the corresponding northern latitudes except for the ITCZ. Poleward of 60° in both hemispheres, the decrease of cloud amount causes the DSW to increase, especially over Antarctica. The NSW follows the DSW very closely between 60°S and 60°N, due to the low albedo of the surface, especially over the oceans. Poleward of 60°, the high albedo of ice- and snow-covered surfaces causes the zonal annual mean NSW to decrease to 25 W m−2.
Bias errors in the dataset appear in the annual mean maps, but the random errors do not (except as they affect the estimate of the bias). Similarly, bias errors do not appear in the principal components and EOFs, but random errors increase the variability to be represented by the principal components and EOFs.
b. Eigenvalues
The eigenvalues of the covariance matrix are the variances associated with each of the principal components. The fraction of variance that is described by each of the first 4 EOFs is listed in Table 2 for the variation of TOA insolation, DSW, and NSW about the annual mean values for each location. Discussion of these values will be included with the discussion of the principal components.
c. Principal component analysis of TOA insolation
Because TOA insolation governs the annual cycles, the principal components of TOA insolation are first considered. The TOA insolation is described by two terms to 0.999 of the variance. Smith et al. (1990) show the first three principal components pj(t), (j = 1, 2, 3) and their EOFs. The first principal component is the annual cycle of insolation, which accounts for 97.5% of the seasonal variance. The second term accounts for 2.4% of the variance and is a semiannual cycle. For TOA insolation, the third term accounts for less than 0.001% of the variance.
d. Principal component analysis of DSW
The eigenvalues of DSW variation are also shown in Table 2 and do not converge nearly as rapidly as do the eigenvalues of TOA insolation. Figure 2b shows the histories of the first 5 principal components. The first term accounts for 92.4% of the variance and its principal component is a sine wave with an amplitude of 80 W m−2 (i.e., about half that of the first principal component of TOA insolation). The zonal mean of the first EOF of DSW is shown by Fig. 2c and is not the simple sine of latitude shape of EOF-1 of TOA insolation (Smith et al. 1990), but is far more irregular. Figure 3a is a map of EOF-1 of DSW. Antarctica stands out with its value of −1.8, creating the strong minimum seen in Fig. 2c. Likewise the Arctic ice pack and Greenland cause the maximum in Fig. 2c. In the subtropics the zonal variations indicate the movement of clouds with season, especially over the regions of India, Bangladesh, and Southeast Asia.
Table 2 shows that the second term accounts for 4.1% of the variance of DSW. Figure 2b shows that p2(t) for DSW is a semiannual sine wave with amplitude of about 20 W m−2. The zonal mean of EOF-2 for DSW, seen in Fig. 2c, resembles EOF-2 for TOA insolation, rising rapidly from small values at 60° in each hemisphere toward nearly symmetric maxima at the Poles. Figure 3b is a map of DSW EOF-2. The zonal patterns in low latitudes are due to seasonal movements of cloud patterns; in particular, the local maximum along the equator is due to ITCZ movements. These cloud movements increase the variance of this term. In the midlatitudes (30°–60°) in each hemisphere, EOF-2 has a small magnitude (i.e., there is very little semiannual variation of DSW in the midlatitudes).
The third eigenvalue of DSW shows that this term accounts for 2.4% of the variance of DSW, whereas the third term of TOA insolation accounts for less than 0.1% of its variance. Figure 2b shows that p3(t) for DSW is very nearly a sine wave of a 1-yr period but 90° out of phase with DSW p1(t). The first principal component of DSW is mainly due to TOA insolation and the change of the clouds in phase with the solar declination. The third term delineates the annual cycle of the part of the response of the atmosphere that lags the TOA insolation. The zonal mean of EOF-3 as seen in Fig. 2c has no clear interpretation. The map of EOF-3 in Fig. 3c shows a complex pattern. There is an irregular band across the northern Tropics, with a high over India. EOF-3 is large in the marine stratocumulus regions of the eastern Pacific and off the coast of Nambia. These are areas that show a seasonal cycle of cloud forcing (Klein and Hartmann 1993). Stratus clouds occur in areas of subsidence and have a large impact on the DSW. Their annual cycle is tied to the circulation patterns of the oceans and the atmosphere. There are negative regions south of the equator over the deep convective regions of South America, South Africa, and the Maritime Continent of the Philippines, with positive regions between these. A spatial pattern of adjacent high and low values with a sinusoidal time variation describes a cyclical movement. In this case these patterns indicate north–south movement of cloud patterns. EOF-3 is very small over the vast expanse of the southern oceans from 30°S to Antarctica. There is a band of low EOF-3 between 30° and 45°N, north of which is a band of highs, notably over Russia.
