## 7 Conclusions  
This study is the first experiment to assimilate ultraviolet radiances for ozone amount analysis in the troposphere and stratosphere. The initial result is encouraging, although the improvement in the atmospheric ozone is small. The assimilation experiments were accomplished through several developments:  
* Through this study, we found that assimilating the \(N_{value}\) can overcome the difficulty of handling the large dynamic range of the normalized radiance (see Figures 4 and 6). The definition of the \(N_{value}\) is given in Equation (8), which is the logarithm (base 10) of the normalized radiance. The Jacobian of the \(N_{value}\) can be calculated from Equation (9). * Specifying an accurate surface reflectance is the most challenging aspect of the problem. The reflectance depends on many variables such as the surface type, surface roughness, sensor and solar zenith, and azimuth angles, with the coarse spatial resolution of the measurements (50 by 50 km\({}^{2}\)) contributing to sub-FOV inhomogeneity. In addition, the bias correction is more challenging than the bias correction in assimilating microwave and infrared measurements. In this study, the bias correction is mitigated in the treatment of surface reflectance. Since the assumption of a single constant surface reflectance is not accurate for the radiance simulation over longer wavelengths (see Figure 4), we propose using two estimated surface reflectance by fitting OMPS normalized channel radiances at 347.6 and 371.8 nm. The normalized channel radiances at 347.6 and 371.8 nm do not have significant sensitivity on at  
Figure 9: The total ozone amount in Dobson Unit difference between the two absolute differences (see Equation (10)). Ana represents the ECMWF analysis and 6 hF is the ECMWF 6-h forecast. “New” is the OMPS NM radiance assimilation. The unit is the Dobson Unit. mospheric ozone (see Equation (4)). By assuming that the instantaneous surface reflectance changes linearly with wavelength, the spectral surface reflectance at 331 nm can be calculated from these two estimated surface reflectance values. This approach mitigates the uncertainty due to unknown surface reflectance and the bias between the measurements and simulations. This approach can also mitigate errors by using scalar radiative transfer calculations. * To date, the CRTM model has not had the capability of simulating either fully polarized or scalar ultraviolet radiances. In this work we have extended the capability to simulate and assimilate ultraviolet radiances and have treated the radiances as scalar measurements for computational reasons. Fully polarized radiance calculations require more than 20 times the CPU time than the scalar radiance assimilation. In a fully polarized calculation for the four components of the Stokes vector, all of matrices are expanded by a factor of 4 by 4; therefore, the matrix inversion requires more than 16 times the computational resources compared with the scalar representation. Other aspects to be considered:
* As part of the enhancements to CRTM allowing for both the scalar and polarized treatment of ultraviolet radiances, CRTM 3.0 will allow users to load cloud and aerosol optical look-up tables in either the current binary format or in the netCDF format. In addition to the current operational GOCART global aerosol modeling, Community Multi-scale Air Quality (CMAQ), which is more focused on regional applications, is also included in the CRTM. The openMP function is implemented in the CRTM as well. Users can simulate radiances using parallel computations at the atmosphere profile level or at the sensor channel level. However, as noted above, the computational requirements for fully polarized calculations are considerably larger than those for scalar calculations. The result of this experimental OMPS NM radiance assimilation shows that the error in bias correction, surface reflectance, and neglecting polarization in radiative transfer calculations are largely mitigated by using the two estimated surface reflectance values.