Pseudoadiabatic chart / sonde diagram

p

p

cR

cR

pconstT

ppT

⋅⋅=

⎟⎟⎠

⎞⎜⎜⎝

⎛=

θ

θ 0

This can be plotted with a logarithmic scale for the pressure.

The lines for constant potential temperature is following the dry adiabatic lapse rate.

We are most interested in the stippled area in Fig. 2.6.

Temperature – Entropy (pot.temp.) diagramThe chart in Fig. 2.6 may be plotted as a temperature-entropy diagram (Fig. 2.20a).

Again, we are only interested in the atmospheric temperature interval (stippled), which is usually rotated (ca. Fig. 2.20b).

Skew-T – ln p diagram (Fig. 2.20b)

Saturated air

When saturated air is lifted adiabatically, water vapor will condense. All the heat formed in the phase change is assumed to warm the air parcel and the liquid water removed.

The lapse rate for this process is called pseudoatiabatic lapse rate (fuktigadiabat).

It is a good idea to plot both adiabats in the same diagram!

And they are, as a function of pressure and temperature in the chart in the back of the book.

Also plotted are the saturated mixing ratios at given T and p.

dTdw

cLdz

dTs

p

ds

+

Γ=−=Γ1

Stability

Why do we want both adiabats in the same chart?

Because dry/unsaturated air follows the dry adiabat, while saturated air follows the moist (pseudo) adiabat.

( )Γ−Γ= dTdzd 11 θ

θ

0

0

0

>

=

<

dzddzddzd

θ

θ

θ Unstable

Neutral

Stable

Unsaturated air Saturated air

Condensing water will free energy: dq = -Ldws

Where L is latent heat, and dws is the amount condensed.

But we have

And it can be shown (Ex.2.33) that

So that

spp

dwTc

LTc

dqd −==θθ

⎟⎟⎠

⎞⎜⎜⎝

⎛=

TcLwddw

TcL

p

ss

p

⎟⎟⎠

⎞⎜⎜⎝

⎛=+=−

ep

s constTc

Lwθθθ lnln

es Tw θθ →⇒→ 0/

Convective instability

We have convective instability when

0<dzd eθ

0<dz

d wθ

or when

Conditional instability

We have conditional instability when

ds Γ<Γ<Γ

The Amble sonde diagram1050hPa – 500hPa: Skew-T – ln p diagram

500hPa – 20hPa: Skew-T – p diagram

Moist adiabatDry adiabatTemperatureSat. mix. rat.

Pot.temp. on the dry adiabat

Pressure

Thickness of layer

Height of the standard atmosphere

Exercise 2.48Pressure 200hPa, temperature T=-60˚C. Find the potential temperature using a sonde diagram.

200hPa

T=-60˚C

θ =70˚C

θ =60˚C

Approximately θ =66˚C

CKKppT

pcR

o64337200

10002131004

287

0 ==⎟⎠⎞

⎜⎝⎛×=⎟⎟

⎠

⎞⎜⎜⎝

⎛=θ

Exercise 2.49ap=1000hPa

T=15˚C

Td=4˚C

Mixing ratio (w)Relative humidity (RH)Potential temperature (θ)Wet-bulb temperature (Tw)Wet-bulb potential temperature (θw)

TTd

ws(Td) ws(T)

Dew point temperature

The final temperature when cooling air at constant pressure untill it is saturated.

The saturated mixing ratio at Td is then the mixing ratio of the air.

w(T) = ws(Td) = 5.1g/kg

Must NOT be confused with saturated mixing ratio at T: ws(T).

Relative humidity

RH = 100% w(T)/ws(T)

= 100% ws(Td)/ws(T)

= 100% x 5.1/10.8

= 47%

Potential temperature

We are at 1000hPa, so

θ = T = 15˚C

Wet-bulb temperature

The temperature we get after evaporating water into the air until saturation.

This is easily done on this chart, lifting the air along the dry adiabat until saturation, and then along the pseudoadiabat on its way down.

Tw = θw = 9.3˚C

Exercise 2.49bp=1000hPa

T=15˚C, Td=4˚C

Lift the air to 900hPa.

T

Td(900hPa)

ws(Td) ws(T)

900hPa

w = 5.1g/kgRH = 100% x 5.1/6.8 = 73%θ = 15˚C as before. (Conserved)Tw = 4.7˚Cθw = 9.3˚C as before. (Conserved)

Td Tw

Tw(900hPa)

Exercise 2.49cp=1000hPa

T=15˚C, Td=4˚C

Lift the air to 800hPa.

T

ws(Td) ws(T)

Td Tw

ws(Td(800hPa)

w = 4.4g/kgRH = 100% x 4.4/4.4 = 100%θ = 17˚C. (Not conserved for moist adiabatic processes)Tw = -1˚Cθw = 9.3˚C as before. (Conserved)

800hPa

How to find different properties on the chart

Potential temperature: Follow the dry adiabat to 1000hPa and read off the temperature.

Mixing ratio: At the dew point temperature, follow the lines for constant water vapor content downwards.

Saturation mixing ratio: At the actual temperature, follow the line for wdownwards.

Wet-bulb temperature: Follow the dry adiabat from the actual pressure upwards until saturation (the lifting condensation level), and then downwards along the moist adiabat to the starting pressure level.

Wet-bulb potential temerature: From the wet-bulb temperature, follow the moist adiabat to 1000hPa.

Equivalent potential temperature: Lift the parcel to saturation, and then along the moist adiabat until there is no water vapor left (where only the dry adiabat is plotted), and then downwards along the dry adiabat.

Static stability: Look at the lapse rate compared to the dry adiabat. Or look at potential temperature. Stable means θincrease with height.

Conditional instability: If the lapse rate is between the dry and the moist adiabat, we have conditional instability.

Level of free convection: In case of conditional instability only. Lift the parcel to saturation, and upwards along the moist adiabat.

Convective instable air: If θe or θw decreases with height.

When this occurs, an initially stable layer will destabilize as it is lifted, since the top of the layer will cool faster than the bottom, thereby steepening the lapse rate. In reality, whole layers may not be lifted at once; instead, parcels often lift from the boundary layer to their level of free convection (LFC) to form thunderstorms. Thus, the physical process that potential instability represents may or may not occur often during convection.

However, θe (which is more sensitive to moisture than temperature) decreasing with height IS important, since it represents the presence of dry air above moist air which enhances downburst and possibly hail potential if thunderstorms develop.

http://www.crh.noaa.gov/lmk/soo/docu/indices.php

T

ws(T2) ws(T)

Td

T2

Td = 13.9˚CLiquid water: ws(T)-ws(T2) = 10-6 = 4g/kgLose 80% of water: w=10-0.8*4 = 6.8g/kgT(900hPa) = 19.5˚C

700hPa

Exercise 2.52p=1000hPa

T=20˚C

w=10g/kg

Air is lifted when passing a mountain to 700hPa.