We quantify the seasonal and spatial variations of cloud radiative impacts in the tropical tropopause layer (TTL) by using cloud retrievals from Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO), International Satellite Cloud Climatology Project (ISCCP) and CloudSat. Over the convective regions including Western Pacific, Africa, South America, and South Asia, we find pronounced solar heating and infrared cooling in the lower part of the TTL (<∼16 km). The solar heating weakens above 16 km and nearly diminishes at 18 km, whereas the infrared cooling extends vertically throughout the TTL. The net cloud radiative forcing, which is the summation of cloud solar and infrared radiative forcing, has heating below ∼16 km and turns to mostly cooling above 17 km. The net cloud radiative heating over the convective regions is mainly contributed from solar radiation, whereas the weak net cloud radiative heating surrounding these regions is due to infrared heating. To further examine the impacts of different cloud types in the TTL, we classified TTL clouds in terms of cloud optical depths (τ) as thin cirrus (τ < 0.3), thick cirrus (0.3 ≤ τ < 3), and opaque clouds (τ ≥ 3). In the solar part, thin and thick cirrus play a relatively small role and the impact of cloud-free air above clouds is negligible. The solar heating is dominantly contributed from the solar absorption near the top of opaque clouds. In the infrared part, the thick cirrus heating is mainly confined over the convective regions in the lower part of TTL while the thin cirrus infrared heating is more prevalent both vertically and horizontally in the TTL, which is the dominant infrared heating source. The infrared cooling in cloud-free air above clouds is dominant above 17 km, whereas the infrared cooling near the top of opaque clouds is dominant below. Despite the infrared heating effects of thin and thick cirrus clouds, the infrared cooling from the opaque cloud top and cloud-free air above clouds outweighs the heating effects so that the ensemble mean cloud infrared radiative forcing is mostly cooling except outside the convective regions.
 Air enters the stratosphere preferentially through upwelling in the tropics, and the upper tropical troposphere is thus the most important region for understanding the troposphere to stratosphere exchange [e.g., Holton et al., 1995]. It is now well recognized that the tropical tropopause is not a material surface but there is a transition region between the troposphere and the stratosphere [e.g., Highwood and Hoskins, 1998; Folkins et al., 1999]. The transition layer is known as the tropical tropopause layer (TTL) [e.g., Fueglistaler et al., 2009]. The TTL connects the convectively dominated overturning circulation of the Hadley cell to the slow wave-driven upwelling of the lower stratospheric Brewer-Dobson circulation. The base of the TTL is usually defined as the level of zero net radiative heating rate (∼14.5–15 km) [e.g., Folkins et al., 1999; Gettelman et al., 2004; Fueglistaler et al., 2009], at which the net radiative heating rate profile changes from cooling to heating. Air below this level will tend to sink back to the troposphere while air above this level will tend to rise into the stratosphere. The top of the TTL is often defined as the level at which upward convective mass flux becomes small compared to the Brewer-Dobson circulation (∼18.5 km) [Fu et al., 2007].
 The TTL is the region where most air enters the stratosphere. However, how air enters the stratosphere through the TTL is still uncertain. Vigorous “fountain”-like convection is observed to lift air directly into the stratosphere through convective overshooting [e.g., Kelly et al., 1993], but this type of transport is too infrequent to be responsible for the troposphere to stratosphere transport (TST) [Gettelman et al., 2002; Küpper et al., 2004]. The general view is that convection transports air at least to the base of the TTL, and then air is radiatively lifted further up through the TTL into the stratosphere. The bulk of evidence suggests that the large-scale slow vertical ascent dominates mass transport across the TTL and that the slow ascent is required for effective dehydration [e.g., Folkins et al., 1999; Holton and Gettelman, 2001]. Nonetheless, this slow motion that is balanced by clear-sky radiative heating rates in the TTL is too slow to explain the observed tracer measurements [Boering et al., 1994; Corti et al., 2006]. An alternative explanation is that thin cirrus clouds, widespread in the TTL, would enhance radiative heating rates and therefore speed up the upwelling [Corti et al., 2006]. A single thin cirrus cloud layer in the TTL with no clouds underneath induces a strong local heating at the cloud layer by absorbing infrared radiation from below and thus strengthens the upwelling. However, if a thin cirrus cloud layer overlaps lower clouds, then the layer could be either heated or cooled, depending upon the contrast between the amounts of radiation that thin cirrus absorbs and emits [e.g., Hartmann et al., 2001a]. If a thin cirrus cloud layer in the TTL is cooled as sufficient cold thick clouds underlie it, it can result in a weakening of the upwelling that slows down the TST.
 Therefore, accurately quantifying the radiative energy budget in the TTL is an important and necessary step to improve our understanding of the physical processes responsible for the TST. Newly available satellite data from CALIPSO that could detect thin cirrus clouds offer an opportunity to address the radiative impacts of clouds in the TTL. In this paper, we will use a radiative transfer model to derive the radiative heating rates in the TTL, employing cloud information from CALIPSO, ISCCP and CloudSat along with balloon-borne measurements of temperature, ozone and water vapor. We will focus on the spatial and seasonal variations of cloud radiative forcing in the TTL.
