Three Dimensional Radiative Effects in Passive Millimeter/Sub-Millimeter All-sky Observations

This study was conducted to quantify the errors prompted by neglecting three-dimensional (3D) effects, i.e., beam-filling and horizontal photon transport effects, at millimeter/sub-millimeter wavelengths. This paper gives an overview of the 3D effects that impact ice cloud retrievals of both current and proposed (Ice Cloud Imager) satellite instruments operating at frequencies of ≈186.3 and ≈668 GHz. The 3D synthetic scenes were generated from two-dimensional (2D) CloudSat (Cloud Satellite) observations over the tropics and mid-latitudes using a stochastic approach. By means of the Atmospheric Radiative Transfer Simulator (ARTS), three radiative transfer simulations were carried out: one 3D, one independent beam approximation (IBA), and one-dimensional (1D). The comparison between the 3D and IBA simulations revealed a small horizontal photon transport effect, with IBA simulations introducing mostly random errors and a slight overestimation (below 1 K). However, performing 1D radiative transfer simulations results in a significant beam-filling effect that increases primarily with frequency, and secondly, with footprint size. For a sensor footprint size of 15 km, the errors induced by neglecting domain heterogeneities yield root mean square errors of up to ≈4 K and ≈13 K at 186.3 GHz and 668 GHz, respectively. However, an instrument operating at the same frequencies, but with a much smaller footprint size, i.e., 6 km, is subject to smaller uncertainties, with a root mean square error of ≈2 K at 186.3 GHz and ≈7.1 K at 668 GHz. When designing future satellite instruments, this effect of footprint size on modeling uncertainties should be considered in the overall error budget. The smallest possible footprint size should be a priority for future sub-millimeter observations in light of these results.