## Climate sensitivity radiative forcing and feedback

The simple model we have been studying affords us the opportunity to introduce the concepts of radiative forcing, sensitivity coefficient and feedback factor. These diagnostics can be applied across the whole spectrum of climate models, from the simplest to the most comprehensive. Suppose that the mean surface temperature depends on some parameter A, and we wish to know how sensitive T is to changes in that parameter. For example, this parameter might be the Solar constant, or the radiating...

## H Jh kT

Solving for the ice thickness, we find This determines the ice thickness once Tg is known. The physical content of this statement is that the ice thickness grows until it is just thick enough to let through the amount of heat delivered to the bottom of the ice. Ice can exist in equilibrium if Tg < Tf, and the ice thickness approaches zero as Tg warms to the freezing point. Increasing the heat flux or decreasing the thermal conductivity would also thin the ice. The fact that it is the harmonic...

## AnSn en effTi En

AT Tg - Tsa y--nb n+ , n + sa-0 (6.35) The numerator in this expression is the energy imbalance the surface would have if the ground temperature were equal to the overlying air temperature. It can be either positive or negative and its sign determines the sign of AT, since all three terms in the denominator are positive. The denominator is a stiffness coefficient. For any given magnitude of the numerator, the denominator determines how much the ground and air temperature differ. In other words,...

## Close to home

When the young Carl Linneaus set off on his journey of botanical discovery to Lappland in 1732, he left on foot from his home in Uppsala. He didn't wait until he reached his destination to start making observations, but found interesting things to think about all along the way, even in the plant life at his doorstep. So it is with climate as well. To the discerning and sufficiently curious observer, a glance out the window, a walk through the woods or town, a short sail on the ocean, all raise...

## At dtdt

The decay rates of A and B are equal because each reaction consumes one particle of A and one of B, producing a particle of C. The rate depends on the product of the activities of the two reactants, since the product gives the probability of particles of the reactants encountering each other. Now, the first equation given only determines the decay of A owing to the reaction with B. This will be the net reaction when there is no C present, but after the reaction proceeds a while in a closed...

## DG dR dG

For example, if R represents the concentration of water vapor on Earth, or of methane on Titan, and if R varies as a function of temperature, then the feedback would influence G through the OLR. Writing OLR OLR(T, R(T), A), then the feedback parameter is assuming the albedo to be independent of temperature in this case. Now, since OLR increases with T and OLR decreases with R, the feedback will be destabilizing ( < 0) if R increases with T. (One might expect R to increase with T because...

## Basic Formulation of Plane Parallel Radiative Transfer

We will suppose that the properties of the radiation field and the properties of the medium through which it travels are functions of a single coordinate, which we will take to be the pressure in a hydrostatically balanced atmosphere. (Recall that in such an atmosphere there is a one to one correspondence between pressure and altitude). This is the plane-parallel assumption. Although the properties of planetary atmospheres vary geographically with horizontal position within the spherical shell...

## Escape of an atmosphere to space

Atmospheric escape calculations play a role in determining how a planet got to be the way we see it today, and what kind of atmosphere it may have had in its past escape calculations can also indicate how long a planet can maintain a habitable climate, and can inform investigations into the mechanisms needed to maintain an atmosphere in a given state. For example, does there need to be an source of N2 outgassing to maintain Titan's largely N2 atmosphere The answer to that hinges primarily on...

## Basic concepts

The atmosphere can be considered to be a mix of particles, some of which absorb, some of which scatter, and some of which do both. The particles could be molecules, or they could be macroscopic particles of a condensed substance, as in the case of cloud droplets or dust particles. One builds up the absorbing and scattering properties of the atmosphere as a whole from the absorbing and scattering properties of the individual particles. In keeping with the usage in the preceding chapters, we will...

## Contents

1.1 Overview 1.2 Close to 1.3 Into deepest time Faint Young Sun and habitability of the Earth 8 1.4 Goldilocks in space Earth,Mars and 1.5 Other Solar System planets and satellites 1.6 Farther afield Extrasolar 1.7 Digression About climate proxies 1.7.1 Overview of proxy 1.7.2 Isotopic 1.7.3 Hydrogen and Oxygen isotopes in sea water and marine sediments 34 1.7.4 Forams to the rescue 1.8 The Proterozoic climate revisited Snowball 1.9 The hothouse icehouse dichotomy 1.9.1 The past 70 million...

## Dr HaD gr mAgr

Where mA is the mass of a molecule of species A. Thus, the particle density decays exponentially with scale height Ha. Note that this is identical in form to the particle density given by hydrostatic balance, except that the equation we have just derived applies to the particle density of each species separately, and not just to the particle density of all species together. In fact, in equilibrium each species acts as if it were in hydrostatic equilibrium separately, and has the same...

