How Much Does A Cloud Droplet Increase In Size To Become A Raindrop

Deject Dynamics

Robert A. Houze , in International Geophysics, 2014

3.one.3 Fallspeeds of Drops

Deject aerosol are subject area to downward gravitational forcefulness, which tin can atomic number 82 to their fallout. Withal, every bit a particle is accelerated downward by gravity, its motility is increasingly resisted past frictional force. Its final speed is called the terminal fallspeed Five. For drops of water in air, V is a function of the drop radius R. Cloud droplets, which are <   100   μm (Department 3.1, Figure 3.1), accept very low, barely detectable fallspeeds, <   one   one thousand   s^{−   1}. Cloud aerosol are the pocket-sized particles that course all the familiar visible nonprecipitating clouds described in Affiliate one (stratus, stratocumulus, cumulus, altostratus, altocumulus, and cirriform clouds). Although their fallspeeds are slight, cloud droplets do undergo very slow sedimentation, and this tiresome sedimentation of cloud droplets must be accounted for in accurately describing certain types of clouds. ¹² Precipitation particles are those that fall more rapidly, generally at speeds >   1   thousand   s^{−   ane}. The smallest liquid precipitation particles are chosen drizzle, and as noted in Department 3.1, Figure three.one, are generally considered to be ~   fifty to a few hundred microns in diameter in radius. Drops greater than a few hundred microns in dimension are called rain. Drizzle and raindrops take terminal fallspeeds that increase monotonically with increasing driblet radius. We will represent this function every bit V(R). For drops <   500   μm in radius, V increases approximately linearly with increasing drop radius (Figure three.3). For larger drops, V(R) increases at a slower rate (Figure 3.iv), becoming constant at a radius of about 3   mm. This asymptotic behavior is associated with the fact that a driblet becomes increasingly flattened, into the shape of a horizontally oriented disc, at larger sizes (see Figure 4.v).

Figure iii.3. Fall velocity of h2o drops &lt;   500   μm in radius for diverse atmospheric conditions.

From Beard and Pruppacher (1969). Republished with permission of the American Meteorological Guild.

Effigy three.iv. Fall velocity of water drops &gt;   500   μm in radius.

From Bristles (1976). Republished with permission of the American Meteorological Society.

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Deject drib nucleation

Ari Laaksonen , Jussi Malila , in Nucleation of Water, 2022

9.1 Köhler theory

Deject aerosol nucleate generally at very low supersaturations, on the lodge of 0.i–ane%. This is due to the fact that there are usually plenty of condensation nuclei available, and some of them sufficiently hygroscopic to initiate deject drib germination almost immediately every bit the air becomes supersaturated with water vapor. In most cases, cloud drop nucleation is a deterministic rather than a stochastic process, and therefore the term activation is often used in identify of nucleation. ^one

The theory of cloud droplet nucleation was adult in the 1920s by the Swedish scientist Hilding Köhler [ii,3]. The starting point of the theory is that cloud drops are formed by hygroscopic aerosols such as salt particles, which go deliquescent (i.e. take up water vapor and dissolve into aqueous solution droplets) already at subsaturation. For example, the deliquescence point of sodium chloride particles is 75% RH. The basis of Köhler theory is the consideration of the equilibrium vapor pressure of water to a higher place small solution aerosol. The equilibrium vapor pressure of water (denoted with subscript w) higher up aqueous solution of substance s is given past

(9.i) $P_{\mathrm{eastward}}({\mathrm{10}}_{\mathrm{due\; west}})=a_w{P}_{\mathrm{eastward}}=f_w{x}_{\mathrm{west}}{P}_e,$

where $a_w$ denotes water activity, $P_e$ is equilibrium vapor force per unit area of pure water, and the action coefficient $f_{\mathrm{westward}}$ of water depends on temperature and the concentration of the solution. Cloud drops course above saturation, which in most cases guarantees that the solution droplets are very dilute, permitting the use of Raoult'due south law $f_{\mathrm{westward}}=\mathrm{ane}$ [4]. The dissolved substance thus causes water vapor pressure to be depressed by a gene equal to the mole fraction of water. Substances that dissociate in water depress the vapor pressure more than efficiently, as ${\mathrm{10}}_w={\mathrm{northward}}_w/(n_w+i{n}_s)$ , where i is the van't Hoff factor, which effectively equals the number of ions that the molecule southward dissolves into in a dilute solution.

Opposite to the Raoult consequence, the curvature of a pocket-size aqueous droplet causes an increase of the saturation vapor pressure of water on its surface that can exist described using the Kelvin equation

(9.2) $P_e(R)=\exp \left(\frac{2\gamma (x_w)v_w(x_w)}{k_{\mathrm{B}}TR}\right).$

Hither, the surface tension and the molecular volume of water depend on the mole fraction, simply in dilute solutions they can be approximated by the pure h2o values. Combining Eqs. (ix.i) and (ix.2), we can write the saturation ratio of h2o above an aqueous droplet that is in equilibrium with humid air every bit

(9.3) $\mathrm{Southward}=\frac{P_e(x_w,R)}{P_e}=f_w{x}_w\exp \left(\frac{2\gamma (x_w){\mathrm{five}}_w(x_{\mathrm{west}})}{k_{\mathrm{B}}TR}\right)\approx \frac{n_{\mathrm{west}}}{n_{\mathrm{west}}+i{\mathrm{due\; north}}_{\mathrm{south}}}\exp \left(\frac{\mathrm{two}{\gamma }_{\mathrm{due\; west}}{v}_w}{m_{\mathrm{B}}TR}\right).$

In the final, estimate equation, the solution surface tension and fractional tooth book have been replaced by those of pure water, based on the fact that at supersaturation the droplet becomes very dilute.

