Reflection of visible light from a dense vegetation canopy—a physical model

Abstract Monitoring vegetation condition by remote sensing is made difficult by the variation of canopy brightness (radiance) with view direction and sun position. In this paper, we develop a physical model of canopy radiance that models this variation as a product of three functions, each being expressed as a simple analytical formula. The first function, the S function, represents the proportion of canopy seen as sunlit, excluding the hotspot. The second function, the hotspot function, corrects the S function for the higher probability of seeing sunlit leaves near the anti-solar point. The third function represents the average radiance of sunlit leaves. The model was fitted to densely-sampled, multi-view radiance measurements of pine forest ( Pinus radiata ) and pasture ( Lolium spp.), taken at a large (⋍ 60°) sun zenith angle. Radiance predictions for multiple views were then made for a small sun zenith angle (⋍ 20°). Comparison of predicted with measured radiances showed that the model out-performed the linear Roujean et al. model ( J. Geo. Res. , 97: 20,455–20,468) and the non-linear Verstraete et al. model ( J. Geo. Res. , 95: 11,755–11,765). The improvement is due to two factors: The hotspot function has a sun zenith angle dependence; and the S function allows the average projected leaf area to vary with off-nadir view angle.

[1]  A. Kuusk,et al.  A reflectance model for the homogeneous plant canopy and its inversion , 1989 .

[2]  B. Hapke.  Bidirectional reflectance spectroscopy: 4. The extinction coefficient and the opposition effect , 1986 .

[3]  A. Strahler,et al.  Geometric-Optical Modeling of a Conifer Forest Canopy , 1985, IEEE Transactions on Geoscience and Remote Sensing.

[4]  J. Otterman,et al.  Effects of leaf-transmittance versus leaf-reflectance on bidirectional scattering from canopy/soil surface: An analytical study , 1995 .

[5]  Robert J. Woodham,et al.  Photometric Method for Radiometric Correction of Multispectral Scanner Data , 1985 .

[6]  Donald W. Deering,et al.  A simple analytical function for bidirectional reflectance , 1992 .

[7]  G H Weiss,et al.  Reflection from a field of randomly located vertical protrusions: errata. , 1984, Applied optics.

[8]  B. Hapke.  Bidirectional reflectance spectroscopy: 1. Theory , 1981 .

[9]  J. Roujean,et al.  A bidirectional reflectance model of the Earth's surface for the correction of remote sensing data , 1992 .

[10]  B. Hapke.  Bidirectional reflectance spectroscopy , 1984 .

[11]  S. Idso,et al.  Light relations in plant canopies. , 1970, Applied optics.

[12]  B. Pinty,et al.  A physical model of the bidirectional reflectance of vegetation canopies , 1990 .

[13]  J. Dymond,et al.  Directional reflectance of vegetation measured by a calibrated digital camera. , 1997, Applied optics.

[14]  R. Myneni,et al.  A review on the theory of photon transport in leaf canopies , 1989 .

[15]  J. Ross.  The radiation regime and architecture of plant stands , 1981, Tasks for vegetation sciences 3.

[16]  H. Rahman,et al.  Coupled surface‐atmosphere reflectance (CSAR) model: 1. Model description and inversion on synthetic data , 1993 .

[17]  D. Kimes.  Dynamics of directional reflectance factor distributions for vegetation canopies. , 1983, Applied optics.

[18]  R. Myneni,et al.  Radiative transfer in vegetation canopies with anisotropic scattering , 1988 .

[19]  M. Minnaert.  The reciprocity principle in lunar photometry , 1941 .

[20]  B. Hapke.  A THEORETICAL PHOTOMETRIC FUNCTION FOR THE LUNAR SURFACE , 1963 .

[21]  D. Kimes.  Modeling the directional reflectance from complete homogeneous vegetation canopies with various leaf-orientation distributions , 1984 .

[22]  Philip Lewis,et al.  Topographic effects in AVHRR NDVI data , 1995 .

[23]  G. Campbell,et al.  Simple equation to approximate the bidirectional reflectance from vegetative canopies and bare soil surfaces. , 1985, Applied optics.

[24]  A. Kuusk.  A fast, invertible canopy reflectance model , 1995 .

[25]  W. Verhoef.  Light scattering by leaf layers with application to canopy reflectance modelling: The SAIL model , 1984 .

[26]  R. Myneni,et al.  A Three-Dimensional Radiative Transfer Method for Optical Remote Sensing of Vegetated Land Surfaces , 1991, [Proceedings] IGARSS'91 Remote Sensing: Global Monitoring for Earth Management.