Development of An Improved BRDF Hotspot Model and its Use in VLIDORT to Study the Impact of Atmospheric Scattering on Hotspot Directional Signatures in the Atmosphere
The term “hotspot” refers to the sharp increase of reflectance occurring when incident (solar) and reflected (viewing) directions almost coincide in the backscatter direction. The accurate simulation of hotspot directional signatures is important for many remote sensing applications. The RossThick-LiSparse-Reciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model is widely used in radiative transfer simulations, and the hotspot model mostly used is from Maignan- Bréon but it typically requires large values of numerical quadrature and Fourier expansion terms in order to represent the hotspot accurately. To improve its use in atmospheric radiative transfer (RT) model simulations, in this paper we have developed a modified version based on the Maignan-Bréon’s hotspot BRDF model that converge much faster numerically, making it more practical for use in RT models that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures. Using the vector linearized discrete ordinate radiative transfer model (VLIDORT), we found that reasonable TOA hotspot accuracy can be obtained with just 23 Fourier terms for clear atmospheres, and 63 Fourier terms for atmospheres with aerosol scattering. One advantage of this modified model is that the new hotspot model agrees very well with the original RossThick model away the hotspot region, making it is very convenient to use in the condition with and without hotspot in applications. This model can calculate the amplitude of hot spot accurately, and has been added in the most recent version of VLIDORT. However, there are some difference of this modified model with the original model for scattering angle close the hot spot, and it may not be appropriate for those who need an exact representation of the hot spot angular signature close to hot spot.