Radiative transfer II: attenuation by non- gaseous atmospheric … · 2014-01-21 · Radiative transfer II: attenuation by non-gaseous atmospheric constituents IMPRS Atmosphere and

Radiative transfer II: attenuation by non-gaseous atmospheric

constituents

IMPRS Atmosphere and Ocean CourseMay 3, 2011Julia Marshall

Outline• What attenuates

the radiation?

• Mie regime

• the size parameter

• Rayleigh regime

• geometric regime

• aerosol particles

• direct effect of aerosols

• aerosols as cloud condensation nuclei

• indirect effects of aerosols

• radiative impacts of different types of clouds

What attenuates the radiation emitted from the sun before it

reaches the earth?

What attenuates the radiation emitted from the sun before it

reaches the earth?

• clouds

• aerosols

• gases

• haze

Visibility in the atmosphere

• the scattering and absorption from small particles determines our experience of visibility in the atmosphere

Seinfeld and Pandis, 1998

Consider a spherical scatterer:

• we’re considering here only elastic scattering, i.e. the wavelength of light is not changed


Plane wave encountering particle:

• resultant scattering produces a spherical wave

• scattering and absorption (together = extinction) determined by the composition and relative size of the particle

Goody and Yung, 1989

The Mie regime

• the complete, formal theory of the interaction of a plane wave with a dielectric sphere, published by German physicist Gustav Mie in 1908

• mathematically very cumbersome, and not widely applied until the late 20th century as a result

• required for cases where the scatterer diameter and λ are comparable

http://en.wikipedia.org/wiki/File:GustavMie.gif



The Mie regime

• scattering phase function greatly influenced by the size of the scattering particle

• or rather, the relative size of the scatterer to the wavelength of incident radiation

• can this figure explain the colour of desert sunsets?


Optical phenomena in the Mie regime:

• the glory

• seen around the shadow of the observer on a cloud

• wonderfully difficult to explain!

http://www.atoptics.co.uk/droplets/glofeat.htm



The glory:

• can be well predicted by full Mie calculations, but this doesn’t explain exactly how it happens

• has to do with the interaction of surface waves at the site of internal reflections within the droplet




The size parameter:• less important than the size of the particle

is the ratio of the particle size to the wavelength of the incident radiation

• often given as the size parameter,

• for very large and small values of x, simpler formulations can explain the physical phenomena

• the Mie solution is always correct (and complete), but can obscure the actual physics

The size parameter: extinction from a water droplet

• the wavelength is fixed at 0.5 microns and the diameter is varied

• the diameter is fixed at 2 microns and the wavelength is varied


Rayleigh’s solution

• named after British physicist John William Strutt, the third Baron Rayleigh

• when x << 1, the Mie formulation reduces to the simple case where

• Qabs α 1/λ

• Qsca α 1/λ4

http://en.wikipedia.org/wiki/File:John_William_Strutt.jpg



Rayleigh’s solution

• scattering phase function for a particle in the Rayleigh regime


What it means:

http://upload.wikimedia.org/wikipedia/commons/6/69/Rayleigh_sunlight_scattering.png



For large size parameters:

• when x >> 1, the wave nature of light doesn’t matter as much

• at this point, ray-based estimations suffice

• this is known as the “geometric regime”

• associated with all sorts of interesting optical phenomena

The rainbow:• centred at anti-solar

point

• due to internal reflection from rain drops with large radius with respect to the wavelength of light

• refraction separates colours like a prism

• can be approximated as rays


The rainbow:

• single internal reflection forms the brightest bow

• double internal reflection forms the secondary bow

• refraction without reflection forms coronae

http://hyperphysics.phy-astr.gsu.edu/hbase/atmos/ligsky.html



Alexander’s dark band, and the light sky beneath:




The rainbow:

• always centered at the anti-solar point?

• reflection bows can be formed over still water or wet sand

http://www.atoptics.co.uk/rainbows/reflect.htm



The rainbow:

• always centered at the anti-solar point?

