Interactive comment on “ Link between the Outgoing Longwave Radiation and the altitude where the space-borne lidar beam is fully attenuated

According to climate models’ simulations, cloud altitude change is the dominant contributor of the positive ensemble mean longwave cloud feedback. Nevertheless, the cloud altitude longwave feedback mechanism and its amplitude struggle yet to be verified in observations. An accurate, stable in time, and potentially long-term observation of a cloud property summarizing the cloud vertical distribution and driving the longwave cloud radiative effect is needed to hope to achieve a better understanding of the cloud altitude longwave feedback mechanism. This study proposes the direct lidar measurement of the atmosphere opacity altitude is a good candidate to derive the needed observed cloud property. This altitude is the level at which a space-borne lidar beam is fully attenuated when probing an optically opaque cloud. By combining this altitude with the direct lidar measurement of the cloud top altitude, we derive the radiative temperature of opaque clouds that linearly drives, as we show, the outgoing longwave radiation. This linear relationship provides a simple formulation of the cloud radiative effect in the longwave domain for opaque clouds and so, helps to understand the cloud altitude longwave feedback mechanism. We find that in presence of an opaque cloud, a cloud temperature change of 1 K modifies its cloud radiative effect by 2 W m −2 . We show that this linear relationship holds true at single atmospheric column scale with radiative transfer simulations, at instantaneous radiometer footprint scale of the Clouds and the Earth's Radiant Energy System (CERES), and at monthly mean 2° x 2° gridded scale. Opaque clouds cover 35 % of the ice-free ocean and contribute to 73 % of the global mean cloud radiative effect. Thin clouds cover 36 % and contribute to 27 %.

