Leaf Angle Distribution Research Articles

Light distribution and foliage structure in an oak canopy

Leaf angle distribution and shoot bifurcation ratio were measured and related to photon flux density (PFD) distribution in an oak canopy. Leaf angle distribution deviated substantially from random and changed markedly throughout the canopy. The observed leaf angle distribution was described by an ellipsoidal function with the single parameter of the distribution, x, changing from 1.6 at the top of the canopy to 3.2 in the lowest branches. In vertically homogeneous canopies, the extinction coefficient for diffuse radiation is expected to decline with increasing leaf area index (LAI). However, in the canopy studied here, the leaf angle distribution changed with height such that the effective extinction coefficient remained constant. Both shoot bifurcation ratio and leaf number per shoot declined with decreasing PFD inside the canopy. Based on these observed relationships, a simple canopy growth model that assumes horizontal homogeneity of the canopy was constructed. Calculations showed that a steady state, when growth in the upper of the canopy is in equilibrium with decline of lower canopy, the total canopy LAI should equal to 4.3. This predicted value of equilibrium LAI is larger than that estimated from measurements of PFD transmission (LAI=3.3), but smaller than that directly determined by litter collection (LAI=6.2 in 1998). Possible reasons for these discrepancies are discussed.

Inverting a canopy reflectance model using a neural network

An off-nadir canopy reflectance model, the Liang and Strahler algorithm for the Coupled Atmosphere and Canopy (CAC) model, was used to simulate multi-angle reflectances based on various combinations of canopy biophysical parameters. Biophysical parameters such as leaf angle distribution (LAD) and leaf area index (LAI) were input to the CAC model along with reflectances of leaf and soil and aerosol optical depth. The CAC model, however, can only be inverted through numerical iterations and it is extremely difficult to use for retrieval of those biophysical parameters with ordinary inversion methods. In order to retrieve those biophysical parameters, we employed an error backpropagation feed-forward neural network program. We constructed a number of neural network models based on the simulated results from the CAC model. In this paper, we report the results obtained from retrieving any individual parameter from multi-angle reflectances and results obtained from simultaneously retrieving some combinations of two parameters and five parameters. We tested the use of a different number of multi-angle reflectances as input to the neural networks. This number varied in the range 1-64. The test results showed that a relative error between 1 and 5% or better was achievable for retrieving one parameter at a time or two parameters simultaneously. The relative errors for two of the five simultaneously retrieved parameters were less than 17%. The amount of computation required by simultaneous retrieval of five parameters was prohibitively high for a regular workstation.

Aspects of maize modelling in eastern Canada

Maize (Zea mays L.) is a crop of growing importance in Eastern Canada. Modelling the temperature effects on phenological development, crop architecture and disease infection in maize contributes to the development of well-adapted, early-maturing varieties. Details of modelling these three aspects of maize growth were presented. The first focussed on quantifying the effect of air or soil temperature on maize phenological development. Crop growth was divided into two periods: vegetative (planting to silking) and grain filling (silking to maturity). A third period (planting to emergence) was separated within the vegetative period. Heat unit systems based on daily temperature response functions were developed to produce the most consistent heat unit sums for each period. The best fits of these functions were determined by minimizing standard deviations and coefficients of variation of these sums for each thermal period over locations and years. Calculated temperature response functions estimated thermal periods more consistently than growing degree days (GDD) for all three periods. The largest improvement was made in the silking to maturity period.The second aspect was a study of crop architecture. Methods were developed to mathematically characterize the structure of a canopy in terms of leaf area and leaf angle distributions with crop height and across the row. These calculations, in turn, were input to a soil–plant–atmosphere model to calculate interception of photosynthetically active radiation (PAR). Model calculations of PAR interception compared well with measurements for a range of plant types and plant population densities (R2 = 0.76).The third aspect was quantifying growth of Fusarium in maize. Differential equations were used to relate Fusarium rates of growth in maize ears to air temperature, relative humidity and precipitation. Integration of these equations over time produced quantitative estimates of fungal infection. Model calculations were compared to visual ratings of fungal infection for two Fusarium species over three years (R2 = 0.92).In each of the three aspects of this study, modelling tested our understanding of the processes involved and the dominant factors controlling these processes. Thus, modelling was an integral part of the scientific approach, synthesizing experimental data in a quantitative conceptual framework and identifying dominant factors and parameters which required additional focussed experimental evaluation. Key words: Phenological development, crop architecture, Fusarium infection