To simplify Eq. (nine.3) further, we note that in dilute solutions $i{n}_{\mathrm{southward}}\ll n_{\mathrm{due\; west}}$ , and thus ${\mathrm{northward}}_{\mathrm{west}}/({\mathrm{northward}}_w+i{n}_s)\approx 1-i{n}_{\mathrm{southward}}/{\mathrm{due\; north}}_{\mathrm{westward}}$ . The number of water molecules in the droplet is $n_w\approx \mathrm{iv}\pi R^{\mathrm{iii}}/3v_{\mathrm{due\; west}}$ . Cogent $b=3i{n}_s{\mathrm{five}}_{\mathrm{due\; west}}/(\mathrm{iv}\pi )$ , we accept

(9.4) ${\mathrm{10}}_w\approx 1-\frac{b}{R^3}.$

We next denote $a=\mathrm{two}{\gamma }_w{5}_{\mathrm{westward}}/(k_{\mathrm{B}}T)$ , and write the Kelvin term as a series: $\exp (a/R)\approx 1+a/R+\dots$ . Because the magnitude of a is on the lodge of 1.two nm, and the radius of the droplet is 100 nm or more, the higher lodge terms of the series can exist dropped:

(nine.five) $\exp \left(\frac{a}{R}\right)\approx 1+\frac{a}{R}.$

Combining Eqs. (nine.4) and (nine.5), nosotros obtain an oft used, simplified grade of the Köhler equation:

(9.half-dozen) $S\approx 1+\frac{a}{R}-\frac{b}{R^{\mathrm{three}}}.$

Note that the cross term $ab/R^2$ has been dropped from the higher up equation on the ground that information technology is small compared to the other terms.

Fig. ix.one shows a "Köhler curve", saturation ratio as a office of droplet diameter, for 100 nm (dry diameter) ammonium sulfate particles calculated using Eq. (9.iii). Also shown are curves calculated with the Raoult and Kelvin terms separately. An aqueous ammonium sulfate droplet in humid air that is out of equilibrium will either have up more h2o or evaporate h2o until it is in equilibrium, i.e. at the Köhler bend. Out-of-equilibrium droplets below the bend will evaporate, and those to a higher place the curve will have upward more water as indicated by the arrows. The maximum of the Köhler curve indicates the signal of nucleation; droplets at the maximum (or to the right of the descending part of the curve) grow by unlimited condensation and become deject drops. A droplet at the Köhler maximum is said to have a critical radius $R^{⁎}$ and the supersaturation at the maximum is termed critical supersaturation ${\mathrm{South}}^{⁎}$ . These can be obtained analytically past setting the derivative of Eq. (nine.6) to nothing; thus

Effigy 9.1. Köhler bend is a sum of the Raoult and Kelvin curves. Droplets that are out of equilibrium (below the bend or to the left from it) will either shrink or grow until they are at the Köhler curve. When a droplet reaches the maximum of the bend, information technology starts growing rapidly due to condensation of water vapor.

(ix.7) $R^{⁎}=\sqrt{\frac{3b}{a}},$

(9.8) $S^{⁎}=\mathrm{one}+\sqrt{\frac{4a^3}{27b}}.$

Fig. 9.two shows the outcome of dry out particle size on the Köhler curves. In the atmosphere, aerosol particles are of of varying sizes and compositions, and therefore their equilibrium curves also tend to show large variation. A cloud is formed when relative humidity increases for some reason, east.yard. due to adiabatic expansion of a rising air bundle. Equally the RH exceeds 100%, those particles with the lowest critical supersaturations nucleate first to form deject drops. Every bit the supersaturation continues increasing, particles with increasingly high ${\mathrm{Due\; south}}^{⁎}$ nucleate, until the vapor depletion rate due to condensation to nucleated droplets is then high that relative humidity ceases to increase (release of latent heat of condensation likewise influences the cessation as it tends to warm the air bundle).

Figure 9.two. Köhler curves for dissimilar sized ammonium sulfate particles. D _d = dry bore.

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SATELLITES AND SATELLITE REMOTE SENSING | Precipitation

G. Liu , in Encyclopedia of Atmospheric Sciences (Second Edition), 2015

Infrared Effulgence Temperature

Cloud droplets are very absorptive in the thermal infrared spectrum. A consequence of this high absorption is that the cloud superlative may be viewed as the surface of a blackbody having a temperature the same equally the air temperature at the level of the deject top. Therefore, the infrared brightness temperature indicates the cloud top temperature except for in the instance of optically thin cirrus clouds. At least in the tropics, near rainfalls are associated with well-developed convective systems that have tall deject tops. Statistically, colder infrared brightness temperatures ofttimes indicate higher rainfall rates at the surface. Yet, shallow convections with warm cloud tops do sometimes produce substantial rainfall. On the other mitt, nonprecipitating cirrus clouds do not produce rainfall, although they also have cold cloud top temperatures. Problems associated with the infrared sensing of rainfall are more serious in the midlatitudes, where almost precipitation is produced by frontal stratiform clouds, for which cloud top temperature and atmospheric precipitation are less correlated than for deep tropical convections.