2. Cloud Optical Depth Retrieval
 On 28 April 2006, the CALIPSO satellite was launched into the nearly identical Sun-synchronous polar orbit of the Aqua satellite and about 1 min behind it. The primary active sensor carried by CALIPSO is a two-wavelength polarization-sensitive backscatter lidar, which provides high-resolution vertical distributions of clouds and aerosols along with their optical properties [Winker et al., 2007]. The CALIPSO lidar probes clouds up to a maximum optical depth of ∼3.0–4.0. With sufficient averaging, the CALIPSO lidar is able to detect thin clouds with optical depth of 0.01 or less. The CALIPSO lidar cloud observations from space provide an unprecedented opportunity to probe the vertical structures of tropical thin cirrus clouds [e.g., Fu et al., 2007; Sassen et al., 2008].
 In this study, we use 1 year CALIPSO L2 5km V2.01 cloud product from June 2006 to May 2007 to investigate the radiative impacts of clouds in the TTL. The cloud optical depths were retrieved from the CALIPSO cloud observations following the lidar equation given by Platt . The observed cloud layer-integrated attenuated backscatter γ′ is related to the true cloud backscatter coefficient β(z) by
where zt and zb are cloud top and base height, η is the layer effective multiple scattering factor that represents a correction factor to the Beer-Lambert law to account for the multiple scattering captured by the lidar receiver and σ is the volume extinction coefficient. Usually, the lidar ratio Sc = is introduced to simplify the equation (1) so that
where the visible optical depth τ = σ(z)dz and τc is the cloud layer optical depth (i.e., τc = σ(z)dz). Performing the integration, γ′ becomes
Thus, the cloud layer optical depth τc can be retrieved from
where γ′ can be obtained from the CALIPSO L2 5km V2.01 cloud product. According to Liu et al. , the observed γ′ from CALIPSO has a systematic uncertainty of about 3% (note that the random noise associated with γ′ can be larger).
2.1. Multiple Scattering Factor η
 Since the spaceborne lidar has a long range to the target atmosphere, even a narrow field of view (FOV) angle yields a large footprint. Therefore, the multiple scattering effect has to be taken into account in retrieving cloud optical depths [e.g., Platt et al., 1999; Völger et al., 2002; Winker, 2003]. In previous studies, Monte Carlo simulations that adopted the specific space lidar configurations were performed to estimate the values of multiple scattering factor. Platt et al.  showed that the simulated η for thick ice clouds has the value smaller than 0.54 with large variation. Such variation may be partly due to the different approximations used in a given multiple scattering simulation [Platt et al., 1999]. Völger et al.  showed that η is about 0.4 for cirrus clouds for the Experimental Lidar In Space Equipment (ELISE) which has a footprint of about 116 m. They also found similar η in cirrus clouds for the Lidar In-Space Technology Experiment (LITE) 286 m footprint. Winker  showed that η has a value between 0.6 and 0.75 for cirrus clouds detected by CALIPSO. Both Völger et al.  and Winker  found that η is nearly constant throughout the cloud layers. Below, we derive η for cirrus clouds based on simple physical arguments.
 The CALIPSO receiver has an FOV angle of 130 μrad that corresponds to a footprint of ∼100 m by considering its orbiting altitude of 705 km. Since the lidar FOV is very small relative to the geometric angle transected by the lidar footprint within one cloud layer (see θ in Figure 1), the incident lidar beams can be treated as parallel beams. For a cirrus cloud layer with a typical cloud thickness of 1 km, the angle θ is about tan−1(100/1000) ≈ 6°.
 As the incident lidar beam hits the cirrus cloud layer, the forward diffraction beam, which is half of the scattered incident energy, should largely remain within the lidar footprint (process 1 in Figure 1). Thus, the downward first-way effective optical depth is half of the original one, i.e., ηdiff = 0.5. Note that if the incident beam is close to the edge of the footprint, then half of the diffracted energy would escape. By using a triangular smoother with the minimum weighting of 0.5 and the maximum weighting of 1, we obtained a ηdiff equal to 0.6. For ice particles with smooth surface, there is ∼15% of the scattered light that is related to the forward delta transmission [e.g., Fu, 2007]. In reality, there are also contributions from sideward scattering that is scattered back to the lidar receiver through secondary scatterings. But for cirrus, this sideward scattering plays only a minor role that can be ignored compared to the strong forward diffraction [Völger et al., 2002]. So the downward first-way multiple scattering factor should range from 0.45 to 0.6, depending on the smoothness (or roughness) of ice particle surfaces.
