Albedo

Ground albedo (r) is the ratio between reflected and incoming radiation within the short wave (0.3-3.0 mm wavelength) portion of the solar spectrum.

Both direct and diffuse light components are partially reflected, depending on the kind of soil, its humidity, geometry and cover. Ross (1975) weights albedo as a function of the direct and diffuse radiation and the reflectivities associated with those components:
 

 

rd: surface albedo for diffuse solar radiation

rb: surface albedo for beam solar radiation

Ri(t): hourly (t=hr, MJ m-2 h-1) or daily (t=d, MJ m-2 d-1) ground reflected diffuse irradiance on an inclined surface

Di(t): hourly (t=hr, MJ m-2 h-1) or daily (t=d, MJ m-2 d-1) diffuse irradiance on an inclined surface

In general, the values of 0.2 or 0.15 are mostly used for r. Typical albedo values for a variety of ground surfaces are listed in numerous literature sources. Table below reports a sample of values from Extraído de Aguiar and Page (1999). See also Scharmer and Greif (2000).

 

 

The following is a similar list of values for a range of vegetation type and soil type (Davies and Idso, 1979; Oke, 1987; Campbell and Norman, 1998).
 

 

Methods do exist to estimate soil albedo. According to Meteotest (2003), albedo can be approximated by a linear a relationship against daily mean air temperature (T(d), °C)
 

 

Reference values for the parameters are: p=0.618, q=-0.044 for areas with a large amount of snow, approximately characterized by sum of precipitation for three winter months > 150 mm and mean air temperature for the same period < -3°C; p=0.423, q=-0.042 otherwise. The graph below show how albedo changes with air temperature for both conditions (estimated vales are conveniently bounded between 0.2 and 0.8).

 

Some authors introduced the relationships between surface albedo and solar elevation angle (or its complement, zenith angle), including the surface albedo at the maximum solar elevation angle (r'=0.05 or lower) as an input. According to Geiger (1965), the surface albedo varies with solar zenith (Y(t), rad):

 

 

Iqbal (1983) proposed a parameterization of albedo with the solar elevation angle (B(t)) in degrees:
 

 

where r' is the albedo at . The graph below is exemplary of albedo variations (from r'=0.05 to 0.57) as a function of solar elevation angles computed at solar noon for different latitudes (l) and days of the year (i).

Another parameterization obtained from a set of data recorded at the South Pole was proposed by Carroll and Fitch (1981). In clear sky conditions and for B(t)≤20°, the relation is:
 

 

so that for high elevation angles the albedo reaches a minimum value of 0.83. For B(t)≤18°, in overcast conditions, parameterization changes in:
 

 

so that for B(t)>18° the albedo value is 0.84. See Orsini et al. (2000) for a more detailed parameterization.

Soil albedo depends on the surface color and on the moisture content. Albedo values for dry soil vary from 0.14 (clay) to 0.37 (dune sand). Ten Berge (1986) described the dependence of the albedo value on soil moisture in relation to the average water content of the top soil layer (table below).
 

 

Surface roughness influences soil albedo other than wet/dry conditions. See Matthias et al. (2000) for a study on two soils with diverse combinations of roughness and wet/dry conditions. The summary in the table below shows albedo values measured at six solar angle values and means (plus standard deviation) for each smooth reference soil, as occurred in generally cloudless days between April and August in 1995 and 1996 at the University of Arizona Campus Agricultural Centre in Tucson (latitude: 32.25° N, longitude: 110.95° W, elevation: 745 m).
 

 

A range of roughness conditions was created by tillage treatments. Next table summaries the mean of six albedo measurements (at six solar angle values ranging from 20° to 70°) for each of tillage treatment of two soils in both 1995 (north-south tillage) and 1996 (east-west tillage).
 

 

 

 

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