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AEROSOLS | Aerosol–Cloud Interactions and Their Radiative Forcing

U. Lohmann , in Encyclopedia of Atmospheric Sciences (Second Edition), 2015

Cloud Droplet Formation

Cloud droplet germination is not a nucleation process because cloud aerosol form on soluble or hydrophilic aerosol particles, which already take taken upwardly large amounts of water below 100% RH. Cloud formation is best described by the Koehler equation:

[i] ${\mathit{east}}^{\ast }\left(\text{r}\right)/{\mathit{e}}_{\text{southward}}\left(\infty \right)=\text{S}=1+\mathit{a}/\mathit{r}-\mathit{b}/{\mathit{r}}^3$

The Koehler equation describes the ratio between the equilibrium vapor pressure over a solution droplet e∗(r) with radius r to the saturation vapor pressure level over a plane surface of h2o east _south(∞) with a and b as described beneath. due east _s(∞) depends exponentially on temperature (T) as described by the Clausius–Clayperon equation:

[two] $d{e}_{\text{s}}/dT={\mathit{L}}_{\text{5}}{\mathit{e}}_{\text{south}}/\left({\mathit{R}}_{\text{v}}{\mathit{T}}^2\right)$

where R _v is the specific gas constant of water vapor (R _v = 461.5 J G^−one kg⁻¹) and 50 _v is the latent heat of vaporization. The Koehler equation has two contributions, the increase in vapor pressure that is associated with the germination of the surface (Kelvin equation) and the decrease in vapor pressure due to soluble substances in water (Raoult'south law). The Kelvin equation is given every bit:

[3] ${\mathit{e}}_{\text{south}}\left(\mathit{r}\right)/{\mathit{e}}_{\text{due south}}\left(\infty \right)=\mathit{S}=\exp \left(2\mathit{\sigma }/\left(\mathit{r}{\mathit{\rho }}_{\text{w}}{\mathit{R}}_{\text{five}}\mathit{T}\right)\right)$

where σ is the surface tension between water and air. At 273.2 Thou, σ is 0.0756 N m⁻¹ and ρ _w, the water density, is 1000 kg m⁻³. The terms of the Kelvin equation other than the radius of the droplet are summarized in term a of the Koehler equation: a = twoσ/(r ρ _w R ₅ T). Kelvin's equation describes that the equilibrium vapor pressure is larger over a droplet with radius r than over a plane or bulk surface. It inversely relates the critical radius for droplet formation to the necessary supersaturation. At S = 1.01, a typical value found in the temper, the critical radius of the droplet needs to exist 0.12 μm. This can never occur past chance every bit it involves 0.25 million water vapor molecules. A more reasonable number of 20 h2o vapor molecules forming a cluster with a critical radius of 0.5 nm requires a saturation ratio Southward of x, i.east., an RH of thousand%, which does non be in Earth's temper.

The second contributor to the Koehler equation, Raoult'south law, is given for a airplane surface of water equally follows:

[4] ${\mathit{e}}^{\ast }\left(\infty \right)/{\mathit{e}}_{\text{s}}\left(\infty \right)={\mathit{north}}_0/(\mathit{north}+{\mathit{n}}_0)$

where e∗ is the equilibrium vapor pressure level over a solution consisting of due north ₀ water molecules and n solute molecules. This equation shows that if the vapor force per unit area of the solute is less than that of water and if the total number of molecules remains constant, the vapor force per unit area over the solution is reduced in proportion to the amount of solute present. The vapor pressure level reduction arises from solute molecules at the surface that limit the substitution of water molecules between the water surface and the overlying vapor to those places where water molecules occupy the surface. For dilute solutions and applied to droplets of size r, Raoult'due south law can be approximated as:

[5] ${\mathit{e}}^{\ast }\left(\mathit{r}\right)/{\mathit{e}}_{\text{s}}\left(r\right)=\mathrm{one}-\mathit{b}/{\mathit{r}}^3,\text{where}\mathit{b}=3\mathit{i}{\mathit{Thousand}}_{\text{s}}{\mathit{grand}}_{\text{w}}/\left(\mathrm{iv}\mathrm{\pi }{\mathit{m}}_{\mathrm{s}}{\mathit{\rho }}_{\mathrm{w}}\right)$

The contest between Kelvin'due south equation and Raoult's law is summarized in the Koehler equation. Figure 3 displays the Koehler curves, i.eastward., the equilibrium vapor pressure as a function of the droplet radius, for droplets containing different amounts of salt. Note that every salt particle with a dry radius r _d has its own individual Koehler curve. Because Raoult's law applies to the droplet volume, it dominates over the Kelvin effect, that depends on droplet size, at modest radii and lowers the equilibrium vapor pressure at small radii below Southward = 1. The Kelvin upshot is negligible for droplets larger than ane μm where all curves arroyo S = 1.

Figure 3. Koehler curves for NaCl (solid lines) and (NH₄)_twoSO_four (dashed lines) for droplets originating from common salt particles with different dry radii r _d. In improver, the Kelvin bend (mutual for all particles) is shown in olive and Raoult's police for (NH₄)_iiAnd then_iv as dot-dashed lines.

The peak in the saturation ratio called critical saturation ratio (South _c) and the corresponding critical radius (r _c) can be obtained by differentiating the Koehler equation with respect to r and setting the derivative to 0:

[vi] ${\mathit{r}}_{\text{c}}={\left(3b/\mathit{a}\right)}^{1/2};{\mathit{S}}_{\text{c}}=1+{\left(4{\mathit{a}}^{\mathrm{three}}/27\mathit{b}\right)}^{1/\mathrm{ii}}$

S _c of a specific Koehler curve is the minimum saturation ratio that is required for the corresponding solution droplet to grow to cloud droplet size. Theoretically, information technology could grow even larger, but the growth becomes increasingly slower the larger the droplet and more efficient growth mechanisms such as growth by collision-coalescence with other aerosol volition have over (come across Clouds and Fog: Cloud Microphysics). If the droplet has grown to r >r _c, information technology is called an activated droplet. All droplets that have a critical saturation ratio S _c <S, where S is the supersaturation reached in the ambience air, tin can thus exist activated. If S <Southward _c, a deliquesced salt particle tin but abound to the radius at which the Koehler curve takes the value S.