 Due to the narrow lidar FOV angle, one would expect only exactly upward backscattered beam can be received by the lidar. However, the backscattered beam within the scattering angle between about 177° and 183° can also be received by the lidar through a forward diffraction to the exact upward direction (process 2 in Figure 1). According to the reciprocity principle, the chance that a beam undergoes process 2 is equivalent to the chance with process 1. Therefore, the upward second-way effective transmittance is equal to that for the downward first way. In summary, the multiple scattering factor for ice clouds ranges from 0.45 to 0.6. The value of 0.6 should be the upper limit in which delta transmission is ignored. The lower limit should not be smaller than 0.35 where all diffracted rays along with the delta transmission are considered as the unscattered light. In this study, we choose a η value of 0.5 with an uncertainty of ±0.1 for ice clouds.
 For water clouds that can be penetrated by the lidar, there is less forward diffraction remained within the lidar sampling volume and there is no delta transmission. But the sideward scattering is more significant owing to much shorter mean photon free path length. A Monte Carlo simulation study [Hu, 2007] has demonstrated that the multiple scattering factor of water clouds is a function of depolarization ratio δ,
For the 1 year CALIPSO observation, we found that η has a mean value of about 0.6 ± 0.2 for water clouds.
2.2. Lidar Ratio Sc
 Another parameter that needs to be determined in the retrieval of cloud optical depth from equation (4) is Sc that is the ratio of cloud extinction coefficient to backscatter coefficient. The lidar ratio Sc is equivalent to the inverse of the normalized backscattering phase function, 4π/P(π), where P(π) is primarily a function of particle shape [Liou, 2002]. For ice clouds, lidar ratio Sc is variable due to the irregular ice particle shapes. Nonetheless, one can estimate the value of effective lidar ratio, which is the product of lidar ratio and multiple scattering factor ηSc. From equation (3), if cloud is opaque, the two-way transmittance exp(−2ητ) comes close to zero, so that
In this study, we find that ηSc ≈ 17 sr with a standard deviation of about 4 sr based on the CALIPSO observations. This value of ηSc is consistent with previous studies [e.g., Platt et al., 1999; Hu, 2007]. The uncertainty associated with the use of the constant effective lidar ratio in retrieving ice cloud optical depths will be discussed in section 2.3. For water clouds, it is found that Sc ≈ 19 sr for spherical particles [Pinnick et al., 1983; O'Connor et al., 2004; Hu, 2007].
 Using η = 0.5 and ηSc = 17 sr for ice clouds, equation (4) can be rewritten as
We do not perform the optical depth retrieval for the columns containing the cloud layers with 1 − 34γ′ < 0. The impact of treating these columns on the radiative forcing in the TTL will be discussed in section 5.3.
2.3. Uncertainty in the Retrieved Ice Cloud Optical Depth
 Before carrying out the uncertainty analysis, it is of interest to compare our retrieved ice cloud optical depth with the CALIPSO official ice cloud optical depth. In the CALIPSO L2 5 km V2.01 cloud product, there are three categories of ice cloud optical depth retrievals. They are (1) clear air transmission (CAT) retrieval, (2) lidar equation (i.e., equation (4)) retrieval using a ηSc of 15 sr, and (3) lidar equation retrieval with adjusted lidar ratios to avoid unphysical optical depths. The CAT method employs layer transmittance that is measured from clear air returns on both sides of cloud layers. It has the Extinction QC flag of one in the CALIPSO cloud product and is considered to be the most reliable retrieval. The multiple scattering factor has to be considered in retrieving cloud optical depth from space satellite. However, there is no multiple scattering correction (i.e., multiple scattering factor = 1) in CAT retrieval in the Version 2 official product (D. Winker, personal communication, 2009). The latter two retrievals use a multiple scattering factor of 0.6. The optical depths retrieved from the third method that utilizes adjusted lidar ratios are not reliable and more like random numbers (D. Winker, personal communication, 2008). These three retrievals account for about 2.7%, 89.4% and 7.9% out of all ice cloud optical depth retrievals. By applying the multiple scattering correction of 0.6 to the CAT retrieval, the difference between our retrieved ice cloud optical depth and the CAT retrieval is about 3%. For the cases where the second CALIPSO official retrieval is available, our retrieved ice cloud optical depth is about 30% larger because the effective lidar ratio and multiple scattering factors that we used are 12% larger and 20% smaller, compared to those used in the official retrieval.
 From equation (4), the uncertainty in the retrieved ice cloud optical depth is mainly attributed to the uncertainties associated with multiple scattering factor η, effective lidar ratio ηSc and observed layer-integrated attenuated backscatter γ′.
 As discussed in section 2.1, η for ice clouds ranges from about 0.4 to 0.6. Since η of 0.5 is used in this study, η has an uncertainty of about 20%. For the effective lidar ratio, we used a constant value of 17 sr in the retrieval. To access the error in the retrieved ice cloud optical depths due to the use of the constant effective lidar ratio, we deduce a set of effective lidar ratio using the cases where CAT retrieval is available. From equation (3), we have
where ηcat = 1, τc,cat is the CALIPSO official ice cloud optical depth retrieved from the CAT method and γ′ is the observed layer integrated attenuated backscatter. Compared with (ηSc)cat, the uncertainty in using the constant effective lidar ratio of 17 sr is about 14.7%. This is a stringent test by comparing the effective lidar ratio derived from opaque clouds with those from thin cirrus.
