The Surface Longwave Cloud Radiative Effect derived from Space Lidar Observations

. Clouds warm the surface in the longwave (LW) and this warming effect can be quantified through the surface LW cloud radiative effect (CRE). The global surface LW CRE is estimated using long-term observations from space-based radiometers (2000–2021) but has some bias over continents and icy surfaces. It is also estimated globally using the combination of radar, lidar and space-based radiometer over the 5–year period ending in 2011. To develop a more reliable long time series of surface LW CRE over continental and icy surfaces, we propose new estimates of the global surface LW CRE from space-based lidar observations. We show from 1D atmospheric column radiative transfer calculations, that surface LW CRE linearly decreases with increasing cloud altitude. These computations allow us to establish simple relationships between surface LW CRE, and five cloud properties that are well observed by the CALIPSO space-based lidar: opaque cloud cover and altitude, and thin cloud cover, altitude, and emissivity. We use these relationships to retrieve the surface LW CRE at global scale over the 2008–2020 time period (27 Wm -2 ). We evaluate this new surface LW CRE product by comparing it to existing satellite-derived products globally on instantaneous collocated data at footprint scale and on global averages, as well as to ground-based observations at specific locations. Our estimate appears to be an improvement over others as it appropriately capture the surface LW CRE annual variability over bright polar surfaces and it provides a dataset of more than 13 years long. of the humidity and temperature profiles (from the surface to 1 km above the surface) over ocean and over land. We also perform radiative transfer computations for numerous combinations of cloud opacity and vertical distribution. We prescribe the vertical extent of each cloud, the effective size of cloud particles and the infrared optical thickness. For a column fully overcast by an opaque cloud, the cloud is represented by a 1 km thick cloud layer with an emissivity equal to 1 at Z FA−G ( Z Top ) above optically uniform cloud layers for different vertical extents with vertically integrated emissivity equal to 0.8. For a column fully overcast by a thin cloud, the cloud is represented by optically uniform cloud layers with vertically integrated emissivities equal to 0.1, 0.3, 0.5, or 0.7. The cloud top altitude varies according to latitude and 17 in and only 11 in polar regions. For each same cloud properties (i.e., same altitude and emissivity) will warm a surface with a high elevation more than a low elevation. For instance, an opaque cloud at an altitude of 5.5 km msl (mean sea level) will warm a surface at sea level by 58 W m -2 and a surface with an elevation of 4 km msl by 102 W m -2 . These results are consistent with Wang et al. (2019) who found that the surface LW CRE increases over Summit station in Greenland due to the dry atmosphere at high elevations. We performed radiative transfer simulations for different surface elevations at all latitudes and months (not shown) and used these to retrieve the surface LW CRE from space-based lidar observations over land. Thus, the regression coefficients over land depend in addition on surface elevation, with a 100 m resolution ( a(RH,T,SE), b(RH,T,SE)) . of uncertainty in climate change


Introduction
Small changes in the surface irradiance may lead to large climatological responses (Chylek et al., 2007;Kwok and Untersteiner, 2011). Therefore, quantifying irradiance at the Earth's surface is a useful step to better understand the climate system. Clouds exert a very important effect on the energy balance at the surface of the Earth through their effects on shortwave (SW) and longwave (LW) radiation. They radiatively warm the surface in the LW domain because they absorb upward LW radiation that would otherwise escape the Earth system and reemit it back towards the surface. They cool the surface in the SW domain because they reflect solar radiation back to space that would otherwise partly be absorbed by the surface. These effects are usually quantified using the surface cloud radiative effect (CRE), defined as the change in the SW and LW radiation reaching the surface induced by the presence of clouds. Globally, clouds radiatively cool the Earth's surface by 20 W m -2 according to Kato et al. (2018) and by 25 W m -2 according to L'Ecuyer et al. (2019), with the (negative) surface SW CRE cooling being two times larger in magnitude than the (positive) surface LW CRE warming. Nevertheless, in some specific regions like at high latitudes or over the tropical ocean below persistent stratocumulus clouds, the surface LW CRE warming can be larger than the surface SW CRE cooling, such that the clouds exert a net radiative warming of the surface.
As an example, SW effects vanish in the winter-hemisphere polar regions, leading to positive net CRE as LW effects dominate (Henderson et al., 2013). While climate warming in the Arctic is already visible with the sea ice melting (Stroeve et al., 2011), previous works showed that clouds may exert some control on future Arctic climate trajectories (Kay et al., 2016) because they play a primary role in regulating the surface energy balance (Ramanathan et al., 1989;Curry et al., 1996, Shupe andIntrieri, 2004) which influences the surface melting (van den Broeke et al., 2009). Over Greenland specifically , van Tricht et al. (2016) showed that clouds increase the radiative fluxes into the surface and therefore could modulate the Greenland ice sheet mass balance (van Tricht et al., 2016;Hofer et al., 2017), which is a large contributor to global sea-level rise (Shepherd et al., 2012;IPCC, 2021). In the Southern high latitudes, clouds likely exert an important role on the surface energy budget of Antarctica (Shepherd et al., 2012;Kopp et al., 2016), but their radiative impact in this region remains largely unexplored (Scott et al., 2017), in spite of the fact that Antarctica contains the largest reservoir of ice on Earth. King et al. (2015) showed large errors in Antarctic surface energy budget and surface melting rates in models and underlined the importance of improving observations of cloud radiative properties in this region. Acquaotta et al. (2014) underlined the current urgent need to develop long term reliable and high-quality climatic time series, in order to better understand, detect, predict and react to global climate variability and change. Given the importance of the surface LW CRE and the need of long time series, it is necessary to get reliable estimates of the surface LW CRE over multiple years, everywhere around the globe including over continents and ice-covered regions. The main motivation for the current work is to derive a long time series of the global surface LW CRE that can be used to better understand the cloud property that have driven the evolution of the surface LW CRE during the last decade (Vaillant de Guélis et al., 2017b, Norris et al., 2016. This is a necessary step toward understanding how clouds might interact with the surface in the future as

Data
This section describes the CALIPSO cloud observations used to retrieve the surface LW CRE and the independent spacebased and ground-based datasets used to evaluate it.

