## 1. Introduction

The diurnal cycle is created by the response of the surface and atmosphere to solar heating over a single day, a time scale at which the details of surface properties, planetary boundary layer, clouds, and precipitation are all important. The importance of a GCM correctly simulating the diurnal cycle of outgoing longwave radiation (OLR) was pointed out by Slingo et al. (1987). Yang and Slingo (2001) demonstrated the utility of the observed diurnal cycle for validation of numerical models and for finding areas that require further development. Although great strides have been made in the development of GCMs, this is still an important consideration today.

The Earth Radiation Budget Experiment (ERBE) instruments aboard the Earth Radiation Budget Satellite (ERBS) provided data for the diurnal cycle of OLR and reflected solar radiation. ERBS was one of three spacecraft carrying instruments of the Earth Radiation Budget Experiment (Barkstrom and Smith 1986) and was placed in an orbit with an inclination of 57°, precessing through all local standard times every 72 days to provide the first direct observations of the diurnal cycle of the earth’s OLR and albedo (Harrison et al. 1983). The satellite provided 5 yr of data from the scanning radiometer between 1985 and 1989. Harrison et al. (1988) used the scanner data to demonstrate the range of the diurnal cycle of the OLR. Smith and Rutan (2003, hereinafter SR03), used these data to compute the diurnal cycles of OLR for 2.5° latitude × 2.5° longitude regions from 55°S to 55°N, which was the portion of the earth observed by ERBS. These data are the only broadband measurements of OLR and reflected solar radiation that cover all local times around the earth.

The OLR is sensitive not only to the temperature variations at the surface and profile through the atmosphere but also to the humidity profile and clouds. Comparisons of the simulated diurnal cycle of the OLR with satellite measurements can thus provide a stringent test of many aspects of a model. The objective of this paper is to validate the diurnal cycle of OLR computed by version 3 of the Hadley Centre Atmospheric Model (HadAM3) by comparison with the diurnal cycle as observed by ERBS. Where differences are noted, potential causes are discussed.

Whether the purpose of a model is to simulate climate or to forecast the weather, the diurnal cycle of the interaction of the surface with the atmosphere and other processes must be described well. Given the nonlinear response of the atmosphere to surface–atmosphere interactions over a wide range of time and space scales, errors within these interactions cannot be expected to average out in the longer term. For example, the depth of convection is governed by heating during the day. If the computed convection is too deep, water vapor will be carried too high into the upper troposphere, affecting the radiation balance, which in turn will affect the subsidence and dynamics of that level on a longer time scale. Thus, the diurnal cycle will affect the climate generated by the model.

Some authors have examined the quality of the simulation of the diurnal cycle by climate models. Surface and related observations provide the most direct validation source (e.g., Betts and Jakob 2002; Dai and Trenberth 2004). Global satellite data also provide important observations, often in the form of narrowband or broadband thermal radiation fields that provide information on surface and cloud-top temperatures (e.g., Yang and Slingo 2001; Tian et al. 2004). Half-hourly data from *Meteosat-7* were used by Slingo et al. (2004) to evaluate HadAM3. A sensitivity to the frequency with which the radiative heating fields are updated in the model has also been found (e.g., Slingo et al. 2004). While the details vary from model to model, a common theme in these comparisons is that the simulated convection and associated rainfall tend to peak far too early in the day, although the precise cause is still under investigation.

Geostationary satellites are a particularly valuable resource because of the high time resolution available. These radiometers measure in the infrared window as opposed to broadband radiometers. The inference of broadband OLR from window channel measurements is sensitive to water vapor and thus has errors as large as 15 W m^{−2}. Nevertheless, much useful information has been derived from these data (e.g., Minnis and Harrison 1984). Measurements from the Geostationary Earth Radiation Budget (GERB) instruments (Harries et al. 2005) aboard the *Meteosat*-*8* and -*9* spacecraft are now available for the Meteosat sector of the earth and are an excellent dataset for studying the diurnal cycle over this part of the earth. In the near future, the Clouds and Earth Radiation Energy System (CERES) project will provide OLR for every third hour (UTC) starting at midnight, based on geostationary satellite data calibrated by CERES radiometers (Wielicki et al. 1998). The ERBS data used in this study cover all longitudes for latitudes between 55°S and 55°N.

In this paper, we compare the HadAM3 simulations of OLR with OLR data from ERBS using the principal component analysis (PCA) technique employed by SR03. PCA has the advantage that the data define the temporal variations in order to maximize the information in each successive term. For this comparison, the June–August case is used. Most of the land area of the planet is in the Northern Hemisphere, and the diurnal cycle is strongest in summer. Over the globe, this case tests the model through a large range of climatological behaviors; thus, it is not necessary to examine each month of the year.