 Assuming that η, ηSc and γ′ are independent, the uncertainty in the retrieved ice cloud optical depths can be calculated from
It is found that the relative uncertainty in the retrieved ice cloud optical depth induced by η, ηSc and γ′ is about 20%, 15% and 3% respectively. Thus, our retrieved ice cloud optical depth has a relative uncertainty of about 25%.
3. Combined CALIPSO, ISCCP, and CloudSat Cloud Fields
 For the cloud column that CALIPSO can penetrate without getting saturated, the optical depths retrieved from CALIPSO observations are used. The cloud vertical extent is obtained from the cloud top/base height reported in the CALIPSO L2 5 km V2.01 product. The radiative heating rate in cloudy conditions is obtained by inputting CALIPSO cloud information along with the mean atmospheric profiles into the radiative transfer model.
 For the column where the lowest cloud layer is opaque to CALIPSO, the cloud optical depth and vertical structure retrieved from CALIPSO are used for the nonopaque cloud layers above while the ISCCP cloud optical depth and CloudSat cloud vertical structure are blended in for the opaque cloud layer.
 ISCCP data have been widely used to study the influence of clouds on the radiative energy budget [e.g., Hartmann et al., 2001b; Yang et al., 2008]. Based on the analysis of available weather satellite radiance measurements, ISCCP identifies every pixel as clear sky or a single cloud layer with a cloud top pressure and a total cloud optical depth. The ISCCP D1 data set [Rossow and Schiffer, 1999] provides cloud fractions for 42 cloud categories according to seven cloud top pressures (10–180–310–440–560–680–800–1000 hPa) and six cloud optical depths (0.02–1.27–3.55–9.38–22.63–60.36–378.65).
 In consideration of the seasonal and spatial variations of clouds, we use monthly mean ISCCP cloud fields averaged over 10 years from 1995 to 2005 with a spatial resolution of 2.5° × 2.5°. In this study, the last four optical depth bins from ISCCP (3.55–9.38–22.63–60.36–378.65), which exceed the threshold of CALIPSO detect limit, are used. Since the optical depth that ISCCP provides is the total optical depth for the whole column, the optical depth for the opaque cloud layer is calculated by subtracting the total optical depth above the opaque cloud layer from the ISCCP optical depth
where τISCCP,i is the optical depth from each of the last four midbin used in ISCCP (6.46, 16.0, 41.5 and 219.5) and is the summation of the optical depths retrieved from the CALIPSO observations for the nonopaque cloud layers above the opaque cloud layer. Thus, blending in ISCCP cloud information for the lowest opaque cloud layer results in four different cloud profiles which have the same cloud optical depths from CALIPSO for the nonopaque cloud layers and four different cloud optical depths from ISCCP for the lowest opaque cloud layer. The cloudy heating rate for such cases that have an opaque cloud layer is obtained by
where QR,i is the heating rate corresponding to the four blended cloud profiles, and CISCCP,i is the ISCCP cloud fraction corresponding to the highest cloud top pressure detected by CALIPSO and the last four ISCCP optical depth bins.
 CloudSat flies 10–15 s ahead of CALIPSO and overlaps the footprint of CALIPSO. The Cloud Profiling Radar (CPR) onboard CloudSat is a 94 GHz, nadir-looking radar [Im et al., 2005]. The CPR could not well capture thin cirrus clouds but could penetrate optically thick clouds. For the opaque cloud layers to which CALIPSO gets saturated, we use cloud top height from CALIPSO and cloud base height from CloudSat to better represent the cloud vertical extent. In this study, the CloudSat level 2 geometrical profiling product (GEOPROF) [Mace et al., 2007; Marchand et al., 2008] is used. Pixels with GEOPROF cloud mask greater than 20 are identified as clouds.
4. Atmospheric Profiles and Radiative Transfer Model
4.1. Atmospheric Profiles
 Balloon-borne observations of temperature, ozone and water vapor were collected from the tropics. In total, 3303 simultaneously measured temperature and ozone profiles of at least up to 28 km were obtained from fourteen Southern Hemisphere Additional Ozonesonde (SHADOZ) [Thompson et al., 2003] stations during 1998–2007 (Figure 2). A total of 137 water vapor profiles, measured by the cryogenic frost-point hygrometer as well as the NOAA/CMDL (now NOAA/ESRL) frost-point hygrometer balloon soundings, were obtained from seven tropical stations (Figure 2) (see Figure 2c of Yang et al.  for details of the profiles). In order to obtain accurate radiative heating rate calculations in the TTL, the observed atmospheric profiles are extended up to 0.2 hPa by blending in the United Kingdom Meteorological Office (UKMO) monthly stratospheric analysis of temperature data and HALogen Occultation Experiment (HALOE) monthly ozone and water vapor data [Swinbank and O'Neill, 1994; Russell et al., 1993; Gettelman et al., 2004], following Yang et al. . In this study, monthly and zonal/latitudinal mean atmospheric profiles are used as the inputs to the radiative transfer model. The seasonal variation associated with atmospheric profiles in the TTL radiative heating rate is negligible except above 17 km (∼0.2 K/d). For our purpose of evaluating the cloud radiative effects in the TTL, it is accurate enough to use the tropical mean atmospheric profiles since the variation of cloud radiative effects is mainly determined by the variation in cloud fields. In the radiative transfer calculations, the atmospheric profiles have a vertical resolution of 100 m below 30 km and a vertical resolution of 1 km above 30 km.
