# A Geostationary Instrument Simulator for Aerosol Observing System Simulation Experiments
## 2 Methodology and Data
### Surface Reflectance Models  
For each satellite domain and observation wavelength, the highest resolution available surface reflectance dataset was used. For simplicity, this first version of the simulator we considered only land surfaces, while future versions will consider water leaving radiance. Over land, for visible and near infrared channels, we used the Ross-Thick Li-Sparse (RTLS) model [35] to represent the variations in surface reflectance as a function of measurement and illumination angles (i.e., the bidirectional reflectance distribution (BRD)). In this model the BRD is calculated by a linear combination of three semi-empirical kernel functions:  
\[\rho(\theta_{s},\theta_{v},\phi)=K_{iso}\rho_{iso}+K_{geo}\rho_{geo}(\theta_{s },\theta_{v},\phi)+K_{vol}\rho_{vol}(\theta_{s},\theta_{v},\phi) \tag{1}\]  
where \(\rho_{iso}\), \(\rho_{geo}\), \(\rho_{vol}\) are the isotropic (Lambertian), geometric [36], and volumetric [37] kernel functions, and \(K_{iso}\), \(K_{geo}\), and \(K_{vol}\) are their respective amplitudes (or weights). The kernels represent different modes of surface scattering. The kernel weights are derived from MODIS observations, such that when the three kernels are scaled by their weights the modeled surface reflectance matches the observations. Equations (2)-(4) show the formulations for the three kernels based on the solar zenith (\(\theta_{s}\)), viewing zenith (\(\theta_{v}\)), and relative azimuth (\(\phi=\phi_{v}-\phi_{s}\)) angles, which are defined according to the photon travel direction, such that \(\phi=0\) is the forward scattering direction (\(\phi_{v}\) and \(\phi_{s}\) are the viewing and solar azimuth angles, respectively). In Equation (3), for the Li-Sparse (geometric) kernel, \(h\), \(b\), and \(r\) represent the height of the crown center, the vertical crown radius, and horizontal crown radius, respectively. The crown relative height (\(\frac{h}{b}\)) was set to 2, and the crown shape parameter (\(\frac{b}{r}\)) was set to 1 (consistent with the MODIS retrievals). The MCD43D product provides daily kernel weights [35] on a 30 arc second grid. The dataset was gap-filled with a seasonal climatology. Eight-day RTLS kernel weights at 1 km resolution from the MAIAC (Multi-Angle Implementation of Atmospheric Correction) algorithm [38; 39] (only available over North America at the time of this work) were used for the TEMPO domain. When using the RTLS model to represent surface reflectance, VLIDORT treats surface reflectance as \"scalar\", i.e., reflectance is only applied to the total intensity (I) term of the Stokes vector; only the (1,1) component of the BRD matrix is non-zero. \[\rho_{iso}=1 \tag{2}\]  
Figure 6: Same as Figure 5 but for the southern Africa biomass burning region (\(10^{\circ}\) W - \(30^{\circ}\) E, \(0^{\circ}\) S - \(30^{\circ}\) S). \[\theta_{s}^{\prime}=tan^{-1}\bigg{(}\frac{b}{r}tan\theta_{s}\bigg{)} \tag{3}\] \[\theta_{v}^{\prime}=tan^{-1}\bigg{(}\frac{b}{r}tan\theta_{v}\bigg{)}\] \[cos\xi^{\prime}=cos\theta_{v}^{\prime}cos\theta_{v}^{\prime}- sin\theta_{s}^{\prime}sin\theta_{v}^{\prime}cos\phi\] \[D^{\prime}=\sqrt{(tan\theta_{v}^{\prime})^{2}+(tan\theta_{s}^{ \prime})^{2}+2 tan\theta_{v}^{\prime}tan\theta_{s}^{\prime}cos\phi}\] \[cos(t)=min\bigg{\{}1,\frac{h}{b}\sqrt{\frac{D^{\prime 2}+(tan \theta_{s}^{\prime}tan\theta_{v}^{\prime}sin\phi)^{2}}{sec\theta_{v}^{\prime}+ sec\theta_{s}^{\prime}}}\] \[O=\bigg{(}1-\frac{1}{\pi}(t-sin(t)cos(t))\bigg{)}(sec\theta_{v} ^{\prime}+sec\theta_{s}^{\prime})\] \[\rho_{geo}(\theta_{s}^{\prime},\theta_{v}^{\prime},\phi)=\frac{ 1}{2}(1+cos\xi)sec\theta_{v}^{\prime}sec\theta_{s}^{\prime}-O\]  
\[\rho_{iso}=1 \tag{2}\]0 \[\rho_{iso}=1 \tag{2}\]1  
Figure 7 shows an example of the change in surface reflectance at 670 nm as would be observed by TEMPO due to the changing sun-sensor geometry on a typical day, and indicates the importance of using a rigorous radiative transfer model with a non-Lambertian surface.