Heterosphere ➡ Deviations from Hydrostatic Balance: Diffusive and Chemical Time Constants

高层大气环境

完全电离（无碰撞）逃逸层/磁层

热层/电离层部分电离

中间层

中性气体平流层（碰撞）对流层 Ionosphere-Thermosphere Basics - I Neutral Atmosphere Vertical Structure

Topics

• Thermal Structure and Thermal Balance ➡ Energy Sources and Sinks ➡ Molecular Conduction and Thermal Gradient • Hydrostatic Balance ➡ Thermosphere Composition ➡ Mean Molecular Weight vs. Height ➡ Homosphere-Heterosphere ➡ Deviations from Hydrostatic Balance: Diffusive and Chemical Time Constants

2 Ionosphere-Thermosphere Basics - I Neutral Atmosphere Vertical Structure

3 Ionosphere-Thermosphere Basics - I Neutral Atmosphere Vertical Structure

4 Global Mean Temperature Structure

Tropo (Greek: tropos); “change” Lots of weather

Strato (Latin: stratum); Layered

Meso (Greek: messos); Middle

Thermo (Greek: thermes); Heat

Exo (greek: exo); outside

5 Discussion for Temperature Structure

ØWhy do most of aircrafts ﬂy in the Stratosphere? ØWhy is the Stratosphere is more stable than the Troposphere? ØCan we use a conventional thermometer to measure temperature in the upper atmosphere? Alternately, why do astronauts in space shuttle feel cold in ionosphere/thermosphere even if the upper thermosphere temperature is so high?

Satellite Bias and Temperature

Yue et al., 2011; Lin et al., 2015 Satellite Bias and Temperature

Zhong et al., 2015 Global Mean Temperature Structure

It is important to distinguish between three types of velocities:

• the actual particle velocity • the flow velocity • and random (thermal) velocity of a gas particle

Wind! Global Mean Temperature Structure

It is important to distinguish between three types of velocities:

• the actual particle velocity • the flow velocity • and random (thermal) velocity of a gas particle

? Global Mean Temperature Structure

How about the mean random velocity ?

For the earth’s atmosphere, Reduce temperature different species of gas have the same temperature! Global Mean Temperature Structure

Question （ homework）: At what altitudes different species of neutral gas do not have the same temperature? Global Mean Temperature Structure

Tropo (Greek: tropos); “change” Lots of weather

Strato (Latin: stratum); Layered

Meso (Greek: messos); Middle

Thermo (Greek: thermes); Heat

Exo (greek: exo); outside

13 Energy source of the upper atmosphere

(1)Absorption of solar ultra-violet and X-ray radiation, causing photodissociation, ionization and consequent reactions that liberate heat. (2)Energetic charged particles entering the upper atmosphere from the magnetosphere . (3)Joule heating by ionospheric electric currents (4)Dissipation of tidal motions and gravity waves by turbulence and molecular viscosity.

High latitude region especially during stormtime Energy source of the upper atmosphere

Energy source of the upper atmosphere

Deposition of solar EUV energy in the thermosphere as a function of wavelength and altitude Qian and Solomon, JGR, 2005 Altitude of Maximum Solar Radiation Absorption

18 Solar Radiation Absorption in the Thermosphere

Absorbing gas is thin here; therefore little absorption. Q F Three factors determine the rate of solar radiation absorption, Q: N ≈ 120 - • No. of photons (solar flux, F) 160 km • No. of absorbing molecules, N • Efficiency of absorption (cross-section)

Few photons left here; Heating per volume! therefore little absorption.

