Effects of 3D Thermal Radiation on Cloud Development

We investigate the effects of thermal radiation on cloud development in an idealized setup in large-eddy simulations with the UCLA-LES model. We investigate single convective clouds (driven by a warm bubble) and a large cumulus cloud field at 50 m horizontal resolution. We compare the newly developed 3D "neighboring column approximation" with the independent column approximation and a simulation without radiation and their respective impact on clouds. Thermal radiation causes strong local cooling at cloud tops accompanied by a modest warming at the cloud bottom, and in the case of a 3D scheme, 5 also cloud side cooling. 3D thermal radiation causes systematically larger cooling when averaged over the model domain. In order to investigate the effects of local cooling on the clouds and to separate these local effects from a systematically larger cooling effect in the modeling domain, we apply the radiative transfer solutions in different ways. The direct effect of heating and cooling at the clouds is applied (interactive thermal radiation) in a first simulation. Furthermore, a slab-averaged applications of the 1D and 3D radiation is used to study the effect of local cloud radiation as opposed to the domain averaged effect. 10 These simulations exhibit a cooling profile, with stronger cooling in the cloudy layers. In a final setup, we replace the radiation simulation by a uniform cooling of 2.6 K/d. For the simulations of isolated single cloud, or the cumulus cloud field with interactive radiation, we find that thermal radiation changes cloud circulation, by causing stronger updrafts and stronger subsiding shells. In our cumulus cloud field simulation we find that interactive radiation, acting locally on clouds, enhances the circulation 15 compared to the averaged radiation applications. In addition we find that thermal radiation triggers the organization of clouds. Comparing the effects of 3D and 1D thermal radiation, we find that organization effects of 3D thermal radiation are usually stronger than the 1D counterpart (either interactive or averaged). Interactive radiation leads to an earlier onset of the organization both in 1D and 3D compared to the averaged radiation application. Applying a constant cooling to the simulations leads to a similar development of the cloud field as in the case of averaged radiation, but less water condenses overall in the simulation. 20 Generally, clouds contain more liquid water if radiation is accounted for. Furthermore, thermal radiation enhances turbulence and mixing as well as the size and lifetime of clouds. Interactive thermal radiation produces larger clouds with longer lifetimes.


Introduction
Clouds are a the key element for accurate climate and weather prediction and cause large uncertainties in the prediction of both (Boucher et al., 2013).Clouds play an important, yet poorly quantified role in climate change.Key questions arising from the and causes an additional downward motion at the interface between the cloud and the atmosphere.They used a 3D radiative transfer approximation, which, however was limited to axially symmetric clouds.The change in cloud circulation in turn promoted vertical cloud development.The vertical differential local heating and cooling causes a destabilization of the cloud (Fu et al., 1995), which increases buoyancy (Sommerai, 1976) and also turbulence production in clouds (Davies and Alves, 1989;Fu et al., 1995;Petters et al., 2012).Fu et al. (1995) also found that the clear sky cooling enhances convection and precipitation.Larson et al. (2001) showed that thermal cooling on the one hand enhances condensation and thus increases liquid water content; on the other hand, radiation causes more entrainment and therefore a decrease in liquid water content.Xu and Randall (1995) found a longer lifetime of clouds when simulating clouds with interactive radiation.They compared simulations with interactive radiation to a homogenized application to look at the local effects of differential heating and cooling on deep convective clouds.Thermal radiation increased turbulence on short time scales, and on longer time scales the cloud development itself.A similar approach was followed by Xiao et al. (2014).In this case, simulations with interactive and homogenized radiation where performed, with a focus on stratocumulus to cumulus transition.Again, an increase in turbulence, due to the destabilization of the clouds by thermal radiation was found.Xiao et al. (2014) state that because they only used a common 1D approximation for the radiation calculation the effects might be larger with 3D radiation.The hypothesis of destabilization of the cloud layer by thermal radiation was originally proposed by Lilly (1988).Tao et al. (1993) found an increase in precipitation of 14-31% due to thermal effects and Tao et al. (1996) saw an increase in relative humidity, enhanced circulation and microphysical processes.In a recent study, Bellon and Geoffroy (2016a) investigated the stratocumulus radiative effect in a set of equilibrium simulations.It was found that depending on the sea surface temperature, radiative cooling at cloud top is either crucial for the existence of the stratocumulus clouds or causes enhanced turbulence by buoyancy production, more entrainment and a deepening of the boundary layer.Based on the results of the first study (Bellon and Geoffroy, 2016a), Bellon and Geoffroy (2016b) investigated how good the stratocumulus radiative effect has to be represented.Applying different radiative solutions, such as column or horizontally averaged radiation, Bellon and Geoffroy (2016b) found that the radiative effect has to be represented in some detail at the cloud top to account for the enhanced turbulence and mixing and therefore determining the existence of the stratocumulus.Studies by Muller and Held (2012); Muller and Bony (2015) suggest that interactive thermal radiation is essential to trigger self-organization in radiative-convective-equilibrium simulations.Emanuel et al. (2014) found that clear sky thermal cooling is also a key component for self-organization.
The microphysical aspect was further addressed e.g. by Harrington et al. (2000); Marquis and Harrington (2005).They showed that thermal emission enhances cloud droplet growth by diffusion.An earlier onset of collision and coalescence of cloud droplets was found by Hartman and Harrington (2005a) and Hartman and Harrington (2005b) when thermal radiation is considered.Recent studies of Brewster (2015) and de Lozar and Muessle (2016) emphasize the hypothesis that thermal radiation might influence droplet growth significantly and lead to a broadening of the droplet size spectra and thus enhance the formation of precipitation.
These former studies were mostly based on 1D radiative transfer approximation.Studies accounting for 3D effects are rare.
This paper aims to address the interaction of radiation and clouds, including a comparison of the effects of 1D and 3D thermal radiation.For this 3D interactive radiation (the "Neighboring Column Approximation", NCA; Klinger and Mayer (2016)) was incorporated into the UCLA-LES (Stevens et al., 2005;Stevens, 2007) and a set of idealized simulations was developed, aiming to isolate the effect of 1D and 3D thermal radiation on clouds.The model and model setup are described in Section 2. The results are presented in Section 3.
The spectral integration is accounted for with a correlated-k molecular absorption parameterization (Fu and Liou, 1992).In addition the Monte Carlo spectral integration (MCSI; Pincus and Stevens (2009)) is used in this study for the simulation of the cumulus cloud field to save computational time.The UCLA-LES was adapted for 3D interactive thermal radiation by implementing the "Neighboring Column Approximation", (NCA; Klinger and Mayer (2016)) for the calculation of 3D thermal heating and cooling rates.
Two passive scalar tracers were implemented into UCLA-LES, following Park et al. (2016).With the help of the tracers, we performed an octant analysis (Park et al., 2016) to extract coherent structures in simulation data.For further analysis of the results, we used the cloud tracking algorithm Cb-TRAM (Zinner et al., 2008).

