1

Topics in Space WeatherTopics in Space Weather

Lecture 11

The Upper Atmosphere

Topics in Space WeatherTopics in Space Weather

Lecture 11

The Upper Atmosphere

Robert R. Meier

School of Computational SciencesGeorge Mason University

rmeier@gmu.edu

CSI 76915 November 2005

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Remaining Lectures

• Lecture 11 – November 15– Upper Atmosphere

• Lecture 12 – November 22– Ionosphere– Geomagnetic storms

• Lecture 13 – November 29– Geomagnetic storms & magnetosphere

connection– Aurora and Airglow

• Lecture 14 – December 6– Effects on Technological Systems– John Goodman will give last lecture

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Topics - Lecture 11

• Sun as a star

• Solar effects on the atmosphere

• Upper atmospheric processes

• Temperature

• Density and composition

• Winds

surface

particles and magnetic fields

SUN EARTH

Sun-Earth SystemSun-Earth System:: Energy Coupling Energy Coupling

photons

core

convection zoneradiative zone

surface atmosphere

magnetosphere

sunspotplage

coronal mass ejection

bow shock

plasmasphere

not to scale

solar wind

heliosphereatmosphere

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SOLAR - TERRESTRIAL SOLAR - TERRESTRIAL ENERGY SOURCESENERGY SOURCES

Source Energy Solar Cycle Deposition (Wm-2) Change (Wm-2) Altitude

Solar RadiationSolar Radiation• total 1366 1.2 surface• UV 200-300 nm 15.4 0.17 10-80 km• VUV 0-200 nm 0.15 0.15 50-500 km

ParticlesParticles• electron aurora III 0.06 90-120 km• solar protons 0.002 30-90 km• galactic cosmic rays 0.0000007 0-90 km Peak Joule Heating (strong storm)Peak Joule Heating (strong storm)• E=180 mVm-1 0.4 90-200 km

Solar WindSolar Wind 0.0006 above 500 km

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Sun as a StarSun as a Star

SPEC

TRU

M

SPEC

TRU

M

VAR

IAB

ILIT

YVA

RIA

BIL

ITY

TOTA

L TO

TAL

IRR

AD

IAN

CE

IRR

AD

IAN

CE

VAR

IAB

ILIT

YVA

RIA

BIL

ITY

8magnetic fields have different effects on radiation at different wavelengths

sunspot

faculae

UV radiation varies more than visible radiation because UV faculae are brighter

The Sun’s Radiation SpectrumThe Sun’s Radiation Spectrum

EUV Radiation is Emitted from the Sun’s EUV Radiation is Emitted from the Sun’s Outer Atmosphere: Outer Atmosphere: Chromosphere, CoronaEUV spectrum:

>1500 lines5 continua

emission line temperatures vary over 2 orders of

magnitude

19960304 20000502EIT

304Å

0.0

8MK

284Å

2M

K

quiet Sun

He+ 304

quiet Sun

750K Exospheric Temperature 1300Kflares and

27-day rotations superimposed on

11-year cycles

Warren et al., 2001

GOES

SOLAR IRRADIANCE VARIABILITY MECHANISMSSOLAR IRRADIANCE VARIABILITY MECHANISMS

SOLAR ROTATION SOLAR ACTIVITY CYCLE

11

Ap

spacecraft drag

critical frequency

solar EUV photon energy

solar wind kinetic energy

corona

chromosphere heliosphere

16 JAN 03

Sun and Thermosphere-IonosphereSun and Thermosphere-Ionosphere

400 km

quiet Sun

response to EUV photons

response to particles, plasma, fields

NRLMSIS:500 km

temperature

neutral density

electron density

nemax=1.24×104fo2

NAVSPACECOMsolar wind

energy

EUV Radiation is Emitted from the Sun’s EUV Radiation is Emitted from the Sun’s Outer Atmosphere: Outer Atmosphere: Chromosphere, Corona

EUV spectrum: >1500 lines5 continua

emission line temperatures vary over 2 orders of

magnitude

19960304 20000502EIT

304Å

0.0

8MK

284Å

2M

K

quiet Sun

304

quiet Sun

Primary EUV Sources of Upper Atmosphere Heating: ch chromospheric cr coronal ch+cr mixed