## 2. Model and observed data

This study uses results from an integration of HadAM3, analyzed by Slingo et al. (2004). The model has 30 vertical levels and a horizontal resolution of 2.5° latitude × 3.75° longitude. Full radiation and dynamics calculations are made every one-half hour, as opposed to the standard version of the model in which the full radiation computation is made every 3 h. HadAM3 is the atmosphere-only version of the climate model, in which the model is forced with the observed sea surface temperatures and sea ice extent for 1984. This was a year in which El Niño was not active. The model also includes a land surface that is partitioned into multiple layers for heat and hydrology computations. This treatment of the surface is necessary for the simulation of the diurnal cycle over land. A full description of the model and of its simulations in this mode is given by Pope et al. (2000). Results are shown for the northern summer season (June–August).

The ERBS measurements are for the period from January 1985 through February 1990. The sea surface temperature for the ERBS data period thus contains interannual variations that are not in the model. For the analysis, SR03 used only the fluxes that were measured at the local time of flyover. (To compute a daily mean value of OLR from two measurements per day, one must use a model to interpolate over the part of the day measured. These modeled values were not used for this work.) The ERBS precessed around the earth every 72 days, so that all regions between 57°N and 57°S are viewed at all local times every 72 days. Because the ascending and descending parts of the orbit are 180° or 12 h of local time apart, regions at low latitudes were covered for all local times every 36 days. The analysis of the ERBS measurements was limited to the latitude range from 55°S to 55°N. There was not sufficient sampling to compute monthly mean diurnal cycles; thus, seasonal means were considered and that is for June–August. The first three principal components are very similar for all four seasons, indicating the robustness of these results.

## 3. Analysis procedure

Diurnal cycles were computed from ERBS measurements by SR03 for 2.5° regions from 55°S to 55°N, which requires 6336 regions for coverage. HadAM3 provides diurnal cycles for grid points covering 2.5° latitude × 3.75° longitude over the globe, which requires 6912 regions. The problem is how to compare several thousand diurnal cycle curves qualitatively and quantitatively. The approach used by SR03 was principal component (PC) analysis, which provides the most economical basis set possible; that is, the first PC describes the maximum amount of variance of the diurnal cycle in time and space that is possible with one function, and each successive PC explains the maximum amount of variance of the residual. The set of PCs provides an orthogonal basis set for describing the time variation of the diurnal cycles. The diurnal cycle for each region is expressed by use of the PCs, for which the resulting coefficients are the empirical orthogonal functions (EOFs), describing the geographical variation of the diurnal cycles. As such, these results are descriptions that are mainly useful to the extent that one can physically interpret them. The attribution of the physical mechanism requires asking what could cause the observed behavior, and the answer is not always unambiguous. The physical interpretation depends on the shape of the PC, the geographical location of the large EOF values, and recognition of the processes that occur in these regions. Various investigators apply PC/EOF analyses in different ways, so the following subsections specifically define the method applied here.

### a. Computation of diurnal cycle

*x*,

*τ*,

*t*) denote the OLR for region

*x*for local time

*τ*on day

*t*, where

*τ*has 48 values and

*t*has up to 31 values. The monthly average OLR for a given local time is then

*N*is the number of days in the month. The daily average OLR for the region during the month is

*x*is then

### b. Principal component analysis

*w*(

*x*) is the area weighting for the

*x*th region and the summation is over all regions. Because

*τ*takes on values from 1 to 48 for the model, the covariance matrix is 48 × 48. The eigenvectors of the covariance matrix are the principal components PC

*(*

_{n}*τ*), where

*n*∈ [1, 48]. The corresponding empirical orthogonal functions provide the geographic distribution and are computed as

*τ*. Therefore, the diurnal cycle for a region can be expressed as

*n*.

### c. Variability comparison

The root-mean-square (RMS) variance of the diurnal cycle of OLR is computed as the square root of the trace of **Γ**(*τ*, *τ*′), which is the area-weighted sum of the squares of all *D*(*x*, *τ*) values for all *x* and *τ*. The RMS of the diurnal cycle is the Euclidean norm in the function space of the diurnal cycle and provides a basis for comparison between model and ERBS results. Figures 1a,b show the RMS of the diurnal cycle from the ERBE measurements and from HadAM3. Relative to ERBS observations, the model has less variation over the oceans everywhere, and there is less variation in model results over North America, India, China, and Southeast Asia. Over the deserts of North Africa and the Middle East, however, the model has greater variation than the ERBS observations. Over the western North Pacific Ocean, the southwest Pacific convergence zone, and across the eastern Pacific Ocean over the intertropical convergence zone (ITCZ), north of the equator, ERBS observations show a RMS of 6–12 W m^{−2}. Over the subsidence zone of the eastern Pacific Ocean on and south of the equator, the RMS values from ERBS and the model are less than 3 W m^{−2}.

