## ATSQ 4eaT4115

For almost any form of the function a(T) between values that are constant when the planet is completely ice covered or completely ice free, this expression has at least three solutions for T. flG. 11.1. A 'single-slab atmosphere' model of the greenhouse effect, in which the atmosphere is treated as a homogeneous layer of temperature Ta that is perfectly transparent to solar radiation and perfectly opaque in the thermal infra-red. The surface receives the equivalent of two solar constants,...

## Introduction

Many of the radiative processes that govern the climate system of the Earth are also important on the other planets of the Solar System. The different boundary conditions that apply, especially distance from the Sun, give rise to different histories and surface and atmospheric properties, but parallels can often be drawn that test our understanding of the physics involved, which of course is everywhere the same. Comparisons between the planets are instructive, therefore, as are attempts to...

## Rv Ro x RiA x R2f x Rsxy x R404 941

Thus, the overall response Rv of the system depends on all three domains, so that, for example, increasing spectral resolution reduces the energy throughput and hence the signal. In general however the variables are not coupled, so that this change should not directly affect the field of view, for example. System definition begins with a consideration of which properties are fixed by the application and which are free parameters in the optimization of the design. It is also necessary, of...

## A v2U2 rcHc GMmk Trc124

We usually also define a characteristic escape time given by Te Hc ve (s). clearly this must be appreciably less than the age of the Solar System ( 1017 s) for the loss of a given species from any particular planet to be important for the climate on earth, oxygen is safe, by this criterion at least, while hydrogen and helium are long gone (Table 12.2). on Jupiter, the combination of low temperature and high gravity means that this condition is not met, even for hydrogen (Table 12.3). Jeans'...

## Preface

Interest in the Earth's climate is at an all-time high, due in large part to concerns that it may be changing to a degree that will soon adversely affect the habitability of the planet. This realization coincides with rapid improvements in the tools needed to study and understand the physical processes that produce and maintain the climate, including remote-sensing instruments and observing platforms in space, and fast computers and sophisticated algorithms to analyse large amounts of data and...

## Oxford

Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland...

## [s20 s20Sm0d0 [

The extinction cross-section per particle, aext, computed by Mie theory needs some care. The extinction (scattering plus absorption) of an EM wave by an infinitesimal layer, dz, of a medium is given, according to Mie theory (see van de Hulst), by the reduction in the magnitude of the electric-field components 3ext 2nk-2N dzRe S(0) , (6.43) with N the number density of the scatterers, all assumed to be of the same radius and refractive index. We have taken the real part of the complex scattering...

## Info

Where here RH is the Rydberg constant for atomic hydrogen given by where e is the electron charge and m the reduced mass of the electron-proton system of H, so that ft.RHc is equal to 13.60 eV. Thus, if we set n 1 and nj to then the energy difference is the ionization limit that is equal to 13.60 eV and corresponds to radiation at the wavelength 912 A. Generally, the ionization FlG. 5.3. The mean solar spectral irradiance, Sq above the atmosphere of the Earth, corresponding to a solar constant...

## Theory Of Radiation Measurements

Radiation measurements are crucial for understanding the climate system and monitoring its behaviour. Increasingly, the most important measurements are made from instruments in space, orbiting the Earth on platforms that offer global coverage of the atmosphere and surface beneath. These remote sensing instruments are the subject of the following chapter. Here, we consider the basic design and operating principles of the instruments that produce both remote and in-situ climate measurements. We...

## The Climate System

We define climate as the mean state of the atmosphere, averaged over several years and all seasons, with particular emphasis on those factors that affect the temperature of the Earth's surface, in both a local and a global mean sense. The climate system includes the Sun, the Earth's surface and some aspects of its interior, for example that which gives rise to outgassing and volcanism, as well as the atmosphere, hydrosphere, biosphere and cryosphere. In this chapter, we provide an overview of...

