PUBLICATIONS. Journal of Advances in Modeling Earth Systems

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1 PUBLICATIONS Journal of Advances in Modeling Earth Systems RESEARCH ARTICLE /2013MS Key Points: LES isolates radiative and thermodynamic positive low cloud feedback mechanisms Thermodynamic cloud thinning due to entrainment liquid-flux adjustment ELF thinning mechanism affects all subtropical Sc-topped cloud regimes Correspondence to: C. S. Bretherton, Citation: Bretherton, C. S., and P. N. Blossey (2014), Low cloud reduction in a greenhouse-warmed climate: Results from Lagrangian LES of a subtropical marine cloudiness transition, J. Adv. Model. Earth Syst., 6, , doi: /2013ms Received 9 JULY 2013 Accepted 2 JAN 2014 Accepted article online 16 JAN 2014 Published online 24 FEB 2014 Low cloud reduction in a greenhouse-warmed climate: Results from Lagrangian LES of a subtropical marine cloudiness transition Christopher S. Bretherton 1 and Peter N. Blossey 1 1 Department of Atmospheric Sciences, University of Washington, Seattle, Washington, USA Abstract Lagrangian large-eddy simulations of a composite stratocumulus to cumulus transition case over the subtropical northeast Pacific Ocean are subject to perturbed forcings that isolate the cloud response to CO 2, to overall tropical warming, and to increased inversion stability over the subtropical subsidence regions. These simulations show that a tropical surface warming of 4 K induces substantial stratocumulus thinning via a thermodynamic mechanism: increased cloud layer humidity flux in a warmer climate induces an entrainment liquid-flux adjustment that dries the stratocumulus cloud layer, whether well mixed or cumulus coupled. A radiative mechanism amplifies this response: increased emissivity of the free troposphere due to increased CO 2 and water vapor reduces radiative driving of turbulence in a stratocumulus-capped boundary layer; a thinner stratocumulus layer accompanies less turbulence. In combination, a 4 K warming and CO 2 quadrupling greatly reduce low cloud and weaken the simulated shortwave cloud radiative effect by over 50%. Large increases in inversion stability in the stratocumulus regions could counter much of this cloudiness reduction. 1. Introduction Low-latitude marine boundary-layer cloud feedbacks remain a key contributor to uncertainty in simulating climate sensitivity with global climate models [Bony and Dufresne, 2005; Soden and Vecchi, 2011; Zelinka et al., 2013]. One reason is that they are maintained by small-scale turbulence unresolved by a climate model grid, on which cloud radiative and latent heating have strong feedbacks, and are highly heterogeneous, making accurate representation of boundary-layer cloud controlling processes challenging. A second reason is that the global radiative effect of boundary-layer clouds is an aggregate over many large-scale circulation regimes, but the dynamic effect of circulation shifts on clouds largely cancel out on global scales [Bony et al., 2004]. Third, the processes controlling the space-time distribution of cloud in the present climate may not be equally dominant for controlling cloud changes in a greenhouse-warmed climate [Bretherton et al., 2013]. With this background, it is useful to develop a process-level understanding of likely mechanisms of lowlatitude marine boundary-layer cloud feedback which can organize our observational analysis and global model parameterization development. Three-dimensional large-eddy simulation (LES) has become an attractive tool for this purpose. LES explicitly simulates the dominant scales of cloud-turbulence interaction, so it does not need a complex and uncertain representation of subgrid turbulence and cloud heterogeneity. With a coarse vertical grid, the grid spacing, the choice of advection scheme and the subgrid turbulent mixing can substantially affect results [Bretherton et al., 1999]. However, for stratocumulus-capped boundary layers, fine vertical grid spacings of 5 10 m bring different LES models into reasonable (factor of two) mutual agreement about the thickness of simulated marine stratocumulus (Sc) cloud layers [Stevens et al., 2005; Blossey et al., 2013]. The simulated characteristics of deeper or aerosol-starved cloud layers that form precipitation can be sensitive to the choice of microphysical parameterization [Ackerman et al., 2009], but this is not a major concern for the cases presented in this paper, for which precipitation is minimal. In recent years, it has become computationally reasonable to run LES of cloud-topped marine boundary layers (CTBLs) with 5 m vertical resolution over domains of 5 10 km horizontal extent for periods of several days. This has encouraged several LES studies of the response of Sc and shallow trade cumulus (Cu) cloud layers to externally specified global-warming relevant perturbations, whose effects on the CTBL may take days to fully realize. Perturbations that have been studied include vertically quasi-uniform warming [e.g., BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 91