Cloud observations from CALIPSO-GOCCP
We use cloud properties from the GCM Oriented CALIPSO Cloud Product (GOCCP v3.1.2;Chepfer et al., 2010;Guzman et al., 2017) over the period 2008-2020. We do not use data collected between 2006 and 2007 because the laser tilted off nadir in November 2007, which introduced some change in the CALIPSO signal. In this product (hereafter, CALIPSO-GOCCP), lidar profiles are classified into three types: clear sky profile when no cloud is detected, thin cloud profile when one or several cloud layers and a surface echo are detected, and opaque cloud profile when one or several cloud layers are detected but no surface echo is detected. Surface echo is not detected typically when the profile contains a cloud with visible optical depth > 3-5 depending on the cloud microphysical properties. The cloud base height corresponds to the lowest cloud layer detected. From this classification, five fundamental cloud properties for CRE studies are derived:  C Opaque : the opaque cloud cover, i.e. the number of opaque cloud profiles divided by the total number of profiles within a grid box.
 Z T Opaque : the altitude of opaque cloud, i.e. the average between the altitude of the highest cloud layer in the profile ( Z Top ) and the altitude of the layer where the lidar beam is fully attenuated ( Z FA ) is computed for each profile, a schematic illustrating these altitudes is presented in Fig. 1. Then the gridded Z T Opaque is the average value of all the Z T Opaque profiles within a grid box.  C Thin : the thin cloud cover, i.e. the number of thin cloud profiles divided by the total number of profiles within a grid box.  Z T Thin : the altitude of thin cloud, i.e. the average between the altitude of the highest cloud layer in the profile ( Z Top ) and the altitude of the lowest cloud layer ( Z Base ) is computed for each profile, a schematic illustrating these altitudes is presented in Fig. 1 Figure 1 presents the altitudes of interest of an opaque cloud and a thin cloud seen from a downward space-based lidar beam and from an upward ground-based lidar beam. A thin cloud ( Fig. 1 left) is characterized by three altitudes: Z Top , Z Base and Z T Thin , which is the average value of the previous two ones. These three altitudes are the same when observed from a spacebased lidar or a ground based lidar for an ideal case.
An opaque cloud ( Fig. 1 right) is characterized by three altitudes. When the lidar is based on the ground, we measure the altitude of the lowest cloud layer (Z Base ), the altitude where the lidar beam is fully attenuated ( Z FA −G ), and Z T Opaque −G which is the average of the two. When the lidar is on board a satellite, we measure the highest cloud layer (Z Top ), the altitude where the lidar beam is fully attenuated (Z FA ), and the average of the two ( Z T Opaque ).  (Guzman et al., 2017) was applied only to nighttime data when noise is lower than daytime. The GOCCP v3.1.2 is applied to nighttime and daytime observations. As expected, the multi-year, annual mean opaque and thin cloud altitudes (Fig 2c, 2d) reach maxima (> 9 km) in the presence of deep convective clouds over the warm pool and over tropical continents, and minima (< 3 km) in subsidence regions such as over stratocumulus along the West coast of continents. The thin cloud emissivity (Fig. 2e) is larger along the ITCZ, the continental regions and around the Antarctica peninsula.

Surface LW CRE from satellites
In this subsection, we describe the already existing global surface LW CRE datasets derived from satellite measurements, against which we will evaluate our satellite new product.

CERES
(i) CERES-EBAF. The first dataset is the Clouds and the Earth's Radiant Energy System (CERES) Energy Balanced and Filled (EBAF)-Surface Ed4.0 product (Kato et al., 2013(Kato et al., , 2018. CERES EBAF-Surface (hereafter, CERES-EBAF) is a monthly mean 1°×1° gridded dataset derived from the CERES radiometers onboard the Aqua and Terra platforms. The Aqua satellite was flying in the same orbit as CALIPSO until September 2018. As CERES is a passive radiometer, CERES-EBAF is less reliable over ice surfaces and continents than over oceans. It is also less reliable in the presence of multi-layered clouds where the lower cloud may be obscured by the overlying cloud (Liu et al., 2010;Stubenrauch et al., 2013). This study uses the Edition 4.1 of the product, which differs by +0.2 W m -2 in global annual mean from the previous edition (Kato et al., 2018 C3M Kato et al., 2010). This product stops in 2011 because of the CloudSat battery anomaly.

