Arthur J. Richardson

Interaction of Light with a Plant Canopy

The Kubelka–Munk (K–M) theory has been applied to light interaction with leaves stacked in a laboratory spectrophotometer. The theory can also be applied to an actual field plant canopy. The K–M theory is a two-parameter generalization of the one-parameter Bouguer–Lambert, or Beer’s law, relation. The older theory accounts for transmittance of a medium but not for reflectance. The K–M theory, however, yields a theoretical value both for reflectance and transmittance. The K–M theory is applied in this paper to the reflectance and transmittance of stacked mature cotton leaves over the spectral range 0.5–2.5 μ. The standard deviation between theory and experiment, after known biases are calculated and removed from the data, is about 1%—a discrepancy well within experimental error. A procedure is developed to apply the K–M theory to an actual plant canopy. The method involves regression analysis to light flux measurements within a plant canopy. Differential coefficients are derived for use in both stacked-leaf and canopy applications.

Interaction of Isotropic Light with a Compact Plant Leaf

A transparent plate with rough plane-parallel surfaces is used as a theoretical model to explain the interaction of diffuse light with a compact plant leaf. Effective optical constants of a corn leaf have been determined from leaf reflectance and transmittance measured over the spectral range 0.5–2.5 μ with a recording spectrophotometer. The effective index of refraction at 0.5 μ for the corn leaf is not inconsistent with the refractive index of epicuticular wax. The effective absorption spectra of the corn leaf appears to be a superposition of the absorption coefficients of chlorophyll and pure liquid water. Residual spectral data from other leaf constituents are at the resolution limit of the spectrophotometer. The plate model of a leaf is also used to determine moisture content of the corn leaf from reflectance and transmittance measurements.

Plant-canopy irradiance specified by the Duntley equations

The Duntley equations for propagation of unidirectionally incident light through a diffusing medium have been generalized and interpreted to account for the diurnal nature of near-infrared radiation measured in an Ithaca, N. Y. corn canopy. The Duntley optical coefficients associated with the specular component of light were assumed to vary as the secant of the sun’s zenith angle. Generalization of the Duntley relations was required in order to predict values of irradiance within the canopy and to account for the effect of background reflectance from the soil. Five independent measurements of canopy irradiance suffice to determine the Duntley parameters. Twenty-four measurements of transmittance within the canopy were used, however, in a least-squares calculation to obtain the best fit of the Duntley equations to irradiance within the corn canopy. The Duntley equations fit the experimental results within a standard deviation of 3.2% for a period from noon to sundown. If the laboratory measurements of optical constants for a single corn leaf are used as constraints, the Duntley equations fit the data to within 3.7%. The best fit to near-ir-transmittance measurements occurs when zero absorptance is assumed for the canopy. The Duntley equations reduce to a three-parameter representation for the special case of no absorptance.

Mean Effective Optical Constants of Cotton Leaves

The plate description of a typical, thin, compact plant leaf, introduced previously, has been generalized to the noncompact case and applied to experimental data including average reflectance and transmittance measurements on 200 mature, field-cotton leaves. A compact leaf has few and a noncompact leaf has many intercellular air spaces in the mesophyll. No statistically significant difference was found between the average leaf thickness and the mean effective water thickness of the leaves. The Kubelka–Munk scattering coefficient s for a typical leaf, measured at the 1-μ spectral region, is approximated by the relation s = r/t, where r and t, respectively, are the reflectance and transmittance of the leaf. The approximate equality of r and t, noted by previous investigators, is explained on the basis of the scattering of diffuse light within the leaf by critical internal reflections. Predictions from the plate (P) model for cotton leaves compare favorably with those of the Kubelka–Munk (K–M) and Melamed (M) theories. Applied to vegetation, all three theories predict a characteristic linear dimension related to the cellular structure of the leaf.

Measurement of reflectance factors under daily and intermittent irradiance variations

A technique for measuring reflectance factors in diurnal and intermittent cloud insolation conditions using hand-held radiometers has been developed. Simultaneously collected reference panel and total insolation measurements were obtained during the South Texas summer growing season (April and May 1980) at Weslaco, Tex., using the GSFC MARK2 three-band hand-held radiometer. The estimated reflectance factors of four reference panels using the hand-held radiometer agreed closely with the expected reflectance as measured with a laboratory spectrophotometer over a wide range of insolation readings (from 20 to 91 mW/cm(2)). These results indicate that this technique could prove useful for achieving uniform reflectance factor measurements for remote sensing studies.