4.2. Radiative Transfer Model
 The radiative transfer model we use is the NASA Langley Fu-Liou radiative transfer model [Fu and Liou, 1992, 1993; Fu, 1996; Fu et al., 1998; Rose and Charlock, 2002]. The radiative transfer scheme is based on the delta-four-stream method for both solar and infrared spectra [Liou et al., 1988; Fu and Liou, 1993] which are divided into six and twelve bands, respectively. The correlated k-distribution method is used to parameterize the nongray gaseous absorption by H2O, CO2, O3, N2O and CH4 [Fu and Liou, 1992] with the addition of CFCs and CO2 in the window region [Kratz and Rose, 1999]. The H2O continuum absorption using the CKD 2.4 [Tobin et al., 1999] is included in the whole thermal infrared spectra (0–2850 cm−1). For ice clouds, the single-scattering properties are parameterized using ice water content and a generalized effective particle size [Fu, 1996; Fu et al., 1998]. For water clouds, the single-scattering properties are parameterized based on Mie calculations using liquid water content and mean effective radius [Slingo, 1989]. The difference of heating rates between the Fu-Liou model and line-by-line calculations is less than ∼0.04 K/d in the TTL [Fu and Liou, 1992; Gettelman et al., 2004].
5.1. Cloud Distributions From CALIPSO
 The latitude-longitude distributions of cloud fractions at 18 km, 17 km, 16 km, 15 km and 14 km are shown in Figure 3 for each season. The cloud fraction, derived from the CALIPSO cloud observations, is defined as the number of cloud pixels divided by the total number of observations within each 2.5° × 2.5°grid box at a given level. Shown in Figure 3, the clouds above 14 km originate mainly from Western Pacific, Africa, South America and South Asia where the tropopause temperature is cold and convection frequently occurs [e.g., Sassen and Wang, 2008]. The cloud systems over these regions exhibit strong seasonal migrations. Over Western Pacific, the cloud systems intensify from the Northern Hemisphere (NH) fall to a maximum strength in the NH winter and then weaken in the NH spring. These cloud systems appear to be weakest in the NH summer whereas strong cloud systems appear over South Asia associated with the Indian summer monsoon. Over South America, the cloud systems are relatively stable throughout the year except during the NH summer when the cloud systems shift northward to Mexico. Over Africa, the cloud systems are of minimum strength in the NH summer, intensify during the NH fall and NH summer and reach its maximum in the NH spring. In general, the belt of maximum cloud occurrence above 14 km is near the equator in the NH spring, and moves northward to about 15°N in the NH summer. It remains around 10°N in the NH fall and shifts southward to 10°S in the NH winter. The movement of the maximum cloud occurrence in the tropics is consistent with the seasonal shifting of the InterTropical Convergence Zone (ITCZ).
 We also examine the seasonal and spatial variations of different types of clouds classified by optical depths. They are thin cirrus (τ < 0.3), thick cirrus (0.3 ≤ τ < 3) and opaque clouds (τ ≥ 3) [Sassen and Cho, 1992]. For our interest in the TTL, we focus only on the cloud columns with the highest cloud top higher than 14 km. Figures 4 and 5 show the seasonal and spatial distributions of cloud fractions for the highest cloud layer with different cloud optical depths and for whole cloud column with different integrated cloud optical depths, respectively. The seasonal and spatial variations of the thin cirrus clouds in Figure 4 resemble the characteristics as seen in Figure 3 for the clouds at 14 km and 15 km. In the TTL, most of the highest clouds are thin cirrus (Figure 4) and majority of the cloud columns have integrated cloud optical depths of greater than 3.0 (Figure 5). Thus, we can conclude that majority of the thin cirrus clouds reside above optically thicker cloud layers, resulting in the whole cloud column to be opaque. This result can be more clearly seen from Figure 6 that depicts the probability density function of column integrated cloud optical depths. Over 30°S–30°N, the cloud fraction of the cloud columns with the highest cloud top within the TTL is 28%. About 50% of the cloud columns are opaque. The cloud fractions of thin and thick cirrus cloud columns are nearly equal.
