Atmospheric Thermodynamics Outline - IAP · N. K ampfer Atmospheric Thermodynamics Aim Gas law...
Transcript of Atmospheric Thermodynamics Outline - IAP · N. K ampfer Atmospheric Thermodynamics Aim Gas law...
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Atmospheric Thermodynamics
N. Kampfer
Institute of Applied PhysicsUniversity of Bern
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Outline
Aim
Gas law
PressureHydrostatic equilibriumScale heightMixingColumn density
TemperatureLapse rateStability
CondensationHumiditySaturation vapor pressureClouds
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Aim
A planetary atmosphere consists of different gases hold tothe planet by gravityThe laws of thermodynamics hold
I pressure structureI pressure as vertical coordinate→ some planets have no solid surface
I hydrostatic equilibriumI scale heightI column densityI mean free path
I temperature structureI lapse rateI stabilityI latent heat and condensation → cloudsI wet lapse rate
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Ideal gas law
pV = NkT
N amount of particlesk = 1.381 · 10−23 J/K is Boltzmann’s constantn = N/V is the number density, particles per Volume
a mole contains NA = 6.022 · 1023 particlesa kmole contains NA = 6.022 · 1026 particleswith q moles of a substance N = qNA and the gas law gets
pV = qNAkT = nRT
where R = kNA
R = 8.314 J mol−1 K−1 resp.R = 8314 J kmol−1 K−1 is the universal gas constant
The mass of a mole of substance is called molar weight:Mwater = 18.016 kg/kmol Mair = 28.97 kg/kmol
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Ideal gas lawmass of q moles is m = qMdensity ρ can be expressed as
ρ =m
V=
qM
V=
Mp
RT
very often gas law is expressed as
pV =m
MRT = m
R
MT = mRGT
orp = ρRGT
RG is the gas constant for the gas under discussion!for dry air Rd = 287 JK−1 kg−1
for water vapor Rv = 461 JK−1 kg−1
Don’t mix up RG and R !!In the literature often R is written as R∗ and RG as R!
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Partial pressureAn atmosphere is a mixture of gasesDalton’s law: The total pressure p is the sum of the partialpressures of each component pj
p = p1 + p2 + p3 + ... =∑
pj
The partial pressure of water vapor is denoted by e and iscalled vapor pressure
For relative amounts of gases it follows
Nj
N=
Vj
V=
pj
p
This is the volume mixing ratio, or VMR often expressed inppm or ppb or even ppt → trace gases
The mass mixing ratio is defined as
MMR =ρi
ρ=
mi
min gkg−1
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Most abundant gases in planetary atmospheres
copied from Y.Yung: Photochemistry of planetary atmospheress
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
VMR of gases in Earth atmosphere
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Mean molecular weight versus height for Earth
copied from C.Bohren: Atmospheric Thermodynamics
Why this shape of the curve?→ we have to look in more detail at the pressure behavior
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Hydrostatic equilibrium
As a gas is compressible → density falls with altitude
Vertical pressure profile can be predicted by consideringchange in overhead force, dF , for a change in altitude dz ina column of gas with density ρ and area A
dF = −ρgAdz
Pressure and altitude are related by hydrostatic equilibrium
dp = −ρgdz
For an ideal gas at temperature T → ρ = MpRT
p(z) = p(z0) exp
(−∫ z
z0
Mg
RTdz
)M, g ,T depend on the planet and on height
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Scale heightAssume T does not vary much and take an average Tav
p(z) = p0 exp
(− Mg
RTavz
)The quantity RTav
Mg has dimensions of a length
→ scale height (Skalenhohe) H
H =RTav
Mg=
RGTav
g=
kTav
mg
Hydrostatic law expressed with H
p = p0 exp(− z
H
)n = n0 exp
(− z
H
)ρ = ρ0 exp
(− z
H
)
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Scale height for different planets
from Y.Yung
Physical properties of planetary atmospheres at 1 bar
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Discussion of hydrostatic lawHow well do these expressions fit with reality?
from Y.Yung
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Discussion of scale height
Discussion:
I pressure decreases with height faster for lower T
I as T 6= const also H will change
I H depends on mass → each constituent would have itsown scale height → own pressure distribution → VMRof unreactive gases would depend on altitude
but this is not observed!