In order to understand the feedback mechanisms, it is useful to identify the fundamental variables that drive the climate radiative response, and then decompose the overall radiative response as the sum of individual radiative responses due to changes in each of these variables.This classical feedback analysis has been largely applied to outputs from numerical climate system simulations in order to estimate the effects of water vapor, temperature lapse rate, clouds and surface albedo on the overall climate radiative response (e.g.Cess et al., 1990;Le Treut et al., 1994;Watterson et al., 1999;Colman, 2003;Bony et al., 2006;Bates, 2007;Soden et al., 2008;Boucher et al., 2013;Sherwood et al., 2015;Rieger et al., 2016).Focusing only on the cloud feedback mechanisms, such approach (Zelinka et al., 2012a) has been used to isolate the role of each fundamental cloud variables that contribute to the radiative response: the cloud cover, the cloud optical depth or condensed water (liquid and ice), and the cloud altitude (or cloud temperature).The shortwave (SW) cloud feedback is driven by changes in the cloud cover and the cloud optical depth, whereas the longwave (LW) cloud feedback is driven by changes in the cloud cover, the cloud optical depth and the cloud vertical distribution (e.g.Klein and Jakob, 1999;Zelinka et al., 2012aZelinka et al., , 2012bZelinka et al., , 2013)).
Verifying cloud feedback mechanisms that have been predicted by climate models simulations using observations requires two steps: 1) First, establish a direct and robust link between the observed fundamental cloud variables and the cloud radiative effet (CRE) at the top of the atmosphere (TOA); so that any change in the fundamental cloud variables can be unambiguously translated within a change in the CRE at the TOA, 2) Second, establish an observational record of these cloud fundamental variables that is long enough, stable enough and accurate enough to detect cloud changes due to greenhouse gases forcing (Wielicki et al., 2013).Such records do not exist yet.Despite this last limitation, Klein and Hall (2015) suggested that some cloud feedback mechanisms, namely the "emergent constraints", could be tested with shorter records in comparing the simulated and the observed current climate interannual variabilities.
The current paper focuses on the LW cloud feedback.Current climate models consistently predict that the cloud altitude change is the dominant contributor to the LW cloud feedback (Zelinka et al., 2016) in agreement with previous works (e.g.Schneider, 1972;Cess, 1975;Hansen et al., 1984;Wetherald and Manabe, 1988;Cess et al., 1996;Hartmann and Larson, 2002).If the models agree on the sign and the physical mechanism of the LW cloud altitude feedback, they predict different amplitudes.Coupled Model Intercomparison Project Phase 5 (CMIP5) climate model simulations suggest that the cloud altitude would rise up by 0.7 to 1.7 km in the upper troposphere in all regions in a warmer climate (+4 K), which is a significant change compared to the currently observed variability, and thus, could be a more robust observable signature of climate change than the CRE (Chepfer et al., 2014).Nevertheless, the cloud altitude LW feedback mechanism and its amplitude still struggle to be verified in observations.There is still no observational confirmation for the altitude LW cloud feedback mechanism because 1) there is no simple direct and robust formulation linking the observed fundamental cloud variables and the LW CRE at the TOA 2) there is no accurate and stable observations of the vertical distribution of clouds over several decades.Thus, a preliminary step to progress on the LW cloud feedback is to establish a direct and robust link between the LW CRE at the TOA and fundamental cloud properties that can be accurately observed and which can also be simulated in climate models.In the SW, Taylor et al. (2007) Taylor et al. (2007) and in the attempt made by Yokohata et al. (2005), establishing a simple radiative transfer model that robustly expresses the LW CRE as a function of a limited number of properties (which can be reliably observed and which can also be simulated in climate models), is more challenging in the LW than in the SW because the LW involves three variables instead of two: the cloud cover, the cloud optical depth and the cloud vertical distribution.
Complete radiative transfer simulations allow to accurately compute the LW CRE for a well-defined atmosphere (clear sky and clouds): detailed information on the atmospheric columns collected by active sensors have been used to estimate TOA CRE and surface CRE (e.g.Zhang et al., 2004;L'Ecuyer et al., 2008;Kato et al., 2011;Rose et al., 2013).In contrast, the definition of a simple and robust linear formulation between the LW CRE at the TOA and a limited number of cloud variables, that would be useful for climate cloud feedback decomposition, cannot use the details of the entire cloud vertical distribution: first, one needs to summarize the entire cloud vertical profile within a few specific cloud levels that drives the LW CRE at the TOA, and second, this specific cloud levels need to be accurately observed at global scale from satellites.
