## Radiationtransfer Theory

The production of radiation by bodies around us is usually from what are essentially blackbody surfaces, or surfaces that absorb most of the thermal radiation incident on them. Planetary atmospheres are usually non-ideal blackbodies, unless they contain high amounts of absorbing molecules. Radiation that is emitted by a surface or an atmospheric layer undergoes absorption and or scattering, by the molecules that constitute the atmosphere, as it is transferred through the atmosphere. Over very...

## Temperature K

Variation of the global mean vertical atmospheric temperature with increasing atmospheric carbon dioxide levels (1 PAL 365 ppmv). The RC model has fixed cloud cover of 0.5, surface relative humidity of 0.8, and surface albedo of 0.1. Water vapour and moist lapse rate feedbacks are included, as are changes to atmospheric composition through the inclusion of the photochemistry. Table 11.3 Climatic effects of increasing atmospheric CO2 levels (1, 2, 4 and 8 PAL), without feedbacks....

## Mediterranean Sea heat budget

The Mediterranean Sea, being a semienclosed system, is an ideal test basin for the climate-research community, because it provides a good opportunity to investigate the closure of its hydrological and heat budgets. The closing of such budgets engenders more confidence that our understanding in many geophysical fields, such as sea air interactions, modelling and measuring solar and terrestrial fluxes and hydrological quantities, is adequate. Evaporation losses from the Mediterranean Sea are...

## Ts BT02Tsy118

If we set ts 0.85, for the total grey optical depth of the present atmosphere, and 255 K then we obtain To 214 K, Ts 288 K and the near-surface air temperature is then T(ts) 263 K. We see that there is a discontinuity of 25 K between the surface temperature and the near-surface air temperature. We also see that for ts 1, the atmospheric layer above the blackbody surface is also a blackbody, eqn (3.83), and so from the above equations we have T(ts) Ts. Thus, in radiative equilibrium, the...

## Bn sin Hn

Thus the mean daily solar flux (W m 2) on day n can be calculated from f Sqfi,ndn (j- j . (5.65) We note that at the equinoxes S 0 and so H n 2 so that d 1 2. In the polar regions it is possible for H to be zero, d 0, i.e. polar night (or winter) that can last up to six months depending on latitude. At this time the other pole has H n, d 1 polar day (or summer). The polar night can happen for latitudes that satisfy tan 0 cot S for S 0. This occurs for 0 > 90 S 66.56 . During the polar day H n...

## GCM climate projections

The IPCC 2001 report distinguishes between climate prediction and climate projection. A climate projection describes the response of the climate system to emission or concentration scenarios of greenhouse gases and aerosols, or radiative-forcing scenarios, based upon simulations by climate models. Climate projections depend upon the forcing scenarios used, which are based on assumptions, concerning, e.g. future socio-economic and technological developments, that may or may not be realized, and...

## Fpg nBj [T pdtj ppg4119

Note that we need to enforce the normalization condition nJ2j Bj(T) aT4. In Chapter 8 we give actual computations for the global distribution of the Earth's thermal infra-red budget. For further reading related to band-absorptance formulations see Goody and Yung and references therein Cess and Trewari Tien and Ramanathan. For the molecular spectroscopy of rotational-vibrational bands see the classic texts by Herzberg, and also Banwell and McCash. Numerical computations of the Voigt function can...

## Longwave radiation budget at TOA

Over the past three decades, considerable effort has been expended in the global measurement of the TOA longwave radiation budget. The Earth Radiation Budget Experiment (ERBE) provides the most comprehensive set of data for the TOA energy budget. The calculated global long-term (1984-2004) average of the outgoing longwave radiation (OLR) at the top of the atmosphere is found to be 239 W m 2, based on model runs with ISCCP climatological data. Fig. 8.25. Model long-term (1984-2004) outgoing...

## Bibliography

For a more detail description of the pp chain see Sturrock and Tayler. A more detailed discussion on photon escape from the centre of stars may be found in the book by Bohm-Vitense. For more details on the solar cycle see the early work of Eddy. For the faint-young-Sun paradox and for conditions on the early Earth see 12.2. The article by Walter and Barry in the Sun in Time text by Sonnet et al. and the text itself provide details on solar flux evolution see also Zahnle and Walker, and Chyba...