The Koehler bend represents equilibrium conditions and therefore has some limitations of its applicability. Big particles have large equilibrium radii and may have insufficient time to abound to their equilibrium size in clouds that do not final long, such every bit convective clouds. Figure 3 shows that the higher S, the more and the smaller aerosols can exist activated. It as well shows that the largest aerosols are the best CCN because they crave the smallest supersaturations to be activated. However, there are only few of them available. Also, because the diffusional growth depends inversely on the size of the droplets with the smallest droplets growing the fastest (come across Clouds and Fog: Cloud Microphysics), the big aerosols may not reach their critical size by diffusional growth. On the other hand, the smallest aerosols crave college supersaturations to activate than exist in the atmosphere. Thus, these aerosols are not efficient for cloud formation either. Mainly accumulation and coarse mode, and partly Aitken mode aerosols act as CCN and go activated into cloud droplets.

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Cloud MICROPHYSICS

D. Lamb , in Encyclopedia of Atmospheric Sciences, 2003

Growth by Condensation

Private cloud droplets that are actively growing in an updraft deed in outcome equally tiny sinks of water vapor. During internet condensation, the concentration of vapor immediately over each droplet surface (within a few mean free paths of the air molecules) is reduced relative to the boilerplate vapor concentration far from the droplet. The radial gradients of vapor concentration thus established give rise to a net flux of vapor molecules toward the drop by the procedure of molecular diffusion. Even though the water molecules must also exist transported across the liquid–vapor interface, information technology is the vapor improvidence step that tends to limit the mass transport under most deject conditions. Nevertheless, the change of phase from vapor to liquid results in a slight warming of the droplet owing to the added enthalpy of condensation, energy that must be conducted through the air and abroad from the droplet. This free energy consequence of condensation raises the equilibrium vapor pressure of the liquid and imposes an additional limitation to the growth rate.

The theory that simultaneously accounts for the exchanges of vapor and free energy between a growing droplet and the surrounding air was first developed by Maxwell in the nineteenth century. The resulting expression for the linear growth rate is

[6] $\frac{\text{d}r}{\text{d}t}=K(\mathrm{due\; south}-s_{\text{1000}})\frac{\mathrm{ane}}{r}$

where Thou is a growth parameter that varies slowly with the temperature and force per unit area. Note that a droplet grows merely to the extent that the ambience supersaturation, south, exceeds the equilibrium value, s _K. Equally r becomes large, s _K→0 and the growth rate dr/dt∝1/r, indicating that the aerosol grow relatively more slowly as they go bigger. Calculations based on eqn [6] show that individual aerosol experiencing a supersaturation of ane% require hundreds of seconds to grow to radii much beyond x   μm.

A population of growing cloud aerosol derives its water from a common supply, namely the vapor initially carried with the ascent air parcel. Competition for the available vapor among all the droplets sets up a potent interplay between the condensation kinetics and the vapor field. Results from numerical computations of droplet growth within an adiabatic parcel are shown in Figure five for the case of a relatively clean maritime environment. The supersaturation (dashed curve) builds up until vapor is removed at a rate comparable to the rate that excess vapor is generated due to adiabatic ascension. Once the maximum in the ambience supersaturation is reached, no new particles can be activated, so the initial number concentration of deject droplets is established low in the cloud. The shut packing of the curves on the correct-hand side of Figure 5 indicates that the droplets tend to agglomeration together in radius. This narrowing of the drop spectrum is an inherent belongings of adiabatic condensation and poses a hindrance to the formation of precipitation.

Figure v. Results from numerical computations of droplet growth in an air parcel ascending adiabatically at the charge per unit of 15   cm   southward^−one. The total concentration of particles in the population is 50   cm⁻³. Solid curves: droplet radii (lower calibration) at diverse heights above deject base for droplets each containing the indicated number of moles of nonvolatile solute. Dashed curve: the ambient supersaturation (upper calibration). (Based on calculations of Mordy (1959); figure reproduced with permission from Lamb D (2000) Rain production in convective systems. In Doswell CA. (ed.) Severe Local Convection. Boston: American Meteorological Club.)

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CLOUDS AND FOG | Cloud Microphysics

D. Lamb , in Encyclopedia of Atmospheric Sciences (Second Edition), 2015

Growth by Condensation

Each cloud droplet acts equally a tiny sink of h2o vapor during active growth in an updraft. Every bit condensation gain, the concentration of vapor immediately over each droplet surface (inside a few mean complimentary paths of the air molecules) is reduced relative to the average vapor concentration far from the droplet. The radial gradients of vapor concentration thus established requite rise to a net flux of vapor molecules toward the drop past the procedure of molecular diffusion. The h2o molecules must besides be transported across the liquid–vapor interface, only it is the vapor diffusion step that tends to limit the mass transport under almost deject conditions. Nevertheless, the change of stage from vapor to liquid at the surface results in a slight warming of the droplet due to the added enthalpy of condensation, energy that must be conducted abroad from the droplet through the air. This free energy consequence of condensation raises the equilibrium vapor pressure level of the liquid and imposes an additional limitation to the growth rate.