## H EE E cpp s d pp sd V d e 811

Where p is the average pressure, s the salinity, 0 the potential temperature, p the density, V the volume, cp the specific heat content of the water cell in location (j,l,k), and 90 is a reference potential temperature. Quantities p, 9, p, and cp can be calculated using the MATLAB Seawater Library of the Commonwealth Scientific & Industrial Research Organisation (CSIRO) Marine Research Division given the salinity, temperature and depth for a specific water cell. Knowing the seasonal...

## To

The variation of the flux ratios is close to those of Ribas et al. who obtained power-law fits of 3.10t '72 and 6.40t 1'23 for the scaled Lya and XUV (1-1200 A) ratios, respectively, at 1 AU. Similarly, Wood et al. (2005) found for G V and F V stars a power-law fit of Lya flux at the stellar surface x P_1- 9 8, which when combined with the age-rotation relationship P < x t 6 gives Lya flux oct -65 -12. 5.5.5 Solar XUV and Ly-a emission flux evolution The method can be applied to calculate the...

## Log10 w g cm2

Band absorptance as a function of CO2 amount (g cm 2) for the 15 m bands, depicting the linear, square root and logarithmic limits at effective broadening pressures of 1.0 and 0.001 atmospheres, at T 300 K. equilibrium, we can write the ratio of the population n of the lower vibrational-rotational level and the total population, n, of the molecule in terms of the Boltzmann distribution where, Ev is the energy of the lower vibrational level v, there is no degeneracy associated with v,...

## J BTdtZAX dz BX T t0 A AA

Where the Planck function, B and the transmittance from level z, t depend strongly on A but more weakly on AA, provided AA is narrow. If AA is in a strongly absorbing region, t(0, A, AA) tends to zero, the second term that represents the contribution from the surface to space vanishes and the radiance leaving the top of the atmosphere is just the integral over height of the Planck function weighted by the derivative with respect to height of the atmospheric transmittance along the viewed path....

## KTehve

Which, in addition to choosing material with large n and G, implies a low temperature T and a large equivalent resistance R. The detector is then said to be photon-noise limited. If the power P originates mainly in the background rather than the source then the detector is said to be operating in the 'BLIP' (background limited intrinsic photoconductor) condition. Figure 9.7 shows how most detectors approach this condition at their wavelength of peak performance. Photovoltaic mode detectors are...

## Dt

Thus A0 Z0, which varies as T, and hence the main temperature dependence of kf comes from the exponential term. For large molecules their orientation on collision becomes important and a correction to Ao is required. This is usually introduced as the steric factor or probability factor P, so that Ao PZo, with P < 1. The steric factor requires a more complex treatment than that from simple collision theory and this is manifested within the transition-state model that involves a transition...

## GT Pt98

Where G* and C* are the thermal conductance and capacitance, respectively, of the element. The amplitude of the temperature cycle is FlG. 9.4. The response of a pyroelectric detector as a function of frequency for several values of the load resistance RL. The responsivity can be improved by increasing RL, but at the expense of frequency response. The device will normally be operated in the plateau region, so that output is less sensitive to frequency fluctuations. (After Boyd 1983). FlG. 9.4....

## BuT buTByTTB bcT bcTsTsT n

Table 4.2 The terrestrial infra-red region divided into spectral intervals with centres w cm-1 and width Aw within which there are important overlapping bands of water-vapour, carbon dioxide, methane and ammonia. (Vardavas and Carver 1984) Table 4.2 The terrestrial infra-red region divided into spectral intervals with centres w cm-1 and width Aw within which there are important overlapping bands of water-vapour, carbon dioxide, methane and ammonia. (Vardavas and Carver 1984) H2O rot-cont, CO2...

## Vo Vs Vn

V0 can be determined by noting the voltage across the detector when the incoming flux is zero, i.e. by calibration of the detector or instrument using a shutter or, on a satellite, a view of cold space. Most detectors take a finite time to reach a steady output after being exposed to a flux of radiation. The time constant for this process t, which determines how rapidly measurements can be repeated, is defined by the expression so t t is the time taken to reach 63 ( 1-1 e) of the steady-state...

