# Light Transmission in Fog: The Influence of Wavelength on the Extinction Coefficient
## 4 Extinction Coefficient Results
### Analysis of the Extinction Coefficient as a Function of Wavelength  
The influence of wavelength on the extinction coefficient was examined by analyzing Figure 9, representing \(k(\lambda,V)\) as a function of \(\lambda\) for different MORs from 15 m up to 175 m. Each sub-figure of Figure 9 contains two graphs constructed from spectroradiometer measurements and the method proposed in the previous section: one corresponding to radiation fog (blue scatter-style crosses and circles) and the other corresponding to advection fog (red scatter-style crosses and circles) produced in the PAVIN BP facility. Two graphs were added to each sub-figure of Figure 9 from the data measured by the PSA for both types of fog (simple dashed line for the Mie model). The PSA data were pre-processed using the Mie formulas in Section 2.3. The Mie theory proposed in the previous section did not take into account molecular absorption and scattering or the phase function in the radiative transfer function. The data from the PSA were then also processed with MODTRAN to estimate the extinction coefficient with greater accuracy [9]. The corresponding two graphs were then added to each sub-figure of Figure 9 (continuous line for the MODTRAN model). For each of these, the reference extinction coefficient \(k_{ref}\) at \(\lambda=550\) nm was calculated from the MOR measured by the transmissometer, considered as a reference. This coefficient \(k_{ref}\) was used to normalize all the curves, in order to have the same extinction coefficient for 550 nm. This choice was made by MODTRAN and had the advantage of focusing more closely on the influence of wavelength, particularly for analyzing data from the PSA, without taking into account the total concentration of fog droplets. Many conclusions can be drawn from these graphs. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**MOR (m)**} & \multicolumn{5}{c}{**Radiation Fog**} & \multicolumn{5}{c}{**Advection Fog**} \\ \cline{2-10}  & \(\lambda\) & **360** & **550** & **1000** & **2000** & **2400** & **360** & **550** & **1000** & **2000** & **2400** \\ \hline
1  
Figure 9: Extinction coefficient (\(k\)) as a function of wavelength (\(\lambda\)) for different MORs (\(V\)). In all the sub-figures, the grid has constant steps of 0.01 m\({}^{-1}\). First of all, it can be noted that for both types of fog (advection and radiation), the spectroradiometer measurements (scatter-style crosses and circles) have the same behavior as the curves from the two models + PSA measurements (simple dashed line for the Mie model and continuous line for the MODTRAN model). This shows that the two methods and the sensors used agreed, showing differences in the extinction coefficient according to wavelength, MOR, and fog type. However, the model + PSA combination would tend to underestimate systematically the extinction coefficient compared to spectroradiometer measurement. This occurred especially for the densest fogs (\(V<100\) m). This may be due to the fact that the PSA would miss drops when confronted with extremely dense fogs. This was because the sensor performed filtering to prevent several drops from being counted at the same time. In the case of very dense fogs, these filters may have an impact on the measurement. Moreover, at wavelengths of 440-1600 nm and \(V<125\) m, the extinction coefficient from the spectroradiometer measurements varied more than the extinction coefficient from the two models + PSA measurements. The PSA may underestimate fog droplets with a diameter between 2 and 5 and overestimate droplets with a diameter higher than 5 (see Figure 3a). In the case of radiation fog (blue curves) and an MOR greater than 100 m, underestimation of the extinction coefficient by the model + PSA measurement may also result from the fact that the sensor cannot detect drops whose diameter is less than 0.3. Again, all the drops may not be counted.