The theory that simultaneously accounts for the exchanges of vapor and energy betwixt a growing droplet and the surrounding air was first adult fully past Maxwell in the nineteenth century. The resulting expression for the linear growth rate is

[7] $\frac{dr}{dt}=G\left(s-{\mathrm{southward}}_{\text{K}}\right)\frac{1}{r}$

where Thousand is a growth parameter that acts equally an effective diffusivity and varies slowly with the temperature and pressure. Annotation that a droplet grows only to the extent that the ambience supersaturation (south) exceeds the equilibrium value (due south _K). As r becomes large, $s_{\text{K}}\to 0$ and the growth rate $dr/dt\propto 1/r$ , indicating that the droplets grow relatively more than slowly as they become larger.

A population of growing deject aerosol obtains its h2o from a common supply, namely the vapor initially carried with the rising air parcel. Competition for the available vapor among all the aerosol sets upwards a strong interplay between the condensation kinetics, the aerosol population, and the vapor field. Results from numerical computations of droplet growth within an air packet rise adiabatically are shown in Figure five for the case of a relatively clean maritime surround. The ambience supersaturation (dashed bend) builds up in the ascension parcel because of the subtract in temperature with pinnacle and the consequent lowering of equilibrium vapor pressure level. Droplets particles with relatively large solute contents, those having low critical supersaturations, activate and get cloud droplets that abound rapidly (seen in Effigy five by the sudden changes in slope). Condensation onto the activated droplets removes water vapor from the air, so the supersaturation increases progressively more than slowly as the aerosol grow and deplete the vapor. At some signal, usually inside several meters higher up cloud base of operations, the rate of vapor removal exceeds the rate at which excess vapor is generated, and the supersaturation then steadily decreases. The maximum supersaturation, s _{ma x}, attained in the cloud is influenced strongly by the affluence of droplets particles and becomes an of import determinant of the microstructure of warm clouds. Once the maximum in the supersaturation is reached, no new particles can exist activated. The initial number concentration of deject droplets is thus established low in the deject and reflects the properties of the droplets population present at the fourth dimension of deject germination.

Figure 5. Results from numerical calculations of activation and growth of droplets in an air parcel ascending adiabatically at the rate of fifteen cm southward^−one. The total concentration of particles is 50 cm⁻³. Solid curves: droplet radii (lower scale) at various heights in a higher place deject base of operations for droplets containing the indicated solute contents (number of moles of nonvolatile solute per particle). Dashed curve: ambient supersaturation (upper calibration).

Adapted from Mordy, West., 1959. Computations of the growth by condensation of a population of cloud droplets. Tellus 11, sixteen–44.

The interaction between the aerosol population and the vapor field can be understood with the help of Figure half dozen (also available equally a sequence of PowerPoint slides in the supplementary fabric). Early in the development of supersaturation, say at betoken 1 in panel (a), the just particles that can activate are those with small disquisitional supersaturations (respective point in panel (b)). Such particles are relatively large so have large solute contents. These initially activated particles typically reside in the tail of the aerosol size distribution ('Number' curve in panel (c)) and so represent but a small fraction of the total droplets population. Nonetheless, these are the largest particles and so represent a meaning fraction of the total solute incorporated into the cloud h2o (run across 'Book' curve in panel (c)).

Figure 6. Graphical relationships between the evolution of ambience supersaturation in an adiabatically ascending package (panel a), the disquisitional supersaturations of private aerosol particles (b), and the size distributions of the aerosol number and book concentrations (c). The circled numbers prove specific values of each variable at selected supersaturations; the shaded regions place portions pertaining to the activated droplets afterward the supersaturation has reached its maximum value (s _{ma 10}).

Every bit the supersaturation continues to increase (e.g., point 2 in panel (a) of Figure six), progressively smaller particles (those with increasing disquisitional supersaturations; panel (b)) are activated and added to the population of droplets. The greater the number of growing aerosol, the greater are the opportunities for vapor to be consumed. Once the maximum supersaturation has been reached (point 3 in panel (a)), all the particles that can be will take been activated. The limiting diameter of the dry aerosol particles activated, those with critical supersaturations equal to or less than the maximum ambient supersaturation, is chosen the activation bore (D _act). With additional uplift of the cloud parcel, the supersaturation decreases (e.g., betoken 4) below the critical supersaturations of the remaining particles in the aerosol population. The inactivated set of particles is the haze droplets and the activated set up, the cloud droplets. As long as the air continues to ascent, the supersaturation stays positive, and the activated aerosol continue to abound.

The close packing of the curves almost the summit on the correct-hand side of Effigy 5 is consequent with eqn [7] and indicates that the droplets tend to bunch together in radius. This narrowing of the drop spectrum is an inherent property of adiabatic condensation and poses a hindrance to the germination of precipitation. Detailed calculations prove that private droplets experiencing a supersaturation of 1% require hundreds of seconds to abound past condensation to radii much beyond 10 μm. Significant additional growth depends on collisions between particles.

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AEROSOLS | Soot

P. Chylek , ... R. Pinnick , in Encyclopedia of Atmospheric Sciences (2d Edition), 2015

Soot and Absorption of Solar Radiation by Clouds

Soot within cloud droplets will once more increase the droplets' absorption of electromagnetic radiation and subtract their single scattering albedo. This leads to an increased absorption of solar radiation inside a cloud layer, to heating, and to a possible increased rate of evaporation of cloud aerosol.