2 Blossey et al., 2009; Xu et al., 2010; Rieck et al., 2012; Blossey et al., 2013], an increase in CO 2 concentration [Wyant et al., 2012; Bretherton et al., 2013], a change in capping inversion strength [Sandu and Stevens, 2011], in subsidence [Blossey et al., 2013], horizontal wind speed, and free-tropospheric humidity [Sandu and Stevens, 2011; Bretherton et al., 2013]. Blossey et al. [2013] presented an LES intercomparison study from CGILS (the Cloud Feedback Model Intercomparison Project/Global Atmospheric System Study Intercomparison of Large-eddy and Single Column Models) [Zhang et al., 2012]. They found that different LES models simulate Sc cloud thinning in response to a warming perturbation, but if subsidence is also significantly reduced, some LES models produce more cloud and some less in Sc and Cu-under Sc regimes. Bretherton et al. [2013] considered the response of an LES model to six different perturbations, and used a multimodel mean from a global model intercomparison to estimate their amplitudes in a realistic global warming scenario. They found Sc-reducing factors (warming and CO 2 increase) are partly compensated by Sc-enhancing factors (reduced subsidence and inversion stability increase), and they suggested this compensation of feedbacks helps rationalize the large spread of subtropical GCM cloud responses to global warming. Some of the LES-predicted cloud responses to individual forcing perturbations have been qualitatively corroborated in analyses of satellite observations [Myers and Norris, 2013; Christensen et al., 2013; Qu et al., 2013] and GCM intercomparison studies [e.g., Kamae and Watanabe, 2012]. Except for Sandu and Stevens [2011], these studies all used an Eulerian framework in which control and perturbed horizontal advective forcings are specified. This has the benefit of allowing an LES model to be run for many days into a steady state with robust statistical properties. However, appropriate specification of advective forcings is tricky. Velocity and thermodynamic property gradients across a sharp, strong trade inversion, as well as a downstream inversion deepening, mean the advective forcings should be interactive with the mean inversion height, but it is inobvious how to do this without biasing the simulated inversion to a particular height or including artificial feedbacks in the column energy and moisture budgets. Choices made about Eulerian forcings can strongly affect the simulated cloud-topped boundary-layer response to a climate perturbation [Bretherton et al., 2013]. Sandu and Stevens [2011] used a composite Lagrangian transition case to assess the CTBL response to a free-tropospheric humidity perturbation. In this approach, a time-varying sea-surface temperature (SST), representative of the surface conditions under a CTBL air column advecting in the low-level trade wind flow, is used instead of specifying horizontal advective forcings. This has strengths and weaknesses complementary to the Eulerian approach. The Lagrangian approach does not require uncertain horizontal advective forcings in the CTBL. It can smoothly sweep across cloud regimes from Sc to Cu, allowing the representativeness of particular Eulerian cases to be assessed. A drawback is that the assumed initial CTBL thermodynamic profile and especially the initial inversion height can affect the entire length of a Lagrangian simulation of a few days. In this study, we use the Lagrangian framework of Sandu and Stevens [2011] to investigate the CTBL response in a Sc-Cu transition to climate perturbations similar to those considered in the Eulerian CGILS studies of Bretherton et al. [2013] and Blossey et al. [2013], with a focus on CO 2 increases, warming of SST and quasi-uniform warming of the whole atmospheric profile with constant relative humidity, and extra warming of the free troposphere, as these appear from CGILS to be particularly important. If the cloud responses simulated in the Lagrangian and Eulerian approaches are comparable, that would increase our confidence in conclusions drawn from either approach. We also analyze the thermodynamic mechanism whereby Sc cloud thins in our Lagrangian simulations when the entire atmospheric profile is warmed, even if the radiative driving and inversion strength and depth (and hence entrainment rate) are unchanged; our novel explanation is based on a concept we call entrainment liquid-flux adjustment of the cloud layer, which encompasses a positive cloud feedback mechanism for Sc-capped mixed layers discussed by Bretherton et al. [2013] and is related to a surface-flux desiccation feedback hypothesized by Rieck et al. [2012] to reduce trade cumulus cloud cover in a warmer climate. 2. Simulated Cases The control case follows Sandu and Stevens [2011]. It uses a fixed reference latitude and longitude of 25 N, 125 W and a calendar date of 15 July. As explained further in the Appendix, we made a slight modification to their time-independent specification of mean vertical motion. Our goal was to more closely balance the BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 92

3 lower free tropospheric ( hpa mean) radiative cooling and subsidence warming across a range of climate perturbations, and to better match the observed summertimemean subsidence rate at the trade inversion along the composite trajectory in the current climate. Our control time-varying subsidence profile, specified in the Appendix, is shown in Figure 1. Unlike locations nearer to the California coast, the mean subsidence is quite weak, allowing rapid deepening of the cloud layer. The small differences between our subsidence Figure 1. Time-varying subsidence profile for the control simulation. specification and that of Sandu and Stevens [2011] induce changes of less than 100 m in the LES inversion height evolution for the control climate and similarly small changes in simulated cloud properties, but are important for simulating the climate perturbations, for which a constant-subsidence assumption leads to undesirable perturbation-dependent imbalances between free-tropospheric subsidence and radiative cooling. The control case (CTL) is perturbed with four different climate perturbations given in Table 1. For simplicity, all perturbations use the same geostrophic wind profile and free-tropospheric relative humidity profile. The time series of SST for CTL and the four perturbed cases are shown in Figure 2. Figures 3a and 3b show their initial profiles of the moist-conserved variables, liquid static energy s l 5c p T1gz2Lq l (rescaled to temperature units) and total water mixing ratio q t 5q v 1q l. Here c p is the specific heat of dry air at constant pressure p, T is temperature, g is gravity, z is height, L is the latent heat of vaporization, q v is vapor mixing ratio, and q l is cloud liquid water mixing ratio. Figure 3c shows the initial profile of the generalized relative humidity, R5q t =q s ðp; T l Þ; (1) where q s ðp; TÞ is the saturation mixing ratio and T l 5T2Lq l =c p is liquid water temperature. R reduces to the conventional relative humidity for an unsaturated state and is easily expressed in terms of our moistconserved variables. For a saturated state R1 (extending from 650 to 900 m in Figure 3c) and the liquid water content is proportional to R21, as detailed further in equation (12). The initial CTL profile has a maximum R near 1.2 and a corresponding maximum liquid water content of 0.8 g kg 21. The first perturbation, 4CO2, is a quadrupling of CO 2 without any change to SST or initial free-tropospheric temperature profile. The mean subsidence is reduced by approximately 10% to compensate for the lessened free-tropospheric radiative cooling (see equation (A3) for the exact subsidence for all simulated cases). The second perturbation, P4, is a 4 K increase in SST along the entire trajectory. The free-tropospheric temperature is also increased following a moist adiabat corresponding to a 4 K surface temperature increase over the tropical oceanic warm pool regions. The mean subsidence is again reduced by 10% compared to CTL to compensate for the lessened free-tropospheric radiative cooling. The third perturbation, P4CO2, is a linear superposition of the first two. Estimated inversion strength [Wood and Bretherton, 2006] is a bulk measure of inversion stability, computed in this paper as EIS 5hð700 hpa Þ2hðp 0 Þ2C p ð850 hpa Þ½700 hpa 2p LCL Š: (2) Table 1. Simulations Performed Case Types Description a CTL D, U, A b Intermediate case of Sandu and Stevens [2011] 4CO2 D, U, A Quadrupled CO 2, subsidence reduced 10% P4 D, U, A CTL with 4 K local and ITCZ SST increase, subsidence reduced 10% P4CO2 D Combination of P4 and 4CO2 EIS D CTL with 4 K ITCZ SST increase, subsidence reduced 10%, local SST increase starting at 2 K a All simulations have the same free-tropospheric relative humidity profile and geostrophic wind speed. b DorU5 diurnally varying or uniform insolation. A 5 U but with different advection scheme. BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 93

