Effective radiation

I!				Notations			B0
			Short wavelength radiation								Terrestrial Rad.
		Atmosphere absorbs some
					BA				Atmospheric counter Rad.
		terrestrial radiation
					The flux of atmospheric counter
						radiation BA is amount of long
					wavelength radiation coming from
			Earth’s surface		the atmosphere in a unit of time on
					a unit of area of the Earth surface.
			absorbs rad.

Since the surface is not ABB, it absorbs just a part of incoming radiation BA

1

B* B0 BA

Usually	T	A	T	Therefore	B B	A	and B* 0
			s		0

Difference between Earth’s surface own radiation B0 and absorbed by the surface the long wavelength atmospheric back radiation is called effective radiation of the Earth surface.

It means that through the long wave radiation the surface always looses the energy.

2

In some rare cases, the effective radiation may turn out to be negative (B*<0)

When?

- may arise at clear nights, the surface becomes very cold.

Effective radiation has an important bearing on the temperature regime of the Earth surface.

It plays a significant role in radiation frost and fog formation and in snow melting.

3

Effective radiation and water vapor in the atmosphere

Effective radiation greatly depends on:

•the water vapor content in the atmosphere

•presence of cloudiness. It decreases with increase of the water

vapor content.
			B* B0	BA		Increase of humidity
B*						results in increase of
			BA a T14			BA value, and, hence,
						decrease of B* value.
	WVC	Absorption			Air temperature at the
		coefficient			level z1

Value z1 is arbitrary chosen quantity, it can be equal to 2 meters. Coefficient “a” specifies emissivity of the atmosphere, depends on humidity, amount and altitude of the cloudiness.

The increase of water vapor pressure and cloud amount results in

coefficient “a” growth up.	4

Application of Angstrem’s formula

BA T14 A1 10 ce1 D

Here, e1 is water vapor pressure at the level z1,A1 0; D 0; c 0 are

empirical constants.

BA a T14

A1 D 10 ce1 a

Combining formulas

B* B0 BA

We obtain

B0* T04 aT14

4

Let’s add

Effective radiation in cloud

B0 T0

0 T 4 T 4

free atmosphere

1

1

B0* T04 aT14 T14 T14

1 a T14 T04 T14

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Let’s denote 1 A1 A; T04 T14 B0*

B0* A D 10 ce1 T14 B0*

A=0,18 and D=0,25 (dimensionless quantities); c=0,95 if e1 in hPa

There is also well known Brent’s formula

BA T 4 a1 b1 e

a1 0,526

b1 0,065

“e” in hPa

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		Cloudiness impact on counter and
		effective radiation
		Effective radiation depends upon following factors
	•	Cloudiness thickness	Numerous influencing factor combinations
	•	Cloudiness altitude
			make theoretical approach to the problem
	•	Cloudiness form
			to be very complicated or even not
	•	Cloud amount	possible.

To understand the essence of the impact, an example will be considered.

Initial conditions are: overcast, cloud base height is a few hundred meters.

Notation: T0 is the surface temperature, T1 is air temperature in shelter, Tk is

	air temperature at the cloud base.			T
	At these conditions: T0 T1 ; Tk	T1 Zk ;			const lapse rate
				z
	within the layer from the surface up to the cloud base.				7

Counter (earthward) flux from the cloud layer

Bk

4

Tk

Since clouds, air and surface

are not ABB factor δ is to be

Z cloud base

introduced

height

a Tk4 The energy loss when passing the layer 0 - Z

a A1 D 10 ce1

B

A

a T 4

Radiation of the layer 0Z

1

B* T 4

a T 4

1 a T 4

0

1

k

B*

The cloudiness radiation

that reaches the surface

0

Tk4 a Tk4 1 a Tk4

Effective radiation at

cloud free condition

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At overcast condition T0 T1

B* T04 a T14 1 a Tk4

B* T 4				a T				4	1 a T 4
		1				1										k
B* T14 1 a 1 a Tk4 1 a T14 Tk4
		4		4			4				T	4
		T1 Tk			T1			1			k
										T
				T 4							1
4
B* T1 1 a					k
			1		4
	B*			T1
																			4
0														*		Tk
This formula suggests that at
overcast ER decreases since the											B*	B			1
quantity in brackets <1													0				1				9
																T

Let’s transform the ratio			4
	Tk
		T
		1

Tk T1 Zk

T1 Tk Tk Zk

T

4

T T

4

T

4

T T T

k

1

k

1

k

k

1

k

T

T

T

1

1

1

T

4

4 T

1

k

1

k .....

T

T

1

1

*

T

4

*

4 T

B* B0

1

k

B0 1

1

k

T

T

1

1

*

4 T

* 4

k

B* B0

Zk

B* B0 T1

T1

Decomposing into raw and restricting our self with only first member, we obtain

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B* B*	4	Z
0 T			k
1

Thus, ER at overcast condition depends on following factors;

1. Air temperature (T1).

Angstrem’s formula

2. Stratification of the atmosphere (γ).

3. Cloud base height (Zk)

B0* T14 A D 10 ec1

T04

T14

4. Humidity of the atmosphere

At overcast condition T0≈T1

B0* T14 A D 10 ec1

T04 T14 0

4

4

A D 10

ec

Zk

1

k

B* 4 T

A D 10

Z

B* T1

1

3

ec

T1

1

A=0,18; D=0,25; c=0,95 (e in hPa)

If n=±1 (10 points)

Bn B0* 1 CLnL CM nM CH nH

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