2BFLX
The 2B-FLXHR-LIDAR P1_R04 (hereafter, 2BFLX) product is derived from combined measurements of CloudSat, CALIPSO, and the MODIS radiometer Henderson et al., 2013). It takes advantage of inferred vertical profiles of cloud properties to compute surface irradiances using a broadband radiative transfer model. The dataset currently stops in 2011 when CloudSat experienced its battery anomaly. This product is sensitive to retrieval errors and biases introduced by the limited spatial and temporal characteristics of CloudSat and CALIPSO. Surface fluxes derived from a combination of radar and lidar observations in 2BFLX are also less susceptible to uncertainties due to undetected multi-

Surface LW CRE from ground-based sites
As the retrieval of the surface CRE from space observations is not direct, we will evaluate the surface LW CRE retrieved from space against that derived from surface radiation measurements collected directly at ground-based sites. For this purpose, we selected three sites located in different regions.
The first site is located in the Arctic, where constraining radiative transfer is challenging with the limited cloud, atmospheric temperature profile and humidity profile observations that are available (Kay et al., 2015) and where the surface CRE may influence the Greenland ice-cap melt (van Trich et al., 2016;Hofer et al., 2017;Shupe et al., 2013). This Summit station (Shupe et al., 2013;Gallagher et al., 2018) is located at the top of the Greenland ice cap (72.6° N-38.5° W) with an elevation of 3250 m. Summit is unique because it is the only place where we have enough observations to make a robust assessment of the surface CRE over Greenland (Lacour et al., 2018). Here, the clear sky flux is computed using a radiative transfer algorithm with measurements of temperature and humidity profiles (eg., Shupe and Intrieri, 2004;Intrieri et al., 2002). Here, the clear sky flux is computed from measurements of near surface temperature and vertical distribution of humidity (Dupont et al., 2008).
The third site is located in the tropical belt where clouds influence the global climate and heat transport (Loeb et al., 2016), and where extensive deep convective clouds reach the cold tropical tropopause. Here, the surface LW CRE is small since much of the surface downward LW radiation originates from emission by the moist near-surface layers of the atmosphere (Prata, 1996). This Kwajalein station (KWA, Roesch et al., 2011), which is also part of BSRN, is located in the Northern Pacific Ocean (8.72° N-167.73° E) with an elevation of 10 m.
Over the 3 ground-based sites, the radiative flux measurements at the surface are carried out using two Kipp and Zonen

Cloud heights used for the surface LW CRE estimate
A schematic representing the cloud altitudes seen from space and ground lidars, and the radiative transfer computations associated with each case, are represented in Figure 3.  To retrieve the surface LW CRE, we could use Z Base from CloudSat but this would limit our time series to 2011 only instead of 2021. We chose to use what we have access to with CALIPSO: a first option consists in using Z FA , the lowest opaque cloud altitude observable by space lidar ( Z FA < 3 km above the surface most of the time, Guzman et al., 2017), which is close to the actual cloud base height except in deep convective towers. A second option is to use Z T Opaque . which might represent the altitude of emission of the cloud in some cases. This second option will overestimate the mean altitude of the deep convective towers where the downward space-based lidar beam attenuates quickly without seeing much of the cloud bottom. The bias will be larger when the cloud base temperature is far from that of Z FA . Moreover, this bias will depend on the opacity of the part of the cloud lying under Z FA that is not observable by space lidar.
In our study we considered option 1 ( Z FA ) and option 2 ( Z T Opaque ). For the sake of simplicity, hereafter we describe the method with Z T Opaque only.

Definition of the radiative quantities
In order to get simple notation, and because we are only interested by the CRE at the surface and in the LW domain in this study, the surface LW CRE will be simply noted CRE in the following equations.
To infer CRE, the net LW radiative fluxes over all type of scenes ( F Allsky net ) may be compared with corresponding fluxes where the influence of clouds has been removed (F Cloudy −freesky net ). Then, we define the surface LW CRE as follow:

CRE=F Allsky net − F Cloudy − freesky net
(1) Using downwelling (↓) and upwelling (↑) fluxes, the surface LW CRE is expressed as follow: Rearranging the terms on the right-hand side of this equation, we get: Which can also be expressed as: Where CRE ↓ represents the surface CRE on the LW downward fluxes and CRE ↑ the surface CRE on the LW upward fluxes. CRE ↑ does not exceed 1 W m -2 in annual global average (Allan, 2011) and in the radiative transfer computations.
Therefore, the error in the surface properties plays a minor role.
Nevertheless, in the LW domain, clouds can warm the surface, changing the surface temperature, which is then related to the upwelling LW radiation. This is a subtle but important issue and is dependent to some degree on the surface type (i.e., land surface will warm more than ocean). If CRE is determined in a hypothetical way, one could assume that the surface temperature is the same. However, this does not capture the full impact of the clouds. To understand the full impact of the clouds, one would need to consider the adjustments of all other parameters, most importantly here being the surface temperature. In this study we assume that the surface temperature is the same under clouds and clear skies, consistently with the definition used in previous satellite-derived products (eg. Kato et al., 2018;L'Ecuyer et al., 2019).
Thanks to the CALIPSO-GOCCP data, it is possible to decompose the surface LW CRE into contributions due to opaque clouds and thin clouds:

Radiative transfer simulations
We use a radiative transfer code to compute the surface LW CRE due to an opaque cloud (CRE Opaque ) or an optically thin cloud (CRE Thin ) in an atmospheric column fully overcast by that cloud. In these 1D atmospheric columns, molecules and clouds are evenly distributed within each layer and each layer is considered infinite and homogeneous. For a single column fully overcast by an opaque cloud, we establish the relationship between CRE Opaque and the opaque cloud altitude Z T Opaque (see Sect. 2.1). For the single column fully overcast by a thin cloud, we establish the relationship between CRE Thin , the thin cloud altitude Z T Thin (see Sect. 2.1) and the thin cloud emissivity ε Thin as in Vaillant de Guélis et al. (2017) The radiative transfer simulations are performed with GAME (Dubuisson et al., 2004). This radiative transfer code computes LW fluxes at 40 different levels with a vertical resolution of 1 km. The fluxes are spectrally integrated between 5 and 200 µm consistently with CERES measurements. We prescribe various surface temperatures and the atmospheric profiles of humidity, temperature, ozone and pressure based on ERA Interim reanalysis (Dee et al., 2011) over oceans and lands for each month and latitude. Humidity and temperature profiles over land for January are presented in figure A2 in Appendix A. Figure A3 presents the seasonal and latitudinal behavior of the first layer of the humidity and temperature profiles (from the surface to 1 km above the surface) over ocean and over land. We also perform radiative transfer computations for numerous combinations of cloud opacity and vertical distribution. We prescribe the vertical extent of each cloud, the effective size of cloud particles and the infrared optical thickness. For a column fully overcast by an opaque cloud, the cloud is represented

Retrieval of surface LW cloud radiative effect from CALIPSO observations and radiative transfer simulations
The surface LW CRE is retrieved from a theoretical expression derived from radiative transfer simulations that involves five observed CALIPSO-GOCCP cloud properties (see Sect. 4). Two surface LW CRE datasets are built from CALIPSO-GOCCP observations using this theoretical relationship over the 2008-2020 period. An orbit dataset at the CALIOP footprint resolution of instantaneous cloud property observations and a 2°x2° gridded dataset of mean cloud properties. In the retrievals, we tested both Z FA and Z T Opaque for estimating the mean altitude of opaque clouds (as discussed in Sect. 3.1).
An evaluation of the retrievals against independent datasets (Sect. 5) suggests that Z T Opaque leads to retrievals that are similar to other space borne retrievals while Z FA leads to better agreement with ground base retrievals (Sect. 6).

Modeled CRE sensitivity to cloud properties
This section establishes parameterizations of the surface LW CRE against cloud altitude and emissivity over a single cloudy column using radiative transfer computations (Sect. 4.1). Then it analyzes the sensitivity of the surface LW CRE to the humidity and temperature profiles (Sect. 4.2), and to the surface elevation (Sect. 4.3).

Sensitivity of the CRE to cloud altitude
Where a(RH,T) and b(RH,T) are constants whose values depend on the humidity and temperature profiles as discussed hereafter. For the specific case presented in Fig. 4, a = -6 and b = 88.

Sensitivity of the CRE to humidity and temperature profiles
The temperature and humidity profiles in the first layers of the atmosphere largely vary according to seasons and location as presented in Fig. A3 in appendix A. As these are variables that influence the surface LW CRE, their variations must be taken into account in order to retrieve the global surface LW CRE.
As an example, Figure 5.a presents the surface LW Opaque CRE for a standard humidity profile and Figure 5.b presents the surface LW Opaque CRE for an enhanced humidity profile (shown in Fig. A4). A 10% change in humidity in the first few km of the tropical atmosphere leads to a surface LW CRE change of 7.7 W m -2 for a cloud at 1 km and by 5 W m -2 for a cloud at 4 km. To capture some variability of humidity and temperature, we have established similar relationships as in columns for an atmospheric state over land in January at a latitude of 39° N (same as Fig. 4 but over land instead of ocean).
At this latitude, the amount of humidity is lower over land than ocean, therefore the LW F Cloudy −freesky net over land is lower and the surface LW CRE would be larger than over the ocean. The surface LW CRE is greater than that over ocean and decreases with a rate (a(RH,T)) of 6.5 W m -2 km -1 instead of 6 W m -2 km -1 over ocean. Figure 6 presents the latitudinal and seasonal behavior of the linear regression coefficients (a(RH,T) and b(RH,T)). The shape of these coefficients spatiotemporal variation is influenced by the shape of the seasonal cycle of humidity and temperature in the first layers of the atmosphere (Fig. A3). For instance, the behavior of the intercept (b(RH,T)) over ocean and land ( Fig. 6b and Fig. 6d, respectively) is driven by the shape of the humidity amount where the largest humidity amount (in tropical regions) causes the smallest intercept coefficients. The seasonal cycle of the surface LW CRE is more pronounced over land than over ocean because the seasonal cycles of humidity and temperature are more pronounced over land than over ocean due to the heat capacity of the surface (Chepfer et al., 2019).

Sensitivity of the CRE to surface elevation
To take into account the surface elevation in the simulation, we consider that the surface temperature is the temperature of the atmospheric layer located at the same altitude as the surface elevation with respect to sea level, and we discard all the layers located between the sea level and the surface elevation altitude. Then we performed numerous radiative transfer simulations corresponding to different clouds as described in section 3.2.
The results presented in Figure 7 show the sensitivity of the surface LW CRE to the surface elevation over continents in January at a latitude of 39° N. As the surface elevation increases, the atmosphere is dryer so the F Cloudy −freesky net decreases, and the surface LW CRE increases. The same cloud with the same cloud properties (i.e., same altitude and emissivity) will warm a surface with a high elevation more than a low elevation. For instance, an opaque cloud at an altitude of 5.5 km msl (mean sea level) will warm a surface at sea level by 58 W m -2 and a surface with an elevation of 4 km msl by 102 W m -2 .
These 3.3. As expected, the surface LW CRE is larger for opaque clouds (Fig. 8a, ~22 W m -2 ) than for thin clouds (Fig. 8b, ~5 W m -2 ) for almost the same atmosphere. Over continents, the weakest CRE GOCCP (< 5 W m -2 ) occurs over Wadi Abadi basin in the Egyptian desert (25° N, 33° E), a cloud free region most of the time (80%). The largest CRE GOCCP (60-65 W m -2 ) occurs over the Tibet Autonomous Region (29° N, 97° E) where the opaque cloud cover is high (58%) and the mean surface elevation is high (4.42 km) over 2.5 million km². Here, the high amount of moisture is uplifted toward southern Tibet, amplified by Rayleigh distillation as the vapor moves over the Himalayan mountains (He et al., 2015), which enhances the formation of opaque clouds.

