# 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
Concerning the relationship between the extinction coefficient and the wavelength, it appears that the extinction coefficient clearly depends on the wavelength. In particular, the extinction coefficient was higher for near-infrared wavelengths than for visible wavelengths, particularly for the densest fog (\(V<30\) m). The ratio can reach 1.5 for an MOR of 15 m. This means that dense fogs have a greater impact on the near-infrared than on the visible domain. For lighter fogs, the difference becomes smaller (ratio less than 1.25). As a reminder, by definition, the extinction coefficient is considered constant in the visible range (350 nm-800 nm) as the MOR is based on human perception [10], but the latter had a ratio of 1.30 on the curves. In the particular case of light advection fog (MOR higher than 100 m), a wavelengths above 2200 nm had a lower attenuation coefficient than the visible one: this was due to the fact that in this case, the drops were very small (lower than 1 ). The longer wavelengths were less affected, as previously shown in Figure 3a. Concerning the comparison between the two models + PSA measurements (Mie and MODTRAN), it can be said that the two models were quite similar. However, the MODTRAN model tended to underestimate globally slightly the extinction coefficient compared to the Mie model, except for the molecular scattering peaks. This was due to the assumption of multiple scattering made by MODTRAN (as opposed to the assumption of single scattering made by the Mie model) [5]. On the other hand, it was interesting to see that the complex MODTRAN model made it possible to highlight extinction peaks around the wavelengths of 1340 nm-1440 nm and 1910 nm-1950 nm. This was due to the molecular absorption of \(H_{2}O\), as we can see in Figure 10. Spectroradiometer measurements also showed the same instability in these areas. The latter had a much smaller amplitude than for MODTRAN + PSA measurements. However, this can be explained by the fact that the values were integrated over ranges of 10 nm in the case of the spectroradiometer. This result confirmed previous work [6]. Concerning the impact of the type of fog, it appears that advection and radiation fogs had exactly the same impact on light at any wavelength from 350 nm-1000 nm, for all MORs. This was in accordance with the literature, since whatever the type of fog, the definition of the extinction coefficient is the same. For the densest fogs (\(V<40\) m), the extinction was the same for both types (advection and radiation). This result was confirmed by the fact that the DSDs were similar for both types of fog below an MOR of 40 m, as shown in Figure 7. On the other hand, above 1000 nm, and for less dense fog (\(V>40\) m), the extinction coefficient was lower for radiation fog than for advection fog. Radiation fog produced in the PAVIN BP facility therefore had less impact on light than advection fog for wavelengths above 1000 nm. This can be explained by the presence of small fog droplets only (with a diameter of less than 1), which had little impact on the highest wavelengths. The results obtainedwith the spectroradiometer were then confirmed by the model + PSA measurements. The impact measured was around 10%.