at least the lower parts of atmospheres behave as theywere built up of a single species with a mean molar massEarth: 28.8, Venus and Mars: 44, Jupiter 2.2
Homogeneity of lower atmospheres is a consequence ofmixing due to fluid motions
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Homosphere - Turbosphere
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Homosphere - TurbosphereMixing on a macroscale by
I convection
I turbulence
I small eddies
does not discriminate according molecular mass
Relative importance of molecular and bulk motions dependson relative distances moved between transport eventsFor bulk motions → mixing lengthFor molecular motion → mean free path: λm
λm ≈1
nσ≈ 1
σ
kT
p
Collision cross section σ of air molecule: ≈ 3 · 10−15 cm−2
At sea level number density n ≈ 3 · 1019 cm−3
Average separation between molecules d = n−1/3 ≈ 3.4nmMean free path λm ≈ 0.1µm, i.e. ≈ 30d
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Homosphere - Turbosphere
Transition region in an atmospherefrom turbulent mixing to diffusion isknown as the turbopause orhomopause
For the Earth both lengths are approx. equal at 100-120 km
Well mixed region below turbopause: homosphereGravitationally separated region above: heterospehre
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Column density
The total content in a column of unit cross section of anatmosphere with a constant scale height is given by thecolumn density
Nc =
∫ ∞0
ndz = n0 exp(− z
H
)dz = n0H =
p0
mg0
Column density in its general form is also used for particledistributions that do not obey the exponential law
Total mass of a planetary atmosphere can be expressed by
Matm =
(p
g
)s
4πR20
where s is at the surface (whatever this is /)
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Temperature profile of Earth
from Jacobson: Atmospheric modeling
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Thermal structureThe thermal structure of an atmosphere is the result of aninteraction between radiation, composition and dynamics
Equation that governs the thermal structure (without proof)
ρcpdT
dt+
dΦc
dz+
dΦk
dz= q
Cp = heat capacity per unit mass at constant pressureq = net heating rate = rate of heating - rate of coolingΦc = conduction heat fluxΦk = convection heat flux
Φc = −KdT
dz
Φk = −KHρcp
(dT
dz− g
cp
)K=thermal conductivity and KH=eddy diffusivity
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Thermal structure
ρcpdT
dt+
dΦc
dz+
dΦk
dz= q
I First term only important for modeling diurnal variations
I Third term (convection) dominates in the troposphere
I Fourth term dominates in the middle atmosphere
I Second term (conduction) balances the fourth term inthe thermosphere
Thermal structure of a planetary atmosphere depends on thechemical composition
Chemical composition may be affected by
I temperature through temperature dependent reactions
I condensation of chemical species
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Temperature profile of inner planets
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Temperature profile of outer planets
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Lapse rate
Radiative transfer tends to produce highest temperatures atthe lowest altitudes→ hot, lighter air lies under cold, heavier air→ one would guess that convection would arise, BUT
gases are compressible and pressure decreases with height→ rising air parcel will expand, will do work on theenvironment→ air is cooled
Consequence:Temperature drop from expansion can exceed decrease intemperature of surrounding atmosphere→ in that case convection will not occur!
What is the decrease in temperature with altitude?What is the lapse rate?
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Lapse rateConsider air parcel thermally insulated from environmentAir parcel can move up and down under adiabatic conditions
First law of Th.D. dU = dq + dW = dU − pdVEnthalpy dH = dU + pdV + Vdp
For our case → dH = VdpHeat capacity at constant pressure Cp = (dH/dT )p
CpdT = Vdp
dp = −ρgdz from hydrostatic equilibrium
CpdT = −V ρgdz
For a unit mass of gas (cp) we get
−dT
dz=
g
cp= Γd
Γd is called the dry adiabatic lapse rate
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Lapse rate for different planets
from Y.Yung
Physical properties of planetary atmospheres at 1 bar
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Stability
Actual temperature gradient of atmosphere: Γ = −dTdz
I Γ < Γd
→ any attempt of an air packet to rise is counteractedby cooling → packet gets colder and denser, it sinks→ any attempt of an air packet to sink is counteractedby warming → packet gets warmer and lighter, it rises→ atmosphere is stable
I Γ > Γd
→ any attempt of an air packet to rise is enforced bywarming → packet gets warmer and lighter, it continuesto rise→ any attempt of an air packet to sink is enforced bycooling → packet gets colder and denser, it continuesto sink→ convection is working → atmosphere is unstable
Actual Γ rarely exceed Γd by more than a very small amount
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Stability
DALR=dry adiabatic lapse rate
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Condensation
However: Presence of condensable vapors in atmosphericgases complicates matters!
