Shallow Cumulus Cloud Feedback in Large Eddy Simulations Bridging the Gap to Storm Resolving Models

. The response of shallow trade cumulus clouds to global warming is a leading source of uncertainty to interpretations and projections of the Earth’s changing climate. A setup based on the Rain In Cumulus over the Ocean ﬁeld campaign is used to simulate a shallow trade wind cumulus ﬁeld with the Icosahedral Non-hydrostatic Large Eddy Model in a control and a perturbed 4K warmed climate, while degrading horizontal resolution from 100 m to 5 km. As the resolution is coarsened the basic state cloud fraction increases substantially, especially at cloud base, lateral mixing is weaker and cloud tops reach higher. 5 Nevertheless, the overall vertical structure of the cloud layer is surprisingly robust across resolutions. In a warmer climate, cloud cover reduces, alone constituting a positive shortwave cloud feedback: the strength correlates with the amount of basic state cloud fraction, thus is stronger at coarser resolutions. Cloud thickening, resulting from more water vapor availability for condensation in a warmer climate, acts as a compensating feedback, but unlike the cloud cover reduction it is largely resolution independent. Therefore, reﬁning the resolution leads to convergence to a near-zero shallow cumulus feedback. This 10 dependence holds in experiments with enhanced realism including precipitation processes or warming along a moist adiabat instead of uniform warming. Insofar as these ﬁndings carry over to other models, they suggest that storm resolving models may exaggerate the trade wind cumulus cloud feedback.


Introduction
How shallow cumulus clouds respond to global warming has been recognized as a critical source of uncertainty to process-  In this Section we present characteristics of the simulated shallow cumulus regime in the control case and highlight similarities and differences as the resolution is coarsened. This lays out the ground to study in the following how shallow cumulus clouds respond to a perturbed warmer climate and how this depends on horizontal resolution in Sect. 4.

Standard Case
At 100 m resolution a typical trade wind cumuli field is simulated that is in line with the range of LES analyzed in the RICO 90 LES intercomparison case (van Zanten et al., 2011). Total cloud cover is 15 % (Fig. 2) which is slightly lower than the cloud cover of 17 % observed during the RICO field study (Nuijens et al., 2009) and the ensemble mean cloud cover of 19 % in the RICO intercomparison case (range 9 -38 %). The vertical structure is consistent with the general picture of trade wind cumuli cloud layers (Fig. 3). Cloud fraction peaks at cloud base (6 %) near 700 m , then decreases sharply with height, thereafter keeping a value of about 2% through the cumulus layer until 2 km (Fig. 3). Above this height, cloud fraction increases again due to 95 detrainment at cloud top before declining sharply under the trade inversion at around 2.5 km height. Temperature increase and sharp humidity decrease mark the inversion and top of the cloud layer.
At coarser resolutions the overall structure of the boundary and cloud layer is surprisingly similar to the 100 m resolution simulation. The vertical structure of cloud fraction is in all experiments characterized by a dominant peak at cloud base and 100 a second smaller peak near the inversion (Fig. 3). Therefore, at all resolutions cloudiness at cloud base contributes most to total cloud cover. All experiments simulate a well-mixed subcloud layer, a transition layer which is most evident in the moisture gradients, a cloud layer, and an inversion layer into which the clouds penetrate and detrain (Fig. 4). However, at coarser resolutions the transition layer is more pronounced exhibiting a stronger moisture gradient and the inversion height is more distributed in the vertical. These variations translate into the most notable differences between the resolutions.  . Temporal evolution of total cloud cover in ctl at 100 m, 500 m, 1 km, 2.5 km and 5 km resolution (solid lines) and ctl-P at 100 m and 5 km resolution (dotted lines). Ordinates on the right axis display the second day domain averaged total cloud cover for 100m.ctl and 5km.ctl (see Table 2 and 3 for more statistics).
Most importantly, we note that at coarser resolutions cloud cover is substantially enhanced (Fig. 2). At 5 km resolution total cloud cover is more than three times higher than at 100 m (50 vs 15 %). This increase in cloud cover is mostly due to enhanced  shown as contours evenly spaced every 0.5 g kg −1 and cloud fraction is grey shaded.
cloudiness at cloud base and to a smaller extent from an increase in cloud fraction near the inversion (Fig. 3). The ratio between cloudiness at cloud base and total cloud cover rises from 0.4 with the 100 m to 0.6 with the 5 km resolution, that is, cloud base cloud fraction contributes more to total cloud cover in the coarser resolution simulations. Further, at coarser resolutions clouds 110 reach higher (Fig. 3). At 5 km resolution clouds deepen up to an inversion height of about 3.2 km, around 700 m higher than at the finest resolution. Both characteristics can be confidently linked to resolution and not domain size as a sensitivity experiment shows (see Appendix B1).
Larger cloud cover and higher cloud tops at coarser resolutions can be attributed to weaker small-scale mixing. At coarse reso-115 lutions the subcloud layer ventilates less efficiently and the subcloud and cloud base layer are therefore moister and cooler and as a result associated with stronger surface sensible but weaker latent heat fluxes (Table 2). Moister and colder conditions are consistent with weaker cumulus massfluxes and weaker entrainment of warm dry air from aloft. Because conditions are moister and colder in the boundary layer, relative humidity is enhanced and saturation is more likely leading to more widespread cloud formation at coarser resolutions. Hohenegger et al. (2020) found similar characteristics in global simulations with explicit con-120 vection and grid spacings ranging between 2.5 and 80 km.
Additionally, at coarser resolutions small-scale lateral mixing between cumulus clouds and their environment is markedly weaker which explains the higher cloud tops. Figure 5 displays the fractional entrainment and detrainment rates as a measure for lateral mixing intensity diagnosed after Stevens et al. (2001). The entrainment rate at 100 m resolution decreases from 125 2 km −1 near cloud base to 1.2 km −1 in the cloud layer, which is similar to the rates found in the RICO LES intercomparison case (van Zanten et al., 2011). At 500 m resolution the mean entrainment rate in the cloud layer is around 0.8 km −1 , in 5 km around 0.4 km −1 , thus notably weaker. This might be attributed to larger cloud structures that offer less surface area for dilution compared to smaller cloud structures that are resolved at finer resolutions. Because they dilute less, clouds retain more buoyancy and reach higher at coarser resolutions.