4 Here h denotes potential temperature, p 0 is surface pressure, p LCL is the mean lifting condensation pressure of near-surface air, and C p < 0 is the derivative of potential temperature with respect to pressure on a saturated moist pseudoadiabat through the ambient 850 hpa temperature. This stratification correction accounts for the approximately moist-adiabatic change in freetropospheric stratification expected over the lowlatitude oceans as the climate warms, so EIS gives a meaningful measure of inversion stability changes that might accompany a perturbed climate. The P4 and P4CO2 climate perturbations produce only small changes in EIS. However, GCMs suggest that because the continents warm Figure 2. SST evolution for the simulations. faster than the oceans, EIS may increase in the adjacent subtropical stratocumulus regions [Caldwell et al., 2013; Qu et al., 2013]. The fourth perturbation, deis, tries to mimic an SST increase that is larger over the warmest parts of the tropical ocean than over the subtropical stratocumulus regions, as seen in multimodel-mean geographic distributions of 21st century SST change in the A1B scenario from Phase 3 of the Coupled Model Intercomparison Project (CMIP3). IPCC [2007, Figure 10.8] shows 2.5 K increases near the California coast, increasing to 3 K along the equatorial upwelling zone of the east Pacific. Case deis uses the same free-tropospheric temperature and humidity profiles as P4, but the SST (and the initial boundary-layer temperature profile) is increased only 2 K at the start, gradually ramping up to 3.6 K at the end, when the trajectory is approaching the warm pool region. This relatively extreme case with only half as much SST increase in the stratocumulus region as in the warm pool is chosen to contrast with to the uniform warming case P4. The mean subsidence is reduced by 4% compared to CTL; this reduction is much smaller than for P4 because the colder cloud top temperature increases radiative cooling in the overlying layer. Simulations of the above cases are performed including a diurnal cycle of insolation with a solar constant of 1367 W m 22 starting at 10:00 local time at the reference position and date, denoted by appending the suffix D to the case name. Other sensitivity studies in Table 1, denoted by appending U and A to the case name, are described in section 3.3. Figure 3. Initial s l =c p, total water and generalized relative humidity. The initial cloud layer profile corresponds to the gray dashed line in Figure 3c where R exceeds one. BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 94

5 3. Description of Models Used 3.1. SAM LES Model The LES model used in this study is version 6.7 of the System for Atmospheric Modeling (SAM), kindly supplied and maintained by Marat Khairoutdinov and documented by Khairoutdinov and Randall [2003] and Blossey et al. [2013]. There are four advected scalars, liquid static energy s l, total nonprecipitating water mixing ratio q t, rain water mixing ratio q r, and rain number concentration N r. The cloud liquid water and temperature are diagnosed from the advected scalars using the assumption of exact grid-scale saturation in cloudy grid cells. The Khairoutdinov and Kogan [2000] scheme is used for conversion between cloud and rain water as well as rain evaporation and sedimentation. Cloud droplet sedimentation is included following equation (7) of Ackerman et al. [2009], based on a lognormal droplet size distribution with a cloud droplet number concentration N d 5100 cm 23 and a geometric standard deviation r g 51:2; in cloud, the effective radius is calculated from the above cloud droplet size distribution. Radiative fluxes are updated every 60 s using the RRTMG scheme [Mlawer et al., 1997] Domain Size and Grid Resolution Following Sandu and Stevens [2011], a doubly periodic domain of horizontal size 4.48 km km is used. The horizontal resolution is 35 m. The vertical grid spacing is 5 m in the height range m with a stretched grid above, extending to a domain top of 4.4 km, with a total of 512 vertical levels Sensitivity Studies For cases CTL, P4, and 4CO2, additional simulations are conducted using diurnally averaged ( uniform ) insolation with a solar constant of W m 22 at an insolation-weighted solar zenith angle of 38.7, denoted by appending a U to the case name. These simulations are used for analyzing cloud response mechanisms. In a second set of simulations with uniform radiation, denoted by appending an A to the case name, the advection scheme of Blossey and Durran [2008] is used for advected scalars in place of the default advection scheme of Smolarkiewicz and Grabowski [1990]. As noted by Blossey et al. [2013], this produces less numerical diffusion at the sharp, poorly resolved inversion that caps the stratocumulus cloud layers that we are simulating, resulting in higher liquid water paths. This is used to test the robustness of the simulated cloud responses to the advection scheme. 4. Diurnally Varying Simulations Figure 4 shows time-height sections of horizontal-mean cloud fraction for the five simulated cases. The logarithmic color scale distinguishes between stratocumulus grid layers of nearly 100% cloud fraction (red) and cumulus grid layers with cloud cover less than 10% (blue). Cumulus-under-stratocumulus boundary layers predominate in all the simulations. These have a red region over a blue region (with a secondary cloud cover maximum at the base of the cumulus layer, which approximately coincides with the lifting condensation level of subcloud-layer updrafts). In the control simulation, there is a brief period around Day 0.6 in which the blue region becomes very thin: this corresponds to a well-mixed nocturnal stratocumuluscapped boundary layer. In all simulations, the simulated cloud has the expected diurnal cycle; it thickens at night and thins in early afternoon. Due to the small domain size, there is substantial high-frequency variability in horizontal-mean cloud and turbulence statistics. Here it is visible mainly as slight random fluctuations in the 3 h averaged cloud fraction in the cumulus layer; it will be much more prominent in some of the turbulence statistics to be discussed later. The 3 d evolution of inversion height and of cumulus cloud base in CTLD matches Sandu and Stevens [2011] to within 100 m, despite the slight differences in the formulation of subsidence rate. Its liquid water path (LWP) evolution, discussed below, is also within 20% of their results throughout the diurnal cycle, except during the first night, for which their LWP was % larger than we obtained. This discrepancy has also been observed in other intercomparisons [van der Dussen et al., 2013; Blossey et al., 2013] and likely reflects differences in the advection scheme and microphysical parameterization used in the two models. Overall, the good overall agreement between the two LES models lends confidence to the sensitivity studies done with both of them. BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 95