• reflection bows can be formed over still water or wet sand




The rainbow:

• usually only two bands (at most) are seen due to the spread over various drop sizes obscuring the finer features


Rare supernumerary rainbows

http://www.atoptics.co.uk/rainbows/supers.htm



Other optical phenomena:

• the halo

• full circle 22 degrees from the sun

• formed by high cirrostratus ice clouds

http://www.atoptics.co.uk/halo/circular.htm




• sundogs or parahelia

Roy Antal (Regina Leader-Post)

• subset of halos, but with the hexagonal ice crystals vertically aligned due to gravitational settling

• situated at 22 degrees on either side of the sun, sometimes with colour separation


• complete set of potential halo effects, depending on type of ice crystal and solar position

http://www.atoptics.co.uk/halo/common.htm




• Heiligenschein:

• centred on anti-solar point

• seen about the observer when there is dew on grass

http://www.atoptics.co.uk/droplets/heilfrm.htm



Other optical phenomena:• Heiligenschein:

• size of particles isn’t crucial, but they need to be small enough to be suspended on the tiny hairs on a leaf’s surface

• the droplets focus the light, which is reflected from the leaf’s surface




• Coronae

• from thin clouds in front of the sun

• rings are much smaller than halos

• due to diffraction rather than reflection


http://www.atoptics.co.uk/droplets/pollen1.htm

pollen corona



Non-spherical particles

• all treatment thus far has assumed that the scatterers are homogeneous, spherical particles

• this is not always the case!

• the difference is irrelevant for the Rayleigh regime, but can be important for the Mie regime

Non-spherical particles• the Mie formulation

can be (relatively) easily extended to describe ellipsoids and concentric shells, but this is still rather limited

• in reality, some aerosols are much more complex than this


Non-spherical particles

• the real world:

• from left: volcanic ash, pollen, sea salt, and black carbon - not to scale!

http://earthobservatory.nasa.gov/Features/Aerosols/



Aerosol particles:

• aerosols (or aerosol) are solid or liquid particles suspended in the air

• they are of both natural and anthropogenic origin

• common sources are dust, sea spray, combustion, and volatile organics

Aerosol particles:size distribution

• they range from a few nanometers to tens of microns, depending on the source and particle history

• often described by multiple overlapping log-normal modes, partly for simplicity

Aerosol particles: number density

• can be as low as a few hundred per cubic centimeter for clean marine environments

• typically a few thousand per cubic centimeter for remote continental areas

• tens to hundreds of thousands per cubic centimeter in urban environments

• declining logarithmically with altitude

Aerosol particles: lifetime

• on average on the order of a week

• lost to gravitational settling (for the larger particles), rain-out, dry deposition...

• hydrophobic particles last longer, but slowly become hygroscopic

Aerosol composition

• “Atmospheric aerosol particles contain sulfates, nitrates, ammonium, organic material, crustal species, sea salt, hydrogen ions, and water.” Seinfeld and Pandis, 1998

Aerosol composition: dust• mineral dust

(crustal)

• generally large particles

• hydrophobic (at first)

• usually short lifetime due to gravitational settling

NASA: MODIS Rapid Response Team

Aerosol distribution: dust

• number distribution

• surface distribution

• volume distribution


Aerosol composition: sea salt

• production via bubble bursting

• many small film drops containing organics

• few large jet drops

• a function of wind speed, often parameterized as ∝U3+

Rogers and Yau

Aerosol distribution: marine


Aerosol distribution: urban


Aerosol size distribution: urban vs. rural


Idealized size spectra by source 94 A Short Course in Cloud Physics

0,

NI

C4z00m004‘as

400-a

FIG. 6.4. Idealized aerosol spectra, showing typical ground-level background distributions and the general dependence of the spectra on height,wind speed, distance from source, and surface heating- (From Slinn, 1975.)

captured by droplets as they continue to grow by diffusion from thevapor, or are swept out by falling precipitation particles. All suchparticles are lost from the aerosol population~ although new aerosols arecreated as residue from evaporating cloud and precipitation particles.Figure 6.4 is a schematic illustration of aerosol particle size distributions that typify different background and extreme conditions. Thecoagulation mode between 0.1 and I pm is evident in most of thedistributions representative of conditions near the ground. The coarseparticle mode (diameter > 10 pm) is pronounced in samples that areinfluenced by nearby combustion sources or high winds, which stir updust from the ground.From the entire aerosol population~ the particles thought to be mostimportant in natural cloud formation are those in the accumulationmode, which corresponds approximately to the size interval of theso-called large aerosols. Particles smaller than about 0.1 pm, even ifhygroscopic, would require higher saturation ratios than those thoughtto exist in the free atmosphere to be activated. Particles larger than 4 or5pm are much fewer in number (except near sources) but may serve asnuclei for some of the cloud droplets that are much larger than averagesize.The chemical composition of ~joud-forming nuclei is difficult to inferbecause they comprise such a small fraction of the total atmosphericaerosol population. Evidence indicates that sea salt is the predominantconstituent of condensation nuclei in the size range above 1 pm. The