Gridded Product
CALIPSO space-based lidar differentiates well opaque clouds from thin clouds. Therefore, we can decompose the surface LW CRE derived from CALIPSO-GOCCP observations into contributions due to opaque clouds (CRE Opaque : Fig. 9b) and thin clouds (CRE Thin : Fig 9c). This decomposition shows that 85% (23 W m -2 ) of the overall annual global mean Orbit A passes over the East Pacific Ocean and observes a deep convective tower, a mid-level opaque cloud at an altitude of 7 km and a low opaque cloud. The differences in surface LW CRE between the three spatial restitutions do not exceed 5 W m -2 . Nevertheless, within a small part of the orbit between 11.3° N and 11.8° N (Fig. B1) we observe that the CALIPSO -GOCCP retrieval is lower than the other two products because the lidar does not detect a low cloud below Z FA that is detected by CloudSat (shown in Fig. B1.b) Orbit B passes over the West Pacific Ocean and observes variable yet shallow clouds in the boundary layer (< 2 km). The CRE GOCCP is intermittently larger than the other two products by ~15 W m -2 . CALIPSO-GOCCP (90 m cross track, 330 m along orbit track) detects shallow clouds in the boundary layer and, during the thickest of these, retrieves a surface LW CRE that is larger than the CERES (CloudSat) retrieval, which is based on a 20 km (5km) footprint and might miss these clouds.
Orbit C passes over ocean stratocumulus regions and observes a low opaque cloud. Between 12° S and 19° S, the CRE GOCCP (almost 60 W m -2 ) is smaller than CRE 2 BFLX by ~5 W m -2 and smaller than CRE CERES by 15 W m -2 .
Orbit D passes over Antarctica and observes opaque clouds at high (10 km) and mid-level (4-5 km) altitudes. In the presence of high opaque clouds (between 68° S and 71° S or between 73° S and 77° S), CRE GOCCP is lower than CRE CERES by up to 20 W m -2 and CRE 2 BFLX by up to 40 W m -2 , but typically compares most favourably with CRE CERES over the full scene. We see a strong correlation between the surface LW CRE from CERES-CCCM observations and the surface LW CRE from CALIPSO-GOCCP observations (R=0.85). Two significant departures from the one-to-one comparison line are observed:

Global Statistical comparison with other satellites products at footprint scale over ocean
one for high values of the surface LW CRE and the other one for low values. In the first pattern for surface LW CRE greater than 70 W m -2 , CRE GOCCP is larger than CRE CERES . This pattern corresponds to some low marine opaque clouds in midlatitude regions (not shown). To reconcile the two products, CRE GOCCP should be smaller by almost 5 W m -2 . One way to reduce this difference would be to increase the altitudes of clouds but, due to attenuation of the signal in opaque clouds, the space-based lidar would already potentially overestimate the overall height of the clouds. Thus, the cloud height is likely not the source of this difference. Another way to reduce the surface LW CRE is by decreasing the cloud cover or the cloud opacity. However, the space-based lidar measures with precision the cloud cover thanks to its high spatial resolution and it shouldn't overestimate the cloud opacity. Thus, the source of this apparent bias is more likely an underestimation of the humidity profiles used to retrieve the surface LW CRE in the presence of clouds. An increase in the humidity at these times would increase the F Cloudy −freesky net and therefore decrease the surface LW CRE. A final possibility for the difference is that each product has a unique estimate of the cloud cover due to vastly different fields-of-view. CALIOP footprints are only a small fraction of the CERES footprint, so part of the CERES footprint could be cloud free even if the 40 CALIOP profiles are opaque. A study by Kato et al. (2010) demonstrated that the differences between CERES and CloudSat/ CALIPSO cloud fractions decrease when averaged over area and time, so this difference is likely not the primary source of bias when comparing large statistical datasets.
The second regime of differences among the products is for surface LW CRE less than 30 W m -2 (Fig. 11a), which corresponds to high opaque clouds over the warm pool region (not shown). Here, CRE GOCCP is smaller than CRE CERES .
The underestimate of surface LW CRE by CALIPSO-GOCCP compared to CERES-CCCM could be caused by the full attenuation of the laser beam in deep convective clouds such that CALIPSO-GOCCP overestimates the mean altitude of opaque clouds. The differences shown in Fig. 11 are expected when comparing satellite products at footprint scales that use different remote sensing techniques. However, when looking at the gridded product distributions ( fig. B4) instead of instantaneous collocated data, the 2BFLX and CALIPSO-GOCCP agree well. Figure 12 shows global maps of differences between CALIPSO-GOCCP and the other satellite-derived products (CERES-EBAF and 2BFLX). This comparison gives an overview of the differences between the three surface LW CRE spatial products but it may mask some differences given the fact that the three spatial products are averaged in time (monthly) and
Compared to CERES-EBAF (Fig. 12a), CRE GOCCP is larger than CRE CERES over the oceans (except in stratocumulus regions) while CRE GOCCP is smaller than CRE CERES over icy surfaces and over ocean stratocumulus regions. The larger differences (-14 to -18 W m -2 ) occur over Greenland, Antarctica and tropical stratocumulus regions. Over icy areas like Greenland and the Antarctic ice sheet, CERES-EBAF has limited ability to differentiate the radiative fluxes emitted by the surface from those emitted by the clouds (Liu et al., 2010;Stubenrauch et al., 2013). The retrieval of surface LW CRE with CERES rely on the cloud detection from MODIS-CERES, which detects more clouds than others satellites over icy surfaces (GEWEX Cloud Assessment;Stubenrauch et al., 2012). Similarly, since stratocumulus clouds are low warm clouds at temperatures close to the surface temperature, the CERES radiometer can also have some bias when differentiating the LW cloud fluxes from LW surface fluxes over these regions.
Compared to 2BFLX (Fig. 12b), CRE GOCCP is slightly larger than CRE 2 BFLX over tropical oceans. Over lands, CRE GOCCP is slightly lower than CRE 2 BFLX . The maximum difference occurs over land along the western coasts of the North and South American continents and the Himalayan mountains where the surface elevation is above 2.5 km. This difference might be due to the CloudSat CPR's long powerful pulse (Fig. B2), which generates a surface clutter echo that tends to partially mask signals from cloud forming below ~1 km (Marchand et al., 2008). Over icy polar areas, the two products are very similar. Figure 12c shows the difference between CRE 2 BFLX and CRE CERES . The same patterns are observed over continent polar regions as in Fig. 12a, where CERES-EBAF overestimates the surface LW CRE compared to the 2BFLX product.
Zonal averages of the surface LW CRE for 2008-2010 (Figure 12d) show that the surface LW CRE is generally low in tropical regions and increases towards the mid-latitudes as the atmospheric moisture decreases. Values do not vary by much northward of about 50° N. To the south, a maximum occurs at about 60° S, with a decline towards the far south due to declines in cloudiness. Over the broad domain reaching from 60° N to 60° S the three satellites techniques show similar zonal means with differences among the three typically not exceeding 3 W m -2 . Over polar regions, the surface LW CRE from CERES-EBAF is generally higher than the other two products derived from active sensors.