Roble, 1987

750K Exospheric Temperature 1300K

Solar Cycle EUV Spectrum Variability

He II “304” He II “304” Å Irradiance VariabilityÅ Irradiance Variability

11-year cycle

27-day rotation

episodic flaring

SEM “304”Å5 min irradiance

NRLEUV HFG EUVACSOLAR2000

particlecontamination

model

SOHO/

TIMED/

SOHO EIT 195ÅSolar EUV Radiation Alters Ionosphere Solar EUV Radiation Alters Ionosphere

- Bastille Day 2000 solar eruption

pre-flare

flare

Meier et al., GRL, 2001

ionosphericelectron density

response

X-ray and EUV

irradiancevariation

TRACE

NRL SAMI2 model(Huber and Joyce)

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Availability of Solar XR, EUV & UV Data

• Solar Extreme Ultraviolet (SEE) data from NASA/TIMED satellite– http://lasp.colorado.edu/see/

• Solar Radiation and Climate Experiment (SORCE)– http://lasp.colorado.edu/sorce/

• Solar EUV model (EUV81) [Hinteregger et al., Geophys. Res. Lett. 8, 1147-1150, 1981]– Can be found at SEE website, along with other

models (click on Data-General information and other data-Solar Irradiance Models)

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Solar Effects on the Solar Effects on the AtmosphereAtmosphere

GLOBAL CHANGE

SPACE WEATHER

EUV FUV MUVRADIATION

Solar Energy Solar Energy DepositionDeposition

Atmospheric Atmospheric StructureStructure

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Radiative energy deposition follows Beer’s Law

Change in solar flux

n = # absorbers/cc = absorption cross

section

Integrating,

dF n F dz

F

F+dF

dz’

z

n(z ')dz '

F(z) F( ) e

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Optical Depth

• Definition

• For several species– i = N2, O2, O

• Altitude of unit optical depth: F(z)= F() e-1 – Solve (z) = 1 for z (See slide 16)

z

(z) n(z ')dz '

i ii z

(z) n (z ')dz '

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Column Density

• If const.,

• Vertical Column Density

number of atoms/molecules in a 1 cm2 column above altitude z

z

(z) n(z ')dz ' N(z)

z

N(z) n(z ')dz '

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Slant path optical depth

Assume plane parallel atmosphere– H << earth radius– Away from terminator

s = z / cos and

(s) = (z) / cos solar zenith angle

What happens at the terminator ( = 90o)?

(z)

0(s)

z

F()

s

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Large solar zenith angles• Allowing for earth curvature and isothermal atmosphere,

then:

(s) = (z) Ch(x, )

– X = (Re + z)/H– Re = earth radius– H = scale height– Ch(x, ) = Chapman function

where + > 90o and - < 90o

• Must do numerical integration along slant path from Sun:– If not isothermal– If accounting for oblate spheroid shape of Earth

2

2xcos χ 0.50.521 xcos χ

Ch(x, χ) π x sinχ e 1 ± erf2 2

*

* From Rishbeth and Garriott, Intro. To Iono. Phys.

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Solar Energy in the Upper Atmosphere

ENERGETIC SUNLIGHT AND PARTICLES

EXCITATION

IONIZATION DISSOCIATION

ION CHEMISTRY NEUTRALCHEMISTRY

COLLISIONALDEACTIVATION

PHOTOELECTRONS

ELECTRON HEATING ION HEATING NEUTRAL HEATING

SPECTRALEMISSIONS

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Atmospheric Absorption Processes

• Ionization– O2 + h O2

+ + e*, …

• Dissociation– N2 + h N + N, …

• Excitation– O + h O*

• O* O + h ’ radiation• O* + X O + X quenching or deactivation

• Dissociative ionization – excitation– N2 + h N+* + N + e, …

...

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Energy Thresholds for Processes*

Species Dissociation

(Å)

Dissociation

(eV)

Ionization

(Å)

Ionization

(eV)

H

He

O

O2

N2

NO

2423.7

1270.4

1910

5.11

9.76

6.49

911.75

504.27

910.44

1027.8

796

1340

13.6

24.58

13.62

12.06

15.57

9.25

* From Heubner et al., Astrophys. Space Sci., 195, 1-294, 1992

Useful relationship: E(eV) x (Å) = 12397

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N2 Absorption Cross Section*

* Pl. Space Sci. 31, 597, 1983

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O2 Absorption Cross Section*

* Pl. Space Sci. 31, 597, 1983

28R. Conway and Brendan McLaughlin, personal communication

SOLAR CYCLE CHANGES IN EUV RADIATION SOLAR CYCLE CHANGES IN EUV RADIATION IMPACT UPPER ATMOSPHERE IMPACT UPPER ATMOSPHERE TEMPERATURE and DENSITYTEMPERATURE and DENSITY

Solar Cycle Changes Solar Cycle Changes at 700 km:at 700 km:

Neutral Temperature:Neutral Temperature: 2 times2 times

Neutral Density:Neutral Density: 50 times50 times

Electron Density:Electron Density: 10 times10 times

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Atmospheric Processes

Described by Thermospheric Global Circulation Models

(GCMs)

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GCM Physics: Upper AtmosphereGeoff Crowley

Atmospheric & Space Technology Research Associates (ASTRA)

11118 Quail PassSan Antonio, TX 78249

210-691-0432

Objective:

What’s required to build a GCM?