## CiPi Sei Sdi72

Where t is time, z is altitude, and i is the total vertical diffusive flux. The net production term Ci from collisionally driven reactions is determined from the expression where vlj is the reactant stoichiometric coefficient of species l involved in each collisional reaction j with forward reaction rate kj (T,p). We recall that the general elementary reaction can be written as where Xi is species l taking part in reaction j, vj is the product stoichiometric coefficient and lj is the net...

## J

Where tox is the total optical depth of the atmosphere and 1 > 0 defines the upward non-vertical direction of the emitted radiation. If we perform the transformation w dw --Trd j, d j, --tt i e-T jdj I u-3e-TxUdw, J 0 J where nBx is the surface spectral emission (W m-2jm), integrated over all directions, and the special function En is the exponential integral defined by t-ne-xtdt xn J t-ne-tdt, (3.87) which obeys the recurrence relations - 7n_i(z) En(0) -- (n > 1) The diffusivity...

## DT RT2779

And on integrating we get the form of the Arrhenius equation that was first obtained based on experiment where A is the integration constant. More generally, in the Arrhenius expression, A can be weakly dependent on temperature. We can see this from simple collision theory. The probability that two molecules A and B collide with a combined energy of at least Ef is given by the exponential term in the above equation. This is equal to the fraction of effective collisions, where the total number...

## Cloudysky fluxes

Clouds are an important determinant of atmospheric radiation as they have lower temperatures then the surface and hence reduce the thermal emission of the planet. Optically thick clouds, like the low-level and middle-level clouds, emit essentially as blackbodies with emissivity close to 1, where ecX 1 e TcA and rcX is the cloud optical depth at wavelength A. High-level clouds, are usually not ideal blackbodies and can have an emissivity well below unity. In Fig. 4.19 we see that the...

## N

Where the total columnar number of particles (particles per unit cross-section of atmospheric column or column number density) of all sizes is N ni. We can also define an effective aerosol radius for the whole aerosol column based on the columnar volume size distribution The effective radius for the fine mode shown in Fig.6.14 is about 0.13 pm throughout the year, while that of the coarse mode varies within the range 2.00-2.32 pm. Table 6.5 Seasonal averages of aerosol volume size distribution...

## F3986

The mean annual hemispherical and global average values over the 14-year period from 1984 to 1997, for the incoming, outgoing, net incoming (i.e. absorbed) SW radiation at TO A, and planetary albedo, are given in Table 8.8 and compared against ERBE data and other published values. In Table 8.9 are given the incoming and outgoing SW radiation, and the net incoming and planetary albedo for the hemispheres and the globe. On a 14-year basis (1984-1997), the Earth is found to reflect back-to-space...

## Ni gj exp Ej EvkT nQvQr

Where r hcBr k is a characteristic temperature of rotation and depends on the rotational constant Br. Thus, we see that since hc k 1.439 cm K and Br is typically about 2 cm1, then r is about 3 K, and hence for atmospheric temperatures r T 1 and hence the sum in the above equation can be replaced by an integral to give while for polyatomic molecules of atmospheric interest, the rotational partition function varies as T3 2 (Herzberg 1945). The partition function for vibration of a diatomic...

## Mipnynx 1pnynx

With the prime superscript denoting a first derivative with respect to the argument of a function, x kr and y mx, r is the radius of the particle, m its refractive index. In the above Mie solution, the medium surrounding the scattering particle was taken to be vacuum (m 1), however, if the surrounding medium has a real refractive index m2 (no absorption), then we obtain the solution by replacing m by m m2 and A (in vacuum) by X m2. Also 7T (cos 0) P.* (cos 0), (6.53) r (cos0) - Pn1(cos0)....

## UpA

Where t is the thermal time constant C* G* (s). The load resistor RL is in parallel with the internal resistance of the detector R0 so the output voltage depends on the combination R R0RL (R0 + Rl). Similarly the capacitance is C C0 + CL, if there is any external capacitance CL, stray or otherwise. The electrical time constant is RC, so the (voltage) responsivity is The responsivity is plotted as a function of the load resistance RL in Fig. 9.4. It is desirable to operate at frequencies in the...

