The Idea

The idea that clouds are sensitive to their environment, dramatically illustrated through Figure 8.1, should surprise no one. In introducing Scorer's (1972) cloud atlas, F. H. Ludlam wrote:

Clouds have an infinite variety of shapes, but a limited number of forms corresponding to different physical processes in the atmosphere which are responsible for their formation and evolution.

Ludlam continued then to trace the history of the modern cloud classification, beginning with the work of Lamarck (1802) and Howard (1802) and culminating with the 1887 treatise of Abercromby and Hildebrandsson, which presents a cloud classification scheme that is identical, in all essential respects, to that

Figure 8.1 MODIS image from July 5, 2002, showing marine stratocumulus in the vicinity of the Canary Islands off the West African coast.

used by meteorological observers today. It took 85 years to work out the basic forms by which we classify clouds; however, the task of relating these forms to specific physical processes (their physical environment if you will)—now some 120 years later—has not yet been completed.

This relating process to form is the focus of this chapter. We concentrate on what one might call a supergenus—low clouds—which includes the familiar genera of stratus and cumulus (dating from Howard's classification) and stratocumulus (dating from the 1836 monograph by Kamtz). Our emphasis is on stratocumulus and cumulus. From the point of view of the climate system, the shallowness of the cloud layer (or the property of being "low") is principally manifest as a temperature difference (T0 - T) between the surface, T0, and cloud top, Tc. This temperature difference is related to the physical height of the cloud top; however, it is more fundamental as it helps meter the relative effects of clouds on the effective emissivity of the atmosphere as compared to its albedo. The emissivity (or greenhouse) effect of clouds increases with the difference in temperature between the surface and cloud top, whereas the albedo effect of clouds need not. Because these effects tend to compete with one another, perturbations to the properties and statistics of low clouds affect albedo disproportionately and hence alter more profoundly the net radiative balance of the system as a whole. Contemporary efforts to relate process to the form of low clouds is motivated by this decisive fact.

There are, however, additional, less appreciated motives for studying the physical processes that control the statistics of low clouds. For instance, low clouds are by definition thin, which means the difference between their cloud top and base temperatures is also small. Because of the potential condensation in an adiabatic current spanning the depth of the cloud scales with this temperature difference, the liquid water content in the cloud (even in the absence of precipitation) remains a small fraction of the total water content. We will argue that this removes a constraint from the system that renders the state of shallow clouds more susceptible to environmental perturbations. In plain terms, the development of rain in shallow clouds is not necessary. This is just one way in which they are delicate.

In addition to being decisive and delicate, low clouds are ubiquitous. This property arises from the fundamental asymmetry of moist convection coupled with the need for circulations to conserve mass, which requires ascending air currents to be more vigorous and less spatially extensive than descending currents (Bjerknes 1938). Hence, conditions of gentle subsidence, which favor low clouds, prevail.

Combining their decisiveness with their ubiquity, we estimate that a one percentage-point change in the albedo of low clouds (equivalently a 2-3 percentage-point increase in the average cloud fraction) could result in a 1 W m2 change in the net solar radiation at the top of the atmosphere. Alternatively, such a perturbation could be effected by just a 6 percentage-point increase of the albedo in only the stratocumulus regions, which is on the order of what one might expect from a 0.2 g kg1 moistening of the marine boundary layer, or an increase in ambient droplet concentrations from 75-150 cm3. In the end, and in light of the perceived delicacies of the system, calculations such as these motivate attempts to answer our phrasing of Ludlam's challenge of relating process to form:

Quantitatively, what is the relationship between the large-scale environment and the statistics of low clouds?

The answer is paramount to understanding both how clouds may change in the future and, by implication, the climate system.

Our discussion of physical controls on cloudiness is divided in two parts: (a) meteorological controls and (b) the role of the atmospheric aerosol. By meteorology we mean the large-scale dynamic and thermodynamic state that is thought to govern principally cloud macro-structure. The aerosol, by which we mean cloud condensation nuclei (CCN), is principally thought to govern cloud micro-structure. Of course, one is not independent of the other, and a considerable amount of our subsequent discussion will be devoted to the ways in which this fact confounds attempts to meet Ludlam's challenge.

Meteorology

Of the varied forms of moist convection, low clouds are the simplest. They embody fewer processes, and those that are operative typically encompass shorter temporal and smaller spatial scales, making them more amenable to both measurement and simulation. Thus on a phenomenological as well as on a theoretical level, our understanding of shallow clouds is more advanced than that of other cloud forms.

Among the observed relationships between low cloud amount and ambient meteorological conditions, the most compelling are those between seasonal variations in lower tropospheric stability and low-cloud amount in regions where low clouds predominate. Introducing the symbol s to denote the sum of the fluid enthalpy and geopotential, often called the dry-static energy, and adopting a subscript notation so that "s0" and " s+" denote values of s at the surface and just above cloud top, respectively, we can define the lower tropospheric stability:

where A is used throughout to denote the difference between a quantity just above cloud top and at the surface. This definition follows most closely what Wood and Bretherton (2006) call the estimated inversion strength (EIS). The observation that cloud incidence tends to increase with As goes back to the early stratocumulus studies by Blake (1928) and to some extent Clayton (1896). Recent studies have increasingly shown such relationships to be compelling (Slingo 1987; Klein and Hartmann 1993; Wood and Bretherton 2006), with the latest showing that, if properly constructed, As can explain over 80% of interseasonal variance in low-cloud amount. Although deficient because it relates cloud incidence (a non-dimensional quantity) to As (a dimensional quantity), these observations are the basis for the long-standing hypothesis that stratocumulus cloud amount will increase in a warmer climate (e.g., Miller 1997). As in a warmer climate, As will increase (and does so robustly in general circulation models), as the tropical thermal structure adjusts to a warmer moist-adiabat.

Are there, however, other factors? For instance, surface wind speeds might be thought to play an important role in setting the rate of coastal ocean upwell-ing, and hence surface temperatures, and thus might provide an important link between cloudiness and the state of the local circulation. To the extent that surface wind speeds are enhanced because of increased cloudiness (and hence large-scale, near-surface cooling), this constitutes a regional-scale feedback process which some suggest might be central to explain features of the current climate (e.g., Philander et al. 1996; Nigam 1997). To the extent that they exist, such feedbacks are likely to compound effects associated with the tendency of greater winds to increase mechanical and biochemical production of the marine aerosol (e.g., Charlson et al. 1987; Latham and Smith 1990).