QI()() e−τλ(,h00 , χ ) ( hv )×ρ EUV = ∑ ∞ λσ λλλ ε λ heating per mass 19 Global Mean Temperature Structure

Tropo (Greek: tropos); “change” Lots of weather

Strato (Latin: stratum); Layered

Meso (Greek: messos); Middle

Thermo (Greek: thermes); Heat

Exo (greek: exo); outside

20 Energy source of the upper atmosphere

(1) Radiation, particularly in the infra-red; the mesosphere is cooled by radiation from CO2 at 15 μm and from ozone at 9.6μm (2) Heat transport • Radiation • Molecular conduction • Eddy diffusion, or convection • Transport by large-scale winds • Chemical transport of heat

Energy sink of the upper atmosphere

Molecular conduction (2) • more efﬁcient in the thermosphere (above 150 km); here Heat transport the thermal conductivity is large because of the low pressure and the pressure of free electrons • Radiation • Molecular conduction • Eddy diffusion, or convection • Transport by large-scale winds • Chemical transport of heat

Radiation • the most efﬁcient process at the lowest levels. Eddy diffusion • The atmosphere is in radiative equilibrium between 30 and • more efﬁcient than conduction below the turbopause. 90 km Thus, below about 100 km eddy diffusion carries heat from the thermosphere into the mesosphere. •This is a major loss of heat from the thermosphere but a minor source for the mesosphere Global Mean Energy Sources and Sinks

Thermosphere: • Energy sources: • Absorption of EUV (200-1000Å; photoionizing O, O2, N2) and UV (1200-2000 Å), photodissociating O2), leading to chemical reactions and particle collisions, liberating energy • Joule heating by auroral electrical currents • Particle precipitation from the magnetosphere • Dissipation of upward propagating waves (tides, planetary waves, gravity waves)

• Energy sinks: • Thermal conduction into the mesosphere, where energy is radiated by CO2, OH and H2O • IR cooling by CO2 NO, O

Mesosphere: • Energy sources: Troposphere: • Some UV absorption by O3 (lower heights) • Energy sources: • Heat transport down from thermosphere • Planetary surface absorption (IR, visible), (minor, upper heights only) convection & conduction to atmosphere • Chemical heating • Atmospheric absorption of terrestrial • Energy sinks: and solar IR • IR radiation by CO2 H2O, OH • Latent heat release by H2O • Energy sinks: Stratosphere: • IR radiation • Energy sources: • Evaporation of H2O • Strong absorption of UV by ozone (causing stratopause temperature peak) • Energy sinks:

• IR radiation by O3 , CO2 , H2O

26 Thermodynamic energy equation

heat conduction Advection z ∂T ge ∂ ⎧K ∂T 2 ⎛ g 1 ∂T ⎞⎫ ! ⎛ ∂T RT ⎞ T K H C V T w = ⎨ + E P ρ⎜ + ⎟⎬ − ⋅∇ − ⎜ + ⎟ ∂t P0C p ∂z ⎩ H ∂z ⎝ CP H ∂z ⎠⎭ ⎝ ∂z CP m ⎠ Q − L + C p adiabatic heating or Heating and cooling cooling

where T is neutral temperature, t is time, g is gravity, Cp is specific heat

per unit mass, KT is the molecular thermal conductivity coefficient, H is

the pressure scale height, KE is the eddy diffusion coefficient which is assumed to be equal to the eddy thermal conductivity, rho is the neutral mass density, z is the model vertical coordinate, P is pressure and a reference pressure (5 x 10-4 mb) at z = 0; V is the horizontal velocity vector, w is the vertical velocity defined by , R is the universal gas

constant, and m is the mean molecular mass of neutral gas. 27 Heating rate profiles of the thermal budget

• QT total neutral heating rate • SRB and SRC O2 absorption heating • e-i collision heating between thermal electrons, ions and neutrals

• Qic ion-neutral chemistry heating • Qnc neutral-neutral chemistry heating

• QJ Joule heating • O(3P) fine structure cooling by O • O3 heating • heating from quenching of O(1D)

Roble, 1995

28 Radiative Cooling by CO2, NO, O is also important to the thermal budget

• QT total neutral heating rate • Km molecular thermal conduction • Ke eddy thermal conduction • NO cooling at 5.3 mm

• CO2 total CO2 rate • O(3P) fine structure cooling by O

• IR total of O, NO, CO2

• NO cooling rate can increase by two orders of magnitude during a storm.