e. Principal component analysis of NSW
Table 2 shows that the fraction of variance of NSW explained by each of the first three terms is close to that for DSW. For NSW the first term accounts for 92.4% of the variance, the same as DSW. Figure 4a shows the time histories of the first 3 principal components of NSW. The first principal component of NSW is a sine wave in phase with TOA insolation, with amplitude of 60 W m−2. Figure 4b shows the zonal means of the first 3 EOFs of NSW. The zonal mean of EOF-1 for NSW varies approximately as the sine of latitude except in polar regions, where it decreases due to the reflection of the snow and ice cover. Figure 5a is a map of EOF-1 for NSW and is interesting for its lack of longitudinal structure, in contrast to the longitudinal variations of the annual mean NSW noted in Fig. 1b, mostly in the Tropics.
The second term of NSW accounts for 3.9% of its variance and Fig. 4a shows that the second principal component is a semiannual cycle plus an annual cycle 90° out of phase with the annual cycle of the first principal component of NSW, so that p2(t) for NSW is relatively flat between June and December with only a hint of the September minimum of p2(t) for DSW. The p2(t) for NSW has a range of 30 W m−2 with peaks in July and December. The zonal mean of EOF-2 for NSW is quite complex, with no similarity to the EOF-2 of TOA insolation or DSW. Because of the high surface albedo of the polar regions, the semiannual cycle of the TOA insolation and DSW, described by p2(t) for these cases, does not dominate p2(t) for NSW. Instead, the p2(t) for NSW is a combination of the semiannual cycle and the annual cycle component, which is 90° out of phase with that of p1(t).
Figure 5b is a map of NSW EOF-2. The patterns seen here are suggested by the patterns of EOF-2 and -3 for DSW-2. There are strong patterns in the Tropics and in the neighborhood of 30°N over the Pacific and Atlantic Oceans, which resemble combinations of patterns of DSW EOF-2 and -3. These are due to seasonal changes of cloud patterns (e.g., the Azores/Bermuda high pressure region) with reduced cloudiness in summer. The negative band in the Tropics is due to the movement of the ITCZ; in particular, the large negative feature over the Indian Ocean is due to the monsoon. Also, the high over the Amazon basin and the low over the Pacific Ocean west of Central America are due to the annual movement of the deep convection zone. More insight into this principal component and EOF is given from examining the next term.
The third term accounts for 2.1% of the variance of NSW, slightly less than for DSW. The p3(t) is a combination of semiannual cycle, out of phase with that of p2(t), and an annual cycle. The zonal distribution of EOF-3 is complicated and defies simple explanation, as did EOF-3 of DSW. Figure 5c is the map of EOF-3 for NSW. As for EOF-2, the high-latitude regions have large values due to changes of insolation and albedo patterns. There are also patterns in low latitudes due to seasonal cloud pattern movements.
The semiannual cycles of cloud patterns are not in phase with the TOA insolation for all regions. Also, the cycle is not purely semiannual, but has an annual component that accounts for the differing peak values. As a consequence, two principal components [i.e., p2(t) and p3(t)] are required to describe these cycles. Whereas the EOF-2 for TOA insolation is symmetric in longitude (except for the small variation due to orbital eccentricity), the NSW is not so symmetric, due to the asymmetry of the Northern and Southern Hemispheres. This asymmetry will result in an annual cycle component. The NSW variations at high latitudes combine with the variations of cloud patterns in low latitudes to separate into the second and third terms, p2(t) and p3(t) with EOF-2 and -3, as descriptors. Figure 3 of Smith et al. (2002) shows that for savanna (tropical wet/dry), the monthly means of NLW radiation flux as a function of NSW radiation flux describe a figure-eight pattern due to a semiannual cycle of NSW. The second and third terms describe this behavior for the savanna regions.