6 Figure 4. Time-height profiles of horizontal-mean cloud fraction for the diurnally varying simulations. The stratocumulus layer is thickest in the CTLD and deisd simulations, and becomes particularly thin and broken in the P4CO2D simulation, which includes both the thermal and radiative effects of CO 2 -induced warming. The P4CO2D simulation also has the lowest cloud top at the end of the simulation, despite having the smallest subsidence rate, implying that it has a smaller mean entrainment rate than the other simulations. The differences between the simulations are more clearly seen in the time series of Figure 5. The LWP is largest in the CTLD and deisd simulations, up to 25% smaller in 4CO2D, about 50% smaller in P4D, and smallest in P4CO2D. The relative differences are largest at night but still substantial during the day, when they are also accompanied by lower cloud fraction in the low-lwp simulations. Hence, the shortwave cloud radiative effect (SWCRE) is substantially weaker (less negative) for the P4D and P4CO2D simulations than for CTLD, with much less weakening for 4CO2D and very little SWCRE change for the deisd simulation. Table 2 gives daily and 3 d mean SWCRE for each of these simulations, showing that 3 d mean SWCRE is reduced 7 Wm 22 in 4CO2D, 29 W m 22 in P4, and 47 W m 22 (more than half) in P4CO2D, compared to CTLD. The SWCRE reduction in P4CO2D is larger than the sum of the SWCRE reductions in P4D and 4CO2D. This superlinear amplification of the cloud response may be due to the partial Sc breakup during P4CO2D, which reduces the CTBL radiative cooling compared to a linear sum of the component responses, feeding back on the cloud reduction. Except for deisd (which has a time-varying forcing difference from the other simulations), these changes are fairly consistent from one day to the next. In all simulations, the surface precipitation rate is less than 0.1 mm d 21, even during the night. Figure 6 shows time series of inversion height z i and mean lifting condensation level of near-surface air at a height of 100 m, entrainment rate w e, latent heat flux (LHF), and boundary-layer radiative flux divergence DR, defined as the difference between the net upward radiative flux at z i 125 m and the surface. The inversion height is computed as the height where the mean relative humidity profile crosses 50%, and w e is computed as described in the appendix of Yamaguchi and Randall [2011]. The deepening of z i is similar between the simulations, but is affected by systematic differences in their entrainment rates. The P4CO2D BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 96

7 Figure 5. Time series of (a) column cloud fraction, (b) LWP, and (c) SWCRE for the diurnally varying simulations. simulation, which deepens least, entrains 20% less than the control, which deepens most. These differences mirror those in DR, which is stronger at night in CTLD than in P4CO2D. This reflects the key role of boundary-layer radiative cooling in driving turbulence, and is consistent with a dominant balance between entrainment warming, radiative cooling, and sensible heat storage in the s l budget of the warming and deepening boundary layer. During the day, DR briefly becomes negative in all simulations due to absorption of insolation by boundary-layer cloud and water vapor; at these times, the differences in DR between the simulations largely vanish. During the daytime, the simulated clouds are particularly thin and patchy during some of the simulations. The similarity of DR between simulations during this time may be due to solar absorption thinning the clouds, which in turn reduces solar absorption faster than it reduces boundarylayer longwave cooling, producing a stabilizing feedback on DR during the daytime. The nearly 30% increase in LHF for P4D and P4CO2D compared to the other simulations is an expected consequence of the Clausius- Clapeyron relationship; to the extent that the subcloud layer relative humidity remains unchanged, at a given wind speed there should be an approximately 7% K 21 increase in LHF. The LHF in deisd begins half-way between its CTLD and P4D values, then approaches the P4D LHF later in the simulation, consistent with the deis SST specifications. In GCMs, the global hydrological cycle is mainly radiatively rather than thermodynamically controlled [Held and Soden, 2006]. As part of this, GCM-simulated LHF over the subtropical oceans increases less fast with temperature in greenhouse warming scenarios (approximately 3% K 21 ) than Clausius-Clapeyron predictions, associated with slight reductions in wind speed and air-sea temperature difference [Richter and Xie, 2008; Lu and Cai, 2009]; this is important to keep in mind when interpreting our results. Table 2. Daily and 3 Day Mean SWCRE (W m 22 ) for All Simulations Sim Day 1 Day 2 Day 3 Overall CTLD CO2D P4D P4CO2D deisd CTLU CO2U P4U CTLA CO2A P4A BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 97

