Longwave emission from a plant/soil surface as a function of the view direction: dependence on the canopy architecture
We examine the longwave emission from a structured surface: soil partially covered by an incomplete (not very dense) plane-parallel canopy. The soil (seen through the gaps) is assumed to be at uniform temperature and warmer than the plants. Different canopy architectures are constructed by varying the ratio kappa of the projection of the vertical elements (thin cylinders, or blades with a uniform distribution in azimuth) to the area of the horizontal facets, while specifying that the gap function (the probability of non-interception, that is, of seeing the soil through the canopy) remains constant (at about 0.5) when viewing the surface at a zenith angle theta v of 50 . Assuming initially that the temperature is uniform throughout the canopy, we note that the observed emission (the measured surface temperature) decreases with increasing zenith angle of observation, as more canopy and less soil is seen in the field of view. The pattern of the change is commonly applied to infer both canopy and soil temperatures. When the architecture tends to be more vertical (as quantified by a higher kappa), the pattern is modified: the emission becomes appreciably higher in the nadir region (more soil is seen) but lower towards the limb, that is, at larger theta v (more plants are seen). Thus, when interpreting the pattern of the emission for a range of theta v to estimate the temperature difference between the soil and the canopy, an overestimate results if the tendency to the vertical is underestimated. The analysis of the radiance as a function of the view zenith angle is extended to a canopy with plant-element temperature increasing with the optical depth in the canopy (where the rate specifying the increase of the emission from the plants with the optical depth is adjusted to maintain the continuity of the temperature at the canopy bottom (canopy/soil interface)). The pattern with theta v of the emitted radiance is, in these cases, closely similar to that for a warm soil/uniform-temperature canopy, especially if the canopy optical depth is large. This analysis indicates that information about the properties of the canopy (optical (radiative transfer) depth, and characterization of the architecture) should be available for an appropriate interpretation of the longwave radiances in terms of the canopy temperature, and through this interpretation, assessment of the evapotranspiration rate. Inversion of the solar bidirectional reflectances measured simultaneously with the longwave measurements is likely to be the best source of this information.
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