Roble, 1995

29 Molecular Conduction Determines Thermosphere Temperature Profile Shape

Thermal conduction (molecular and turbulent) removes heat from the thermosphere to the mesosphere (here collision frequencies are

high enough that polyatomic molecules CO2, O3, H2O can radiate energy away in infrared). dT Let Φ = heat flux due to conduction = k dh As a first approximation, heat input is balanced by loss due to conduction:

dΦ Q ≈ dh ⇒ Φ ≈ ∫ Qdh

€

€ € dT 1 ∞ Therefore ≈ ∫ Qdh dh z k z

dT must always be sufficiently large to conduct away

dh heat deposited at higher levels. Therefore

• dT above 200 km → 0 dh

• also dT is maximum around dh 120 - 130 km

€

€ Diurnal variation and heating sources

32 Diurnal variation and heating sources

中性温度

离子温度

地方时

Midnight temperature enhancement Altitude of Maximum Solar Radiation Absorption

34 Solar Radiation and Thermosphere Variability Radiative Cooling by CO2, NO, O is also important to the thermal budget

• QT total neutral heating rate • Km molecular thermal conduction • Ke eddy thermal conduction • NO cooling at 5.3 mm

• CO2 total CO2 rate • O(3P) fine structure cooling by O

• IR total of O, NO, CO2

• NO cooling rate can increase by two orders of magnitude during a storm.

Roble, 1995

36 “Greenhouse Cooling ” Roble and Dickinson [1989] ﬁrst pointed out the effects of CO 2×CO2 2 enhancement in the troposphere on the upper atmosphere.

Cicerone [1990] “Roble and Dickinson’s report opens our eyes to further disturbances to the global atmosphere that are primarily due to human activities.”

36 Roble and Dickinson [1989]

0.5×CO2 2×CO2

[Roble and Dickinson, Geophys. Res. Lett., 16, 1441-1444, 1989] 37 38 Long-Term Decrease in Thermosphere Density - CO2 Cooling Effect?

Average behavior for 5 satellites near 400 km

Model consistently overestimates density during solar minimum, so this trend is removed

Marcos et al, GRL, 2005; see also Emmert et al., 2004; Keating et al., 2000

39 Mesopause Climatology from SABER

40 Stratopause Indentification

41 DE-2 temperature CHAMP mass density

Raghavarao et al., GRL, 1991 Liu et al., JGR, 2007

42 plasma-neutral collision heang Control simulaons

-320K

Plasma-neutral collision heating is the major contributor to the formation of the ETA crests!

[Lei et al., 2012a, JGR] Solar heating

Conduction

Adiabatic cooling

Advection

Joule heating

[Lei et al., 2012a, JGR] 44 Lecture 3 Hydrostatic Balance & Thermosphere Composition

45 Ionosphere-Thermosphere Basics - I Neutral Atmosphere Vertical Structure

HYDROSTATIC EQUILIBRIUM

If ….. P + dP n = # molecules per unit volume, and

m = mass of each particle, then dP

nm dh = total mass contained in a cylinder of air (of unit cross -sectional area)

and the force due to gravity on the cylindrical mass = nmg dh nmgdh P

The difference in pressure between the lower and upper faces of the cylinder balances the above force in an equilibrium situation: (P+ dP) − P = −nmgdh

€ dP R*= 8.314 Jmol-1K-1 M = N m = 28.97 gmol-1 ⇒ = −nmg a dh for air R* = kN a Assuming the ideal gas law holds,

R* n P R = = kT M Then the previous expression may be written:

1 dP 1 where H is called the scale height = − and P dh H

€ kT RT 2 RE H = = g = g(0) 2 mg g (RE + h)

€ €

€

€ €

€ This is the so-called hydrostatic law or barometric law.

h Integrating, where dh −z z = ∫ P = P0e H 0

and z is referred to as the "reduced height" and the subscript zero refers to a reference height at h = 0. T Similarly, n = n 0 e −Z 0 T

For an isothermal atmosphere, then,

−h −h −h P P e H H e H = o n = noe ρ = ρo

€ € € Now, the efficiency of molecular diffusion increases according to the mean free path of atmospheric particles, and hence inversely with atmospheric density. At sufficiently low altitudes in the atmosphere, molecular diffusion is not able to compete with the various mixing processes in the atmosphere (turbulent diffusion, wave and general dynamical transport, etc.).

