Linear Functionals of the Foliage Angle Distribution as Tools to Study the Structure of Plant Canopies

1984 ◽  
Vol 32 (2) ◽  
pp. 147 ◽  
Author(s):  
RS Anderssen ◽  
DR Jackett ◽  
DLB Jupp
Keyword(s):  
Synthetic Data ◽  
Angle Distribution ◽  
Linear Functionals ◽  
General Transformation ◽  
Area Index ◽  
Plant Canopies ◽  
Contact Frequency ◽  
Numerical Experimentation ◽  
Actual Evaluation ◽  
Foliage Density

In 1967, Miller showed how average foliage density could be computed from contact frequency data. It formalized mathematically the idea posed earlier by Warren Wilson of estimating the leaf area index as a linear combination of measured values of the contact frequency. Recently, it has been shown that Miller's result is a special case of a general transformation that allows linear functionals defined on the (generally unknown) foliage angle distribution (foliage angle functionals) to be evaluated as linear functionals defined on the (measured) contact frequency (contact frequency functionals). This result has important consequences for the use of foliage angle functionals in the study of the structure of plant canopies. For example, it allows Warren Wilson's idea to be extended to the evaluation of such functionals, and thereby simplifies greatly their actual evaluation. In this paper, we first motivate and review the use of foliage angle functionals in the study of plant canopies; then we introduce new functionals (the segmented foliage density and the moments); and finally, we use numerical experimentation with synthetic data to illustrate the advantages of having formulas for the foliage angle functionals of interest that are defined explicitly in terms of the (measured) contact frequency.

scholarly journals Linear functionals of foliage angle density

1984 ◽  
Vol 25 (4) ◽  
pp. 431-442 ◽  
Author(s):  
R. S. Anderssen ◽  
D. R. Jackett
Keyword(s):  
Integral Equation ◽  
Environmental Monitoring ◽  
Fredholm Integral Equation ◽  
Inversion Formula ◽  
Canopy Reflectance ◽  
Linear Functionals ◽  
General Transformation ◽  
Area Index ◽  
Contact Frequency ◽  
Special Case

AbstractKnowledge about the foliage angle density g(α) of the leaves in the canopy of trees is crucial in foresty mangement, modelling canopy reflectance, and environmental monitoring. It is usually determined from observations of the contact frequency f(β) by solving a version of the first kind Fredholm integral equation derived by Reeve (Appendix in Warren Wilson [22]). However, for inference purposes, the practitioner uses functionals defined on g(α), such as the leaf area index F, rather than g(α) itself. Miller [12] has shown that F can be computed directly from f(β) without solving the integral equation. In this paper, we show that his result is a special case of a general transformation for linear functionals defined on g(α). The key is the existence of an alternative inversion formula for the integral equation to that derived by Miller [11].

The quality of short-wave radiation within plant canopies

1969 ◽  
Vol 47 (12) ◽  
pp. 1989-1994 ◽  
Author(s):  
T. B. Daynard
Keyword(s):  
Leaf Area Index ◽  
Leaf Area ◽  
Plant Communities ◽  
Short Wave ◽  
Wave Radiation ◽  
Leaf Angle ◽  
Visible Radiation ◽  
Area Index ◽  
Plant Canopies

In this paper, a mathematical attempt is made to predict the effects of leaf area index, leaf angle, and leaf spectral properties on changes in the relative composition of short-wave radiant fluxes as they penetrate plant canopies. Results of this theoretical analysis indicate that a sizeable change in the quality of visible radiation will only occur if the canopy is sufficiently dense to intercept at least 98% of the incident flux one or more times. By contrast, a significant increase in the proportion of infrared radiation is predicted within plant communities, even those of a low effective leaf area index. For natural plant communities, the results would indicate a minimal change in the composition of penetrating radiation at solar noon and a maximal change at sunrise or sunset.The implications of these phenomena to plant morphogenesis and to radiation-measuring techniques are discussed.

scholarly journals Sensitivity Analysis of Canopy Structural and Radiative Transfer Parameters to Reconstructed Maize Structures Based on Terrestrial LiDAR Data

