Atmospheric and Emissivity Corrections for Ground-Based Thermography Using 3D Radiative Transfer Modelling

Methods to retrieve urban surface temperature (T_s) from remote sensing observations with sub-building scale resolution are developed using the Discrete Anisotropic Radiative Transfer (DART, Gastellu-Etchegorry, Grau and Lauret, 2012) model. Corrections account for the emission and absorption of radiation by air between the surface and instrument (atmospheric correction), and for the reflected longwave infrared (LWIR) radiation from non-black-body surfaces (“emissivity” correction) within a single modelling framework. The atmospheric correction a) can use horizontally and vertically variable distributions of atmosphere properties at high resolution (< 5 m); b) is applied here with vertically extrapolated weather observations and MODTRAN atmosphere profiles; and c) is a solution for ray tracing and cross section (e.g. absorption) conflicts (e.g., cross section needs the path length but it is typically unavailable during ray tracing). The emissivity correction resolves the reflection of LWIR radiation as a series of scattering events at high spatial (< 1 m) and angular (ΔΩ ≈ 0.02 sr) resolution using a heterogeneous distribution of radiation leaving the urban surfaces. The method is applied to a novel network of seven ground-based cameras measuring LWIR radiation across a dense urban area (extent: 420 m x 420 m) where a detailed 3-dimensional representation of the surface and vegetation geometry is used. Our unique observation set allows the method to be tested over a range of realistic conditions as there are variations in: path lengths, view angles, brightness temperatures, atmospheric conditions and observed surface geometry. The median (5^th and 95^th percentile) atmospheric correction magnitude for pixels with 250 (± 10) m path length is up to 4.5 (3.1 and 8.1) K at 10:10 on a mainly clear-sky day. The detailed surface geometry resolves camera pixel path lengths accurately, even with complex features such as sloped roofs.

The atmospheric correction uses varying surface – sensor path lengths (z^path, m, Figure 1a). The band integrated longwave emission from the atmosphere (L^atm, Figure 1b) and band integrated atmospheric transmissivity (Γ^atm, Figure 1c) combine to enable the atmospheric correction, shown as a difference between uncorrected camera brightness temperatures (T_b^cam) and corrected surface brightness temperatures (T_b^surf) in Figure 1d. The correction is evaluated using simultaneous “near” (~15 m) and “far” (~155 m) observations which has a mean absolute error of 0.39 K. Using broadband approximations, the emissivity correction has clear diurnal variability, particularly when a cool and shaded surface (e.g. north facing) is irradiated by warmer (up to 17.0 K) surfaces (e.g. south facing). Varying the material emissivity with bulk values common for dark building materials (ε = 0.89 → 0.97) alters the corrected roof (south facing) surface temperatures by ~3 (1.5) K, and the corrected cooler north facing surfaces by less than 0.1 K. Corrected observations assuming a homogeneous radiation distribution from surfaces (analogous to a sky view factor correction) differ from a heterogeneous distribution by up to 0.25 K.