Physical Fundamentals of Global Change Processesstock/lectures/lectures_old/GC-Fundamentals… · Global Change Fundamentals stock 3-1 Module: Physical Fundamentals of Global Change

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


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


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, ….• ………………


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


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)


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


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


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).


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.


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


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


Electromagnetic Radiation


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


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


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)


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


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


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%


Atmospheric electromagnetic transmittance or opacity


Insolation and atmospheric absorption


Next Lecture (GC-Fundamentals_04):

The Earth’s Atmospheric Compositionand Climate

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Physical Fundamentals of Global Change Processesstock/lectures/lectures_old/GC-Fundamentals… · Global Change Fundamentals stock 3-1 Module: Physical Fundamentals of Global Change