The present results for surface DSW and NSW can be compared with those for TOA absorbed solar radiation (ASR; Smith et al. 1990). For ASR, DSW, and NSW each the p1(t) describes an annual cycle. For DSW and ASR, p2(t) describes a semiannual cycle, but for NSW, p2(t) is a combination of a semiannual term and an annual term out of phase with p1(t). For ASR and DSW, p3(t) is an annual cycle that is 90° out of phase with p1(t); for NSW, p3(t) is a combination of a semiannual term with other variations.
Given that the solar output is constant to a fraction of 1% over the last few decades, the TOA insolation can be readily computed. However, the effects of clouds are highly variable. The present results quantify the DSW and NSW with the effects of clouds included for the period 1983–91. Any change in cloud distribution and/or annual cycle of a region, which would be expected to accompany any climate change, would appear in a similar principal component analysis as a variation of the EOF values for that region. A more widespread variation would also affect the principal components.
5. Seasonal cycles and climate classes
The relation between the seasonal cycles as expressed in terms of EOFs and the climate classification is now considered. Smith et al. (2002) showed that the climate classification of a region could be defined in terms of the surface radiation so as to match closely that of Trewartha and Horn (1980), who defined climate classes in terms of temperature and precipitation. Earlier work (e.g., Köppen 1936), defined climate classes in terms of vegetation. Except for the change of nomenclature required, the map of Trewartha and Horn (1980) corresponds closely to that of Köppen (1936), as does the map of Smith et al. (2002). For the climate classes defined by surface radiation, histograms of EOF values were computed. These are summarized as box-whisker plots in which the total range (0%–100%) is denoted by the bar and the box indicates the 25th and 75th percentiles The bar inside the box indicates the 50th percentile (median) and the dot denotes the mean.
Figure 6 shows box-whisker plots for DSW for the first three EOFs for land regions of the Northern and Southern Hemispheres separately. There is a clear progression of the range of EOF-1 from polar through boreal and temperate classes, with little overlap in the Northern Hemisphere. The climate classes of savanna (tropical wet/dry) and rain forest (tropical wet), have very little annual cycle of DSW. Just as Smith et al. (2002) found that these classes can be discriminated by the annual mean NSW, there is a relation between climate class and annual cycle. There is some overlap between temperate and the small range of boreal. The range of steppe is quite broad because steppe are caused by a variety of conditions. They border deserts as transition regions, and they occur in the rain shadow of mountains and in highland areas. The zonal mean of EOF-1 of DSW is very roughly skew symmetric, so that the plots for the Northern and Southern Hemispheres are approximately skew symmetric. For EOF-2, the polar class has a much larger value than any other class as Fig. 3b shows. EOF-2 is nearly symmetric with latitude, and the plots are similar for the Northern and Southern Hemispheres, except that for the Southern Hemisphere, the ranges are very small for all climate classes. For EOF-3, the complexity of the spatial pattern manifests itself, with most classes having wide distributions. Savanna and the rain forest, which had small variations with EOF-1 and -2, show large ranges, even greater than for steppe. However, the variance contained in EOF-3 is quite small.
Figure 7 shows box-whisker plots for DSW over oceans. As with land, EOF-1 is nearly skew symmetric between the hemispheres, though the ranges of EOF-1 are not well separated. The ranges of EOF-2 are nearly symmetric between the hemispheres, but in the Northern Hemisphere the polar regions have much larger values of EOF-2 than in the Southern Hemisphere. For EOF-3 in the Northern Hemisphere, the ranges are large for each climate class, but the variance of the term is small.
For NSW over land, Fig. 8 shows box-whisker plots of EOFs. The results are qualitatively similar to those for DSW except for the polar case, where the high albedo of snow and ice causes the polar NSW to be low compared to its DSW. The skew symmetry of NSW over land of EOF-1 appears again between the Northern and Southern Hemispheres. The range of NSW is greater than for DSW in nearly all cases. For EOF-2 in the Northern Hemisphere the ranges are large compared to the ranges for DSW. Figure 9 shows box-whisker plots for the NSW flux over ocean. These are qualitatively similar to those of Fig. 7 for DSW because, as noted earlier, the albedo of the ocean surface is low and the NSW is close to the DSW.