## Effect of long term variation of orbital parameters

The three orbital parameters that govern the seasonal and geographical distribution of insolation are the precession angle, obliquity, and eccentricity. All three change gradually on a scale of many thousands of years, owing basic laws of mechanics which apply to any planet in any solar system. The evolution of the precession angle derives from a fairly elementary property of the mechanics of rigid-body rotation. The rotation axis of a rotating body subject to a net torque executes a rotation...

## FLTsaTg 1 agSg CpPsCDUTsa Tg aT4a T4g 638

If the second two terms on the right hand side were not there, we'd have the result that the latent heat flux is equal to the surface absorbed solar radiation. The two additional terms are positive when Tg < Tsa, and can thus allow the latent heat flux to somewhat exceed the available solar forcing under circumstances when an inversion can form at the surface. The strength of this inversion determines the amount of excess evaporation that can be sustained. We can show that an inversion must...

## For Further Reading

For a comprehensive reference to the planetary boundary layer and atmospheric turbulence, see Garrett JR 1994 The Atmospheric Boundary Layer. Cambridge, 334pp. Meaurements of the hottest ground temperature on Earth are discussed in Mildrexler, Zhao and Running 2006 Where are the hottest spots on Earth EOS 87. A discussion of Monin-Obukhov scaling functions for the unstable case, with particular attention to the free-convection limit, can be found in Delage Y and Girard C 1992 Stability...

## Kt dz Tzo Sieiut bT722

If pcp is constant, this boundary condition can be satisfied by a solution of the diffusion equation of the form T Aei(kz-Ut),h , -1 (7.23) where A is a constant and D is the diffusivity kt (pcp). The complex vertical wavenumber k has been determined by substitution of the exponential form of T' into the diffusion equation. A will be determined by substitution of the solution into the boundary condition, but before doing so it is worth pausing to make some remarks on the solution Eq. 7.23. This...

## Mars present and past

Asymmetries between the solstices Southern winter is much colder than Northern winter. CO2 condensation, and the seasonal cycle of surface pressure. Seasonal cycle of Ar as a diagnostic of polar condensation. The strong, deep diurnal cycle on Mars. Factors limiting the polar night temperature drop on Mars, and relevant observations. Seasonal cycle of surface pressure, and mass of polar cap (effective thermal inertia due to latent heat). For latter problem,...

## N

The expression for the downward flux follows a similar form. Bj is the blackbody emission from layer j , and the flux at a given level is a weighted sum of the emissions from each layer below (for upward flux) or above (for downward flux) layer . The weighting coefficient ej characterizes the joint effects of the emissivity at layer j and the absorptivity by all layers between i and j. Exercise 4.4.3 Write down the analogous trapezoidal-rule approximation to I_ Exercise 4.4.4 Write down...

## Real gas radiation Basic principles 441 Overview OLR through thick and thin

It would be exceedingly bad news for planetary habitability if real greenhouse gases were grey gases (see Exercise 4.3.1). Greenhouse gas concentrations would have to be tuned exceedingly accurately to maintain a planet in a habitable temperature range, and there would be little margin for error. Thus, it is of central importance that, for real gases, OLR varies much more gradually with greenhouse gas concentration than it would for an idealized grey gas 2. This is another area in which the...

## Partitioning of CO2 between atmosphere and ocean

How does the presence of a liquid ocean affect the composition of a planet's atmosphere In this section, we'll consider the storage of a substance such as the carbon in atmospheric CO2 in the liquid ocean, neglecting any geochemical processes such as seafloor weathering which could remove dissolved components from the liquid and put them in long-term storage as solids in the oceanic crust. The primary example we have in mind is exchange of CO2 between atmospheres and a water ocean, but some of...

## Precipitationtemperature relations

There is more to climate than temperature, and for atmospheres that contain a condensible substance - e.g. water on Earth or methane on Titan - the precipitation rate is of as much interest as the temperature. Aside from the role of rainfall in making land habitable on Earth, there are many reasons for being interested in precipitation. For example, it is the precipitation of snow that feeds the growth and flow of glaciers. Precipitation of water on Earthlike planets exerts a controlling...

## R2s dr r2rEUv

The heating profile determines the flux (r rs)2F(r), which is needed for use in the energy equation. The flux integration shows that when the heating is shallow, Qo 1 FQ rEUV. The calculations shown in the figure were done with rEUv rs 1, yielding a shallow, low-level heating. Looking at the results, we see that when * is made large, the temperature is monoton-ically decreasing, and at very large escape fluxes the curve looks like the adiabatic escape solution as expected. As * 1, however, the...

## Summary of thermal inertia effects

The preceding discussion has revealed two limiting forms of behavior a planet can exhibit in the course of its seasonal cycle. A waterworld, having high thermal inertia in the ocean-atmosphere system, responds primarily to the annual average insolation. Such a world will be coldest at the poles and warmest at the equator, unless the obliquity exceeds about 54o, in which case the warmest climates will be found near the two poles. A desertworld, having little thermal inertia in either the surface...

