Chapter 2 Shortwave (Solar) Radiation Model

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radiation at the surface consists of direct and diffuse components. The relative magnitude

of these two components depends in a large part on the optical depth of the clouds. As the

cloud optical depth increases, the direct component will decrease, while the diffuse

component may increase initially if the optical depth is small enough. As the optical

depth increases beyond some threshold value, the diffuse component will decrease.

2.1 Downwelling Shortwave Radiation

Shapiro (1987, 1982, 1972) developed a simple model to determine the direct and diffuse

shortwave irradiance at the surface using only standard surface meteorological

observations. The Shortwave Radiation Module (SRM) developed for FASST uses this

model to determine the downwelling shortwave irradiance. The module also uses a

simple reflected shortwave irradiance model based on the downwelling shortwave

irradiance and knowledge of the surface albedo. Surface albedo is parameterized in terms

of the land surface type. For example, the albedo for grass is given as 0.20 and for sand

as 0.40. For each land type there will be an albedo value based on that land type. The

Solar Radiation Module requires cloud information that can be obtained from

observations, climatology or cloud conditions generated by mesoscale forecast models

such as the Army's Boundary layer Forecast Model (BFM).

The basic model approach involves dividing the atmosphere into k layers and assuming

Rk + Tk + Ak = 1 .

(2.1)

R, T, and A are the reflectance, transmission, and absorption of layer k. In the SRM R, T,

and A have been parameterized in terms of the solar zenith angle, φo, and the state of the

atmosphere/clouds using the very extensive SOLMET database (NOAA 1979). The

general form of the flux equations is

I sk↓ = Tk I sk↓-1 + Rk I sk↑

(2.2a)

I sk↑ = Tk +1I sk↑+1 + Rk +1I sk↓ .

(2.2b)

Layer k = 0 is the top of the atmosphere. For operational use, the atmosphere has been

divided into three layers consistent with the concept of low, middle, and high clouds. The

downwelling solar flux at the ground (bottom of layer 3) is given as

I s↓ = T1T2T3 / D2

(2.3)