12.003 Introduction to Atmosphere, Ocean, and Climate Dynamics...
Transcript of 12.003 Introduction to Atmosphere, Ocean, and Climate Dynamics...
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12.003 Introduction to Atmosphere, Ocean, and
Climate Dynamics Topic 6
Vertical Structure of the Atmosphere
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Topic 6 Outline
1. Vertical distribution of temperature2. Hydrostatic balance3. Vertical distribution of pressure and density
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As discussed in earlier lecture... • Ideal gas law
⇤(z) = ⇤0 e�z/H (1)⇤0 = 1.35 kg/m3 (2)H = 6.8 km (3)
� =vr
=2⇥R/day
R=
2⇥day
= 7.27⇤10�5s�1 (4)
Ve =�
2GM/R (5)
Vm =�
2kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ⇤Rg
mT = ⇤ RT (8)
Rg = 8.314 JK�1mol�1 (9)
R =Rg
ma= 287 Jkg�1K�1 (10)
p = ⇥i
⇤iRg
miT = 78%⇤
Rg
mN2
T +21%⇤Rg
mO2
T + · · · = ⇤Rg
maT (11)
e = ⇤v Rv T (12)pd = ⇤d Rd T (13)p = pd + e⌅ pd (14)
es = A e�T (15)
1
⇤(z) = ⇤0 e�z/H (1)⇤0 = 1.35 kg/m3 (2)H = 6.8 km (3)
� =vr
=2⇥R/day
R=
2⇥day
= 7.27⇤10�5s�1 (4)
Ve =�
2GM/R (5)
Vm =�
2kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ⇤Rg
mT = ⇤ RT (8)
Rg = 8.314 JK�1mol�1 (9)
R =Rg
ma= 287 Jkg�1K�1 (10)
p = ⇥i
⇤iRg
miT = 78%⇤
Rg
mN2
T +21%⇤Rg
mO2
T + · · · = ⇤Rg
maT (11)
e = ⇤v Rv T (12)pd = ⇤d Rd T (13)p = pd + e⌅ pd (14)
es = A e�T (15)
1
⇤(z) = ⇤0 e�z/H (1)⇤0 = 1.35 kg/m3 (2)H = 6.8 km (3)
� =vr
=2⇥R/day
R=
2⇥day
= 7.27⇤10�5s�1 (4)
Ve =�
2GM/R (5)
Vm =�
2kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ⇤Rg
mT = ⇤ RT (8)
Rg = 8.314 JK�1mol�1 (9)
R =Rg
ma= 287 Jkg�1K�1 (10)
p = ⇥i
⇤iRg
miT = 78%⇤
Rg
mN2
T +21%⇤Rg
mO2
T + · · · = ⇤Rg
maT (11)
e = ⇤v Rv T (12)pd = ⇤d Rd T (13)p = pd + e⌅ pd (14)
es = A e�T (15)
1
⇤(z) = ⇤0 e�z/H (1)⇤0 = 1.35 kg/m3 (2)H = 6.8 km (3)
� =vr
=2⇥R/day
R=
2⇥day
= 7.27⇤10�5s�1 (4)
Ve =�
2GM/R (5)
Vm =�
2kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ⇤Rg
mT = ⇤ RT (8)
Rg = 8.314 JK�1mol�1 (9)
R =Rg
ma= 287 Jkg�1K�1 (10)
p = Rg78%⇤mN2
T +Rg21%⇤mO2
T + · · · = ⇤Rg
maT (11)
p V = ⇥i
ni Rg T = ⇥i
Mi
miRg T (12)
e = ⇤v Rv T (13)pd = ⇤d Rd T (14)p = pd + e⌅ pd (15)
es = A e�T (16)
1
⇤(z) = ⇤0 e�z/H (1)⇤0 = 1.35 kg/m3 (2)H = 6.8 km (3)
� =vr
=2⇥R/day
R=
2⇥day
= 7.27⇤10�5s�1 (4)
Ve =�
2GM/R (5)
Vm =�
2kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ⇤Rg
mT = ⇤ RT (8)
Rg = 8.314 JK�1mol�1 (9)
R =Rg
ma= 287 Jkg�1K�1 (10)
p = Rg78%⇤mN2
T +Rg21%⇤mO2
T + · · · = ⇤Rg
maT (11)
p V = ⇥i
ni Rg T = ⇥i
Mi
miRg T (12)
e = ⇤v Rv T (13)pd = ⇤d Rd T (14)p = pd + e⌅ pd (15)
es = A e�T (16)
1
ρ
Universal gas constant Gas constant of a specific gas
⇤(z) = ⇤0 e�z/H (1)⇤0 = 1.35 kg/m3 (2)H = 6.8 km (3)
� =vr
=2⇥R/day
R=
2⇥day
= 7.27⇤10�5s�1 (4)
Ve =�
2GM/R (5)
Vm =�
2kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ⇤Rg
mT = ⇤ RT (8)
Rg = 8.314 JK�1mol�1 (9)
R =Rg
ma= 287 Jkg�1K�1 (10)
p = Rg78%⇤mN2
T +Rg21%⇤mO2
T + · · · = ⇤Rg
maT = ⇤ R T (11)
p V = ⇥i
ni Rg T = ⇥i
Mi
miRg T (12)
e = ⇤v Rv T (13)pd = ⇤d Rd T (14)p = pd + e⌅ pd (15)
es = A e�T (16)
1
Dry air gas constant
Lines of constant temperature
