# MODIS Retrieval of Aerosol Optical Depth over Turboid Coastal Water
## 3 Retrieval Algorithm
### Algorithm Implementation and Steps  
The retrieval algorithm is designed to supplement the existing DT algorithm. Hence, the lookup table (LUT) from the MODIS DT-ocean AOD retrieval algorithm is also used here [4; 9]. That LUT is created by using [PERSON]'s [18] radiative transfer code, assuming aerosol optical properties from four \"fine\" (effective radius \(<1\) um) and five \"coarse\" (effective radius \(>1\) um) lognormal mode. The fine modes include two water-insoluble and two soluble modes, whereas the coarse modes are separated into three soluble sea-salt like, and two insoluble dust-like modes ([[http://darktarget.gsfc.nasa.gov/algorithm/ocean/aerosol-models](http://darktarget.gsfc.nasa.gov/algorithm/ocean/aerosol-models)]([http://darktarget.gsfc.nasa.gov/algorithm/ocean/aerosol-models](http://darktarget.gsfc.nasa.gov/algorithm/ocean/aerosol-models))). This LUT is defined at various 0.55 um AOD values in the range of 0 to 3 and at different Sun-Earth-satellite geometries [4; 9]. Furthermore, as water surface reflectance depends on surface wind speed, the LUT is constructed at four wind speeds, specifically 2 m s\({}^{-1}\), 6 m s\({}^{-1}\), 10 m s\({}^{-1}\), and 14 m s\({}^{-1}\). Like the DT algorithm, combination of a fine mode and a coarse mode is required for AOD retrieval. In the retrieval procedure, MxD02 TOA reflectance at 2.1 um is used to fit the corresponding LUT value \(\rho_{2.1}^{\text{LUT}}\big{(}\tau_{0.55}^{tot}\big{)}\) which is a weighted sum of pure fine mode LUT value \(\rho_{2.1}^{\text{f}}\big{(}\tau_{0.55}^{tot}\big{)}\) and pure coarse mode LUT \(\rho_{2.1}^{\text{c}}\big{(}\tau_{0.55}^{tot}\big{)}\) at a given 0.55 um AOD value \(\tau_{0.55}^{tot}\). \[\rho_{2.1}^{\text{LUT}}\big{(}\tau_{0.55}^{tot}\big{)}=\eta\rho_{2.1}^{\text{ f}}\big{(}\tau_{0.55}^{tot}\big{)}+(1-\eta)\rho_{2.1}^{\text{c}}\big{(}\tau_{0.55}^{tot} \big{)} \tag{1}\]  
The value of reflectance weighting parameter \(\eta\) equals the fraction of total AOD at 0.55 um contributed by the fine mode [9]. In addition, the LUT is calculated under the assumption of \"gas free\" (gas absorption is not included), thus correction [4] of MxD02 TOA reflectance is required to match the LUT before retrieving AOD. Figure 2: (**a–d**) are MODIS Aqua true color image, 0.55 μm AOD, 0.65 μm TOA reflectance, and 2.1 μm TOA reflectance at Bohai Sea, China on 23 February 2017, respectively. Red box is the region where water is turbid and atmosphere is clean. (**e,f**) are simulation (solar zenith angle is 24\({}^{\circ}\), view zenith angle 54\({}^{\circ}\), and relative azimuth angle 60\({}^{\circ}\)) of 0.65 μm and 2.1 μm TOA reflectance with fine aerosol model, respectively. (**g,h**) are similar to (**e,f**) but for coarse aerosol model. (**i,j**) are gradient of 0.65 μm and 2.1 μm MODIS digital signal (dn**) with respect to 0.55 μm AOD with fine aerosol model. (**k,l**) are similar to (**i,j**) but for coarse aerosol model. Values in the legends are surface reflectance used to simulate TOA reflectance at corresponding wavelength. Figure 3 shows the steps of our algorithm to retrieve AOD over coastal water, and hereafter, we call this algorithm the Coastal Water (CW) algorithm. Each step of CW is described below with a note that these steps essentially follow DT-Ocean algorithm except CW uses the 2.1 \(\upmu\)m to retrieve AOD for those cloud-free turbid coastal water scenes. Hence, for each valid cloud-free turbid coastal water scene (i.e., a box of 20 \(\times\) 20 pixels at 500 m resolution or at 10 km resolution at nadir, as available in the standard MODIS aerosol product), the following steps are implemented. 1. Collect and organize 20 \(\times\) 20 pixels at 500 m resolution, remove pixels that are defined by land/sea mask as \"land\", designated by ice/snow mask to be \"ice\", designated by the cloud mask to be \"cloud\", or removed by other tests. 2. Discard the brightest 25% and darkest 25% pixels defined with 0.86 \(\upmu\)m reflectance. 3.