UCLA-LES Setup
Two different types of idealized cloud studies have been performed, with either a single cloud or a complete cumulus cloud field.

Single Cloud
A single cloud, induced by a heat bubble is investigated to study the effects of thermal radiation on individual clouds.We compare the effects of a simulation without radiation (No-Radiation) to simulations with 1D independent column approximation interactive (1D Thermal ICA) and simulations with 3D thermal radiation (3D Thermal NCA) using the NCA.For the simulation, the full thermal spectrum was simulated.
As the strength of the radiation effect on cloud development likely depends on the shape and dynamics of a cloud, we choose four different clouds for our investigation.
-A weakly driven, axially symmetric cloud.The heat bubble is introduced by a elliptical shaped volume of warmer air close to the surface.The temperature perturbation is 0.4 K.
-A weakly driven, non-symmetric cloud.The heat bubble is introduced by a uniform random perturbation varying between 0.0 -0.8 K in the same elliptical shaped volume as the weakly driven symmetric cloud, giving the same average perturbation of 0.4 K as above.The cloud is comparable in strength to the weakly driven axially symmetric cloud.
-A stronger driven, axially symmetric cloud.The heat bubble is introduced by a elliptical shaped volume of warmer air close to the surface.The temperature perturbation is 0.8 K.
-A stronger driven, non-symmetric cloud.The heat bubble is introduced by a uniform random perturbation varying between 0.0 -1.6 K in the same elliptical shaped volume as the stronger driven symmetric cloud, giving the same average perturbation of 0.8 K as above.The cloud is comparable in strength to the stronger driven axially symmetric cloud.
A stable background profile was chosen in order to cause only moderate updraft velocities of a few m/s.The simulation is performed over 80 min.More setup details are summarized in Tab. 1.The random noise in the non-symmetric cloud simulations was initialized with the same random seed in all simulations in order to simulate clouds of similar shape which allows a direct comparison of the development of the clouds.The simulations are performed with 50 m horizontal and vertical resolution in a 6.4 x 6.4 km 2 domain.

Cumulus Cloud Field
Large scale simulations of a cumulus cloud field in a 50x50 km 2 domain with 50 m horizontal resolution have been performed.
The environment was a warm ocean surface without orography.All simulations are run for 30 hours at Deutsches Klima Rechenzentrum (DKRZ) in Hamburg on Mistral supercomputer (Intel-Haswell) on 512 cores.We focused on the effects of thermal radiative heating and cooling at the clouds itself.Therefore, surface fluxes of latent (180 W/m 2 ) and sensible heat (18 W/m 2 ) were fixed throughout the simulation.The initial atmospheric profiles for this simulations were taken from Stevens (2007).We allow for warm microphysics (Seifert and Beheng, 2001), but omit the development of rain to reduce possible feedbacks that rain might cause (e.g.cold pool dynamics).Due to the high computational costs of radiation simulations, we used the Monte Carlo Spectral Integration (MCSI, Pincus and Stevens (2009)) in a version adapted for 3D interactive radiation described in Jakub and Mayer (2015).Further details are given in Tab. 2.
Again, we compare different radiation types (1D Thermal ICA and 3D Thermal NCA).Those are the interactive radiation applications, where heating and cooling acts locally where it is generated.In addition, we averaged the thermal heating and cooling of the 1D Thermal ICA and 3D Thermal NCA radiation solution in each time step in each layer (1D Thermal AVG and 3D Thermal AVG).This allows us to separate the effects of local heating/cooling in comparison to a systematically higher cooling that is introduced by thermal radiation.In addition we can separate possible feedbacks that might arise from the different amount of cooling introduced by the 1D and 3D radiative transfer solutions.The overall cooling in a modeling domain is generally stronger in case of 3D thermal NCA radiation.Additionally, we apply a constant cooling of 2.6 K/d throughout the simulation in the modeling domain.The constant cooling differs from the averaged radiation simulations in the profile of the cooling.The averaged radiation simulations cause more cooling in the cloudy layers.
All simulations are analyzed after a 3h initialization run, where the first clouds are allowed to form.