Free tropospheric humidity may also play a critical role in setting cloudiness. For example, through its critical role in a hypothesized instability process (Deardorff 1980; Randall 1980), Aq is thought to help select among cloud regimes. Well-mixed greenhouse gases, and for that matter, q+, may also play a role in determining the cloud-top cooling potential of stratocumulus layers, and hence the susceptibility of the cloud layer to decoupling; this, in turn, is thought to be a factor in regulating cloud amount (Turton and Nicholls 1987). During DYCOMS-II, satellite imagery showed that stratocumulus regions break up conspicuously as they drift toward the equator under the influence of increasingly humid mid-free-tropospheric air associated with the North American Monsoon.

Underlying many of the ideas expressed above is the uncertainty about the role of the large-scale divergence of the horizontal wind, V, whose vertical integral is the large-scale vertical motion. The climatology of divergence helps select regions where low clouds predominate, and hence divergence is controlled for when investigating sensitivities between low-cloud amount and other parameters. Climatologically, low clouds are favored in regions of stronger divergence. However, on short time and small spatial scales, such relationships are nontrivial. For instance, all other things being constant, increasing V lowers cloud top and produces a thinner cloud. In the limit, during periods of offshore flow and strong divergence, stratocumulus is often suppressed as the boundary layer becomes insufficiently deep to support clouds (Weaver and Pearson 1990); if the vertical motion is sufficiently weak, areas of stratiform cloudiness may break down into more cumuliform patterns.

Theory, of course, exists to order the empiricism. To begin, one could simply list the parameters previously discussed and, in doing so, identify what one might call a zeroth-order meteorological vector, m = {so, qo, V, V, s+, q+, F+}, (8.2)

consisting of ostensibly external factors regulating clouds. In addition to the previously introduced variables, V denotes a surface exchange velocity (proportional to the mean wind) and F+ denotes the net downwelling longwave radiation above the cloud layer. This vector identifies seven parameters. After multiplying q by L , the enthalpy of vaporization, all except V carry the units of velocity to some power and, because given a surface at saturation and fixed pressure q0 is given by s0, m identifies at least a four-dimensional parameter space in which we expect the properties of low clouds to be manifest. The meteorology is neither homogeneous nor stationary; thus, spatial and temporal gradients of m, as well as covariance among its components, will (even in the absence of variations in the aerosol) render the effective dimensionality of the space much larger. This explains why Ludlam's challenge of relating process to form has proved to be much more difficult than Howard's challenge of relating name to form.

For both cumulus and stratocumulus, the theory largely attempts to describe the bulk or integral state of the cloud and subcloud layers (for a review, see Stevens 2006). Because the theory is expressed differently, depending on whether we consider stratocumulus versus shallow cumulus, we discuss each in turn.

Stratocumulus

Lilly's 1968 mixed-layer theory identifies key environmental factors that influence stratocumulus cloud amount (or thickness). In the absence of advective forcing, Stevens (2006) used this theory to derive an expression for the steady-state cloud thickness:

where h denotes cloud-top height, zb cloud-base height, ae the nondimensional entrainment, ni = ^

1 AF

gv qQ

Here g denotes gravity and Rv the gas constant for water vapor. The cloud albedo is an increasing function of its optical thickness, r, which to a first approximation can be expressed as:

where C represents the liquid water path and re the effective radius. They are given as:

where yi is taken as the cloud-averaged value of dq1 /dz, Nthe expected number of activated cloud droplets for an adiabatic cloud, and a some unspecified measure that encodes effects as a result of the shape of the drop distribution and diabatic (collisions, mixing) effects. Equation 8.6 provides a basis for relating cloud optical properties (or albedo) to cloud geometrical properties. These relationships show that m largely determines the cloud geometric properties, whereas the optical properties depend additionally on the cloud microphysical structure, which in turn may be expected to reflect, at least in part, the properties of the aerosol.1

However, especially to the extent clouds precipitate, cloud geometric properties may also be regulated by N.

Relationships such as those above, and the ideas that underlie them, should explain and extend the existing empiricism. There is evidence that the theory is beginning to rise to this challenge. For example, the ideas behind Equation 8.3 can also be used to show that the approach to equilibrium is slow, which means the past matters. This point helps to explain the finding made by Klein et al. (1995) and Pincus et al. (1997) that in a Lagrangian sense, cloud optical properties lag environmental conditions by 12-24 hours, which corresponds roughly to the thermodynamic timescale of the mixed-layer model. The same theory shows that multiple timescales emerge and can lead to differential short- and long-term behavior (e.g., Zhang et al. 2005; Wood 2007), which is also inferred in the observational study by Pincus et al. (1997).

Likewise, the role of microphysical processes identified in Equation 8.6 is the basis for the so-called cloud-water feedback. The idea, first explored by Paltridge (1980), is that y depends on a fixed way to its adiabatic value, which in turn depends on Rvs0/(cpLv), and hence on temperature. The sensitivity of re to cloud microphysical alterations through a has been explored by Chosson et al. (2007). By distributing cloud water according to different mixing scenarios ex post facto, they show that the impact of inhomogeneous mixing processes on the droplet size distribution at the top of a stratocumulus layer can affect the optical thickness of the layer more efficiently than the heterogeneous spatial distribution of liquid water (cf. Burnet and Brenguier 2007).

Notwithstanding these initial steps, a full-scale evaluation of the theory has not been attempted for at least two reasons: (a) the theory remains incomplete, or deficient; (b) many of the parameters upon which it is based (most notably q+, F+, and T>) are difficult to measure. The principal deficiencies in the theory are the lack of a compelling specification of a,, and the breakdown of a key assumption (well mixedness) under certain conditions. Next, we discuss these two points.

Entrainment

The entrainment rate is expressed non-dimensionally, following Stevens (2006), as a = EAs/AF, in Equation 8.3. Doing so obscures the fact that it (through the entrainment velocity, E) may depend on m, which means that the full parameter sensitivity of even the equilibrium states of the mixed-layer model remains uncertain.