## T rrfk11

Where I (t) is the luminosity of the Sun at time t and t is the current age of the Sun, usually taken as 4.6 billion years. This formula was originally proposed to describe the younger Sun, but it continues to be reasonably accurate out to times 4 billion years in the future as well. It follows from Eq. 1.1 that 4 billion years ago the Earth received solar energy at only 75 of the rate it does today. All other things being equal - atmospheric composition in particular - that means the Earth...

## Things that go bump in the night Infraredscattering with gaseous absorption

Traditionally, the problem of dealing with the joint effects of scattering and gaseous absorption has been considered to be one of the scariest problems in radiative transfer. The problem appears scary only if one intends to mount an attack on it by some kind of modification of the band-averaged transmission function approach. The problem here stems from the fact that band-averaged transmission functions do not satisfy the multiplicative property, so that the path that one feeds to the...

## Partially absorbing atmospheres

The assumption underpinning the blackbody radiation formula is that radiation interacts so strongly with matter that it achieves thermodynamic equilibrium at the same temperature as the matter. It stands to reason, then, that if a box of gas contains too few molecules to offer much opportunity to intercept a photon, the emission will deviate from the blackbody law. Weak interaction with radiation can also arise from aspects of the structure of a material which inhibit interaction, such as the...

## Into deepest time Faint Young Sun and habitability of the Earth

The Solar system was not always as we see it today. It formed from a nebula of material collapsing under the influence of its own gravitation, and once the nebula began to collapse, things happened very quickly. The initial stage of formation of the Solar system was complete by about 4.6 billion years ago. By this time, the Sun had begun producing energy by thermonuclear fusion the formation of the outer gas giant planets and their icy moons by condensation, and the formation of the inner...

## Other Solar System planets and satellites

For the gas giant planets - Jupiter and Saturn - many of the most striking questions that arise are fluid dynamical in nature. These questions include the origin of the banded multiple-jet structure of the atmospheric flow, and the dynamics of long-lived atmospheric vortices, most famously Jupiter's Great Red Spot. We shall have little to say about such fluid dynamical questions in this book. However, the thermal structure of the atmosphere provides an essential underpinning for any dynamical...

## Optically thin atmospheres The skin temperature

Since the density of an atmosphere always approaches zero with height, in accordance with the hydrostatic law, one can always define an outer layer of the atmosphere that has so few molecules in it that it will have low infrared emissivity. We will call this the skin layer. What is the temperature of this layer Suppose for the moment that it is transparent to solar radiation, and that atmospheric motions do not transport any heat into the layer thus, it is heated only by infrared upwelling from...

## Absorbed stellar radiation Wm

Figure 8.2 Effect of the abiotic form of the silicate weathering feedback on the variation of surface temperature with stellar luminosity. The luminosity in this graph is translated into absorbed stellar radiation per unit surface area of the planet, allowing for a 20 albedo. The pCO2 curve gives the value of pCO2 in equilibrium with a fixed outgassing rate for the case including the weathering thermostat. Supposing this planet to have enough silicates to support silicate weathering, and...

## Thermal Inertia

At several points in the preceding discussion, we have needed to make reference to the thermal response time of the system. In the present section, we shall make this notion precise. The heat storage in the planet's solid or liquid surface, and in its atmosphere means that it takes time for the system to heat up or cool down. The strength of this effect, known as thermal inertia, determines the extent to which the seasonal and diurnal fluctuations are averaged out in the climate response.

## FeSiOss CO2g FeCO3s SiO2s

In all of these reactions, the carbon in gaseous CO2 exchanges with the silicon in solid silicate minerals, to form a solid carbonate mineral plus solid silica (SiO2, of which quartz is one form, and which is also common in beach sand). The reader should keep in mind that the actual silicate minerals involved in the formation of carbonates can be considerably more complex than the simple chemical compounds referred to in the above reactions, and may have different equilibrium and kinetic...

## Farther afield Extrasolar planets

Up until 1988, the Solar system was the only field of play for students of planetary climate, and it provided the only example against which theories of planetary formation could be tested. Revolutionary improvements in detection methods led to the first confirmed detection of a planet orbiting another star in that year, and instrumentation for planetary detection has continued to improve by leaps and bounds. As of the time of writing, over 228 planets orbiting stars within 200 parsecs (652.3...

## Simple models of sea ice in equilibrium

There are many circumstances in which one would like to know the thickness attained by a layer of ice floating on an ocean once it comes into a state of thermal equilibrium. This problem is relevant to the state of the sea ice cover which forms in the polar regions on Earth today and in other icy climates. It is also relevant to the thick-ice regimes prevailing on a globally glaciated Snowball Earth. Another application is the determination of the ice-crust thickness for icy moons such as...

## Po

Where iH2 is the mass path of Hydrogen in the box, in kg m2, and p0 is a standard pressure. The coefficient kH2 has dimension m2 kg and can be used in precisely the same way as the absorption 0 100 200 300 400 500 600 700 800 Wavenumber (cm ') 0 100 200 300 400 500 600 700 800 Wavenumber (cm ') Figure 4.23 The N2 N2 and N2 H2 collision-induced continuum absorption coefficients as a function of temperature (indicated on curves). The coefficients are given at an N2 partial pressure of 100mb....

