The effect of radiometer placement and view on inferred directional and hemispheric radiometric temperatures of an urban canopy

Abstract. Any radiometer at a fixed location has a biased view when observing a convoluted, three-dimensional surface such as an urban canopy. The goal of this contribution is to determine the bias of various sensors views observing a simple urban residential neighbourhood (nadir, oblique, hemispherical) over a 24 hour cycle under clear weather conditions. The error in measuring a longwave radiation flux density (L) and/or inferring surface temperatures (T₀) is quantified for different times over a diurnal cycle. Panoramic time-sequential thermography (PTST) data were recorded by a thermal camera on a hydraulic mast above a residential canyon in Vancouver, BC. The data set resolved sub-facet temperature variability of all representative urban facets in a 360° swath repetitively over a 24-hour cycle. This data set is used along with computer graphics and vision techniques to project measured fields of L for a given time and pixel onto texture sheets of a three-dimensional urban surface model at a resolution of centimetres. The resulting data set attributes L of each pixel on the texture sheets to different urban facets and associates facet location, azimuth, slope, material, and sky view factor. The texture sheets of L are used to calculate the complete surface temperature (T_0,C) and to simulate the radiation in the field of view (FOV) of narrow and hemispheric radiometers observing the same urban surface (in absence of emissivity and atmospheric effects). The simulated directional (T_0,d) and hemispheric (T_0,h) radiometric temperatures inferred from various biased views are compared to T_0,C. For a range of simulated off-nadir (φ) and azimuth (Ω) angles, T_0,d(φ,Ω) and T_0,C differ between −2.6 and +2.9 K over the course of the day. The effects of effective anisotropy are highest in the daytime, particularly around sunrise and sunset when different views can lead to differences in T_0,d(φ,Ω) that are as high as 3.5 K. For a sensor with a narrow FOV in the nadir of the urban surface, T_0,d(φ=0) differs from T_0,C by +1.9 K (day) and by −1.6 K (night).

Simulations of the FOV of hemispherical, downward-facing pyrgeometers at 270 positions show considerable variations in the measured L and inferred hemispherical radiometeric temperature T_0,h as a function of both horizontal placement and height. The root mean squared error (RMSE) between different horizontal positions in retrieving outgoing longwave emittance L_↑ decreased exponentially with height, and was 11.2, 6.3 and 2.0 W m⁻² at 2, 3, and 5 times the mean building height z_b. Generally, above 3.5z_b the horizontal positional error is less than the typical accuracy of common pyrgeometers. The average T_0,h over 24 h determined from the hemispherical radiometer sufficiently above an urban surface is in close agreement with the average T_0,C. However, over the course of the day, the difference between T_0,h and T_0,C shows an RMSE of 1.7 K (9.4 W m⁻²) because the relative contributions of facets within the projected FOV of a pyrgeometer do not correspond to their fractions of the complete urban surface.