A model for inferring canopy and underlying soil temperatures from multi-directional measurements

Abstract

Thermal emission is modeled from a canopy/soil surface, where the soil and the leaves are at different temperatures,T g andT c respectively. The temperatureT m corresponding to a radiometer reading is given by $$B_\lambda (T_m ) = \chi B_\lambda (T_g ) + (1 - \chi )B_\lambda (T_c ) ,$$ whereB λ denotes the Planck blackbody function at wavelength λ, χ specifies the fraction of the field of view occupied by the soil at a given view direction, and an emissivity of 1.0 is assumed for the plants and the soil. The dependence of the soil-fraction χ on the view direction and the structure is expressed by the viewing-geometry parameter, which allows for concise and simple formulation. We observe from our model that at large view zenith angles, only the plants are effectively seen (that is, χ tends to zero), and thereforeT c can be determined from observations at large zenith angles, to the extent that such observations are practical. Viewing from the zenith, χ = exp(-L hc), whereL hc is the projection of the canopy leaf-area (per unit surface area) on a horizontal plane. For off-zenith observations, the soil-fraction χ depends on the distribution in the azimuth of the projected areas of various leaf categories, in addition to the dependence on the sum total of these projections,L hc.L hc, rather than the leaf-area index, emerges as the parameter characterizing the optical thickness of the canopy. Inferring bothT c andT g from observations from the zenith and from large zenith angles is possible ifL hc is known from other measurements. Drooping of leaves under water-stress conditions affects the observed temperatureT m in a complicated way because a leaf-inclination change produces a change inL hc (for the same leaf area) and also a change in the dependence of χ on the view direction. Water stress can produce an increase of the soil-fraction χ and thus tends to produce an exaggerated increase in the observed temperature compared to the actual increase in canopy temperature. These effects are analyzed for a simulated soybean canopy.