## 6 Experimental OMPS Radiance Assimilation
The land surface reflectance is interpolated or extrapolated from the surface reflectance at 347.6 nm and 371.8 nm. The latter two reflectance are calculated by fitting OMPS NM measurements at the two wavelengths. The scalar model uses the same surface reflectance as Stokes. The modified scalar model uses the surface reflectance by fitting the measurements with the scalar model calculations at the two wavelengths. OMPS observations and the CRTM simulations for solar zenith angles less than 80 degrees. The CRTM radiative transfer model is a plane-parallel model that does not take the Earth's curvature into account. Therefore, for solar zenith angles larger than 80 degrees, the CRTM simulation is not accurate. The collocated ECMWF forecast and the OMPS NM global data between 03Z and 09Z on 2 March 2021 were used. Since the collocated data for aerosols and clouds are not available, we did not apply the data control except for in the condition where the relative difference between the OMPS observations and the CRTM simulations were within 10%. Applying the condition excludes 4% of the data. In Figure 7, the standard deviations vary from 1.0% to 2.6%. The averaged bias and standard deviation are 1.4% and 1.8%, respectively. Figure 6: \(N_{value}\) for OMPS NM measurements (red), CRTM simulation using a constant surface reflectance (black), and CRTM simulations using interpolated/extrapolated surface reflectance from the estimated reflectance at two wavelengths (cyan). In the following, we directly assimilate OMPS NM UV radiance. Due to the very limited computational resource, this radiance assimilation is based on a one-dimensional variation technique that is different from the three-dimensional variation algorithm used at NWP centers. This radiance assimilation technique is different from the MiRS retrieval algorithm. The similarity and difference among this algorithm, the MiRS retrieval algorithm, and three-dimensional radiance assimilation are given in Table 1. Figure 8 is the ECMWF global total ozone amount (DU) distribution from the 06Z analysis. The ozone amount in northern hemisphere is higher than that over southern hemisphere. The 6-h forecast is relatively close to analysis. The global mean difference and standard deviation between analysis and the 6-h forecast is about 0.22 DU and 3.60 DU, respectively (not shown). The difference for some small regions can be up to 50 DU. Our OMPS NM radiance assimilation slightly improves the ozone product. For the areas where the OMPS NM covers and the solar zenith angles are less than 80 degrees, our OMPS NM radiance assimilation  
Figure 7: Comparison of the normalized radiance between OMPS NM measurements and the CRTM simulations. The data for solar zenith angles less than 80 degrees are used. The surface reflectance is either interpolated or extrapolated using two reflectance by fitting normalized radiances at 347.6 nm and 371.8 nm. slightly improves the ozone product. For example, the bias and standard deviation between the ECMWF analysis and our OMPS NM radiance assimilation at 06Z 2 March 2021 are 0.286 and 5.262 DU, respectively (not shown), while the bias and standard deviation between the ECMWF analysis and the ECMWF 6-h forecast for those radiance assimilated data points are 0.348 and 5.269 DU, respectively. The standard deviation improvement from our radiance assimilation is quite small. Nevertheless, the result is encouraging for a first demonstration of ultraviolet radiance assimilation. To look at the differences on a global map, one can look into the differences between two absolute differences: the absolute difference between the ECMWF ozone analysis and the ECMWF 6-h forecast and the absolute difference between the ECMWF ozone analysis and our OMPS NP radiance assimilation:  
\[\Delta O_{3}=|O_{3}(analysis)-O_{3}(6h\ forecast)|-|O_{3}(analysis)-O_{3}(OMPS \ radiance)| \tag{10}\]  
Equation (10) is often used in data analysis.