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Required Reading: Jacob Chapter 2

Atmospheric Chemistry

ATOC-5151 / CHEM-5151

Spring 2013Prof. Jose-Luis Jimenez

Atmospheric Structure I

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Review Questions

1. Oxygen has a constant mixing ratio in the atmosphere. How would you expect its number density in surface air to vary between day and night?

2. Give a rough order of magnitude for the number of molecules present in a typical 1 micrometer aerosol particle.

3. Does it make sense to talk about the mixing ratio of aerosolparticles in air? To express the concentration of soot aerosol in units of ppbv?

2From Heald

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Radius = 6000 kmAtm = 12 km

Radius/atm = 500

Radius = 75 mmskin = 0.5 mm

Radius/skin= 150

Atmosphere is a thin planetary skin

From Tolbert

Atmosphere is locally flat

• For most practical purposes, lower atmosphere can be regarded as flat. Earth curvature only needs to be considered in very special cases.

• Earth does drag a veil of gas with itself (“exosphere”) with the size of approximately 10,000 km, however it is extremely dilute.

• For reference, space shuttle @ 300-600 km above the Earth surface

4Figure from Brasseur & Jacob

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Measurement of atmospheric pressure with the mercury barometer:

vacuum

A Bh

Atmospheric pressure P = PA = PB = Hg gh

Mean sea-level pressure: P = 1.013x105 Pa = 1013 hPa

= 1013 mbar (mb)= 1.013 bar= 1 atm= 760 mm Hg (Torr)

Atmospheric Pressure

From Jacob

Sea Level Pressure MapQ1: is P in Boulder correct?A.YesB. NoC. It dependsD. I don’t know

Q2: why is P variation relatively small?A. Because T is also smallB. Because of stormsC. Because of windsD. Because it is an “El Niño” yearE. I don’t know

Adapted from Jacob

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Sea-Level P can only vary over a narrow range

Consider a pressure gradient at sea level operating on an elementary air parcel dxdydz:

P(x) P(x+dx)

Vertical area dydz

Pressure-gradient force ( ( ) ( ))d P x P x dx dydz F

Acceleration1 dP

dx

For P = 10 hPa over x = 100 km, a ~ 10-2 m s-2 100 km/h wind in 3 h!

Effect of wind is to transport air to area of lower pressure and dampen P

On mountains, however, the surface pressure is lower, and the pressure-gradient force along the Earth surface is balanced by gravity:

P(z)

P(z+Dz) P-gradient

gravity

This is why weather maps show “sea level” isobars; The fictitious “sea-level” pressure at a mountain site assumes an air column to be present between the surface and sea level

From Jacob

8http://en.wikipedia.org/wiki/International_Standard_Atmosphere

• Questions:– Physical basis for P

variation?

– Physical basis for T variation?

Vertical Structure I

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From Tolbert

Vertical Structure II

Troposphere: 0 – 15 km

Greek “tropo” = turningStrong vertical motions (days/hrs)

• T decreases with altitude• Air mostly transparent to visible radiation, not a lot of heating• Sun heats surface: warm air below cold• Creates buoyancy and convection

Adapted from Tolbert

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Stratosphere: 17 – 50 km

Latin “stratus” = layeredSlow vertical mixing - years

T increases w/ altitude, warm above coldStable, temperature inversion

From Tolbert

CQ: Where is the tropopause higher?

a. Tropicsb. Polesc. About equal in both placesd. Tropics in summer and poles in wintere. I don’t know

Adapted from Tolbert

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Mesosphere: 50 – 80 km

Temperature drops off again

T increases w/ altitude, warm above coldStable, temperature inversion

This is where small meteors burn up – “shooting stars”

From Tolbert

Thermosphere: > 80 km

T increases w/ altitude, warm above coldStable, temperature inversion

Air is heated by absorption of x-raysHighly ionized

This class: Troposphere and Stratosphere

From Tolbert

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AS II: Pressure Variation

• Write force balance for slab

From Jacob

15

height" scale" is where

)0()(

: oft independen are and that Assuming

:get we two theseCombining

:law gas ideal From

)]()([

:laws sNewton'

a

Hz

a

a

a

gM

RTH

ePzP

zMT

dzRT

gM

P

dP

RT

PM

gdz

dP

AdzzPzPgAdz

AS II: Pressure Variation Solution

“Hydrostatic equation”

CQ: H in troposphere?A: 7 km B: 7 K/km C: 2 km D: 0.5 atm E: dunno

Ada

pted

from

Nid

koro

dov

2/7/2013

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Required Reading: Jacob Chapter 2 + 4.3