Precipitating Case
Trade wind cumulus clouds rain frequently as observations show (Nuijens et al., 2009). We activate precipitation processes to test if the identified resolution dependence is robust in simulations with 100 m, 500 m and 1 km horizontal resolution.
We find that including precipitation processes mainly acts to limit cloud layer deepening. Whereas the 100 m resolution 100m.ctl 500m.ctl 5km.ctl 5 km around 350 m lower than in the non-precipitating case (Table 3). In the RICO LES intercomparison case van Zanten et al. (2011) also found that precipitating simulations with 100 m resolution cause an approximate 100 m reduction in the depth of the cloud layer. Precipitation acts to limit cloud layer deepening because it removes moisture available for evaporation near the inversion. The precipitating cloud field is therefore also characterized by less cloud fraction near the inversion (Fig. 3). Furthermore, we find that the precipitating cloud fields exhibit more cloud fraction in the lower parts of the cloud layer as compared to the non-precipitating cloud field (Fig. 3) Tables 2 and 3). However, changes between the non-precipitating to precipitating cloud field are small and additionally similar across resolution. Therefore, the resolution dependencies remain dominant in the precipitating case as in the non-precipitating case: cloud cover is substantially enhanced and clouds are deeper at coarser resolutions.

Cloud response to warming across resolutions
Here, we investigate how the cloud field responds to warming in dependence of resolution. First, the response to a uniform 155 temperature shift in the standard non-precipitating case is discussed and how the resolution dependence of the basic state cloud field affects the cloud field's response to warming. Second, the robustness of our results are investigated by testing whether warming along a moist adiabat or in the precipitating case alters the response across resolution.