Comparison with ground-based stations at gridded scale
Comparisons between ground-based measurements and the satellite-derived products (CRE GOCCP , CRE CERES , CRE 2 BFLX ) provide a direct evaluation of the satellite retrievals, but are limited by the difference in the spatial resolution of the satellitederived product (2°×2°) and the ground station observations (a few meters). The locations of the three ground-based sites are reported in the maps (stars in Fig. 12c).
Over the Summit Station, Greenland site, on average compared to ground-based observations, CALIPSO-GOCCP underestimates the surface LW CRE by 8.5 W m -2 , while 2BFLX underestimates it by 16.4 W m -2 and CERES-EBAF overestimates it by 36.6 W m -2 (Fig. 13a). where CERES-EBAF overestimates the surface LW CRE comparing to CALIPSO-GOCCP is observed over the map of difference (Fig. 12a) in icy polar regions, for instance over Greenland and Antarctica ice sheet. While this comparison suggests that CALIPSO-GOCCP could be biased somewhat low compared to the ground-station perspective over Greenland, it is also clear that this approach does appropriately capture the annual variability, while the CERES-EBAF approach appears to be significantly biased high with an unrealistic annual cycle.
Over the mid-latitude continental site (Fig. 13b) on average, CALIPSO-GOCCP underestimates the surface LW CRE by 5.7 W m -2 compared to ground-based observations, while 2BFLX underestimates it by 9.4 W m -2 and CERES-EBAF underestimates it by 12.1 W m -2 .
Over the tropical ocean site (Fig. 13c) on average, CALIPSO-GOCCP underestimates the surface LW CRE by 2.3 W m -2 compared to ground-based observations, while CERES-EBAF underestimates it by 2.7 W m -2 and 2BFLX underestimates it by 4.1 W m -2 . This same behavior is found on the map of differences between CRE GOCCP and CRE 2 BFLX (Fig. 12b) along the tropical Pacific and tropical Atlantic oceans where 2BFLX underestimates the surface LW CRE comparing to CALIPSO-GOCCP.