Most of the cloud climatologies derived from space observations rely on passive satellites, which do not retrieve the actual cloud vertical distribution, and only retrieve the cloud top pressure and estimates of high-level, mid-level, and lowlevel cloud covers.These last estimates have been coupled with ranges of cloud optical depth to define different cloud types (Hartmann et al., 1992) associated to different values of CRE.These cloud types have been used to analyze the interannual cloud record collected by the Moderate Resolution Imaging Spectroradiometer (MODIS) (Zelinka and Hartmann, 2011), as well as the International Satellite Cloud Climatology Project (ISCCP) and the Pathfinder Atmospheres Extended (PATMOSx) (Marvel et al., 2015;Norris et al., 2016)  Radar (CPR) from CloudSat (Stephens et al., 2002) to re-build similar cloud types as in Hartmann et al. (1992).Stephens et al (submitted) and Hartmann et al. (1992) found very different results because passive sensors cannot retrieve reliable cloud altitude contrarily to active sensors (e.g.Sherwood et al., 2004;Holz et al., 2008;Michele et al., 2013;Stubenrauch et al., 2013).Today, ten years of satellite-borne active sensors data provide a detailed and accurate view of the cloud vertical distribution, which can be used to build for the first time, a simplified radiative transfer model that robustly expresses the LW CRE as a function of the cloud cover, the optical depth (or emissivity) and the cloud altitude, and that can be tested against observations.To do so, in the current paper, we summarize the entire cloud vertical profile observed by active sensors with three specific cloud levels that drive the LW CRE at the TOA and that can be accurately observed by spaceborne lidar: the cloud top altitude, the cloud base altitude, and the altitude of opacity where the laser beam gets fully attenuated when it passes through an Opaque cloud.This altitude of opacity together with the Opaque cloud cover, are both observed by space-borne lidar, and are strongly correlated to the LW CRE (Guzman et al., 2017) because emissions of layers located below the altitude of opacity have little influence on the outgoing LW radiation (OLR).Previous studies (Ramanathan, 1977;Wang et al., 2002), suggested that the link between the Opaque cloud temperature and the OLR is linear, which would be mathematically very convenient for the study of cloud feedbacks (derivatives), but these studies are limited to radiative transfer simulations only.We propose to build on these studies by adding the space-borne lidar information.
In Section 2 we present the data and tools used in this study.In Section 3 we define radiative temperatures of Opaque clouds and Thin clouds derived from lidar cloud altitude observations and reanalysis, and present the observed distributions over the mid-latitudes region and the ascending and subsiding regime areas in the tropics.In Section 4 we use Product (GOCCP)-OPAQ (GOCCP v3.0; Guzman et al., 2017) segregates each atmospheric single column sounded by the CALIOP lidar as one of the 3 following single column types (Fig. 1): • The Clear sky single column (brown, center) is entirely free of clouds.In other words, none of the 40 levels of 480 m vertical resolution composing the atmospheric single column is flagged as "Cloud" (Chepfer et al., 2010).
• The Opaque cloud single column (orange, right) contains a cloud into which the laser beam of the lidar ends fully attenuated at an altitude termed  "#$%&' | . "#$%&' | (as well as any  | variable used later on in the paper) refers to a single column, i.e. a 1D atmospheric column from surface to the TOA where each altitude layer is homogeneously filled with molecules and/or clouds, as mentioned by the exponent symbol "|".Such single column is directly identified by the presence of a level flagged as "z_opaque".Full attenuation of the lidar is reached for a visible optical depth, integrated from the top of the atmosphere (TOA), of about 3 to 5 (Vaughan et al., 2009).This corresponds to a cloud LW emissivity of 0.8 to 0.9, if we consider that cloud particles do not absorb visible wavelengths and that diffusion can be neglected in the LW domain.
• The Thin cloud single column (brown and blue, left), contains a semi-transparent cloud.Such single column is identified by the presence of at least one level flagged as "Cloud" without a level flagged as "z_opaque".Opaque cloud single columns.The total gridded OLR will be computed from the 3 single column OLRs weighted by their respective cover:  -./0 ,  12'$3 ,  "#$%&' .
Figure 2 shows the global covers of these 3 single column types, using 2°´2° grids.(as well as any  ⊞ variable used later on in the paper) refer to 2°´2° grid box as mentioned by the exponent symbol "⊞".
Opaque clouds cover is very high at mid-latitudes and, in the tropics, high occurrences clearly reveal regions of deep convection (warm pool, ITCZ) and stratocumulus regions at the east part of oceans.Thin clouds cover is very homogeneous over all oceans, with some slight maxima in some regions, namely near the warm pool.These results are discussed in detail in Guzman et al. (2017).) levels flagged as "Cloud", using the temperature profiles of the NASA Global Modeling and Assimilation Office (GMAO) reanalysis (Suarez et al., 2005) provided in CALIOP Level 1 data and reported in GOCCP v3.0 data.
• Thin cloud emissivity  -./0 | of a Thin cloud single column is inferred from the mean attenuated scattering ratio of levels flagged as "Clear" below the cloud, that we note ′ B'2<C and which approximately corresponds to the apparent two-way transmittance through the cloud.Indeed, considering a fixed multiple scattering factor  = 0.6, we retrieve the Thin cloud visible optical depth  -./0 JKL (Garnier et al., 2015).Then, as the cloud particles are much larger than the visible and infrared wavelengths and considering no absorption by cloud particles is occurring in the visible domain, the Thin cloud LW optical depth  -./0 MN is approximately half of  -./0 JKL (Garnier et al., 2015).In order to avoid all possible uncertainties due to solar noise, results presented in this paper are only for nighttime conditions.Furthermore, we restricted this study to observations over oceans to avoid uncertainties due to the ground temperature diurnal cycle over land.And, in order to not be influenced by major changes of surface physical properties across the seasons, we also removed from this study all observations over iced sea, based on sea ice fraction from the European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-Interim reanalysis (Berrisford et al., 2011).