Atmospheric Chemistry

ATOC-5151 / CHEM-5151

Spring 2013Prof. Jose-Luis Jimenez

Atmospheric Structure II

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Business Items• Dr. Christoph Knote (NCAR) will teach lecture on

simple models– He is an atmospheric modeler

– Tricky conceptually, if you haven’t done this before

– Do the reading before the lecture if you can, and especially if you are having issues with the simple models in the problems (e.g. Radon problem in HW2.2, pollution problem in HW3.7)

• HW programming notes– Pay attention to conventions of the course, points shall be

taken off for not following them

– If a problem requires doing the same calculation for several time steps, you need to reuse the same code. It is inefficient (esp. on your time) to e.g. write a separate routine or loop for each time step

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Mass of the Atmosphere from force balanceRadius of Earth:6380 km

Mean pressure at Earth's surface:984 hPa

Total number of moles of air in atmosphere:

201.8 10 molesaa

a

mN

M

Mol. wt. of air: 29 g mole-1 = 0.029 kg mole-1

2184

5.13 10 kgSurfacea

R Pm

g

• Clicker Q: approx. number of moles in the mesosphere?– A: 1.8 x 1014 B: 1.8 x 1015 C: 1.8 x 1017

– D: 1.8 x 1012 E: I don’t know

The sea breeze

circulation

From Jacob section 2.5

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Vertical Profile of Temperature

Mean values for 30oN, March

Alt

itu

de,

km

Surface heating

Expansion coolingConvective Transport & Latent heat release

Radiativecooling (ch.7)

- 6.5 K km-1

+ 2 K km-1

- 3 K km-1

Radiativecooling (ch.7)

Radiative heating:O3 + hO2 + OO + O2 + M O3+M

heat

Heating by Absorption

• In the absence of local heating, T decreases with height

• Exceptions: Stratosphere: Chapman Cycle (1930s)O2 + hv → 2O

O + O2 + M → O3 (+ heat)

O + O3 → 2O2

O3 + hv → O + O2 (+ heat)

– Q: what is heat at the molecular level?

• Mesosphere: absorption by N2, O2, atoms…

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Adiabatic Lapse Rate

For adiabatically expanding gas:

(internal energy) (work)

where is molar heat capacity of air at constant .

Combining this with ideal gas law,

we get:

where is molar hea

v

v

p

p

nc dT PdV

c V

PV nRT

dT RT

dP c P

c

t capacity of air at constant .

is called "dry adiabatic lapse rate"

dp p

P

dT RT dP MW g

dz c P dz c

Clicker Q: What is the approx. lapse rate for Earth if Cp for air is 29.1 J mole-1 K-1?

A.10 K/kmB.1 K/km

C.0.01 K/mD.10 km/atmE.Don’t know

(rate of temperature decrease with altitude)

Adapted from Nidkorodov

Atmospheric (Vertical) Stability I• Adiabatic Lapse Rate ()

– vertical temperature profile when air ascends or descends adiabatically, i.e. w/o giving or receiving heat

– For Earth, = 9.8 K km-1

• Buoyancy force on an air parcel that has rapidly (adiabatically) ascended or descended: Fb = ’g – g

Figure from Jacob’s book 24

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Atmospheric (Vertical) Stability II

• Q: which of the following profiles are stable?– Stable: a small vertical motion is damped (Unstable: it is

amplified)

– A: 1 & 2 B: 2 C: 3

– D: 2 & 3 E: I don’t know F: All of the above

T

z z z

“Inversion”

T T

adiabatic Actual

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1 2 3

Dilution of Power Plant Plumes• Question: which

plume dispersion corresponds to each T profile?

26From Jacob’ s book (problem 4.1)

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How does the Temperature Profile Evolve?

• An atmosphere left to evolve adiabatically from an initial state would eventually tend to neutral conditions (-dT/dz = ) at equilibrium

• Solar heating of surface and radiative cooling from the atmosphere disrupts that equilibrium and produces an unstable atmosphere:

Initial equilibriumstate: - dT/dz = G

z

T

z

T

Solar heating ofsurface/radiative cooling of air: unstable atmosphere

ATM

ATM

z

Tinitial

final

buoyant motions relaxunstable atmosphere back towards –dT/dz = G

• Fast vertical mixing in an unstable atmosphere maintains the lapse rate to .Observation of -dT/dz >= is sure indicator of an unstable atmosphere.

From Jacob

Temperature Inversions in the Troposphere

Condition under which temperature increases with altitude (negative lapse rate) instead of decreasing.

CONSEQUENCE

Air in the inversion layer is not mixed efficiently, which results in local trapping of pollutants.

Atmospheric Boundary Layer

Air contained below the inversion layer, where mixing is rapid. This layer is directly affected by the surface. Air pollutants emitted on the ground rapidly distribute through the boundary layer and accumulate in the inversion layer.