## Nird2

For example, for N2 at a pressure of 1 atm, at 300 K the number density is 2.4x1019 molecules cm-3 and for a typical molecular diameter of 2x10 8 cm we get l 3 x 10 5 cm. From Avogadro's number, the mass is equal to 28 (6 x 1023) g, and so the mean speed is 5x104 cm s-1. Thus, the diffusion coefficient is 0.5 cm2 s-1 and the collision frequency is 5x109 s-1. In the atmosphere if we consider diffusion of a molecule i in the vertical direction and define the flux to be positive in the direction...

## Atmospheric temperature HIRS and AIRS

Atmospheric vertical temperature profiles obtained by infra-red remote sensing from satellites are now routinely used by the meteorological services to augment traditional sources such as balloon-borne radiosondes. The High-resolution Infrared Radiation Sounder or HIRS, which has been in use for many years for this purpose, featured a large number of channels (20) with the highest spectral resolution that can be obtained with interference filters (about 10 cm-1), in order to separate the...

## Surface properties Thematic Mapper and MODIS

For observations from space of the land, the key variables are the reflectivity (in the near-IR) and the emissivity (in the thermal-IR). Figure 10.8 shows how these 'fingerprints' vary for some common materials. Careful choice of wavelength filters (for example, isolating the chlorophyll bands) enhances sensitivity to vegetation types and different stages of growth, or can address the mineralogy and physical state of the surface, with a view to studying desertification, for example, or even...

## Solar luminosity evolution

5.4.1 The role of mean molecular weight For the Sun we can assign an effective blackbody temperature, Tq, so that its luminosity is given by where Rq is its radius. For a dwarf star like the Sun its luminosity during its MS evolution varies approximately as where j is the solar mean relative molecular weight with respect to the proton mass that, as we shall see, controls the luminosity on timescales of billions of years. The mean molecular weight needs to be calculated with some care as it is...

## Plane of reference

Scattering of electric vectors of a plane wave by a homogeneous spherical scatterer. Plane of reference taken through incident and scattered wave. Plane of polarization contains the orthogonal electric field, E and magnetic field H vectors. The Poynting vector P, is in the direction of wave propagation. scattering albedo, u> , defined by eqn (3.36), and knowing the asymmetry factor we can solve the multiple-scattering problem within an atmosphere, as we shall see in 6.4. Details on...

## Solar ultraviolet flux evolution

It is well known that stellar chromospheric activity, as measured by the strength of emissions lines such as Ca II HK (3934 A), Mg II (2800 A), C iv (1550 A), N v (1240 A) and Lya (1216 A), decreases with main-sequence age, t. Magnetic activity, which controls chromospheric, transition region and coronal activity, is driven by the interaction of stellar rotation, internal differential rotation and convection (the dynamo action). The primary indicator of MS activity is thus the stellar rotation...

## Validation data

Validation of model results both for the downward fluxes reaching the surface of the Earth and the outgoing fluxes at TOA is only possible through comparison with ground-based measurements at specific sites for the downward fluxes, and with satellite measurements for the outward fluxes. Table 8.3 summarizes a sample of validation data sets that are available. Table 8.3 Validation data sets. Fluxes at the top of the atmosphere (TOA) are outgoing to space. Fluxes are both longwave and shortwave....

## General circulation models

While radiative-convective models are very useful tools for investigating how the atmospheric composition affects the radiation field, and in turn the role of the radiation field on atmospheric photochemistry, the fact that they have only one spatial dimensional (height) poses some fundamental limitations. The real earth is a three-dimensional distribution of atmospheric and surface properties that are linked by atmospheric dynamics and ocean circulation, whose accurate Table 11.7 Climatic...

## Longwave radiation budget at surface

The estimation of the Earth's longwave radiation budget represents a major objective of the World Climate Research Programme as demonstrated by its Global Energy and Water Cycle Experiment (GEWEX), and in particular the Table 8.14 Model computed mean annual hemispherical (NH Northern Hemisphere, SH Southern Hemisphere) and global average outgoing longwave radiation, OLR (1984-2004) and net incoming shortwave radiation NISR (1984-1997) at the top-of-at-mosphere, and net incoming all-wave...

## Sv 1 Uv Bv Uv Jv

3.4.7.2 Complete frequency redistribution In the case of complete redistribution in frequency, R(v , v) (v )4> (v), and we have nv KvBv + ovp(v) p(v )Jv> dv (3.66) J 0 Sv (1 - Uv)Bv + Uvp(v) p(v )Jv'dv . (3.67) 3.4.7.3 Non-isotropic coherent redistribution The volume emission for the case of coherent scattering in frequency but non-isotropic redistribution in photon direction, as defined by the angle between incoming and outgoing photon direction, is J p(cos )Iv n ,4> d(j> , (3.68)...

