Circumsolar LUT

The spectral circumsolar normal irradiance ($\text{CSNI}_{\lambda}$) is the spectrally resolved diffuse contribution to the solar beam. This component consists of all scattered photons, including those travelling along the direct beam after multiple scattering events, in the angular vincinity of $\pm \alpha_{0}$ about the non-scattered direct normal beam ($\text{DNI}_{\lambda}^{strict}$). Here, the direct normal direction is indicated by the red dashed line, and the boundaries of $\pm \alpha_{0}$ are indicated by the red solid line.

$\text{CSNI}_{\lambda} = \int_{2\alpha_{0}}\int_{2\alpha_{0}} F_{\lambda}(\Omega) cos(\theta - \theta_{z}) sin(\theta)d \theta d \phi \; \; \; \; \text{ and } \; \; \; \; \text{CSR}_{\lambda}=\frac{\text{CSNI}_{\lambda}}{\text{CSNI}_{\lambda}+\text{DNI}_{\lambda}^{strict}} $

where $F_{\lambda}(\Omega)$ is the diffuse radiance, $\alpha_{0}$ is the aperture half angle of the viewing instrument and $\theta_{z}$ is the solar zenith angle. $\text{CSR}_{\lambda}$ is the circumsolar ratio, which quantifies the contribution of the CSNI to the total direct normal beam. This CSNI lookup table has been precomputed using DISORT with LibRadtran running at 32 streams under a stanrdard 'afglms' atmosphere. $\text{CSNI}_{\lambda}$ has been parameterised with solar zenith angle (SZA), aerosol optical depth at 500nm (AOD) and seven of the OPAC aerosol types.