Estimating Direct and Diffuse Short-wave lrradiance

11.2 Estimating Direct and Diffuse Short-wave lrradiance

Computation of the solar or shortwave component of the radiant energy budget of an organism requires estimates of flux densities for at least three radiation streams: direct irradiance on a surface perpendicular to the beam

diffise sky irradiance on a horizontal plane and reflected radiation from the ground

In addition to these, sometimes

Radiation Fluxes in Natural Environments

irradiance of a horizontal surface need to be known. is sometimes reffered to as the global

These last two quantities are related to the

(1 1.9) where is the solar zenith angle.

Reflected radiation is the product of the average surface reflectance for the solar waveband and the total shortwave irradiance of the surface:

The shortwave surface reflectance is called albedo. Typical albedos for several surfaces are given in Table 11.2. These values are influenced by

amount of cover, color of soil or vegetation, and sun elevation angle, so the values in the table should be regarded as approximate. Tall canopies and water surfaces have reflectances that depend strongly on solar zenith angle. The values in Table 11.2 are for small (midday) zenith angles.

Though a number of models are available for estimating clear sky and

with considerable accuracy and Porter, 197 they require data that are not generally available to the ecologist without special measurements, and are quite complicated to use. We use a simpler model based on Liu and Jordan (1960). We expect

to be a function of the distance the solar beam travels through the atmosphere, the transmittance of the atmosphere, and the incident flux density. A simple expression combining these factors is:

where is the extraterrestrial flux density in the waveband of interest, normal to the solar beam. The term is the atmospheric transmittance and m is the optical air mass number, or the ratio of slant path length

T A BLE 11.2. Shortwave reflectivity (albedo) of soils and vegetation canopies.

Surface Reflectivity Surface Reflectivity

Grass 0.24-0.26

Snow,

Wheat

Snow, old

Maize 0.18-0.22 Soil, wet dark 0.08 Beets

0.18 Soil, dry dark 0.13 Potato

0.19 Soil, wet light 0.10 Deciduous forest 0.10-0.20

Soil, dry light 0.18 Coniferous forest

Sand, dry white 0.35 Tundra

0.15-0.20 Road, blacktop 0.14 Steppe

0.20 Urban area (average) 0.15

Solar Radiation under Clouds 173

through the atmosphere to zenith path length. For zenith angles less than refraction effects in the atmosphere are negligible, and m is given by:

Pa 101.3 cos

The ratio is atmospheric pressure at the observation site di- vided by sea level atmospheric pressure, and corrects for altitude effects. Equation (3.7) can be used to calculate this ratio. It can be shown that Eq. (1 1.11) is mathematically equivalent to Beer's law (Eq. (10.4)).

Liu and Jordan (1960) measured t on clear days, and found values ranging from 0.75 to around 0.45 at two sites. When is lower than about

0.4, one would consider the sky to be overcast. Gates (1980) suggests values of between 0.6 and 0.7 to be typical of clear sky conditions. Values on the clearest days would be around 0.75.

Of the radiation that starts through the atmosphere, part reaches the ground as beam radiation

part is absorbed by the atmo- sphere, part is scattered back to space, and part is scattered downward toward the ground. The down scattered part is called the sky

ra- diation. The actual amount of diffuse radiation reaching the ground is difficult to compute because it depends, in part, on the albedo of the ground. All else being equal, the sky is brighter when the ground is snow covered than it is when the ground is covered with dense, dark vegeta- tion. Without getting into these complications, approximate values can

be computed for sky radiation on clear days using an empirical equation adapted from Liu and Jordan (1960):

The factor partially compensates for the effect of the cosine factor in Eq. (1

so that the radiation remains relatively constant throughout clear days. In fact, Peterson and

(1981) found that the ratio

is nearly constant on clear days. Figure 11.2 shows the beam, diffuse, and total radiation computed using Eqs. (1 1.1 1) and 1.13) for a clear atmosphere. Figure 11.3 shows these same radiation streams, but for a turbid atmosphere. Note that as the dust and haze increase, beam radiation is decreased and

radiation increases.