From Nidkorodov

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Diurnal Ventilation of Urban Pollution

z

T0

1 km

MIDDAY

NIGHT

MORNING

Mixingdepth

Subsidenceinversion

NIGHT MORNING AFTERNOON

PBLdepth

Potential Temperature I

1 10

0

1 2

7

0 0

If the adiabatic approximation applies, we have

constant

where is reference pressure ( 1 atm)

7

5

The quantity

is known as the "potential temperature

P

V

T P P

P

Cγ

C

P PT T

P P

"

• Potential temperature, , is the temperature an air parcel would assume if it were adiabatically compressed from its initial pressure P to some reference pressure P0

(usually 1 atm).

USEFULNESS

• Air parcels approximately conserves its potential temperature and tend to move along lines of constant .

• Air parcels with constant can be assumed to be well mixed

• In other words, potential temperature is a convenient indicator of atmospheric stability: Adapted from Nidkorodov

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Stability w/ Potential Temperature

• Q: which of the following profiles are stable?– Stable: a small vertical motion is damped (Unstable: it is

amplified)

– A: 1 & 2 B: 2 C: 3

– D: 2 & 3 E: I don’t know F: All of the above

z z z

adiabatic Actual

31

1 2 3

Potential Temperature III

0 when

well mixed atmosphere

0

poorly mixed atmosphere

dp

d dT MW g

dz dz c

d

dz

Clicker Q: An air parcel has a temperature of 10 C and a pressure of 650 mbar. Is this parcel likely to have the same composition as the air at the ground level below it?A. YesB. Only partiallyC. It depends on additional infoD. No way JoseE. E. I don’t know Adapted from Nidkorodov. Fig. from Jacob

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In Cloudy Air

Air parcel

Cloud forms

Cloud deepens

RH > 100%:Cloud forms

“Latent” heat releaseas H2O condenses

9.8 K km-1

W 2-7 K km-1

RH

100%

T

z

W

Clicker Q: Does the stability criterion that we discussed based on q apply to cloudy air?A. Yes B. Only partially C. It depends on additional infoD. No E. I don’t know Adapted from Jacob

cloud

boundarylayer

Discuss: why do the clouds start where they do? why do they stop? Air is turbulent (cf. airplane take off and landing) below the cloud base and inside the cloud and usually smooth above—why?

A picture to illustrate. Not the same place/time, but the same phenomenon

Adapted from Jacob

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Clouds and Subsidence Inversions• Very common,

otherwise air would rise to tropopause, precipitating along the way.

• Lateral distance between the point of ascent and descent for the air mass can be as short as several kilometers and as large as thousands of kilometers. Subsidence over subtropical cities (LA, Mexico City, Athens, Sao Paulo) adds to pollution.

typically 2 km

From Jacob & Nidkorodov

FT

PBL

FT = Free Troposphere

Species Variation?• H(z) = RT(z)/(MWair * g)

• Dalton’s law: each component behaves as if it was alone in the atmosphere

• Hi(z) = RT(z)/(MWi * g)– O2 at lower altitudes than N2?

– Some scientists: CFCs could not cause stratospheric O3 depletion; too heavy to rise to stratosphere

• Q: What’s wrong with that picture?

36

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Homosphere: Turbulent fluid mixing faster than diffusion

Heterosphere:Above 100 kmDiffusion fasterthan turbulent fluid mixingGravitation separationbased on MW

From Tolbert

Persistence of Planetary Atmospheres• Molecules in the high velocity tail of the Maxwell-

Botzmann distribution can escape the atmosphere

• The molecules are held back by the gravitational pull of the planet. The critical parameter is the ratio of their gravitational and thermal energy (r = planet radius; G =6.675×10-11 m3/(kg s2 ) = gravitational constant; M = planet mass; m = mass of the molecule; k = Boltzmann constant)

• Escape rate per unit area per second can be estimated as (nc = density at the critical level). This is known as the Jeans escape formula.

• Escape velocity is the ratio of the escape rate and the gas concentration

322

( ) exp2 2Max Boltz

m mp

kT kT

potential

thermal

E GMm

E rkT

(1 )2

cnRate e

Planet Exospheric Temperature (K)

H Vescape

(cm/s)Has

atmosphere?

Uranus 810 33 1.6×10-8 Yes

Venus 400 16.2 0.11 Yes

Earth 1200 6.3 1700 Yes

Moon 390 0.9 55000 No

Io 700 0.8 66000 No

2kT

m

(1 )2

escapec

RateV e

n

Solve in class: Calculate O

and Vescape for the oxygen atom on Earth. The mass of

the Earth is 5.981024 kg, and its radius is 6371 km. Do a similar calculation for the

Moon, M = 7.351022 kg, r = 1738 km)

Earth answer: O = 100; Vescape = 0.00 cm/s

Moon answer: O = 13.9; Vescape = 0.24 cm/s

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Spatial and Temporal Scales• Tight link

between spatial & temporal scales

From S&P

39