One idea would be to use large-eddy simulation to estimate a , and indeed this has been a strategy adopted by a number of investigators (e.g., Lock and MacVean. 1999; Moeng et al. 1999). This strategy, however, has proved challenging, largely because the fine scale of the entrainment processes makes it difficult to represent with fidelity. This point formed the focus of an intercom-parison study by Stevens (2005), who showed that entrainment is sensitive to the detailed numerical formulation of a simulation. As shown in Figure 8.2, even at a relatively fine resolution, the representation of the cloud layer is

0.0 pseudo albedo 1.0 UCLA-0 UCLA-1

0.0 pseudo albedo 1.0 UCLA-0 UCLA-1

Figure 8.2 Visualization of flow fields from two simulations using the UCLA large-eddy simulation model which differs only in the representation of small-scale (sub-grid) mixing. Shown are plan-view images of the albedo estimated from the liquid water path, and cross sections showing vertical velocity (shaded) and cloud water (contoured). Cross-section cuts are indicated by the white dashed line in the plan-view plots. These fields were drawn from simulations wherein N = N = 192 and Ax = A y = 20 m, x y 7

Figure 8.2 Visualization of flow fields from two simulations using the UCLA large-eddy simulation model which differs only in the representation of small-scale (sub-grid) mixing. Shown are plan-view images of the albedo estimated from the liquid water path, and cross sections showing vertical velocity (shaded) and cloud water (contoured). Cross-section cuts are indicated by the white dashed line in the plan-view plots. These fields were drawn from simulations wherein N = N = 192 and Ax = A y = 20 m, x y 7

sensitive to the representation of the smallest scales, as manifest in this inter-comparison of differences in the representation of the subgrid-scale mixing. The simulations are an example of numerical delicacy. For this particular case, the result on the left (labeled UCLA-0) conforms better to the data. As a point of reference, this simulation was only constructed after it was determined that the default configuration of the model (which produced the image on the right) yielded results that were incompatible with the data. Nonetheless, our ability to begin constraining the models with data in these respects represents a significant step forward and provides an example of the increasingly critical interplay between models, theory, and data.

Decoupling

The mixed-layer limit is believed to become energetically inconsistent in certain regions of parameter space. Roughly speaking, when surface fluxes become significant, relative to the effective cloud-top radiative driving, one can expect a transition to a more cumulus-coupled layer. This transition is often referred to as decoupling because it is associated with increased differentiation (decoupling) between the thermodynamic properties of the cloud and subcloud layer. It was developed as a theory of the stratocumulus to cumulus transition by Bretherton and Wyant (1997), following on ideas developed by Turton and Nicholls (1987) to explain the diurnal cycle. Stevens (2000) used idealized simulations to show that such transitions are sharp, or threshold-like, in parameter space, suggesting the existence of distinct regimes or attractors of the fl ow. In the decoupled regime one expects significant differentiation between the cloud and subcloud thermodynamic properties, which results in marked reductions in cloudiness (see also Lewellen and Lewellen 2002), as compared to the well-mixed regime.

Regime transitions are thought to underlie the types of numerical delicacies seen in Figure 8.2, wherein small changes in the efficacy of cloud-top mixing may engender profound differences in cloud structure. Because this is an energetic threshold, such a transition may be triggered by a variety of processes (e.g., precipitation). The emergence of such nonlinear behavior implies that the statistics of cloudiness may depend on a richer characterization of the meteorological vector. Thus, for instance, small values of T> imply small values of n3 and hence, by Equation 8.3, favor an increase in r. However, to the extent such states are effectively forbidden, one might expect r to depend less on m and more on the character of its spatial and temporal fluctuations.

Cumulus

A compelling theoretical framework for cumulus has proved to be more difficult to establish (cf. Albrecht et al. 1979; Bretherton 1993; Bellon and Stevens 2005; Bretherton and Park 2007). In some respects this is surprising, because in certain limits cumulus convection is much simpler than stratocumulus convection. For instance, because radiative fluxes are important primarily to the long-time behavior of boundary layers topped by cumulus convection, they are only indirectly coupled to the turbulent fluxes through the evolution of the mean state and hence surface fluxes. As such it is possible to construct compelling, but purely transient, representations of layers of cumulus convection by replacing the surface temperature description with a surface flux prescription. In such a framework one need not make explicit reference to either T> or F+, which somewhat simplifies the zeroth-order meteorological vector, m (Stevens 2007). To the extent a stationary description is desired, such simplifications are not warranted. Simple bulk theories, such as the one layer model of Betts and Ridgway (1989), may be useful. However, even these are complicated by the fact that the radiative cooling is distributed through the layer (rather than concentrated at cloud top as in stratocumulus), so that the fraction of cooling within just the subcloud layer emerges as an additional parameter.

Energetics and Mixing

One of the chief challenges for simple theories of shallow cumulus is the difficulty of reconciling the internal vertical structure with the energetics of the layer. Most research to date focuses on the question of this internal structure; for example, the cloud-base mass flux and its distribution through the cloud layer as constrained by models of lateral mixing (Siebesma 1998; Neggers et al. 2004). Work in this regard suggests that the convective mass flux is well constrained by both the thermodynamic and energetic state of the subcloud layer (Neggers et al. 2007), thereby providing guidance, albeit relatively unexplored, as to how convective cloudiness may change in response to factors like changing surface winds or fluxes, or perhaps changes in the effective saturation pressure of the free troposphere. Recent work also clarifies the mechanism through which the cloud layer deepens and the energetic constraints placed on this process by the subcloud layer (Stevens 2007). In this respect, one important finding is that the cumulus layer deepens primarily as a result of the flux of liquid water into the inversion. This implies that the development of precipitation may help arrest the growth of the cloud layer (Stevens and Seifert 2008). This has implications for cloud feedbacks that exercise microphysical pathways. Clouds that rain less can be expected to deepen more efficiently, but deeper clouds rain more. Similar effects are evident in layers of stratocumulus convection, but are not thought to be so dominant (Stevens et al. 1998; Ackerman et al. 2000; Bretherton et al. 2006).

Convective versus Stratiform Cloudiness

Another important challenge is to determine the respective roles and parameter sensitivity of convective versus stratiform (large-scale) cloudiness. Conceptually, the convective cloudiness can be expected to be proportional to the mass flux and hence constrained by the energetics of the layer; even if processes like the vertical shear of the horizontal wind may yield different cloud distributions for the same mass flux, just as a function of cloud overlap. Stratiform, or large-scale cloudiness in the cloud layer, is less directly related to the convective fluxes and at times may have its own (somewhat more stratocumulus like) dynamics. This complicates the theoretical development and is why most simple models of cumulus layers do not have any predictive skill in determining the amount of cloudiness within the layer (cf. Betts and Ridgway 1989).

Early models (e.g., Slingo 1980) simply tied the large-scale, or stratiform, cloud amount to the relative humidity in a model layer, such that c = f (U), (8.7)

where U is the large-scale (grid-cell) relative humidity and / is a non-decreasing function between zero and one. Models of the form contained in Equation 8.7 specify implicitly a distribution of the humidity within a grid cell and, through the constancy of the form of /, assume it to be universal. Adaptations of this approach condition the form of / on the cloud regime, for instance by letting it depend on the large-scale vertical velocity or the strength of the cloud-capping inversion (Slingo 1987), or by predicting parameters of a distribution function whose form, and degrees of freedom, are assumed a priori (e.g., Bougeault 1982; Smith 1990; Lewellen and Yoh 1993). Another approach has been to couple the stratiform and convective cloud representations directly (e.g., Sundqvist 1978; Albrecht 1989; Xu and Randall 1996). Doing so introduces different parameter sensitivities, and hence articulates the possibility of different meteorological and microphysical feedbacks. Work on these issues is making increasing use of cloud-resolving or large-eddy simulation models to help decide which strategy is best (e.g., Tompkins 2002), further exemplifying the increasing maturity in the use of models, theory, and data.