Comparing biophysical properties of the Streletskaya Steppe Reserve and the Konza Prairie∗

Reflected radiation by a crop canopy can be influenced by changes in the biological processes and physical attributes of the canopy. The study was conducted to characterize the effective leaf area index (LAI) and leaf angle distribution of the Streletskaya Steppe Reserve of the Russian Republic and the Konza Prairie in Kansas and to determine dependence of leaf optical properties on leaf water potentials of some dominant species in discrete wavebands in the visible and near‐infrared (NIR) (spanning 400–1000 nm range). Biophysical properties were measured in July 1991 during the Kursk Experiment (KUREX‐91) and in the summer of 1989 during the First ISLSCP Field Experiment (FIFE‐89). Leaf area index, leaf angle distribution, mean tilt angle, canopy height, leaf optical properties, and leaf water potential were measured. Generally, the KUREX‐91 steppe sites were characterized by high leaf area index and an uniform leaf angle distribution, while the FIFE‐89 prairie sites were characterized by low leaf area index and an erectophile canopy. There were differences in leaf reflectances between plant groups (grass versus forb) and between plant communities (prairie versus steppe), but not generally for transmittance. Leaf optical properties (visible and NIR) were not related to leaf water potential (over the ‐0.5 to ‐3.5 MPa range) for dominant plant species observed at the KUREX‐91 and FIFE‐89 sites. Characterization of the biophysical properties during the FIFE‐89 and KUREX‐91 experiments provide information useful in understanding the differences in canopy bidirectional reflectance observed at the two grasslands.

Biophysical and Biochemical Sources of Variability in Canopy Reflectance

Analyses of various biophysical and biochemical factors affecting plant canopy reflectance have been carried out over the past few decades, yet the relative importance of these factors has not been adequately addressed. A combination of field and modeling techniques were used to quantify the relative contribution of leaf, stem, and litter optical properties (incorporating known variation in foliar biochemical properties) and canopy structural attributes to nadir-viewed vegetation reflectance data. Variability in tissue optical properties was wavelength-dependent. For green foliage, the lowest variation was in the visible (VIS) spectral region and the highest in the near-infrared (NIR). For standing litter material, minimum variation occurred in the VIS/NIR, while the largest differences were observed in the shortwave-IR (SWIR). Woody stem material showed opposite trends, with lowest variation in the SWIR and highest in the NIR. Leaf area index (LAI) and leaf angle distribution (LAD) were the dominant controls on canopy reflectance data with the exception of soil reflectance and vegetation cover in sparse canopies. Leaf optical properties (and thus foliar chemistry) were expressed most directly at the canopy level in the NIR, but LAI and LAD strongly controlled the relationship between leaf and canopy spectral characteristics. Stem material played a small but significant role in determining canopy reflectance in woody plant canopies, especially those with LAI<5.0. Standing litter significantly affected the reflectance characteristics of grassland canopies; small increases in the percentage of standing litter had a disproportionately large affect on canopy reflectance. The structural attributes of ecosystems determine the relative contribution of tissue, canopy, and landscape factors that drive variation in a reflectance signal. Deconvolution of these factors requires an understanding of the sources of variance at each scale (which is ecosystem dependent) as well as an adequate sampling (spectral, angular, and temporal) of the shortwave (400–2500 nm) spectrum.

Measurements of leaf orientation, light distribution and sunlit leaf area in a boreal aspen forest

A new instrument called a Multiband Vegetation Imager (MVI) ( Kucharik et al., 1997), which uses a 16-bit charge-coupled device (CCD) camera and filter exchange mechanism to capture 2-band (visible and near-infrared) image pairs of plant canopies, has been used to measure the light distribution over sunlit leaves and indirectly infer leaf area index (LAI), sunlit LAI and leaf angle distribution (LAD) in a boreal aspen ( Populus tremuloides) forest during the Boreal Ecosystem–Atmosphere Study (BOREAS). One purpose of this study is to demonstrate that by combining MVI measurements with numerical Monte Carlo simulations of forest canopy architecture, the LAD and sunlit LAI of aspen can be obtained indirectly. Our results show that this boreal aspen stand exemplifies an erectophile LAD, with a mean leaf inclination angle near 70°. We also find that the values of the measured and modeled sunlit leaf area in aspen do not change dramatically for typical northern boreal latitude solar zenith angles (i.e. 30–70°). A major problem with determining the sunlit LAI is deciding what range of light intensities constitute a sunlit leaf because penumbra create a smooth continuum of light intensities over sunlit and shaded leaves in the canopy. Therefore, we show that the upper and lower limits can be placed on sunlit LAI values in aspen by using different leaf illumination threshold levels to determine sunlit and shaded LAI in the canopy. Typically, sunlit LAI values in aspen (LAI=3.3) range between 0.8–1.0 at a 70° sun zenith angle and 1.1–1.6 at a 30° sun zenith angle. Monte Carlo simulations and MVI measurements suggest that canopy sunlit leaf area estimates are possible from below the canopy at modest LAI values (<∼4.0) but become unreliable in higher LAI (>5.0). Since a substantial fraction of the total sunlit leaf area can be viewed from below the canopy in aspen (40–60% of the total sunlit LAI), a representative light distribution can be measured and used to quantify the canopy leaf angle distribution.

