12.003Atmosphere, Ocean and Climate Dynamics
InstructorRaffaele Ferrari, 54-1420
Teaching AssistantsTAs: Allison Wing and Rebecca Dell
Webpagehttp://www.mit.edu/~raffaele/12.003
Sunday, August 21, 2011
12.003Atmosphere, Ocean and Climate Dynamics
Meeting timesMonday, Wednesday and Friday 11.00-12.00
Classroom54-1615
PrerequisitesMultivariable Calculus (18.02)
Physics I: Classical Mechanics (8.01)
Sunday, August 21, 2011
12.003Atmosphere, Ocean and Climate DynamicsCourse description: This undergraduate class is designed to introduce students to the physics that govern the circulation of the ocean and atmosphere. The focus of the course is on the processes that control the climate of the planet.
Grading: The assessment will be in three parts (with weight toward final grade):1. Homework assignments will be handed out each week. These will serve a multiple purpose: As a component of the teaching process, as an assessment of performance, and as a means of providing feedback to me. (35%; the two lowest marks will be given half-weight)2. Class participation. (5%)3. A mid-term test. (20%)4. A final, closed book, exam on all assessable course material. (40%)
Commitment: 3 hours of lectures1 hour of recitation 10 hours per week6 hours of homework (on average)
Sunday, August 21, 2011
12.003Atmosphere, Ocean and Climate Dynamics
Other Useful Reading Material
Hartmann. Global Physical Climatology. International Geophysics Series. Vol. 56. San Diego, CA: Academic Press, 1994. This book should prove useful for both atmospheric and oceanic sections of the course, especially chapters 1-7 of the book, which cover the first two months of class material.
Houghton. The Physics of Atmospheres. Cambridge, UK: Cambridge University Press, 1977. For the atmosphere, detailed treatment of radiation, and simple and intelligible treatment of dynamics.
Wallace and Hobbs. Atmospheric Science: An Introductory Survey. New York, NY: Academic Press, 1977. Good qualitative discussion of many of the topics we will cover in atmospheric science.
Stewart. Introduction to Physical Oceanography. Available for free as a PDF file. A not-too-technical introduction to physical oceanography.
Textbook
Marshall, John, and R. Alan Plumb. Atmosphere, Ocean, and Climate Dynamics: An Introductory Text. Boston, MA: Elsevier Academic Press, 2007.
Sunday, August 21, 2011
12.003Atmosphere, Ocean and Climate Dynamics Course syllabus
(1) The global energy balance of the Earth(2) The equations of fluid motion(3) The general circulation of the atmosphere(4) The general circulation of the ocean(5) Climate and climate variability
Laboratory experiments• Rotating flow experiments• GFD Lab (Green Building 54-1510) and portable rotating tank
Sunday, August 21, 2011
12.003Atmosphere, Ocean and Climate Dynamics Course syllabus
(1) The global energy balance of the Earth(2) The equations of fluid motion(3) The general circulation of the atmosphere(4) The general circulation of the ocean(5) Climate and climate variability
Laboratory experiments• Rotating flow experiments
Sunday, August 21, 2011
12.003Atmosphere, Ocean and Climate Dynamics
Lecture IICharacteristics of the Atmosphere
Sunday, August 21, 2011
Lecture II Outline
1. Geometry of the Earth2. Chemical composition of the atmosphere
Sunday, August 21, 2011
Components of the Climate System
1. Atmosphere• fast timescales (days to weeks)
2. Hydrosphere• intermediate timescales (decades to millenia)
3. Cryosphere• slow timescales (> 100 years)
4. Lithosphere• very slow timescales (> 10,000 years)
5. Biosphere• all timescales
Sunday, August 21, 2011
Geometry of litosphere
