# A Geostationary Instrument Simulator for Aerosol Observing System Simulation Experiments
## 2 Methodology and Data
### Aerosol Optical Properties  
In GOCART, aerosols are assumed to be external mixtures, thus the total layer aerosol optical thickness, \(\tau_{aer,l}\), can be calculated from the sum of individual aerosol species (dust, sea salt, sulfate, and carbonaceous aerosol) optical thicknesses:  
\[\tau_{aer,l}=\sum_{\kappa}\beta_{s,l}m_{s,l}^{d} \tag{17}\]  
where \(m_{s,l}^{d}\) is the aerosol dry mass concentration, and \(\beta_{s,l}\) is the mass extinction efficiency for species \(s\), which is calculated according to Equation (18) ([PERSON] and [PERSON], 1997). The aerosol mass extinction efficiency is a function of the aerosol effective radius (\(r_{e}\)), density (\(D_{s}\)), wet mass (\(m_{s}\)), and extinction coefficient (\(\epsilon_{s}\)), which, for hygroscopic aerosols, are all functions of layer relative humidity (RH). \[\beta_{s}=\frac{3\epsilon_{s}(\lambda)m_{s}}{4D_{s}r_{e,s}m_{s}^{d}} \tag{18}\]  
In Equations (18)-(20) below, we have dropped the layer subscript, \(l\), for clarity, but all aerosol physical properties are model layer properties. The parameters in Equation (18) were derived from the prescribed particle size distribution, density, and refractive index of each species. The size distributions for sulfate, OC, and BC were described by a lognormal distribution function:  
\[n(r)=\frac{N_{0}}{r\ln S\sqrt{2\pi}}\exp{-\frac{(\ln r-\ln r_{M})^{2}}{2(\ln S)^{ 2}}} \tag{19}\]  
where \(r\) is the particle radius, \(n(r)\) is the number concentration of particles with radius \(r\), \(N_{0}\) is the total number of particles per unit volume, \(S\) is the geometric standard deviation, and \(r_{M}\) is the radius of the number mode of the distribution. The distributions were truncated between a minimum and maximum radius of \(r_{Min}\) and \(r_{Max}\), respectively. The values of \(S\), \(r_{M}\), \(r_{Min}\), and \(r_{Max}\) for sulfate, OC and BC are listed in Table 4.  
The sea salt and dust size distribution were described by five size bins. Each bin has a minimum and maximum radius, which are listed in Tables 5 and 6 for dry sea salt and dust, respectively. The particle size distribution in each sea salt bin is described by Equation (2) in Gong [49]. While for dust, for the four largest bins, the particle size distribution within the bin is \(n(r)=N_{0}^{i}r^{4}\), where \(N_{0}^{i}\) is the total number of particles per unit volume in bin \(i\). The smallest dust size bin is broken into 4 sub-bins with mass weighting factors equal to 0.009, 0.081, 0.234, and 0.676. Within each sub-bin the size distribution is also \(n(r)=N_{0}^{i}r^{4}\). Except for dust and hydrophobic OC and BC, all aerosols are hygroscopic. The size distributions of sulfate, hydrophilic OC, and hydrophilic BC grow with RH according to a growth factor, \(GF(RH)\), that was taken from the Global Aerosol Data Set (GADS) [50] and depends on RH. For some RH equal to \(r\)l, the lognormal size distribution mode and maximum radius increases by the factor \(GF(rh)\). For sea salt, particle growth as function of RH was taken from [PERSON] et al. [51] (see Equation (3) and Table 2). The size of each sea salt bin changes as the particles grow. The effective radius, \(r_{e}\), for each species at a GEOS-5 downscaled sub-grid layer RH is the area-weighted mean radius of the size distribution. For dust and sea salt, the effective radius is calculated for each size bin. The aerosol particle density is then simply the sum of the dry aerosol density \((D_{g}^{d})\) and water density \((D_{w})\) weighted by the volume fraction of dry aerosol \((f^{d})\) and water \begin{table}
\begin{tabular}{l c c} \hline \hline
**Bin** & \(r_{Min}\) [\(\mu\)m] & \(r_{Max}\) [\(\mu\)m] \\ \hline
1 & 0.1 & 1.0 \\
2 & 1.0 & 1.8 \\
3 & 1.8 & 3.0 \\
4 & 3.0 & 6.0 \\
5 & 6.0 & 10.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Minimum and maximum radius of the five size bins that describe the dust size distribution.