## 5 Uncertainty Estimation
### Estimation of Model Parameters
When the SSA is 0.89 under NA conditions, the effect of surface reflectance on the surface reflectance is more significant. The effect of surface reflectance on the surface reflectance is more significant than the underestimation of surface reflectance. an overestimation of surface reflectance of 40% results in an SSA error of \(-0.033\), while a \(-40\%\) underestimation causes and SSA error of \(-0.005\). Figure 12: Retrieval error in **(a)** AOD, **(b)** SSA and **(c)** ALH (km) due to errors in surface reflectance for each aerosol type. Gray: HAF, pink: Dust and blue: NA. Errors are obtained by testing the algorithm with four LERs that are \(-40\%\), \(-20\%\), \(20\%\) and \(40\%\) from the true condition of \(0.06\). Each box-and-whisker plot for a given LER error condition shows the retrieval error distribution derived from the 108-member ensemble for AOD and SSA and 81-member ensemble for ALH. An underestimation of surface reflectance results in an overestimation of atmospheric scattering and thus leads to an underestimation of the shielding effect of aerosols. Therefore, an underestimation (overestimation) of surface reflectance results in an underestimation (overestimation) of ALH. However, under NA conditions the underestimation of molecular scattering due to an overestimation of surface reflectance results in an underestimation of ALH. The absolute ALH error caused by errors in surface reflectance ranges between \(-1.18\) and \(1.40\) km and the highest error was found for HAF aerosols. After correcting for measurement geometry in the measured spectrum, the most important parameter for simulating the TOA spectrum is the aerosol model chosen for the RTM simulation, which consists of the volume size distribution and indices of refraction. With respect to spectral variations in the simulated TOA reflectance, assumptions related to the wavelength dependence of the imaginary component of the refractive index play a crucial role [52]. This dependence leads to spectral variations in the Aerosol Absorbing Optical Depth (AAOD). A parameter which represents the slope of the AAOD-wavelength relationship in log space is commonly used to describe this spectral dependence [52] and is known as AAE. Numerous studies have investigated the AAE in the UV range for various aerosol types and the values 3.9 [39], 1.8 [40] and 0.0 [41] were adopted for HAF, dust and NA aerosols, respectively, in this study. The AAE affects simulations of the spectral variation of the backscattered radiance and the accuracy of the OE method by affecting a priori retrieval and spectral fitting. Errors in classifying aerosols by type lead to errors in AAE. For example, the classification of dust as HAF (NA) results in an overestimation (underestimation) of AAE. Figure 13 and Table 6 show the retrieval errors caused by incorrect aerosol classification. For this error analysis, the algorithm is forced to use an incorrect aerosol type by deactivating the aerosol type selection process. The effect of classification errors is more dramatic than that of surface reflectance errors. The median error in AOD for the reference condition of 1.5 reaches 5.51 when HAF aerosol is incorrectly classified as NA and the SSA error ranges from \(-0.040\) to 0.048 under various reference conditions. In terms of ALH, an overestimation of 3.9 km occurs at a reference condition of 1 km. As shown in Figure 3, the ratio between radiances at 354 and 388 nm decreases with increasing AOD and this decrease accelerates as AAE increases. Thus, the higher the AAE, the lower the AOD for a given radiance spectrum; i.e., \(\text{AOD}_{\text{NA}}\) > \(\text{AOD}_{\text{dust}}\) > \(\text{AOD}_{\text{HAF}}\). The radiance increases in the UV region due to increasing SSA becomes more dramatic as the AAE increases. This means that the SSA retrieved under the assumption of high AAE is larger than that for low AAE.