5.2. Cloud Radiative Forcing
 In this paper, cloud radiative forcing is defined as the difference between radiative heating rates (in unit of K/d) for all-sky and clear-sky conditions. It describes the vertical distribution of cloud contribution to atmospheric radiative heating rate. In the paper, we will show the ensemble mean cloud radiative forcing results over each 2.5° × 2.5° grid box,
where the overbar represents the ensemble mean over each 2.5° × 2.5° grid box, R,all-sky and R,clear are ensemble means of all-sky and clear-sky heating rate profiles within each grid box. The vertical profile of all-sky heating rate R,all-sky is given by
where Fraccloudy is the cloud fraction for the given grid box that is obtained from the CALIPSO cloud observation. A radiative transfer calculation is performed for every cloud profile along with the mean atmospheric profile. We then do the ensemble mean over each grid box to get R,cloudy. The clear-sky heating rate R,clear is calculated by using the mean atmospheric profiles.
 In the radiative transfer calculations, the monthly and latitudinal dependence of solar insolation and the diurnal variation of solar radiation are taken into account explicitly. The solar surface albedo and thermal surface emissivity are set to be 0.07 and 0.99, respectively. All chemical gases concentrations are set to be the average values between June 2006 and May 2007 (CO2: 380 ppmv; CH4: 1.775 ppmv; N2O: 0.32 ppmv; CFC-11: 0.25 ppbv; CFC-12: 0.535 ppbv and CFC-22: 0.18 ppbv). Clouds with cloud top height higher than 7 km (∼−20°C) are assumed to be ice with a mean effective ice particle radius of 30 μm.The sensitivity to the assumed ice particle size will be discussed in section 5.3. Clouds with cloud top height below 7 km are assumed to be water with a mean water droplet radius of 10 μm. Cloud extinction coefficient is considered to be vertically homogenous within a given cloud layer.
5.2.1. Radiative Forcing of All Clouds
Figure 7 shows the seasonal and spatial dependences of cloud solar radiative forcing at 18 km, 17 km, 16 km and 15 km. We find pronounced solar heating at 15 km and 16 km over Western Pacific, Africa, South America and South Asia with the seasonal migrations of cloud systems. The heating decreases above 16 km and nearly diminishes at 18 km. The cloud solar radiative forcing is due to two contributions. One is the solar heating related to the absorption of clouds. Another is related to the enhanced absorption of solar radiation by cloud-free air above clouds due to the underlying clouds that reflect solar radiation upward. The second contribution is found to be small in the TTL (not shown). Thus, the solar heating shown in Figure 7 is mostly contributed from the cloud absorption of solar radiation.
Figure 8 is the same as Figure 7 but for the cloud infrared radiative forcing. From 15 km to 16 km, the strong infrared cooling surrounded by infrared heating is found over the four regions (i.e., Western Pacific, Africa, South America and South Asia). Similar to the solar heating shown in Figure 7, the strength of infrared cooling weakens at 17 and 18 km. The infrared cooling above 17 km with the magnitude of smaller than 0.5 K/d is found to be cloud-free air cooling due to the underlying clouds (not shown). Below 17 km, the infrared cooling contributed from clouds is dominant.
Figure 9 shows the seasonal and spatial dependences of net cloud radiative forcing which is the summation of cloud solar and infrared radiative forcing. The net cloud radiative forcing varies with the seasonal migrations of cloud systems shown in Figure 3. In the NH spring, the maximum net cloud radiative heating at 15 km is found over the central Africa. The maximum moves to South Asia in the NH summer and South America in the NH fall. In the NH winter, the maximum net cloud radiative heating is located over the Western Pacific warm pool. As also shown in Figure 9, net cloud radiative heating is strongest at 15 km and decreases to mostly radiative cooling above 17 km. The net cooling above 17 km with a typical value of smaller than 0.5 K/d is found to be contributed from the infrared cooling in cloud-free air. Combining Figure 7, Figure 8 and Figure 9, the net cloud radiative heating found over the convective regions in the lower part of TTL is mainly contributed from solar heating and the weak net radiative heating outside these regions is due to infrared heating.
 The vertical profile of the annual mean cloud radiative forcing over 30°S–30°N is shown in Figure 10. The cloud solar radiative forcing increases with height from 10 km to a maximum of ∼0.24 K/d around 14 km and then decreases with height. Above 18 km, the cloud solar radiative forcing is nearly constant with the value of about 0.03 K/d. The cloud infrared radiative forcing exhibits an “s”-like shape. It has radiative heating from 10 km to 13.5 km and turns to cooling above 13.5 km. The maximum cooling of 0.1 K/d is found at about 15 km. The net cloud radiative forcing shows heating from 10 km to 17 km and cooling above 17 km. In the TTL, we found positive solar cloud radiative forcing and negative infrared cloud radiative forcing. Solar heating is dominant below 17 km. Above 17 km, infrared cooling is dominant.
5.2.2. Radiative Forcing of Thin Cirrus Cloud
 To further understand the cloud radiative impacts in the TTL shown in Figure 7 and Figure 8, we performed the radiative heating rate calculations by removing the thin cirrus clouds (τ < 0.3), with cloud top height higher than 14 km. By subtracting the cloud radiative forcing fields in which thin cirrus is removed from the original cloud radiative forcing (Figures 7–9), we obtain the impacts of thin cirrus clouds on the cloud radiative forcing in the TTL (Figures 11–13).
