Application of Characteristic Vector Analysis to the Spectral Energy Distribution of Daylight and the Spectral Reflectance of American Soils

Abstract

Measurements have been made of the spectral energy distribution of daylight (sunlight plus skylight) and skylight in the near-uv and visible region of the spectrum as a function of solar altitude for various atmospheric conditions as measured on planes of different orientation. A characteristic vector analysis was made of the digitized data. From these data, a variance-covariance matrix was computed for the daylight energy data and another for the skylight energy data. The four vectors were capable of accounting for 98.2% of the trace of the variance-covariance matrix for daylight and 99.4% for the skylight data. Spectral reflectances extending from 320 nm to 1000 nm have been obtained for 160 soil samples collected from thirty-six states. Measurements were made of both wet and dry samples, which vary widely in color and reflectance. An examination of the 160 sets of curves indicates that they can be classified into three general types with respect to their curve shapes. A characteristic vector analysis was made of the spectral reflectance data; it showed that by linear combinations of four vectors and the mean curve, each set of data could be reconstituted to a high degree of accuracy (99.9% of the trace). Empirical regression equations have been derived that relate spectral reflectance data at thirty-five wavelengths spaced at 20-nm increments to measurements made at only five specially selected wavelengths. To the extent that soils may be identified by their reflectance characteristics, this abridged technique seems to have sufficient accuracy for the 160 samples that have been measured.