Response to uniform warming
At 100 m resolution we find a slight cloud cover reduction as response to uniform warming in line with earlier LES-based 160 studies (Rieck et al., 2012;Blossey et al., 2013;Vogel et al., 2016). Total cloud cover decreases from 15.3% to 14.3% (Table   2). It seems plausible that drying (Fig. 6), that results from mixing due to the stronger vertical gradient in specific humidity within the warmer case, could explain much of this reduction in cloud cover (Bretherton, 2015;Brient and Bony, 2013). It has further been suggested that enhanced surface latent heat fluxes envigorate convection, deepening the cloud layer and leading to further drying by mixing (Stevens, 2007;Rieck et al., 2012). However, as more refined experiments (Sect. 4.2) do not result 165 in substantial deepening, this process appears to be of secondary importance. The cloud cover reduction on its own constitutes a positive shortwave cloud feedback.  Also at coarser resolutions, we find cloud cover reductions as response to uniform warming (Table 2). Across resolutions the cloud layer is drier, cloud cover reduced and cloud tops reach higher (Fig. 7). The magnitude of cloud cover reduction, 170 however, differs: at 100 m resolution total cloud cover reduces by 1% point, whereas at 5 km resolution total cloud cover reduces by roughly 9% points. At coarse resolutions it is distinctly cloud base cloudiness that reduces with warming. This low resolution behavior is in contrast to the results of previous high resolution LES studies and observations which suggest a relatively invariant cloud base fraction (Nuijens et al., 2014;Siebesma et al., 2003), but is a common feature in global climate model simulations (Brient and Bony, 2013;Brient et al., 2015;Vial et al., 2016). We find that the strength of cloud reduction 175 correlates well with the amount of cloud cover in the basic state (Fig. 8). The more clouds are present in the basic state, the more cloudiness reduces in the warmer climate. Hence, because cloud cover increases at coarser resolutions, in particular near cloud base, they show a stronger cloud reduction than at high resolutions. cloud fraction 500m.ctl 500m.unifw 1km.ctl 1km.unifw 2.5km.ctl 2.5km.unifw 5km.ctl 5km.unifw From the reduction in cloud amount, a positive shortwave feedback would be expected, however, the total shortwave feedback 180 at high resolutions is close to zero, e.g. at 100 m with a value of 0.05 Wm −2 K −1 (Fig. 9). This is due to a compensating feedback from cloud thickening. The cloud liquid water path increases at all resolutions with warming ( Fig. 9). Clouds become more reflective contributing a negative shortwave feedback. In contrast to the cloud amount reduction though, cloud thickening is not strongly resolution dependent. An increasing cloud water content with warming is to be expected as more water vapor is available for condensation (Paltridge, 1980); an argument that is not reliant in any meaningful way on resolution. Consequently, 185 the total shortwave feedback shows the same dependence on resolution as the cloud reduction and correlates well with the basic cloud cover, too (Fig. 8). Hence the shortwave cloud feedback is weak or close to zero for high resolution and positive for coarse resolutions.

Sensitivity of response to refined experimental setups
The base case studied above was admittedly simplistic in that there is no precipitation and a vertically uniform warming was 190 applied. Here we explore the effects of these assumptions. The free tropospheric temperature profile in the Tropics is set by the regions of deep convection that are close to a moist adiabat. Therefore, the tropical temperature is expected to warm close to a moist adiabat, leading to more warming aloft than at the surface and has been used in other modelling studies (e.g Blossey et al., 2013;Bretherton et al., 2013). With moist adiabatic warming an increase in dry static stability is introduced: the initial lower tropospheric stability (LT S = θ 700 − θ 0 ) increases from 13.1 K to 14.4 K, and as a result, with moist adiabatic warming gions change only little. The inversion height in the moist adiabatic warming case varies compared to the control case by only around 50 to 100 m, whereas in the uniform warming case the inversion height increased markedly by around 300 m (Table   2). Therefore, cloud deepening is at all resolutions slightly weaker. Nevertheless, total cloud cover reduction is only slightly dampened. (Fig. 9). Overall the changes are small, though, and therefore, the total shortwave cloud radiative feedbacks is only With precipitation processes activated, the cloud field in a warmer climate responds with a cloud amount reduction across all resolutions, similar to that of the non-precipitating case, though the reductions in total cloud cover are slightly smaller (Tab. 3 vs. Tab. 2). We are aware of two main mechanism that could be contributing to the dampening. First, precipitation 205 has a constraining effect on cloud deepening, noted by Blossey et al. (2013) and Bretherton et al. (2013). At 500 m resolution the boundary layer deepening with warming is half and at 5 km only a third as much as in the non-precipitating simulations. Therefore, especially near the inversion changes in cloud fraction are reduced (Fig. 10). Second, evaporation of precipitation in the lower cloud layer counteracts drying. Vogel et al. (2016) who integrated for a longer time period reported likewise that precipitation reduces deepening and drying with warming. In this way, precipitation is thought to promote the robustness of 210 shallow cumulus clouds to warming. Regardless, though, we find the same dependency on resolution of how shallow cumulus cloud coverage responds to warming as in the non-precipitating simulations.
To summarize, the different experiments all exhibit the same horizontal resolution dependency on the representation and response of shallow cumulus clouds to warming (Fig. 9). The resolution induced differences are larger than those between 215 the different experimental setups. This confirms that horizontal resolution affects the representation and therewith response of shallow cumulus clouds to warming to first oder: the simulated shortwave cloud radiative feedback differs between the resolutions mainly in proportion to the basic state cloud fraction (Fig. 8) and therefore the cloud feedback strength increases at coarse resolutions. Hohenegger et al. (2020) who investigated grid spacings ranging from 2.5 km to 80 km found that cloud cover increases up to 80 km horizontal resolution, which would, provided the results found here carry over also to even coarser resolutions, translate into further increased cloud feedback. At high resolutions, on the contrary, the trade wind cumulus cloud feedback converges to near-zero values.