Cb-TRAM Cloud Tracking Algorithm
To gain some statistics on the cloud size, lifetime and number of clouds in the simulations, we use a cloud tracking algorithm to track individual clouds over time.Cb-TRAM was originally setup to work with satellite imagery by (Zinner et al., 2008), but is easily adapted to any other map of 2D information.Here fields of liquid water path are tracked.Cb-TRAM identifies objects as contiguous areas with a specific common characteristic.We set two thresholds to define a cloud: first, only cloud columns of a liquid water path larger then 20 g/m 2 are considered; second, a cloud must consist at least of 16 grid connected boxes.
Objects defined this way at one time step are found in the water path field of the next time step using an optical flow analysis of the liquid water field deformation and a simple object overlap analysis.This way cloud objects are detected and tracked over time, allowing us to estimate cloud size and lifetime distributions. the surface, which we ignore in our analysis.Also, cooling rates are sampled and averaged over grid boxes belonging to this single cloud, to show heating and cooling generated by the cloud.A running average over 300 s was applied to the averages in order to smooth the results.A gray shaded area covers the first 40 min of the simulations in Fig. 3 and Fig. 4.During this time, the cloud development is dominated by the heat perturbation of the warm bubble.Updraft vertical velocities are strong in this initial stage.We only expect an significant effect of thermal radiation on cloud development after that initial stage.Interestingly, 40 min is about the time it takes for the thermal cooling to compensate the original heat perturbation of the bubble (not shown).

Single Cloud Simulations
Both, the symmetric and non-symmetric clouds show the impact of thermal radiation on the cloud development.Focusing on the liquid water path (top row of Fig. 3) we can split the cloud development into three stages.Both cloud types show a fast development at the beginning (up to about 20 min, gray shaded area, until first gray line).We refer to this first development of the cloud as the "first stage".During that time, the development is dominated by the heat perturbation at the surface.Both liquid water quantities develop similarly in all simulations, with only little differences due to thermal radiation.
After the first stage, liquid water path decreases and finally, from about 30 min onward the cloud stays rather constant at a certain height (not shown).Updrafts become weaker (top row of Fig. 4) and radiation acts more significantly on the cloud.
All simulations show that the liquid water path (top row of Fig. 3) is reduced by thermal radiation in this "second stage" (from about 20 min to 40 min).The "last stage" of cloud development (about 40 min to 80 min) is dominated by a second growth-period of the cloud.In this stage, thermal radiation can act on the cloud.From this time on, the initial heat perturbation is compensated by thermal cooling.Both non-symmetric clouds show a second rise in liquid water path, in case of the stronger forced cloud exceeding the No-Radiation simulation.Interestingly, when comparing the development of liquid water path to the development of maximum liquid water mixing ratio over time (lower row of Fig. 3) the rise in liquid water mixing ratio in the last phase becomes more evident.Maximum values of liquid water mixing ratio in the radiation simulations exceed the No-Radiation simulation in this last phase.Looking at the location of these maximum values of liquid water mixing ratio and the shape of the cloud (not shown), we find that clouds become narrower (have a reduced horizontal extent) over time when radiative effects are accounted for and maxima of liquid water mixing ratio are enhanced in the center of the cloud.Vertical velocities show stronger upward and downward values for both thermal radiation simulations.The upward and downward motion at this time results from the initial temperature perturbation and the resulting overturning circulation.
Looking at the differences between 1D Thermal ICA and 3D Thermal NCA we find stronger cooling in the 3D Thermal NCA radiation simulation which affect the further development of the cloud (bottom row of Fig. 4).Differences occur in terms of liquid water when comparing both thermal radiation simulations.The differences are small though, but in general slightly stronger in the case of 3D Thermal NCA simulation.In the last stage, differences in vertical velocity between the No-Radiation and the thermal radiation simulations are evident.Both radiation simulations show stronger upward and downward vertical velocities.Vertical velocities are usually a bit stronger in case of 3D Thermal NCA radiation than in case of 1D thermal radiation.The region of subsiding motion around a cloud, the "subsiding shell" is known from previous work of Heus and Jonker (2008); Jiang et al. (2006); Small et al. (2009).Heus and Jonker (2008) studied the subsiding shell of cumulus clouds from measurement data in comparison to model simulations and concluded that negative buoyancy at the cloud sides causes the subsiding shell to develop.Jiang et al. (2006) and Small et al. (2009) again compared measurement data and simulations.They found a stronger subsiding shell due to more cloud condensation nuclei and enhanced evaporative cooling in their study.Stronger downward motion at cloud sides was also found by Guan et al. (1995) and Guan et al. (1997) due to the effect of thermal radiation.