(Equations, numerical techniques, parameterizations, boundary conditions, input specifications, validation with data)

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Important Inputs to the Thermosphere – Ionosphere System

Solar UV Input

Upper Atmosphere (Thermosphere – Ionosphere)

Tides and Gravity Waves

E-fields Particles?

Neutral density temperature wind electron density

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Simplified Physics of Upper Atmosphere

Composition

Temperature

Winds

E-fields

Electron Density

Diffusion Coeffs

Boundary Conds

Chemistry

Joule Heating Particle Heating

Solar EUV Chemical HeatingTides

Gravity Waves

Solar EUV

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The leap-frog method is employed with vertical thermal conductivity treated implicitly to second order accuracy. This leads to a tridiagonal scheme requiring boundary conditions at the top and bottom of the domain as implied by the differential equation. Advection is treated implicitly to fourth order in the horizontal, second order in the vertical

Energy equation

ppp

e

p

i

po

s

c

Q

Hc

RTTV

c

aT

c

aT

sK

H

1

scp

ge

t

T

Molecular conduction radiation advection adiab. heating

Many terms

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NEUTRAL GAS HEATING

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Continuity equation

RSdz

dV

dz

dezK

dz

deL

T

T

m

m

dz

de

dt

d zz125.0

0

N

1z

2

molecular diffusion eddy diffusion Horiz. advection

Vert. adv.

Production

Recombination

i is the mass mixing ratio for species i: i = I(z) / I(z), where is the mass density

The leap-frog method is employed leading to a tridiagonal scheme requiring boundary conditions at the top and bottom of the domain.

37

Example: Nitrogen Chemistry (Simplified)

Each species equation includes horizontal and vertical advection, photo-chemical production and loss, and vertical molecular and eddy diffusion.

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Neutral Species

The model includes 15 separate neutral species, not counting some excited states which are also tracked.

CO2, O, N2, CO, O2, O3, H, H2, H2O, HO2,

N, NO, NO2, Ar, and He.

Ionized Species

The model includes 7 ion species

O+, N+, CO2+, O2

+, N2+, NO+, and H+

with ionization primarily from solar EUV and x-ray. The ions are assumed to be in photochemical equilibrium with one another and the free electrons.

39

Momentum equations

Zonal velocity

Meridional velocity

The Leap frog method is employed with vertical molecular viscosity treated implicitly to second order accuracy. Since the zonal and meridional momentum equations are coupled through Coriolis and off-diagonal ion drag terms, the system reduces to a diagonal block matrix scheme, where (2 x 2) matrices and two component vectors are used at each level. Boundary conditions for the zonal (u) and meridional ( v) wind components are needed at the top and bottom of the model.

GWU + F + u + + t

cosr

g u vu RAYK* ) tan

r

u + (f +

s

u

H

) K+ K(

s

P

eg =

t

uxIxxIxyxxuxy

EM

o

s

GWV+ F + + u z

r

g v RAYK* u) tan

r

u + (f

s

H

)K + K(

s

P

eg =

tIyyIyxxxxy

EM

o

s

Viscosity (Molecular and Eddy)

Coriolis

gravity wave drag

Pressure gradientsRayleigh friction

ion drag momentum advection

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Upper atmospheric temperature, density and

composition

Some simplified concepts

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78% N2

21% O2

1% other

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Thermodynamics

• Temperature equation very difficult to solve• Even under simplified 1-D geometry, the

temperature equation is a 2nd order time-dependent PDE– See Equation 8.77 of Gombosi

• Net heating rate (Production – Loss) is positive in the thermosphere (low cooling rate)– Leads to increase in temperature with altitude– Heat conducted downward and radiated to space in the

lower thermosphere by CO2, NO, and small amount of O fine structure radiation

43

Schematic of Energy Deposition in Thermosphere

44

Bates [1959] Temperature Profile

Analytic approximation for temperature profile:

T(z) = T - (T - Tzo) e-s(z – zo)

– s = shape function » Varies with conditions» typical ~ 0.02 km-1

– Matches observations– Functional form agrees with GCM models

o

o

z

z

dTdz

s =T - T

45

Fitting Bates Temperature Profile to GCM Model

• Non-linear least squares fit– “+” are model– Lines are function

• Worst error: few % • Therefore, can use

Bates profile for simple models of the thermosphere

• Note– Some places, T ~ const.– Some places, T ~ linear

Low solar activity

High solar activity

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Diffusion

• Eddy diffusion– Turbulent mixing/wave breaking approximated

by diffusion of small eddys

• Molecular diffusion– Each species follows its own scale height

• Turbopause– Where eddy and molecular diffusion rates are

equal– Typically ~ 105 km

• But transition is smooth over some altitude interval• Below is called the homosphere• Above is the heterosphere

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Turbopause

Gombosi, Fig 8.3

Turbopause

Ho

mo

sp

her

eH

ete

rosp

he

re

48

• Maxwell-Boltzmann velocity distribution

• No net vertical diffusion velocity• No chemistry • Steady-state, static equilibrium

– Ignore velocities

• Chapter 8 [Gombosi]

Diffusive Equilibrium

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Area A

(p+dp)A

pA

dw

Diffusive Equilibrium

The Gibbs-Dalton Law of partial pressures applies. For any species, force balance yields:

dw + (p+dp)A = pA

but dw = g A dz

Then

dp = - g dz = - nm g dz where p = pressure

= mass density

n = molecules cm-3

m = molecular massg = grav. acceleration

Forces balance on slab of gas in equilibrium

at altitude z

dz

z

zo

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Combine with Ideal Gas Law

p = n k T

dp = kT dn + nk dT = - nm g dz

dividing by nkT

dn/n + dT/T + dz/H = 0

where H = kT/(mg)

If T and g constant, then

n(z) = n(zo) e-(z-zo)/H

Note-Earth is an oblate spheroid:- Equatorial Radius: 6378 km & g = 9.78 m/s2

- Polar Radius: 6357 km & g = 9.83 m/s2

- Mean Radius: 6371 km

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Barometric Equation

From Ideal Gas Law

p = n k T

And with

n(z) = n(zo) e-(z-zo)/H

Substituting:

p(z) = p(zo) e-(z-zo)/H

This applies over small altitude intervals or at high altitudes where T is ~ constant

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Non-isothermal Atmosphere

Diffusive equilibrium:

dn/n + dT/T + dz/H = 0

d Log n + d Log T = - dz/H

Integrating:

n(z) = n(zo) T(zo)/T(z) e-dz/H

or

p(z) = p(zo) e-dz/H

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Multi-constituent AtmosphereTotal Pressure:

p(z) = pi

where i = N2, O2, O

Test for Diffusive Equilibrium

dpi = - ni mi g dz = - pi mi g dz / (kT)

Solving for g/(kT) for species I and j, leads to:

Integrating,

I=atomic mass of i

ji

i i j j

dpdp1 1=

mp dz m p dz

i

j

1

μi

1

μj

n T= const. = R

n TMeier et al.JGR, 106, 15519, 2001

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Diffusive Equilibrium for TIE-GCM and MSIS: O

• Plot R for two models– TIE-GCM first

principles model– MSIS empirical model

• Solar medium conditions– June

• Models qualitatively similar for O

Meier et al.JGR, 106, 15519, 2001

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Diffusive Equilibrium for TIE-GCM and MSIS: O2

• Important differences in O2

• Major discrepancies exist in measure-ments of O2

– After 50 years of space research, O2 remains uncertain

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A Couple of Shortcuts

• Isothermal Scale Heights– Hi = kT/(mig)

for g(200 km)

HN2 = 0.032* T

HO2 = 0.028* T =37 km

HO = 0.0567* T

• Estimate scale height: n(z)/n(zo) = 0.1 = e-(z-zo)/H

or H = (z-zo)/loge (10)

H = (z-zo)/2.3

Altitude interval where density decreases by 10:277 km – 205 km = 72 km

H = 72 km/2.3 = 31.3 km

ON2

O2

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Bates-Walker Model Atmosphere[Walker, J. Atmos. Sci, 22, 462, 1965]

Using the Bates T(z):

T(z) = T – (T - Tzo) e-s(z-zo))

And diffusive equilibrium: ni(z) = ni(zo) T(zo)/T(z) e-dz/Hi

And changing to geopotential altitude:

= (z-zo)(Re+ zo)/(Re+ z)

Then

where

1+

-μς(z)oi i o

T(z )n (z) = n (z ) e

T(z)

i o

e o

m g(z )1μ = s + =

R + z μkT

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Bates-Walker Model Atmospherecont.