A small amount of soot, of the order of 10⁻⁹ to ten⁻⁷ by volume, in cloud droplets has little effect on deject optical properties. Yet, soot in highly polluted regions, produced past industrial activities or biomass burning, can touch on cloud absorption. Soot in deject water concentration of the guild of 10⁻⁶ and above will increase cloud absorption significantly. The effect of soot volume fraction, varying from 10⁻⁷ to 10^−iv, on the reflectivity of cloud is quite pronounced at visible wavelengths, as shown in Effigy v. Near accumulation-size soot particles tin can propagate up to several thousands miles away from their sources without a meaning decrease in soot concentration. Thus, for example, an extensive biomass burning can affect cloud absorption and regional climate in regions several hundred miles abroad from source.

Effigy v. Cloud reflectivity as a part of radiation wavelength for an optically thick (semi-infinite) cumulus cloud. The cases of pure water cloud droplets and for varying soot volume fractions in cloud aerosol are shown.

Adapted with permission from Chylek P, Ramaswamy 5, and Cheng RJ (1984). Outcome of graphitic carbon on the albedo of clouds. Journal of the Atmospheric Sciences 41: 3076–3084. A significant reduction of deject reflectivity at visible and near-infrared wavelengths is obtained for soot volume fractions at and above 10⁻⁶.

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Cloud processes of the primary precipitating systems over continental tropical regions

Daniel Alejandro Vila , ... Micael Amore Cecchini , in Precipitation Science, 2022

18.seven.1 Aerosol effects on the formation of Amazonian clouds

A deject droplet forms over an embryo and grows via the diffusion of h2o vapor from the surrounding air. The embryo is usually referred to as nucleus and the germination of a deject droplet as nucleation. In principle, the embryo can consist of either h2o vapor molecules that randomly coagulate together or droplets particles. If the atmospheric water vapor force per unit area is high enough, they volition condense onto the embryos and the droplet starts growing. This can simply occur if the air around the droplet surface is initially supersaturated, significant that it contains more water vapor than it can sustain for a given temperature. Withal, the energy needed to condense water vapor over an embryo is inversely proportional to its size. Therefore information technology is much harder for a droplet to course over a small-scale embryo such as water vapor molecules. Aerosol particles have sizes of tens of nanometers to a few micrometers, meaning that they are ii–iv orders of magnitude larger than a water molecule. The energy cost difference implies that the condensation onto water molecule embryos is unfeasible under observable atmospheric conditions. This leads to the decision that every cloud droplet was formed over an droplets particle.

The subset of aerosols that are able to nucleate droplets are called Cloud Condensation Nuclei (CCN) and their characteristics help determine the initial conditions for cloud formation. In the Amazon, most of the natural CCN come from the wood itself, either via direct emissions or through the oxidation of volatile organic compounds (VOCs). The latter stand for to the secondary generation of particles considering the starting time require the emission of VOCs, which only then grow through oxidation into CCN-sizes. Co-ordinate to Pöschl et al. (2010), this is the most of import source of natural CCNs. Other sources include long-range transport of ocean common salt, naturally- or anthropogenically triggered biomass burning events and pollution downwind from cities and settlements (Martin et al., 2017; Wendisch et al., 2016).

The fashion in which droplets particles grow into deject droplets is described by the Köhler equation, which was more than recently adjusted by Petters and Kreidenweis (2007):

(18.1) $\mathrm{Southward}\left(D\right)=\frac{D^3-D_d^3}{D^{\mathrm{iii}}-D_d^3\left(\mathrm{one}-\kappa \right)}\exp \left(\frac{A}{D}\right)$

where $A=8.69251\times {10}^{-6}\sigma /T$ and $\sigma$ and T are the surface tension of the droplet and temperature, respectively. This bend describes the evolution of the saturation ratio (actual water vapor pressure divided by its saturation value) over the droplet surface equally the office of the droplets dry diameter D _d , the droplet diameter D, and the hygroscopicity parameter $\kappa$ . The latter synthesizes the droplets chemic composition and has a value for each compound. If the aerosol consists of multiple compounds, the $\kappa$ should be combined into one constructive value. For the Amazon, $\kappa$ averages to about 0.17 (Pöhlker et al., 2016) and is consequent with high fractions of organic aerosol. For reference, $\kappa$ =0.61 for ammonium sulfate (Petters & Kreidenweis, 2007), meaning that inorganic compounds tin can exist more efficient at nucleating aerosol. The overall behavior of Eq. 18.1 is as follows. Starting from D _d , the saturation ratio S increases with D, meaning that larger aerosol require higher supersaturation [ $\mathrm{Southward}S=\left(\mathrm{South}-1\right)\times 100$ , given in %] to attain equilibrium with the surround. The equation reaches a superlative so S starts decreasing with D and reaches $S=1$ for $D\to \infty$ . At the peak the saturation ratio and droplet size reach their critical values S _c and D _c , respectively. Because South decreases for D>D _c , this means that if the environmental supersaturation is higher than S _c the droplet volition continue growing even if the supersaturation later decreases (as long every bit it does non reach subsaturation). Therefore if the droplet reaches D _c , it is said to be activated.

The way in which physical and chemic properties of aerosol collaborate to produce cloud droplets can exist analyzed using the approximated equation (Petters & Kreidenweis, 2007):

(18.2) $\mathrm{fifty}{n}^2{S}_c=\frac{4A^3{\sigma }^3}{27T^{\mathrm{iii}}\kappa D_d^3}$

For a given supersaturation, Eq. (eighteen.2) defines what are the hygroscopicity and D _d requirements for droplet activation. More than hygroscopic and larger aerosols crave less supersaturation to activate. Typical supersaturation values are normally in the range of 0.1%–1.0%, meaning that Amazonian aerosols only activate if they exceed 200–xl   nm (respectively) in diameter. If aerosols are equanimous exclusively of ammonium sulfate, then the required sizes would reduce to 130–xxx   nm, meaning that potentially more aerosols of a given population activate. The average size distribution of Amazonian aerosols under natural conditions presents 2 modes at 70 and 150   nm approximately (Martin et al., 2010). Therefore under low supersaturation weather condition, the chemic composition of the aerosols will play a pregnant office in determining the number of activated droplets in a deject. The sensitivity report of Hernández Pardo et al. (2019) quantifies this effect and confirms that for larger aerosols their hygroscopicity plays a bottom role.