## Pleistocene Glacial Interglacial cycles

Now we'll take a closer look at what's been going on in the past five million years. The earlier portion of this time is known as the Pliocene epoch, and the latter portion, beginning around 1.8 million years ago, is the Pleistocene. The choice of the Pliocene-Pleistocene boundary is based on Figure 1.11 Evolution of geography over the Phanerozoic 1.8. The numbers give the time in millions of years ago. Figure 1.11 Evolution of geography over the Phanerozoic 1.8. The numbers give the time in...

## Thermal inertia for a mixedlayer ocean

The concept of thermal inertia is well illustrated by consideration of heat storage in the mixed layer of an ocean. Consider a layer of incompressible fluid with density p and specific heat cp, which is well-mixed by turbulence to a depth H. The assumption of well-mixedness implies that any heating or cooling applied to the surface is distributed instantaneously throughout the depth of the mixed layer, whose temperature thus remains uniform. Let S(t) be the solar flux heating the mixed layer,...

## OLR and backradiation for an optically thin grey atmosphere

The OLR and surface back-radiation for an optically thin grey atmosphere are obtained by integrating Eq. 4.27 over all frequencies. The result is I+ (1 - tto)'+(0) + T aT4 I-,s (1 - tx)I-,x + T aT4 where the mean atmospheric emission temperature is given by The first term in the expression for is the proportion of upward radiation from the ground which escapes without absorption by the intervening atmosphere, while the second is the emission to space added by the atmosphere. In the expression...

## Optical thickness and the Schwarzschild equations

Although the radiation field varies in space only as a function of pressure, p, its intensity depends also on direction. Let I(p, n, v) be the flux density of electromagnetic radiation propagating in direction n, measured at point p. This density is just like the Planck function B(v, T), except that we allow it to depend on direction and position. The technical term for this flux density is spectral irradiance. Now we suppose that the radiation propagates through a thin layer of atmosphere of...

## Digression About climate proxies 171 Overview of proxy data

Instrumental records of climate - that is, records of measurements of temperature and other quantities by scientific instruments - date back at most a few hundred years. The first accurate thermometer was invented in 1654 by Ferdinando II de'Medici, and two hundred years passed before anything like a global network of reliable temperature measuring stations began to become available. Written historical records of such events as frost dates, encounters with sea ice and depictions of mountain...

## OLR AaT p14 AaLR4494

ypV ln (p* J f20gsJKo) 4 v where p* is defined as before and A' is an order unity constant which depends on L R An examination of the g dependence of the calculated Kombayashi-Ingersoll limit in Figure 4.37 shows that over the range 1m s2 < g < 100m s2, the numerically computed dependence can be fit almost exactly with this formula if we take A' .7344 and ko .055 (assuming po 104Pa). Though the pressure dependence of absorption causes the limiting OLR to vary more slowly with g than was...

## Similarity theory for the surface layer

The surface layer theory based on dimensional analysis tells us most of what we need to know, but it doesn't tell us how the drag coefficient depends on the height at which the top-of-layer conditions are applied, nor does it say precisely how the coefficient depends on stratification or the surface roughness. We will now re-do the surface layer theory using a more precise form of the similarity assumption. The most important thing we will get out of this is a quantification of the suppression...

## Spectroscopic properties of selected greenhouse gases

Now we will provide a survey of the infrared absorption properties of a few common greenhouse gases, with particular emphasis on the big 3 that determine much of climate evolution of Earth, Mars and Venus from the distant past through the distant future CO2, H2O and CH4. In each case, the spectral results shown are for the dominant isotopic form of the gas, e.g. 12C16O2 for the case of carbon dioxide. Other isotopic forms (isotopologues) can have significantly different spectra, particularly...

## Goldilocks in space Earth Mars and Venus

Until well into the 1960's, science fiction stories about Venus generally portrayed it as a steamy jungle planet, but one where intrepid explorers could perhaps survive unprotected on the surface. The idea of a jungle and breathable air was of course unfounded speculation, but the general picture of the climate was not wholly without merit. After all, the dense reflective cloud deck of Venus was readily observable - it is what makes Venus so bright as the evening star - and the reflection of...

## [w cpT 22gsrs 828

Note that 2gsrs is the square of the escape velocity from the surface, and when multiplied by rs r it becomes the square of the escape velocity from radius r. Let us defer for the moment the business of making sense of the term SQ dr - which is a bit of a mathematical monstrosity - and explore the adiabatic case, for which SQ 0. In this case, the expression E -w2 + cpT - -2g.srs r (8.29) must be independent of r. E is the energy per unit mass of the fluid, the three terms representing kinetic...

