## 4 Community Radiative Transfer Model (CRTM)
However, un-polarized natural light can be polarized by scattering from molecules, aerosols and clouds, and by the reflection and scattering from surfaces [24]. The polarization of light in the atmosphere-surface system contains important signals that have led to major scientific breakthroughs that could not have been achieved by only studying scalar radiance [25]. For example, the polarization measured by microwave sensors provides unique information to calculate the sea surface wind speed [26], sea surface wind vector [27], and sea ice [28]. The French satellite-based POLarization and Directionality of the Earth Reflectance (POLER) instrument has been used to obtain the particle shape of ice clouds [29]. In the CRTM version 3.0 beta, major work was conducted to extend the unpolarized treatment to a fully polarized treatment with an update to the radiative transfer solver and to add polarized atmospheric optical property calculations and surface emissivity/reflectance calculations. For the reasons of computational efficiency and easy software maintenance, we used a polarized radiative transfer form that holds the reciprocity principle [30]. With the reciprocity principle, we extended the CRTM Advanced Doubling-adding (ADA) algorithm to vectorized radiative transfer just by changing the dimension size from n_Angles to n_Angles x n_Stokes and saved about 50% in computational time in the radiative transfer solver. The extension of the CRTM AMOM is slightly more complicated [30]. For a scalar RT model, a single element of the phase matrix for intensity is sufficient, while all six independent elements in the phase matrix are required for a fully polarized RT model. In addition to the software changes, there is significant effort to generate aerosol and cloud optical look-up tables offline. The look-up tables contain the extinction scattering coefficients, six expansion coefficient sets for the Greek matrix used in fully polarized radiative transfer, and asymmetry factors. Backscattering coefficients are newly added for active sensor applications. The OpenMP function was also implemented so that one can perform parallel CRTM calculations either at a profile level or at a channel level. Solar irradiance is important to UV and visible radiance simulation, although normalized radiance and the N value (see Section 6) are independent from the solar irradiance. One can see from Equations (1) and (2) in [30] that the radiation source is linearly proportional to solar irradiance in the radiative transfer equation within the ultraviolet and visible spectrums, where the thermal emission is negligible. The radiance solution of the radiative transfer equation is linearly proportional to solar irradiance as well. To understand the physics behind this, one can imagine the atmosphere and surface systems as a black box and as having a boundary at the top of the atmosphere (e.g., Karman line at 100 km). The satellite measured UV and visible radiation are the reflected solar irradiance from the boundary, which is a linear product of solar irradiance and the reflectance at the boundary. The reflectance will not be changed because the solar radiation does not alternate the optical properties of the atmosphere and the surface during the very short period of time. Solar irradiance is also subject to non-local thermodynamic equilibrium (non-LTE) effects [31; 32]. It was found that below 210 nm, the non-LTE effects contribute significantly to the solar spectral irradiance (SSI) and SSI variability. However, above 210 nm, the non-LTE SSI variability from the non-LTE and LTE results are very similar, and the SSI difference between the LTE and non-LTE are very small (less than 1%) and should be understood as unimportant to our current study, which applies to OMPS Nadir Mapper wavelengths from 300-380 nm without considering the non-LTE effects. With the changes described above, CRTM version 3.0 therefore has a new capability for UV radiance simulation and assimilation.