The Temperature Control of Cloud Adiabatic Fraction and Coverage

The fraction of cloud water compared to its adiabatic value is defined as the adiabatic fraction, fad. The accuracy of cloud representation in climate models is highly sensitive to mixing rate, manifested in fad. Here, we present the first fad distribution of marine boundary layer clouds over global oceans, retrieved by satellite observations. The fad is shown to decrease exponentially with cloud base temperature (CBT) and cloud depth, in agreement with the increasing evaporation capacity of entrained warmer air. Cloud cover decreases with increasing CBT, but to a much lesser extent than fad. The dependence of fad on CBT has little dependence on relative humidity or precipitation. The relationship between CBT and fad highlights the importance of CBT as a core control factor on cloud evaporation. The simultaneous decrease in cloud water content and cover with increasing CBT can lead to positive cloud feedback, resulting in greater future climate warming.

Supporting Information may be found in the online version of this article.(Quaas et al., 2006;Rausch et al., 2017).However, dynamical processes in clouds, represented by entrainment, are essential modulators of cloud microphysical properties, often leading to sub-adiabatic clouds (f ad < 1) (Barlakas et al., 2020;Richardson & Stephens, 2017).Chin et al. (2000) indicated that low-level clouds' sub-adiabatic prop erty strongly influences the radiative energy balance, especially in the shortwave.This sub-adiabaticity stabilizes the cloud layer by reducing the contrast of radiative heating/cooling within the cloud, which also simultaneously affects the cloud amount, albedo, and rain rate.Current climate models and passive satellite retrievals of cloud drop number concentrations (N d ) are usually performed based on the adiabatic assumption (assuming f ad = 1) with large uncertainties, which also leaves most of the mechanisms involved in aerosol-cloud interaction unclarified (Grosvenor et al., 2018;Grosvenor & Wood, 2014;Szczodrak et al., 2001).Efraim et al. (2020) and Wang et al. (2021) showed that applying a f ad correction can reduce the uncertainty of satellite-retrieved N d caused by cloud sub-adiabaticity.Accurate acquisition of f ad is therefore essential for an improved understanding of aerosol-cloud interactions and atmospheric model simulations.
Most of these studies are based on ground-based radar or aircraft observations and are conducted for short periods and regions based on field campaigns (Merk et al., 2016).These studies provided systematic values of f ad , with a mean value of 0.6.Min et al. (2012) indicated that the average f ad value for thin clouds was higher than that for thicker clouds through multi-aircraft observations.However, f ad varies considerably from region to region (Min et al., 2012).The limited number of f ad measurements is insufficient to support large regional or global climate change studies.Passive satellites cannot calculate f ad accurately due to the high uncertainties in cloud geometric parameters retrieval (Merk et al., 2016).Thus, relying on satellite observations to estimate f ad and its impact on entrainment and mixing using spaceborne lidar would be highly desirable for global-scale analyses.
Climate and large-eddy simulation (LES) models have shown that increasing cloud base temperature (CBT) will increase the adiabatic liquid water content (LWC) and further drive the increase in cloud water (Charlock, 1982;Rieck et al., 2012).Increasing the water vapor content contrast between the cloud and the surrounding environment would further enhance the entrainment and vertical mixing in the boundary layer (van der Dussen et al., 2015).This variation of entrainment mixing will inevitably cause f ad to vary with environmental temperatures.Unfortunately, current studies based on the model simulations have focused only on the relationship between the f ad and the cloud boundary without exploring the effect of temperature on f ad (Eytan et al., 2021(Eytan et al., , 2022)).
Changes in CBT and the subsequent changes in entrainment and vertical mixing can also lead to changes in cloud cover fraction (CF), which will further modulate the global energy budget (Dagan et al., 2018;Qu et al., 2015).
Although climate model simulations of low-level cloud cover involve several complex iterative processes, including entrainment mixing, radiative transfer, and cloud feedback (Klein et al., 2017), the results are still subject to controversies and uncertainties.This uncertainty is likely because cloud cover is also heavily influenced by atmospheric aerosols in addition to environmental factors (Rosenfeld et al., 2019).
Consequently, current researches on variability in cloud coverage remain controversial, particularly in the context of global warming.It is evident from existing studies that changes in atmospheric entrainment, mixing, precipitation, temperature, and aerosol concentration can lead to changes in f ad and CF (Albrecht, 1989;Bender et al., 2019;Bretherton & Blossey, 2014;Bretherton et al., 2013).However, a comprehensive understanding of the synergistic variation of temperature and cloudiness and f ad has not been studied in depth, and the exact quantitative relationships need to be further explored.
We first retrieved f ad at a global scale using satellite observations.Further, we studied the dependences of f ad and CF of global marine low clouds on CBT, cloud depth, precipitation, and other meteorological parameters.The results provide the dependence of f ad and CF on CBT based on the observed data.Finally, we discuss the significance of the findings.

