SURFACE RADIATION BUDGET

The surface radiation budget is comprised of four different terms:

Q* = SW_up + SW_down + LW_up + LW_down (1)

where:

Q* = is the net surface radiation (Wm^-2)

SW_up is the upwelling reflected short wave solar radiation

SW_down is the downwelling short wave radiation that is transmitted through the atmosphere, originating from the sun.

LW_up is the upwelling longwave (IR) radiation emitted by the earths surface

LW_down is the diffuse downwelling radiation (usually emitted by greenhouse gasses in the atmosphere

Downward fluxes are negative, upward fluxes are positive.

So you ask, what do each of these terms look like during the course of a day??? Take a look -->

Let's now look at each of these terms in more detail.

Shortwave Radiation

The intensity of solar radiation at the top of the atmosphere is often called the "solar constant (S)".
This terminology is misleading since S varies with time from about -1360 Wm^-2 to -1380 Wm^-2. We'll use a value of -1370 Wm^-2 (note the negative sign indicating a downward directed flux).
At the earth's surface, however, we do not observe 1370 Wm^-2 of down welling solar radiation. Why? Answer
Hence, we can define the net transmissivity (T_sw) as as the fraction of down welling solar radiation that makes it to the surface.
The net transmissivity is also a function of the solar elevation angle, Y. The solar elevation angle is simply the angle of the sun above the local horizon.
So, considering the effects of clouds and the solar elevation angle, the net transmissivity can be approximated (parameterized) as:

T_sw = (0.6 + 0.2 sin Y)(1-0.4s_hc)(1-0.7s_mc)(1-0.4s_lc) (2)

where s represents the cloud-cover fraction for high (hc), middle (mc), and low (lc) clouds.

Q: When the sun is directly overhead and there are no clouds, what is the net transmissivity? Answer

Q: When the sun is directly overhead and there is full sky coverage of clouds at all levels, what is the transmissivity? Answer

So, the expression for the down welling short wave radiation at the surface is approximately:

SW_down = ST_swsinY for daytime hours (i.e., sin Y is positive)

= 0 for nighttime hours (i.e., sin Y is negative)

Q: How does one determine the local elevation angle?????

easy: (3)

where f and l_e are the latitude (positive north) and longitude (positive west) in radians. d_s is the solar declination angle (angle of the sun above the equator, in radians) given by:

(4)

where f_r is the latitude of the Tropic of Cancer (23.45 degrees), d is the Julian day of the year, d_r is 173, the Julian day of the summer solstice, and d_y is the average number of days in the year (365.25).

The upwelling short wave radiation is much easier....,

SW_up = -aSW_down

where a is the albedo of the earth's surface.

Long wave Radiation

As you can see in the above figure, the upward and downward-directed long wave radiation contribute significantly to the total radiation budget at the surface.
Also notice that both LW_up and LW_down do not vary much diurnally.
An approximation to the net upward longwave radiation, i.e., LW_net = LW_up + LW_down is given by:

LW_net= (0.08 Kms^-1)(1-0.1s_hc)(1-0.3s_mc)(1-0.6s_lc) (5)

This parameterization for LW_net is very much oversimplified.
Really, one must consider LW_up and LW_down separately.
To calculate LW_up is easy, just use the Stefan-Boltzman Law for a gray body:

LW_up = e_lsT⁴ (6)

where e_l is the spectral emissivity and s is the Stefan-Boltzman Constant = 5.67 x10^-8 Wm^-2K^-4.

To calculate LW_down is much more difficult and is frankly beyond the scope of this class (we touch upon this issue in Physical Met.).

So, putting this altogether, based on the aforementioned approximations for SW_up, SW_down, LW_up, and LW_down, we can rewrite (1), our original radiation budget equation as:

Q* = (1-a)ST_swsinY + LW_net during the daytime

Q* = LW_net during the night time

Questions??????????????????????

OK, let's do the radiation budget lab.