SURFACE LAYER

State of the surface layer has a significant impact on vegetable and animal kingdoms, on the activity and state of humanity as a whole, and on individual people.

All kind of exchange between surface and the atmosphere come about through the surface layer.

(heat, momentum, water vapor fluxes go through it)

Processes within the surface layer are different from all other layers of the atmosphere.

1

Some characteristics of the surface layer

•Surface layer (SL) is greatly influenced by the underlying surface. The latter supplies the SL with heat, water vapor, and admixtures and here the air currents experience the friction effect.

•Meteorological parameters experience variations with time and altitude that are much stronger than in the rest of the atmosphere.

	γ°C/100 m	Diurnal temperature	Diurnal wind speed
		variation °C	variation m/s
SL	-2…10	0…20	6…10
F. A.	0,6 – 0,7	0…4	2…4

•Inversions are frequent phenomena in the surface layer.

•The most important process in the surface layer is EDDY MIXING.

2

T	u		T	v
					T		w		K
			x
t								z		z
					y		a

r ph

cp

For more clear reasoning, let’s assume the following conditions: no advection

vertical motion close to zero

εr=0, fair weather (no water phase transfer)

T

z

z

cp

cp

K

cp

T dz cp

K

dz

t

z

z

0

t

0

z

z

c

z

K dz c

z d

K

c

K

c

K

p

p

p

p

0

z

z

0

z

z z

z 0

Q

Q0

z

T dz c

c

T

z Q Q

T

p

t

p

t

0

Q Q0

cp

t

z

0

3

Let’s define the altitude z=h, up to which the ratio remains very small.

For instance ε=0,1

cp			T				h
			t
	Q0

Q0

cp

T

h

Q0

h

“h” is altitude of SL

t

cp

T

According to measurements,

t

Q0=40…250 w/m².

Suppose, temperature variation is 5°C for 12 hours

h 0,1 40 12 3600

28m

1

1005 1,25 5

h2 0,1 250 12 3600 172m 1005 1,25 5

4

From the previous discussion we know

Q Q	c	z			T		dz
0		p			t
		0

The layer 0 – Z is relatively small. Therefore, within this layer temperature variation has the same sign at any altitude. It means that Z increase results in increase the integral too, and at Z<h the integral can not exceed the product Q0

Thus, within the layer 0 – h Q≈Q0. The error will not be more than 10%

5

Temperature profiles in the surface layer

the New Bridge, Bratislava, Slovakia; Temperature inversion; 11 Nov 2005

Author: --Ondrejk 23:33, 21 Mar 2005 (UTC)

6

eddy coefficient k grows up with z in the surface layer

assume there’s linear growth of k:

k k0 az	(13.5)
k0 is k value at z 0
a const det er min ing	k increase with altitude

7

Let’s multiply both parts of (13.4) by dz

C	k		Q	(13.4)
p		z	0

Cp k

dz Q0dz

or

dz

Q0 dz

z

z

Cp

k0 az

Since

dz d ,

d

Q0

dz

(13.6)

Cp k0

az

z

8

Let’s integrate (13.6) from z=0 ( 0 ) to arbitrary chosen z

	(z) 0			Q0	ln k0 az	(13.7)
			Cp 0a
					k0
	we adopted that			0 const

(13.7) is a logarithmic law of air temperature distribution in the surface layer.

As known

(z) T (z) a z

9

(13.7) can be rewrittenQas					k		az
	T (z) T		0	ln		0		z	(13.8)
0			Cp 0a				k0	a

T0 is measured just at the surface (significant inaccuracy). Let’s reduce such errors (13.8 for z=z1 ):

T T		Q0	ln	k0 az1	z	(13.9)
1 0		Cp 0a		k0	a 1

T T			Q0					ln k0 az1 z
0 1			Cp 0a						k0	a 1
substitute in (13.8)
T (z) T1			Q0		ln		z		a (z z1 )	(13.10)
		Cp 0a
						z1				10

	T (z) T1		Q0	ln	z	a (z	z1 )	(13.10)
			Cp 0a		z1

sign of temperature variation with height depends on sign of heat flux Q0

the air temperature decreases with height at

Q0 0

the air temperature increases with height at

Q0 0

11