Methods
Adiabatic fraction is defined as the ratio between the measured actual cloud LWC (g/m 3 ) and the adiabatic theoretical cloud LWC at a specific height (H) above the cloud base (Eytan et al., 2021), as shown in Equation 1.
f ad_h (H) is the adiabatic fraction at the specific height H, LWC act (H) is the measured LWC at H, and LWC ad (H) is the theoretical liquid water content that a parcel would have if it was lifted adiabatically from the cloud base to the specific height above cloud base.Liquid water path (LWP; g/m 2 ) is the integral of LWC with height.Thus, when the specific H is equal to the geometric thickness of the cloud, the following relationship exists.
where  LWCact and  LWCad are the averaged LWC act and LWC ad over the cloud thickness; LWP act is the actual liquid water path; and LWP ad is the adiabatic theoretical liquid water path.That is, for any cloud, the vertically averaged f ad is the ratio of LWP act to LWP ad , as shown in Equation 3. where c is a constant usually taken as 5/9, ρ w is the water density, τ is the cloud optical thickness, and r e is the cloud drop effective radius (Grosvenor et al., 2018).LWP act can be retrieved by satellite observations of τ and r e .It is obtained in this study from MODerate Imaging Spectroradiometer (MODIS) MYD06 Level 2 cloud products with a resolution of 1 km.To ensure data quality, MODIS LWP act when the solar zenith angle is greater than 65° is excluded in this study (Zhu et al., 2018).The LWP ad is retrieved from the CBT and pressure based on the plane parallel cloud adiabatic assumption consistent with the methods in Min et al. (2012) and Merk et al. (2016).
The cloud base height (CBH), CBT, cloud geometric thickness (CGT), and CF are obtained from the active Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) observations on board Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observation (CALIPSO) base on the method of X. Lu et al. (2021).The retrieval methodology is built on the highest resolution low-level water cloud data obtained from the Vertical Feature Mask (VFM) product of CALIPSO.The retrieval domain is each 1° scene along the CALIPSO trajectory.The phase (water cloud and ice cloud) and confidence information from VFM product were used to extract high-confidence water clouds.For more details of the CALIPSO CBH retrieval methodology, please refer to the Supporting Information S1 (Text S1) and X. Lu et al. (2021).The National Centers for Environmental Prediction (NECP) reanalysis data was also used in this study.Due to the poor quality of the atmospheric temperature data provided by CALIPSO satellite itself, after obtaining the CBH for each 1° scene through the CBH retrieval method in X. Lu et al. (2021), the height and temperature profile data provided by NCEP was used to linearly interpolate and obtain the CBT corresponding to the CALIPSO CBH.Lower-tropospheric stability (LTS), used to characterize the stability state of the atmosphere, was calculated as the potential temperature difference between the sea surface and 700 hPa and calculated from NECP reanalysis data.For more information about data matching between CALIPSO and MODIS, please refer to the Supporting Information S1 (Text S1 and Figure S1).