The Aerosol

The idea that clouds depend on the atmospheric aerosol, and not just the dynamic and thermodynamic properties of the atmosphere (meteorology), dates back to the earliest cloud studies. In a series of pioneering measurements, Squires and colleagues showed that droplet concentrations in maritime clouds are significantly less than the concentrations characteristic of similar clouds forming in air masses of continental origin (Squires 1956; Squires and Twomey 1966). Squires's (1958) casual observation that shallow marine clouds often rain in less than 30 minutes foreshadowed the mystery of warm rain formation. Subsequent studies, which suggested that anthropogenic perturbations to the aerosol could modulate the propensity of clouds to rain (Warner and Twomey 1967; Warner 1968), stimulated decades of research in weather modification. Twomey's recognition that changes in the aerosol could be important to cloud optical properties (Twomey and Wojciechowski 1969) further motivated research into aerosol-cloud interactions, so that by now they are a major focus of climate research (e.g., Rosenfeld 2006).

Twomey's Calculation

In the absence of other changes, the albedo of clouds with intermediate optical depths (e.g., marine stratocumulus) is especially susceptible to perturbations in cloud drop number concentrations and, by inference, the atmospheric aerosol (Twomey 1974, 1977). Satellite imagery and in-situ measurements of ship tracks similar to those shown in Figure 8.3 have provided observational support for these ideas (Radke et al. 1989), as have closure studies on the cloud system scale (e.g., the ACE-2 measurements described by Brenguier et al. 2000). Attempts to incorporate these processes into physically based models have, however, been frustrated by the poor representation of underlying cloud

Figure 8.3 MODIS image from NASA's Aqua satellite showing ship tracks over the Pacific Ocean, just west of British Columbia on January 21, 2008.

processes in existing climate models, as well as a poor understanding of the pathways through which perturbations to the aerosol manifest themselves on the climate system.

Proliferating Pathways

Since Twomey's pioneering studies, the literature has seen a proliferation of hypothesized indirect aerosol-cloud interactions.2 Perhaps the simplest of this class of effects is that changes in the aerosol, by modifying clear-sky radiative fluxes, may alter the stability of the cloud layer, and hence subsequent cloudiness (e.g., Hansen et al. 1997). Fine-scale modeling studies provide some support for this idea. Ackerman et al. (2000) show that the effect of enhanced absorption of solar radiation by soot in the cloud layer can lead to a reduction in cloudiness to an extent that is not inconsistent with the observational record. Similarly, Feingold et al. (2005) suggest that the reduction in surface fluxes associated with an increase in the aerosol can also reduce cloudiness, thereby counteracting the effects discussed by Twomey. This study, however, begins to hint at the complexity of aerosol-cloud interactions, as the effect of smoke on cloudiness may depend not only on the chemical properties of the aerosol particles (relative role of absorption versus CCN) but also its distribution in the vertical.

Among the more complex ideas are those that connect Squires's interest in aerosol controls on precipitation, with Twomey's focus on cloud optical properties. As an example, Albrecht (1989) argued that changes in the precipitation

This is not to be confused with indirect aerosol-climate interactions, of which the direct aerosol-cloud interaction described by Twomey is a classic example.

rate affected by changes in the aerosol would affect cloud fraction. His hypothesis follows naturally from his cloud model, wherein following Sundqvist (1978), Albrecht couples cloudiness to condensate amount, thereby linking the former to the propensity of clouds to precipitate, as that acts as a sink for the latter. The effects articulated by Albrecht are sometimes called cloud lifetime effects because they hinge on the idea that cloudiness depends on condensate amount, which in turn is limited by precipitation. Notwithstanding that most (if not all) work linking cloud lifetime to precipitation actually connects the lifetime of radar echoes to precipitation (e.g., Saunders 1965; Cruz 1973), investigations of these effects using fine-scale models have, just as often, found countervailing processes. For example, Xue and Feingold (2006) and Xue et al. (2008) have shown that the tendency to produce larger drops leads to more cloudiness, as these drops linger. Only when the rain production becomes very efficient does one see a tendency for cloudiness to decrease with more rain, although in such situations secondary effects, such as the formation of cold pools (which are well known to promote the longevity of cloud systems), may counteract this.

Pincus and Baker (1994) introduced a related but conceptually distinct idea, wherein they proposed that increased precipitation could affect the thickness and hence the radiative properties of stratocumulus by altering cloud dynamic processes. Although the details of the mechanism by which this result was manifest in their model (i.e., condensation heating affected a reduction in surface fluxes which in turn reduced the deepening of the layer by entrainment) is probably incorrect, their work was among the first to articulate a cloud-aerosol connection mediated by dynamic (rather than thermodynamic) processes. Their study also merits attention in that it was specifically formulated for layers of stratocumulus, which has been the dominant focus of large-scale model and satellite observational-based attempts to quantify the radiative effects of the aerosol on the climate system as a whole. The observational record is, however, not definitive, and most insight has been developed on the basis of fine-scale modeling studies. As discussed above, large-eddy simulation of stratocumulus-topped layers support the idea that increased precipitation leads to less entrain-ment (Stevens et al. 1998; Ackerman et al. 2004; Bretherton et al. 2006) and less cloudiness. This is perhaps most dramatically evident in the results of Savic-Jovcic and Stevens (2008), for which precipitating and non-precipitating stratocumulus are represented simply by changing the droplet concentrations from 25 to 200 cm3. The albedo of these simulated clouds is shown in Figure 8.4 and suggests that precipitation can also have a profound effect on cloud morphology, most likely as a result of the regime transitions discussed above, and not unlike what is observed in pockets of open cells (Stevens et al. 2005). These calculations may also help explain the observed tendency of ship tracks to generate closed-cell cloud forms in regions otherwise consisting of open cells (e.g., on the eastern side of Figure 8.3).

Figure 8.4 Visualization of cloud albedo from large domain simulations with (NS, upper left) and without (DS, upper right), as a function of radiative forcing. Lower simulations show the effect of eliminating the radiative forcing, which we use to represent crudely the effect of solar radiative heating, which to a first approximation can be thought to compensate longwave cooling.