• Gives good representation of atmosphere in diffusive equilibrium

• Basis of many atmospheric studies

• Basis of MSIS-class empirical models of the upper atmosphere– Needs to be modified for O and O2

photochemistry, which is important below ~ 200 km

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Departures from Diffusive Equilibrium: Simplified O2 Photochemistry*

• LossO2 + h O + O j = 4.2 to 6.8 x 10-6 s-1 solar min to max

tL = j-1 = 2.4 to 1.5 x 105 s

• ProductionO + O + M O2 + M k = 2.76 x 10-34 e710/T cm6 s-1

tP = (k nO nM)-1 s

• Diffusion timetD = H2/D tD(110km) ~ 2.4 x 105 s

tD(120km) ~ 1.2. x 105 s

• Therefore O2 not in diffusive equilibrium (tL ~ tD)

* Other O2 photochemistry also involved: Gombosi, 8.8.2

60From Rees, Phys. & Chem. of Upper Atmos.

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MSIS Class Empirical Atmospheric Models

• MSIS-class Models Are the Community Standard• Inputs: Day, Time (UT, Apparent Solar Local Time),

Location, Solar EUV Flux Proxy (F10.7 , F10.781 day

ave), Magnetic Activity (ap, Ap)

• Outputs: Composition (N2, O2, O, N, He, Ar, H, Oa), Total Mass Density, and Temperature, 0 - 1000 km

• Empirical, Analytic, Assimilative– Spherical Harmonics + Bates-Walker Altitude Profile– Interpolates Among Or Extrapolates Numerous Data Sets To

User-Specified Inputs– Nominal 1s Error 15-25 % (vs Altitude/Latitude)

• NRLMSIS 2000E supercedes MSISE-90: Automated/Web Distribution

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MSIS Data Bases

• Data Sets Incorporated Into NRLMSIS– Satellites (Mass spectrometer [MS], EUV

absorption)– Rockets (MS, Pressure gauge, falling sphere,

grenade)– Ground-based Incoherent Scatter Radar (ISR)– Middle Atmosphere Program (MAP) Handbook

Tables– Satellite Drag, Accelerometer– Recent O2 Data: Solar Maximum Mission (SMM)

• Data Sets Yet To Be Incorporated– Upper Atmosphere Research Satellite (UARS)– NRL/DOD UV Remote Sensing: ARGOS, SSULI

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MSIS Accessibility

• Description and downloading:– http://uap-www.nrl.navy.mil/models_web/msis/msis_home.htm– http://modelweb.gsfc.nasa.gov/models/msis.html

• MSIS 90 (earlier version)

• Reference to NRLMSIS2000– Picone, J. M., A. E. Hedin, D. P. Drob, and A. C. Aikin, J.

Geophys. Res., 107(A12), 1468 (2002)

• MSIS solar-geophysical inputs can be found at:

– ftp://ftp.ngdc.noaa.gov/STP/GEOMAGNETIC_DATA/INDICES/KP_AP/– http://www.sec.noaa.gov/today.html

64

NRLMSIS Example: March 21F10.7 = 150, Ap = 4 , Altitude = 300 km

65

NRLMSIS Example: June 21F10.7 = 150, Ap = 4, Altitude = 300 km

66

How Good are the Models?

• Compare MSIS & TIE-GCM Models

Solar-Geophysical Conditions• Summer Solstice June 19

• Solar Medium F10.7=150

• Low Geomagnetic Ap = 4• Latitudes -60 to + 60o

• Longitudes all• Altitude Range 110 – 478 km• GMT 00:00 H

• Plot Ratios of GCM/MSIS Parameters

67

Thermospheric Global Circulation Model and MSIS Empirical Model Show Major Discrepancies

Meier et al. JGR, 106, 15519, 2001

68

Upper Atmospheric Dynamics

Short Summary

(More after ionosphere and geomagnetic storm lectures)

69

Atmospheric Momentum Sources

• Solar (Heating) Tide

• Coriolis Force

• Ion Drag

• Gravity Waves

70

71

Altitude-Latitude Variation of Thermospheric Circulation from GCM Model

Quiet

Average

Storm

GeomagneticActivity