The atmosphere, in fact, remains well-mixed below about 100 km. This regime is called the homosphere and is characterized by a constant mean molecular weight as a function of height:

∑ mini -1 m = = 28.97 g mole ∑ ni A mean scale height is thus defined:

78.1% N 20.9% O kT 2 2 .9% Ar .03% CO2 H = .002% Ne .0005% He Variable H O mg 2 51

€

€ ………… and all constituents possess the same scale height and number density (and pressure) distributions with height: T n = n = n 0 e −h / H i 0 T

§ It is not until about 100 km (the exact height is species dependent, due to the dependence of molecular diffusion velocity on mean molecular weight) that molecular diffusion begins to take over, and each species separates according to its individual scale height. § This separation occurs at the homopause, sometimes called the turbopause. Above the homopause is the heterosphere; homosphere below.

52 Strictly speaking, since m varies from constituent to constituent

(i.e., H, He, O, O2, N2, ....), the above relations apply to individual constituents, i.e., h h h − H − H − H i n n e i ρ = ρ e i P = Pioe = io io

where P is the partial pressure and kT i H = i mig

Thus, each individual constituent has the tendency to distribute vertically according to its own individual scale height (see following figure). The process which makes this possible is molecular diffusion.

€ € €

€ Variation of the density in an atmosphere with constant temperature (750 K).

54 Helium is produced by radioactive decay in the Earth’s crust, and it diffuses up through the atmosphere, eventually to escape into space.

Atomic hydrogen also flows constantly up through the atmosphere but its source is the dissociation of water vapour near the turbopause.

55 Solar activity dependence of neutral composition

56 Prolong solar minimum of solar cycles 23/24

大气密度

F107

MgII

SOHO flux Coplanar of CHAMP and GRACE Satellites

Bruinsma, S. L., and J. M. Forbes (2010), Anomalous behavior of the thermosphere during solar minimum observed by CHAMP and GRACE, J. Geophys. Res., 115, A11323, doi :10.1029/2010JA015605. 58 CHAMP to GRACE Density Ratio Feb 2007 (10LT)

ρ 1 C ∝ ρG Hρ Dec 2008 (8LT)

[Thayer et al., 2012, JGR] Helium is produced by radioactive decay in the Earth’s crust, and it diffuses up through the atmosphere, eventually to escape into space.

Atomic hydrogen also flows constantly up through the atmosphere but its source is the dissociation of water vapour near the turbopause.

• Question: H and He are not produced in the upper thermosphere. What are they observed there?

60 Deviations from Hydrostatic Equilibrium: Diffusive and Chemical Time Constants

61 Distributions of atmospheric constituents in the atmosphere are not just affected by gravity, but also by chemical processes and transport by winds and diffusion.

The continuity equation expresses the balance between these competing processes. The equation of continuity for the number density of the ith constituent

Ni is ∂N ! i = P - L - ∇⋅Φ ∂t i i i ! ! Φ i = flux NiVi due to mass transport ! with velocity Vi

Generally, vertical variations ! ∂ are most important for many ∇⋅Φ i ≈ Niwi atmospheric problems: ∂z 62

€

€ From gas kinetic theory (i.e., Chapman & Cowling 1961):

& 1 dN i 1 (1 +α i ) dT ) Φi = N iwi ≈ −N iDi ( + + + molecular diffusion ' N i dz H i T dz *

& 1 dN i 1 1 dT ) − N iK( + + + eddy diffusion ' N i dz H T dz *

Note: 1 dPi Magnitude Pi dz Niwi ~ NiDi/Hi

1 dPi 1 1 dPi 1 Note: for wi = 0 we have = − or = − Pi dz Hi Pi dz H

R *T R * T kT Hi = H = Di = ν = collision frequency mig m g mν

Note: Di increases exponentially with height

63 See two paper sheets (Rees 82-85; Brekke 96-99, first edition)

€

€ ∂N i ∂ N iDi We can define a time ~ N iw i ~ 2 ∂t ∂z H constant for the diffusive i 1 D process. ∂ i − t /τ D N i ~ 2 ⇒ N i ~ N ioe N i ∂t H i Suppose diffusion is the H 2 H 2 only process acting. i where τD ~ (or τ M ~ ) Di K