Combining the development of liquid water with upward and downward vertical velocities (top and middle row of
We found that thermal radiation has an effect on the cloud development from the end of the second stage on, when the cloud stays at a constant height and the initial temperature perturbation is compensated by thermal cooling.To further investigate this question and the development of the cloud, with a special focus on the possible change in cloud circulation and the subsiding shell, Fig. 5 shows transects of liquid water (bottom of each figure) and vertical velocity (center of each figure) in the last stage of cloud development, averaged in 900-1200 m height (in the cloud layer).
In the time series analysis, the cloud development is accompanied by stronger updrafts and stronger downdrafts in the radiation simulations.Fig. 5 shows the stronger upward and downward motion in the transect.The subsiding shells are clearly visible at the cloud side region.Liquid water content is enhanced in the radiation simulations in the cloud center and the cloud is narrower (Fig. 5).This is in agreement with the results of the time development of liquid water path and maximum liquid water (Fig. 3) that indicated narrower clouds with enhanced liquid water content in the cloud center.Stronger downdrafts are found for all radiation simulations.Again, clouds simulated with the radiative feedback are narrower.
Finally, Fig. 6 shows the horizontally averaged vertical profile of negative and positive buoyancy, sampled in the cloudy region (all grid boxes where liquid water is larger than zero).Data is sampled for 8 min, starting after 50 min of the simulation.All simulations including thermal radiation show stronger negative buoyancy which is slightly larger in the 3D Thermal NCA is slightly larger than in the 1D case.This might be due to the thermal cooling at cloud tops, and in case of 3D Thermal NCA radiation at cloud sides.The negative buoyancy can cause the observed subsiding motion, as already found by Heus and Jonker (2008) and Small et al. (2009).The stronger horizontal buoyancy gradient (difference between positive and negative buoyancy in Fig 6 ) generates enhanced turbulence and therefore stronger evaporation.This explains the narrowing of the clouds in the horizontal.

Cumulus Cloud Field Model Experiments
In this section, we explore the effects of thermal radiation on the development of cumulus clouds in the 50 x 50 km 2 domain.to differentiate afterwards.Maximum liquid water mixing ratio exceeds 2 g/kg after 20 hours.In a rain permitting simulation rain would likely form at that time.We ran the simulations for 30 hours, to see what would theoretically happen to the clouds, but as we are aware that the simulations become more and more unrealistic from 20 hours on, our main analysis will be on the time interval between restart and 20 hours.After 20 hours, a strong increase in cloud fraction in all radiation simulations is found.This increase is particularly strong for the two averaged radiation simulations.Looking at the maximum liquid water mixing ratio (and the liquid water path, not shown) an oscillatory behavior of liquid water is found, indicating strong formation of clouds and their decay.To study whether the observed differences are simply caused by the systematic bias introduced by 1D or 3D radiation, or if the local effects are relevant, we compare the averaged and interactive thermal radiation simulations.Although the averaged amount of cooling per domain is (in the beginning of the simulation) the same for both 1D Thermal ICA and 1D Thermal AVG (or 3D Thermal NCA and 3D Thermal AVG) simulations, the averaged radiation simulations produce higher cloud cover than their corresponding 1D or 3D interactive radiation simulation.Interestingly, liquid water path and maximum liquid water content is lower for the averaged radiation simulations until 20 hours.The development of all quantities shown here can be related to the location where thermal radiation acts.In the interactive radiation simulations, cooling (and some warming at the cloud bottom) acts directly at the cloud edges.Cooling rates can locally be up to several hundred K/d and can destabilize the cloud layer, thus promoting updrafts, more condensation and an increase in cloud height.For the averaged radiation simulations, cooling occurs in the cloud layers, but as it is averaged and applied everywhere in a layer, independent of the location of the clouds, a destabilization occurs in the whole area, which is however weaker than the local destabilization of the interactive radiation simulations.Finally, in the constant cooling simulation, the cooling is distributed equally over all heights, cooling in the cloud layer is thus smaller compared to the simulations with radiation which explains the lower liquid water path.This explains the lower values of liquid water.Cooling in the cloud layer, where condensation occurs is reduced in this case.
For both averaged radiation simulations, a sudden and strong increase (and decrease) in cloud fraction (and liquid water path, not shown) is found from 22 hours on.This might indicate stronger organization of clouds in the averaged radiation simulations after 22 hours of simulations time.However, as stated before, prohibiting the formation of rain leads to unrealistic values of liquid water in this idealized setup of our simulations after 20 hours.