The combination of aerosol properties (size distribution and size-dependent chemical limerick) and the updraft speed (w) ascertain the initial characteristics of cloud formation. The updraft speed is the primary source of supersaturation due to adiabatic cooling of the ascending air parcels. This supersaturation will then activate a number of droplets depending on the aerosol properties. However, the process is not stationary since the condensation of water vapor onto one droplet reduces the bachelor humidity for another 1. For a fixed updraft speed (and assuming adiabaticity), the droplets volition continually actuate until the supersaturation is fully consumed, when no new droplet formation is possible. If the number of CCN is increased (with the same updraft and humidity atmospheric condition), the same corporeality of water vapor is spread into more droplets. This is known every bit the h2o vapor competition process and results in more but smaller droplets at cloud base.

Cecchini et al. (2016) addressed the aerosol–deject interaction in the Amazon by contrasting clouds discipline to background and polluted aerosol weather downwind from Manaus during the wet flavor. This was achieved by comparison aircraft measurements of clouds located inside or outside the pollution plumage that usually disperses southwestward from the metropolis. This setup allowed the comparison of clouds bailiwick to different aerosol atmospheric condition while embedded in similar thermodynamic environments. They constitute that the pollution increased CCN number concentrations from 100–150   cm⁻³ to 250–550   cm⁻³ on boilerplate (for SS betwixt 0.25% and 0.v%, respectively), which resulted in meaning differences of deject-base of operations properties of polluted and background clouds. For instance the LWC (representing the total amount of condensed water per cubic meter) was found to scale with updraft speed for polluted clouds, going from 0.2   one thousand   one thousand⁻³ for w=0.ane   yard   s⁻ⁱ up to 0.8   g   m⁻³ for w=4   m   s⁻¹. For the same w range the background clouds did non present such scaling, presenting average LWC consistently close to 0.2   g   m⁻³. This indicates that natural clouds over the Amazon operate under the aerosol-limited government (Reutter et al., 2009), where increases in CCN lead to college amounts of condensed water. Using the LWC=0.two   thousand   one thousand⁻³ point as reference, the boilerplate droplet size of polluted clouds was 10   µm, beingness v   µm lower than in groundwork clouds. The corresponding droplet number concentrations were 400   cm⁻³ for polluted and 200   cm^−three for background clouds.

The aerosol issue on cloud base formation will affect the early cloud evolution, since different DSD will nowadays dissimilar growth rates during the warm stage. This issue will exist addressed in the next department.

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Radiations

Kristian Pagh Nielsen , ... Emily Gleeson , in Uncertainties in Numerical Weather condition Prediction, 2021

3.2.1 Liquid water clouds

If liquid cloud droplets are causeless to be spherical, their optical properties tin can exist accurately calculated from Mie theory ( Mie, 1908; Wiscombe, 1980). It was shown past Nielsen et al. (2014) that many deject liquid optical property computations that are used in NWP and climate models are inaccurate. Thus, negative errors of the lodge of tens of W grand⁻² were found for clouds with cloud h2o loads of the order of 0.1   kg m² when the Slingo liquid cloud optical property scheme (Slingo, 1989) was used. The Nielsen liquid cloud optical property scheme for the RRTM SW spectral bands is given in Eqs. (10)–(12) and Tables one and 2.

Table 1. Coefficients used for the Nielsen liquid cloud optical parameterization.

i	2	3	four	v	6	7
[μm]	0.2632–0.3448	0.3448–0.4415	0.4415–0.6250	0.6250–0.7782	0.7782–1.242	1.242–ane.299
a i	1.614	1.633	ane.649	i.677	i.719	ane.788
b i	−1.018	−one.021	−ane.022	−one.026	−1.032	−1.042
c i	ane.000	1.000	one.000	1.000	0.99998	0.9999
d i	0.000	0.000	−four × 10−8	−1 × x−6	−two.seven × 10−5	−ix.7 × 10−v
due east i	0.861	0.869	0.874	0.870	0.869	0.870
f i	2.five × 10−4	1.one × 10−4	4.0 × 10−v	2.iii × ten−iv	two.iii × 10−4	ii.3 × 10−4
h i	−0.050	−0.064	−0.060	−0.067	−0.088	−0.095
j i	−0.30	−0.25	−0.19	−0.19	−0.19	−0.fifteen

Note: The columns show the wavelength bands (i) 2–7.

Table 2. Coefficients used for the Nielsen liquid cloud optical parameterization.

i	8	nine	ten	11	12	13
[μm]	ane.299–1.626	1.626–i.942	1.942–2.150	2.150–2.500	two.500–3.077	3.077–3.846
a i	1.869	1.845	one.740	1.832	1.870	ii.098
b i	−1.054	−i.049	−1.028	−i.043	−1.049	−1.080
c i	0.9985	0.9993	0.988	0.993	0.525	0.775
d i	−9 × 10−4	−6 × 10−4	−iii.1 × 10−3	−ii.2 × ten−3	1.1 × x−3	−4.8 × 10−iii
e i	0.867	0.863	0.863	0.862	0.944	0.871
MMR f i	iv.v × ten−iv	5.1 × ten−4	ane.0 × 10−3	1.0 × x−three	2.viii × 10−4	i.7 × 10−3
h i	−0.092	−0.17	−0.78	−0.78	−0.22	−0.48
j i	−0.xv	−0.xx	−0.xl	0.40	−0.40	−0.thirty

Notation: The columns show the wavelength bands (i) 8–thirteen.

