An improved BRDF hotspot model and its use in VLIDORT for studying the impact of atmospheric scattering on hotspot directional signatures in the atmosphere

Abstract

Abstract. The term “hotspot” refers to the sharp increase in the 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 for its use coupled with atmospheric radiative transfer modeling (RTM). In this paper, we have developed a modified version based on the Maignan–Bréon's hotspot BRDF model that converges much faster numerically, making it more practical for use in the RTMs that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures, such as in the RTM models using the Doubling–Adding or discrete ordinate method. 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 atmosphere and 63 Fourier terms for atmosphere with aerosol scattering. In order to study the impact of molecular and aerosol scattering on hotspot signatures, we carried out a number of hotspot signature simulations with VLIDORT. We confirmed that (1) atmospheric molecule scattering and the existence of aerosol tend to smooth out the hotspot signature at the TOA and that (2) the hotspot signature at the TOA in the near-infrared is larger than in the visible, and its impact by surface reflectance is more significant. As the hotspot amplitude at the TOA with aerosol scattering included is smaller than that with molecular scattering only, the amplitude of hotspot signature at the surface is likely underestimated in the previous analysis based on the POLDER measurements, where the atmospheric correction was based on a single-scatter Rayleigh-only calculation. This modified model can calculate the amplitude of the hotspot accurately, and, as it agrees very well with the original RossThick model away from the hotspot region, this model can be simply used in conditions with and without hotspots. However, there are some differences in this modified model compared to the original Maignan–Bréon model for the scattering angles close to the hotspot point; thus, it may not be appropriate for those who need an exact representation of the hotspot angular signature.