2021 ◽  
Vol 13 (18) ◽  
pp. 3751
Author(s):  
Bitam Ali ◽  
Feng Zhao ◽  
Zhenjiang Li ◽  
Qichao Zhao ◽  
Jiabei Gong ◽  
...  
Keyword(s):  
Hausdorff Distance ◽  
Leaf Angle ◽  
Phenotypic Traits ◽  
Lidar Data ◽  
Angle Distribution ◽  
Area Index ◽  
Terrestrial Lidar ◽  
Scale Parameters ◽  
Gap Fraction ◽  
Macro Scale

The maturity and affordability of light detection and ranging (LiDAR) sensors have made possible the quick acquisition of 3D point cloud data to monitor phenotypic traits of vegetation canopies. However, while the majority of studies focused on the retrieval of macro scale parameters of vegetation, there are few studies addressing the reconstruction of explicit 3D structures from terrestrial LiDAR data and the retrieval of fine scale parameters from such structures. A challenging problem that arises from the latter studies is the need for a large amount of data to represent the various components in the actual canopy, which can be time consuming and resource intensive for processing and for further applications. In this study, we present a pipeline to reconstruct the 3D maize structures composed of triangle primitives based on multi-view terrestrial LiDAR measurements. We then study the sensitivity of the details with which the canopy architecture was represented for the computation of leaf angle distribution (LAD), leaf area index (LAI), gap fraction, and directional reflectance factors (DRF). Based on point clouds of a maize field in three stages of growth, we reconstructed the reference structures, which have the maximum number of triangles. To get a compromise between the details of the structure and accuracy reserved for later applications, we carried out a simplified process to have multiple configurations of details based on the decimation rate and the Hausdorff distance. Results show that LAD is not highly sensitive to the details of the structure (or the number of triangles). However, LAI, gap fraction, and DRF are more sensitive, and require a relatively high number of triangles. A choice of 100−500 triangles per leaf while maintaining the overall shapes of the leaves and a low Hausdorff distance is suggested as a good compromise to represent the canopy and give an overall accuracy of 98% for the computation of the various parameters.

scholarly journals Quantitative Evaluation of Leaf Inclination Angle Distribution on Leaf Area Index Retrieval of Coniferous Canopies

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Guangjian Yan ◽  
Hailan Jiang ◽  
Jinghui Luo ◽  
Xihan Mu ◽  
Fan Li ◽  
...  
Keyword(s):  
Remote Sensing ◽  
Leaf Area Index ◽  
Leaf Area ◽  
Inclination Angle ◽  
Three Dimensional ◽  
Good Choice ◽  
Optical Remote Sensing ◽  
Angle Distribution ◽  
Area Index ◽  
Leaf Inclination

Both leaf inclination angle distribution (LAD) and leaf area index (LAI) dominate optical remote sensing signals. The G-function, which is a function of LAD and remote sensing geometry, is often set to 0.5 in the LAI retrieval of coniferous canopies even though this assumption is only valid for spherical LAD. Large uncertainties are thus introduced. However, because numerous tiny leaves grow on conifers, it is nearly impossible to quantitatively evaluate such uncertainties in LAI retrieval. In this study, we proposed a method to characterize the possible change of G-function of coniferous canopies as well as its effect on LAI retrieval. Specifically, a Multi-Directional Imager (MDI) was developed to capture stereo images of the branches, and the needles were reconstructed. The accuracy of the inclination angles calculated from the reconstructed needles was high. Moreover, we analyzed whether a spherical distribution is a valid assumption for coniferous canopies by calculating the possible range of the G-function from the measured LADs of branches of Larch and Spruce and the true G-functions of other species from some existing inventory data and three-dimensional (3D) tree models. Results show that the constant G assumption introduces large errors in LAI retrieval, which could be as large as 53% in the zenithal viewing direction used by spaceborne LiDAR. As a result, accurate LAD estimation is recommended. In the absence of such data, our results show that a viewing zenith angle between 45 and 65 degrees is a good choice, at which the errors of LAI retrieval caused by the spherical assumption will be less than 10% for coniferous canopies.

The distribution of foliage density on single plants

1965 ◽  
Vol 13 (3) ◽  
pp. 411 ◽  
Author(s):  
JR Philip
Keyword(s):  
Radial Distribution ◽  
Axial Symmetry ◽  
Area Index ◽  
Patterns Of Distribution ◽  
Foliage Density

Means are developed for estimating the radial distribution of foliage density and of "foliage area index" from laterally observed distributions on single plants. The analysis depends on the assumption of axial symmetry. The analysis is applied to Warren Wilson's observations on saltbush. Characteristic patterns of distribution of leaves, stems, and inflorescences are found. The estimated "foliage area index" exceeds 13 at the plant axis.

