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Calculation of the angular radiance distribution for a coupled atmosphere and canopy

The radiative transfer equations for a coupled atmosphere and canopy are solved numerically by an improved Gauss-Seidel iteration algorithm. The radiation field is decomposed into three components: unscattered sunlight, single scattering, and multiple scattering radiance for which the corresponding equations and boundary conditions are set up and their analytical or iterational solutions are explicitly derived. The classic Gauss-Seidel algorithm has been widely applied in atmospheric research. This is its first application for calculating the multiple scattering radiance of a coupled atmosphere and canopy. This algorithm enables us to obtain the internal radiation field as well as radiances at boundaries. Any form of bidirectional reflectance distribution function (BRDF) as a boundary condition can be easily incorporated into the iteration procedure. The hotspot effect of the canopy is accommodated by means of the modification of the extinction coefficients of upward single scattering radiation and unscattered sunlight using the formulation of Nilson and Kuusk. To reduce the computation for the case of large optical thickness, an improved iteration formula is derived to speed convergence. The upwelling radiances have been evaluated for different atmospheric conditions, leaf area index (LAI), leaf angle distribution (LAD), leaf size and so on. The formulation presented in this paper is also well suited to analyze the relative magnitude of multiple scattering radiance and single scattering radiance in both the visible and near infrared regions.

Liang, Shunlin↗

TLSLEAF: Automatic Leaf Angle Estimates From Single-Scan Terrestrial Laser Scanning

Leaf angle distribution (LAD) in forest canopies affects estimates of leaf area, light interception, and global-scale photosynthesis, but is often simplified to a single theoretical value. Here, we present TLSLeAF (Terrestrial Laser Scanning Leaf Angle Function), an automated open-source method of deriving LADs from terrestrial laser scanning. TLSLeAF produces canopy-scale leaf angle and LADs by relying on gridded laser scanning data. The approach increases processing speed, improves angle estimates, and requires minimal user input. Key features are automation, leaf–wood classification, beta parameter output, and implementation in R to increase accessibility for the ecology community. TLSLeAF precisely estimates leaf angle with minimal distance effects on angular estimates while rapidly producing LADs on a consumer-grade machine. We challenge the popular spherical LAD assumption, showing sensitivity to ecosystem type in plant area index and foliage profile estimates that translate to c. 25% and c. 11% increases in canopy net photosynthesis (c. 25%) and solar-induced chlorophyll fluorescence (c. 11%). TLSLeAF can now be applied to the vast catalog of laser scanning data already available from ecosystems around the globe. The ease of use will enable widespread adoption of the method outside of remote-sensing experts, allowing greater accessibility for addressing ecological hypotheses and large-scale ecosystem modeling efforts.

3D↗

The reflection for dense plant canopies from the one-angle radiative transfer equation

An essential component of remote sensing of vegetation canopies from satellites is fundamental understanding. Since passive remote is driven by photons, the modeling of photon interactions with vegetation is a basic building block in that understanding. Several such photon transport models have been developed during the past two decades and continue to be developed. Different approaches have been followed including monte carlo, radiosity methods, geometric shadowing, and radiative transfer. In general, each approach has application for canopies with specific attributes. This presentation concerns the application of radiative transfer to dense vegetation canopies in which the soil does not participate. The approach taken here is novel in that a consistent theory for photon transport for non-rotationally invariant leaf scattering is developed in a canopy with a general leaf angle distribution (LAD). The theory is limited to the one-angle approximation (azimuthally averaged radiance) and is based on Chandrasekhar's analytical theory. While such a model is admittedly only approximate, it does fulfill a unique function in our search for understanding. In particular, the model is simple in its construct yet contains the essential features of canopy architecture that are mainly responsible for observed responses. Thus, this model will not only be a predictive tool but also an educational one. The mathematical setting is the radiative transfer equation in a dense (semiinfinite) canopy. The leaf scattering phase function is assumed to be Lambertian with different reflectance and transmittance. In addition, abaxial and adaxial differentiation is allowed which effectively destroys optical reciprocity. The analytical solution for the canopy BRDF is obtained by manipulation of the integral transport equation (a la Chandrasekhar) for a general LAD. With discretization of the. leaf angle, the resulting set of integral equations are solved iteratively including an acceleration procedure when the single scatter albedo is near one (in the NIR). Results will be compared to the LARS soybean canopy radiances as well as to broadleaf results from a recent Ames experiment.