IC., IO~’ lO~~ irpARtIcLE DIAMETER, I””

Rogers and Yau, 1989

Modelled aerosol particles:

Aerosol particles: their role in the climate system

• attenuate incoming radiation both directly and indirectly (more on that later)

• act as cloud condensation nuclei, i.e. the little speck of dirt on which cloud droplets form

The importance of a dirty atmosphere

• without any particles on which to form, the atmosphere would require ~800% relative humidity before clouds could form!

Aerosols as cloud condensation nuclei• CCN = Cloud Condensation Nucleus

• cloud droplets consist of mostly water, usually condensed onto an existing aerosol particle

• the equilibrium behaviour between the droplet and water vapour is described by the Köhler equation

The Köhler curve

• two separate and competing effects need to be taken into account:

• the reduction of the saturation vapour pressure due to the solute effect (Raoult’s law)

• the enhancement of the saturation vapour pressure due to the curvature effect (Kelvin’s law)

The Köhler curve: curvature effect

• the equilibrium vapour pressure over a droplet’s surface depends on its curvature, and is given by:

with

or

The Köhler curve: solute effect

• for a plane water surface the reduction in vapour pressure due to the presence of a nonvolatile dilute solute can be expressed as:

• with n molecules of solute and n0 molecules of water

The Köhler curve: solute effect

• the number of effective ions in a solute of mass M is given by

• and the number of water molecules can be written as

• now we can substitute the mass of water by

• making Raoult’s law:

with

The Köhler curve: combined

or, for not too small values of r, the more common form:

The Köhler curve:

88 A Short Course in Cloud Physicswhere a = 2aIq,fl ~T. For r not too small, a good approximation to thisequation is

(6.6)

In this approximate form, air may be thought of as a “curvature term”which expresses the increase in saturation ratio over a droplet ascompared to a plane surface. The term b/r3 may be called the “solutionterm”, for it shows the reduction in vapor pressure due to the presence ofa dissolved substance. Numerically, a 3.3 x W5IT (cm) and b4.3iMitfl, (cm3). For given values of T, M, and in5, (6.6) describes thedependence of saturation ratio on the size of a solution droplet. Theresultant curve is called a KOhler curve, an example of which is illustratedinFig. 6.2.The curve shows that the solution effect dominates when the radius issmall, so that a very small solution droplet is in equilibrium with thevapor at relative humidities less than 10001°. If the relative humidity isincreased a small amount, the droplet will grow until it reaches equilibrium once again. This process of increasing the ambient humidity andallowing the droplet to grow to equilibrium size can be continued up tothe relative humidity of 100% and slightly beyond. Finally the criticalsaturation ratio S is reached that corresponds to the peak of the Kohlercurve—in this example a supersaturation of 0.6%, corresponding to a

00ccC0

0

0U,

1001 r-Droplet RadiuS, pm

FIG. 6.2. Equilibrium saturation ratio of a solution droplet formed Ofl anammoflium sulfate condensation nucleus of mass

The Köhler curve:what it means

• depends on the solute: some things are more hygroscopic...

• depends on the particle size

The direct effect of aerosols

• simple scattering and backscattering of radiation from non-absorbing aerosols

• when radiation is scattered back into space, it doesn’t reach the surface

• net cooling effect

global sulphate aerosol distribution


Resultant radiative effect


Pinatubo aerosol load:

• the idea behind stratospheric aerosols as a geoengineering climate fix


The semi-direct aerosol effect

• some aerosols are absorbing (like soot)

• this can lead to local heating, which, depending on the location, can be either a warming or a cooling effect


Do aerosols heat or cool?

