A model for soil surface roughness influence on the spectral response of bare soils in the visible and near-infrared range

Abstract A mathematical model dealing with the influence of soil surface roughness on soil reflectance in the visible and near-infrared range is discussed. The model is based on the assumption that the reflectance from anisotropic rough soil surfaces is strongly correlated with the area of shadowed soil fragments, and therefore depends on the degree of soil roughness as well as on the illumination and the viewing geometry. A rough soil surface is simulated by equal-sized spheres arranged such that their centers form a square grid on a freely sloping plane. This model converts the bare soil reflectance data obtained for smooth samples into data relating to any natural rough surface states under conditions of unlimited illumination, which are defined by the solar altitude, the angle of a slope, and the sloping of the soil surface relating to the sunbeams direction. A simple parameter of the state of soil roughness expressing a proportion of the aggregates' and clods' area in top view in a given soil surface area is used here. The correctness of this model was evaluated on spectral data from 12 air-dried undisturbed soil samples obtained by means of a field spectrophotometer in outdoor conditions at solar altitudes from 31° to 59°. The measurements were taken for soil surfaces sloping at angles of 0°, 10°, 20°, and 30° forward and backward to the direction of sunbeams. Linear regression analysis indicates that for the studied spectral range the correlation coefficient of the relationship between all the 368 data point measured and calculated using this model reaches values of approximately 0.99. It has been found that relation between measured and predicted reflectance coefficient is similar for all the tested soils.