Boundary Layer and Cloud Layer Development
We investigate the development of the boundary layer and cloud layer by examining the profiles of different quantities at three time periods of the simulation.Starting with the initial profile at the restart time (3 hours), we show in addition the averaged profile from 9-11 hours (noted as 10 hours) and from 19-21 hours (noted as 20 hours).
The initial profiles at 3 hours (Fig. 10  The first clouds appear shortly after the restart in all simulations.From this time on, thermal radiation (that is cloud top cooling and cloud bottom warming, and in the case of 3D Thermal NCA cloud side cooling) changes the development of the boundary layer and of the clouds themselves.Due to the imposed constant surface fluxes of latent and sensible heat, the atmosphere warms over time.When thermal radiation is applied in the simulations, this warming is partially compensated by thermal cooling.At 10 hours, the whole atmosphere is about about 1 K cooler in the thermal radiation simulations (see Fig. 10) which in turn leads to a higher relative humidity and more condensation of water vapor.The increase in liquid water over time was already shown in Fig. 9. Here, in addition to the increased liquid water (which is strongest for the 3D Thermal NCA radiation case at 10 hours) a deepening of the cloud layer occurs in the simulations including thermal radiation.Thermal cooling at the cloud boundary (interactive radiation simulations) and in the cloud layer (averaged radiation simulations) cause more condensation.The constant cooling simulations produces less water, because the cooling is not directly produced by the clouds but imposed in the simulation setup in the whole atmosphere.Therefore, less cooling is found in the cloud layer compared to the other radiation simulations.The difference in the temperature profiles between the No-Radiation and the radiation simulations increases (up to 3 K), which again, leads to an increase in relative humidity in the sub-cloud layer and more condensation.We note here that in the cloud layer, the relative humidity decreases in the interactive radiation simulations.The production of TKE through buoyancy is shifted upward into the cloud layer and upward velocities increase in the cloud layer, which becomes deeper (see the deepening of liquid water profile, Fig. 10).While at the beginning of the simulation, the 3D Thermal NCA simulations produced the largest amount of liquid water, the averaged radiation simulations produce the largest amount at the end of the simulation.The development of liquid water, relative humidity and the TKE production by buoyancy and the development of vertical velocities suggest that more mixing/entrainment of dry air from aloft the cloud layer occurs in the interactive radiation simulations.
We summarize therefore that 1D Thermal and 3D Thermal heating and cooling at clouds destabilizes the cloud layer, promoting the development of strong updraft cores and the transport of water vapor into the cloud layer.In addition, the cooling of the atmosphere leads to enhanced condensation.Mixing in the cloud layer is stronger.In addition to the stronger updraft velocities, downdrafts increase as well.
The local cooling at the cloud boundary itself in the interactive radiation simulations (in comparison to the averaged radiation effect), increases the earlier described development by destabilizing the cloud layer locally at the clouds stronger than in the averaged radiation simulations.Entrainment is stronger in the interactive radiation simulations, causing less condensation and lower relative humidity.The simulation with constant cooling usually shows the weakest effect of all radiation simulations.We hypothesize that thermal radiation, and in the interactive case, localized thermal heating and cooling (as was already shown for the single cloud simulation) leads to stronger development of the cloud circulation in terms of updrafts and subsiding shells.
3D Thermal NCA radiation, in comparison to 1D thermal radiation increases these shown effects by an additional cloud side cooling and overall stronger cooling in the modeling domain.

Cloud Development
The preceding section (Sec.3.2.1)analyzed the effects of thermal radiation on the development of the cloud-topped boundary layer.In this section, we further investigate the effects of thermal radiation on cloud development.It was shown before that the cloud circulation changes due to the effects of thermal radiation, promoting updrafts and subsiding shells, a deepening of the clouds, and depending on the radiation type, increases liquid water within the clouds.Another hypothesis raised earlier is the possible organization of clouds (see beginning of Sec.3.2) due to thermal radiation.In addition, thermal radiation may alter cloud lifetime.In the following we will address these possible changes.For the cloud field simulations, we used the octant analysis described by Park et al. (2016) to extract updrafts and subsiding shells from our simulations.By the signs of flux perturbations, eight parts (octants) are derived from the spatial field of three variables (vertical velocity and two passive scalars).Those octants include updrafts and subsiding shells.The analysis is restricted to cloudy layers (layers, where liquid water mixing ratio is larger than 0.1 g/kg).Figure 12 shows the averaged and maximum updraft and downdraft velocities over time.Updrafts are stronger in all thermal radiation simulations, compared to the No-Radiation case.The updraft velocities of the interactive radiation simulation are slightly stronger than the updrafts in the averaged radiation simulations.The interactive radiation simulations produce stronger subsiding shells, noted in the averaged as well as maximum values.Updrafts and downdrafts in the 3D radiation cases are in general slightly stronger than their 1D counterparts.Therefore an overall stronger circulation, induced by local heating and cooling is found.These results agree with the increase in buoyancy production, the development of relative humidity and upward vertical velocity as shown in Sec.3.2.1.In terms of updrafts and subsiding shells we find the constant cooling simulations produces similar results as the averaged radiation simulations.

Cloud Organization
Apart from the changes in the cloud circulation, clouds organize differently.Cloud cover and liquid water developed differently for the individual simulations.The horizontally averaged radiation simulations showed a larger cloud cover over time than the interactive radiation simulations.
To investigate how the cloud structures change over time, we calculated the temporal variation in the autocorrelation length (defined by the shift where the correlation coefficient drops below 1/e) from the liquid water path of the cloud field (Fig. 13).
Autocorrelation is a measure for the size of the clouds.At about 9 hours, the simulations start to develop differently.Both In the No-Radiation simulation, no organization occurs.Clouds remain small with little liquid water content throughout the simulation.This is different if thermal radiation is accounted for.If we compare the five different radiation simulations, one notices that both interactive radiation simulations and both horizontally averaged radiation simulations as well as the constant cooling simulation show a similar behavior.
Larger structures with more liquid water content form much earlier in the simulations with interactive thermal radiation.
Patches of dry and wet regions form (blue till red vs. white areas) and the cloud patterns in the interactive radiation simulations contain more liquid water and show larger structures.The simulations with the horizontally averaged radiation also show growing structures but they contain less liquid water and are smaller during the shown simulation time.Also, no significant differences exists between the 1D and 3D averaged radiation simulations (which was also evident in Fig. 13).Comparing the 1D and 3D interactive thermal radiation simulations, we find larger structures earlier in the 3D Thermal NCA radiation simulation.Also, clouds in the interactive radiation simulations contain more liquid water.The fiber-like structures of the hovmoeller diagrams usually give a hint on the movement of the clouds.Here, however, the structures show that clouds move very little during their lifetime and mostly remain at one location, as our simulation is performed without any background mean wind.
We can therefore summarize the following findings: Interactive thermal radiation enhances cloud organization in our simulations in the first 20 hours.
For a matter of completeness, it shall be mentioned that strong organization occurs after 24 hours in the averaged radiation simulations, exceeding the cloud organization in the interactive radiation simulations.

