Moist adiabatic processes

An adiabatic process in moist, saturated air is called

MOIST ADIABATIC PROCESS

This process is significantly different form that in the dry or non-saturated air

1

P	Dry adiabat		dTi	1 /100m
		Moist adiabat			0
			dz
Pk		Lifting
			dSi	0
		Condensation level
			dz
		T	d RH
	S0=Sm, Tk,	So, Ti0,			0
			dz
	RH=100%	RH<100%

RH 100%

Sm S0 ;Ti Tk

RH 100%

S0 Sm ;Ti Tk

So, Ti0, RH<100%

Continuous ascent results in further temperature fall and water vapor condensation that makes the rate of the temperature fall less than 1°/100 m.

Lifting Condensation level

Initial level

The rate of temperature variation of the ascending saturated air without heat influx or outflow is called MOIST ADIABATIC LAPSE

RATE 2

From the above reasoning it follows:

Temperature of an ascending parcel of air decreases with height,
•	m.a. a ).
but slower that at dry adiabatic process (

•Due to condensation, the particle specific humidity Sm decreases with height

•Relative humidity remains equal to 100%.

Adiabatic ascent of the moist air till attaining saturated state is called DRY STAGE.

Further ascending of the saturated air above the condensation level is called MOIST STAGE

PDry adiabat

Moist stage

Condensation level Dry stage

T

3

First law of thermodynamics for the moist, saturated air

Suppose a parcel of the saturated air has got some amount of heat dq. This heat will be laid out for:

•Inner energy increase

•Expansion work

•Evaporation of some amount of water

Reason for evaporation

dq 0	dTi 0	RH 100% RH 100%			RH 100%
		The parcel becomes non-saturated +		dSm evaporation
dq cvdTi pdvi LdSm			As we know, pdv RT		dP
			i	i	P

dq c	dT	RT	dP LdS	m
	p i	i	P		4

For adiabatic process

cpdTi

RTi

dP LdSm 0

c dT pdv

LdS

m

0

v i

i

P

Accounting for static equation,

cpdTi gTi

dz LdSm 0

c dz

we get:

Te

p

dT

gT

L

dS

dTi

g

Ti

i

i

m

0

Since

m.a.;

a ; T 1

dz

c

cp

dz

cpTe

dz

p

e

dSm

0

m.a a

L dSm

m.a a

dz

Value of the moist adiabatic

cp

dz

a

const

lapse rate depends on pressure

m.a const

and temperature only and does

not depend on humidity

5

Sm 0,622 E	ln Sm ln 0,622 ln E ln P
P

	1	dSm	1 dE			1 dP
	Sm		E dz			P dz
		dz

E E T

1

dSm

1 dE dTi

1 dP

1 dP

g

dT

dz

dz

;

i

dTi

dz

dz

dz m.a

Sm

E

P

P

RT

e

dSm

Sm dE

Sm g

E

g

m.a dE

dz

E dTi

m.a

RTe

0,622 P

dT

RT

E

i

i

m.a a

L dSm

m.a

a 0,622

L E

g

m.a

1 dE

P

dT

c

dz

p

c

p

RT

E

i

i

6

		0,622	L E			g		1 dE
			c		P RT
m.a	a			p			m.a E dT
						i			i

Opening brackets we obtain

m.a

L 2,5 106 J kg

and solving the equation with respect to m.a ,

		0,622		L			E		g
	a			cp P RTe
	1 0,622			L			1 dE
			c		p		P dT
									i

	dE		L		E
	dT		R	T 2
			w

	P 0,622			LE
				RT
m.a a				e
	P 0,622			L2 E
		c		R T 2
			p w i

7

Values of the moist adiabatic lapse rate at different temperature and pressure

Pressure				T°C
hPa	-50	-20	0	10	20	30
1000	0,966	0,856	0,658	0,532	0,435	0,363
800	0,964	0,831	0,614	0,489	0,398	0,335
600	0,960	0,793	0,557	0,436	0,356	0,303
400	0,952	0,730	0,478	0,371	0,307	0,267
200	0,928	0,597	0,361	0,286	0,247	0,223

8

Criterion of instability for the moist air

aaa

m.am.am.a

Unstable atmosphere

Stable atmosphere Dry, non-saturated air

Neutral atmosphere

a m.a

Unstable atmosphere

Stable atmosphere Moist, saturated air

Neutral atmosphere

.a m.a	Absolute instability			Combine criterion of instability
m.a a	Absolute stability
a m.a	Conditional instability
	The air is unstable, it is saturated				9

Some additional information

Equivalent-potential temperature is the potential

temperature of an air parcel, the water vapor containing in it had been condensed due to adiabatic ascent and the heat obtained has been laid out to rise up the air parcel temperature,

Θ+dθ, e=0

		Pseudo-potential
		temperature
Θ, e	Initial level	Θp.p, e=0

Θe, e=0	1000 hPa
Equivalent-potential temperature		10