Geographic Distribution of Cloud Adiabatic Fraction and Cover
Using 1-year satellite observations of CALIPSO and MODIS, we obtained the f ad over global oceans in 2014 based on Equation 3. The original spatial resolution of the retrieved f ad data is 1° scene along the CALIPSO trajectory.The joint distributions of CALIOP CGT and the average f ad are shown in Figure 1, which indicates that the f ad decreases almost exponentially with increasing CGT and stabilizes near f ad of ∼0.05 when the clouds are thick.This decrease of f ad with CGT occurs because cloud parcels mix as they rise, and a given rate of mixing would lead to this shape of decreasing f ad (Merk et al., 2016), by dilution, evaporation, and precipitation of the LWC, making the f ad generally smaller (Min et al., 2012).The variation range of the f ad is significantly greater for smaller CGT, which is influenced by the smaller LWP of thin clouds.Slight deviations in the retrieval of LWP act of thin clouds may lead to large fluctuations in f ad , because of the division of two small values with large relative uncertainties in Equation 3. We also compared our retrieved f ad from CALIPSO and MODIS satellite observations with f ad data in other studies based on aircraft observations (Braun et al., 2018;Efraim et al., 2020;Min et al., 2012) (Figure 1, represented by blue and cyan lines).For detailed information regarding the aircraft validation data, please refer to Table S1 in Supporting Information S1.Both previous studies pointed out that the f ad decreases in an approximately linear relationship as the CGT observed by the aircraft increases (Figure 4 2020)), which is consistent with our findings.However, in these previous studies, the maximum CGT is essentially less than 1,000 m, especially in Min et al. (2012), where the CGT is below 500 m.We provide trends in f ad at large CGTs that were unavailable from previous studies.
Figure 1 highlights that for small CGT, there are cases where the indicated f ad is greater than 1, as shallow clouds tend to have small LWP.However, small absolute errors in LWP as represented in Equation 3, could translate into large relative errors of f ad .To account for the uncertainties, we excluded all cases where f ad > 1 (accounting for 9.3% of all data) for all figures except for Figure 1.This decision is based on recognizing that such cases (with f ad > 1) are likely to be influenced by measurement and retrieval uncertainties.Furthermore, "superadiabatic" cloud profiles, where f ad > 1, are not physically realistic.This rationale aligns with the approach taken by Merk et al. (2016) in their analysis of in situ observations.It is also worth noting that f ad values greater than 1, particularly in thin clouds, fall outside the standard deviation range of the average line (black line) shown in Figure 1.However, it is worth mentioning that CALIPSO lidar is more capable of detecting thin clouds, and the retrievals for thin clouds are more accurate in terms of CBH than thick clouds, as confirmed in both works of Mülmenstädt et al. (2018) and X. Lu et al. (2021).Therefore, the primary source of uncertainty in f ad in this study is highly likely to be the MODIS-observed LWP product (1 km resolution) of thin clouds.To accurately determine this impact, higher-resolution satellite observations or LES models may be necessary in future research.
The global geographic distributions of annual average f ad , CALIOP CGT, and CF in 2014 are provided in Figure 2. When creating geographic plots, the retrieved f ad data was aggregated into 3° × 3° latitude-longitude grids.We also provide the spatial distribution of the number of samples for each grid, as shown in Figure S2 in Supporting Information S1.The result shows that low f ad occurs mainly in tropical regions (30°S-30°N) with an average of 0.24, much lower than at middle and high latitudes (90°S-30°S and 30°N-90°N) with an average of 0.48.The highest f ad in low latitudes mainly occurs in South America and Africa offshore areas, exceeding 0.5.Combined with the CGT distribution in Figure 2b, it can be seen that the f ad pattern is inverse to that of CGT.Regions with lower f ad are concentrated in the equator and the tropical western Pacific, where clouds are thicker.These regions are characterized by high sea surface temperatures (SSTs) (X.Lu et al., 2021).The higher mean f ad line shown in Efraim et al. (2020) and Braun et al. (2018) with an average SST of 10°C in Figure 1 also confirms this finding compared to Min et al. (2012) with an average SST of 17°C.The distribution of CF in Figure 2c shows a similar pattern to the f ad in Figure 2a.The zones with high f ad usually have high cloud cover, especially in the downwind region of the continent.