Light attenuation by early successional plants of the boreal forest

2001 ◽  
Vol 31 (5) ◽  
pp. 812-823 ◽  
Author(s):  
Christy Shropshire ◽  
Robert G Wagner ◽  
F Wayne Bell ◽  
Clarence J Swanton
Keyword(s):  
Boreal Forest ◽  
Plant Species ◽  
Jack Pine ◽  
Rubus Idaeus ◽  
Pteridium Aquilinum ◽  
White Birch ◽  
Area Index ◽  
Plant Canopies ◽  
Crown Cover ◽  
Green Alder

The influence of eight early successional plant species from the boreal forest on photosynthetically active radiation (PAR) were compared using a controlled plant competition study. Four woody (green alder, Alnus crispa (Ait.) Pursh; upland willow, Salix humilis Marsh.; white birch, Betula papyrifera Marsh.; wild red raspberry, Rubus idaeus L.) and four herbaceous (eastern bracken fern, Pteridium aquilinum L.; bluejoint grass, Calamagrostis canadensis Michx.; large-leaved aster, Aster macrophyllus L.; fireweed, Epilobium angustifolium L.) plant species were studied using an additive density experiment with jack pine (Pinus banksiana Lamb.) seedlings. The transmission of PAR through the plant canopies was measured using a line quantum sensor under six plant density treatments at the time of maximum canopy development each year. Four measures of plant abundance (planting density, actual density, projected leaf area index, and crown cover) were evaluated for their ability to predict PAR transmission through the plant canopies. Visual estimates of crown cover provided the best models each year. Vertical profiles of PAR transmission were used to compare the canopy structure among plant species and were used to refine the models. During the second growing season, increasing crown cover of bluejoint grass and large-leaved aster had the largest influence on PAR. In the third season, green alder, upland willow, and white birch (along with bluejoint grass and fireweed at the jack pine crown level) had the greatest influence on PAR. PAR measurements taken from a nearby forest for several of the plant species indicate that the models developed from our controlled experiment are reasonably applicable to naturally occurring plant populations.

scholarly journals Evaluation of the FluorWPS Model and Study of the Parameter Sensitivity for Simulating Solar-Induced Chlorophyll Fluorescence

2021 ◽  
Vol 13 (6) ◽  
pp. 1091
Author(s):  
Chiming Tong ◽  
Yunfei Bao ◽  
Feng Zhao ◽  
Chongrui Fan ◽  
Zhenjiang Li ◽  
...  
Keyword(s):  
Chlorophyll Fluorescence ◽  
Radiative Transfer ◽  
High Performance ◽  
Forest Canopy ◽  
Structural Parameters ◽  
Coefficient Of Determination ◽  
Leaf Angle ◽  
Angle Distribution ◽  
Structural Factors ◽  
Area Index

Solar-induced chlorophyll fluorescence (SIF) has been used as an indicator for the photosynthetic activity of vegetation at regional and global scales. Canopy structure affects the radiative transfer process of SIF within canopy and causes the angular-dependencies of SIF. A common solution for interpreting these effects is the use of physically-based radiative transfer models. As a first step, a comprehensive evaluation of the three-dimensional (3D) radiative transfers is needed using ground truth biological and hyperspectral remote sensing measurements. Due to the complexity of forest modeling, few studies have systematically investigated the effect of canopy structural factors and sun-target-viewing geometry on SIF. In this study, we evaluated the capability of the Fluorescence model with the Weighted Photon Spread method (FluorWPS) to simulate at-sensor radiance and SIF at the top of canopy, and identified the influence of the canopy structural factors and sun-target-viewing geometry on the magnitude and directional response of SIF in deciduous forests. To evaluate the model, a 3D forest scene was first constructed from Goddard’s LiDAR Hyperspectral and Thermal (G-LiHT) LiDAR data. The reliability of the reconstructed scene was confirmed by comparing the calculated leaf area index with the measured ones from the scene, which resulted in a relative error of 3.5%. Then, the performance of FluorWPS was evaluated by comparing the simulated at-sensor radiance spectra with the spectra measured from the DUAL and FLUO spectrometer of HyPlant. The radiance spectra simulated by FluorWPS agreed well with the measured spectra by the two high-performance imaging spectrometers, with a coefficient of determination (R2) of 0.998 and 0.926, respectively. SIF simulated by the FluorWPS model agreed well with the values of the DART model. Furthermore, a sensitivity analysis was conducted to assess the effect of the canopy structural parameters and sun-target-viewing geometry on SIF. The maximum difference of the total SIF can be as large as 45% and 47% at the wavelengths of 685 nm and 740 nm for different foliage area volume densities (FAVDs), and 48% and 46% for fractional vegetation covers (FVCs), respectively. Leaf angle distribution has a markedly influence on the magnitude of SIF, with a ratio of emission part to SIF range from 0.48 to 0.72. SIF from the grass layer under the tree contributed 10%+ more to the top of canopy SIF even for a dense forest canopy (FAVD = 3.5 m−1, FVC = 76%). The red SIF at the wavelength of 685 nm had a similar shape to the far-red SIF at a wavelength of 740 nm but with higher variability in varying illumination conditions. The integration of the FluorWPS model and LiDAR modeling can greatly improve the interpretation of SIF at different scales and angular configurations.