The Sensitivity of the OSAVI Vegetation Index to Observational Parameters

OSAVI is a soil-adjusted vegetation index optimized for agricultural monitoring. The SAIL–SOILSPECT–PROSPECT–KUUSK model was applied to test the sensitivity of OSAVI to a number of observational and environmental parameters, with the constraint that the parameter ranges were chosen to be representative of conditions encountered during operational monitoring by SPOT and Landsat of the U.K. sugar beet crop in the summer months. Within these defined limits, variations in solar and viewing angles introduced no more than 4% systematic (and rectifiable) error in estimation of crop canopy cover while errors associated with atmospheric correction were of a similar magnitude. Although sugar beet has large leaves close to the ground and was expected to generate a large hot spot effect, the effect of uncertainty in leaf size appears to be negligible. Leaf angle distribution is effectively accounted for by the use of crop cover as an index of productivity, except when the crop is wilting, but this is unlikely to occur in sugar beet at the time of satellite overpass. Subject to the uncertainties of modeling, the estimation of crop canopy cover within an absolute error of 5% appears to be achievable.

Seasonal changes in leaf nitrogen pools in two Salix species.

Leaf nitrogen distribution pattern was studied four times during the growing season in a 2-year-old Salix viminalis L. and Salix dasyclados Wimm. plantation in Estonia. We measured the vertical distributions of leaf nitrogen concentration, dry mass, leaf area and light environment (as fractional transmission of diffuse irradiance, a(d)) in the canopy. The light-independent nitrogen pool was evaluated as the intercept of the leaf nitrogen concentration versus a(d) relationship, and the nondegradable nitrogen pool was evaluated as the nitrogen remaining in abscised leaves. A strong vertical gradient of mass-based leaf nitrogen concentration was detected at the beginning of the growing season, and decreased steadily during canopy development. This decline had at least three causes: (1) the amount of nitrogen in the foliage was larger at the beginning of the growing season than at the end of the growing season, probably because of pre-existing root systems; (2) with increasing leaf area index (LAI) during the growing season, the proportion of leaf nitrogen in total canopy nitrogen that could be redistributed (light-dependent nitrogen pool) decreased; and (3) the photosynthetic photon flux density gradient inside the canopy changed during the season, most probably because of changes in leaf area and leaf angle distributions. Total canopy nitrogen increased almost proportionally to LAI, whereas the light-dependent nitrogen pool had a maximum in August. Also, the proportion of the light-dependent nitrogen pool in the total canopy nitrogen decreased steadily from 65.2% in June to 17.2% in September in S. dasyclados and from 63.3 to 15.1% in S. viminalis. The degradable nitrogen pool was always bigger than the light-dependent nitrogen pool.

Inverting optical reflectance to estimate surface properties of vegetation canopies

An inversion method using a simple bidirectional reflectance model and data on optical reflectances remotely-sensed from satellites has been improved to derive surface properties such as the leaf area index (LAI). Such properties are important in deriving the resistance of the vegetative canopy to uptake of gaseous trace chemicals from the atmosphere and in the study of radiation transfer processes. We found that a multi-pass retrieval technique can greatly improve a model's ability to retrieve surface properties. Because the sensitivity of the model inversion to initial values is an important issue that depends on (1) the partial derivative of reflectance with respect to each parameters to be retrieved ( R / x ) and (2) the degree of independence among model parameters, we investigated the issue with synthetic data constructed by a bidirectional reflectance model. The results revealed that, although the surface optical properties are mostly independent of each other, their initial values did have some effect on the retrieved value of the LAI, with the worse case caused by leaf angle distribution index, n, at close-to-nadir solar and view zenith angles of the reflectance data. At nearnadir angles, n and LAI were strongly correlated, and their retrieval was not unique. When applied to satellite remote sensing data obtained with the advanced very-high-resolution radiometer (AVHRR), the model-retrieved seasonal variation of surface properties agreed reasonably well with independent ground measurements made in the First International Satellite Land-Surface Climatology Project (ISLSCP) Field Experiment (FIFE) campaign. Application to Landsat data to retrieve spatial variation was less successful, largely because of the close-to-nadir solar and view zenith angles in the data.

