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

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.