scholarly journals Estimation of LAI with the LiDAR Technology: A Review

2020 ◽  
Vol 12 (20) ◽  
pp. 3457
Author(s):  
Yao Wang ◽  
Hongliang Fang
Keyword(s):  
Laser Scanning ◽  
Large Scale ◽  
Scale Validation ◽  
Canopy Structure ◽  
Impact Factors ◽  
Future Research ◽  
Lidar Data ◽  
Biophysical Parameters ◽  
Area Index ◽  
Contact Frequency

Leaf area index (LAI) is an important vegetation parameter. Active light detection and ranging (LiDAR) technology has been widely used to estimate vegetation LAI. In this study, LiDAR technology, LAI retrieval and validation methods, and impact factors are reviewed. First, the paper introduces types of LiDAR systems and LiDAR data preprocessing methods. After introducing the application of different LiDAR systems, LAI retrieval methods are described. Subsequently, the review discusses various LiDAR LAI validation schemes and limitations in LiDAR LAI validation. Finally, factors affecting LAI estimation are analyzed. The review presents that LAI is mainly estimated from LiDAR data by means of the correlation with the gap fraction and contact frequency, and also from the regression of forest biophysical parameters derived from LiDAR. Terrestrial laser scanning (TLS) can be used to effectively estimate the LAI and vertical foliage profile (VFP) within plots, but this method is affected by clumping, occlusion, voxel size, and woody material. Airborne laser scanning (ALS) covers relatively large areas in a spatially contiguous manner. However, the capability of describing the within-canopy structure is limited, and the accuracy of LAI estimation with ALS is affected by the height threshold and sampling size, and types of return. Spaceborne laser scanning (SLS) provides the global LAI and VFP, and the accuracy of estimation is affected by the footprint size and topography. The use of LiDAR instruments for the retrieval of the LAI and VFP has increased; however, current LiDAR LAI validation studies are mostly performed at local scales. Future research should explore new methods to invert LAI and VFP from LiDAR and enhance the quantitative analysis and large-scale validation of the parameters.

The distribution of foliage density with foliage angle estimated from inclined point quadrat observations

1965 ◽  
Vol 13 (2) ◽  
pp. 357 ◽  
Author(s):  
JR Philip
Keyword(s):  
Integral Equation ◽  
Standard Deviation ◽  
Leaf Angle ◽  
Frequency Data ◽  
Sampling Errors ◽  
Contact Frequency ◽  
Foliage Density ◽  
The Mean ◽  
Point Quadrat ◽  
The Given

Estimation of the distribution of foliage density with foliage angle from contact frequency data for a number of quadrat inclinations involves solution of a Fredholm integral equation of the first kind. The kernel is known from the work of Warren Wilson and Reeves, and the observed contact frequencies constitute the given function f(β). The solution is g(α), the foliage angle density function. f (β) is known at only a finite number of points, and each value contains inevitable sampling errors. The structure of the solution is such that g(β) is consequently subject to serious errors. A technique involving smoothing of the data is developed with the aim of minimizing this difficulty. The technique is critically discussed and applied to observations of Warren Wilson on lucerne leaves. The analysis indicates that the distribution of leaf angle is roughly symmetrical about the mean angle, with a standard deviation of about 15°.

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