Fluxes observations collocated with lidar clouds observations
CERES radiometer, on-board the Aqua satellite, measures the OLR at the same location where the CALIOP lidar, on board the CALIPSO satellite, will shoot 2 minutes and 45 seconds afterwards.So, the instantaneous Single Scanner 1°´1° product (Loeb et al., 2009), that we average over 2°´2° grid boxes.

Radiative transfer computations
For all radiative transfer computations needed in this study, we use the GAME radiative transfer code (Dubuisson et al., 2004) combined with mean sea surface temperature (SST) and profiles of temperature, humidity and ozone extracted from the ERA-Interim reanalysis.GAME is an accurate radiative transfer code to calculate the radiative flux and radiance over the total solar and infrared spectrum.The radiative transfer equation is solved using DISORT (Stamnes et al., 1988) and gaseous absorption is calculated from the k-distribution method.This code accounts for aerosol and clouds scattering and absorption as well as interactions with gaseous absorption.GAME radiative transfer code does not take into account cloud , where  denotes the Stefan-Boltzmann constant.We present distributions of these cloud radiative temperatures derived from lidar measurements over the mid-latitudes region and the tropics.

Definition and approximations of the cloud radiative temperature
Considering .This occurs in lidar observations for  12<&[ MN| greater than a limit situated between 1.5 to 2.5.Below this limit clouds are declared as (blue area) Thin clouds.Clouds with  12<&[ MN| between 1.5 and 2.5 could be (gray area) either Opaque or Thin clouds depending on the limit.
We will now approximate  Opaque single columns over the number of all single columns.We do this in order to take into account the sampling differences in each grid box.Because the radiative impact of the Thin clouds will also depend on the cloud emissivity of the cloud, we also computed the distributions of  -./0 | among Thin clouds.Figure 4d shows these distributions.For all regions, the maximum is located around 0.25.So, emissivities of Thin clouds are usually small, and clouds with small emissivities have less impact on the OLR.This, once again, goes in the sense that the role that play Thin clouds on the total CRE should be significantly smaller than that of Opaque clouds.).Then, we verify this relationship against observations at instantaneous 20 km footprint scale, using high spatial resolution collocated satellite-borne broadband radiometer and lidar data, and at monthly mean 2° latitude ´ 2° longitude gridded scale.

Linear relationship deduced from radiative transfer simulations over single cloudy column
The goal of this sub-section is to establish a simple and robust relationship between 1) the OLR over an Opaque where decreases of 1 K (e.g. if the Opaque cloud rises up) then the OLR decreases by 2 W•m -2 .This linear relationship, firstly found by Ramanathan (1977), has a slope which is consistent with previous work that found 2.24 W•m -2 /K (Wang et al. (2002) using the radiative transfer model of Fu andLiou (1992, 1993) and the analysis of Kiehl (1994)).Linear regressions done on other regions with different atmospheric conditions give a similar coefficient.This means that, in spite of the significant differences in the atmospheric temperature

Contributions of Opaque clouds and Thin clouds to the cloud radiative effect
In the previous section, we found a clear linear relationship for Opaque clouds between  "#$%&' and  "#$%&' at different scales.The relationship for Thin clouds, though quite simple, is not linear and agrees less with observations than for Opaque clouds.In this section, we evaluate the contributions of Opaque clouds and Thin clouds to the total CRE.

Tropical Opaque cloud CRE and Thin cloud CRE in dynamical regimes
Figure 11 shows the cloud properties as a function of dynamical regime in the tropics (whose PDF according to the 500-hPa pressure velocity is given Fig. 11h).In the tropical convective regimes ( ƒ"" < 0 hPa•day -1 ),  "#$%&' ⊞ is strongly driven (25 % to 45 % increase from 0 hPa•day -1 to -100 hPa•day -1 ) by the velocity of ascending air, whereas  -./0 ⊞ seems to be poorly dependent of it, with an almost constant cover around 40 %.In subsidence regions, the mean  "#$%&' ⊞ is also increasing when the air descending velocity is larger but with a wide range of variation from month to month (Fig. 11a).

Evaluation of the OLR over Thin clouds
We saw that the theoretical linear expression of  -./0 | for a fixed  -./0 | overestimates the simulated one, up to +10 W•m -2 for many cases (Section 4.1).This is partly due to the fact that the linear theoretical expression does not take into account the diffusion of the LW radiation within the clouds.It could partly explain why  -./0 ⊘ (MK †) is large compared to the measured  -./0 ⊘ (1‹OE‹L) (Fig. 6b).However, we do not think it should really affect the global scale partition of  -< defined such a simplified radiative transfer model by robustly expressing the SW CRE as a function of the cloud cover and the cloud optical depth.This linear relationship has been largely used for Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License.decomposing the SW cloud feedbacks into contributions due to cloud cover change and optical depth change.Contrary to the SW, the LW CRE does not only depend on the cloud cover and the cloud optical depth, but also on the cloud vertical distribution.As stated in in order to identify LW CRE changes associated to cloud properties changes.But recently, Stephens et al. (submitted) used combined passive observations and active sensors observations (2B-FLXHR-LIDAR product; Henderson et al., 2013) collected by the Cloud-Aerosol LIdar with Orthogonal Polarization (CALIOP) from the Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) and the Cloud Profiling Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License.and Thin clouds observations by space-borne lidar Eight years (2008-2015) of CALIPSO observations are used in this study.The GCM-Oriented CALIPSO Cloud