(10) $\begin{array}{ll}\hfill k_i& =a_i{r}_{\mathrm{due\; east},\mathrm{liq}}^{b_i},\hfill \end{array}$

(11) $\begin{array}{ll}\hfill {\omega }_i& =c_i+d_i{r}_{e,\mathrm{liq}},\hfill \end{array}$

(12) $\begin{array}{ll}\hfill g_i& ={\mathrm{eastward}}_i+f_i{r}_{\mathrm{due\; east},\mathrm{liq}}+h_{i}exp(j_i{r}_{\mathrm{eastward},\mathrm{liq}}).\hfill \end{array}$

Here, the showtime RRTM SW spectral band is omitted because UV radiation with wavelengths shorter than 270   nm does not attain the atmospheric clouds. RRTM SW spectral band 14, which covers the wavelength range three.846–12.195   μm, is omitted because this spectral band has almost no SW irradiance.

The LW cloud liquid optical backdrop can be parameterized in a similar manner. This has been done by Lindner and Li (2000).

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Ice nucleation

Ari Laaksonen , Jussi Malila , in Nucleation of Water, 2022

10.11 Freezing in mixed-phase and rainclouds

Freezing of cloud droplets initiates rain. This was start realized past Alfred Wegener in 1911 [109] while observing and thinking about frost on trees. Because the saturation vapor pressure of ice is lower than that of liquid h2o, freezing of super-cooled droplets will accelerate the growth of frost. Wegener idea that a similar procedure could occur in clouds, and initiate rain formation. After, Tor Bergeron [110] and Alfred Findeisen [111] suggested that the rapid condensation of water vapor onto water ice particles will crusade the water vapor concentration to decrease, and droplets that have not frozen volition kickoff to evaporate. The water ice thus grows in the expense of the liquid water. This process is called the Wegener–Bergeron–Findeisen (WBF) mechanism.

Mixed stage clouds, consisting of liquid droplets and ice particles, are ubiquitous and occur all around the world. They are e'er in not-equilibrium state, evolving from one land to some other. The process of a supercooled liquid cloud turning into an ice cloud is chosen glaciation. The speed of glaciation is important not only because it may turn a non-precipitating cloud into a raincloud, just also because the radiative backdrop of ice clouds differ considerably from those of liquid clouds. Glaciation time depends on temperature, the number concentration of water ice particles, initial ice and liquid h2o mixing ratios, and updraft velocity of the cloud [112]. If the updraft velocity is cipher, glaciation times tin can vary from minutes to hours. Information technology turns out that at not-naught updraft, the matter is circuitous, and the WBF mechanism is not ever operational. At high updrafts it is possible, depending on the other parameters, that ice particles and water droplets grow simultaneously. At very low updrafts it is even possible that both the water ice particles and the droplets evaporate simultaneously [112].

Supercooled cloudwater and mixed stage clouds tin can occur at temperatures from the freezing signal down to about −xl   °C, the homogeneous freezing limit. A satellite study [113] has indicated that about half of mixed phase clouds glaciate at temperatures in a higher place −20   °C. It is generally thought that the primary ice nucleation mode in mixed phase clouds is immersion freezing with contact nucleation perhaps playing a smaller role [114]. The concentrations of water ice nucleating particles limit the extent of immersion freezing in mixed stage clouds, and as their ice nucleating efficiency varies according to particle type, the types of INP's available impact the glaciation time and temperature. It should be noted that ice nucleation alone does not dictate the ice crystal concentrations every bit so called secondary ice product mechanisms have an upshot likewise. In the Hallett–Mossop process, interim at temperatures between −3 and −viii   °C, pressure buildup inside a freezing droplet with an water ice crush causes it to burst and produce ice splinters. Water ice–water ice collisions accept too been suggested to pb to mechanical fragmentation of the colliding crystals, producing secondary ice [115].

Because of the importance of glaciation to precipitation and cloud radiative backdrop, it would exist important to represent water ice nucleation in climate models equally realistically equally possible. In the case of mixed phase clouds, i problem is that the knowledge of the INP types that cause immersion freezing is lacking [114]. It is likely that mineral dusts and various biological particle types known to be constructive ice nucleators play a major office, just much more field information is needed to obtain a good agreement of what INP types probable play a role at various regions of the globe.

An interesting question is related to the ice nucleating properties of anthropogenic aerosols, and to what extent they may have indirect climate effects via ice nucleation in mixed phase clouds. Lohmann [116] suggested that hydrophilic soot particles may crusade contact nucleation. Increased anthropogenic soot concentrations would then cause increased glaciation in mixed stage clouds, and lead to increased precipitation and decreased cloud lifetime. Blackness carbon particles take been shown to be inefficient immersion freezing nuclei [117], but an interesting question relates to the immersion freezing efficiency of wing ash. Coal wing ash appears to have decreasing immersion freezing efficiency the longer the particles have been immersed in h2o before ice nucleation temperatures are reached, perhaps because of deactivation of the particle surface resulting from hydration of CaSO_four and CaO [76]. Even so, more experimental studies on different fly ash types would clearly be desirable.

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How Much Does A Cloud Droplet Increase In Size To Become A Raindrop,

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