Albedo of a Forest Modeled as a Plane with Dense Protrusions

Abstract

A model is developed that treats, in a simplified way, the reflection of the direct solar radiation by a surface consisting of a soil-plane and protruding vertical plant elements, such as needles of pine trees or stalks of a wheat field. Such a surface is treated as a Lambertian reflectivity soil-plane (reflectivity ri) and thin, vertical cylinders are also characterized as Lambertian reflectors (reflectivity rc). Each cylindrical section is randomly located with respect to the other sections. The first hemispheric reflection of the direct beam from this surface is computed exactly, expressed as diri + dcrc, where di and dc are the geometrical factors governing the reflection from the soil-plane and from the protrusions respectively. These geometrical factors are a function of the solar zenith angle ?0, and the area s of the projections on a vertical plane of the cylindrical plant elements per surface unit area. The light trapping in such a complex surface is assessed by analyzing di and dc. For the case rc = ri, we analyze the combined geometrical factor de = di + dc. In the range 20° < ?0 < 80°, the factor de decreases with increasing zenith angle for low values of s, but for a large s it increases, sharply so for ?0 > 60°. When s tan?0 ? 1, the albedo accrues from the protrusions only and can be stated as a product of rc and an explicit function of ?0, which increases monotonically with ?0. The above analytical results apply to the direct solar beam. For the scattered component of the irradiance or for the global irradiance under cloudy conditions, a constant albedo, independent of the solar zenith angle, seems applicable. A comparison with the albedo measurements reported over a pine forest indicates that our simple analytic model reproduces quite well the dependence of the albedo on the solar zenith angle and the overall light trapping characteristics of such a complex surface. Determination of the parameter s for any vegetated area over which albedo measurements are taken will enhance the meaning of the measurements for meteorological-climatological studies.