• β is upscatter fraction

• ω is the single scattering albedo:Qscat/(Qscat+Qabs)

• Rs is the surface albedo


Radiative effect of clouds in general

• can be separated generally into low, optically thick clouds (like stratocumulus) and high, optically thin clouds (cirrus)

• can be further separated into shortwave and longwave components

Low clouds

• short wave (solar) radiation

• highly reflective (they look “white”)

• low absorption

• low transmission

• cooling effect

114 Clouds and Radiation

Figure 6.1: Low clouds and solar radiation.

Figure 6.2: Low clouds and terrestrial radiation.

Low clouds

• longwave (terrestrial) radiation

• thermal emission from both the surface and the cloud determined by temperature, according to Planck’s Law

• because the clouds are only slightly cooler than the surface, this results in a very slight warming effect


Figure 6.1: Low clouds and solar radiation.

Figure 6.2: Low clouds and terrestrial radiation.

High clouds

• shortwave (solar) radiation

• optically thin, so little reflection

• substantial transmission

• low absorption

• very little cooling

6.1 Warming or Cooling by Clouds 115

6.1.2 High, Optically Thin Clouds (Cirrus)

• Solar:

– Little reflection (optically thin cirrus),

– Low absorption, and

– High transmission.

– Quite Little Cooling.

– See Figure 6.3

Figure 6.3: High clouds and solar/terrestrial radiation.

• Terrestrial

– Thermal infrared radiation emitted by the surface (as a function of surface tem-perature) corresponding to Planck’s law.

– Cirrus absorbs and emits this radiation.

– Emission by the clouds takes place at very low temperature.

– Moderate Warming (Greenhouse effect, because of temperature differences be-tween surface and high clouds).

– See also Figure 6.3

High clouds• longwave (terrestrial) radiation

• clouds absorb terrestrial radiation and emit it as well according to Planck’s Law

• because they’re high in the atmosphere and so much colder than the surface, this results in substantial warming

• similar to greenhouse effect

6.1 Warming or Cooling by Clouds 115

6.1.2 High, Optically Thin Clouds (Cirrus)

• Solar:

– Little reflection (optically thin cirrus),

– Low absorption, and

– High transmission.

– Quite Little Cooling.

– See Figure 6.3

Figure 6.3: High clouds and solar/terrestrial radiation.

• Terrestrial

– Thermal infrared radiation emitted by the surface (as a function of surface tem-perature) corresponding to Planck’s law.

– Cirrus absorbs and emits this radiation.

– Emission by the clouds takes place at very low temperature.

– Moderate Warming (Greenhouse effect, because of temperature differences be-tween surface and high clouds).

– See also Figure 6.3

Summary of cloud effects:

• low clouds are generally cooling due to their high reflectivity and near-surface temperature

• high clouds are generally warming due to their low reflectivity and much cooler thermal emission

Net radiative effect of clouds


6.1.3 Net Effect (Solar Plus Terrestrial)

• Strong solar cooling of the low clouds overbalances the rather moderate warming bythe cirrus in the terrestrial spectral range.

• Please have a look at Figure 6.4

Figure 6.4: Net cloud effect, as observed by ERBE (Earth Radiation Budget Experiment) 1998.

• Strong cooling effect of low clouds dominates

Aerosols and clouds


First indirect aerosol effect:

6.2 Indirect Cloud Effects 117

6.2 Indirect Cloud Effects

Aerosol particles principally act to:

• Decrease droplet size,

• Increase cloud geometrical thickness,

• Increase cloud reflectivity,

• Reduce precipitation,

• Prolong life time of clouds, except for the case of strongly absorbing aerosol particles(burn–off of clouds).

Figure 6.5: Cloud first indirect effect: Increase of albedo in polluted clouds.

Clean environment Polluted environment

Cloudalbedo

First indirect effect (Twomey effect):

• for the same amount of cloud water, the droplets are spread over more CCNs

• this results in more, smaller, cloud droplets

• this increases the albedo of the cloud, causing more radiation to reflect back into space

• this is a net cooling effect

• shows cloud albedo as a function of cloud droplet number concentration

• liquid water content fixed at 0.3 g/m3

• typical for clean marine stratocumulus


Radiative impact:

• calculated perturbation in radiative quantities from uniform increase in cloud droplet number concentration

• made with assumption that perturbation affects only non-overlapping marine St and Sc clouds


Why are we only talking about marine

clouds?

