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A GEOMETRICAL MODEL OF SOIL BIDIRECTIONAL REFLECTANCE IN THE 
VISIBLE AND NEAR-INFRARED RANGE 
J. CIERNIEWSK1 
Adam Mickiewicz University, Institute of Physical Geography, Frediy 1, 61-701 Poznan (Poland) 
M. VERBRUGGHE 
I.N.R.A. Bioclimatologie, B.P. 91, 84143 Montfavet Cedex (France) 
ABSTRACT: 
A model dealing with the influence of soil surface roughness, solar illumination and the viewing of soil surface 
on soil reflectance in the visible and reflective near-infrared range along the solar principal plane is discussed. 
The model is based on the assumption that the reflectance from anisotropic rough soil surfaces is strongly 
correlated with the area of sunlit soil surface being essentialy reduced by the area of shaded soil fragments. 
Wave energy leaving the sunlit soil fragments is directly proportional to the energy coming to them, i.e., it 
depends on the incidence angle of the sunbeams directly illuminating these fragments. Spheroids, 
characterized by their horizontal and vertical radii, lying on an horizontal surface at a given distance, simulate 
the soil surface. The model was tested using soil bidirectional reflectance data acquired on a bare field of an 
alluvial plain covered by regularly spread pebbles. The spectral data were measured by a three-channel field 
radiometer CIMEL simulating the SPOT (HRV) bands. The regression analysis was performed separately for 
the three channels using 169 pairs of data for 15 solar zenith angles (SZA) varied from 25° to 66°. The relative 
reflectance factor may be predicted with a mean deviation from the measured reflectance data lower than 0.09 
for the SZA lower than 50° and lower than 0.14 for the SZA higher than 50°. 
KEY WORDS: Geometrical model, Bidirectional soil reflectance,Visible and Near-infrared range 
1. INTRODUCTION 
Remotely sensed data on soil surfaces like vegetation canopies have non-Lambertian reflectance properties. 
Rough soil surfaces usually display variations in brightness due to the direction of irradiation and also the 
direction along which reflection is observed. A soil surface seems to be the brightest from the direction which 
give the lowest proportion of shaded fragments. The scattering properties of bare soil, showing a backscatter 
reflectance peak towards the position of the sun, are displayed by field reflectance measurements of bare soils 
taken by Kimes and Sellers (1985). Milton and Webb (1987) present the results of ground measurements of 
ploughed bare soils, clearly indicating the angular asymmetry of reflectance around the nadir. The reflectance 
of the soils increases with the increase in the view zenith angle if the sensor was directed towards the solar 
beam. The peak of backscatter radiation become less pronounced at a low solar zenith angle. Deering et al. 
(1990) have supplied evidence that soil reflectance could clearly have both a backscatter and a forwardscatter 
character. They demonstrated it on an example of bidirectional reflectance data of an alkali flat bare soil and a 
dune sand flat surface with uniform ripples and composed of nearly pure gypsum crystals. 
Soil reflectance generated by most of the existing models characterizing minimum 
shadowing from anti-solar directions has shown a strong backscattering regime. Otterman and Weiss's model 
(1984) treats soils as a field of randomly located thin vertical cylinders, illuminated by a direct solar beam. The 
model of Norman et al. (1985) was developed on the assumption that the shadowing of larger soil particles or 
a ggregates, simulated by cuboids, had a stronger influence on the soil reflectance distribution than scattering 
properties of bare soil particles of silt and clay. The smaller the shadowing, the higher the reflectance of the 
modeled surface. The Monte Carlo reflectance model of soil surfaces, created by Cooper and Smith (1985), 
assumes that the soil is a perfect diffuse scatterer at a microscopic level. The probability that a photon will be 
scattered at a given angle depends only on the orientation of the micro soil surface. Hapke's model, used by 
Pinty et al. (1989) for modeling soil reflectance, describes a soil surface as a substrate composed of particles 
which multiply scatter solar radiation of an isotropic character. Simple soil surface roughness parameters are 
replaced here by five others connected with the physical principles of reflectance. Jacquemoud et al. (1992), 
using the radiative transfer model based on the same model of Hapke, found that the single scattering albedo is 
only dependent on wavelength. The roughness parameter belongs to wavelength-independent parameters. The 
model of Irons et al. (1992) describes soil surfaces as uniform opaque spheres regularly spaced on a horizontal