## T Earth m

Given the weak variation of the factors multiplying nh (Earth) in typical cases, a good rule of thumb for use in making crude estimates of escape fluxes is to simply assume the homopause density to be the same as Earth's, though of course where observations are available it is better to use the observed value. For most escape calculations, it is not necessary to know the homopause altitude, though it can be estimated from the lower atmosphere scale height if it is desired. The homopause...

## Pure radiative equilibrium for a grey gas atmosphere

For the temperature profiles discussed in Sections 4.3.2 and 4.3.3, the net infrared radiative heating computed from Eq. 4.14 is nonzero at virtually all altitudes generally the imbalance acts to cool the lower atmosphere and warm the upper atmosphere. In using such solutions to compute OLR and back-radiation, we are presuming that convective heat fluxes will balance the cooling and keep the troposphere in a steady state. The upper atmosphere will continue to heat, and ultimately reach...

## Milankovic cycles on Earth

Earth's precessional cycle is shown in Figure 7.12. The precession angle increases at a nearly constant rate, completing a cycle every 22,000 years. Though the variation in rate is not evident over any one cycle, the rate is not exactly constant, and therefore the phase drifts over the course of hundreds of thousands of years. The precessional cycle is very rapid, and the precession angle has changed markedly even over historical times. Eight thousand years ago, when the first Sumerians poured...

## A homebrew radiation model

We have now laid out all the ingredients that go into a real gas radiation model, and are ready to begin assembling them. The ingredients are A means of computing the band-averaged transmission over a specified wavenumber range The band-averaged integral (Eq. 4.11,4.12, or 4.13) giving the band-averaged solution to the Schwartzschild equation in terms of the preceding transmission functions Divide the spectrum into bands of a suitable width Prepare in advance Malkmus coefficients or exponential...

## Forams to the rescue

As it happens, Nature has provided a handy way of determining the isotopic composition of past ocean waters, via the good works of single-celled shelly amoeba-like organisms known as foramanifera, nicknamed forams (see Fig. 1.6). These creatures build distinctive calcium carbonate (CaCO3) shells which record the state of the water in which they grew. Because the shells have such diverse and unmistakable shapes, it is easy to recognize and select out the species which live at the the depth level...

## Behavior of the bandaveraged transmission function

Although the absorption spectrum has very complex behavior, the band-averaged transmission function averages out most of the complexity. The definition of the transmission guarantees that it decays monotonically as p1 p21 increases and the path increases, but in addition the decay is invariably found to be smooth, proceeding without erratic jumps, kinks or other complex behavior. This smoothness is what makes computationally economical radiative transfer solutions possible, and the various...

## Effects of atmospheric solar absorption

On the present Earth the idealized picture of climate in which all solar absorption occurs at the ground is useful, but even for the present Earth about 20 of solar radiation is absorbed within the atmosphere. For other atmospheres, the proportion absorbed in the atmosphere could be much greater. The effect of this absorption on climate depends very much on the vertical distribution of the absorption, and that is what we will explore here for selected real gases. The two key questions we have...

## Global warming and the surface budget fallacy

A common fallacy in thinking about the effect of doubled CO2 on climate is to assume that the additional greenhouse gas warms the surface by leaving the atmospheric temperature unchanged, but increasing the downward radiation into the surface by making the atmosphere a better infrared emitter. A corrollary of this fallacy would be that increasing CO2 would not increase temperature if the lower atmosphere is already essentially opaque in the infrared, as is nearly the case in the Tropics today,...

## XRTe xkTexf2

Where Tex is the exobase temperature, m is the actual mass (in kilograms) of the molecule which makes up most of the exosphere and k is the Boltzman thermodynamic constant. For the more general case, one must extend the hydrostatic relation to account for the decay of gravity with altitude. This case is important for light constituents like H or H2, which have a large scale height because low molecular weight implies large gas constant R. The exosphere can also be very extended even for heavier...

## About Extreme Ultraviolet

Extreme ultraviolet (EUV) consists of electromagnetic radiation with wavelengths between 0.12 pm and 0.01 pm. EUV makes up only a tiny part of the spectrum of stars with photospheric temperatures under 10000 K - main sequence stars of spectral class B,A,F,G,K and M. (Recall that our Sun is a class G star). It nonetheless fuels the chemistry and physics of the outer atmosphere. EUV photons have sufficient energy to break up otherwise stable atmospheric compounds, allowing their components to...

## The absorption spectrum of real gases

We will now take a close look at the absorption properties of CO2, in order to introduce some general ideas about the nature of the absorption of infrared radiation by molecules in a gas. Continuing to use CO2 as an example, these ideas will be developed in Sections 4.4.3,4.4.4 and 4.4.6 into a computationally efficient means of calculating infrared fluxes in a real-gas atmosphere. A survey of the spectral characteristics of selected other greenhouse gases will be given in Sections Figure 4.7...