8 Figure 6. Time series of (a) inversion height and mean lifting condensation level of near-surface air at a height of 100 m, (b) entrainment rate, (c) boundary-layer radiative flux divergence, and (d) latent heat flux for the diurnally varying simulations. Figure 7a shows time series of EIS. Except for the deisd simulation, all the simulations have very similar EIS evolution, with EIS decreasing almost 5 K over the 3 days. The EIS in the simulations with 4 K warmer SST is marginally ( K) larger. The deisd simulation has a 3 K larger EIS at the start than the other simulations; this difference is halved over the course of the simulation. Figure 7. Time series of (a) EIS, (b) inversion Ds l =c p, (c) Dq t, and (d) Db for the diurnally varying simulations. BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 98

9 Figure 8. Time series of (a) turbulent dissipation averaged over the 200 m below the inversion, (b) entrainment efficiency A, and (c) moist stability parameter j for the diurnally varying simulations. Figures 7b and 7c show the local inversion jumps Ds l =c p and Dq t,whered denotes a horizontal-mean difference between the inversion top and base heights z 1 and z 2 identified by the method of Yamaguchi and Randall [2011]. Despite the large EIS reduction across the 3 days, the liquidtemperature based inversion strength Ds l = c p stays approximately constant throughout all the simulations except for deisd, where it slightly decreases. This shows a fundamental ambiguity in using EIS or other bulk measures such as lowertropospheric stability [Klein and Hartmann, 1993] as estimators of inversion strength; given two profiles with exactly the same above-inversion temperature profile and near-surface temperature and lifted condensation level, but different inversion heights, that with the deeper inversion will tend to have a larger Ds l =c p because the mean stratification between the LCL and inversion is usually much weaker than that between the inversion top and a reference height within the free troposphere. In particular, from equation (2), we see that the EIS is designed to estimate the strength Ds l =c p of an inversion that is relatively close to the LCL, e.g., for well-mixed Sc, but will underestimate the strength of an inversion that is substantially higher than the LCL, as in the later parts of our simulations. The inversion humidity jump is larger for the P4D and P4CO2D simulations compared to CTLD and 4CO2D, and intermediate in the deisd simulations, as expected from Clausius-Clapeyron considerations. Figure 7d shows the inversion buoyancy jump Db5 g DT q 1gðz 1 2z 2 Þ=c p ; T q which we use for calculating entrainment efficiency. Here the density temperature T q 5Tð110:61q v 2q l Þ:Db is slightly smaller for the warmer simulations P4D and P4CO2D than the others, mainly because of their increased humidity jump. Figure 8a shows time series of turbulent dissipation averaged over the 200 m below the inversion. We find that is a skillful measure of how turbulence intensity affects entrainment rate. It is much stronger at night when the boundary layer is being strongly radiatively destabilized, and larger late in the simulations, when updrafts from a deeper underlying cumulus layer contribute to the turbulence near the inversion. Figure 8b shows time series of a nondimensional entrainment efficiency A 5w e Db=: (3) BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 99

10 Figure 9. Time-height profiles of horizontal-mean cloud fraction for the diurnally uniform simulations. After model spin-up, A 3 for all times in all simulations. The diurnal cycle is nearly invisible in A, showing how w e correlates with the strong diurnal cycle of. This suggests that the variations of w e within and between our simulations can be attributed mainly to changes in the turbulence profile within the CTBL, as manifest in, rather than poorly resolved changes in inversion structure. We also computed entrainment efficiencies based on common measures of turbulence such as convective velocity w or vertical velocity variance [e.g., Nicholls and Turton, 1986; Stevens, 2002; Caldwell and Bretherton, 2009]. These efficiencies make the assumption that the eddy length scale is proportional to the boundary-layer depth, which is fails for a cumulus-coupled boundary layer. An advantage of A is that already has the same dimension as w e Db, sidestepping the need for assuming an eddy length scale. With reasonable length scale choices, other tested entrainment efficiencies based on statistics exhibited a variety of behaviors in time and across our simulations, and none collapse to a constant quite as well as A. However, we are not proposing that A is necessarily the basis of a better entrainment closure for simple CTBL models. Theoretically, there is no reason that entrainment efficiency need be constant, and past entrainment closures have hypothesized dependences on cloud top liquid water content and inversion jump ratios [e.g., Nicholls and Turton, 1986; Moeng, 2000]. Also, to use equation (3) as a practical entrainment closure, one would have to predict the vertical profile of turbulent dissipation. Figure 8c shows the moist stability parameter j511ldq t =Ds l. In the warm-sst simulations, the larger inversion humidity jump makes j larger by than in the control-sst simulations, such that it reaches 0.5 much of the time. MacVean [1993], Moeng [2000], and Lock [2009] suggested that a larger j in this range should correlate with a thinner cloud and a smaller cloud fraction, and indeed this is seen in P4D and especially P4CO2D. A larger humidity jump increases the evaporative cooling that can be induced by entrainment mixing. One plausible explanation for the cloud thinning is that this makes entrainment more efficient (larger A ) for a given level of turbulence, drying out and thinning the cloud layer; this is not supported by Figure 8b, which shows the same A in all simulations. Instead, Figure 8b supports an alternative explanation that increased evaporative cooling enhances buoyant production of turbulence within the cloud layer, allowing less cloud to produce a given entrainment rate through a mechanism we articulate in section Diurnally Uniform Simulations A goal of this paper is to better understand the decrease in cloud thickness and fraction that accompanies greenhouse warming in our simulations. This is more easily isolated by averaging the insolation across the diurnal cycle so that the cloud structure evolves systematically as the SST increases. These diurnally uniform BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 100

