Parameterization of albedo, thermal inertia, and surface roughness of desert scrub/sandy soil surface

Spectral albedo, A sub n, for the direct solar beam is defined as A sub n (r sub i,s, theta sub 0) = r sub i exp(-s tan theta sub 0)1-I(s) where I(s) is the integral over all reflection angles describing the interception by the absorbing plants of the flux reflected from the soil, r sub i soil reflectance, assumed Lambertian, S the projection on a vertical plane of plants per unit surface area, and theta sub 0 is the solar zenith angle. Hemispheric reflectance for the direct solar beam equals 1-I(s) times the reflectance to the zenith. The values of s of 0.1, 0.2, and 0.3 respectively quantify sparse, moderately dense, and very dense desert scrub. Thin plants are assumed to be of negligible thermal inertia, and thus directly yield the absorbed insolation to the atmosphere. Surface thermal inertia is therefore effectively reduced. The ratio of surface roughness height to plant height is parameterized for sparse, moderately dense, and very dense desert-scrub as a function of s based on data expressing the dependence of this ratio on plant silhouette.