6378
6356
• Earth is a rotating oblate spheroid• 70% of the litosphere is covered by ocean• 70% of emerged land is in Northern Hemisphere
ρ(z) = ρ0 e−z/H (1)
ρ0 = 1.35 kg/m3 (2)H = 6.8 km (3)
Ω =v
r=
2πR/day
R=
2πday
= 7.27×10−5s−1 (4)
Ve =
2GM/R (5)
Vm =
2kT/m (6)
uuueTe · ∇T (7)
(∂t +uuug · ∇) T +ΓT v+N2T
w = DT (8)(∂t +uuug · ∇) S +ΓS v+N
2S
w = DS (9)
(∂t +uuug · ∇) ρ +Γρ v+N2ρ w = Dρ (10)
(∂t +uuug · ∇) C +ΓC v = DC (11)
ρ = ρ0 [1−α (T −T0)+β (S−S0)] (12)
C = ρ0
1−
N2S
N2ρ
α (T −T0)+N
2T
N2ρ
β (S−S0)
(13)
(14)
1
Sunday, August 21, 2011
Geometry of litosphere• Emerged land rarely exceeds 2 km
• atmosphere flows above slightly corrugated surface • Oceans are on average 4 km deep
• oceans sit in deeply corrugated basins
Sunday, August 21, 2011
Characteristics of the amosphereρ(z) = ρ0 e
−z/H (1)ρ0 = 1.35 kg/m3 (2)H = 6.8 km (3)
ρ Duuu
Dt= Pressure and frictional forces (4)
κ|∇T |2 (5)
uuueTe · ∇T (6)
(∂t +uuug · ∇) T +ΓT v+N2T
w = DT (7)(∂t +uuug · ∇) S +ΓS v+N
2S
w = DS (8)
(∂t +uuug · ∇) ρ +Γρ v+N2ρ w = Dρ (9)
(∂t +uuug · ∇) C +ΓC v = DC (10)
ρ = ρ0 [1−α (T −T0)+β (S−S0)] (11)
C = ρ0
1−
N2S
N2ρ
α (T −T0)+N
2T
N2ρ
β (S−S0)
(12)
(13)
1
Sunday, August 21, 2011
6370 km10 km
Characteristics of the amosphere
Sunday, August 21, 2011
6370 km10 km
• Gravity is approx. constant throughout atmosphere• g ≈ 9.81 m/s2
Characteristics of the amosphere
Sunday, August 21, 2011
Chemical composition of atmosphereThe chemical composition of Earth’s atmosphere differs from that of other planets in the solar system
Sunday, August 21, 2011
Abundance of chemical elements in the solar system
Sunday, August 21, 2011
Atmospheric loss• Atmospheres can lose atoms, especially low mass ones, if they can exceed escape velocity (Jeans escape) • Escape velocity ⇒
• Mean molecular velocity at top of the atmosphere (exosphere, 500-1000 km, T =1000 K) ⇒
• Boltzmann distribution implies that negligible number of molecules have V > 3Vm• Molecular hydrogen has 3Vm = 12 km/s• Jupiter has Ve = 60 km/s, Earth has Ve = 11 km/s• H2 cannot escape from gas giants like Jupiter, but is easily lost from lower-mass bodies like Earth or Mars
ρ(z) = ρ0 e−z/H (1)
ρ0 = 1.35 kg/m3 (2)H = 6.8 km (3)
Ω =v
r=
2πR/day
R=
2πday
= 7.27×10−5s−1 (4)
Ve =
2GM/R (5)
Vm =
2kT/m (6)
uuueTe · ∇T (7)
(∂t +uuug · ∇) T +ΓT v+N2T
w = DT (8)(∂t +uuug · ∇) S +ΓS v+N
2S
w = DS (9)
(∂t +uuug · ∇) ρ +Γρ v+N2ρ w = Dρ (10)
(∂t +uuug · ∇) C +ΓC v = DC (11)
ρ = ρ0 [1−α (T −T0)+β (S−S0)] (12)
C = ρ0
1−
N2S
N2ρ
α (T −T0)+N
2T
N2ρ
β (S−S0)
(13)
(14)
1
ρ(z) = ρ0 e−z/H (1)ρ0 = 1.35 kg/m3 (2)H = 6.8 km (3)
Ω =vr
=2πR/day
R=
2πday
= 7.27×10−5s−1 (4)
Ve =
2GM/R (5)
Vm =
3kT/m (6)
p V = n Rg T =Mm
Rg T (7)
p = ρRg
mT = ρ RT (8)
Rg = 8.314 JK−1mol−1 (9)
R =Rg
ma= 287 Jkg−1K−1 (10)
p = Rg78%ρmN2
T +Rg21%ρmO2
T + · · · = ρRg
maT = ρ R T (11)
p V = ∑i
ni Rg T = ∑i
Mi
miRg T (12)
p = pd + e≈ pd (13)
e = ρRg
mvT (14)
pd = ρRg
mdT (15)
1
Sunday, August 21, 2011
Chemical composition of atmosphere
Life changed the chemical composition of Earth’s atmosphere
Photosynthesis Nitrogen Cycle
Sunday, August 21, 2011
Earth’s atmospheric composition• Atmospheric composition is constant below 50 km• Water vapor and CO2 are strongest absorbers in infrared
0.000004%O3*Ozone
0.00003%N2O*Nitrous Oxide
0.00005%H2Hydrogen
0.00017%CH4*Methane
0.0005%HeHelium
0.0018%NeNeon
0.0360%CO2*Carbon Dioxide
0.93%ArArgon
0 to 4%H2O*Water
20.95%O2Oxygen
78.08%N2Nitrogen
Percent VolumeChemical FormulaGas Name
* variable gases
Atmospheric Composition
Sunday, August 21, 2011
CO2 concentration and climate
Sunday, August 21, 2011
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