The relative importance of various process can be determined by comparing their time constants. The smaller time constant indicates the dominant process. For instance, we may define the homopause or turbopause according to the relative lifetimes of a constitutent with respect to molecular diffusion or mixing:

τD << τM z > 105 km ⇒ “heterosphere”

τD >> τM z < 105 km ⇒ “homosphere”

τD ~ τM z ~ 105 km ⇒ “turbopause”

€ 2 2 Hi H τ D ~ and τ M ~ Di K

are the time constants relevant for re -establishing hydrostatic equilibrium if the species are driven from hydrostatic equilibrium by some process (i.e., vertical motion due to sudden heating; introduction of a reactive chemical into the atmosphere; sudden lifting of the ionosphere by electric fields).

65 An Example Atomic Oxygen at Mesosphere O + hν "J"→O + O Atomic Oxygen 2 k2 O + O + M ""→O2 + M ∂[O] ! = P - L - ∇⋅V [O] ∂t

Total rate of Rate of change of Rate of change of change of [O] [O] within volume V [O] within volume V within volume V due to chemical due to transport in production (P) and or out of the loss (L) volume.

Photochemical equilibrium 2 implies a balance between 2J[O2 ] = k2 [O] [M ] production and loss, i.e., P = L. 1 2 "2J[O2 ]% Note: The law of mass action says that the ∴ [O]=# & rate of a chemical reaction is proportional $ k2 [M ] ' to the product of the densities of species taking part in the reaction.

€ Thus, given [O2], J, k and [M], one can calculate the atomic oxygen profile in Earth’s atmosphere:

However, this profile does not agree with measurements, particularly the height of the peak.

68 We can define a time constant for the diffusive process. SupposeJ diffusion is the only process acting: O2 + hν ""→O + O So we ask,

k2 after photo-dissociation, what ThenO + O + M ""→O2 + M is the most likely fate for O?

∂[O] 2 ~ −k2 [O] [M ] ∂t Near 95 km, 1 ∂ ~100 d −t /τ L τL [O] ~ − k2 [O][M ] ⇒ [O] ~ [O] e [O] ∂t o 1 Similarly, a time constant forwhe oxygenre τ L ~ recombination can be defined: k2 [O][M ]

Near 95 km, K~100 m2s-1 (no H 2 τ ~ systematic height dependence), M K and H~8 km, so tM~ 6 d

69 At 80-100 km, the time constant for mixing is more efficient than recombination, so mixing due to turbulence and other dynamical processes must be taken into account (i.e., photochemical equilibrium does not hold).

Mixing transports O down to lower (denser) levels where recombination proceeds rapidly (the "sink" for O).

O Concentration

After the O recombines to produce O2, the O2 is transported upward by dynamical mixing to be photodissociated once again (the

"source" for O). 70 Thus, “hydrostatic equilibrium” for a particular atmospheric constituent implies

• Steady-state conditions

• Chemical production and loss have long time constants compared to diffusion

• There is no net diffusion between the constituent and the other major species

Planetary escape by atomic hydrogen is another case where the mean vertical profile of a thermosphere constituent deviates from hydrostatic balance. This is because there is a net escape flux of H from the atmosphere

71 Minor species: water vapour (H2O)

• source of hydrogen

+ + • H 3O, H (H2O)6…

72 Minor species: water vapour (NO)

+ • O2 + NO à NO + O2 (E region ionosphere)

Stratosphere:

N2O + O à NO NO + hvà N + O

NO + Nà N2 + O

Mesopshere-thermosphere

N(2D)+O2 à NO + O 4 N( S) + NO à N2 + O NO + hvà N(4S) + O

73 Minor species: water vapour (NO)

74 Minor species: ozone (O3)

• Peak at 20 km

O + O2 + M à O3 +M

O3 +hv à O2 + O

O3 +O à O2 + O2

ozone hole

Cl O ClO O + 3 → + 2

ClO + O → Cl + O2 − − − − − − − − − − − − −

O3 + O → 2O2

75 Global ozone structure Minor species: Metals

• Sodium

• Calcium

• iron

• magnesium

77 Upper Atmosphere Variability & Empirical Models of the Thermosphere

78 SABER channels and data product

http://saber.gats-inc.com/ SABER 9 day s=0 Component

[Chang et al., 2009, GRL] SABER 9 day s=0 Component, 50°N & 50°S UARS http://umpgal.gsfc.nasa.gov/uars-science.html http://aura.gsfc.nasa.gov/index.html

Our Early Knowledge of the Thermosphere was Derived from the Observed Effects of

Atmospheric Drag on Satellite orbits

The acceleration due to thermospheric density drag on an object is:

1 2 ｖ! D = − ρB v - V ev−V 2 where B = B-factor (ballistic coefficient) = C D A

ρ = density m v = neutral wind

V = satellite velocity € From radar tracking, one can derive the atmospheric density (the more accurate the tracking, the shorter time required to determine density). Typical resolution is about 1 day below 200 km and 5 days at 500 km. (Much better with laser beacon, etc.)

87 Examples of Simple calculations of satellite life-time

high solar low solar

14 88 01/12/05 99/05/27 01/09/29 5月 3号 How to derive thermosphere temperature

from mass density? Given the equations defining the hydrostatic law, the chemical composition at some height, and an expression for the temperature profile shape, a density profile can be retrieved from the satellite observations. Tex, i.e., 500 K, In practical applications 700 K, ...... 1900 K of this method, if a reasonable initial first guess of the vertical structure is provided, slope and curvature an iterative procedure defined by ”shape‘ leads to an accurate parameters determination that is

independent of the specify [O], [O2], [N2] here and T initial guess. Z ~ 120 km 120

A set of "exospheric temperatures” emerges from this process.

91 Correlation of density and temperature with long- term changes in solar activity.

92 Diurnal and semiannual variations, and correlations with short -term changes in solar activity.

1967 1968 1969 93 Contemporaneous Solar Rotation Effects at Mars and Earth CHAMP 5d Orbit-Integrated Densities - 410 km

solar flux Mars Global Surveyor Orbital Decay (5d) - 390 km

[Forbes et al., Science, 2006] 94 High speed solar wind streams in 2008

266 spotless days

Geospace was not quiet

95 Thermosphere was not quiet under this extreme solar minimum!!

Solar wind density

IMF |B|

Solar wind speed 38 CIRs!

IMF Bz

IMF Bx

Geomagnetic Activity Index

Density - 400km altitude

Lei et al., Solar Phy., 2011 96 Classical CIR

Tsurutani et al., JGR, 1995

Russell-McPherron effect 97 IN THE 1970'S, TWO DATA SETS BECAME AVAILABLE THAT ADDRESS THE PREVIOUSLY-MENTIONED LIMITATIONS FOR DRAG-BASED MODELS:

• determinations of Tex from incoherent scatter radar measurements.

• satellite mass spectrometer measurements of O, O2, N2, He, H, etc., and also measurements of Tex. (satellites like OGO-6, AE, and many others).

HENCE LEADING TO THE

Mass Spectrometer Incoherent Scatter (MSIS) models of A. Hedin (NASA/GSFC).

However, the MSIS models are not optimized with respect to satellite drag, and so have not been widely adopted for ephemeris computations in lieu of the Jacchia models. In principle, though, getting closer to the correct physics should lead to improved orbital predictions.

98 Some of the other models developed during the past 30 years

EMPIRICAL U.S. Standard 1962 Jacchia 1964 U.S. Standard Supplements, 1966 CIRA-1961, 1965 MSIS86, MSIS90, MSISE90 Jacchia-1971, 1977 CIRA-1986 NRLMSIS2000

NUMERICAL/THEORETICAL MODELS

University College London Thermosphere-Ionosphere Model

(now Coupled Thermosphere-Ionosphere-Plasmasphere Model (CTIP) at CU/CIRES)

NCAR Thermosphere-Ionosphere GCM

TGCM TIGCM TIE-GCM TIME-GCM

99 NRLMSIS00

100 NRLMSIS00

101 Model validation

Marcos F. (2006) Model-data comparison

Obs.