The box-whisker plots show the amount of each component of DSW and NSW associated with each climate class. The classes have different dependences of DSW and NSW, emphasizing the complexity of interactions between solar declination, climate class of region, and surface albedo [i.e., savanna (tropical wet/dry)]. The range of NSW is greater than for DSW in nearly all cases, which shows strong and complex interactions during the year. To compute correctly the energetics of processes in the various climate regions, a model must include these interactions correctly. Table 3 approximately summarizes the climate classes for which the EOFs are largest for land and ocean DSW and NSW.
6. Conclusions
The annual cycles of DSW and NSW radiation fluxes at the surface have been examined by principal component analysis using the 8-yr surface radiation budget (SRB) dataset. The principal components describe the time history during the year and the corresponding geographical variation is described by the EOF. Because of its major effect on the surface radiation, the TOA insolation is also examined by principal component analysis to provide insight into the results. One term accounts for 97.5% of the variance of the TOA insolation, as an annual cycle. The second term describes 2.4% of the TOA insolation variance as a semiannual cycle, concentrated in polar regions. At the surface, the DSW is more complex, primarily due to clouds. The first term is an annual cycle and accounts for 92.4% of the variance. The second term describes 4.1% of the variance and is a semiannual cycle that corresponds to the second term for TOA insolation in polar regions and describes the movement of clouds in the Tropics. The third term accounts for 2.4% of the variance of DSW. Its principal component is an annual sine wave 90° out of phase with the TOA insolation and is due to the part of the response of the atmosphere that lags the TOA insolation. The maps of the EOFs of DSW are quite irregular and strongly influenced by intra-annual changes in cloud patterns as well as TOA insolation.
For NSW, the variances described by each term are approximately those for DSW. For NSW the first principal component is an annual sine wave, but the second and third principal components are semiannual cycles with small annual cycles present. EOF-1 of NSW has little longitudinal structure, but EOF-2 and -3 have complex geographical distributions due to cloud pattern movements as well as insolation effects in polar regions. For any region the annual cycles of DSW and NSW each can be described by three parameters, EOF-1, -2, and -3, to account for more than 98% of the variance on a global basis. A similar principal component analysis of data for another epoch would indicate variations of cloud patterns, which would be expected to accompany any change of climate.
Box-whisker plots are used to examine the distribution of EOFs of downward and net SW fluxes for the climate classes. Within each climate class the range of each EOF is small in most cases. These plots relate the seasonal cycles of DSW and NSW to the climate class. The climate classes have differing dependences between DSW and NSW, emphasizing the complexities of the interactions between insolation, climate class, and surface albedo. In order for a circulation model to properly describe the energetics in these various regions, it must describe these interactions well.
Acknowledgments
This work was supported by the Clouds and the Earth Radiant Energy System (CERES) program and the Surface Radiation Budget Program of the Earth Science Enterprise of NASA through Langley Research Center by contract to Analytical Services and Materials, Inc., and the National Institute of Aerospace. Data were provided by the Langley Atmospheric Sciences Data Center.
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(a) Map of the annual mean DSW flux. (b) Map of the annual mean NSW flux
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
(a) Latitudinal variation of the longitudinal mean of the annual mean DSW and NSW fluxes together with the mean annual insolation at the TOA. (b) Principal component time histories of the DSW flux for PC-1, -2, and -3. (c) Latitudinal variation of the longitudinal mean of EOF-1, -2, and -3 of the DSW flux
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Map of (a) EOF-1, (b) EOF-2, and (c) EOF-3 of the DSW flux
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
(a)Principal component time histories of the NSW flux for PC-1, -2, and -3. (b)Latitudinal variation of the longitudinal mean of EOF-1, -2, and -3 of the NSW flux
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Map of (a) EOF-1, (b) EOF-2, and (c) EOF-3 of the NSW flux
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Box-whisker plots of EOFs for the DSW flux over land sorted by climate classification of regions
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Same as in Fig. 6, but for the DSW flux over ocean
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Same as in Fig. 6, but for the NSW flux over land
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Same as in Fig. 6, but for the NSW flux over ocean
Citation: Journal of Climate 19, 4; 10.1175/JCLI3625.1
Annual and interannual variances of shortwaves at the surface
Normalized eigenvalues for TOA insolation, DSW, and NSW
Climate classes for which EOFs are largest. Extratropical denotes polar, boreal, temperate, and subtropical