## DTs GTs

By definition, G 0 at an equilibrium point Teq. Suppose that the slope of G is well-defined near Teq - in formal mathematical language, we say that G is continuously differentiable at Teq, meaning that the derivative of G exists and is a continous function for Ts in some neighborhood of Teq. Then, if dG dTs < 0 at Ts, it will also be negative for some finite distance to the right and left of Ts. This is the case for points a and c in the net flux curve sketched in Fig. 3.9. If the temperature...

## Tropopause height for real gas atmospheres

The radiative equilibrium solutions discussed in the preceding section are all unstable near the ground. As convection sets in, it will mix away the unstable layer and replace it by an adiabat the well-mixed region is the troposphere. The change in lower level temperature profile, however, will alter the upward radiation which heats the stratosphere, and therefore cause temperature changes even above the layers reached directly by convection. When all this sorts itself out, how deep is the...

## Pure CO2 atmospheresPresent and Early Mars and Venus

Figure 4.30 shows the OLR as a function of surface pressure for a pure CO2 atmosphere subject to Martian gravity. The results span the range of surface pressure from those similar to the thin atmosphere of present Mars up to the thick atmospheres commonly hypothesized for Early Mars 6. The calculations were carried out for a fixed surface temperature of 270K, since we are 6 There is no strong reason to exclude the possibility of a substantial amount of N2 in the Early Martian atmosphere....

## Erosion by solar wind

Solar wind erosion is a form of nonthermal escape energized by solar wind particles instead of EUV photons. The corona is basically the exosphere of the Sun, and the solar wind is nothing more nor less than hydrodynamic escape of the Solar atmosphere, which is primarily hydrogen ionized to protons. The mechanism is general and applies to virtually all stars, though we will not attempt to discuss here how the stellar wind characteristics vary from star to star, nor the way the stellar wind...

## Nonthermal escape

Using Planck's constant, the energy of an EUV photon with wavelength 0.05 pm is 4 10-18J. This is sufficient to dissociate the components of many molecules, and to knock off electrons from just about anything - a process called ionization which produces charged particles in the outer atmosphere. In fact, ionization is the principle means by which absorbed EUV heats the outer atmosphere, since ejection of an electron increases the kinetic energy of the ion left behind, as well as imparting...

## Diffusion limited escape

The efficiency of escape of material that reaches the exobase is not necessarily the controlling factor determining atmospheric mass loss. For mass to escape from the exobase, it must first be delivered to the exobase, and in many circumstances the rate of transport of mass to the exobase is the limiting factor. When a minor consituent of an atmosphere is escaping, it must first diffuse through the dominant component on its way to the exobase, and even if the escape from the exobase is very...

## H2oso2h2s

Figure 4.11 Some polar triatomic molecules. Two different modes of rotation are indicated for the H2O molecule. There is a third mode of rotation about an axis perpendicular to the page. Figure 4.11 Some polar triatomic molecules. Two different modes of rotation are indicated for the H2O molecule. There is a third mode of rotation about an axis perpendicular to the page. think of the interaction in semiclassical terms. The reason is that the wavelength of infrared is on the order of 10 pm,...

## Walk the line

An individual spectral line is described by a line position (i.e. the wavenumber at the center), a line shape, a line strength (or intensity), and a line width. The line shape is described by a nondimensional function of nondimensional argument, f (x), normalized so that the total area under the curve is unity. The contribution of a single spectral line to the absorption coefficient for substance G can then be written KG(v,p,T ) Sf (v vc) (4.60) where vc is the frequency of the center of the...

## Greenhouse effect of CO2 vs CH4

There is considerable interest in the idea that on the Early Earth methane may have taken over much of the role of CO2 in offsetting the Faint Young Sun. In part this interest is due to rather sketchy geochemical evidence that at some times in the Archaean CO2 concentrations may not have been high enough to do the trick, but regardless of whether the evidence actually demands a relatively low-CO2 atmosphere, possibilities abound that in an anoxic atmosphere methane could build up to high...

## Effect of atmospheric solar absorption on pure radiative equilibrium

Now we will examine how the absorption of solar radiation within an atmosphere affects the temperature structure of the atmosphere in radiative equilibrium. The prime application of this calculation is to understand the thermal structure of stratospheres. Under what circumstances does the temperature of a stratosphere increase with height The effect of solar absorption on gas giant planets like Jupiter is even more crucial. There being no distinct surface to absorb sunlight, all solar driving...

## Mach Number

Movement of the energy curve through the sonic point means that the gradient of M(r) and w(r) have square-root singularities there - a consequence of the violation of the transonic rule. From a physical standpoint, what is important is not so much the singularity as the fact that solutions cease to exist altogether once r is moved past the sonic point. An examination of Eq. 8.32 shows that the temperature decreases as the sonic point is approached this increases the Mach number by decreasing...