11 Figure 10. Time series of column cloud fraction, (left) LWP and SWCRE for the diurnally uniform simulations and (right) their sensitivity to use of an alternate advection scheme. simulations (denoted by a suffix U ) are particularly useful in separating contributions to cloud thinning that can be attributed to the temperature dependence of the moist thermodynamics operating in the boundary layer from those due to changes in the radiative driving of the cloud-topped boundary layer, and they facilitate the use of domain-mean statistics that are time-averaged for several-hour periods to reduce the impact of high-frequency noise due to the small domain size. The CTLU, 4CO2U, and P4U simulations evolve very much like their diurnally varying counterparts. Figure 9 shows their time-height sections of cloud fraction, which can be compared with Figure 4. Figures 10a 10c shows time series of column cloud fraction, LWP, and SWCRE for the CTLU, 4CO2U, and P4U simulations, and Table 2 gives their daily-mean and simulation-mean SWCRE. As in the diurnally varying simulations, they show some cloud thinning in 4CO2U and more cloud thinning and cloud fraction reduction in P4U compared to CTLU. Due to rectification from daytime cloud thinning, the daily-mean SWCRE is roughly 20% weaker in the diurnally varying simulations than the corresponding diurnally uniform simulations, but the SWCRE sensitivities to the forcing perturbations are similar between the two sets of simulations, as also found in Eulerian LES simulations of a Sc-topped mixed layer by Bretherton et al. [2013] Sensitivity of Diurnally Uniform Simulations to Advection Scheme Figures 10d 10f and Table 2 show results for simulations CTLA, 4CO2A, and P4A, which use the Blossey- Durran scalar advection scheme. They show an approximately 20% larger time-mean LWP and SWCRE in all BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 101

12 Figure 11. Time series of (a) boundary-layer radiative flux divergence, (b) latent heat flux, (c) entrainment rate, and (d) inversion strength for the diurnally uniform simulations. three simulations than for the U simulations which use SAM s default scalar advection scheme. However, the sensitivity of LWP and SWCRE between the A simulations is similar to the U simulations. That is, our results about cloud response to climate perturbations are robust to the choice of advection scheme. 6. Isolating Thermodynamic Cloud Response: 4CO2U Versus P4U Figure 11 shows time series of boundary-layer radiative flux divergence DR, latent heat flux, entrainment rate w e, and inversion strength Ds l =c p for simulations CTLU, P4U, and 4CO2U. As in the diurnally varying simulation, the radiative driving DR of the boundary layer is weaker in both 4CO2U and P4U than in CTLU due to the larger free-tropospheric emissivity associated with increases in CO 2 and water vapor, respectively, while the latent-heat flux is 30% stronger in P4U than the other two simulations due to its Clausius- Clapeyron scaling with temperature. The inversion strength Ds l =c p remains similar in all three simulations, though slightly weaker for 4CO2U. The entrainment rate mainly responds to differences in DR between the simulations. Hence, in the first half of the simulation, it is slightly weaker for 4CO2U and P4U than for CTLU. In the second half of the simulation, the P4U and CTLU entrainment rates are similar, and larger than for 4CO2U. Serendipitously, the time series of DR; Ds l =c p, and inversion height are very similar for P4U and 4CO2U for the first 1.5 days. This allows us to compare two simulations with nearly the same radiative driving, inversion strength and boundary-layer depth, but with one corresponding to a 4 K warmer temperature profile. Hence, we interpret the cloudiness decrease from 4CO2U to P4U during this time as isolating a temperature-driven thermodynamic contribution to low cloud feedback across the Sc-Cu transition. This contribution acts in addition to any cloud responses to changed radiative driving, inversion strength and height, surface wind speed, or free-tropospheric relative humidity. As in the diurnally varying simulations, the entrainment efficiency A 3 in both 4CO2U and P4U (not shown), so the warming-induced cloud thinning cannot be attributed to enhanced entrainment efficiency, but instead must be interpreted as less cloud generating the same amount of turbulence in the warmer climate. A similar thermodynamic response was also suggested by the Eulerian S12 and S11 CGILS simulations [Blossey et al., 2013; Bretherton et al., 2013]. Using a mixed layer model, Bretherton et al. [2013] explained it as a consequence of enhanced upward moisture fluxes in the boundary layer, which cause the buoyancy BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 102