MSIS

TIEGCM

Lei et al., JGR, 2011 Analyses of many satellite orbits led to the so-called "static diffusion models" developed by Jacchia and which form the basis of many operational drag models. These are based on a parametric dependence of density on exospheric temperature.

The derived exospheric temperatures (and the densities) reveal many of the variations typical of the thermosphere: annual, semiannual, solar activity, magnetic activity, diurnal, etc. (see following figures).

DESPITE THE IMMENSE SUCCESS OF THESE MODELS AT THE TIME, THEY SUFFER FROM SOME FUNDAMENTAL LIMITATIONS:

• The derived temperature is more of a 'virtual' temperature than 'real' (kinetic) temperature

• Rocket measurements of O, O2 at the lower boundary are difficult to interpret (i.e., O recombines into O2 against walls of measuring device, meaning that O can be underestimated and O2 overestimated).

• Wind-induced diffusion is also important, i.e., for [O]; The 'static diffusion' or 'hydrostatic' restriction is not amenable to addressing vertical transport (i.e., upwelling) or horizontal transport.

104 • Question: As the increase of solar activity, we did see an increase the light species (e.g. He) observed in O, N2 and O2. Why? Planetary Escape

106 Ionosphere-Thermosphere Basics - I Neutral Atmosphere Vertical Structure

107 Atmospheric Escape Maxwell-Boltzmann Distribution For an ideal gas consisting of perfectly elastic spheres in random thermal motion, and under equilibrium conditions, the number of molecules dN out of a total N having a speed between c and (c+dc) is given by the Maxwell-Boltzmann distribution: mc 2 c +dc 3/2 − dN |c m 2 = 4π e 2kT c dc N ( 2πkT ) The above provides a definition of kinetic temperature valid whenever a gas is in thermal equilibrium. Critical Level Above a certain level the mean free path of the particles becomes so long (i.e., on the order of a scale height) that a molecule traveling upward can go all the way out to space without colliding at all. The level at which this occurs is called the critical level.

108

€ Exosphere and Exobase The region above the critical level is called the exosphere. The critical level is sometimes called the exobase. The exobase is between about 500-800 on Earth (depending on solar activity), and at about 200 km on Venus.

Atmospheric particles escape if their velocities exceed the escape velocity, which is determined by the gravitational field:

1/ 2 2GM u & # l H esc = $ ! < % r "

where G, M and r are the Gravity Above the exobase there exists a substantial fraction of the particles with velocities greater than constant, planet mass and radius. the escape velocity. For Earth, uesc=11.2 km/s.

This produces a net upward flux of atmospheric gases, in practice only relevant for atomic hydrogen, that introduces and additional term in the “hydrostatic equation”.

109

€ Jeans Escape Assuming that particle velocities are thermal, the escape flux is given by: r ….. Exobase radius N(rc )⋅U −λ −2 −1 c FJeans (rc ) = e (λ + 1) [cm sec ] N ….. Number density 2π 1/ 2

where 1/ 2 Mparticle …Particle mass & 2kT # u2 T …….... Temperature U = $ ! and λ = esc $ M ! U 2 k ………. Botzmann const. % particle "

U is the most probable velocity of a Maxwellian distribution of thermal velocity.

So, Jeans escape increases with temperature. A rise in temperature should thus lead to a considerable decrease of N(H) at the exobase.

This decrease in N(H) with temperature is observed, but smaller than expected from Jeans escape. Thus, H escape may be due to other processes less sensitive to temperature changes, such as charge exchange:

H + H + * → H + + H *

110 In Earth’s atmosphere, escape has an

important effect on variations in - - k = 107 Hydrogen densities. __ k = 0

Escape sink

vertical flux

H O, CH 2 4 source H

The thermal or Jeans escape flux increases with temperature, causing the hydrogen density to decrease with increasing solar activity.

111