Figure 8.4 Visualization of cloud albedo from large domain simulations with (NS, upper left) and without (DS, upper right), as a function of radiative forcing. Lower simulations show the effect of eliminating the radiative forcing, which we use to represent crudely the effect of solar radiative heating, which to a first approximation can be thought to compensate longwave cooling.

But here again, one finds evidence that the response of the system may be more complex. For instance, Sandu et al. (2008) examined the coupling between aerosol impacts and the diurnal cycle of stratocumulus in simulations for which the radiative and surface fluxes are allowed to respond to the evolution of the cloud layer. Their simulations, albeit on a much smaller domain, suggest that precipitation in the pristine cases reduces the amplitude of the diurnal cycle, partially by inhibiting turbulent mixing at night which then mitigates decoupling during the day (Figure 8.5).

Discussion

From the above review, several themes emerge: (a) attribution demands theory; (b) theory expresses constraints, of which we have too few; and (c) models are necessarily selective in both their empirical and theoretical content.

Attribution Demands Theory

Consider c(m, a) where a introduces a vector describing those aspects of the aerosol affecting cloudiness. It follows that

For sake of argument, let us suppose that 8c, 8m, and 8a are all observable;

Buoyancy destruction 0 Buoyancy production of turbulance Polluted case, N = 200 cm-3

Diurnal coupling

Liquid water path ~ 30 gm-

Diurnal coupling

ra 400

Liquid water path ~ 30 gm-

ra 400

Figure 8.5 Time-height cross section showing the evolution of the buoyancy flux in the stratocumulus-topped boundary layer. The top panel shows a case where droplet concentrations are 220 cm~3 and drizzle is weak; the lower panel shows a case with droplet concentrations of 50 cm~3 for which drizzle during the night is strong and induces decoupling.

Figure 8.5 Time-height cross section showing the evolution of the buoyancy flux in the stratocumulus-topped boundary layer. The top panel shows a case where droplet concentrations are 220 cm~3 and drizzle is weak; the lower panel shows a case with droplet concentrations of 50 cm~3 for which drizzle during the night is strong and induces decoupling.

then changes in cloudiness that result from changes in the aerosol (the aerosol effect) can be estimated as:

Clearly, our ability to estimate such effects is limited by our ability to control for the meteorology. Although this point is well known, what tends to be less well appreciated is the fact that controlling for meteorology does not simply require one to bound dm (which tends to be the approach in the existing, largely flawed, literature) but rather dm. It is precisely the factor that gives meaning to the statement that dm is small. In plain terms, the ability to rule out meteorological factors is conditioned on the level of our theoretical understanding, which we have previously argued is primitive.

The difficulty in disentangling meteorological effects on cloudiness from those of the atmospheric aerosol is compounded not only by the poor state of theory, but also because m and a depend on each other in ways that are similarly unclear. Indeed, almost all work that looks for aerosol effects on cloudiness distinct from the pathway articulated by Twomey (1974) explores the idea that m(m0, a), where m0 denotes some primitive or initial meteorological state vector whose effects are independent of the aerosol and can presumably be controlled. In this case, one explores the idea that

dc_ dm

a

dc

dc

dm

a dm0

da

m dm

a da

Likewise, the fact that two air masses have different aerosol properties is almost always an indicator of their differing meteorological histories, which makes it nearly impossible to establish causal relationships between c and a from observations of self-perturbed systems.

Thus, the apparently high susceptibility of cloudiness to the meteorology combined with our poor understanding of exactly how meteorological factors control cloudiness confounds attempts to establish observationally the effect of the atmospheric aerosol on cloudiness.

Theory Expresses Constraints

One little heralded but significant advance in our understanding of the climate system is manifest in the statement "the equilibrium climate sensitivity... is likely to be in the range 2°C to 4.5°C," which is contained in the Fourth Assessment Report of the IPCC (2007). Previous estimates, dating back to the Charney Report (Charney et al. 1979), estimated climate sensitivity between 1.5°C and 4.5°C. The basis for the higher lower-bound (2.0 instead of 1.5) is a better understanding of water vapor feedbacks and reflects largely the acceptance of the argument that small perturbations to the climate system will not affect the distribution of relative humidity. The increasing acceptance of this argument, which dates to Manabe and Wetherald (1967), can be traced to the study by Soden et al. (2005) of upper tropospheric humidity in both satellite observations and general circulation model simulations. Underpinning these results is the idea that the constancy of the distribution of relative humidity in the atmosphere measures the constancy of the atmospheric circulation. This constant circulation hypothesis amounts to saying that the change in the relative humidity, SU, is small, equivalently,

Although Equation 8.11 provides a valuable constraint on water vapor feedbacks, it does little to constrain cloudiness in the lower troposphere. Consider anew the case of stratocumulus initial conditions observed during DYCOMS-II. Above we indicated that a roughly 2% change (from 9.05-9.25 g kg1) in the boundary layer total-water mixing ratio could increase the cloud liquid water path by more than 35% and the cloud albedo by more than five percentage points. As far as low clouds are concerned, an order s change in U can lead to an order one change in cloudiness. More generally if we denote cloud-base height by zb, then for a shallow well-mixed layer, with surface temperature T0,

vdJ RvcpTo

RdTo

is a moisture scale height. For a cloud layer whose depth £ = h - zb ~ 200 m, this implies that

where U denotes here the relative humidity with respect to the saturation humidity at the surface temperature, T0. If SUIU is order s, then is order unity by virtue of the fact that zjh is order 1Is. Because, by Equation 8.5, the optical depth is proportional to C which by Equation 8.6 depends on h2, the sensitivity of cloud amount to U is even more pronounced. This makes the point that, at least for stratocumulus, cloud amount is very sensitive to small changes in the humidity within the boundary layer. This may help explain the relative imprecision of simulations of this important cloud regime.

Precipitation, which is central to some of the hypothesized pathways through which the aerosol affects cloudiness, proves even more challenging. Theoretical studies of the droplet collision efficiency (Klett and Davis 1973) suggest that the droplet collection process starts to be significant only when the biggest droplets reach a radius of the order of 20 ^m, which corresponds to a mean volume or effective radius of the droplet population slightly greater than 10 ^m (for empirical support for this idea, see Gerber 1996; Boers et al. 1998). Increased aerosol particle concentrations, which lead to a decrease of the droplet sizes at a specified liquid water content, can therefore significantly impact precipitation when the cloud depth, and hence the maximum liquid water content, is bounded (e.g., in thin stratocumulus clouds). In deeper convective clouds, however, the effect will only be to raise slightly the level where collection starts to be active. Once the threshold diameter is reached, the collection process is much less sensitive to the number concentration of the cloud droplets (as apparent in bulk parameterizations of the accretion process). Hence near the onset of precipitation, small differences in the depth of the cloud layer can prove decisive in the development of precipitation. Indeed, if cloud-base precipitation scales with h3, as has been suggested by a variety of field studies (Pawlowska and Brenguier 2003; Van Zanten et al. 2005; Comstock et al. 2005; Geoffroy et al. 2008) we would expect the precipitation rate sensitivity to be a factor of three larger than the relative cloud thickness sensitivity (i.e., 5p/p =38h/h, where p denotes cloud-base precipitation).

