# MODIS Retrieval of Aerosol Optical Depth over Turboid Coastal Water
## 3 Retrieval Algorithm  
### Retrieval Principal and Sensitivity Analysis  
Like the existing DT algorithm, our new algorithm is based on a lookup table (LUT) approach, meaning that it is attempting to match simulated TOA reflectance to the observed TOA reflectance. The best-match solution represents the AOD and other properties of the aerosol. Over the open ocean, the atmospheric signal tends to dominate that of clear water. Near coastlines, however, sediments and turbid waters can dominate the signal, making aerosol retrieval impossible. However, in longer wavelengths, such as 2.1 um (at which the imaginary part of refractive index for liquid water is several of magnitude larger than that in the visible), the penetration depth is so small, that contribution from the water should be nearly negligible.  
To test this assumption, we compare the sensor sensitivity at 2.1 um at which water-leaving radiance is negligible regardless of water turbidity with that at shorter wavelength which has large water-leaving radiance over turbid coastal water (taking 0.65 um as an example). Figure 2 shows 2.1 um TOA reflectance has better sensitivity to aerosol than 0.65 um in both fine and coarse mode aerosol situations when 0.65 um surface reflectance is large (turboid coastal water). When AOD is small (less than 0.15 at 0.55 um, Figure 2b), the TOA reflectance (Figure 2c,d) is nearly the surface reflectance. Surface reflectance of turbid coastal water is up to 0.4 at 0.65 um (Figure 2c) while it is very small (less than 0.0035) at 2.1 um (Figure 2d). Figure 2e-h present a simulation of TOA reflectance through UNL-VRTM model [17] with various surface reflectances in fine aerosol (average TOA reflectance of the four fine aerosol modes defined in the DT-ocean LUT) and coarse aerosol (average TOA reflectance of the coarse aerosol modes defined in the DT-ocean LUT) situations. In a fine aerosol situation, 0.65 um TOA reflectance is an increasing function of AOD when surface reflectance is small (0.03, clear water) (Figure 2e). However, it first decreases and then increases slowly when surface reflectance is large (0.3 or 0.4, turbid coastal water) (Figure 2e). The gradient of 2.1 um MODIS digital signal (defined as change of MODIS digital count, \(dn**\), with respect to 0.55 um AOD, or \(\partial(dn**)_{2.1}/\partial(AOD)_{0.55}\)) is \(\sim\)25 regardless of AOD values (Figure 2j) while \(\partial(dn**)_{0.65}/\partial(AOD)_{0.55}\) is smaller than 25 when AOD is less than 0.5 (1.2) and surface reflectance is 0.3 (0.4). This means that it is better to use TOA reflectance at 2.1 um rather than 0.65 um to retrieve fine AOD in turbid coastal water situation. Additionally, while the sensitivity of digital signal at 2.1 um to the AOD change is a factor of 3-8 smaller than the counterpart at 0.65 um (e.g., contrasts of blue lines between Figure 2 ij) in the clear water situation, 2.1 um still has significant sensitivity to the change of fine-mode AOD, and its detection limit for fine-mode AOD is \(\sim\)0.04 (i.e., the inverse of \(\partial(dn**)_{2.1}/\partial(AOD)_{0.55}\)). The reason that 2.1 um still has reasonably good sensitivity for fine-mode aerosols is because the ocean surface is nearly black at 2.1 um, albeit fine aerosol extinction decrease significantly.  
In a coarse aerosol situation, \(\partial(dn**)_{0.65}/\partial(AOD)_{0.55}\) is similar to that in a fine aerosol situation and is a little smaller than \(\partial(dn**)_{2.1}/\partial(AOD)_{0.55}\) when 0.65 um surface reflectance is small (Figure 2k,l). However, \(\partial(dn**)_{0.65}/\partial(AOD)_{0.55}\) is a factor of 6-10 smaller than \(\partial(dn**)_{2.1}/\partial(AOD)_{0.55}\) when water is turbid (e.g., contrast of red/green curves between Figure 2k,l). Overall, over turbid water, it is better to use TOA reflectance at 2.1 um rather than 0.65 um to retrieve AOD, regardless of whether fine or coarse mode dominates. In other words, 2.1 um should be used to retrieve coarse-mode AOD regardless of water turbidity.