Cloud Lifetime
Radiation may, in addition to the previously shown changes, alter the cloud's lifetime and size.Figure 15 shows a probability density function (pdf) of cloud lifetime.Each cloud occurring within the first 20 hours of our simulations was tracked and the lifetime was calculated.Interactive thermal radiation leads to less clouds with a small lifetime, but more clouds with a larger lifetime.This result agrees with our previous findings: Enhanced turbulence and mixing in the interactive radiation simulations can lead to a faster decay of small clouds, while larger clouds might live longer and grow due to the enhanced cloud circulation (stronger updrafts and downdrafts).The averaged radiation simulations show more clouds with a longer lifetime than the No-Radiation and the const.cooling case.
Figure 16 shows the pdf compared to simulation time and the cloud size.Many small clouds occur at the beginning of the simulations.In the interactive radiation simulations, these small clouds become fewer over time and more larger clouds occur, while in all other simulations, these small clouds occur throughout the whole simulation.Clouds larger than 1 10 3 km 2 occur in the interactive radiation simulations, but hardly any in the No-Radiation and the const.cooling case.

Dependence of the Results on Resolution and Reproducibility
One important issue of our simulations is the robustness of the results and the dependence on resolution.We therefore repeated the calculation with a resolution of 100 m instead of 50 m and performed three runs for the computationally cheaper 100 m resolution.Although small differences are found in the statistical analysis of profiles and time series of the different variables the organization effect remains.Figures.17 and 18 show the hovmoeller diagrams and autocorrelation length, this time calculated from the 100 m resolution simulations.Again clouds start organizing earlier if interactive radiation, especially the 3D interactive radiation is accounted for.The separation into moist and dry regions is stronger in the simulation with a coarser resolution.The clouds of the interactive radiation simulations also contain more liquid water, similar to the 50 m resolution simulations.The effects of 3D Thermal radiation is even larger than in the 50 m resolution case.Due to the reduced resolution, this simulation is computationally less expensive and we repeated it two times.Although small differences occur (one reason being for example the randomly chosen spectral bands in the MCSI), the effects (e.g.stronger organization or the more locally focused liquid water in the 3D interactive radiation radiation case) remain the same.

Conclusions
We found that thermal radiation affects cloud development.This was first investigated for idealized single clouds induced by a heat bubble perturbation close to the surface as well as for idealized simulations of cumulus cloud fields.Thermal radiation changes the cloud circulation which includes stronger updraft vertical velocities and stronger subsiding shells around the clouds.Overall, we find an increased mixing and entrainment in the simulations with radiation.Both, the mixing and the resulting vertical velocities are due to a destabilization of the atmosphere which results from thermal cooling.
The change in the overall dynamics causes clouds to organize.Clouds also become deeper in vertical extent and contain more liquid water if thermal radiation is accounted for.
One important objective of our simulations was to investigate the effect of 3D interactive thermal radiation.Therefore, we performed four different thermal radiation simulations.We separate between 1D and 3D thermal radiation as well as between interactive and averaged radiation.We find that the effects described above are always stronger if 3D thermal radiation is applied, compared to 1D thermal radiation.Differences in the overall development of the cloud field are evident between the interactive and averaged radiation application.The most pronounced difference between the interactive and averaged radiation simulations is the development of cloud organization.Organization starts earlier if interactive radiation is applied.If the simulations are run beyond 20 hours larger cloud structures form in the simulations with averaged radiation, exceeding the cloud sizes in the interactive radiation simulations.
The main difference between the averaged and the interactive radiation is the location and the strength of the thermal cooling.
In the case of interactive radiation, the cooling (or heating) acts locally at the cloud sides, tops and bottom.Cooling rates can be as large as several 100 K/d.This causes a local destabilizing.This is supported by stronger updrafts and downdrafts for the interactive radiation simulations.In case of the averaged radiation, the resulting cooling is weaker but acts in the entire Atmos.Chem.Phys. Discuss., doi:10.5194/acp-2016-896, 2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 11 November 2016 c Author(s) 2016.CC-BY 3.0 License.modeling domain and the cooling does not distinguish between cloudy and cloudless regions.It therefore takes longer for the averaged radiation to destabilize the atmosphere.However, when a certain destabilization is reached , it causes a rapid cloud development in the entire domain at once (like in our simulations after 20 hours).This might explain why cloud organization starts earlier in the case of interactive radiation, but that cloud organization are eventually larger for the averaged radiation case, if the simulation is run long enough.Fig. 19 summarizes our findings.The main findings of our study are reproducible at coarser horizontal resolution and with perturbed initial conditions.
Obviously, the simulations shown in this study are in an idealized framework to omit feedback mechanisms which would occur otherwise.The fixed surface fluxes omit the surface flux feedback which was found e.g. by Muller and Held (2012) who proposed that this could be a reason for the organization of clouds.Another feedback mechanism which we neglect is the effect of rain and possible cold pool dynamics.Cold pool dynamics are usually associated with cloud organization (e.g.Seifert and Heus (2013)).This cannot be the cause for the cloud organization which we find in our simulations and with our setup we isolated the radiation effects.However, it is obvious that the clouds produced in our simulations are deep enough to cause rain from about 20 hours on, if we would allow it.If we would account for rain effects, the whole system would possibly change.
Rain would set in earlier in all thermal radiation simulations (compared to the No-Radiation case), and most likely earlier in the interactive radiation simulations.We rerun the 1D ICA interactive radiation simulations, allowing for rain, and found rain to occur after 22 hours.In a more realistic framework (e.g.simulations allowing for rain or surface interaction), it is not certain that we would ever reach the stage where clouds organize in the averaged radiation simulations, but we may reach the stage in the interactive ones.Furthermore, in a more realistic setup, one would have to account for solar radiative effects as well, not only for thermal radiative effects.
Previous studies (Emanuel et al. (2014), Muller and Held (2012), Muller and Bony (2015)) used RCE experiments and found thermal radiation to be a key driver for cloud organization.Our simulations are for a much smaller domain, with higher spatial resolution, and without deep convection.Yet, we also find that thermal radiation is a driver for organization.Also, our simulations show that it might be essential how radiative transfer is applied.The effects of interactive and averaged application of radiation differs significantly.In addition 3D, interactive radiation and the thus additional local cooling at cloud sides changes the cloud development stronger than 1D interactive radiation (e.g.downdrafts or organization).The differences between a 1D and 3D averaged radiation application is, in contrast to the differences between 1D and 3D interactive radiation simulations, small.