## 4. Results for land

The diurnal cycle of OLR over land is much greater than that over ocean because of the much larger effective heat capacity of the oceans. SR03 therefore partitioned their analysis into land and ocean segments so that the variation of OLR over land would not overwhelm that over ocean. Also, the physics of the diurnal cycles over ocean differ from those over land, so the partitioning of the globe into land and ocean areas permits the analysis method to show these differences more easily. That approach is also used here. In the partitioning, regions containing both land and ocean are excluded from the analysis.

The PCs and EOFs of the HadAM3 OLR dataset were computed for boreal summer (i.e., averaged over June–August) over the ERBS domain, between 55°S and 55°N, in order to compare directly with the ERBS results.

### a. Variances over land

Table 1 lists the area-weighted RMS over land for the model diurnal cycle over the ERBS domain of 55°S–55°N and for the ERBE results for boreal summer. The model’s RMS is 11.4 W m^{−2} and the ERBS result is 13.3 W m^{−2}, so the model has a slightly smaller diurnal cycle over land than the satellite data. The model values are based on point values of OLR at half-hourly intervals, whereas the observation values are means of OLR within 1-h intervals.

The eigenvalues of the covariance matrix normalized by the trace are also listed in Table 1. The normalized eigenvalues represent the fraction of variance that is described by each PC, and thus quantify the importance of each term. The model eigenvalues decrease more rapidly than those measured, so that fewer terms are required to describe the model diurnal cycles to a given accuracy than are needed for observation, indicating that the diurnal cycles that are observed by the satellite have a greater variety than those computed by the model. For the model, 99% of the variance can be described by five terms, whereas for the observed diurnal cycles, five terms describe only 91% of the variance.

### b. Comparison of model and ERBS for boreal summer over land

Table 1 shows that for the model, the first principal component (PC-1) describes 89% of the variance, compared to 76% for the ERBS PC-1. Figure 2 compares PC-1 from the model and from ERBS. The first principal component is the function that describes the most variance possible with a single function. As such, it may consist of a combination of physical effects. The PC-1 curves are similar for the model and for ERBE. The model PC-1 shows the OLR decreasing slowly from sunset to sunrise, with a sinusoidal increase beginning at sunrise, approximating the cosine of the solar zenith angle. Both curves have a range of about 30 W m^{−2}. The model curve has a peak at 17 W m^{−2} as compared with 21 W m^{−2} for ERBS. However, there are some important differences. The satellite PC-1 crosses zero at 0730 and 1700 LST. The model result crosses zero at 0830 and 1900 LST, so that the model case warms more slowly and retains heat longer than that shown by ERBS. This may be because the effective thermal mass, that is, the thermal conductivity times specific heat of the land, is too high on a global basis in the model. The ERBS PC-1 has a maximum near noon (1230 LST) and little decrease of OLR during the night. This result was also found by Minnis and Harrison (1984) using data from the Geostationary Operational Environmental Satellite (GOES) window channel. In contrast, the model result has a broader peak, which is skewed such that the maximum occurs at about 1330 LST, which is more intuitive than the satellite result, because it represents the delay caused by the finite heat capacity of the surface, which is included in the model. Also, the model PC-1 decreases by 7 W m^{−2} from 2000 to 0600 LST. The ERBS peak is nearer to noon because of an increase in the afternoon cloudiness over many regions of the earth. In addition, the model PC-1 has large curvature near sunrise and sunset, whereas the ERBS PC-1 begins to increase prior to 0600 LST. This early increase of the ERBS PC-1 is the result of the variation of sunrise and sunset times with latitude, which is further described by PC-3, as noted in section 4b.

Figure 3a shows the first empirical orthogonal function (EOF-1), which is the geographically dependent coefficient for PC-1, for the ERBS measurements. Figure 3b shows the map of EOF-1 for the model. The ERBS and model results have similar patterns over deserts and surrounding regions. Over the deserts of North Africa, the Middle East, and southern Asia, the ERBE EOF-1 exceeds 2.0 and the model EOF-1 exceeds 1.5. The PC-1 peak is 21 W m^{−2} for ERBS and 17 W m^{−2} for the model, and the product of PC-1 times EOF-1 is close for both sets of data. For regions of large EOF-1, PC-1 describes the classic signature of the strong response of land surface temperatures to the solar heating through a cloud-free atmosphere. In these regions, particularly the deserts, the OLR closely follows the surface temperature, with a maximum just after noon and slow cooling through the night to a minimum just before dawn. This interpretation is supported by the fact that plots of the OLR obtained directly from the model over the Sahara are identical in shape to that for PC-1 shown in Fig. 2. The major difference between the two maps is the appearance of negative values over large areas in the model EOF-1, which do not appear in ERBE observations. Here, PC-1 is negative because of the diurnal cycle of cloudiness in the model, particularly over the monsoon areas of equatorial South America, West Africa, India, and Southeast Asia. Figure 3a shows ERBS observations to be positive over most of the domain, that is, OLR is greater during the day than at night.

