U.S. Department of Agriculture: Agricultural Research Service, Lincoln, Nebraska


Document Type


Date of this Version



Agronomy Journal Volume 102, Issue 3, 2010, pp. 942-955, doi:10.2134/agronj2009.0393.


U.S. government work.


Th is article describes a geometric model for computing the relative proportion of sunlit vegetation, shaded vegetation, sunlit soil, and shaded soil appearing in a circular or elliptical radiometer footprint for row crops, where the crop rows were modeled as continuous ellipses. Th e model was validated using digital photographs of row crops, where each component was determined by supervised classification. Root mean squared errors (RMSE) between modeled and observed components were 35, 49, 29, and 44% of observed means for sunlit vegetation, shaded vegetation, sunlit soil, and shaded soil, respectively. Mean bias errors (MBE) were, respectively, –5.6, 16.6, –4.0, and –0.5% of observed means. Th e continuous ellipse model was compared to the commonly used clumping index model, where the latter estimates total vegetation and total soil, but does not resolve these into their sunlit or shaded components and does not account for radiometer footprint shape dimensions. Th e continuous ellipse model resulted in RMSE for vegetation and soil of 22 and 19%, respectively, whereas the clumping index model resulted in respective RMSE of 37 and 31%. Th e continuous ellipse model had MBE of 3.3 and –2.6% for vegetation and soil, respectively, which was slightly greater than the respective MBE of –1.5 and 1.4% for clumping index model. Given the model sensitivity and uncertainty of leaf area index (LAI), the RMSE and MBE resulting from the continuous ellipse model would not be expected to be less than 20% of the observed means, and model performance was therefore deemed reasonable in this study.