Figure 2
Figure 2 provides a first impression of the four different single cloud simulation.The visualization shows the weak symmetric, weak non-symmetric, strong symmetric and strong non-symmetric single cloud simulations at 20 min for the No-Radiation simulation.The following section provides a detailed analysis of the development of these single clouds for different radiation setups.A comparison of the time development of liquid water, vertical velocity and cooling rates is shown in Fig. 3 and Fig. 4. Liquid water path is sampled for the original cloud only (conditionally sampled).During the simulations, new clouds form close to Fig. 4), the data suggests that a change in cloud circulation is induced from the second stage onward by the effects of thermal radiation, which enhances updraft vertical velocities in the cloud cores, thus strengthening the cloud development and at the same time, Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-896,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 11 November 2016 c Author(s) 2016.CC-BY 3.0 License.induces stronger downdraft vertical velocities at the cloud sides.

Figure 7
Figure 7 provides a first impression of the cumulus cloud field, for three of the six performed simulations.The figure shows a time snapshot at 20 hours of the simulations.The different development of the cloud fields are subject of this section.

Figure 8
Figure8shows the temporal development of cloud fraction and maximum liquid water mixing ratio from the restart time until 30 hours.In addition to the 3D and 1D Thermal radiation cases, the averaged and fixed radiation scenarios are shown.In the

Figure 9
Figure 9 shows the temporal development of liquid water path, maximum vertical velocity and cloud base and top height until 20 hours.Liquid water path increases with time in all simulations.The increase is more pronounced in the case of 3D Thermal NCA.Each of the interactive thermal radiation simulations produces more liquid water than its averaged counterpart.Liquid water path increases less in the simulation with constant cooling.The maximum vertical velocities are weaker in the No-Radiation simulation and cloud extend is smaller with a heightened cloud base and lower cloud tops.All quantities increase over time.The different development of the No-Radiation simulation and the radiation simulations is related to the missing cooling of the thermal radiation in the No-Radiation simulation.Therefore, less water condenses, reducing the number of clouds, cloud cover and a liquid water path.The higher cloud base is also a result of the missing cooling.The smaller increase in cloud top height might be linked to reduced updraft velocities and missing destabilization in the No-Radiation simulation (see Section 3.2.1).
and Fig. 11, first row) show the typical profiles of a boundary layer over a warm ocean surface.No clouds have developed yet at this stage.The profile of liquid water potential temperature shows a well mixed layer (up to 400 m), the conditionally unstable layer (up to 1200 m) as well as the inversion layer at about 1100 m height.Relative humidity increases with height at first, before decreasing from 400 m height to the inversion, indicating the entrainment of dry air from aloft the inversion.Typical for the boundary layer over a warm ocean, turbulence is produced by buoyancy in the layer close to the warm ocean (rising thermals).The upward motion of this low layer can also be seen in the updraft velocity in the lower layer until 400 m height (Fig. 11, middle).
The cooling at cloud tops (and cloud sides in the 3D radiation case) as well as the bottom warming leads to a destabilization of the cloud layer, promoting the development of clouds by increased buoyancy (Figure11(second column)).Turbulence that is initially only produced through surface flux induced buoyancy tendencies is now additionally produced in the cloud layer, again Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-896,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 11 November 2016 c Author(s) 2016.CC-BY 3.0 License.peaking for the 3D Thermal NCA simulation.Due to the increased buoyancy in the radiation simulations, upward velocities in the clouds are stronger (second column of Fig. 11, middle).Furthermore, all radiation simulations produce stronger downdraft vertical velocities in the subsiding shells, especially the interactive radiation simulations (Fig. 11, bottom).
Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-896,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 11 November 2016 c Author(s) 2016.CC-BY 3.0 License.Results from the single cloud simulation and the statistical analysis of the cloud field simulations suggest that a change in the cloud circulation occurs, promoted by thermal radiative heating and cooling at the clouds.Stronger updrafts and stronger downdrafts/subsiding shells are expected due to the destabilization of the cloud layer and by thermal cooling of the clouds.Therefore, changes in the cloud circulation are expected to be stronger for the simulations with interactive 1D Thermal ICA and 3D Thermal NCA radiation, compared to the horizontally averaged radiation simulations.All radiation simulations are expected to show stronger circulation features than the No-Radiation simulation.
interactive radiation simulations show an increased correlation length from this time on, indicating stronger organization of the clouds.The largest cloud patches are found for the 3D Thermal NCA simulation.Both averaged radiation simulations simulation behave quite similar and show less organization than the interactive radiation simulations, but slightly more than the No-Radiation simulation.The constant cooling simulation is located between the averaged radiation simulations and the No-Radiation simulation.It shall be mentioned here (although not shown) that from about 24 hours on, strong organization occurs in the averaged radiation simulations and the const cooling simulation, in which the clouds oscillate: disappearing and then reappearing.No systematic difference between 1D and 3D radiation is found in these cases.To further investigate how much water the individual clouds contain and if and how they organize, we show hovmoeller di-Atmos.Chem.Phys.Discuss., doi:10.5194/acp-2016-896,2016 Manuscript under review for journal Atmos.Chem.Phys.Published: 11 November 2016 c Author(s) 2016.CC-BY 3.0 License.agrams (Fig. 14).Liquid water path was averaged in x-direction for these diagrams.They thus provide an overview of the spacial and temporal development of the cloud field.Extended patches of liquid water along the spacial dimensions indicate large clouds.Extended patches along the time axis show long living clouds.In additions, the diagrams show how much water is located in the cloud patches.