On the estimation of leaf size and crown geometry for tree canopies from hotspot observations

A computer‐graphics based model for radiation interception in vegetation canopies is used to investigate the feasibility of estimating leaf size and crown size, for deciduous and coniferous trees, from canopy reflectance in the hotspot region. For deciduous trees, as represented by aspen trees, it appears that under certain conditions one can estimate leaf size; we specify optimal Sun‐view geometry, wavelength, and index, which can minimize the impacts of other structural parameters (e.g., leaf area index, leaf angle distribution, and interplant spacing) for the most accurate estimation of leaf size. However, for coniferous trees an accurate estimation of crown size seems unlikely, except possibly for sparsely spaced canopies.

Vertical point quadrat sampling and an extinction factor to calculate leaf area index

The appropriateness of a correction factor to derive leaf area index (LAI) from contact frequency using vertically-inserted point quadrat sampling was investigated. Point quadrat data were collected in a grid pattern over 72 individual shrubs and grass plots comprising eight common Great Basin scrub species of widely divergent ecology and canopy form. Destructive sampling and intercept measurements were used to determine LAI values. Extinction coefficients were then calculated from paired LAI and contact frequency. For all eight species, this extinction coefficient was statistically equivalent to 0·5 as a result of spherical leaf angle distribution, permitting LAI estimation simply by multiplying contact frequency by 2.

Growth of Lettuce, Onion, and Red Beet. 1. Growth Analysis, Light Interception, and Radiation Use Efficiency

A field experiment was carried out to analyse the growth of lettuce, onion and red beet in terms of: ( a) canopy architecture, radiation interception and absorption; ( b) efficiency of conversion of absorbed radiation into biomass; and ( c) dry matter partitioning. Growth analysis, total solar radiation interception, PAR interception and absorption by the crop canopy, ground cover, maintenance respiration of onion bulbs and red beet storage roots were measured. Models for different leaf angle distribution and ground cover were used to simulate light transmission by the crop canopy. The three crops are shown to have contrasting growth patterns from both a morphological and a physiological point of view. Lettuce showed very high light interception and growth after the early growth stages but, throughout the growth cycle, this leafy crop showed the lowest radiation use efficiency due to the respirational cost of the high leaf area. Onion showed a lower early relative growth rate than lettuce and red beet. This was due partly to the low light interception per unit leaf area in the later stages of growth and partly to the low initial radiation use efficiency compared with the other two crops. On the other hand, thanks to more uniform distribution of the radiation inside the canopy, to the earlier termination of leaf development and to the very low level of bulb respiration, onion showed high radiation use efficiency and was able to produce a large amount of dry matter. Red beet leaf posture and canopy structure resulted in high light interception and absorption. Its radiation use efficiency was lower than that of onion, partly perhaps because of the more adverse distribution of the intercepted radiation fluxes within the canopy and partly because of the high respiration cost of a continuous dry-matter allocation to the leaves. However, this crop can accumulate a very large amount of dry matter as leaf blade development and storage root growth can both continue almost indefinitely, providing continuously available sinks. Ground cover gave a good estimate of the PAR interception only at low values of light interception but, in general, it underestimated PAR interception in all three crops. Ratios between attenuation coefficients established by considering PAR or total solar radiation and LAI or ground cover were calculated.

A simple anisotropic reflectance model for homogeneous multilayer canopies

This article deals with the representation of the canopy bidirectional reflectance factor (BRF) with a model that is simple, for inversion purposes, and computationally cheap. The objective was to derive the analytical expressions of radiative transfer in covers that may comprise strongly anisotropic vegetation layers and/or bottom interface. This is carried out through the introduction of an additional upward directional flux that originates from the anisotropic components of the cover, in a widely used and reliable three-flux model, that is, the SAIL (scattering by arbitrarily inclined leaves) model. It results in a multi-layered four-flux model with a fast computer code. Parameters (i.e., r sm and r dm ) that characterize the anisotropic behavior of canopy layers are computed with the same input parameters as the SAIL model. Moreover, at least one additional parameter is used for characterizing the anisotropic behavior of the bottom interface, that is, soil surface. Depending on the LAI (leaf angle index) and LAD (leaf angle distribution) of the upper layer and on the degree of anisotropy of the underlying layers, differences between BRFs that are derived from the four-flux model and from the SAIL model can be large. This stresses the necessity of the introduction of an upward directional flux in presence of covers with strongly anisotropic characteristics.