## Water and ice clouds

Now we'll take a closer look at the way Earth's water and water-ice clouds effect the radiation budget, taking account of the balance between the shortwave albedo effect of clouds which act to cool the planet and the longwave cloud greenhouse effects which act to warm the planet. Much of the general behavior in evidence on Earth applies equally well to water clouds on other planets, or for that matter to any cloud-forming substance which is strongly absorbing in the infrared but fairly...

## The past 70 million years

Figure 1.8 shows the paleogeography at the end of the Cretaceous, 65 million years ago. The continent of Antarctica has approached the South Pole, and will continue to drift over the next 40 million years or so until it is more nearly centered on the pole. There is open water at the North Pole in the late Cretaceous, and the open Arctic Ocean continues throughout the subsequent time through the present. The modern continents of North and South America, Eurasia, and Africa are still early in...

## Ppi Rpicppii pp2 Rp2cpp2i215

P(pi)( pi )R(pi) cp(pi)-1( po )R(p2) cP(p2)-1 < p(p2 ) (2.16) po p2 This yields the same criterion as the correct criterion given in Eq. 2.14 only if I cp is constant. The lack of a globally valid potential density complicates the precise analysis of the static stability of inhomogeneous atmospheres. Strictly speaking, one needs to examine potential density profiles for a range of different po covering the atmosphere. In practice, the potential density based on a single po can often provide a...

## Hydrodynamic escape

Hydrodynamic escape is basically a more efficient means of deploying the energy available to the atmosphere in order to assist escape. The energy involved still comes from EUV absorption or the general thermal energy of the atmosphere, but instead of this accumulating in a more or less random set of motions, in some circumstances the energy can sustain a mean outward escaping flow which carries fluid to space without wasting energy on motions directed toward the planet or on a population of...

## Isotopic proxies

The chemical properties of an element are primarily determined by the number of protons in the nucleus (the atomic number, which also determines the configuration of the electron cloud. Nucleii also contain neutrons, and atoms having the same atomic number can appear in forms with different numbers of neutrons. These differing forms are known as isotopes of the element. Isotopic proxies have proved to be a versatile source of information about past climates. Some isotopes are unstable, and...

## The twostream equations with scattering

The two stream approximations to the full scattering equation are derived from Eq. 5.14 and Eq. 5.15 by constraining the angular distribution of the radiation in such a way as to allow all integrals appearing in these equations to be written in terms of either I+ + I_ or I+ I_. In the resulting equations, flux in the upward stream is absorbed, or scattered into the downward stream, at a rate proportional to the upward stream intensity, and similarly for the downward stream. The two-stream...

## Impact erosion

The two main cases in the solar system where theories of atmospheric evolution call for massive atmospheric loss are the problem of water loss on Venus and the loss of a hypothetical dense CO2 atmosphere on Mars. For Titan the question is the converse - accounting for the lack of atmospheric N2 loss, and that is plausibly accounted for by the solar wind shielding provided by Saturn's magnetic field and the low EUV flux at such large distances from the Sun. There may have been blowoff early in...

## Pure radiative equilibrium for real gas atmospheres

Pure radiative equilibrium amounts to an all-stratosphere model of an atmosphere, and is a counterpoint to the all-troposphere models we have been discussing. Real atmospheres sit between the two extremes, sometimes quite near one of the idealizations. In this section we will focus on pure infrared radiative equilibrium. The effects of solar absorption in real gases will be taken up in From simple analytic solutions, we know essentially all there is to know about pure radiative equilibrium for...

## Greenland GISP Ice Core O

Figure 1.14 Oxygen isotope data from the GISP-2 Greenland ice core. Larger (less negative) values correspond to warmer temperatures. Figure 1.14 Oxygen isotope data from the GISP-2 Greenland ice core. Larger (less negative) values correspond to warmer temperatures. of a glacial lake into the ocean, but generally speaking the mechanisms of both the Younger Dryas and of millennial variability remain as Big Questions that are yet to be resolved. This is an especially important question because the...

## Real gas OLR for alltroposphere atmospheres

Calculation of OLR is one of the most fundamental steps in determining a planet's climate. Now that we are equipped with an ability to compute the OLR for real gases, we can revisit some of our old favorite problems - Snowball Earth, the Faint Young Sun, Early Mars, and so forth -but this time relate the results to the actual atmospheric composition. In this section we present results for the all-troposphere model introduced in Section 4.3.2, occasionally limiting the upper air temperature drop...

## Hydrogen and Oxygen isotopes in sea water and marine sediments

We will turn our attention now to the isotopes of hydrogen and oxygen contained in water and in sediments precipitated from the water column. We'll learn what the concentration of these isotopes tells us about the volume of glacier ice and the temperature of various parts of the ocean. Normal water is H2l6O, but other isotopes of hydrogen or oxygen can substitute for the most prevalent isotopes, leading to various forms of heavy water, notably HD16O and H28O. Figure 1.5 Sketch showing how the...