## Drx

The total downwards flux, FTX, comprises the diffuse and direct components FTx Fi + MoFjx, (6.133) and the net downwards flux is fl x ftx + fx (6.134) The surface boundary condition is then where Rsx is the surface spectral reflectance and both diffuse and direct solar radiation is diffusely reflected upwards at the surface. Thus the total upwards flux is equal to the diffuse component, FTx F_j. At the top of the atmosphere the boundary condition is that there is no incoming diffuse component...

## [H2o [co2

Simple greenhouse models for the present (solid line) and pre-industrial and late-twenty-first century Earth, as discussed in the text. flG. 11.2. Simple greenhouse models for the present (solid line) and pre-industrial and late-twenty-first century Earth, as discussed in the text. were found to fit the past data and hence deemed appropriate for extrapolation into the future. Such crude methods may be used for some of the processes, even in a full GCM, while research goes on to...

## Ig10 P atm

Band absorptance (cm-1) as a function of the effective broadening pressure (atmospheres) for the O3 9.6 m bands, depicting the pressure-independent regions, for different ozone amounts (g cm-2), at T 300 K. root limit is attained for intermediate absorber amounts for the low-pressure case. The criterion for strong lines is satisfied for the CO2 15 m band. For the high-pressure case only the linear and logarithmic limits are attained. 4.5.3 Temperature dependence of absorptance The...

## C N V gunij

Where h is Planck's constant, c the speed of light, l and u refer to the lower and upper state, respectively, N is the molecular number density, n and nu are the populations of each state, g are statistical weights that take into consideration the electronic, vibrational, rotational and nuclear degrees of freedom of the molecule and Blu is the Einstein coefficient for induced absorption in units cm3 (erg s2). For LTE conditions the population of each state is defined by Boltzmann statistics,...

## Orx

Note that we have defined j, cos 0 such that j, > 0 in the outward direction while the optical depth is zero at TOA increasing towards the surface. The solution for a layer defined by the boundaries zmax to z, as shown in Fig. 3.6, is then ix(tx, ) Ia(0, , (3.80) where j < 0 for incoming radiation with the upper boundary value Ix(0,j) at 3.5.4 Solution for thermal emission A planetary atmosphere can absorb and emit thermal infrared radiation, given that it has heteronuclear molecules (e.g....

## K

Where Si and S2 are called the Mie scattering functions ( 6.3.2). The time-average magnitude of the Poynting vector of the scattered wave can be written as F(0,0) Si sin2 0 + S cos2 0. (6.31) The total rate of scattered energy, dL (in W), flowing through an element of area dA is then where n is a unit vector normal to the element of surface. If we now replace dA r2 by d sin OdOd0, an element of solid angle, then the total rate of energy, L, scattered into a sphere around the scattering particle...

## PL

With p and L being the water density and the latent heat of evaporation, as defined before. The equation above is used to calculate the bulk aerodynamic evaporation rate Ea from Qea and the heat-balance evaporation rate Er from 8.9.3 Sea data for computing heat storage For the calculation of the heat storage, AH we need the seawater temperature, salinity and pressure in a three-dimensional grid. We can use such data from two sources. The first is the Mediterranean Data Archaeology and Rescue...

## Radiativeconvective climate models

One-dimensional radiative-convective (RC) climate models are very powerful diagnostic tools for understanding climatic sensitivity to changes in the physical and chemical structure of the Earth's atmosphere and surface. The usefulness of RC models stems from their relative simplicity and their ability to provide a quantitative estimate of climate change produced by variations in, for example, the atmospheric content of carbon dioxide or water vapour, changes in the solar flux and in the Earth's...

## Computation of fluxes

To compute the Earth's longwave radiation budget one needs the following atmospheric, Earth surface, and cloud properties Molecular mixing ratio vertical profile Atmospheric vertical temperature and pressure profiles Earth's surface temperature and emissivity Cloud infrared optical depth Cloud-top temperature and pressure Cloud-base temperature and pressure in order to compute, at each wavelength, the thermal fluxes at the Earth's surface, within the atmosphere and at TO A. The next step is to...

