L14 Physics of dry air and moist air

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L14 Physics of dry air and moist air • Potential temperature • Pseudo-adiabatic charts • Skew T – ln p charts • Moist air • Saturated adiabatic lapse rate • Normand’s Rule: Cloud base

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L14 Physics of dry air and moist air. Potential temperature Pseudo-adiabatic charts Skew T – ln p charts Moist air Saturated adiabatic lapse rate Normand’s Rule: Cloud base. Potential Temperature ( θ ). - PowerPoint PPT Presentation

Transcript of L14 Physics of dry air and moist air

Page 1: L14 Physics of dry air and moist air

L14 Physics of dry air and moist air

• Potential temperature

• Pseudo-adiabatic charts

• Skew T – ln p charts

• Moist air

• Saturated adiabatic lapse rate

• Normand’s Rule: Cloud base

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Potential Temperature (θ)

• The potential temperature of an air parcel is its temperature when compressed (or expanded) adiabatically to surface pressure (p0) (defined as a standard pressure of 1000 hPa).

• Again, start from the 1st Law of Thermodynamics, and make dq=0:

0 dpdTcp

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Ideal Gas Law (see Lecture 8)

RTp p

RT

1so:

0 dpdTcp

0 dpp

RTdTcp

substitute in α:

R is the specific gas constant for air R = 287 J kg-1 K-1

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Divide by RT:

0p

dp

T

dT

R

cp

Integrate both sides, from the starting (p,T) tothe surface (p0,T0), noting cp/R is a constant:

p

p

T

T

p

p

dp

T

dT

R

c

00

Remember integral of 1/x is the natural log of x:

1

212 lnlnln

1 ln 2

1

2

1x

xxxdx

xx

x

x

x

x

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0

lnlnp

pT

R

cp

Remember: abba ln)(ln

0p

pT R

cp

pc

R

p

pT

0

Hence: or:

Rearrange to give potential temperature, θ:

Integrating:

pc

R

p

pT

0

R = 287 J kg-1 K-1

cp = 1004 J kg-1 K-1

Hence R/cp = 0.286

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Happily, we can look at this graphically:e.g., the ‘Pseudo-adiabatic’ chart

• So if you plot: p0.286 on y-axis,T on x-axis

• For a constant θ, (p00.286/θ) is also a

constant, so the graph yields a straight line with gradient given by (p0

0.286/θ), and passing through T=0 and p=0

286.0

0

p

pT

286.00286.0 p

Tp Re-arrange:

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Useful as now we can follow each line and determine graphically temperature at any pressure, assuming adiabatic expansion/compression

Earth’satmosphere

Pseudo-adiabatic chart

y-axis is linear for p0.286

also linear for ln(p)

Page 8: L14 Physics of dry air and moist air

Pseudo-adiabatic chart

Solves Poisson’s equation graphically!

Disadvantage:

Everything happens in small region of the chart…

This can be overcome by skewing the temperature lines rather than plotting them straight up → The Skew T-ln p chart

Earth’s atmosphere

Earth’s atmosphere is never here

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Skew T-ln pchartdifference to pseudo-adiabatic: ln(p) rather than p0.286

T skewed

• Examples:

• Kuching in Malaysia

• Valentia in Ireland.

Vertical T

Skew T

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What are all the

lines on the skew T-ln p

chart?

isobar

isotherm

dryadiabat

saturated adiabat

saturationmixingratio

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Example: airplane air

If an airplane at 250hPa takes air in at

-51oC and adjusts it to cabin pressure (850 hPa), does the air have to be

1. Heated

2. Cooled

to be comfortable?

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Temperature ~43°C

Cabin pressure850 hPa

Followthe dry adiabatto 850 hPa

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Moist air• See: L6 Humidity• Air contains some H2O molecules (water vapour)• Vapour pressure (e):

partial pressure exerted by the gaseous water (hPa)• Mixing ratio (w): mass of water vapour / mass of dry air• Warmer air can accommodate more water molecules; the maximum

for a given temperature is when the air is ‘saturated’• For a given temperature, there is a:

saturation vapour pressure (es)saturation mixing ratio (ws)

• An air parcel can become saturated, e.g. by ascent and cooling• Once saturated, further cooling will result in condensation of liquid

water: i.e. cloud droplets

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Mixing ratio w = mvapour/mdry [normally given units g/kg]

At saturation: evaporation balances condensation

Saturation mixing ratio ws = 0.622 es / p

Relative Humidity = w/ws x 100% = e/es x 100%

evaporation

condensation

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Thermodynamics of saturated air

• As long as air remains unsaturated, it will behave like ‘dry’ air• However, once saturated, the condensation of liquid water

releases latent heat• This means that an ascending air parcel that becomes saturated

will cool less than one that remains unsaturated• We can theoretically derive how much the cooling is modified (not

done here, see Wallace & Hobbs p79-87 if interested), and define the ‘Saturated Adiabatic Lapse Rate’ (SALR)

• The difference between the DALR and a SALR is largest for warmer air, as the water vapour content, and hence latent heat release are larger

• Saturated adiabats are solid green lines on the skew T-ln p chart

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Saturation mixing ratio

Constant p: w increases with T

Constant T: w increases with decreasing p

Derived

Using ideal gas law, and def. of saturation water vapour pressure

(Clausius Clapeyron, Dr Essery)

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Relative humidity: RH = 100*e/es ≈ 100*w/ws

Dewpoint (Td): Temperature to which air must cool at constant pressure to be saturated

Q: Air at 1000 hPa and 18oC has a mixing ratio of 6 g/kg. What is its relative humidity and dewpoint?

RH=6/13*100=46%

Dewpoint ~6.5oC

ws

w = 6 g/kg

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As unsaturated air lifts dry adiabatically, it will eventually saturate: Normand’s Rule

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This level is the lifting condensation level

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LCL = Cloud base

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Let’s look at some real data

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Albemarle, 00z Monday 17 Oct

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Albemarle, 00z Tuesday 18 Oct

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Summary

• Potential temperature – the temperature of air compressed/expanded to 1000 hPa along a dry adiabat

• Pseudo-adiabatic charts – graphically solve equations

• Skew T – ln p charts – will use in labs• Moist air – releases latent heat at saturation point• Saturated adiabatic lapse rate – less than DALR

– typically 6 K/km• Normand’s Rule: Can estimate cloud base height

using surface temperature and moisture