Dependence of Cloud Adiabatic Fraction and Cover on Cloud Base Temperature
Considering the positive correlation between f ad and CF with latitude as shown in Figure 2, we further investigated the dependence of f ad and CF on CBT in Figure 3. Saturation vapor pressure (es) is a parameter positively correlated with CBT based on the Causius-Clapeiron equation.It is shown that the higher f ad and CF occur with colder CBT and lower es (Figure 3a).The increased f ad with decreasing CBT is consistent with the reduced evaporation of cloud water for a given mixing rate (Dagan et al., 2018).The CF increases with the lower CBT and larger f ad , as a probable result of slower loss of cloud water to evaporation in colder environments (Klein et al., 2017).The gray lines in Figure 3a represent the dependences of f ad and CF on es.The higher es in warmer CBT indicates a greater contrast in water vapor between the cloud and its surrounding environment at a fixed relative humidity (RH), resulting in more cloud water being consumed to saturate the entrained ambient air (Dagan et al., 2018;Qu et al., 2015).As a result, f ad and CF decrease.Additionally, given that higher CBTs often imply less stable atmospheric conditions, this instability may also lead to a decrease in f ad .Therefore, the variation in f ad under high-CBT conditions in Figure 3a may also be influenced by smaller atmospheric stability.To eliminate the interference of atmospheric stability on the conclusions drawn in Figure 3a, we further differentiated the changes in f ad and CF with CBT under different LTS conditions in Figure 3b.It can be seen that f ad and CF both gradually increase with greater atmospheric stability.Most importantly, when LTS is fixed, the decreasing trends in f ad and CF (Figure 3b) with increasing CBT align with the trends in all data (Figure 3a).This indicates that CBT dominates the variability of f ad and CF while LTS has a secondary effect.The effects of CBT and LTS on f ad and CF are similar in magnitude.
The causes for the decreasing f ad and CF with increasing CBT are further demonstrated by Figure 3c based on a parcel model, which shows that adiabatic LWC at a given height above the cloud base (which is 300 m in this study and can be changed arbitrarily) increases less than linearly with CBT (red line in Figure 3c), whereas the saturation vapor density for a given RH near the cloud base with a pressure of 900 hPa is growing exponentially with CBT (blue line in Figure 3c).Therefore, at a higher CBT, a larger fraction of the adiabatic LWC is evaporated for a given mixing rate with the ambient air.The resulting increase in water vapor content contrast promotes entrainment-driven drying of the boundary layer as simulated by Bretherton and Blossey (2014) and Bretherton (2015), which leads to a reduction in low-level cloud cover and hence acts as a positive cloud radiative feedback that enhances the initial warming (Qu et al., 2015;Rieck et al., 2012;Sherwood et al., 2014).