## Clearsky fluxes

In Chapter 3, we derived the Schwarzschild-Milne equations, given the source function, for the net upwelling flux at any atmospheric level arising from flux emitted by the surface and by the atmospheric layers below and above that level. For the troposphere and stratosphere, the bulk of the thermally emitting FlG. 4.17. N2O 7.8 m band rotational line intensity, including contributions from isotopic bands. FlG. 4.18. N2O absorption cross-section in the region of the 7.8 m band. FlG. 4.18. N2O...

## Band absorptance formulations

4.5.1 Doppler-broadened rotational limes The absorptance of a molecular band can be calculated based in an analogous way to line absorptance. At low pressure the rotational lines of a band are Doppler broadened and essentially non-overlapping, as the full line width, 2bD, typically 0.002 cm1, becomes smaller than the line spacing, d, typically 1.0 cm1. Ignoring any asymmetries between P and R branches, we can consider, to a first approximation, that the line strength decreases exponentially...

## Ext 4nk2Re[S0Ndz646

Where Ndz has units of inverse area and so we can write the extinction cross-section for a single particle as Knowing the extinction and scattering cross-sections for a single particle we can compute the absorption cross-section of the scattering particle. For a medium consisting of scattering spheres of different radii, a, we can weight a particle cross section by the number density distribution of sizes and we note that the functions Si and S2 are functions of the particle radius and the...

## Av

Where I0 is the radiance from a reference source and Vn is the output noise voltage. The relationship between input radiance and output voltage is assumed to be linear (the system design will be such as to make sure this is the case) and the contributions to the net responsivity of the system from spectral, geometrical, and radiometric factors are independent of each other, so that

## Acknowledgements

The writing of a textbook with the wide scope embraced here involves drawing on the work of a very large number of researchers, past and present. We have acknowledged our main sources in the text and in the notes and references at the end of each chapter, to these and others too numerous to mention go our gratitude and recognition. Any errors or omissions are of course the responsibility of the present authors. FWT would like to thank Jesus College, Oxford, for a travel grant and the Foundation...

## Kncn h uaUb kb

Where n is the number density of each molecule. The equilibrium constant is given by the thermodynamic expression where R is the universal gas constant, and AG the change in the molar Gibb's free energy of the system given by AG Y G (products) - G (reactants), (7.75) with G the free energy of formation of the species involved in the reaction in their standard state, usually at a pressure of 1 atm and room temperature of 298 K. If AG is negative, K will be greater than unity and the forward...

## NET mTM

Unlike NET, NEAT has significance only in terms of viewing a specific source, and is a function of source temperature, Ts. If the target has an emissivity of ev at wave number v cm-1 then It follows that, in principle, the NET and the NEAT have the same value at Ts 0 K, for a blackbody source with ev 1. FlG. 9.13. Conceptual grating spectrometer layout, showing entrance and exit optics and associated optics. In summary, in much the same way that NEP describes the performance of a particular...

## AO Av e yv

Where A is the aperture or collecting area, O the solid angle of the field of view, Av the spectral resolution (or, more generally, the spectral bandwidth) in cm-1, e the efficiency or throughput of the optical components, and to the measurement time in seconds. A modulation factor of 1 2a 2 appears (in the denominator) because the chopper, usually a rotating toothed wheel with equally spaced teeth and gaps, passes this fraction of the total energy if the beam has a circular cross-section. The...

## NEP aA Grv Nep Aav y

The lowest temperature that can be measured is that which produces SNR 1 this is known as the noise equivalent temperature or NET and is given by A more useful quantity is the noise equivalent temperature change (NEAT), given by The NEAT is the amount by which T has to change to produce the smallest detectable change in the detector output, which is by definition equal to the NEP. It is therefore a measure of the sensitivity of the radiometer, and of the uncertainty in any measurement. For a...

## X9

Or 4.577 x lO21- A (l + B X2) (6.69) where A is in pm, the coefficients A and B are tabulated in Allen (1976) for various molecules, while S (6 + 3A) (6 7A), where A is the depolarization factor, whose values are given in Table 6.2, together with the coefficients A and B for various molecules. For a mixture of atmospheric gases we obtain the rayleigh cross-section from where nm is the mixing ratio by volume, of molecules m. The rayleigh reflectivity of an atmospheric layer can be quickly...