Conclusions
This study explores the representation and response of shallow trade wind convection to warming and how that depends on horizontal resolution by varying between 100 m and 5 km. Therewith we aim to bridge the gap between findings based on ex-225 isting large eddy resolving simulations and emerging global storm resolving simulations. Based on the RICO case, simulations representative of trade wind conditions are compared to simulations with a 4 K warmed surface and atmosphere at constant humidity, representative of a simple idealized climate change. First, in a basic experiment the representation of shallow trade wind cumuli and their response to a uniformly warmed state is explored. Second, the sensitivity to resolution is probed in refined experimental setups by including precipitation processes and warming along a moist adiabat in place of uniform warming.

230
At 100 m resolution a typical trade wind cumuli field is simulated that is in line with observations (Nuijens et al., 2009), and the range of LES analyzed in the RICO intercomparison case (van Zanten et al., 2011). Total cloud cover accounts to 15% in the non-precipitating and 13% in the precipitating case with a prominent peak in all cases near cloud base. At coarser resolutions, cloud cover is substantially enhanced and clouds are deeper; in the most extreme case at 5 km resolution total cloud 235 cover is around 3.5 times more extensive. Cloud cover increases mostly due to enhanced cloudiness at cloud base. Weaker subcloud layer ventilation could explain the enhanced cloudiness and a weaker lateral entrainment rate allows the clouds to reach higher. Nevertheless, the overall structure of the boundary and cloud layer bear surprising similarity across resolutions explored here, suggesting that, although distorted, the same set of processes act in all cases.

240
In response to warming a cloud reduction can be observed consistently across resolutions. However, whereas at 100 m grid spacing the cloud reduction is rather small, at coarse resolutions the reductions are substantially enhanced. A robust dependency between cloud cover amount and its change with warming emerges: the more clouds are present in the control climate, the more cloud cover reduces in a warmer climate. Including precipitation processes mainly acts to limit the cloud layer deepening by causing a net warming of the upper cloud layer and thereby stabilising the lower troposphere. A similar effect is 245 found when the warming is done along a moist adiabat. These more refined setups result in nearly constant cloud top height with warming, questioning the idea that a cloud deepening is critical to a positive cloud cover feedback (Rieck et al., 2012).
Regardless, the resolution dependence pertaining to cloud cover change is practically the same. On the contrary, a negative cloud optical depth feedback arises in all simulations due to an increasing cloud liquid water path. Although the magnitude of this feedback varies, there is no obvious dependence on resolution. This is to be expected since increasing amounts of water 250 vapor available for condensation with warming at constant relative humidity is a fundamental physical fact.
All in all, the compensation between the decreasing cloud cover and increasing cloud water with warming results in our case with convergence towards near-zero trade wind cumulus cloud feedback. Both of these effects appear physically appealing: a stronger vertical gradient in specific humidity results in a lowered relative humidity when mixing is activated, and all 255 other things being equal in a slight reduction of the areal fraction where condensation can occur, whereas more availability of water vapor in the boundary layer results in thicker clouds. Provided the identified resolution-dependence of the cloud cover feedback carries over to other model codes, then it implies that storm resolving models may exaggerate trade wind cumulus cloud feedback. It is also interesting to compare with earlier studies, where LES simulations previously have suggested trade wind cumulus feedback in the range 0.3 and 2.3 Wm −2 K −1 (Bretherton, 2015;Nuijens and Siebesma, 2019), and observa-260 tional studies up until recently likewise 0.3 -1.7 Wm −2 K −1 (Klein et al., 2017). A recent observational study, however, finds a near-zero trade wind cumulus cloud feedback (Myers et al., submitted), which is in line with our results.  Table A1 for details. The free tropospheric lapse rate dθ dz is calculated with where the imposed subsidence w balances a radiative cooling Q R of 2.5 Kday −1 as suggested in the RICO setup. The temperature profile thus follows roughly a moist adiabat in the lower free troposphere. At 17 km, a tropopause of 195 K is included.
The specific humidity profile is calculated from relative humidity following a linear decrease from 20% at 4 km height to 1% at 15 km and 0% at 17 km height.
285 Appendix B: Impact of domain size In order to confidently link the observed differences to characteristics of the resolution and not of the domain size, a simulation at the same horizontal resolution (1 km) is performed on two different domain sizes (50 km and 500 km). The simulations show that differences between the cloud field on the two domains are small (Fig. B1). With larger domain size, clouds are slightly deeper and show a narrower cloud fraction profile; total cloud cover is 1% points less (1 km resolution). On the same domain, 290 the cloud cover would hence be even larger with the coarser resolutions.