An optimal estimation based aerosol retrieval algorithm using OMI near-UV observations

An optimal estimation (OE) based aerosol retrieval algorithm using the OMI (Ozone Monitoring Instrument) near-ultraviolet observation was developed in this study. The OE-based algorithm has the merit of providing useful estimates of errors simultaneously with the inversion products. Furthermore, instead of using the traditional look-up tables for inversion, it performs online radiative transfer calculations with the Vector Linearized Discrete Ordinate Radiative Transfer (VLIDORT) model to eliminate interpolation errors and improve stability. The measurements and inversion products of the Distributed Regional Aerosol Gridded Observation Network campaign in Northeast Asia (DRAGON NE-Asia 2012) were used to validate the retrieved AOT and SSA. The retrieved AOT and SSA at 388 nm have a correlation with the Aerosol Robotic Network (AERONET) products that is comparable to or better than the correlation with the operational product during the campaign. The OE-based estimated error better represented the variance of actual biases of AOT at 388 nm between the retrieval and AERONET measurements than the operational error estimates. The forward model parameter errors were analyzed separately for both AOT and SSA retrievals. The surface reflectance at 388 nm, the imaginary part of the refractive index at 354 nm, and the number fine mode fraction (FMF) were found to be the most important parameters affecting the retrieval accuracy of AOT, while FMF was the most important parameter for the SSA retrieval. The additional information provided with the retrievals, including the estimated error and degrees of freedom, is expected to be valuable for relevant studies. Detailed advantages of using the OE method were described and discussed in this paper.

0.5 over the oceans. This modification eliminates the land-ocean discontinuity in UVAI threshold. It 125 is now identical (0.5) for both conditions. The current characterization of ocean reflective properties 126 in the OMAERUV algorithm does not explicitly account for ocean color effects and, therefore, the 127 quality of the retrieved aerosol properties over the oceans for low aerosol amounts would be highly 128 uncertain. For that reason, retrievals over the oceans are only carried out for high concentrations of 129 either desert dust or carbonaceous aerosols as indicated by UVAI values larger than or equal to 0.5. 130 Depending on the magnitude of the UVAI and CO parameters as well as the aerosol type, 131 two retrieval approaches are currently used. They are referred to as two-channel and single-channel 132 retrievals. In the two-channel approach, observations at 354 and 388 nm are used to simultaneously 133 derive AOD and SSA. Over scenes when the aerosol absorption signal is low, the single-channel 134 retrieval is applied. AOD is retrieved from the 388 nm observation assuming a value of 1.0 for SSA. 135 Different CO threshold values are used for the northern and southern hemispheres to remove upper 136 tropospheric CO which may not be necessarily associated with carbonaceous aerosols. A smoothing 137 function in CO is used to transition from SH to NH threshold values. Specific criteria for retrieval 138 approaches are summarized in Table 3 143 The traditional LUT-based inversion method potentially includes errors due to interpolation 144 between the nodal points and the local minimum, despite its high numerical efficiency. Such 145 interpolation error typically depends on the interpolation method, number of the nodal points, and 146 analytic characteristics of the parameters in LUT. In order to reduce the interpolation error, higher 147 resolution of LUT nodal points is necessary which requires larger amount of numerical computation. 148 Furthermore, in order to modify the retrieval algorithm, whole LUT should be re-calculated even for a few number of target retrievals. The errors from the interpolation are also hard to evaluate as 150 the LUT becomes more complicated. 151 On the contrary, online retrieval methods can reduce such errors from the interpolation and 152 are numerically efficient particularly for the smaller number of target retrievals. Thus, online 153 retrieval method is appropriate for the research purposes since retrieval sensitivity study typically 154 use smaller number of sample compared to the operational purposes and prefer rapid and accurate 155 results. In our experience, the online retrieval method was numerically more efficient compared to 156 the LUT-based retrieval method by order of 1 or 2 for less than few thousands of retrievals.

OE-based OMI near UV aerosol algorithm
157 Furthermore, the online retrieval methods are optimized to avoid local minima by employing 158 additional constraints to find more reliable and stable solutions (Kalman, 1960;Phillips, 159 1962;Tikhonov, 1963; Twomey, 1963;Chahine, 1968 using two different measurement matrices are compared in Table 4.

310
The dust event on 28 th April 2012 has been selected to compare the aerosol optical 311 properties from the operational product with the OE-based retrievals in this study. Figure 3 shows and operational algorithm were similar (63.0%). When a measured radiance is affected by 346 parameters that the theoretical radiative transfer model does not consider (e.g., sub-pixel cloud 347 contamination), the χ of the retrieval typically has a high value. In this study, retrievals with χ larger 348 than a certain value (i.e., 2.0 in this study) have been rejected. This limitation on retrievals imposed by the χ reduced the number of retrievals with abnormally high biases, which might be associated 350 with sub-pixel cloud contamination, in the operational algorithm in Figure 6 (a).

351
The SSA values at 388 nm from OMI operational products and OE-based inversion 64.8% and 65.9%, respectively. The Q sol was higher than Q omi despite of the lower mean value of (0.20) than that of (0.21). The error bars and black squares in Figure 8 represent the 375 moving σ and average value of the retrieval biases from AERONET as a function of estimated error, 376 respectively. As shown in Figure 8   there may still be ground pixels contaminated by sub-pixel clouds. As the TOA reflectance is  Table 5) is much lower than the difference between the FMFs of dust type and other aerosols 422 (~0.004, see Table 2), the errors resulting from selection of the wrong aerosol type can be more 423 significant. The estimated of the surface reflectance at 388 nm was higher than the previously

451
An OE-based aerosol retrieval and error characterization algorithm using the OMI near-UV  Basis Documents) and this study.    parameters for n r and n i were obtained from 440 nm AERONET inversion products.    show the degrees of freedom and cost function of the retrieval, respectively.