Model Myopia

Given incomplete theoretical descriptions and insufficient empirical constraints, attempts to evaluate the net effect of environmental changes on cloudiness explore necessarily specific and preconceived pathways. Unexpected behavior can only arise on the resolved scales of the simulation, as on the parameterized scales one is limited to the specific preconceptions built into the model, even more so to the extent that parameterizations of distinct processes interact only through changes to the mean state. This weakness, or even flaw, in the approach to exploring the effect of unresolved processes on the climate as a whole might have been foremost in the minds of the IPCC when they approved the following statement (Denman et al. 2007, p. 566):

The response of the climate system to anthropogenic forcing is expected to be more complex than simple cause and effect relationships would suggest; rather, it could exhibit chaotic behaviour with cascades of effects across the different scales and with the potential for abrupt and perhaps irreversible transitions.

The ultimate clause of this statement suggests that the authors might have had what we call a choleric interpretation in mind; namely, that small changes at the process level can have large consequences that are unanticipated for the system as a whole. Here we prefer to explore a more phlegmatic interpretation and its implications; namely, the idea that large changes at the process level can have small consequences that are unanticipated for the system as a whole.

As a case in point, consider the ideas hypothesized by Albrecht (1989). The standard approach to quantify such effects would be to allow the precipitation efficiency of shallow clouds to depend on the cloud droplet concentration, which in turn is made dependent on the aerosol loading. Then, by comparing simulations with larger and smaller aerosol loadings, one could attempt to quantify the importance of such effects. However, think about the logical structure of such an enterprise: It presumes that an effect on the subgrid scale projects directly onto the resolved scale, which in turn modifies the small scale. If clouds precipitate more readily, will not this information (heating/drying) be most readily evident on the local (cloud) scale, and only gradually work its way through a sequence of scales to the larger scale? Of course, the large-scale model, insofar as its parameterizations are formulated in terms of mean fields (rather than higher-order statistics that incorporate information about the fluctuations and their correlations), is not capable of representing precisely these effects (i.e., those that one would naturally expect to be most predominant). From this perspective, it is not surprising that upon more detailed investigation we find, almost always, that the response of physical systems is much richer and that it is often contrary (e.g., Feingold et al. 1996, 2005; Xue and Feingold 2006; Wood 2007; Xue et al. 2008; Sandu et al. 2008,) to that predicted by the depictions of physical processes studied with the aid of global models or satellite snapshots. Such difficulties are only compounded by bad practice (e.g., the habit of enforcing relationships valid for one scale on entirely other scales or, more specifically, the common practice of applying microphysical concepts designed for single clouds to fields of clouds).

The outcome is that the seduction of using large-scale models to quantify perturbations globally to small-scale physical processes is often greater than the utility; the results can be expected to depend heavily on the (often flawed) conceptual framework underlying particular parameterizations. Moreover, agreement among large-scale models as to the magnitude of a particular effect may just as well represent the poverty of the parameterizations as it does the robustness of an underlying physical principle. In this way, our poor understanding of clouds haunts not only our attempts to estimate aerosol effects on clouds observationally but also numerically.

Outlook

Clearly, these are difficult problems, but science is not afraid of hard problems, particularly important ones. Take, for example, the search for a cure for cancer or the dream of cheap fusion. Both have a long history, and both have seen steady progress. The search for a cancer cure might be a better analogy, because a cloud, like a cancer, finds its expression in many regimes. Given the difficulty of the problem, and the likelihood that progress will be incremental, it appears worthwhile to step back and take stock of which strategies have the best chance of exacting progress.

• Think globally: Processes that simply shift the boundary among regimes are likely to scale with the area across which the regime boundary fluctuates. To the extent that such transitions are localized, these types of effects (changing the precipitation efficiency or decoupling boundary), while locally large, may be expected to be relatively small on a global average. Thus priority should be given to identifying and focusing on those changes most likely to affect patterns of cloudiness on the largest possible scales (e.g., lapse-rate feedbacks or the Twomey effect).

• Look around, not just up (or down): Shallow cumulus clouds are often diffi cult to measure with existing satellites, especially on timescales relevant to their physical evolution. In-situ measurements are sample limited, and radar measurements tend to suffer from greater absorption (because those radars operate at wavelengths where clouds are reflective), thereby limiting their capacity for scanning. However, better use can be made of scanning cloud radars, especially at remote marine sites, to yield a larger empirical database elucidating relationships between low clouds and their environment, which can then be the target of theory.

• Exploit social idiocrasy: Humanity, through its accidental intervention in natural systems, presents the best opportunity to decouple aerosol perturbations from meteorological ones. Well-known examples are ship tracks, but other less exploited ones are fires, which may or may not be set in Santa Ana conditions, or in regions of biomass burnings. Identifying these opportunities of accidental large-scale intervention may be central to advancing the empiricism.

• Replace the fetish for quantification with a curiosity for constraints: By this we mean to suggest that large-scale models might be more fruitfully employed to understand either how the circulations which they do resolve respond to changes made to small-scale physics, or identify robust environmental changes to which clouds should be responding. Such a search for understanding will in the long run better serve the quantitative mandates of our times.

• Worship hierarchy (at least model hierarchies): Here the challenge is to identify processes on small scales and work to investigate their impact through the full range of scales, using a hierarchy of models that can be formally related to one another and which produce signatures that can be tested with data. Those arguments explored in this fashion will, in the end, be most compelling.

• Act locally: Notwithstanding the primitive state of theory, many large-scale models are not even capable of representing the content of our existing understanding. Therefore, acting to ensure that the physical basis of existing models is sound and able to represent key processes and interactions with fidelity should merit reward.

• Theory first! If we can make but only one point, it would be that progress on these and related issues will advance no faster than does the theory. Thus the search for understanding, encapsulating theories of cloud systems capable of explaining the empiricism, should be our pri-ority—not because theory is more important, but rather because it is the crucible in which critical experiments and observations are conducted. Forgetting this compels us to grope forever in the dark.