Willstätter-Stoll Theory of Leaf Reflectance Evaluated by Ray Tracing

The widely accepted Willstätter-Stoll (W-S) theory of leaf reflectance has been investigated by extensive ray tracing through a model (W-S model) in which the leaf cellular structure is approximated by circular arcs. Calculations were performed on an IBM 1800 computer. The W-S model is treated as a two-dimensional, uncentered optical system consisting of a single medium and air. Optical properties of the medium are specified by a complex index of refraction. Given an incident ray, new reflected and transmitted rays are produced at each interface with properties determined by the laws of Snell, Fresnel, and Lambert. Calculations indicate that the W-S model, as exemplified by their artists conception, is too transparent, that is, the magnitude predicted for transmittance is too high. Transmittance is still too high if each interface is treated as a diffusive instead of a smooth surface. The W-S model can be easily improved, however, by introduction of more intercellular air spaces. The modified W-S model promises to be an excellent representation of physical reality. Accurate predictions, however, require an inordinate amount of computer time.

Development of Agrometeorological Crop Model Inputs from Remotely Sensed Information

The goal of developing agrometeorological crop model inputs from remotely sensed information (AgRISTARS Early Warning/Crop Condition Assessment Project Subtask 5 within the U. S. Department of Agriculture (USDA)) provided a focus and a mission for crop spectral investigations that would have been lacking otherwise. Because the task had never been attempted before, much effort has gone into developing measurement and interpretation skill, convincing the Scientific community of the validity and information content of the spectral measurements, and providing new understanding of the crop scenes viewed as affected by bidirectional, atmospheric, and soil background variations. Nonetheless, experiments conducted demonstrate that spectral vegetation indices (VI) a) are an excellent measure of the amount of green photosynthetically active tissue present in plant stands at any time during the season, and b) can reliably estimate leaf area index (LAI) and intercepted photosynthetically active radiation (IPAR)-two of the inputs needed in agrometeorological models. Progress was also made on using VI to quantify the effects of yield-detracting stresses on crop canopy development. In a historical perspective, these are significant accomplishments in a short time span. Spectral observations of fields from aircraft and satellite make direct checks on LAI and IPAR predicted by the agrometeorological models feasible and help extend the models to large areas. However, newness of the spectral interpretations, plus continual revisions in agrometeorological models and lack of feedback capability in them, have prevented the benefits of spectral inputs to agrometeorological models from being fully realized.

Radiometric estimation of biomass and nitrogen content of Alicia grass

Abstract Hand-held MARK-II radiometric measurements were used to estimate biomass yields and nitrogen (N) content of Alicia grass (Cynodon spp.) plots having five levels of nitrogen fertilization. The radiometric RED (630- to 690-nm) and NIR (760- to 900-nm) measurements obtained from the plots were converted to reflectance factors and to perpendicular (PVI) and ratio (RVI = NIR/RED) vegetation indices and then correlated with grass biomass yield and N content. The coefficients of determination (r2) in estimating biomass yield for the RED and NIR reflectance factors were 0.04 and 0.73, 1 respectively, and for PVI and RVI they were 0.68 1 and 0.61, 1 respectively. The correlations for N content were 0.02, 0.71, 1 0.69, 1 and 0.60, 1 respectively. Since beef cattle protein needs are related to grass N content these results may be useful to operational rangeland remote sensing programs for estimating animal carrying capacity using satellite data.

Diurnal patterns of bidirectional vegetation indices for wheat canopies

Abstract The perpendicular vegetation index (PVI) and normalized difference vegetation index (NDVI) were calculated from Mark II radiometer RED (0.63-0.69 μm) and NIR (0.76–0.90 μ) bidirectional radiance observations for wheat canopies. Measurements were taken over the plant development interval flag leaf expansion to watery ripeness of the kernels during which the leaf area index (LAI) decreased from 40 to 2-5. Spectral data were taken on four cloudless days five times (09.30, 11.00, 12.30, 14.00 and 15.30 hours (central standard time, C.S.T.) at five view zenith, Zv (0, 15, 30,45 and 60°) and eight view azimuth angles relative to the Sun, Av (0, 45, 90, 135, 180, 225, 270 and 315°). The PVI was corrected to a common solar irradiance (PVIC) based on simultaneously observed insolation readings. The PVIC at nadir view (Ž=0°) increased as (l/cosZs) increased on all the measurement days whereas the NDVI changed little as solar zenith angle (Zs) changed. Thus, the PVIC responded to increasing path length thro...

Comparison of multispectral video and SPOT-1 HRV observations for cotton affected by soil salinity

Abstract A 15-ha field of cotton (Gossypium hirsuiutn L,) with an erratic pattern of soil salinity was overflown twice during the 1989 growing season with each of two sensor systems, a multispectral videography system and the High Resolution Visible (HRV) scanner of the French polar-orbiting satellite SPOT. The objectives were to compare the responses of the two sensor systems and to relate vegetation indices calculated from them to plant cover and lint yield (kgha−1) observations for 36 sites located at the intersections of a square 60 m grid laid off in the field. The range in responses, expressed as digital counts, was much greater for the video than for the HRV. For paired dates of acquisitions, the agreement between near-infrared and red bands between systems was almost as good as within systems. Yield and plant cover could also be estimated about equally well from vegetation indices calculated from both systems. Consequently, it is concluded that the video observations provided essentially the same ...