Figure 4 shows the model PC-2 and the ERBS PC-2. The two curves agree quite well, especially considering the differences noted earlier for PC-1, which can cause differences to be transferred to higher-order PCs, and the fact that the model PC-2 accounts for only 5.7% of the variance, compared to 10% for the ERBS PC-2. In each case the primary effect of PC-2 is to describe the lead or lag of a given region relative to the gross average, so the similarity of shape is perhaps not surprising. PC-2 represents to first order the modification introduced by the diurnal cycle of the cloudiness.

The EOF-2 for the ERBE and for the model results are shown by Figs. 5a,b. These maps differ considerably. Many regions in Fig. 5b show positive EOF-2 values, which shift the peak heating to later in the day than for PC-1 alone. These regions have more cloud in morning than in afternoon. This is particularly widespread away from the equator in regions where EOF-1 is slightly negative, for example, for North America and Siberia. When combined with a negative EOF-2 value, PC-2 will shift the peak OLR to an earlier time of day, as happens over areas with afternoon cloudiness. This is the case where the deep convection of central Africa has moved north of the equator in July. Slingo et al. (2004) point out that convection as computed by HadAM3 peaks before noon, whereas the observed peak is in late afternoon or evening. The peak in the afternoon will be described by PC-2. Because convection peaks near noon in the model, its effects on OLR will be combined with the peak formed by diurnal heating in PC-1. The incorporation of this variation of OLR into PC-1 will decrease that of PC-2 and increase that of PC-1, in agreement with the comparison of Table 1. Also, the model and ERBS EOF-2 will be quite different as noted here.

The satellite and model PC-3s, shown in Fig. 6, are similar, if one regards PC-3 as being Fourier wavenumber 2 and ignores the higher-frequency variations. PC-3 has valleys at the null points of PC-1, so a combination of the two will either broaden or narrow the peak of the diurnal cycle. This behavior is a response to the dependence of the length of the day on the latitude.

The diurnal cycles as computed for two sites by HadAM3 and from ERBS data are now considered. Figure 7 shows the diurnal cycle for a region in the Sahara Desert (22°N, 22°E) from ERBS data and as computed by the model. The diurnal cycle for this region is one of the largest on Earth. Figure 7 shows a maximum of 340 W m^{−2} for ERBS and 350 W m^{−2} for the model, and a minimum of about 285 W m^{−2} for both. Haywood et al. (2005) showed that over the northern African deserts, dust can have a direct longwave effect of 35 W m^{−2} in the monthly mean. For an optical depth of 1, dust can cause a decrease of the OLR of 30 W m^{−2} at the daily maximum and 14 W m^{−2} at the minimum, so that the dust decreases the diurnal cycle significantly from that computed by the model. For the monthly mean, these effects would be averaged down.

The maxima for both the ERBE and model results occur near 1300 LST. The morning part of the diurnal cycle is close between the model and ERBS at 0600 LST, but the model computes a faster rise in OLR in the morning, from which one infers a faster rise in temperature. Several mechanisms could cause this slow rise in the observations as compared with the model. One possibility is that the reduction of surface insolation by dust slows the rise in the morning and causes a lower maximum near noon, and in the afternoon the surface cools quickly with reduced sunlight. Another explanation is that thin cirrus may be present, which are not computed by the model. A third conjecture for this difference is that the albedo of the model is too low. Finally, the model assumes an emissivity of 1. As a consequence, at a given temperature, the surface will radiate a little more than it should, but in doing so the temperature would decrease so that the observed OLR change would be small. In the afternoon the model decreases more slowly than the ERBS result does, indicating that in the model the ground is retaining heat too long, suggesting that in the model heat transfer to the atmosphere is too slow or that the heat is stored too deep in the ground. Clearly, further studies with additional data are required to resolve the processes involved here.

The diurnal cycle of the model is reconstructed using only PC-1 and is shown in Fig. 7. The first term alone gives an excellent representation of the diurnal cycle, The diurnal cycle based on ERBS measurements is reconstructed using one and two terms, that is, PC-1 × EOF-1 + PC-2 × EOF-2 (Fig. 7). For the ERBS case the first term alone reproduces most of the features of the diurnal cycle, except that PC-1 for ERBS peaks near 1230 LST. The addition of the second term shifts the peak to 1330 LST and gives a close fit, showing that higher-order terms must be quite small.

