# A Geostationary Instrument Simulator for Aerosol Observing System Simulation Experiments
## 2 Methodology and Data
### TOA Radiance Simulations
#### 2.4.2 Forward Radiative Transfer Calculations with VLIDORT  
VLIDORT is a linearized pseudo-spherical vector discrete ordinate radiative transfer model (RTM) for direct and diffuse radiation in a multi-layer atmosphere [43]. The model outputs the Stokes vector and its' derivatives with respect to any atmospheric or surface property for arbitrary viewing geometry and optical depth. The optical property inputs for VLIDORT are the layer extinction optical depths \((\Delta_{l})\), layer total single scattering albedos \((\omega_{l})\), and layer scattering-matrix expansion coefficients \((B_{l})\), and surface reflectance \((\rho)\). For layer Rayleigh scattering optical thickness, \(\delta_{Ray,l}\), molecular absorption optical thickness, \(\alpha_{gas,l}\), aerosol extinction optical thickness, \(\tau_{aer,l}\), aerosol single scattering albedo, \(\omega_{aer,l}\), liquid water and ice cloud extinction optical thicknesses, \(\tau_{Lcld,l}\) and \(\tau_{lcld,l}\), and liquid water and ice cloud single scattering albedos, \(\omega_{Lcld,l}\) and \(\omega_{lcld,l}\), the total layer atmospheric optical inputs are:  
\[\Delta_{l}=\delta_{Ray,l}+\alpha_{gas,l}+\tau_{aer,l}+\tau_{Lcld,l}+\tau_{ lcld,l} \tag{5}\]  
\[\omega_{l}=\frac{\omega_{aer,l}\tau_{aer,l}+\omega_{Lcld,l}\tau_{Lcld,l}+\omega _{lcld,l}\tau_{lcld,l}+\delta_{Ray,l}}{\Delta_{l}} \tag{6}\]\[\mathbf{B}_{l}=\frac{\omega_{aer,l}T_{aer,l}\mathbf{B}_{aer,l}+\omega_{Lcld,l}\tau_{Lcld,l} \mathbf{B}_{Lcld,l}+\omega_{lcld,l}\tau_{Lcld,l}\mathbf{B}_{Lcld,l}+\delta_{Ray,l}\mathbf{B}_{ Ray,l}}{\omega_{aer,l}\tau_{aer,l}+\omega_{Lcld,l}\tau_{Lcld,l}+\omega_{lcld,l} \tau_{Lcld,l}+\delta_{Ray,l}} \tag{7}\]  
Aerosol optical properties, \(tau_{aer,l}\), \(\omega_{aer,l}\), and \(\mathbf{B}_{aer,l}\) were derived from G5 NR vertical profiles of aerosol dry mass mixing ratios interpolated to the TEMPO, GEMS, and SENTINEL-4 grids. However, the downscaled sub-grid 1 km relative humidity profiles described in the previous section were used to determine the aerosol hygroscopic growth, allowing for sub-grid scale variability in aerosol optical properties. Details of the aerosol optical property calculations, as well as surface reflectance datasets are described in Sections 2.3 and 2.6, while the details of the Rayleigh optical thickness calculations are described in Section 2.5. The liquid water and ice cloud optical properties were derived from Mie calculations based on gamma water droplet size distributions with an effective variance of 0.1, and bulk ice cloud phase models developed by [PERSON] et al. [PERSON] et al. (2016), both consistent with the MODIS operational cloud product, MOD06. Because the G5 NR simulation contains limited trace gas information, the calculated TOA radiance includes aerosol, cloud, and Rayleigh scattering terms only, and is effectively trace gas and water vapor corrected. Future implementations of the forward radiative transfer calculations for the geostationary constellation will be based on a global full chemistry nature run and will include trace gas absorption effects. TOA radiance was calculated by running VLIDORT in vector mode with 6 discrete ordinate streams and delta-M scaling for sharply peaked phase functions. The full vector solution to the radiative transfer equation is required for accurate TOA radiance calculations in the UV spectral range VILDORT was also configured to use an exact single scatter correction, the so-called Nakajima-Tanaka procedure, which replaces the truncated single scatter contribution with an exact solution that uses the complete phase function Naka and Tanaka (2016). An additional correction was applied to the single scatter term to account for the Earth's curvature effect on the incoming solar beam and the outgoing line-of-sight (referred to as the \"outgoing\" sphericity correction in VILDORT). See Appendix A for a comparison of VLIDORT forward radiative transfer benchmark calculations with several RTMs, and an estimate of the uncertainty in the simulated TOA radiance.