FUNDAMENTALS OF GLOBAL CLIMATE CHANGE : LEARNING FROM GLOBAL DISASTER LABORATORIES
Physical Fundamentals of Global Change Processesstock/lectures/lectures_old/GC-Fundamentals… ·...
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Global Change Fundamentals www.pik-potsdam.de/~stock 3-1
Module:
Physical Fundamentals of Global Change Processes
07. November 2006 - Lecture 3 Physical Quantities, Laws and Theoretical Fundamentals
of Global Change and Earth Sciences,Planetary Motion, Electromagnetic Radiation and
other Parameters of Climate Variation
University of Applied Sciences EberswaldeMaster Study Program Global Change Management
Manfred Stock Potsdam Institute for Climate Impact Research
Global Change Fundamentals www.pik-potsdam.de/~stock 3-2
Contents of Lecture 3• Resume of the last Lectures• Theoretical Fundamentals of Global Change: Discussion about Module Themes, Work Plan, and Participitation of Students (Presentations)
• The Solar System: Dynamics and Radiation
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Theoretical Fundamentals of Global Change• Equations of motion of particles: location, time, speed, mass • Conservation laws: energy, momentum, angular momentum• Electromagnetic radiation: radiation laws, reflection (albedo),
transmission, refraction, absorption, emission• Thermodynamic systems:
– Isolated Systems – matter and energy may not cross the boundary. – Adiabatic Systems – heat may not cross the boundary. – Diathermic Systems - heat may cross boundary. – Closed Systems – matter may not cross the boundary. – Open Systems – heat, work, and matter may cross the boundary.
• Nonlinear dynamical systems• Earth System Analysis: ecology, economy, climate and social system• Mathematical methods: modelling, statistics, vector calculus, differential
calculus, integral calculus, ….• ………………
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Physical Quantities and Units
W/t, E/tW, J/sPpower
Asphere = 4 π r²Vsphere = 4/3 π r³
m²m³
AV
areavolume
sttime
F/A
0 K = –273.15 °C
W = R1∫R2
F(r) dr
F = m * a
L = r x I
I = m * v
equations
J, NmEenergy
KTtemperature
Pa, N/m²ppressure
J, NmWwork
N, kg m/s²Fforce
kg m²/sLangular momentum
kg m/sImomentum
kgmmass
m/s²aacceleration
m/svvelocity
mrdistance
unitsymbolquantity
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Conservation Lawsa particular measurable property of an isolated physical system does not change as the system evolves:• Conservation of energy• Conservation of linear momentum• Conservation of angular momentum• Conservation of electric charge• Conservation of mass(applies approximately for low speeds)
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Energy = "the potential for causing changes."
There are several types of energy:
Examples associated with
• kinetic energy motion Ekin = ½ m v²
• potential energy position, work Epot = R1∫R2 F(r) dr
• internal energy atomic speed dU = δQ + δWthermal energy temperature T = TdS + pdV
heat Q, entropy S
• radiant energy radiation, luminosity = E/t L = 4πR² σ T4 [ W ]
• chemical energy chemical bonds, type of potential energy
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1. The orbit of a planet about a star is anellipse with the star at one focus.
2. A line joining a planet and its star sweeps outequal areas during equal intervals of time.
3. The squares of the orbital periods of planetsare directly proportional to the cubes of thesemi-major axis of the orbits.
T = orbital period of planeta = semimajor axis of orbit
Kepler’s three laws of planetary motion (1630)
X
tor2 ∝ ror
3
tor = orbital period of planetror = semimajor axis of orbit
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The Three Laws of Motion (Newton 1678)Newton's Laws of Motion describe the motion of a body as a whole and are valid for motions relative to a reference frame:
1. An object will stay at rest or move at a constant velocity in a straight line unless acted upon by an unbalanced force.
2. The rate of change of the momentum of a body is directly proportional to the net force acting on it, and the direction of the change in momentum takes place in the direction of the net force: F = dI/dt
3. To every action (force applied) there is an equal but opposite reaction (equal force applied in the opposite direction).
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Centripetal Motion in the Phase Space R(r,v)
rx
-rxry
-ry vy
-vy
vx
-vx
tor = 2π r / v
vy
-vy-vx
vx
-ay
ay
ax
-ax
tor = 2π v / a
⇒a = v² / rcentripetal acceleration⇒Fc = m v² / rcentripetal force
I
r
m
Using the phase space is a rather elegant and simple method to calculate the centripetal or centrifugal force, compared to the standard method via vector and differential calculus. The phase space is the coordinate system of all variables describing the state of a system.
