Absorption of insolation by land surfaces with sparse vertical protrusions

Abstract

Absorption of insolation by land surfaces is analyzed, applying a previously developed model of a plane with sparse protrusions, in which r₁ and r_c are Lambertian reflectivities of the soil-plane and of the protrusions, respectively, and s is the projection on the vertical plane of protrusions over a unit area. The effective daylong absorption of insolation by this type of surface increases with latitude, sharply for dark protrusions, gradually if the reflectivity of the protrusions is equal to that of the soil-plane.

Inasmuch as the absorbed insolation is transferred to the atmosphere at a different rate by the protrusions than by the soil, the ‘daylong absorption at equinox by the protrusions and by the soil-plane are analyzed separately, as functions of r₁, r_c, s and of the latitude. The dependence on the solar zenith angle of the partitioning of the surface absorption between these two components of our complex surface implies that its effective thermal inertia varies with time of day, season and latitude. Surface models, such as the one discussed, are required to interpret the various measurements of bidirectional reflectivity and/or albedo into a data set appropriate for climate studies, specifying (i) the surface albedo as a function of the direction of its irradiation, and (ii) the partitioning of the absorbed insolation into that by the protrusions, and that by the soil (from which the effective surface thermal inertia can be appropriately assessed). Measurements of s in a global survey over all the continents are needed.