Space lidar missing the opaque cloud base
CALIPSO does not see the cloud base in many stratiform-type clouds, as an example, but this does not lead to as big of an issue in the surface LW CRE retrieval because the stratiform cloud base is not very far from the point of attenuation of the lidar. On the other hand, this attenuation can become a significant issue for circumstances where the lidar signal is fully attenuated at an altitude that is significantly above the actual cloud base, such as in deep convective clouds.
Based on the comparison of orbits (Fig. B1), we observe that when the space lidar does not see the cloud base, CALIPSO LW CRE underestimates the local surface LW CRE compared to 2BFLX. However, the opaque deep convective clouds cover a small part of the overall tropics compared to others clouds, therefore this effect does not dominate the global comparison ( Fig. 12) where CALIPSO-GOCCP surface LW CRE, is on the contrary, slightly larger than the other satellite products.
To test if the differences between CALIPSO-GOCCP and other products come from the space lidar not seeing the cloud base, we used Z FA instead of Z T Opaque in the CALIPSO-GOCCP retrieval. By definition Z FA is always lower in altitude than Z T Opaque , therefore this change should reduce the difference between the CALIPSO-GOCCP surface LW CRE and other surface LW CREs if the differences were due to CALIPSO missing the cloud base. Fig. B3 shows that the difference between CALIPSO-GOCCP surface LW CRE and the other satellite products increases instead of reduces when using Z FA instead of Z T Opaque . This suggests that the differences in surface LW CRE are likely not often due to CALIPSO misrepresenting the cloud base and that the cloud base might not be far from Z T Opaque in the majority of the cases. This result also suggests that the differences between the satellite retrievals come from other sources, such as the assumed humidity and temperature profiles. Indeed, the resolution of these profiles is rough in the CALIPSO retrieval and these profiles have also been identified as the largest sources of LW flux uncertainty in the 2BFLX product (Henderson et al., 2013).
Nevertheless contrarily to the satellite retrieval inter-comparison, using Z FA instead of Z T Opaque leads to slightly better agreement of CALIPSO-GOCCP LW CRE with ground base retrievals (eg. Fig. 13, 14). Ground-based measurements derive directly the surface LW CRE. While there are certainly challenges in comparing ground-based and satellite estimates, we should consider the ground-based estimates to be of pretty high quality. Thus, what these results mean collectively is that: 1)The inability of CALIPSO to observe the cloud base likely does have some effect (with respect to ground-based measurements). And that 2) this effect actually makes the comparison with other satellite products worse, which means that there are other issues (possibly with the other satellite products) leading to further differences. Over the Greenland site (Fig. 14a,d), CALIPSO-GOCCP and 2BFLX find the same seasonal cycle of the surface LW CRE with maxima in July, that correspond to the maximum opaque cloud cover, same as the ground-based seasonal cycle. The CERES-EBAF retrieval maximum is shifted by about three months (October, Fig. 14a,d), to a time of year that shows the minimum opaque cloud cover based on CALIPSO-GOCCP (not shown). This result suggests that during these months the CERES-EBAF retrieval does not successfully distinguish LW upward fluxes from clouds and the surface. This is consistent with CERES-EBAF low-mid and high-mid cloud fractions being biased high over the Summit site except for summer time (not shown). Consistently, Figure 14d shows CERES-EBAF's surface LW CRE is overestimated compared to ground-base retrievals in all season except summer. As a consequence CERES-EBAF does not capture the surface LW CRE annual cycle, contrarily to CALIPSO-GOCCP and 2BFLX retrievals.
Over the mid-latitude continental site (Fig. 14b,e), the surface LW CRE seasonal cycle of  are close to each other and the three satellite-derived products show similar seasonal cycles as the ground station.
Over the tropical ocean site (Fig. 14c,f), the surface LW CRE seasonal cycle is relatively flat. Figure 15a represents the global average seasonal cycle of the three surface LW CRE satellite-derived products. CRE CERES is larger than CRE GOCCP and CRE 2 BFLX from October to February and is lower from May to September. To analyze these differences, we decomposed the globe into Northern Hemisphere (NH : Fig. 15b), NH-ocean (Fig. 15c), NH-land (Fig. 15d),
The NH winter is the main cause for CERES-EBAF being larger than the two other products from October to February (2-3 W m -2 ). The NH-continents have the largest contribution (~6 W m -2 ) and the NH-oceans contribute slightly (~1 W m -2 ) between January to March which corresponds to the maximum of sea ice (Rousset et al., 2015). The SH only contributes a little (~0.5 W m -2 ) for the months of October and November and this comes only from the Antarctic ice sheet, which is covered by ice all year long. Same as in the difference maps (Fig. 12a), MODIS-CERES detects more clouds than other satellites over icy surfaces (GEWEX Cloud Assessment ;Stubenrauch et al., 2012).
The lower CERES-EBAF compared to CALIPSO-GOCCP and 2BFLX (1-2 W m -2 ) from May to September is mostly caused by both the oceans in SH and the land in NH.
20 515 520 525 530 7.1.3 Seasonal evolution of the zonal mean Figure 16 represents the annual evolution of the zonal mean of the surface LW CRE from CERES-EBAF (Fig. 16a), CALIPSO-GOCCP (Fig. 16b), and 2BFLX (Fig. 16c). The two active sensor figures exhibit the same behavior whilst CERES-EBAF has a stronger surface LW CRE in the polar regions during winter months, which corresponds to the minimum of opaque cloud cover and the maximum of sea ice. To see where the largest differences with CERES-EBAF are located, Figures 16d and 16e represent the differences between CALIPSO-GOCCP and CERES-EBAF and the differences between 2BFLX and CERES-EBAF respectively. The same feature is observed in both figures with CERES-EBAF having larger surface LW CRE than the other two products in the polar regions during their respective winters. CERES-EBAF also has smaller surface LW CRE in the mid-latitude regions.
Decomposing the difference (Fig. 16d) into land only (Fig. 16f) and ocean only (Fig. 16g) shows CALIPSO-GOCCP lower than  during winter (September to May) and over the icy Antarctic all year long. The oceans contribute to this difference during months of significant sea ice. These results suggests that the differences in surface LW CRE are likely due to CERES-EBAF detecting clouds over icy surfaces when there are no clouds .
On the contrary, CERES-EBAF is lower than CALIPSO-GOCCP mostly over mid-latitude oceanic regions all year long ( Fig. 16g) and this difference is also observed in the annual mean maps (Fig 12a). These regions contain low altitude thin clouds and few low opaque clouds (1-2 km: Fig. 2b,d). To see if these differences are caused by thin clouds in the boundary layer, we have computed the difference between the surface LW opaque CRE from CALIPSO-GOCCP observations and the CERES-EBAF product (Fig. 16h) over ocean only. The differences over mid-latitude oceans are smaller and close to 0 in this case (Fig. 16h). Thus, the reason for the CERES-EBAF surface LW CRE being weaker than the CALIPSO-GOCCP in these regions is likely because the CERES radiometer does not see the optically thin clouds in the boundary layer over midlatitude oceans. Figure 17a shows the temporal evolution of the surface LW CRE anomaly from the three satellite-derived products over 13 years 2008-2020. A decomposition separating continents from oceans and NH from SH is presented in Figs. 17b-g.