FIG. 1 .
FIG. 1. Partitioning of the atmosphere into 3 single column types thanks to CALIOP lidar: (left) Thin cloud single column, when a cloud is detected in the lidar signal and the laser beam achieve to wholly go through the cloud until the surface, (middle) Clear sky single column, when no cloud is detected, and (right) Opaque cloud single column, when a cloud is detected and the laser beam ends fully attenuated into the cloud at a level called  "#$%&' |

FIG. 2 .
FIG. 2. Maps of (a) Opaque cloud cover (b) Thin cloud cover and (c) Clear sky cover.Only nighttime over ice-free oceans for the 2008-2015 period is considered.Global mean values are given in parentheses.

.
Opaque cloud emissivity cannot be inferred and we do the approximation that it is close to a black body, so  "#$%&' | ≈ 1. Single columns with multi-layers of clouds are also consider in this study, i.e.  -flagged level of the highest cloud in the column and  =$>' | and  =$>' | to the lowest "Cloud" flagged level of the lowest cloud in the column.Also, in this case,  -./0 | is computed from the summed optical depth of all cloud layers present in the column.

Footprint
(SSF) of the CERES swath crossing the CALIPSO ground-track give the OLR over atmospheric single columns sounded by the lidar.Because a CERES footprint has a diameter of ~20 km, whereas the CALIOP lidar samples every 333 m along-track with a footprint of 70 m diameter, several atmospheric single columns sounded by the lidar (up to 60) are located within a single CERES footprint.To collocate the GOCCP-OPAQ instant data and the CERES SSF measurements, we use the CALIPSO, CloudSat, CERES, and MODIS Merged Product (C3M;Kato et al., 2011) which flags the instantaneous CERES SSF of the CERES swath crossing the CALIPSO ground-track.Finally, for each of these flagged CERES SSF, we matched, from geolocation information, all the GOCCP-OPAQ single columns falling into the CERES footprint.We consider that an atmospheric column with CERES footprint base is an Opaque (Thin) cloud column if all matched single columns are declared as Opaque (Thin) cloud single column.We use these Opaque and Thin cloud columns to validate lidarderived OLR.From the C3M product, we also use the estimated Clear sky OLR of the instantaneous CERES SSF of the CERES swath crossing the CALIPSO ground-track.This estimated Clear sky OLR is computed from radiative transfer simulations using the synergy information of the different instruments flying in the Afternoon Train (A-Train) satellite constellation.As C3M is only released through April 2011, during the time period when both CALIPSO and CloudSat are healthy, we also use the Clear sky OLR from 1°´1° gridded data monthly mean CERES Energy Balanced and Filled (EBAF) Edition 2.8 Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License. 3 Radiative temperatures of Opaque clouds and Thin clouds derived from lidar cloud observations and reanalysis We define here an approximation of the Opaque and Thin cloud radiative temperatures which can be derived from lidar measurements.The cloud radiative temperature corresponds to the equivalent radiative temperature of the cloud  3$[ | such as the upward LW radiative flux emitted by a cloud of emissivity  | , at the top of the cloud, is  12<&[ ↑MN| ( ) =  |   3$[ | g FIG. 3. Comparison of (green) the cloud radiative temperature  3$[ | inferred from the RTE (see appendix A) with the lidar-definitions 3$[ | for Opaque clouds and Thin clouds using straightforward formulations which could be derived from lidar cloud observations and reanalysis.In an Opaque cloud single column (Fig. 1, right), the optically very thick cloud prevents LW radiative flux from below to propagate upwards.Thus, atmospheric layers below  "#$%&' | have little influence on the OLR over an Opaque cloud single column  "#$%&' | .Here, we propose that  "#$%&' | is mainly driven by an Opaque cloud radiative temperature defined as: Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License.cloud single column (Fig. 1, left), the cloudy part is optically semi-transparent and lets through a part of the LW radiative flux coming from the cloud-free atmospheric layers and surface underneath.Then, the OLR over a Thin cloud single column  -./0 | depends on one hand on the surface temperature, the surface emissivity, the temperature profile, and the humidity profile, and on the other hand on the cloud emissivity  -./0 | and the Thin cloud radiative temperature defined as: of  -./0 | , the cloud radiative temperature of Thin clouds ( 12<&[ MN| < 1.5, blue area), and  "#$%&' | , the cloud radiative temperature of Opaque clouds ( 12<&[ MN| > 2.5, orange area), with  3$[ | deduced from RTE (green) show good agreement in Fig. 3. Clouds with 1.5 <  12<&[ MN| < 2.5 (gray area) can be either Thin or Opaque clouds depending on the integrated LW optical depth at which  "#$%&' | will occur.Here, computations were performed for a fixed cloud top temperature  -<# | at 250 K and a fixed cloud base temperature  =$>' | at 260 K.  "#$%&' | will depend on the integrated LW optical depth from cloud top  MN| to where  "#$%&' | will occur, which is known to be situated between 1.5 and 2.5:  MN| = w p  JKL| (Chepfer et al., 2014), with  JKL| between 3 and 5 (Vaughan et al., 2009).Then, according to  "#$%&' | possible values given this approximation (black shadow area),  "#$%&' | range is deduced (red shadow area).Computations with other pairs of  -<# | and  =$>' | temperatures (not shown) reveal that the relative vertical position into the cloud of  3$[ | does not depend much of the cloud top and cloud base temperatures.In other words, with other pairs of  -<# | and  =$>' | temperatures, we obtain almost the same figure as Fig. 3 only with the y-axis temperature values changed.This means that the difference between  3$[ | and  -./0 | or between  3$[ | and  "#$%&' | becomes larger as the difference between  -<# | and  =$>' | increases.Naturally, in reality, the error made by using  -./0 | and  "#$%&' | as approximations of  3$[ | will also depend on other cloud properties, such as cloud inhomogeneity and cloud microphysics.However, this simple theoretical calculation allows us to assert that  -./0 | and  "#$%&' | as we defined above are good approximations of the cloud radiative temperature of the Thin and Opaque clouds, with less than a 2 K error for a Thin cloud with a 10 K difference between its cloud base and cloud top temperatures, and less than a 1 K error for an Opaque cloud with  12<&[ MN| > 5 and with a 10 K difference between its cloud base and cloud top temperatures. .Then, we computed the probability density function (PDF) of  "#$%&' | among Opaque clouds and  -./0 | among Thin clouds for 3 different regions: the tropical ascending region between ±30° latitude with monthly mean 500-hPa pressure velocity  ƒ"" < 0 hPa•day -1 , the tropical subsiding region between ±30° latitude with monthly mean  ƒ"" > 0 hPa•day -1 and the mid-latitudes (North and South) region between 65° S and 30° S and between 30° N and 65° N put together.To compute these PDFs, e.g. the PDF of  "#$%&' | among Opaque clouds, we firstly compute a PDF of  "#$%&' | among all single columns on each 2°´2° grid box for the 2008-2015 period.Then, we compute the area-weighted averaged PDF of a region, weighting each 2°´2° grid box PDF by the ratio of the number of Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License.

.
FIG. 5. Relationship between the OLR and the cloud radiative temperature from radiative transfer computations: (a) over an Opaque cloud single column and (b) over a Thin cloud single column.Direct radiative transfer computations are shown in dots.Solid lines represent the linear relationships inferred from a regression on dots in the Opaque case and applied to the Thin clouds case according to Eq. (4).For a fixed value of cloud emissivity (dots colors; 1 [purples] for Opaque clouds and 0.1 [reds], 0.3 [blues], 0.5 [greens], 0.7 [greys] for Thin clouds), the linear relationship does not depend on the cloud altitudes (dots light intensity; 0 km [dark] -16 km [bright]) or the geometrical thicknesses (dots size; 1 km [small] -5 km [large]).Results shown here use the 2008-year mean thermodynamic atmospheric variables over the tropical region [30° S-30° N] from ERA-I reanalysis.
atmospheric column with a CERES footprint base, as mentioned by the exponent symbol "⊘", and are obtained averaging respectively all  "#atmospheric column with a CERES footprint base.