## CH2O hv CO h2

Table 7.6 Model global mean surface emission and deposition rates together with global mean mixing ratios for CH4, CO and H2. Table 7.6 Model global mean surface emission and deposition rates together with global mean mixing ratios for CH4, CO and H2. estimated global emission rate of 51 Tg year-1. estimates for the various sources and sinks of tropospheric hydrogen have varied over the years, with the emission rate varying within a range of 30-70 Tg year-1. Hydrogen sources, beyond methane...

## L9m

Contour plot of the size distribution for the haze particles from Lavvas et al. 2007b. Size in m, number density in cm 3. Dashed curve corresponds to the optically effective radius of the particles. Numbers on contours correspond to the log10 number density. Box is Voyager I estimate. physics. The interaction of solar radiation with the atmosphere (photochemistry) and haze determines the chemical species that are formed and the temperature structure. The chemical rates that depend...

## Thermal Infrared Transfer In The Atmosphere

Absorption of terrestrial thermal infra-red radiation by molecules in the atmosphere depends on their concentration, type and whether they are heteronu-clear (e.g. CO2, H2O, CH4, O3, NH3) or homonuclear (e.g. N2 and O2), that is whether or not they have an electrical dipole that can interact with infrared radiation. The atmosphere consists of mainly homonuclear molecules and hence it is the trace molecules, which strongly absorb infra-red radiation emitted by the Earth's surface to space, that...

## Atmospheric composition Iris Atmos and TES

Infra-red and microwave instruments also measure atmospheric composition. The intensity of the emitted thermal flux depends on the temperature and the abundance of the emitter (i.e. on the probability per molecule of emission of a photon of given wavelength, and on the number of emitting molecules present). So, once the temperature has been determined from the emission by a molecule of known abundance, such as CO2, measurements of the same atmospheric path at a different wavelength in an...

## Methane and hydrogen photochemistry

Methane is an important greenhouse gas that is emitted at the Earth's surface through biological activity in swamps, marshes, rice paddies, lakes and oceans. It is also a product in emissions from agriculture, animal husbandry, mining, landfills and volcanoes. Tropospheric methane concentrations have increased from about 0.70 ppmv pre-1980 to 1.75 ppmv in 1998 (IPCC 2001). About half of the current emissions are of anthropogenic origin. Methane is removed from the atmosphere primarily through...

## FL SxeTx6112

Is the direct solar flux, at optical depth rx, normal to the direction of incidence defined by po, the cosine of the solar zenith angle. SqX is the incoming solar spectral flux (erg cm-2 s-1 pm-1) at the Earth's orbit. We note that the phase function is divided by 4n sr so that SiX(p) has units of radiance (erg cm-2 s-1 If we take positive in the downwards direction (increasing optical depth), integrate over the incoming direction and use the Eddington approximation Ix Jx + 3pHx, eqn (3.89), we...

## A 2A0S f32477

For values of w < 10, the above series converges after 25 terms with an error less than 1 . For values w > 10 the absorptance can be computed, with a maximum error of 3 , from the expression A 2A0S(0.7523b3 2 + 0.6513b1 2 + 0.3013b-1 2 + 0.1231), (4.78) where b ln w, based on an asymptotic expansion for single lines given in Struve and Elvey (1934). Thus, given the total line strength of the band, k, or band strength, the absorber amount (in units corresponding to the band strength), the...

## Info

Projected emissions of carbon dioxide (in units of 1012 tonnes of carbon per year) from fossil-fuel burning for four future emission scenarios, together with estimated emissions from 1850-2000. Crown copyright (UK Met Office Hadley Centre 2005). surface air temperature is accompanied by more frequent extreme high and less frequent extreme low temperatures. There is a decrease in diurnal temperature range in many areas, with nighttime lows increasing more than daytime highs. Results...

## Hp Sx395

On using the Eddington approximation we obtain ld2'd 2X) JX(tx) Sx(Tx). (3.103) Substituting for the source function for coherent and isotropic scattering we have l f1 C1 )(Mrx) Bx(rx)), (3.104) which has the form of a steady-state diffusion equation. The above equation can then be solved for the mean radiance J by any standard technique given the boundary conditions at the surface and deep in the atmosphere (see Chapter 6). 3.5.7 The Schuster-Schwarzschild approximation Another approach for...