Acknowledgments

B. Stevens would like to acknowledge UCLA, which supported him during the time when much of this article was prepared. Comments on early drafts of this manuscript by Louise Nuijens, Pier Siebesma, Graham Feingold, Robert Wood, and the editor greatly improved the exposition. We also thank our colleagues for the stimulating discussions during the course of this Forum.

References

Ackerman, A. S., M. P. Kirkpatrick, D. E. Stevens, and O. B. Toon. 2004. The impact of humidity above stratiform clouds on indirect aerosol climate forcing. Nature 432:1014-1017.

Ackerman, A. S., O. B. Toon, D. E. Stevens et al. 2000. Reduction of tropical cloudiness by soot. Science 288:1042-1046.

Albrecht, B. A. 1989. Aerosols, cloud microphysics and fractional cloudiness. Science 245:1227-1230.

Albrecht, B. A., A. K. Betts, W. H. Schubert, and S. K. Cox. 1979. A model of the thermodynamic structure of the trade-wind boundary layer. Part I: Theoretical formulation and sensitivity tests. J. Atmos. Sci. 36:90-98.

Bellon, G., and B. Stevens. 2005. On bulk models of shallow cumulus convection. J. Atmos. Sci. 62:3286-3302.

Betts, A. K., and W. Ridgway. 1989. Climatic equilibrium of the atmospheric convective boundary layer over a tropical ocean. J. Atmos. Sci. 46:2621-2641.

Bjerknes, J. 1938. Saturated-adiabatic ascent of air through dry-adiabatically descending environment. Q. J. Roy. Meteor. Soc. 64:325-330.

Blake, D. 1928. Temperature inversions at San Diego, as deduced from aerographical observations by airplane. Mon. Wea. Rev. 56:221-224.

Boers, R., J. B. Jensen, and P. B. Krummel. 1998. Microphysical and shortwave radiative structure of stratocumulus clouds over the Southern Ocean: Summer results and seasonal differences. Q. J. Roy. Meteor. Soc. 124:151-168.

Bougeault, P. 1982. Cloud ensemble relations based on the gamma probability distribution for the high-order models of the planetary boundary layer. J. Atmos. Sci. 39:2691-2700.

Brenguier, J.-L., P. Y. Chuang, Y. Fouquart et al. 2000. An overview of the ACE-2 CLOUDYCOLUMN closure experiment. Tellus 52B:814-826.

Bretherton, C. 1993. Understanding Albrecht's model of trade cumulus cloud fields. J. Atmos. Sci. 50:2264-2283.

Bretherton, C., P. N. Blossey, and J. Uchida. 2006. Cloud droplet sedimentations, entrainment effi ciency and subtropical stratocumulus albedo. Geophys. Res. Lett. 34:L03813.

Bretherton, C., and S. Park. 2007. A new bulk shallow cumulus-topped boundary layer model. J. Atmos. Sci. 65:2174-2193.

Bretherton, C., and M. C. Wyant. 1997. Moisture transport, lower tropospheric stability, and decoupling of cloud-topped boundary layers. J. Atmos. Sci. 54:148-167.

Burnet, F., and J. Brenguier. 2007. Observational study of the entrainment-mixing process in warm convective clouds. J. Atmos. Sci. 64:1995-2011.

Charlson, R. J., J. E. Lovelock, M. O. Andreae, and S. G. Warren. 1987. Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate. Nature 326: 655-661.

Charney, J., A. Arakawa, D. Baker et al. 1979. Carbon Dioxide and Climate: A Scientific Assessment. Washington, DC: Natl. Research Council.

Chosson, F., J.-L. Brenguier, and L. Schüller. 2007. Entrainment mixing and radiative transfer simulation in boundary layer clouds. J. Atmos. Sci. 64:2670-2682.

Clayton, H. H. 1896. The origin of the stratus-cloud, and some suggested changes in the international methods of cloud-measurement. Nature 55:197-198.

Comstock, K. K., C. S. Bretherton, and S. E. Yuter. 2005. Mesoscale variability and drizzle in southeast Pacific stratocumulus. J. Atmos. Sci. 62:3792-3807.

Cruz, L. A. 1973. Venezuelan rainstorms as seen by radar. J. Appl. Meteor. 12: 119-126.

Deardorff, J. W. 1980. Cloud top entrainment instability. J. Atmos. Sci. 37:131-147.

Denman, K. L., G. Brasseur, A. Chidthaisong et al. 2007. Couplings between changes in the climate system and biogeochemistry. In: Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, ed. Solomon, S., D. Qin, M. Manning et al., pp. 499-588. New York: Cambridge Univ. Press.

Feingold, G., H. Jiang, and J. Y. Harrington. 2005. On smoke suppression of clouds in Amazonia. Geophys. Res. Lett. 32(2):L02804.

Feingold, G., B. Stevens, W. R. Cotton, and A. S. Frisch. 1996. The relationship between drop in-cloud residence time and drizzle production in numerically simulated stratocumulus clouds. J. Atmos. Sci. 53:1108-1122.

Geoffroy, O., I. Sandu, and J. L. Brenguier. 2008. Relationship between drizzle rate, liquid water path and droplet concentration at the scale of a stratocumulus cloud system. Atmos. Chem. Phys. 8:4641-4654.

Gerber, H. 1996. Microphysics of marine stratocumulus clouds with two drizzle modes. J. Atmos. Sci. 53:1649-1662.

Hansen, J., M. Sato, and R. Ruedy. 1997. Radiative forcing and climate response. J. Geophys. Res. 102:6831-6864.

Howard, L. 1802. On the Modification of Clouds. London: J. Taylor.

IPCC. 2007. Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, ed. S. Solomon, D. Qin, M. Manning et al. New York: Cambridge Univ. Press.

Klein, S. A., and D. L. Hartmann. 1993. The seasonal cycle of low stratiform clouds. J. Climate 6:1587-1606.

Klein, S. A., D. L. Hartmann, and J. R. Norris. 1995. On the relationships among low-cloud structure, sea surface temperature, and atmospheric circulation in the summertime northeast Pacific. J. Climate 8:1140-1155.

Klett, J. D., and M. Davis. 1973. Theoretical collision efficiencies of cloud droplets at small Reynolds numbers. J. Atmos. Sci. 30:107-117.

Lamarck, J.-B. 1802. Annuaire Météorologique, vol. 3, pp. 151-166. Paris: Dentu.

Latham, J., and M. H. Smith. 1990. Effect of global warming on wind-dependent aerosol generation at the ocean surface. Nature 347:372-373.

Lewellen, D. C., and W. Lewellen. 2002. Entrainment and decoupling relations for cloudy boundary layers. J. Atmos. Sci. 59:2966-2986.

Lewellen, W. S., and S. Yoh. 1993. Binormal model of ensemble partial cloudiness. J. Atmos. Sci. 50:1228-1237.