 In the solar part (Figure 11), thin cirrus plays a very minor role above 17 km. At 15 km and 16 km, the thin cirrus solar heating is preferentially found over the convective regions where thin cirrus overlies thick clouds (Figure 4 and Figure 5). There, thin cirrus clouds absorb more solar radiation from the underlying thick clouds which reflect strong solar radiation upward. In the infrared part (Figure 12), we found widespread heating due to thin cirrus cloud layers, which implies that almost all of thin cirrus absorbs more infrared radiation than the radiation it emits in the TTL. The infrared heating decreases above 17 km and is found to be negligible at 18 km. Overall, it is clear that thin cirrus clouds induce prevalent net heating (Figure 13) in the TTL primarily through infrared radiation. We also see that the infrared heating surrounding the convective regions shown in Figure 8 is caused by thin cirrus clouds.
5.2.3. Radiative Forcing of Thick Cirrus Cloud
 The thick cirrus clouds (0.3 ≤ τ < 3) are the cloud category that lies between thin cirrus and opaque clouds, and thus have the characteristics of both thin cirrus and opaque clouds. In general, the smaller the optical depth of these clouds is, the more thin cirrus characteristic they would have. On the other hand, the larger the optical depth is, the more opaque cloud characteristic they would have.
 Analogous to the method used to examine the TTL thin cirrus radiative forcing, we removed the thick cirrus clouds with cloud top height higher than 14 km and performed the heating rate calculations. By subtracting the cloud radiative forcing fields in which thick cirrus is removed from the original cloud radiative forcing, we obtain the radiative impacts of thick cirrus clouds in the TTL (Figures 14–16).
 The impact of thick cirrus clouds is mainly concentrated over the convective regions from 15 km to 16 km (Figures 14–16). In the solar part (Figure 14), thick cirrus clouds induce a comparable heating to the heating from thin cirrus clouds (Figure 11), despite thick cirrus which has larger optical depth tends to have stronger solar absorption. To understand the comparable solar heating found for thin and thick cirrus clouds, we calculate the occurrence of thin cirrus and thick cirrus clouds out of all cloud layers that have cloud top height above 14 km. It is found that thin cirrus cloud layers occur about 70% out of all TTL cloud layers and thick cirrus occurs only about 19% out of all TTL cloud layers. That is thin cirrus occurs about four times more frequent than thick cirrus clouds. Thus, the higher occurrence of thin cirrus cloud compromises its smaller optical depth resulting in the comparable solar heating to thick cirrus. In the infrared part (Figure 15), the thick cirrus clouds have mostly infrared heating at 15 km. The infrared heating decreases with height and becomes mostly cooling above 16 km. The net radiative forcing of thick cirrus clouds is mostly heating at 15 and 16 km (Figure 16).
 In the TTL, the cloud solar radiative forcing is contributed from three sources. They are (1) thin and thick cirrus cloud layer heating, (2) cloud-free air heating due to the underlying clouds (mostly from opaque clouds) which reflect solar energy upward and (3) opaque cloud top heating if the cloud top is in the TTL. Among the three sources, the solar impact of thin and thick cirrus is small and cloud-free air solar heating is found to be negligible in the TTL. Thus, the strong solar heating found in Figure 7 is due to the strong solar absorption near the top of opaque clouds.
 The total cloud infrared radiative forcing in the TTL is the combination of (1) thin cirrus and thick cirrus heating, (2) cloud-free air cooling due to the underlying clouds and (3) thick cirrus and opaque cloud top cooling if the cloud top is within the TTL. The thin cirrus infrared heating is prevalent in the TTL while the thick cirrus heating is mainly confined over the convective regions in the lower part of TTL. The thin cirrus infrared heating effect is the dominant infrared heating source. The cloud-free air infrared cooling is dominant above 17 km while the infrared cooling near the top of thick cirrus and opaque clouds (primarily opaque clouds) is dominant below. Although thin cirrus and thick cirrus clouds have the infrared heating and the cloud fraction of cirrus is dominant in the TTL, the infrared cooling from cloud-free air and opaque cloud top outweigh the heating effects so that the ensemble mean infrared cloud radiative forcing to be mostly cooling except outside the convective regions (Figure 8).
5.3. Uncertainty in the Cloud Radiative Forcing
 It is important to estimate the uncertainty in the derived cloud radiative forcing. In cloud optical depth retrieval, we didn't perform the retrieval for the columns containing the cloud layers with 1 − 34γ′ < 0. The term 1 − 34γ′ becomes negative because of the uncertainty in the lidar ratio combined with the situations when the cloud layer has a large optical depth. For the sensitivity test, we consider these cloud columns by assuming a cloud optical depth of 3 for the cloud layers with 1 − 34γ′ < 0, which is about the upper limit of CALIPSO detection threshold for the cloud layers that are not saturated. The results show that the calculations with and without considering these cloud columns has little effect on the radiative forcing. Below we quantify the uncertainty in the cloud radiative forcing induced by the uncertainties associated with the retrieved ice cloud optical depth, the blended cloud field, and the assumed ice particle sizes.
