# Probing Dust and Water in Martian Atmosphere with Far-Infrared Frequency Spacecraft Occultation
## 3 Results
### Dust and Cloud Losses  
The signal power loss is calculated in four dust storm scenarios [55] using the formulation (Equation (15)) for the dust number density profile [17]. In the given equation, \(n_{dust}(z)\) refers to the density of the dust as a function of altitude. The list of parameters for each dust storm scenario is presented in the table below. Here, \(n_{s}\) is surface dust density, FH is falloff height, PH is pulse height, FL is falloff length, PT is pulse thickness, and B is the ratio of peak to surface dust [17; 55]. Falloff height refers to the altitude to which dust has been measured, and falloff length is a characteristic length scale where the opacity decays from near-surface dust conditions to zero. \[n_{dust}(z) = n_{s}*A(z) \tag{17}\] \[A(z) = [1-e^{-\frac{(z-FH)^{2}}{F^{2}}}]+B.e^{-\frac{(z-FH)^{2}}{PT^{2}}} \tag{18}\]  
We estimate the attenuation due to water ice clouds and compare it with ones from the dust storm scenarios mentioned in Table 1. Signal attenuation is estimated in the Rayleigh  
Figure 3: Maximum expected signal loss at THz frequencies due to major absorbers in gas phase i.e., CO\({}_{2}\), CO, H\({}_{2}\)O, O\({}_{2}\), and O\({}_{3}\) in Martian atmosphere assuming appropriate mixing ratios [50] compared with S- and X-band instrument sensitivity. Losses are calculated from the absorption coefficient using the HITRAN database. scattering regime (Equation (13)) using absorption and scattering coefficients from [56], and the corresponding signal losses at each altitude are computed using the Abel transform for given dust number density profiles (Equation (9)). The complex refractive index of dust between 1 and 10 THz is taken from [57]. In the case of water ice, refractive indices are known to be temperature dependent around 10 THz [58]. At 10 THz frequency, i.e., 30 \(\upmu\)m, the imaginary value of the refractive index changes from 0.03 (T = 176 K) to 0.05 (T = 266 K). The temperature range of the Martian atmosphere shows a wide degree of variation between 130 to 230 K [23]. Therefore, we consider the nominal values for real and imaginary indices [58]. Figure 4 shows the magnitude of real and imaginary refractive indices considered for computing the signal loss. In order to draw a comparison between dust and water ice cloud losses with VeRa absorptivity, we calculate the range of expected absorptivity due to water ice clouds and dust storm scenarios. For dust particles, we present the extreme case: (i) global dust storm at MY 28 and (ii) no dust storm based on the dust distribution parameters presented in Table 1. The effective radius of the dust particles is taken to be 1.5 \(\upmu\)m [41; 42] while the radii of the water ice particles are in the range of 1-3 \(\upmu\)m [59]. For water ice, the maximum number density is computed from the maximum water ice content expected for the Martian atmosphere, i.e., 1 mg/cm\({}^{3}\)[60]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dust Activity** & \(n_{s}\) (cm\({}^{-3}\)) & **B** & **FH (km)** & **FL (km)** & **PH (km)** & **PT (km)** \\
**Scenario** & & & & & & \\ \hline MY25 & 17 & 0.86 & 76 & 12 & 48 & 18 \\ MY28 & 12 & 0.86 & 76 & 12 & 48 & 18 \\ Regional storm & 6 & 0.33 & 45 & 9 & 32 & 4 \\ No storm & 1.2 & 0.75 & 42 & 12 & 25 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for dust activity scenarios. Figure 4: Real and imaginary refractive indices for water ice and dust particles at frequencies in the far-infrared ranging from 1 to 10 THz. Figure 5A,B show dust absorptivity corresponding to the range of dust storm absorptivity can range from \(\sim\)0.001 dB/km to greater than 0.1 dB/km in the case of global dust storms. It shows a wide range encapsulating the S- and X-band absorptivities. Thus, it shows that the range of 1 to 10 THz frequencies provides enough dust absorptivity to be detected from the atmospheric losses during occultation.