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Atmospheric temperature variations • Atmospheric temperature varies in horizontal and vertical• Vertical variations are similar everywhere (pattern mostly set by radiation budget)• Horizontal variations depend on height (radiation and atmospheric circulation)
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Vertical variations of temperature Three hot spots:
1) thermosphere =>
2) stratopause =>
3) surface =>
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Thermosphere • Named from the Greek (heat sphere), begins about 90 km above Earth’s surface• Molecules are dissociated, ionized • Absorbs high-energy UV (λ < 0.1 μm) • Temperature increases with height
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Mesosphere • Named from the Greek (middle sphere), located from about 50 km to 80-90 km above Earth's surface• Composition is similar to troposphere and stratosphere (N2, O2, Ar, CO2) • Absorbs decreasing (with height) amounts of UV through ozone• Temperature decreases with height from 0oC to -100oC
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Stratosphere • Named from the Greek (layered sphere), located from about 10 km to 50 km above Earth's surface
• Contains most of the ozone in the atmosphere
• Ozone absorbs medium wavelength UV (0.1 < λ < 0.35 μm) - heated from above
• Temperature increases with height from -40oC to 0oC
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Ozone layer • Ozone is byproduct of photodissociation of molecular oxygen• Ozone absorbs medium wavelength UV (important for life on Earth)
Ozone hole over Antarctica in Spring (different issue from global warming!)
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Troposhere • Named from the Greek (turn sphere), located within 12 km of the Earth's surface• Contains 85% of the atmospheric mass• Absorbs infrared radiation through H2O and CO2 - heated from below• Temperature decreases with height from 15oC to -40oC
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• Atmospheric layer most dynamically active- weather we experience is confined to troposphere
• Transport modifies temperature profiles
Troposhere
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What determines pressure distribution with height?: Hydrostatic balance d p
dz=�g⌅ (1)
Fg⇧⌅⇤⌃Gravitational force
+ FT⇧⌅⇤⌃Top pressure force
+ FB⇧⌅⇤⌃Bottom pressure force
= 0 (2)
⇤|⇥T |2 (3)
uuueTe · ⇥T̄ (4)
(⇧t +uuug · ⇥) T +�T v+N2T w = DT (5)
(⇧t +uuug · ⇥) S +�S v+N2S w = DS (6)
(⇧t +uuug · ⇥) ⌅ +�⌅ v+N2⌅ w = D⌅ (7)
(⇧t +uuug · ⇥) C +�C v = DC (8)
⌅ = ⌅0 [1�� (T �T0)+⇥ (S�S0)] (9)
C = ⌅0
�1�
N2S
N2⌅
� (T �T0)+N2
TN2
⌅⇥ (S�S0)
⇥(10)
(11)
1
d pdz
=�g⌅ (1)
Fg⇧⌅⇤⌃Gravitational force
+ FT⇧⌅⇤⌃Top pressure force
+ FB⇧⌅⇤⌃Bottom pressure force
= 0 (2)
⇤|⇥T |2 (3)
uuueTe · ⇥T̄ (4)
(⇧t +uuug · ⇥) T +�T v+N2T w = DT (5)
(⇧t +uuug · ⇥) S +�S v+N2S w = DS (6)
(⇧t +uuug · ⇥) ⌅ +�⌅ v+N2⌅ w = D⌅ (7)
(⇧t +uuug · ⇥) C +�C v = DC (8)
⌅ = ⌅0 [1�� (T �T0)+⇥ (S�S0)] (9)
C = ⌅0
�1�
N2S
N2⌅
� (T �T0)+N2
TN2
⌅⇥ (S�S0)
⇥(10)
(11)
1
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How close to isothermal?