sregio 165 "6Figure 1 .
Figure1.Three dimensional heating and cooling rates and surface fluxes in a cumulus cloud field, calculated with the Monte Carlo model MYSTIC(Mayer, 2009;Klinger and Mayer, 2014).

Figure 2 .
Figure 2. Visualization of the four single cloud simulations (first: weak symmetric; second: weak non-symmetric; third: strong symmetric; fourth:strong non-symmetric).The snap shot of the cloud field is taken at 20 min of the simulation of the No-Radiation case.The visualization was performed with the 3D radiative transfer model MYSTIC(Mayer, 2009).The clouds in the background are a feature of the visualization and do not occur in the LES simulation of the single clouds.

Figure 3 .
Figure 3.Time development of conditionally sampled liquid water path and maximum liquid water mixing ratio for the simulations of the single clouds.Only liquid water belonging to the single cloud was considered.The left column shows the weaker forced, the right column the stronger forced single clouds.Solid lines represent the non-symmetric cloud, dashed lines the symmetric cloud.

Figure 4 .
Figure 4. Time development of maximum updraft and downdraft vertical velocity as well as conditionally sampled cooling rates of the single cloud simulations for the simulations of the single clouds.Cooling rates were sample at the single cloud only.The left column shows the weaker forced, the right column the stronger forced single clouds.Solid lines represent the non-symmetric cloud, dashed lines the symmetric cloud.

Figure 5 .
Figure 5. Height and time averaged transects of liquid water mixing ratio (pale color, bottom, right axis) and vertical velocity (middle, left axis).The time average was performed over 3 min at around 60 min simulations time.The vertical average was taken in the middle of the vertical extend of the cloud to cover cloud side areas.Dashed lines show the symmetric cloud, solid lines the non-symmetric cloud.

Figure 6 .
Figure 6.Positive and negative buoyancy profile sampled at 50-58 min of the simulation in the cloudy area.Dashed lines show the symmetric cloud, solid lines the non-symmetric cloud.

Figure 7 .
Figure 7. Visualization of the cumulus cloud field of the constant cooling (top), 3D Thermal Average (middle) and 3D Thermal NCA (bottom) simulations.The snap shot of the cloud field is taken at 20 hours of the simulation.The visualization was performed with the 3D radiative transfer model MYSTIC(Mayer, 2009).

Figure 8 .
Figure 8.Time development of cloud fraction and maximum liquid water mixing ratio from 5 to 30 hours.The two gray lines (at 10 hours and 20 hours) separate the development in different periods for the further analysis.

Figure 9 .
Figure 9.Time development of liquid water path, maximum vertical velocity and cloud base and cloud top height.The gray line (at 10 hours) separates the development in different periods for the further analysis.

Figure 10 .
Figure 10.Time averaged profiles of liquid water potential temperature, liquid water mixing ratio and relative humidity.The profiles are shown at the restart time (3 hours), as an 3 hour averaged around 10 hours and 20 hours of the simulations.

Figure 11 .Figure 13 .
Figure11.Time averaged profiles of buoyancy production of the TKE and updraft and downdraft vertical velocity.The profiles are shown at the restart time (3 hours), as an 3 hour averaged around 10 hours and 20 hours of the simulations.Updraft and downdraft vertical velocities were extracted from the 3D data followingPark et al. (2016)

Figure 15 .
Figure 15.Probability density function of cloud lifetime: The lifetime of each cloud detected by the tracking algorithm was calculated within the first 20 hours of the simulations.

Figure 17 .
Figure 17.Cloud organization in the 100 m resolution simulations shown as hovmoeller diagrams of the liquid water path, averaged in x-direction

Figure 18 .
Figure 18.Temporal development of the correlation length for the 100 m resolution simulation.The correlation length is defined by the shift where the correlation coefficient drops below 1/e.

Figure 19 .
Figure 19.Schematic figure of the effects of thermal radiation in the presented simulations.The figure summarizes cloud development over time and height, showing the enhanced cloud growth, the development of vertical velocity (arrows), a deepening of the cloud layer and the enhanced mixing.Blue and red colors show thermal heating and cooling, either at the clouds itself (for interactive radiation) or averaged in the cloud layer.

Table 2 .
Model input for cumulus simulations.