A region in the ITCZ in eastern Sudan (13.75°N, 35°E) is next examined in Fig. 8. The diurnal cycles for the Sahara Desert site were very smooth, but this ITCZ location has a very irregular diurnal cycle for the ERBS case. These irregularities are due to the limited sampling of the chaotic clouds over the region. Because of the irregular shape of the ERBS result, two terms provide only a rough fit to its diurnal cycle. The observed range of OLR is 180–265 W m^{−2} and the modeled range is 234–256 W m^{−2}, so that the observed range is much greater than that modeled. The observed OLR peaks at 1400 LST, and then drops sharply, indicating cloud formation. From midnight, the observed OLR increases through the remainder of the night, indicating that the clouds are dissipating. On the other hand, the model shows a peak value of 256 W m^{−2} at 1000 LST, after which the OLR decreases to the minimum of 234 W m^{−2} at 1500 LST, showing cloud formation during this time. Then, the clouds dissipate until 1800 LST, and after this the OLR comes to a plateau until midnight, when the clouds further decrease until 1000 LST. The modeled diurnal range of OLR is about one-fourth of that observed, suggesting that the cloud forcing is not adequately modeled. This minimum in the model OLR is several hours before the convection causes the OLR minimum in the ERBS data and is a symptom of model errors discussed by Slingo et al. (2004).

During much of the day, the model OLR is lower than the values at night in Fig. 8. Consequently, when the model OLR is projected onto the principal components, EOF-1 is negative, as was seen in Fig. 3b. These negative EOF-1 values do not occur in the convective regions for the ERBS results of Fig. 3a.

For the ERBS data, PC-1 (with 76% of the variance) peaks near 1230 LST, and PC-2 (with 10% of the variance) describes the shift of peak heating to the afternoon for regions that are clear in the afternoon and to morning for regions that are clear in the morning and develop afternoon cloudiness. For the model, nearly 90% of the variance is explained by the first term, which has a peak later in the day; less than 6% of the variance describes the effect of morning–afternoon clouds on OLR.

## 5. Results for ocean

The surface temperature of land undergoes large changes during the day, especially over deserts, resulting in large changes in the diurnal cycle of OLR. Because of the immense heat capacity of the ocean, the temperature change of its surface is quite small during the day, and the OLR change resulting from temperature change is likewise small. Most of the diurnal variation of OLR over ocean is due to cloud formation and dissipation.

### a. Variances over ocean

Table 2 shows that the RMS for the diurnal cycle of OLR over ocean for the model is 2.8 W m^{−2} for the ERBS domain. The ERBS result shows a RMS of 5.9 W m^{−2}, indicating that the diurnal cycle of OLR over ocean is greater than that computed by the model. In the model, the sea surface temperature is constant during the day. However, in some areas the observed diurnal temperature change can be large enough to change the OLR by 2–3 W m^{−2} (Webster et al. 1996), and air–sea interactions may magnify these changes.

The sum of the first five terms is much smaller for the ocean than for land, so the variance as a function of the order of the term converges far more slowly for the ocean for both the model and ERBS. The larger number of terms required to describe the diurnal cycle over ocean shows that the variety of diurnal cycles is greater than that over land. For ERBS, the sum of the first five terms is only 0.47, as compared with 0.66 for the first term of the model. The complexity is greater for ERBS than for the model, as was found over land.

### b. Comparison of model and ERBS over ocean in boreal summer

PC-1 and EOF-1 will be compared for the ocean case. Because the first term for the model accounts for 66% of the variance over the ERBS domain, whereas for ERBS the first term accounts for only 16% of the variance, the PCs and EOFs cannot be expected to agree very well. Figure 9 shows PC-1 for the diurnal cycle of OLR over the oceans for the ERBS results and for the model. The PC-1 from ERBS increases during the morning with a peak near noon and decreases to a minimum at 2000 LST. There is a subsidiary maximum just after midnight, followed by a decrease to 0630 LST. The increase during the night may be due to the clearing of the clouds that have formed during the day. Kondragunta and Gruber (1994) demonstrated large diurnal variability of cloudiness over the ITCZ and southwest Pacific convergence zone and a paucity of mid- and high-level clouds over the subsidence regions of the oceans. Note that low-level clouds do not have cold tops and thus do not create large decreases from the clear-sky OLR. For the model, PC-1 is very nearly sinusoidal, with a peak near 1600 LST and a minimum near 0400 LST.