Effects of Meteorological Parameters on Cloud Adiabatic Fraction and Cover
The dependences of f ad and CF on other parameters under different CBTs are also provided in Figure 4, including CALIOP CGT and LTS.The division to CBT bins (Figure 4) shows a similar CBT dependence to Figure 3a.More specifically, the results exhibit a decreasing trend of f ad with decreasing LTS for any CBT bins (Figure 4b).The CBT dependences of CF on CGT and LTS (Figures 4c and 4d) are generally similar to the dependence of f ad on these properties, but with a much smaller sensitivity.It is worth noting that we only used scenes with a sufficient number of penetrated thin clouds for cloud parameter retrieval due to the lack of capability of the CALIOP lidar for thick cloud observations (X.Lu et al., 2021), so that the CFs in Figure 4 are mainly distributed between 0.3 and 0.6.The results show that the CF tends to decrease as the CGT increases, but then there is a slight increase when the CGT is greater than 1,000 m, which may also be influenced by other factors, such as aerosols (Rosenfeld et al., 2019).As the LTS increases, the CF keeps increasing (Figure 4d), but the differences between different CBT bins are small.This may be because the LTS itself already reflects changes in CBT.
Increased SST can also lead to decreased CF, so the impact of SST on f ad and CF is explored in Figure S3 in Supporting Information S1.The results indicate that the effects of SST on f ad and CF are similar to that of CBT as shown in Figure 4.This may be due to the fact that CBT is generally correlated with SST, but a range of CBT can exist for the same SST.Moreover, RH (obtained from NECP reanalysis data) at 950 and 850 hPa, as a physical quantity characterizing the dryness of the atmosphere, is also utilized to study its effects on f ad and CF (Figures S4 and S5 in Supporting Information S1).The f ad decreases slightly with increasing RH, especially at 850 hPa.That may be because the higher RH, the less buoyancy, and the reduced buoyancy will lead to an increase in cloud development time under the same path, resulting in an increase in entrainment (C.Lu et al., 2018), while the enhanced entrainment will lead to a reduction in f ad .This entrainment driven by humidity changes has a much smaller effect on f ad than CBT.CF also increases slightly or remains approximately constant with increasing RH.This is similar to the results based on the Coupled Model Intercomparison Project, which indicated that free tropospheric RH has a nearly negligible impact on cloud cover changes (Qu et al., 2015).Overall, the effect of RH on f ad and CF is significantly smaller than that of temperature and LTS.Thus, CBT and its variation are the essential drivers of changes in f ad and CF.
In addition to the above controlling factors of f ad , the effect of precipitation on cloud adiabaticity is also noteworthy due to its significant role in regulating cloud water content.To assess this effect, we used the cloud droplet effective radius (r e ) threshold of 14 μm to distinguish between precipitation and non-precipitation conditions, as proposed by Rosenfeld and Gutman (1994) and Suzuki et al. (2010) (Figure S6 in Supporting Information S1).
When r e is less than 14 μm, it indicates no precipitation; whereas greater than 14 μm suggests precipitation.The results presented in Figure S6a in Supporting Information S1 reveal that the effect of precipitation occurs mainly for CBT above 14°C, with a reduction of cloud water content due to precipitation leading to a decrease in f ad .The trends in f ad with CBT, with and without precipitation, are mostly similar.For cloud cover (Figure S6b in Supporting Information S1), precipitation also results in a decrease in cloudiness, which corresponds to the reduction in cloud adiabatic fraction.In summary, precipitation does not significantly alter the variation of f ad with CBT.