I Condensation to liquid or solid releases latent heat tothe air parcel
I For a saturated vapor, every decrease in temperature isaccompanied by additional condensation
I Saturated adiabatic lapse rate, Γs , must be smallerthan Γd
I Clouds can formI Clouds are mainly made of H2O for the Earth, but not
alone, e.g. PSC are HNO3
I Clouds on giant planets made from NH3, H2S, CH4I Clouds on Mars from CO2 and on Venus from H2SO4
For the derivation of Γs we need Clausius -Clapeyronequation
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Humidity
Different ways to express humidity in the atmosphere:
Mixing ratio g/kg w ≡ mv
md=ρv
ρd=
Mv
Md
e
p − e
where e is the partial pressure of water vapor
As p � e and with MvMd
= ε = 0.622:
w ≈ 0.622e
p
As long there is no condensation or evaporation the mixingratio is conserved!
Specific humidity is defined as
s =ρv
ρ=
ρv
ρd + ρv=
eε
p − (1− ε)e
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Saturation vapor pressureEquilibrium between condensation and evaporation→ saturation vapor pressure es
→ is valid for other gases than water vapor
Relation between saturation pressure and temperature isgiven by equation of Clausius and Clapeyron
des
dT=
1
T
Lv
Vv − Vl=
1
T
lv1ρv− 1
ρl
where: Lv = enthalpy of vaporizationVv resp. Vl are volumina of vapor and liquid phasesfor H2O: lv = 2.5 · 106 J/kg
es ≈ Ce
“− lv
Rv T
”= Ce(−mv lv
kT )
numerator: energy required to break a water molecule freefrom its neighborsdenominator: average molecular kinetic energy available
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Saturation vapor pressure
Useful approximation for water vapor:
lnes
6.11mb=
LMv
R
(1
273− 1
T
)= 19.83− 5417
T
Saturation mixing ratio ws ≈ 0.622 esp
Relative humidity, RH RH = 100 wws
= 100 ees
Dew point is the temperature where RH = 100%
Lapse rate for saturated conditions, Γs , can be shown to be
Γs = −dT
dz=
g
cp
1 + lvws/RT
1 + l2v ws/cpRvT 2
In case of Earth: Γs ≈ 5K/km in contrast to Γd ≈ 10K/km
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Saturation vapor pressure for water vapor
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Clouds, a few facts
I Clouds can form on all planets with condensable gases
I Temperature must drop below the condensation orfreezing temperature of such gases
I Cloud condensation nuclei must be present
I Most terrestrial clouds consist of water droplets and icecrystals but other cloud particles are possible, eg.HNO3·2H2O or H2SO4/H2O in PSCs
I On ♀ exist H2SO4 clouds
I On ♂ exist water ice clouds
I On titan clouds of CH4 are expected
I NH3- ice may form on X and YI H2S-ice may form on Z and [ and also CH4-ice
I Clouds are often related to precipitation
I Clouds are extremely important for radiation budget→ often little is known
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Polar stratospheric clouds
photo from H.Berg, Karlsruhe
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Polar stratospheric clouds
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Clouds on Mars
photo from NASA
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Clouds on Venus
photo from NASA
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Level of cloud formationThe lifting condensation level, LCL, is the level to which aparcel of air would have to be lifted dry adiabatically toreach a RH of 100% → base of clouds
Height of LCL is a function of T and humidity resp.condensable matter
If a parcel with T0 is lifted from z0 to height z then
T (z) = T0 − Γd(z − z0)
For the dew point at any z
Td(z) = Td0 − Γdew (z − z0)
zLCL is reached when both are equal
zLCL = z0 +T0 − Tdo
Γd − Γdewwhere Γdew = −dTd
dz=
g
εlv
T 2d
T
→ Rule of thumb: zLCL − z0 = (T0 − Td0)/8 in km-units
N. Kampfer
AtmosphericThermodynamics
Aim
Gas law
Pressure
Hydrostaticequilibrium
Scale height
Mixing
Column density
Temperature
Lapse rate
Stability
Condensation
Humidity
Saturation vaporpressure
Clouds
Ceilometer at IAP for cloud base measurements
Laser-ceilometerfrom M.Schneebeli
Cloud base as determined with a ceilometer