Figure 10a shows the map of EOF-1 for ERBS. There are negative values over the western oceans and strong positive values for the middle and eastern Pacific and Atlantic Oceans in the Northern Hemisphere (summer), but not in the Southern Hemisphere (winter). Figure 1a shows that the RMS for the observed diurnal cycle is large over the ITCZ areas, but EOF-1 does not have large values in these areas. Thus, the observed variation over the ITCZ is described by higher-order PCs. The map of EOF-1 for the model results for ocean is shown in Fig. 10b. The modeled diurnal cycle is strong at low latitudes, coincident with the convectively active regions, and decreases with increasing latitude. There are maxima near some of the coasts, which may be due to a residual influence of the diurnal cycle over the adjacent land regions. In the regions of the ITCZ the modeled EOF-1 shows a significant diurnal cycle that does not appear in the ERBS EOF-1. Both the model and ERBS show strong positive EOF-1 values over the Indian Ocean at the equator. The features observed over the western and eastern oceans as noted above do not appear in the model results.

For ERBS, PC-2 accounts for 11% of the variance, and for the model, PC-2 describes 23% over the ERBS domain (Table 2). Figure 11 shows PC-2 for both ERBS and the model. The ERBS PC-2 is wavenumber 2. Although the quasi half-sine describing insolation can be expressed by a Fourier series containing a small wavenumber-2 term, PC-2 is a nonlinear response to the forcing by the diurnal cycle. The model PC-2 is a wavenumber-1 sinusoid 90° out of phase with PC-1, the effect of which is to give a sine wave at each region, with the phase determined by the proportions of PC-1 and PC-2.

Over oceans there is a wide range of behaviors of clouds and precipitation, and the OLR will have corresponding behaviors. Yang and Slingo (2001) note that studies have shown that a convection or precipitation maximum occurs early in the morning over some ocean regions. McGarry and Reed (1978) found that over West Africa the convective cloud maximum follows rainfall by up to 2 h, and they attribute this delay to the spreading of convective cloud tops after the peak of the rain. They also showed an afternoon peak in cloudiness and precipitation over some ocean regions, which will produce an afternoon minimum of OLR. Janowiak et al. (1994) showed that the morning peak of cloudiness is due to high clouds and that the afternoon maximum of cloudiness is due to midlevel clouds. These maxima of clouds would result in minima of OLR, and regions with the two peaks will appear as having large EOF-2 values. The model, however, shows for the second principal component a sine wave that is 90° out of phase with the first principal component. For the model, the first two principal components describe sine waves with a 1-day period with various phases and magnitudes that account for 88% of the variance of OLR over the ERBS domain (55°N–55°S). There is little variance remaining for wavenumber-2 features. Improvements of the model results over ocean require additional research into the various processes of the atmosphere–ocean interactions because they vary over the full range of behaviors over the world’s oceans. As the model is developed to include these processes better, the variance in the first two PCs will decrease as other behaviors are described by higher-order PCs.

A region over the Bay of Bengal (6°N, 87.75°E) has a large diurnal cycle for the ERBS observations and was selected for examination. Figure 12 shows the diurnal cycle of OLR for this region from ERBS observations and from the model. The diurnal cycle of OLR from the ERBS observations ranges from 182 to 242 W m^{−2} and has large irregularities that were not smoothed out by the measurements of 15 months, demonstrating the highly variable nature of the clouds over this region. The representation of the diurnal cycle of OLR for this region by use of only the first two terms is also shown. The observations indicate the formation of mid- and high-level clouds, which create minima of OLR near 0600–0800 and 2000–2200 LST. The peak value of 242 W m^{−2} near noon indicates that the mid- and high-level clouds have cleared by this time. The diurnal cycle of OLR for this site as computed by the model is small and has fairly small irregularities resulting from day-to-day variations of clouds, with a maximum of 195 W m^{−2} near 0800 LST and a minimum of 187 W m^{−2} near 2000 LST. The low level of OLR of the model shows that it computes cloud cover all day, rather than clearing in the early afternoon as the observations indicate. Further study is needed to establish the specific causes of these variations in order to direct the improvements that are required for the GCM to recreate these variations.

## 6. Discussion

The robustness of the principal components computed here must be considered, that is, are they significant or are they the results of either errors or the method of treatment? The ERBS results are based on 24 one-hour averages of OLR, so that there are 23 principal components. Only the first three were considered here. The eigenvalues of these three PCs are large and well separated, so that they are significant and are not mixtures of different PCs (North et al. 1982). In terms of Fourier analysis, one could compute 11 wave terms for sine and cosine parts. PC-1 and PC-2 have essentially wavenumber-1 shapes, and PC-2 is wavenumber 2. These simple shapes are easily described by the 24 one-hour averages, and there is no problem with temporal resolution.

We must consider the effects on these results of the following two atmospheric oscillations: the Madden–Julian oscillation (MJO) and El Niño–Southern oscillation (ENSO). The Madden–Julian oscillation (Madden and Julian 1972, 1994) has a period that varies between 40 and 50 days. For the ERBE analysis it was necessary to use a seasonal average for the diurnal cycle, that is, an average over June–August, so that the seasonal averaging time has two to three MJO periods. The ERBE results are based on 5 yr of data, and thus include 10–15 MJO events. The MJO is restricted to being near the equator, and the OLR change occurs in the longitudes between 70° and 130°E, where the OLR varies between 190 and 250 W m^{−2} (Wong and Smith 2003). Thus, any effects of MJO on the diurnal cycle of OLR would be restricted to the equatorial Indian Ocean.