## The Grey Gas Model

We will see in Section 4.4 that for most atmospheric gases k, and hence the optical thickness, has an intricate dependence on wavenumber. This considerably complicates the solution of the radiative transfer equations, since the fluxes must be solved for individually on a very dense grid of wavenumbers, and then the results integrated to yield the net atmospheric heating, which is the quantity of primary interest. The development of shortcuts that can improve on a brute-force integration is an...

## Thermodynamics in a Nutshell

The atmospheres which are our principal objects of study are made of compressible gases. The compressibility has a profound effect on the vertical profile of temperature in these atmospheres. As things progress it will become clear that the vertical temperature variation in turn strongly influences the planet's climate. To deal with these effects it will be necessary to know some thermodynamics - though just a little. This chapter does not purport to be a complete course in thermodynamics. It...

## Distribution of incident solar radiation

The geographical variations of temperature are driven by variations in the amount of sunlight falling on each square meter of surface, and also by variations in albedo. Seasonal variations are driven by changes in the geographical distribution of absorbed sunlight as the planet proceeds through its orbit. Therefore, the starting point for any treatment of seasonal and geographical variation must be the study of how the light of a planet's sun is distributed over the spherical surface of the...

## Upward Flux Wm

Figure 3.7 The Earth's observed zonal-mean OLR for January, 1986. The observations were taken by satellite instruments during the Earth Radiation Budget Experiment (ERBE), and are averaged along latitude circles. The figure also shows the radiation that would be emitted to space by the surface (aTf) if the atmosphere were transparent to infrared radiation. condensed substances absorb infrared as well as water does. Liquid methane (imporant on Titan) and CO2 ice (important on present and early...

## Scattering by particles

Rayleigh theory tells us everything we need to know about scattering from the gas making up an atmosphere, but to deal with cloud and aerosol particles, we need to know about scattering from objects that are not small compared to a wavelength, and indeed could be considerably larger than a wavelength, as is the case for visible light scattering from water or ice clouds on Earth. The answer is provided by Mie theory 2, which is a general solution for scattering of an electromagnetic wave from a...

## A first look at the runaway greenhouse

We have seen in Chapter 2 that the mass of an atmosphere in equilibrium with a reservoir of condensed substance (e.g. a water ocean) is not fixed. It increases with temperature in accordance with the dictates of the Clausius-Clapeyron relation. If the condensible substance is a greenhouse gas, then the optical thickness increases with temperature. This tends to reduce the OLR, offsetting or even reversing the tendency of rising temperature to increase the OLR. What are the implications of this...

## Some elementary orbital mechanics

Sir Isaac Newton showed that the orbit of a single planet revolving about its star takes the form of an ellipse, with a focus of the ellipse at the center of mass of the system. Since stars are typically much more massive than their planets, the center of mass for most purposes is identical to the center of the star. The elliptical nature of orbits has an important effect on the seasonal cycle, since the planet is farther from its sun at some parts of the year than it is at others. This makes...

## Elementary models of radiation balance

Our objective is to understand the factors governing the climate of a planet. In this chapter we will be concerned with energy balance and planetary temperature. Certainly, there is more to climate than temperature, but equally certainly temperature is a major part of what is meant by climate, and greatly affects most of the other processes which come under that heading. From the preceding chapter, we know that the temperature of a chunk of matter provides a measure of its energy content....

## Milankovic cycles on Mars

As expected from general mechanical considerations, Mars has Milankovic cycles analogous to those of Earth. Mars' cycles differ in some key respects, because of the lack of a massive moon, and because of the proximity of Jupiter. As for Earth, the precession angle of Mars increases at a nearly constant rate. However, because Mars does not have a moon as massive as Earth's, the precession is dominated by Solar gravity, and is slower. The Mars precessional cycle has a period of approximately...

## Scattering by molecules Rayleigh scattering

Rayleigh scattering theory is a classical (i.e. non-quantum) electromagnetic scattering theory which began life as a theory for scattering of an electromagnetic plane wave from a small sphere with real index of refraction n. Small in this context means small compared to the wavelength of the light being scattered. The scattering calculation is quite simple in the Rayleigh limit because the incident electric field is nearly constant over the particle, which makes it simple to compute the induced...

## Dr P pgs r812

As in the treatment of the hydrostatic relation in Chapter 2, the equation is closed by using the ideal gas law, p pRT, where R is the gas constant for the mixture making up the uppermost part of the atmosphere. In escape problems it is often more convenient to deal with particle number density rather than mass density. The particle density n(r) is obtained by dividing p by the mass of a molecule, m. If the upper atmosphere is isothermal with temperature To, then the solution expressed as...

## Hothouse and icehouse climates over the Phanerozoic

The Cretaceous hothouse climate and the Pleistocene icehouse climate represent opposite extremes of the Earth's typical climate state of the past half billion years. Going back further in time, the Snowball Earth represents an ultra-extreme on the cold end going further afield in space, the runaway greenhouse represents an ultra-extreme on the hot end, though one that evidently never occurred on Earth. The Earth has experienced many individual hothouse and icehouse episodes in the past half...