13 fluxes to increase within, but not below, the stratocumulus cloud. In the mixed layer model, the entrainment rate is proportional to the vertically integrated buoyancy flux, a measure of turbulence generation. To keep entrainment warming in balance with fixed radiative cooling in a warmer climate, the cloud thins to maintain a fixed vertically integrated buoyancy flux despite a larger in-cloud buoyancy flux. An apparently similar thermodynamic cloud-thinning response robustly emerges throughout the full length of our Lagrangian simulations, even though the cloud layer is not well mixed. This suggests it operates throughout a range of cloud regimes, both well mixed and cumulus coupled, and is not strongly dependent on details of the case setup. Hence, it seems worthwhile to understand in more general terms Liquid Flux and Cloud Generation of Turbulence As a preliminary step toward generalizing Bretherton et al. s [2013] argument beyond mixed layer models, we consider the relationship between buoyancy flux and turbulent liquid flux in a general cloud-topped boundary layer. Bretherton and Wyant [1997] partitioned horizontal buoyancy perturbations into an unsaturated contribution and a contribution from the condensation of liquid water: b 0 5b 0 u 1cgq0 l ; (4) c5 L 21:61 7 at 290 K ; (5) c p T b 0 u 5g T 0 l T 1:61q0 t : (6) The temperature dependence of c (20.4% K 21 ) is negligible for the arguments presented here. Based on equation (4), equation (9) of Bretherton and Wyant [1997] similarly partitioned buoyancy flux into an unsaturated contribution and a contribution from the liquid flux: w 0 b 0 5w 0 b 0 u 1cgw0 q 0 l : (7) In subtropical cloud-topped boundary layers, the unsaturated contribution is often negative above the near-surface LCL (i.e., in the cloud layer), but is overwhelmed by a larger positive liquid flux contribution to create a positive buoyancy flux. Figure 12 illustrates these features, using averages over hours 9 15 of selected vertical profiles in CTL, 4CO2U, and P4U. Figure 12a shows the buoyancy flux and unsaturated buoyancy flux profiles. The negative spike in the unsaturated buoyancy flux near the inversion is due to entrainment occurring above the Sc radiative cooling layer. The difference between the actual and unsaturated buoyancy flux is proportional to the liquid flux, the solid curves in Figure 12b. The liquid flux extends down to the surface-layer LCL, well below the Sc base, due to underlying cumulus convection; in fact, the Sc base is not clearly evident in the liquid flux, unlike in a mixed layer model. In subtropical CTBLs, the liquid flux profile is mainly controlled by the total water flux and the fractional cloud cover profile. This can be understood by writing q l 5max ðq lp ; 0Þ; (8) where the potential liquid water is defined in terms of moist conserved variables (after linearization of the Clausius-Clapeyron equation) as q lp 5 q t2q s ðp; T l Þ ; (9) 11c c5 L c (10) At a cloud-free level, the liquid flux is zero. At a fully saturated level with 100% cloud cover, q l 5q lp everywhere, so the liquid flux is equal to the potential liquid flux. Using equation (9), BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 103

14 Figure 12. Profiles averaged over times 9 15 h in the diurnally uniform simulations of (a) buoyancy flux (solid) and unsaturated buoyancy flux (dashed), (b) turbulent liquid flux (solid) and potential liquid flux (dashed), (c) q t flux, (d) q l, (e) vertical velocity variance, and (f) dissipation rate, In all plots, the subcloud-layer (z m) LCL, stratocumulus cloud base (at which the horizontal-mean cloud fraction is half of its maximum value) and inversion height for each simulation are marked with horizontal dashed lines of the matching color. w 0 q 0 lp c w 0 q 0 t 2w 0 T 0 (11) In subtropical CTBLs, the dominant term in the potential liquid flux is due to the total water flux, shown in Figure 12c. The total water flux is 20 25% larger in the warm-climate simulation P4U than in the other simulations, due to Clausius-Clapeyron temperature dependence. The chain-dashed curves in Figure 12b shows the potential liquid flux. Due to the contribution of the total water flux, potential liquid flux also rises by nearly 10% (2% K 21 ) in the warm-climate simulation. This increase is smaller than for total water flux due to the canceling temperature dependence in the 11c term in the denominator of equation (11). We conclude that in a fully cloud-filled layer, the liquid flux, and hence the buoyancy flux, can be expected to increase with temperature, as is seen in a mixed-layer model [e.g., Bretherton et al., 2013, Figure 10]. Figure 12b shows that within the Sc layer, the liquid flux approaches the potential liquid flux, while in the cumulus layer, the small cloud fraction keeps the liquid flux well below the potential liquid flux. Unlike the potential liquid flux, the actual liquid flux doesn t increase in the warm-climate simulation P4U, suggesting that it is not just controlled by Clausius-Clapeyron temperature dependence. This response is associated with a reduced cloud fraction and a thinner Sc layer (Figure 12d). The buoyancy flux is the main source of TKE in subtropical cloud-topped boundary layers, so the liquid flux profile is a primary control on the TKE near the boundary layer top, which in turn drives entrainment. Figure 12f shows the TKE dissipation profile, which generally resembles the TKE generation by buoyancy fluxes, BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 104

15 Figure 13. Diagram of how entrainment liquid-flux adjustment can lead to cloudiness reduction in cumulus-coupled boundary layers in a warmer climate with unchanged boundary-layer radiative flux divergence DR and inversion strength Ds l =c p. See text for explanation. indicating the importance of the in-cloud buoyancy fluxes for driving this entrainment-relevant measure of turbulence. As with buoyancy and liquid fluxes, the TKE dissipation profile is very similar in all three simulations. Another illuminating measure of turbulence is the vertical velocity variance profile (Figure 12e); this shows a tendency for cloud-layer updrafts and downdrafts to slightly weaken in the warm-climate simulation. 7. Entrainment Liquid-Flux Adjustment and Boundary-Layer Cloud Reduction in a Warmer Climate This section presents a conceptual thermodynamic cloudiness-reduction argument that applies to Cuunder-Sc boundary layers as well as Sc-topped mixed layers. It is phrased in terms of a fast cloud adjustment via entrainment feedbacks to an instantaneous uniform warming with no change in generalized relative humidity. As shown in Figure 13, we consider a turbulent cloud-topped boundary layer in an original climate (blue). It is cumulus coupled, i.e., it has a subcloud layer, a transition layer near the cumulus base in which q t decreases with height and s l slightly increases with height, and an overlying stratocumulus-topped mixed layer through which the cumuli rise. The argument would also apply to a well-mixed boundary layer. In a similar spirit as Rieck et al. [2012], we perturb the entire atmospheric depth and SST so as to increase T l at constant pressure by some uniform amount (e.g., 4 K) everywhere in the boundary layer and through the inversion zone, such that the inversion strength remains constant. We increase specific humidity q t everywhere so as to maintain a constant generalized relative humidity R. The perturbations are specified in terms of the moistconserved variables T l and q t (instead of T and q v ) because this preserves the stratification of a cloudy boundary layer, e.g., a Sc-topped mixed layer in the original climate remains well mixed in the perturbed climate. To isolate thermodynamic effects, we assume there is no accompanying change in the boundary-layer radiative flux divergence DR. For this reason, this scenario is like comparing the first half of the P4U and 4CO2U simulations, i.e., treating the 4CO2U simulation as the original climate for purposes of comparing with LES. For argument, imagine the warming perturbation with constant relative humidity is made instantaneously, respecting the preexisting three-dimensional turbulent structure of the spatially varying fields, so that we can consider how the turbulence might quickly respond to it. To maintain the existing horizontal generalized relative humidity perturbations, specific humidity variations q 0 t will be amplified by the climate perturbation by approximately 7% K 21 due to Clausius-Clapeyron effects. Within the cloud layer, this induces an amplification of horizontal liquid water variations q 0 l. Because T l is increased uniformly, and temperature can be written T5T l 1Lq l =c p, there are horizontal temperature variations T 0 5Lq 0 l =c p associated with liquid water condensation, and their contribution (7) to horizontal buoyancy variations will also be increased. Following equation (9), q 0 l and T 0 increase by only 2 3% K 21 because more than half of the 7% K 21 increase in q 0 t goes BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 105

