## 3 Algorithm Description
### Comparison with CALIOP ALH  
The median value of the retrieved ALH in Figure 7c is located at 0.889 km and 45.36% of the data points are lower than 1.0 km. The ALH in high AOD regions is generally higher than other regions. However, similarly high values are found over the ocean in the southern part of the Korean Peninsula and Japan, because weak aerosol attenuation increases the uncertainty in SSA and thus ALH retrieval. As the ALH of the operational OMI near-UV algorithm is defined according to aerosol type and location, the results are not compared quantitatively. Instead, the results are compared with the heights (Z\({}_{\text{aer}}\)) derived from CALIOP measurements.  
Figure 8 shows the difference between retrieved ALH from the current algorithm using OMI and the estimated \(Z_{\text{aer}}\) from CALIOP (retrieved ALH \(-\)\(Z_{\text{aer}}\)) from March to May 2007. In this comparison, the ALH products were collocated within a 0.5\({}^{\circ}\)\(\times\) 0.5\({}^{\circ}\) range around a CALIOP pixel when the temporal difference between the two measurements was shorter than 30 min. Then, the average value of the collocated dataset was compared with the \(Z_{\text{aer}}\) value from the CALIOP lv2 backscatter coefficient if the standard deviation of the dataset was lower than 50% of the average value.  
Figure 8: Difference between ALH retrieved from the developed algorithm and the attenuated-backscatter-weighted height estimated from the CALIOP 1064 nm product for the period from March to May 2007. The difference values are sorted by (**a**) AOD and (**b**) SSA and the bottom panel only includes values for AOD \(>\) 0.8. Standard deviations of the values sorted by each bin are shown by vertical and horizontal bars. Colors indicate mean (**a**) SSA and (**b**) AOD for each bin.  
In Figure 8a, the differences and retrieved SSA are sorted according to retrieved AOD and divided so as to have the same number of data points in each bin. While mean ALH difference and its standard deviation are represented by symbols and error bars, respectively, the mean SSA is shown by color. The horizontal error bar represents standard deviation of AOD for each bin. The 'binsize' in Figure 8 shows the number of data points in each bin. As shown in Figure 8a, the retrieval error in ALH decreased as the AOD increased from 0.0 to about 0.8, because the contribution of ALH to the normalized radiance increases with aerosol extinction. When the AOD is between 0.8 and 2.0, the mean difference between the ALH and CALIOP \(\text{Z}_{\text{aer}}\) is close to 0.0 km with a standard deviation of about 1.0 km. However, the ALH error increases negatively with increasing AOD in the high-AOD range. It should be noted that data points in the high-AOD bin may be affected by cloud contamination, contributing to the high mean value. In this case, \(\text{Z}_{\text{aer}}\) would be overestimated due to the increase in the backscatter coefficient from high cloud layers and ALH would be underestimated because of the underestimated radiative absorption of aerosols. The high SSA of 0.96 for the highest AOD bin suggests frequent cloud contamination.  
Based on results shown in Figure 8a, the dependence of ALH error on SSA was analyzed for conditions with AOD higher than 0.8 to investigate the sensitivity of ALH retrieval errors to SSA without interference from other retrieval uncertainties. The SSA dependence results are shown in Figure 8b. In this figure, color represents the mean AOD for each bin sorted according to the retrieved SSA. Because of the AOD threshold, the number of data points was reduced from 2806 to 615 and thus the bin size was decreased to 24. Although ALH retrieval error increased with decreasing AOD, the error decreased with decreasing SSA. The maximum error was found for the highest AOD (2.48).