Figure 8 428 Figure 9
Figure8shows the zonal mean observations of the 5 cloud properties ( "#$%&' ⊞ Fig.11c) and an elongation of the cloud vertical distribution which gives even higher  -<# | (see monthly mean 2°´2° gridded dynamic regimes produces a change in the cloud properties and CRE that seem predictable.For example, if an intensification of the upward air motions velocity change  ƒ"" on a region from -40 hPa•day -1 to -80 hPa•day -1 ,  "#$%&' ⊞ would increase by 8 % ( -./0 ⊞ will remain more or less constant),  "#$%&' ⊞ will decrease by 10 K and  -./0 ⊞ by 7 K, and  -./0 will increase by 0.03.These cloud changes would increase the CRE by 17 W•m -2 including 14 W•m -2 from Opaque clouds (Fig.11f).Because  -./0 ⊞ will remain more or less constant whereas  "#$%&' ⊞ will increase with a decrease of  ƒ"" in ascending regime, the relative contribution of Opaque clouds to the total CRE will be more and more important as convection increases.This is why we see in Fig.11ga decrease of the Thin clouds relative contribution from 20 hPa•day -1 to -100 hPa•day -1 .Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License.narrowing of the ascending branch of the Hadley cell (e.g.Su et al., 2014), which means less convective regions and more 491 subsiding regions and which should result in a decrease of the CRE predictable knowing the changes of  ƒ"" all over the 492 tropics.493 Atmos.Meas.Tech.Discuss., https://doi.org/10.5194/amt-2017-115Manuscript under review for journal Atmos.Meas.Tech.Discussion started: 6 June 2017 c Author(s) 2017.CC BY 3.0 License.6 Limitations of the OLR linear expression In this study, from the direct measurement of the atmosphere opacity by spaceborne lidar, termed  "#$%&' | , we were able to infer the radiative temperature of Opaque clouds  "#$%&' | , which we found linearly linked to the OLR.We propose  "#$%&' | as a good candidate to provide an observational constraint on the LW CRE.We tested the linear relationship at different space scales from instantaneous to monthly means.Hereinbelow, we list possible reasons for uncertainties.3.1) only take into account the apparent cloud extremities seen by the lidar ( -<# | and  "#$%&' | or  =$>' | ).A temperature defined by the centroid altitude (Garnier et al., 2012) would take into account the entire cloud vertical profile.It could estimate better the equivalent radiative temperature.However, our results show that the CRE is mainly driven by  "#$%&' | and  -<# | over Opaque clouds and  =$>' | and  -<# | over Thin clouds.Furthermore, observational-based studies from the Atmospheric InfraRed Sounder (AIRS) and CALIOP showed that the radiative cloud height is located at the "apparent middle" of the cloud (Stubenrauch et al., 2010).The authors defining the "apparent middle" of the cloud as the middle between the cloud top ( -<# | ) and the "apparent" cloud base sees by the CALIOP lidar ( =$>' | for Thin clouds and  "#$%&' | for Opaque clouds), consistently with our own definitions (Eqs.(

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between  "#$%&' ⊞ (MK †) and  -./0 ⊞ (MK †) , because, replacing  -./0 ⊞ (MK †) by the difference  -<•$2 ⊞ (1‹OE‹L) −  "#$%&' ⊞ (MK †) , reveals that Opaque clouds contribute to 74 % to the total CRE instead of 73 %.Plotting results of Fig.6in single-cloud-layer situations (not shown) shows better correlation coefficients, with R = 0.99 for Opaque clouds and R = 0.92 for Thin clouds.It reveals that our linear expression can be affected by additional uncertainties in multilayers situations.As an example, all the occurrences far from and over the identity line in Fig. 6a are due to cloud multilayers.For Opaque cloud single columns, taking into account the optical depth of the thinner cloud which overlaps an Opaque cloud in the expression of  "#$%&' | improves the results (R = 0.97).However, this subtlety adds complexity to compute  "#$%&' |, and only gives small improvements to a simple expression with already very satisfying results (R = 0.95 on Fig.6a).Also, the value of  -./0 ⊞ used to construct  -./0 ⊞ (MK †) does not account for Thin cloud single columns where no "Clear" bin is found below the cloud (these clouds are not present in the  -./0PDFs of Fig.4d).This happens when very low clouds are present in the lowest 480 m bin.So, emissivities of Thin clouds close to the surface are not taken into account in the averaged  -./0 ⊞ .But since all these "missed" cloud emissivities are from clouds near the surface, their temperature is certainly close to the surface temperature and their LW CRE should be small.So, this effect should have no significant impact on the presented results.