## Shortwave aerosol radiative forcing

The SW aerosol radiative forcing, AF, or more precisely the 'aerosol flux change', is the effect of aerosols on the SW radiation budget at TOA, at the Earth's surface, or within the atmosphere, and it is given by where Fi and Fciear i are the SW radiative fluxes with and without the presence of aerosols, respectively. The index i involves various aerosol forcings defined in terms of the corresponding SW fluxes. The forcings AFTOa, AFatmo, AFsurf, and AFnsurf, represent the effect of aerosols on...

## Scat nr2 QScatrN rdr660

The asymmetry factor, g, can be computed from 3 -Zsn-Re awaw+1 + 6 6n+1J (6.61) where a* denotes the complex conjugate of a. We recall that the complex conjugate of a complex number is obtained by replacing i by i, wherever it occurs (implicitly or explicitly), and that the product of a complex number and its conjugate is equal to the square of its magnitude. In Fig. 6.5, we present the variation of Qscat as a function of the size parameter x, for n 1.4. We see that if the scattering particle...

## Tables Of Reactions

Table B.1 Photoionization rates and products of atmospheric species, based on the quiet-Sun irradiance in the ultraviolet and visible spectral regions at the top of the atmosphere, for global mean conditions. N2 N(2D) + N+ + e NO NO+ + e O O+ + e N N+ + e N(2D) N+ + e He He+ + e Table B.2 Total photodissociation and photoionization rates of atmospheric species, based on the quiet-Sun irradiance in the ultraviolet and visible spectral regions at the top of the atmosphere, for global mean...

## Detection of climate change

The application of the instruments described in the previous sections to studying the processes involved in climate change is fairly obvious. For example, absolute radiometers (ACRIM) measure the output of the Sun broadband radiometers (ERBE, GERB, CERES) monitor the Earth's radiation budget spec-troradiometers (ATSR, MODIS, HIRS, AIRS) measure surface and atmospheric temperatures interferometers (IRIS, ATM OS, TES) measure composition, including greenhouse-gas amounts. Collectively and in...

## Sea surface temperature ATSR

The surface temperature of the Earth's oceans is a key climate parameter and also a tracer for warm and cold currents near the surface. Again, rather precise measurements are required, with precisions of < 0.1 K and absolute accuracies of better than 0.5 K. Achieving these fairly demanding values from space is made particularly difficult by the presence of the intervening atmosphere, which has absorption features even in the most transparent spectral windows, plus very variable attenuation...

## Atmospheric Physics And Thermodynamics

The atmosphere is a thin shell of gas held gravitationally to the planet and having a thickness of only about 1 of the radius of the solid body. Its original composition, drawn from the solar nebula from which the Sun and the planets formed, will have included many more light elements, especially hydrogen and helium, than are found today, and a complicated evolutionary process, still not fully understood, was involved in the progression from one to the other. Key stages in the evolution of the...

## G

6.7.4 Atmospheres with clouds and aerosols The atmosphere can be divided into layers whose individual optical depth is evaluated, according to its properties, from t Tcs Tca Taers Taera Tma + tr, (6.150) where tcs is the cloud-scattering optical depth, Tca is the cloud-absorption optical depth, raers is the aerosol-scattering optical depth, Taera is the aerosol-absorption optical depth, Tma is that for molecular absorption, and tr is that for Rayleigh or molecular scattering. The single...

## Outgoing solar radiation at TOA

We present global distribution results of the outgoing solar radiation at TOA based on a deterministic radiative-transfer model on a mean monthly and 2.5 x 2.5 longitude-latitude resolution, spanning the 14-year period from January 1984 through December 1997. The model uses data from the ISCCP D2-series supplemented by water-vapour and temperature data taken from NCEP NCAR. Model input data were also taken from other global databases, such as TIROS-TOVS, ISLSCP, and GADS. The model computations...

## Model input data

In order to calculate the longwave and shortwave radiation budgets using the models described in Chapters 4 and 6, various atmospheric, cloud and surface properties are required. These are listed in Table 8.1. Table 8.1 Input data required to model the Earth's radiation budget. For clouds the data required are for each cloud type (low, middle and high-level). Cloud properties Atmospheric properties Surface properties Cloud amounts Scattering optical depth Absorption optical depth Cloud-top...

## Hz LEMsw1119

Where F(z)gW is the net downwelling solar radiation flux at level z, p is the atmospheric density and cp the atmospheric specific heat capacity at constant pressure. In Fig. 11.4 is given the mean global vertical heating rate due to solar radiation absorption for an RC model with mean cloud cover of 0.5, surface albedo of 0.1, with the relative humidity falling with altitude according to (Man-abe and Whetherald 1967) rh vh Ps '02 p ps > 0.02 (11.20) with a surface relative humidity of 0.8,...