 As discussed in section 2.3, the retrieved ice cloud optical depths have a relative error of 25%. This introduces a relative error of 4.9%, 2.8% and 1% in the solar, infrared and net cloud radiative forcing, respectively.
 For opaque cloud layers, we blended in ISCCP cloud information. To test the sensitivity of the blended ISCCP clouds on the cloud radiative forcing in the TTL, one weighted mean optical depth instead of the last four midbin ISCCP optical depths is used for the opaque cases. The mean weighted optical depth is calculated by
where τISCCP,i and CISCCP,i are the last four bins of the 10 year mean ISCCP cloud statistics. The calculated mean optical depth is about 22. The result shows that cloud radiative forcing associated with the blended ISCCP clouds is about 9%, 1% and 0.4% in the solar, infrared and net cloud radiative forcing, respectively.
 In this study, we used a generalized ice particle size of 30 μm in the radiative transfer calculation. This value has been used by Hartmann et al. [2001b] and Yang et al. . To further investigate the uncertainty of using the constant ice particle size in the cloud radiative forcing fields, we test the results by using the ice particle sizes which were parameterized as a function of temperature (in unit of centigrade) [Fueglistaler and Fu, 2006],
based on the data provided by Boudala et al.  and Garrett et al. . The parameterized Dge decreases with decreasing temperature. Using the temperature-dependent ice particle size Dge instead of the constant Dge and keeping other fields as the same, we get a relative error of about 8% for the solar cloud radiative forcing, and about 0.7% and 1.1% for the infrared and net cloud radiative forcing, respectively.
 Therefore, by assuming the errors associated with the retrieved ice cloud optical depth, the blended ISCCP cloud field and generalized particle size are independent, the uncertainty associated with the calculated cloud radiative forcing can be estimated by
which is about 13%, 3% and 1.5% for the solar, infrared and net cloud radiative forcing, respectively.
6. Summary and Conclusion
 Cloud plays an important role in the troposphere to stratosphere exchange. Accurately quantifying the cloud radiative energy budget in the TTL will improve our understanding for the physical processes responsible for the TST. In this study, we derived the cloud radiative impacts in the TTL based on the Fu-Liou radiative transfer model, by employing the cloud information from CALIPSO, ISCCP and CloudSat together with balloon-borne measurements of temperature, ozone and water vapor.
 Space lidar has a large footprint, and thus multiple scattering factor has to be considered in retrieving cloud optical depths. For ice clouds, there are three sources that contribute to multiple scattering factor: forward diffraction, delta transmission (if ice particle surface is smooth) and sideward scattering. By neglecting the sideward scattering for ice clouds, the multiple scattering factor has the range of 0.35–0.6. The uncertainty analysis shows that our retrieved ice cloud optical depth has an uncertainty of about 25% due to the uncertainties in multiple scattering factor, effective lidar ratio and observed layer-integrated attenuated backscatter.
 It is shown that the seasonal and spatial distributions of cloud radiative forcing vary with the seasonal migrations of cloud systems. Over the Western Pacific, Africa, South America and South Asia, we find pronounced solar heating and infrared cooling in the lower part of the TTL (<∼16 km). The solar heating weakens above and nearly diminishes at 18 km while infrared cooling extends vertically throughout the TTL. The net cloud radiative forcing, which is the summation of cloud solar and infrared radiative forcing, has heating below ∼16 km and turns to mostly cooling above 17 km. The net cloud radiative heating over the convective regions is mainly contributed from solar heating whereas the weak net cloud radiative heating surrounding these regions is contributed from infrared heating.
 In the solar part, both thin and thick cirrus clouds play a small role and the enhanced absorption of solar radiation by cloud-free air above clouds is negligible. The solar heating is dominantly contributed from the solar absorption near the top of opaque clouds. In the infrared part, thin cirrus infrared heating is prevalent in the TTL while the thick cirrus heating is mainly concentrated over the convective regions in the lower part of TTL. The thin cirrus infrared heating effect is the dominant infrared heating source. The cloud-free air infrared cooling is dominant above 17 km whereas the infrared cooling near the top of opaque clouds is dominant below. Although thin cirrus and thick cirrus clouds have infrared heating effects, the infrared cooling from cloud-free air and opaque cloud top outweigh the heating effects so that the ensemble mean infrared cloud radiative forcing is mostly cooling except outside the convective regions.
 We also performed uncertainty analysis, and found that the relative uncertainty associated with the calculated solar, infrared and net cloud radiative forcing is about 13%, 3% and 1.5%, respectively.
 Q.Y. thanks David Winker for helpful discussions on the CALIPSO ice cloud optical depth product. Q.Y. thanks Andrew Gettelman for helpful suggestions. The CALIPSO and ISCCP data are obtained from the NASA Langley Research Center Atmospheric Sciences Data Center. The 2B-GEOPROF product is downloaded from CloudSat Data Processing Center. This work is supported by NASA Earth and Space Sciences Fellowship (NESSF) NNX08BA82H and NASA grant NNX08AF66G.