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Laws of Gravitation and Planetary Motiongravitational force between two bodies of mass m1 and m2separated by the distance r12
FG = - G m1 m2 / r122
G = 6.673 10-11 N m² kg-2
centripetal force accelerating a body of mass m1 and speed v1 on an orbit with radius r12
Fc = m1 v1² / r12
1.task: prove that Keplers 3rd law is a consequence of Newton’s3rd law expressed in the the relation: FG + Fc = 0
2.task: calculate the Earth’s orbital speed, using this relation and theparameters: mE = 5.98 1024 kg, mS =1.988 1030 kg, rES = 1.49 1011 mSolution:
Epot = - FG * rES = G mE mS / rES = 5.3*1033 J = Fc * rES = mE vE² ⇒ vE = 29.8*103 m/s
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Titius-Bode rule for planetary distances
30.0639,5038.88Neptune
Pluto1
19.219.67Uranus
9.5410.06Saturn5.205.25Jupiter
2.772.84Ceres1
1.521.63Mars1.001.02Earth0.720.71Venus0.390.40Mercury
real av.distance
DTBnPlanet DTB = 0,4 + 0,3 x 2(n-1) x sgn(n) Distances in astronomical units, AU. One AU is the average distance between Earth and Sun, roughly
AU = 149 598 000 km
The rule was proposed in 1766 by Johann Daniel Titius and "published" without attribution in 1772 by the director of the Berlin Observatory, Johann Elert Bode.
There is no solid theoretical explanation of the rule, but it is likely a combination of orbital resonance and shortage of degrees of freedom.1 dwarf planet
68,0077,29Eris1
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Electromagnetic Radiation
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Black Body Radiation and Temperature
A black body is an object that absorbs all electromagnetic radiation that falls onto it.
The total energy radiated per unit area per unit time Lb by a black body is related to its temperature T in K and the Stefan-Boltzmann constant σ as follows:
Lb = σ T4
with σ = 5.67e-8 Wm-2K-4
spectral intensity according to Planck's law of black body radiation
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Heat radiation from a human bodyThe net power (energy/time) emitted is the difference between what someone absorbs from their surroundings and what they radiate themselves:
Pnet = Pemit – Pabsorb
= A σ (Th4 – T0
4)
Calculate with:A = 2 m², Th = 28°C T0 = 20°C
≅ 100 W
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INSOLATION = INcident SOLar radiATION and IR Radiation
INSOLATION S0
IR Radiation 1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Albedo α
S0 = 1360 W/m² top insolationS = S0(1- α) surface insolation
IR = σ T4 σ = 5.67e-8 Wm-2K-4
T(S,α)
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Calculate Surface Temperatures in the Solar System
DSE = 1.496e11 m, dist. Sun-Earth RS = 0.696e9 mRE = 6.373e6 m
DMe = 5.834e10 m DVe = 1.077e11 mDMa = 2.274e11 mDPl = 5.909e12 m
1. Mean surface temperature T(α) of the Earth for different albedo αwithout greenhouse effect.α surface T(α) K °C 0 black0.1 water, forest0.3 actual mean0.8 ice cover
2. Surface temperature of the SunTS =
3. Surface Temperature of planets(α = 0, no greenhouse effect):a) Mercury (trot=torb)b) Venusc) Marsd) Pluto
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Calculate Surface Temperatures in the Solar System
DSE = 1.496e11 m , dist. Sun-Earth RS = 0.696e9 mRE = 6.373e6 m
DMe = 5.834e10 m DVe = 1.077e11 mDMa = 2.274e11 mDPl = 5.909e12 m
1. Mean surface temperature T(α) of the Earth for different albedo αwithout greenhouse effect.α surface T(α) K °C 0 black0.1 water, forest0.3 actual mean0.8 ice cover
2. Surface temperature of the SunTS =
3. Surface Temperature of planets(α = 0, no greenhouse effect):a) Mercury (trot=torb)b) Venusc) Marsd) Pluto
278, 5271, -2255, -18186, -87
5773, 5500
630, 357328, 55226, -4744, -229
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Insolation: spatial variation and energy balanceTop of atmosphere (global mean) S0 = 1360/4 W/m²
= 340 W/m²
2/3 S0 = 227 W/m²(67%)
IR = 227 W/m²
30% 15%
45%global mean net solar energy
Sne ≅ 100 W/m²for evapotranspiration, photo-synthesis and other processes
45%
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Atmospheric electromagnetic transmittance or opacity
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Insolation and atmospheric absorption
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Next Lecture (GC-Fundamentals_04):
The Earth’s Atmospheric Compositionand Climate