## Rd Rl Rd ARd RlRd

Assuming a log-linear dependence, with coefficient a, between the temperature of the detector element, T, and its resistance RD, and RD RL. In general, VS is accompanied by VN and V0, the noise and offset components of the output voltage as before. The advantages of thermistor bolometer detectors include sensitivity to a wide range of wavelengths, and reasonable performance (D* few x 108 cm Hz1 2) without cooling. The main drawback is the need to provide a high (noise-free) bias voltage....

## D

And depends on the effective broadening pressure, pe (atm), given by where pm is the partial pressure of atmospheric constituent molecule, m, and Z is the broadening coefficient. For CO2, Z takes values 1.3, 1.0, 0.81, and 0.78, for collisions between CO2 molecules and CO2 (self broadening), N2, O2, and argon, respectively. For ozone, we can take pe 1 and Z 1, for ozone-air collisions, as it is a minor constituent of the atmosphere. Care must be taken with the units when the effective...

## HjlTT dJ

Where Mi is the molecular weight, g is gravitational acceleration, T is atmospheric temperature, and R is the universal gas constant. We see that when the molecular density structure follows that given by the stratification structure we have zero Brownian diffusive flux. Similarly, the atmospheric scale height when we have complete mixing is given by where M is the atmospheric mean molecular weight and We can now express the Brownian diffusive flux in terms of the mixing ratio For turbulent or...

## Contents

1.5 Radiative equilibrium and radiative forcing 8 1.6 Atmospheric circulation 10 1.7 The hydrosphere and the cryosphere 12 1.7.1 Oceanic circulation 13 1.7.2 El Nino southern oscillation (ENSO) 15 1.7.3 North Atlantic oscillation (NAO) 17 1.8 The land surface and biosphere 20 1.8.1 Land-surface albedo 20 1.8.2 Carbon dioxide sequestering 20 1.9.1 Temperature trends 21 1.10 Projections of future climate 24 1.10.1 Emission scenarios and global warming 26 1.10.2 Climate projections for the...

## Ku Y Sj wj499

The HITRAN data corresponds to reference temperature and pressure conditions (Tref 296 K and Pref 1 atm). This means that for different conditions, corrections to the line intensities and half-widths must be done, before the calculation of the absorption coefficient. In order to correct for temperature variations in the line strength, we need to know the temperature dependence of the statistical weight and level populations. Based on the condition of LTE, the Boltzmann distribution provides...

## Ivp A dfj d 370

3.5 The equation of radiation transfer The equation of radiation transfer describes the modification of the radiation field as it traverses an atmosphere. It has terms related to absorption, emission and scattering of photons by the atmospheric molecules, but can include surface effects. Planetary atmospheres can, as a first approximation, be considered as plane-parallel or simple layers. It is better to simplify and solve the transfer equation to deal with specific problems rather then attempt...

## R

Where v is the upward velocity of a molecule of mass m. The critical level for collisions, which we now call the exobase, falls between 500 and 600 km altitude on Earth. It occurs when the vertically integrated density accounts for one mean free path, i.e. at radius rc from the centre of the planet where N (r)adr aN (rc )Hc 1, (12.2) where N is the number density, a is the collisional cross-section, H is the scale height, and rc defines the height of the exobase. The Jeans' escape flux Fjeans...

## ItiMV

Where the transmissivity tr 1 Rr, gr is the asymmetry factor set to zero (symmetric scattering). For the atmosphere the flux-mean optical depth over the UV-visible range of the incoming solar radiation is 0.187. The flux-mean rayleigh scattering optical depth can be computed from the incoming solar flux spectral distribution, normalized to a solar constant of 1366 W m 2. For a solar zenith angle corresponding to p 0.5 the rayleigh reflectivity of the atmosphere is about 16 , according to the...