Effects of standing litter on the biophysical interpretation of plant canopies with spectral indices

Litter is frequently present within vegetation canopies and thus contributes to the overall spectral response of a canopy. Consequently, litter will affect spectral indices designed to be sensitive to green vegetation, soil brightness or other features. The main objectives of the current research were to 1) evaluate the spectral properties of green vegetation and litter and 2) quantify the effect of standing litter on the performance of spectral indices. The SAIL (scattering by arbitrarily inclined leaves) model was used to generate canopy reflectance “mixtures” and to estimate fractions of absorbed photosynthetically active radiation (fAPAR) with varying leaf area index (LAI), soil background, combinations of vegetation component spectral properties, and one or two horizontal vegetation layers. Spectral measurements of different bare soils and mature green and senescent leaves of representative plant species at the HAPEX-Sahel (Hydrological Atmospheric Pilot Experiment) study sites were used as input. The normalized difference vegetation index (NDVI), the soil adjusted vegetation index (SAVI), and the modified NDVI (MNDVI) and mixture model spectral indices were selected to evaluate their performance with respect to standing litter and green vegetation mixtures. Spectral reflectance signatures of leaf litter varied significantly, but strongly resembled soil spectral characteristics. The biophysical phyameters (LAI, fAPAR), derived from spectral vegetation indices, tended to be overestimated for randomly distributed, sparse green and litter vegetation cover mixtures, and underestimated for randomly distributed dense green and litter vegetation cover mixtures. All spectral indices and their biophysical interpretation were significantly altered by variability in 1) green leaf, leaf litter, and bark optical properties, 2) the amount and position of standing leaf litter, 3) leaf angle distribution, and 4) soil background. The NDVI response to these variables was inconsistent, and was the most affected by litter. The spectral mixture model indices, designed to be sensitive to litter, were shown to be promising for the identification of litter present among different ecosystems.

Optimal sampling conditions for estimating grassland parameters via reflectance

The sensitivity of grassland bidirectional reflectance to soil, vegetation, irradiance, and sensor parameters is assessed. Based on these results, a vegetation bidirectional reflectance distribution function (BRDF) model is inverted with ground reflectance data from the First ISLSCP Field Experiment (FIFE). Results suggest leaf area index (LAI) is most accurately retrieved from data gathered in near-infrared bands at low solar zenith angles (SZA), and leaf angle distribution is best retrieved from data gathered in near-infrared bands at SZA. Generally, leaf optical properties are more accurately estimated from data acquired at high SZA. Canopy albedo and fraction of absorbed photosynthetically active radiation (fAPAR) are also estimated and compared to measured values. Albedo estimates are accurate to about /spl plusmn/0.01 (4% relative) when model parameters are determined from reflectance data gathered under preferred conditions. Estimates of fAPAR are less accurate. These results provide a guide for efficiently sampling surface reflectance and accurately retrieving parameters for use in climate ecosystem models.

Image analysis estimation of leaf area index and plant size of young hazelnut plants

SummaryA nondestructive method of leaf area estimation was evaluated on two year old hazelnut plants cv. Tonda Gentile Romana grown in the field. Black and white photographs of 22 plants were taken from two directions at 90° and processed by means of a Vidas image analyzer (Kontron Elektronic) to obtain an estimation of leaf area. Plants were then defoliated and actual leaf area was measured by means of a Delta T Device area meter. A good linear relationship between measured leaf areas and canopy silhouette areas was obtained. Nevertheless, silhouette area measured through image analysis resulted consistently lower than actual leaf area, because of leaf angle distribution and the overlapping of the different leaf layers. Leaf area index (LAIplant) was reliably calculated as the ratio between total leaf area estimated by image analysis and the area of canopy projection on the ground. Plant size parameters (height, width, canopy cross-sectional area and volume) were correctly predicted by image processing. Once calibrated, the method is simple and rapid and seems to be an effective tool for measurements of within-crown leaf area index and plant growth repeated in time and space.