## Climate Observations By Radiometryspectrometry

Quantitative and spectroscopic measurements of radiation are at the heart of observations made to understand and monitor the climate system (Fig. 10.1). The time-dependent complexity of the system under observation requires that the measurements span the globe, including the vertical dimension. Many of the important processes, for example those involved in ozone depletion, are associated with transient dynamical phenomena and occur on local and diurnal scales, calling for high-resolution...

## A ko T [M

B a k (T), c log b, d (1 + c2)-1 and f is a constant that for atmospheric conditions a value of about 0.6 adequately fits the reaction data. There are simpler limiting forms for kf depending whether or not we have low or high pressure. At low pressures If the number density M of the catalytic third body is in units of molecules cm 3 then the units of ko are cm6 cm3 molecules 1 s 1. Usually, ko(300), ka 2006, IUPAC 2006, NIST 2006). while the units of kare (300), n and m are tabulated (JPL In...

## Terrestrial radiation transfer in GCMs

11.4.3.1 HadAM3 Scheme The longwave fluxes are calculated by a two-stream approximation, where the spectrum is divided into 8 bands with the following boundaries (in cm-1) 0-400 400-550 550-800 (excluding 590-750) 590-750 800-1200 (excluding 990-1120) 990-1120 1200-1500 and 1500-3000. Gaseous absorption data are again derived from HITRAN and continuum absorption by water vapour is treated using a continuum model. 11.4.3.2 NCAR CAM 3.0 Scheme Longwave absorption by ozone and carbon dioxide is...

## The shortwave radiation budget at surface

Figure 8.16 shows the geographical distribution, on a 2.5x2.5 degree resolution, of the 17-year (1984-2000) average downwelling shortwave radiation (DSR) at flg. 8.16. Long-term (1984-2000) average global distribution of downward shortwave radiation (W m 2) at the Earth's surface for the month of January. (Hatzianastas-siou et al. 2005) flg. 8.16. Long-term (1984-2000) average global distribution of downward shortwave radiation (W m 2) at the Earth's surface for the month of January....

## F vnAAOs

The above series converges very slowly for y > 10 and for this range of values, wD can be evaluated, with a relative error < 1 , from the truncated series wB(v(y)) v +--- +- , (4.43) where v(y) i lny. The Lorentz equivalent width can be computed from Table 4.1 The coefficients b and c used to evaluate the Ladenburg-Reiche function L(x) for x < 7 using eqn (4-45). (Vardavas 1993) where x(a,y) y (2a Tr) and L(x) is the Ladenburg-Reiche function given by L(x)...

## O2 hv O3P O3P750

With atomic oxygen in the ground state. This Herzberg dissociation continuum is weak, extends from 185 nm to 242 nm, and is the main source of O atoms for altitudes below 60 km in the Earth's atmosphere. The absorption cross-section of O2 as a function of wavelength for the Herzberg continuum is given in Fig. 7.4. FlG. 7.3. Idealized potential energy curves for O2 and vibrational-rotational energy levels, with dissociation limits at 7.047 and 5.080 eV. Bound-bound transitions from Xto B3 -...

## [1 wl togc2 ts tajj

And the cloud single scattering albedo is with ts and Ta being the scattering and near-infra-red absorption cloud optical depths, respectively, while the asymmetry factor gc is set to a lower value of about 0.8. The cloud absorption is then given by a rc 1 Rirc tirc. 6.5 Aerosol absorption and scattering A major difference between aerosols and greenhouse gases is that aerosols have a much shorter atmospheric lifetime (from 10 4 days for natural, to tens of days for anthropogenic aerosols)...

## NSTp i Afi Y666

Thus, we can write 2nNSTP V A2 If we replace k in the expression for the cross-section we have Table 6.2 Coefficients for computing the Rayleigh scattering cross-section. Table 6.2 Coefficients for computing the Rayleigh scattering cross-section. and so the cross-section (cm2 ) can be computed from

## B2 a21 e2

E(year) eo - 7.22 x 10V(year - 2000), FlG. 5.15. The celestial sphere and the plane of the ecliptic. FlG. 5.15. The celestial sphere and the plane of the ecliptic. where year is years AD. The arc SD 6 is the solar declination with a maximum value equal to e. The arc YD a is called the right ascension of the Sun, and corresponds to the solar longitude as measured on the celestial equator, measured from the vernal equinox where a 0. Thus, a and 6 define the coordinates of the Sun, point S, on the...