## POJFdV6122

We can divide the equation by a and differentiate a second time to obtain the radiation diffusion equation, cf. eqn (6.95), on replacing the derivative of H in terms of J from eqn (6.114) where a 1 3a and b 3 a. For the case of isotropic scattering, g 0, and for no incoming solar flux a 1 3 and b 0, and so we obtain the radiation diffusion equation given by eqn (6.97). If we now substitute for the source function Sx from eqn (6.116) we get a second-order differential equation

## Tlto

Which is the expression known as Schottky's formula. (in)2 N f 2e A , (9.34) In photovoltaic mode, the resistive (Johnson) noise contribution is generally negligible compared to that due to the photon flux P. If the background contribution to the power at the detector is also negligible compared to that originating in the source, i.e. P Ps, then the noise current is so the signal-to-noise ratio, in terms of dwell time t0, is The noise equivalent power, defined as the signal power that results...

## O

The variation of the global cloud cover based on ISCCP data for the period 1984-2004. cloud cover and the radiative properties of the many types of cloud. Cloud cover is highly variable both temporally and spatially. Cloud overlap can modify rapidly the resultant scattering and absorbing properties of the cloudy sky. The radiative properties of droplets are different from ice crystals, and different condensation processes can occur rapidly. In addition to the airborne droplets or ice...

## Solar evolution

The Sun started its life as a cloud of very tenuous hydrogen gas that contracted to a protostar in about one million years (Myr). As it contracted its interior temperature increased until its surface temperature rose to over 1000 K and it became an infra-red emitter. A possible next phase is what is called the T-Tauri star stage with an effective temperature of several thousand degrees and a radius of several times the present value, as shown in Table 5.5. The T-Tauri phase of a star is...

## FTJ rRJ

Solar and proxy solar (stars of Table 5.6) results for r 1 AU are shown in Figures 5.11 and 5.12. At an age of 100 Myr the solar XUV and Lya emission flux ratios are 104.0 and 15.6, decreasing to 5.7 and 2.7, respectively, at an age of 1 Byr (3.56 Byr ago). However, beyond the present age, for the next several billion years the solar emission flux ratios decrease very slowly up to 8 Byr. Although the Rossby number increases over this time interval its effect is compensated by a corresponding...

## Atmospheric molecular absorption

In Fig. 6.3 is shown the solar irradiance, at low resolution (see 5.2.4), and the atmospheric molecules that absorb it, mainly in the near-infra-red. In Table 6.1 are shown the main absorbing molecules in each spectral interval, including Rayleigh scattering, from the ultraviolet to the near-infra-red. 6.2.1 Ultraviolet-visible absorption The most important molecular absorption relevant to the 0.20-0.85 m range of solar radiation is that of O3. The absorption is temperature-dependent in the...

## Solar flux at the Earths orbit

According to Kepler's first law, the orbit of a planet around the Sun is an ellipse, with the Sun one focus. The Sun-Earth distance, r, thus varies with time as the Earth's orbit around the Sun is elliptical. The elements of this elliptical orbit are shown in Fig. 5.14 where S is one focus corresponding to the Sun (the second focus is its reflection on the segment BO across the KO plane) A is perihelion B is aphelion a OA is the semimajor axis b OK is the semiminor axis e OS OA is the...

## Intruduction Of Earth Surface

The Sun is a dwarf main-sequence star with an age of about 4.6 Byr (billion years) whose luminosity has increased slowly, by about 30 , from the time it joined the main sequence. At the same time, the XUV (1-1200 A) and ultraviolet emission decreased as the rotation rate of the Sun became slower, and its magnetic activity declined. Thus, the incoming solar radiation (ISR) at the Earth's orbit is determined by solar evolution on timescales of billions of years. Luminosity variations affect...

## Climate Signal White Noise

Where to is the integration time (s) of the measurement. Figure 9.6 illustrates graphically the effect of integrating the signal (i.e. reducing the bandwidth) in observations of the signal returned from a lidar (optical radar) system viewing the atmosphere vertically upwards from the ground. This is an example of an active system, that is, one that includes its own source. A real lidar system, used to observe the backscatter from thin cloud layers in the atmosphere, uses two lasers, one to...

## 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...

## 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...