Variations of 13 years (2008-2020)
There is consistent amplitude in the annual variability in the global surface LW CRE anomaly between the three datasets.
This appears to be because of the annual cycle variations in the SH and NH, which are out of sync from each other, and the fact that the SH annual amplitude (and magnitude) are larger. Thus, the annual variation of the global surface LW CRE is most closely aligned with the annual variation of the SH.
The The phasing of the annual cycle for the CERES-EBAF product is actually quite consistent with the others for both NH and SH over both land and ocean, except for the NH land ( Fig. 17d; because of false cloud detection as already explained and shown in Figs. 14-16). However, it is interesting that even over NH land the annual minima match pretty well. Thus, the overall two months shift (Fig. 17a) is in part due to the differences in NH land annual maximum but apparently also somewhat due to the different amplitudes of the annual cycles for different areas and how they combine in unique ways for the different datasets.
The inter-annual variability is pretty interesting. For example, the NH winter max in CERES-EBAF and CALIPSO-GOCCP products appears to vary by up to about 3 W m -2 from year to year. That is the kind of variability that might have significant impacts on climate-relevant processes like melting of the cryosphere.
22 575 580 8 Conclusion In this paper, we build a new surface LW CRE dataset from five cloud properties observed with space-based lidar (CALIPSO-GOCCP). The robustness of the new surface LW CRE dataset at global scales is evaluated by comparing it against existing independent space-based surface LW CRE retrievals from CERES and CloudSat (Kato et al., 2018;L'Ecuyer et al., 2019) at footprint instantaneous scale as well as at 2°x2° gridded scale globally. It is also evaluated locally by comparison against observations collected at three ground stations in polar (Shupe et al., 2013), mid-latitude (Haeffelin et al., 2005;Chiriaco et al., 2018) and tropical (Roesch et al., 2011) locations. The (admittedly limited) ground-station comparisons actually showed that the CALIPSO-GOCCP product agreed the best with the ground measurements compared to the other satellite products, especially in capturing the annual variability. Additionally, there are other specific aspects where the CALIPSO-GOCCP product appears to be an improvement over others, including over bright polar surfaces.
This might be surprising given the simplicity of the surface radiation retrieval method used to produce the CALIPSO-GOCCP product, but it is understandable because of the two following physical elements: i) The CALIPSO-GOCCP method directly retrieves the surface LW CRE without retrieving the surface radiative fluxes first.
This approach minimizes the impact of the uncertainties due to surface characteristics (surface emissivity, roughness, deserts and frozen surfaces), which strongly influence the fluxes but not the surface LW CRE.
ii) The surface LW CRE is primarily driven by the cloud cover, the cloud opacity and the cloud altitude, which are quite well measured by space-based lidar over all types of surfaces. Moreover, the lidar approach distinguishes quite well the opaque clouds from the optically thin clouds. Lastly, it documents the detailed vertical cloud profile, except below the altitude where the laser is fully attenuated where we overestimate the mean altitude of opaque clouds. This last limitation only weakly influences the surface LW CRE retrieval because the lidar is fully attenuated at an altitude lower than 3 km above the surface most of the time (Guzman et al., 2017)  This new global dataset extends over more than a decade thanks to the long CALIPSO mission. The global mean temporal evolution over 13 years (2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018)(2019)(2020) shows that the anomaly of the surface LW CRE derived from CALIPSO-GOCCP is shifted by about two months compared to that derived from the passive CERES radiometer. This shift is mostly due to differences over the NH lands during winter when the surface is icy. This new dataset will be extended in time by including future data acquired by CALIPSO, as well as with data collected by forthcoming space lidars on board the European Earth Cloud, Aerosol and Radiation Explorer mission (EarthCARE; Illingworth et al., 2015) and the next generation of US cloud/aerosols lidar space missions.
The dataset presented in this paper will be used in a future study to better understand the mechanisms of cloud radiative feedbacks at the Earth's surface, i.e. how a change in surface temperature modifies the cloud properties that change the surface LW CRE, which in turn influences the temperature. An essential first step is to understand which cloud variables have driven the surface LW CRE variations over the last decade in regions that are most sensitive to global warming, such as the polar regions, as well as on a global scale. Several recent studies (eg. Taylor et al., 2007;Zelinka et al., 2012aZelinka et al., , 2012bVaillant de Guélis et al., 2017a, 2017b, 2018 have shown that it is possible to attribute changes in CRE to variations in cloud properties when 1) the CRE is related to a limited number of cloud properties by sufficiently simple relationships that they can be derived analytically, 2) the CRE retrieved by these analytical relationships is sufficiently reliable, i.e. within the uncertainty domain of the existing datasets, and 3) the CRE is retrieved using reliable observations over all surface types and on long global time scale. The CALIPSO-GOCCP surface LW CRE dataset developed in this study satisfies these three conditions. The next step of this work will therefore be to analyze this 13 years dataset to understand these mechanisms. The goal of this research is to improve our understanding of the response of clouds to the warming induced by anthropogenic activities, which is a major source of uncertainty in climate change predictions.