An Introduction to Twomey’Effect Guillaume Mauger

Aihua Zhu

Mauna Loa, Hawaii on a clear day Mauna Loa, Hawaii on a dusty day

Non-selectivescattering.

Rayleighscattering

Miescattering

The impact ofclouds

Clouds have two competing influences in theradiation budget:

1) They reflect solar radiation and prevent itfrom reaching the surface of earth, similar to anumbrella, and preventing the warming of theatmosphere through absorption of theradiation.

2) They absorb the infrared radiation escapingfrom the surface of the earth and thus trap thewarmth in atmosphere, similar to a greenhouse.

Low cloud

Middle cloud

High cloud

Cloudtypes

Different impacts of differentclouds

Low level clouds: large albedo, weak absorption of infrad radiation-----coolingUpper level clouds: weak albedo, strong absorption of infrad radiation----warming

is the extinction efficiency, is given by Mietheory, nearly equal to 2is the extinction efficient

For solar wavelengths and for realistic (polydisperse)drop distributions we can eliminate the integrationand adopt the simple formula

Where N is the drop concentration per cubic centimeterand can be any representative of mean or model radius

Opticalthickness

Extinction efficiencies: general behaviour anddeviations

Size dependence ofthe extinction efficiencyfactors forhomogeneousspherical particles. Theinfluence of variationsof the real part (upperpanel) and imaginarypart (lower panel) ofthe refractive index isillustrated.Typical refractiveindex m of clouddroplet is:m=1.333-1.96*10-9i

The liquid water content W is given by the volume-meanradius W (in number)

=W (in mass)=

ρwater W (in number)

A water content of 1/3 gm-3 (which is typical at least oflower level clouds) was adopted to calculate values ofextinction coefficient kE (cm-1) and optical thickness perkilometer of cloud depth hrNkm

22πτ =22 rNkE π=

Parameters needed to give theextinctionOptical thickness:

es ββω /0 =

∫∫+

−

+

−= 1

1

1

1

)(

)(

duuP

duuuPg

Single scatteringalbedo:

Asymmetry factor:

hrNkm22πτ =

ase βββ +=)cos(θ=uWhere P(u) is the phase function

is the extinction coefficientis absorption opticalthickness

)1( 0ωττ −=a

Increase pollution (pollution index x) will increase thealbedo if dS/dx is positive:

=dxdS

because:

so we need to prescribeand

)1( 0ωττ −=aBecause:

¬Clean air over the tropical oceans 10-100 cm-3¬Continental concentrations run from 500-1000cm-3;¬Moderate to heavy pollution has values >5000cm-3

Typical cloud nucleiconcentration

The values 0.01 and 0.1 represent a reasonable and anextreme value of , respectively, for the absorptionkm-1 depth in continental conditions when N=1000cm-3

∫ ∫ ΦΦΦ==↑

πµµµµ

πµµ

2

0

1

0 000

0 ),;,(1*)0(

)( ddRF

Fr dif

*)/(),;0(),;,( 000 FIR r µµπµµ Φ=ΦΦ

∫==↑ 1

0 0002 )(2*)0(

µµµπ

drFa

fr

Spherical (or global) albedo:As=

Spherical albedo eliminates geometric variables and gives a reasonablyrepresentative global value of albedo, It represents the fraction ofincident radiation reflected by a sphere covered by a layer of theprescribed properties.

According to Liou, spherical albedo can becalculated as:

Frequency distributions ofthe reflectances at 1,535nm versus reflectances at754 nm determined duringthe ACE-2 experiment.Isolines of geometricalthickness (H) and dropletnumber concentration (N)demonstrate the higherreflectance in pollutedcloud if normalised by asimilar geometricalthickness (Brenguier et al.2000).

Indirect Forcingof Aerosols

Flow chart showing theprocesses linking aerosolemissions or production withchanges in cloud optical depthand radiative forcing. Barsindicate functional dependenceof the quantity on top of the barto that under the bar. Symbols:CCN (Cloud conden-sationnuclei); CDNC (Cloud dropletnumber concentration); IN (Icenuclei); IP (Ice particles); OD(Optical depth); HC(Hydrometeor concentration); A(Albedo); fc (Cloud fraction); Dc(Cloud optical depth); tc(Radiative forcing).

¬Pollution may increase or decrease the brightnessof clouds depending on the optical thickness of theclouds and the way in which cloud nucleusconcentration varies with absorption opticalthickness.¬In all but the thickest clouds the pollutionincreases the albedo. Since most of the earth’scloud cover is not very thick this result suggest thatthe planetary albedo also will increase with increaseof pollution.

conclusion