A framework for monitoring crop growth by combining directional and spectral remote sensing information

For monitoring agricultural crop production, growth of crops is modeled, for example, by using simulation models. Estimates of crop growth often are inaccurate for practical field conditions. Therefore, model simulations must be improved by incorporating information on the actual growth and development of field crops, for example, by using remote sensing data. Such data can be used to initialize, calibrate, or update crop growth models, and it can yield parameter estimates to be used as direct input into growth models: 1) leaf area index (LAI), 2) leaf angle distribution (LAD), and 3) leaf colour (optical properties in the PAR region). LAI and LAD determine the amount of light interception. Leaf (or crop) color influences the fraction of absorbed photosynthetically active radiation (APAR) and the maximum (potential) rate of photosynthesis of the leaves. A framework is described for integrating optical remote sensing data from various sources in order to estimate the mentioned parameters. In this article, the above concepts for crop growth estimation are elucidated and illustrated using groundbased and airborne data obtained during the MAC Europe 1991 campaign. Quantitative information concerning both LAI and LAD was obtained by measurements at two viewing angles (using data from the CAESAR scanner in dual-look mode). The red edge index was used for estimating the leaf optical properties (using AVIRIS data). Finally, a crop growth model (SUCROS) was calibrated on time series of optical reflectance measurements to improve the estimation of crop yield.

Influences of canopy architecture on relationships between various vegetation indices and LAI and Fpar: A computer simulation

Abstract Vegetation Indices (VIs) are often used to estimate important biophysical parameters, like LAI and Fpar, from vegetation canopy reflectance data. In this study, a three‐dimensional model (Diana) is utilized to generate architecturally realistic tree and crop canopies in various development stages and to calculate bidirectional reflectance factors in the principal plane. We investigate the influence of various factors like soil brightness, optical properties of canopy elements, leaf angle distribution, spacing distance between plants and solar and view geometries on relationships between VI and Fpar, LAI and percentage ground cover (GC) in order to determine optimal VI and viewing conditions for the estimation of Fpar and LAI/GC. These simulation studies suggest that: (1) in most cases, Vis using off‐nadir reflectances are more informative and useful than those based on nadir reflectances; (2) the optimal VI and sun/view geometries are usually different for inferring different parameters, depending on canopy architecture; (3) LAI can be practically estimated by VI only for homogeneous canopies while GC and Fpar can be inferred even for an inhomogeneous canopy; and (4) when optical properties of vegetation elements vary within a canopy, neither LAI/GC nor Fpar can be estimated by means of VI method with an acceptable accuracy.

Estimating the fraction APAR by means of vegetation indices: A sensitivity analysis with a combined prospect‐sail model

Abstract A sensitivity analysis is performed for both crop parameters and external factors, using the SAIL canopy reflectance model and the PROSPECT leaf reflectance model, towards the possibilities of using vegetation indices (VIs) in estimating the fraction of absorbed photosynthetically active radiation (FPAR). Results from this theoretical study show that a linear relationship may be assumed between WDVI (Weighted Difference VI) or NDVI (Normalized Difference VI) and FPAR as an approximation. External factors (soil background, ratio diffuse/total irradiation, solar zenith angle) do not have a large influence on the relationship between FPAR and the WDVI. Moreover, leaf parameters (such as leaf chlorophyll content, leaf mesophyll structure and hot spot size‐parameter) also have quite a small influence for green leaves, as concluded from simulations with the combined PROSPECT‐SAIL model. The main crop parameter influencing the relationship between WDVI and FPAR is the leaf angle distribution (LAD). So, ...

Mathematical characterization of maize canopies

Leaf area and its distribution in space largely determine canopy photosynthesis and dry matter accumulation. Methods were developed to characterize the morphology of maize plants in order to calculate leaf area and leaf angle distributions. Plants were placed against a grid where ligule heights and leaf curvature characteristics were measured. Leaf widths were then measured every 10 cm along the length of the leaf. The curvature of each leaf was characterized by a general quadratic equation expressed in terms of the initial leaf angle, the coordinates of the maximum height of the leaf and the coordinates of the leaf tip. A third order polynomial, expressed in terms of leaf width at the ligule, the length of the leaf and two empirical shape coefficients, was used to describe leaf shape. From these equations leaf areas were calculated as a function of plant height and distance between rows. Leaf angle distributions were also calculated. In order to reduce the number of coefficients needed to describe a canopy, the various parameters involved with leaf curvature and shape and internode length were fitted by least squares to second order polynomial functions of leaf number. These second order polynomial functions were used to generate leaf area and angle distributions which compared favourably with the original measurements.