The data span of the ERBS record used to compute the diurnal cycle of OLR is 1985 through 1990 and includes the ENSO of 1986/87, so that the computed diurnal cycle averages over any effects of this ENSO. Figure 1a shows that the RMS of the diurnal cycle for the subsidence region of the Pacific Ocean east of the date line is less than 3 W m^{−2} for the 1985–90 data period of ERBS. This implies that the diurnal cycle is small during both the warm and cool phases of ENSO. North of this region the RMS has a local maximum variation up to 12 W m^{−2} in the ITCZ. Because of the large amount of clouds and their activity in this region, one would expect that the diurnal cycle would be at least this large during either phase of ENSO.

The better description of the relevant processes remains in order to improve our understanding of the diurnal cycles. There are two sources of observation that should be exploited for the investigation of the diurnal cycles of OLR—the instruments aboard *Meteosat*-*8* and -*9*, and *GOES*-*8* and its successors. The GERB instruments aboard *Meteosat*-*8* and -*9* (Harries et al. 2005) provide excellent temporal sampling of OLR, from which Comer et al. (2007) have computed the diurnal cycle for the Meteosat sector by using principal component analysis for 1 month of data. This part of the earth includes the Sahara Desert and the Congo basin, whose diurnal cycles are among the strongest on the planet. By defining the diurnal cycle with 1 month of data, questions of ENSO or other large long-term variations are averted. These diurnal cycle results will be useful for model comparisons over the Meteosat sector.

Ellingson et al. (1989, 1994) developed a technique of retrieving OLR from High Resolution Infrared Radiation Sounder (HIRS) measurements aboard operational meteorological satellites. Ellingson and Ba (2003) have extended this method for application to the data from the five channels of the sounder aboard *GOES*-*8* and -*9* to compute OLR. Their use of information from the sounding channels minimizes the errors that are inherent when extracting OLR from window channels. The purpose of their paper was to report the method, so the scientific results were limited. The Ellingson and Ba (2003) method should be used to investigate the diurnal cycle over the Americas sector, which includes the Amazon basin and the Great Plains of North America. The GOES sounders also provide information about clouds, surface temperature, and atmospheric profiles of temperature and humidity with which to diagnose the dynamics that create the diurnal cycle of OLR and related parameters.

In July the ITCZ has moved to a northern location, bringing the monsoon to India, Southeast Asia, and northwest Africa. The surface insolation causes intense evapotranspiration in these rain regions, after which the resulting latent heat is released to create a powerful diurnal cycle of deep convection with its outflow. This resulting outflow at middle and high levels in the troposphere causes a flow at low levels that brings additional moisture into the region. These regions may be regarded as steam engines driven by the net radiation, which is large for the areas, and these high, cold clouds have very low OLR. The ability of a GCM to replicate these features is important to its validity and should be tested further using the GERB and GOES sounder data.

Cess et al. (1997) use both short- and longwave results from ERBE in their model comparisons of the seasonal changes of cloud radiative forcing, thus demonstrating the power of including the shortwave behavior. Shortwave variations are sensitive to cloud at any level, depending on thickness, but OLR is affected largely by high clouds and only a little by low clouds. The results of Rutan et al. (1998) for the diurnal variation of albedo could be compared with GCM results to learn more about low clouds as computed by the GCM. To proceed beyond this point, additional information regarding clouds is needed in order to know what parameters are responsible for significant differences between the observations and the model results. These parameters include cloud fraction, cloud-top pressure (temperature), and cloud optical depth. Existing datasets, for example, the dataset produced by the International Satellite Cloud Climatology Project (Rossow and Schiffer 1991), should be analyzed to get this information in an understandable and easy-to-use form.

## 7. Conclusions

The method of principal component analysis has been used to extract the features of the diurnal cycle of outgoing longwave radiation as generated by HadAM3 of the Hadley Centre and to compare these features with those derived from the measurements from the Earth Radiation Budget Experiment aboard the Earth Radiation Budget Satellite. The diurnal cycle of OLR differs in range and physical mechanisms over land and over ocean, so the earth is partitioned into land and ocean for the analysis.