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Vertical distribution of pressure
• Isothermal atmosphere
• Non-isothermal atmosphere
d pdz
= �g⇤ (1)
Fg⌦ �↵Gravitational force
+ FT⌦ �↵Top pressure force
+ FB⌦ �↵Bottom pressure force
= 0 (2)
p(z) = ps exp�� z
H
⇥H =
RT0
g(3)
p(z) = ps exp⇤�
⌥ z
0
dz⇤
H(z⇤)
⌅H(z) =
RT (z)g
(4)
uuueTe · ⇥T̄ (5)
(⌅t +uuug · ⇥) T +�T v+N2T w = DT (6)
(⌅t +uuug · ⇥) S +�S v+N2S w = DS (7)
(⌅t +uuug · ⇥) ⇤ +�⇤ v+N2⇤ w = D⇤ (8)
(⌅t +uuug · ⇥) C +�C v = DC (9)
⇤ = ⇤0 [1�� (T �T0)+⇥ (S�S0)] (10)
C = ⇤0
⇧1�
N2S
N2⇤
� (T �T0)+N2
TN2
⇤⇥ (S�S0)
⌃(11)
(12)
1
d pdz
= �g⇤ (1)
Fg⌦ �↵Gravitational force
+ FT⌦ �↵Top pressure force
+ FB⌦ �↵Bottom pressure force
= 0 (2)
p(z) = ps exp�� z
H
⇥H =
RT0
g(3)
p(z) = ps exp⇤�
⌥ z
0
dz⇤
H(z⇤)
⌅H(z) =
RT (z)g
(4)
uuueTe · ⇥T̄ (5)
(⌅t +uuug · ⇥) T +�T v+N2T w = DT (6)
(⌅t +uuug · ⇥) S +�S v+N2S w = DS (7)
(⌅t +uuug · ⇥) ⇤ +�⇤ v+N2⇤ w = D⇤ (8)
(⌅t +uuug · ⇥) C +�C v = DC (9)
⇤ = ⇤0 [1�� (T �T0)+⇥ (S�S0)] (10)
C = ⇤0
⇧1�
N2S
N2⇤
� (T �T0)+N2
TN2
⇤⇥ (S�S0)
⌃(11)
(12)
1
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Vertical distribution of density
• Isothermal atmosphere
• Non-isothermal atmosphere
d pdz
= �g⇤ (1)
Fg⌦ �↵Gravitational force
+ FT⌦ �↵Top pressure force
+ FB⌦ �↵Bottom pressure force
= 0 (2)
p(z) = ps exp�� z
H
⇥H =
RT0
g(3)
p(z) = ps exp⇤�
⌥ z
0
dz⇤
H(z⇤)
⌅H(z) =
RT (z)g
(4)
⇤(z) =ps
RT0exp
�� z
H
⇥H =
RT0
g(5)
⇤(z) =ps
RT (z)exp
⇤�
⌥ z
0
dz⇤
H(z⇤)
⌅H(z) =
RT (z)g
(6)
uuueTe · ⇥T̄ (7)
(⌅t +uuug · ⇥) T +�T v+N2T w = DT (8)
(⌅t +uuug · ⇥) S +�S v+N2S w = DS (9)
(⌅t +uuug · ⇥) ⇤ +�⇤ v+N2⇤ w = D⇤ (10)
(⌅t +uuug · ⇥) C +�C v = DC (11)
⇤ = ⇤0 [1�� (T �T0)+⇥ (S�S0)] (12)
C = ⇤0
⇧1�
N2S
N2⇤
� (T �T0)+N2
TN2
⇤⇥ (S�S0)
⌃(13)
(14)
1
d pdz
= �g⇤ (1)
Fg⌦ �↵Gravitational force
+ FT⌦ �↵Top pressure force
+ FB⌦ �↵Bottom pressure force
= 0 (2)
p(z) = ps exp�� z
H
⇥H =
RT0
g(3)
p(z) = ps exp⇤�
⌥ z
0
dz⇤
H(z⇤)
⌅H(z) =
RT (z)g
(4)
⇤(z) =ps
RT0exp
�� z
H
⇥H =
RT0
g(5)
⇤(z) =ps
RT (z)exp
⇤�
⌥ z
0
dz⇤
H(z⇤)
⌅H(z) =
RT (z)g
(6)
uuueTe · ⇥T̄ (7)
(⌅t +uuug · ⇥) T +�T v+N2T w = DT (8)
(⌅t +uuug · ⇥) S +�S v+N2S w = DS (9)
(⌅t +uuug · ⇥) ⇤ +�⇤ v+N2⇤ w = D⇤ (10)
(⌅t +uuug · ⇥) C +�C v = DC (11)
⇤ = ⇤0 [1�� (T �T0)+⇥ (S�S0)] (12)
C = ⇤0
⇧1�
N2S
N2⇤
� (T �T0)+N2
TN2
⇤⇥ (S�S0)
⌃(13)
(14)
1