Discussion and Conclusions
We obtained the first-ever global distribution of f ad for marine low-level clouds by combining measurements of radiometer and lidar onboard satellites.Based on the retrieved f ad result, we explored the control of CBT, CGT, SST, LTS, RH, and precipitation on f ad and cloud cover.It was found that the f ad decreases exponentially with increasing cloud thickness.Variations in CBT are an essential driver of changes in f ad and, to a lesser extent, of CF.Increased SST can also lead to decreased CF and f ad .Nevertheless, although CBT is usually associated with SST, it's essential to recognize that there can be a range of CBT values for the same SST.This means that the impacts of SST on f ad and CF are comparable to those of CBT.Additionally, higher SST corresponds to lower atmospheric stability.In such conditions, clouds tend to grow deeper, resulting in lower cloud covers.Deeper clouds also have more time and opportunities to mix with the surrounding air, leading to lower f ad .Therefore, changes in SST are actually associated with variations in lower atmospheric stability, which, in turn, play a significant role in controlling cloud development.Lower atmospheric stability doesn't directly influence f ad but rather suppresses the vertical growth of clouds, which tends to increase f ad levels.f ad and CF show low sensitivity to changes in RH.Precipitation and LTS do not change the variation shape of f ad and CF with CBT.Both f ad and CF increase systematically with colder CBT.This finding lends support to the proposition that both f ad and CF are manifestations of the extent of cloud evaporation due to entrainment.It is also noteworthy that the results of this study, which are based on satellite observations, suggest concomitant variations in both f ad and CF.Consequently, any process that triggers a reduction in CF would likewise manifest as a decrease in f ad .However, the change in cloud adiabaticity cannot be fully explained by the variation in cloud cover.As shown in Figure 3b, the relative change in f ad is triple the relative change in CF for a given change in CBT.This means that the indicated change in f ad is dominated by the real (unknown) change in CF.Disentangling the effects of controlling factors on f ad and CF necessitates measurements of exceedingly high resolution at the scale of the cloud mixing, that is, the satellite sub-pixel cloud scale, which is beyond the scope of this study.Addressing this limitation, future research may employ LES models and higher-resolution satellite observations to gain a more precise comprehension of the cloud microphysical processes in a single cloud scale.Rosenfeld et al. (2019) have shown that aerosols dominate the variability in cloud cover for a given meteorological condition.They showed that the meteorological leading factors were CGT and LTS, but didn't address CBT as they focused on the 0 to 40°S latitude band.Here we show that CBT is a leading meteorological cause for variability in CF and f ad , and quantify these effects.Quantifying the synergistic variation of cloud cover and adiabatic fraction with CBT provides the conditions for a better understanding of cloud processes based on observations.Most importantly, the decrease in f ad and cloud cover for increasing CBT is expected to decrease cloud albedo.This is because as CBT increases, the associated changes in entrainment and turbulent mixing typically lead to a decrease in CF.This reduction in cloud cover is already recognized as a major cause for positive radiative feedback of clouds to warming, a crucial factor to consider in climate models.In the context of global warming, climate change assessment parameters such as N d and cloud thickness are closely associated with f ad .The finding that f ad is even more susceptible to CBT than CF implies an added component to the positive cloud feedback with global warming, which would increase the overall magnitude of the positive cloud feedback and the respective climate sensitivity.It may be already accounted for by the observed response of LWP.Introducing this highly susceptible relationship between CBT and f ad into climate models provides a unique perspective for assessing cloud feedback.

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The first-ever global climatology of cloud adiabatic fraction of marine boundary layer clouds was retrieved by satellite observations • Cloud base temperature and cloud depth dominate the variation of the cloud adiabatic fraction • Cloud adiabatic fraction is positively correlated with cloud cover Supporting Information: in Min et al. (2012) and Figure 8 in Efraim et al. (

Figure 1 .
Figure 1.Joint distribution of Cloud-Aerosol Lidar with Orthogonal Polarization cloud geometric thickness and average f ad with the color of case frequency for each bin in 2014.The black line is the average line.The I-shaped line is the standard deviation of the average line.The solid blue dots and blue line are from Min et al. (2012), and the cyan hollow dots and cyan line are from Efraim et al. (2020) and Braun et al. (2018).

Figure 3 .
Figure 3.The dependence of the average f ad (solid blue line) and cloud cover fraction (CF) (dotted red line) on cloud base temperature (CBT) and cloud base saturation vapor pressure (es, solid, and dotted gray line for f ad and CF, respectively).(a) is for all data; (b) is the same as (a) but under different lower-tropospheric stability bins (unit: K).The "fraction" in the y-axis heading indicates the adiabatic fraction and cloud cover.(c) The dependences of simulated adiabatic liquid water content (LWC) (red line) and saturation vapor density (blue line) on CBT are based on a parcel model of a 300 m deep cloud, with a cloud base pressure at 900 hPa.The blue line represents 0.1 times the saturation vapor density, allowing for a comparative display of the relative trends of saturation vapor density and adiabatic LWC on the same coordinate system.The calculation of adiabatic LWC follows the formula provided by Zhu et al. (2018); the vapor density is calculated based on the Clausius-Clapeyron equation.The plots are based on the retrieved f ad and cloud cover of this study.

Figure 4 .
Figure 4.The dependences of f ad and cloud cover on different parameters as a function of cloud base temperature (CBT).Panels (a) and (c) are for Cloud-Aerosol Lidar with Orthogonal Polarization CGT; (b) and (d) are for lower-tropospheric stability (LTS).Bins of cloud geometric thickness or LTS and CBT are shown only if they contain at least 100 cases.The plots are based on the retrieved results in 2014.