Heat fluxes in the atmosphere

Climate_Change_Attribution.

Heat flux notion

Convective and advective heat fluxes

Eddy heat flux

Individual and local (partial) derivatives

Energy equation

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Презентации по физике атмосфере на английском / 12-Heat fluxes in the atmosphere.ppt

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Heat to the atmosphere comes mainly from the underlying surface. Processes responsible for the heat transfer are:

Eddy flux	Convective flux

L.w. radiation

Evaporation

L.w. radiation

The quantity сpT being transferred by the air parcels in a unit of time through a unit of area facing the

transfer direction is called HEAT FLUX.

There are convective heat flux and eddy heat flux.

Convective heat flux, in turn, is divided into advective one (horizontal heat transfer) and real convective

(vertical heat transfer).

In meteorology, the horizontal heat flux is called advective flux (Qa), and the vertical one is called

convective flux (Qc).

cp CT

kg m

m s

1m²

kg K

kg K m

Q c

Qa cp CT

Any air particle contains some amount of heat. When moving, it carries this heat along. By this way the heat is distributed in the atmosphere. However, that is not the only way for the heat distribution. Not less effective way is EDDY MIXING (EXCHANGE)

Incoming heat flux is positive, outgoing flux is negative.	4

Eddy heat flux is caused by wind velocity pulsation

General conditions for eddy exchange

•Permanency

•Conservation

•Passivity

Quantity сpTdoes not satisfy this conditions. Air temperature changes as the air ascending or descending. However, potential temperature satisfy.


Q c		A		c	K			a
E	p		z	p		z	z

QE cp K a

с* с с'

Qa cp c T

103 101 100 104

с* с с'

QE cp k a

103 101 10 1 103

w* w w'

Qc cp w T

103 10 2 100 101

103

10 1

cp 103 100 103

100

10 2

101

104

The strongest flux

100 C

103

101

The weakest flux

Along with vertical eddy flux there are horizontal fluxes.

At the same level

QEx cp K '

Q c K '

Eddy heat exchange differs from that of other substances. Coefficients A and K (for eddy heat exchange) are called coefficient of eddy heat conductivity and temperature conductivity respectively.

As the stratification is stable ( a ) eddy heat flux directed downward QE 0

As the stratification is unstable ( a ) eddy heat flux directed upward QE 0

Heat influx (outflow) notion

Q	Heat influx

When an air parcel moves, its state parameters are not necessarily constant; they are function of coordinates and time.

F F x, y, z, t

For the moving parcel, the coordinates, in turn, are functions of time.
x x t ; y y t ; z z t					dx	u; dy	v; dz	w
				dF	dt	dt	dt
	z	y			F F dx F dy F dz

			x Local derivative	dt	t	x dt	y dt	z dt

dF	F	u	F	v	F	w	F
dt	t		x		y		z

Convective derivative

Advective derivative

Individual derivative

Heat influx = incoming heat flux – outgoing heat flux

Heat outflow

Temperature variation is of prime interest for meteorologists. It depends on heat influx. It can be determined on the base of the energy conservation equation.

dq cp dT		RT dP	Heat influx:			dq	E r ph k
dt	dt	P dt	Heat influx:			dt		J
1m2	(Q dQ)z	Qz Q dQ z dQz						J	Heat influx
1m2	(Q dQ)z	Qz Q dQ z dQz
								kg s
	z dz	dQz Qz dz						kg s	unit
	z dz					E r ph k
	z					E r ph k
	z		z
	Qz Mass of the volume is 1 m2 dz dm
		dQz	dQz	1	Qz dz
		dQz	dQz		Qz dz
		dm	dz	z dz

dQz dQz 1 Qz dm dz z

The same reasoning can be applied for horizontal heat fluxes

1	Q	x	Qy	Q
				z	divQ
				z	divQ
	x		y
	x		y	z

c A'

cp A'

QE z cp A

сp

Eddy heat influx

Since the horizontal exchange is much smaller the vertical one, for practical purposes this formula can be simplified

сp		A	Qz	cp		K	Qz

	z		z		z		z	10

RT dP

dt cp dt

P dt

∆t

m/s

P 10

10 2

∆P

102

10 2

m/s

104

1 102

∆Pz

104

∆x

105

∆T

100

∆y

105

10 105 10

∆Tz

∆z

2 104

103 10

All members of this

formula have the same

u x v y w z

order of magnitude

Substituting

and

100

104

100

into energy equation, we

obtain

See the next slide

y T

102 101

103

T		u	T	v	T	w	T	RT	w	P
E r ph k сp	t		x		y			P		z
							z

(

)

сp P z

This quantity is

RT w

P w

RT g w gRT

neglected

small and can be

сp P z

cp P

cp P RT

w a w a

w z

After substituting into the basic equation

and solution with respect to

, we obtain

r ph

T		T		T	w				r ph
	u		v				K
	u		v				K
t		x			a	z		z	cp
t		x		y		z		z	cp

T			T	v	T
		u		v
			x
	t ad		x		y

Air temperature variation due to advection

T	w a
	w a
t w

T				K

		z			z
t E		z			z

T			r		ph

					cp
t r, ph					cp

Air temperature variation due to vertical motion

Air temperature variation due to eddy mixing

Air temperature variation due to radiation and water phase transfer

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