16 to increasing the saturation mixing ratio perturbation q 0 s 5ðdq s=dtþt 0 rather than increasing q 0 l [Betts and Harshvardan, 1987]. Within the cloud layer, updrafts tend to have more liquid water, warmer temperature, and higher buoyancy than downdrafts. The immediate result of the T l increase (shown in red on Figure 13) is to increase liquid water everywhere by the same proportion, 2 3% K 21 (shown by increasing the size of all the red cloud droplets), without changing the cloud boundaries. This amplifies the existing updraft-downdraft differences in liquid water and hence in temperature, causing an immediate increase in the buoyancy flux, by 2 3% K 21, both in the stratocumulus and cumulus layers. The increased buoyancy flux amplifies the turbulent updrafts and downdrafts (shown in Figure 13 by increasing the length of the vertical arrows indicating the updraft and downdraft velocities). More cloud-layer turbulence induces a burst of increased entrainment of dry, warm air through the inversion, indicated as a larger circular arrow in Figure 13. Within a few large-eddy turnover times, the result is an adjusted cloud layer (magenta colors in Figure 13) in which the burst of entrainment has slightly dried and warmed the upper mixed layer (profiles on left), thinning the capping stratocumulus cloud layer from its base (gray dashed line). Liquid water in Sc updrafts and downdrafts is reduced (shown by removing an equal mass of liquid water from each red droplet to get the magenta droplets) and possibly completely evaporated in some Sc downdrafts. The reduction of Sc thickness and fraction also decreases upward liquid flux, buoyant generation of turbulence, and updraft/ downdraft velocities (pink arrows), until the entrainment rate is reduced sufficiently that the radiative destabilization DR can again maintain the cloud. We call this internal cloud-regulating feedback entrainmentliquid flux (ELF) adjustment; more liquid flux and entrainment favor thinner Sc, which reduces the liquid flux and entrainment, keeping them adjusted to the fixed radiative cooling. For a Sc-capped mixed layer, ELF adjustment is equivalent to Bretherton et al. s [2013] thermodynamic mechanism that was based on a mixed layer model analysis. Note that any associated reduction in Sc cloud cover would reduce boundarylayer radiative cooling, just like increased CO 2 or water vapor aloft, creating a positive feedback on the ELFinduced Sc thinning. This horizontally uniform drying is envisioned to affect the mean liquid water in the Sc layer much more than its horizontal variability; hence, the ratio of mean liquid water to its standard deviation can be expected to be smaller in the adjusted state compared to the original state (confirmed in section 7.2). The adjustment of the cumulus layer may be more complicated; these arguments suggest a decrease in updraft fractional area (converging gray arrows in Figure 13) but do not make a clear prediction about the change in updraft liquid water content. The uncertainty in these two predictions is indicated by the gray and magenta question marks in Figure 13. There is no guarantee that ELF adjustment is the main cause for LWP differences in the original and perturbed climates. Slower time scale processes involving changes in horizontal relative humidity variability, vertical temperature stratification, surface fluxes, precipitation, etc., could also be important; this can best be tested using LES. We next turn to one such test ELF Adjustment and Rapid Spin-Up of Warm-Cold Cloud Thickness Differences With some effort and technical complication, the above conceptual experiment could be performed using LES. So far, we have performed a simpler though less decisive analog, which is to compare the first few hours of the spin-up of the P4U, 4CO2U, and CTLU simulations. All three are initialized with identical inversion pressures and generalized relative humidity profiles; the small initial differences in inversion height and LWP are due to reduced air density and the stronger liquid-water lapse rate in a warmer climate. The P4U initial profile is 4 K warmer in the boundary layer than the other two simulations but has a nearly identical inversion jump in s l. The P4U and 4CO2U simulations are an excellent pair with which to test the predictions of our conceptual model, since they closely satisfy the forcing assumptions made in that model. They have nearly identical subsidence rates, and induce nearly identical radiative flux-divergence across the cloud-topped boundary layer. The key difference with the conceptual experiment is that the simulations are not started from a fully turbulent initial state so there is no true analog to the instantaneously perturbed (red) state in Figure 13; however, we can still look for a rapid development of the predicted differences between the cloud statistics of the simulations. The CTLU simulation is also an interesting comparison, since its main difference from 4CO2U is having a stronger radiative driving of the boundary layer, so we can test if this is also important to the initial development of the cloud layer. BRETHERTON AND BLOSSEY VC American Geophysical Union. All Rights Reserved. 106