Lilly, D. K. 1968. Models of cloud topped mixed layers under a strong inversion. Q. J. Roy. Meteor. Soc. 94:292-309.

Lock, A. P., and M. K. MacVean. 1999. A parametrization of entrainment driven by surface heating and cloud-top cooling. Q. J. Roy. Meteor. Soc. 125:271-299.

Manabe, S., and R. T. Wetherald. 1967. Thermal equilibrium of the atmosphere with a given distribution of relative humidity. J. Atmos. Sci. 24:241-259.

Miller, R. L. 1997. Tropical thermostats and low cloud cover. J. Climate 10:409-440.

Moeng, C.-H., P. P. Sullivan, and B. Stevens. 1999. Including radiative effects in an entrainment-rate formula for buoyancy driven PBLs. J. Atmos. Sci. 56:1031-1049.

Neggers, R. A., A. P. Siebesma, and G. Lenderink. 2004. An evaluation of mass flux closures for diurnal cycles of shallow cumulus. Mon. Wea. Rev. 132:2525-2538.

Neggers, R. A., B. Stevens, and J. D. Neelin. 2007. Variance scaling in shallow cumulus topped mixed layers. Q. J. Roy. Meteor. Soc. 133, 1629-1641.

Nigam, S. 1997. The annual warm to cold phase transition in the eastern equatorial Pacific: Diagnosis of the role of stratus cloud-top cooling. J. Climate 10:2447-2467.

Paltridge, G. W. 1980. Cloud-radiation feedback to climate. Q. J. Roy. Meteor. Soc. 106:895-899.

Pawlowska, H., and J.-L. Brenguier. 2003. An observational study of drizzle formation in stratocumulus clouds for general circulation model (GCM) parameterization. J. Geophys. Res. 33:L19810.

Philander, S. G. H., D. Gu, D. Halpern et al. 1996. Why the ITCZ is mostly north of the equator. J. Climate 9:2958-2972.

Pincus, R., and M. B. Baker. 1994. Effect of precipitation on the albedo susceptibility of marine boundary layer clouds. Nature 372:250-252.

Pincus, R., M. B. Baker, and C. S. Bretherton. 1997. What controls stratocumulus radiative properties? Lagrangian observations of cloud evolution. J. Atmos. Sci. 54: 2215-2236.

Radke, L. F., J. A. Coakley, Jr., and M. D. King. 1989. Direct and remote sensing observations on the effects of ships on clouds. Science 246:1146-1149.

Randall, D. A. 1980. Conditional instability of the first kind upside-down. J. Atmos. Sci. 37:125-130.

Rosenfeld, D. 2006. Aerosols, clouds, and climate. Science 312:1323-1324.

Sandu, I., J.-L. Brenguier, and O. Geoffroy. 2008. Aerosol impacts on the diurnal cycle of marine stratocumulus. J. Atmos. Sci. 65(8):2705.

Saunders, P. M. 1965. Some characteristics of tropical marine showers. J. Atmos. Sci. 22:167-175.

Savic-Jovcic, V., and B. Stevens. 2008. The structure and mesoscale organization of precipitating stratocumulus. J. Atmos. Sci. 65:1587-1605.

Scorer, R. 1972. Clouds of the World: A Complete Colour Encyclopedia. Melbourne: Lothian Publ.

Siebesma, A. P. 1998. Shallow convection. In: Buoyant Convection in Geophysical Flows, ed. E. J. Plate, E. E. Fedorovich, D. X. Viegas, and J. C. Wyngaard, vol. 513, pp. 441-486. Dordrecht: Kluwer Academic Publ.

Slingo, J. 1980. Cloud parameterization scheme derived from GATE data for use with a numerical model. Q. J. Roy. Meteor. Soc. 106:747-770.

Slingo, J. 1987. The development and verification of a cloud prediction scheme for the ECMWF model. Q. J. Roy. Meteor. Soc. 113:899-927.

Smith, R. N. B. 1990. A scheme for predicting layer clouds and their water content in a GCM. Q. J. Roy. Meteor. Soc. 116:435-460.

Soden, B. J., D. L. Jackson, V. Ramaswamy, M. D. Schwarzkopf, and X. Huang. 2005. The radiative signature of upper tropospheric moistening. Science 310:841-844.

Squires, P. 1956. The microstructure of cumuli in maritime and continental air. Tellus 8:443-444.

Squires, P. 1958. Penetrative downdraughts in cumulli. Tellus 10:381-385.

Squires, P., and S. Twomey. 1966. A comparison of cloud nucleus measurements over central North America and the Caribbean Sea. J. Atmos. Sci. 23:401-404.

Stevens, B. 2000. Cloud transitions and decoupling in shear-free stratocumulus-topped boundary layers. Geophys. Res. Lett. 27:2557-2560.

Stevens, B. 2005. Atmospheric moist convection. Ann. Rev. Earth Planet. Sci. 33: 605-643.

Stevens, B. 2006. Bulk boundary layer concepts for simple models of tropical dynamics. Theor. Comp. FluidDyn. 20:379-304.

Stevens, B. 2007. On the growth of layers of non-precipitating cumulus convection. J. Atmos. Sci. 64:2916-2931.

Stevens, B., W. R. Cotton, G. Feingold, and C.-H. Moeng. 1998. Large-eddy simulations of strongly precipitating, shallow, stratocumulus-topped boundary layers. J. Atmos. Sci. 55:3616-3638.

Stevens, B., and A. Seifert. 2008. On the sensitivity of simulations of shallow cumulus convection to their microphysical representation. J. Meteorol. Soc., in press.

Stevens, B., G. Vali, K. Comstock et al. 2005. Pockets of open cells and drizzle in marine stratocumulus. Bull. Amer. Meteor. Soc. 86:51-57.

Sundqvist, H. 1978. A parameterization scheme for non-convective condensation including prediction of cloud water content. Q. J. Roy. Meteor. Soc. 104:677-690.

Tompkins, A. M. 2002. A prognostic parameterization for the subgrid-scale variability of water vapor and clouds in large-scale models and its use to diagnose cloud cover. J. Atmos. Sci. 59:1917-1942.

Turton, J. D., and S. Nicholls. 1987. A study of the diurnal variation of stratocumulus using a multiple mixed layer model. Q. J. Roy. Meteor. Soc. 113:969-1009.

Twomey, S. A. 1974. Pollution and the planetary albedo. Atmos. Environ. 8:12511256.

Twomey, S. A. 1977. The influence of pollution on the shortwave albedo of clouds. J. Atmos. Sci. 34:1149-1152.

Twomey,

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