Why are we only talking about marine

clouds?• other environments are essentially

saturated with cloud condensation nuclei already

• comparatively wet clouds in clean air will be the most affected by an increase in aerosol particles

What other side effects might the smaller droplets have?

What other side effects might the smaller droplets have?

• smaller droplets means we’re less likely to get enough large droplets to start the collision-coalescence process necessary to make rain

• this can make the cloud last longer...

Formation ofCloud Droplets 83

,ironmeflt, which requires highin the atmosphere, is calledin which a free energy barrierid or liquid to ice transitions are

nuclei are present in the atmoshumidities less than 100% andity. The relatively large condencloud droplet size. As moist airye humidity approaches 100%.iucleus population then begin to~nt continues, supersaturation isI by the condensation on nuclei.;s of relative humidity over theth a relative humidity of 101.5%;, there are usually enough nuclein rising much above about 1%. Itimosphere that there are alwayse for cloud formation when the

top may eventually be cooled toplets in the cloud are then said toay not freeze, depending uponire water droplets, homogeneousature of about —40°C is reached.‘ever, freezing can occur at just a~ese aerosols are not completelye rather scarce in the atmosphere,.iclei. Consequently supersaturarcent are extremely uncommon inilets in supercooled form are thedown to —15°C or colder are notthe main methods of artificiallynuclei, as we shall see later.oplets usually numbering severalaving radii of about 10 gm. Thisthe droplets show little tendency

~es except by general growth of theelops when the cloud populationow at the expense of others. Thereoud microstructure may becomesion and coalescence (sticking) ofitant in any cloud. The secondbetween water droplets and ice

crystals and is confined to those clouds whose tops extend to temperatures colder than 0°C.From analysis of the aerodynamic forces it is found that very small

droplets cannot readily be made to collide. A small drop falling througha cloud of still smaller droplets will collide with only a minute fractionof the droplets in its path if its radius is less than about 18 pm. Therefore it is expected that clouds which contain negligible numbers ofdrops larger than l8pm will be relatively stable with respect to growth bycoalescence. Clouds with considerable numbers of larger drops maydevelop precipitation.When an ice crystal exists in the presence of a large number of

supercooled water droplets the situation is immediately unstable. Theequilibrium vapor pressure over ice is less than that over water at thesame temperature and consequently the ice crystal grows by diffusion ofvapor and the drops evaporate to compensate for this. The vapor transferdepends on the difference in equilibrium vapor pressure of water and iceand is most efficient at about — 15°C.Once the ice crystal has grown by diffusion to a size appreciably larger

than the water droplets, it begins to fall relative to them and collisionsbecome possible. If the collisions are mainly with other ice crystalssnowflakes form; if water droplets are collected graupel or hail mayform. Once the particle falls below the 0°C level melting can occur, andthe particle may emerge from cloud base as a raindrop indistinguishable

FIG. 6.1. Comparative sizes, concentrations, and terminal fall velocities ofsome of the particles included in cloud and precipitation processes. (From

McDonald, 1958.)

conventional borderlinebetween cloud drops and

raindrops00

~clId drop

Typical condensation nucleus‘‘01.106

V ‘0 0001

OTypical cloud drop06V-I

KeyJr . radius in micronsn-number per I ierI’-’ -terminal velocityin centimeters~per second

~~Iraindrop rl000 n-I • V’650

Rogers and Yau, 1989

Overview of aerosol-cloud effects


Figure 6.6: Experimental verification of first indirect effect.

Figure 6.7: Second and semi–indirect effects, from IPCC (2007).IPCC (2007)

• IPCC AR4:

• aerosol radiative effects are still very uncertain!

climate

After lunch:

• trying out some little experiments with an online 1-D radiation model

• getting a feeling for 1 W/m2

• so in this picture, “LW up flux” would be 235 W/m2

• “SW net flux” would be 342-107= 235 W/m2

• the “SW net flux” in the model is much higher because it’s for a mid-day summer case with clear sky, and the numbers only have to balance on average (day and night, winter and summer, globally)

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Radiative transfer II: attenuation by non- gaseous atmospheric … · 2014-01-21 · Radiative transfer II: attenuation by non-gaseous atmospheric constituents IMPRS Atmosphere and