Atmospheric and emissivity corrections for ground-based thermography using 3D radiative transfer modelling

Methods to retrieve urban surface temperature (Ts) from remote sensing observations with sub-building scale resolution are developed using the Discrete Anisotropic Radiative Transfer (DART, Gastellu-Etchegorry et al., 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 to 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 (Delta Omega approximate to 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. For pixels with 250 ( +/- 10) m path length the median (5th and 95th percentile) atmospheric correction magnitude 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 method evaluation, with simultaneous "near" (similar to 15 m) and "far" (similar to 155 m) observations, 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 (epsilon = 0.89 -> 0.97) alters the corrected roof (south facing) surface temperatures by similar to 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. Our proposed correction provides more accurate T-s observations with improved uncertainty estimates. Potential applications include ground-truthing airborne or space-borne surface temperatures and evaluation of urban energy balance models.