Over land, the root-mean-squares of the diurnal cycles are comparable, with 11.4 W m^{−2} for the model and 13.3 W m^{−2} for ERBS. The first principal component for the model agrees well with that from ERBS and accounts for 89% of the variance of OLR for the model and 76% for ERBS. However, the model PC-1 has a peak near 1330 LST, whereas the ERBS PC-1 peaks at 1230 LST. The model PC-1 decreases by 3 W m^{−2} between midnight and 0600 LST, whereas the ERBS result does not decrease during this time. Intuitively, both of these features seen in the model result are expected, so more research is needed to resolve this difference. Following sunrise the PC-1 for the model increases more slowly than for ERBS observations; however, over the Sahara Desert the GCM’s OLR increases more rapidly than that of the observations. The empirical orthogonal function map corresponding to PC-1 for the model agrees reasonably well with the map for ERBS.

For the ocean, the diurnal cycle is much smaller than over land, and the RMS is 2.8 W m^{−2} for the model and 5.9 W m^{−2} for ERBS. Also, the variety of patterns to be described by the PCs is considerably greater over the ocean for ERBS than over land. The lack of variation of sea surface temperature during the day and the concomitant feedback processes may be responsible for the low variability of OLR over ocean. For the ocean, the model PC-1 and PC-2 are simple sine waves, whereas the ERBS PC-1 and PC-2 have more irregular structures.

Reasons for the differences between the modeled and satellite-derived results that have been used in this study are discussed. The model computes convection too early in the day, which reduces the variance of the second principal component and causes the first principal component to peak later in the day. Over the region covered by the *Meteosat*-*8* satellite, the Geostationary Earth Radiation Budget instrument (Harries et al. 2005) now provides data with excellent temporal sampling with which to study these issues.

## Acknowledgments

The authors were supported in this work by the Earth Sciences Enterprise of NASA by contract with the Langley Research Center (LaRC) of NASA. ERBE data for the computation of the diurnal cycle of outgoing longwave radiation were supplied by the Atmospheric Sciences Data Center of LaRC. We are indebted to Prof. A. J. Slingo of Reading University for providing the HadAM3 output for outgoing longwave radiation and for invaluable discussions. We also thank the reviewers for the insight of their comments, which improved the paper considerably.

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PC-1 of the diurnal cycle of OLR of ERBS and HadAM3 for 55°S–55°N over land during June–August.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

PC-1 of the diurnal cycle of OLR of ERBS and HadAM3 for 55°S–55°N over land during June–August.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

PC-1 of the diurnal cycle of OLR of ERBS and HadAM3 for 55°S–55°N over land during June–August.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

Map of EOF-1 of diurnal cycle of OLR from (a) ERBS and (b) HadAM3 for 55°S–55°N over land during June–August.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

Map of EOF-1 of diurnal cycle of OLR from (a) ERBS and (b) HadAM3 for 55°S–55°N over land during June–August.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

Map of EOF-1 of diurnal cycle of OLR from (a) ERBS and (b) HadAM3 for 55°S–55°N over land during June–August.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

As in Fig. 2, but for PC-2.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

As in Fig. 2, but for PC-2.

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As in Fig. 2, but for PC-2.

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As in Fig. 3, but for EOF-2.

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As in Fig. 3, but for EOF-2.

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As in Fig. 3, but for EOF-2.

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As in Fig. 2, but for PC-3.

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As in Fig. 2, but for PC-3.

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As in Fig. 2, but for PC-3.

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Diurnal cycle of OLR over the Sahara Desert (22°N, 22°E) and its representation using the first two terms of principal components and EOFs for ERBS and HadAM3.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

Diurnal cycle of OLR over the Sahara Desert (22°N, 22°E) and its representation using the first two terms of principal components and EOFs for ERBS and HadAM3.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

Diurnal cycle of OLR over the Sahara Desert (22°N, 22°E) and its representation using the first two terms of principal components and EOFs for ERBS and HadAM3.

Citation: Journal of Applied Meteorology and Climatology 47, 12; 10.1175/2008JAMC1924.1

As in Fig. 7, but over the intertropical convergence zone in eastern Sudan (13.75°N).

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As in Fig. 7, but over the intertropical convergence zone in eastern Sudan (13.75°N).

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As in Fig. 7, but over the intertropical convergence zone in eastern Sudan (13.75°N).

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As in Fig. 2, but over ocean.

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As in Fig. 2, but over ocean.

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As in Fig. 2, but over ocean.

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As in Fig. 3, but over ocean.

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As in Fig. 3, but over ocean.

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As in Fig. 3, but over ocean.

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As in Fig. 4, but over ocean.

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As in Fig. 4, but over ocean.

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As in Fig. 4, but over ocean.

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As in Fig. 7, but over the ocean in the Bay of Bengal (6°N, 87.75°E).

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As in Fig. 7, but over the ocean in the Bay of Bengal (6°N, 87.75°E).

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As in Fig. 7, but over the ocean in the Bay of Bengal (6°N, 87.75°E).

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Variances for land during boreal summer in ERBE domain.

Variances for ocean during boreal summer in ERBE domain.