Ganapol, B. D.↗

Evaluation of one dimensional analytical models for vegetation canopies

The SAIL model for one-dimensional homogeneous vegetation canopies has been modified to include the specular reflectance and hot spot effects. This modified model and the Nilson-Kuusk model are evaluated by comparing the reflectances given by them against those given by a radiosity-based computer model, Diana, for a set of canopies, characterized by different leaf area index (LAI) and leaf angle distribution (LAD). It is shown that for homogeneous canopies, the analytical models are generally quite accurate in the visible region, but not in the infrared region. For architecturally realistic heterogeneous canopies of the type found in nature, these models fall short. These shortcomings are quantified.

Goel, Narendra S.↗

Potential Sources of Polarized Light from a Plant Canopy

Field measurements have demonstrated that sunlight polarized during a first surface reflection by shiny leaves dominates the optical polarization of the light reflected by shiny-leafed plant canopies having approximately spherical leaf angle probability density functions ("Leaf Angle Distributions" - LAD). Yet for other canopies - specifically those without shiny leaves and/or spherical LADs - potential sources of optically polarized light may not always be obvious. Here we identify possible sources of polarized light within those other canopies and speculate on the ecologically important information polarization measurements of those sources might contain.

Polarized Light↗

Simulations of Seasonal and Latitudinal Variations in Leaf Inclination Angle Distribution: Implications for Remote Sensing

The leaf inclination angle distribution (LAD) is an important characteristic of vegetation canopy structure affecting light interception within the canopy. However, LADs are difficult and time consuming to measure. To examine possible global patterns of LAD and their implications in remote sensing, a model was developed to predict leaf angles within canopies. Canopies were simulated using the SAIL radiative transfer model combined with a simple photosynthesis model. This model calculated leaf inclination angles for horizontal layers of leaves within the canopy by choosing the leaf inclination angle that maximized production over a day in each layer. LADs were calculated for five latitude bands for spring and summer solar declinations. Three distinct LAD types emerged: tropical, boreal, and an intermediate temperate distribution. In tropical LAD, the upper layers have a leaf angle around 35 with the lower layers having horizontal inclination angles. While the boreal LAD has vertical leaf inclination angles throughout the canopy. The latitude bands where each LAD type occurred changed with the seasons. The different LADs affected the fraction of absorbed photosynthetically active radiation (fAPAR) and Normalized Difference Vegetation Index (NDVI) with similar relationships between fAPAR and leaf area index (LAI), but different relationships between NDVI and LAI for the different LAD types. These differences resulted in significantly different relationships between NDVI and fAPAR for each LAD type. Since leaf inclination angles affect light interception, variations in LAD also affect the estimation of leaf area based on transmittance of light or lidar returns.

Seasonal↗

Three-dimensional estimation of deciduous forest canopy structure and leaf area using multi-directional, leaf-on and leaf-off airborne lidar data

Airborne laser scanning (ALS) has been widely used to map gap probability and leaf area index (LAI) distribution at plot and landscape scales. As an indirect measurement, most ALS methods to estimate LAI combine waveform or point density information with supporting field measurements such as the leaf angle distribution, gap probability, or direct LAI measures. The development of a more independent estimation approach would facilitate more widespread use of existing ALS data to investigate patterns of forest structure and build realistic 3-D vegetation scenes to simulate remote sensing imagery and energy balance. Here, we develop a data processing workflow (named PVlad) using ALS point cloud apparent reflectance to estimate LAI and voxel-based leaf area density (LAD), aiming to reduce the need for associated field measurements such as the gap probability. The adaptation of the path volume (PV) concept derived from apparent reflectance integrates information from multi-directional ALS pulses, and quantifies the percentage exploration of each voxel for classification and occlusion correction, such that rigorous volumetric sampling approaches can be developed to derive LAI and LAD. The PVlad workflow was applied to discrete-return lidar data (Riegl VQ480i) acquired by NASA Goddard's LiDAR, Hyperspectral and Thermal Imager (G-LiHT) Airborne Imager during leaf-on (summer) and leaf-off (spring) conditions at the Smithsonian Environmental Research Center (SERC). The estimates of LAI and LAD captured structural differences between mature, logged, and intermediate-aged stands over eight deciduous forest plots. The derived LAI values were compared to field litter collection measurements, and the derived LAD vertical distribution was compared to the output of the VoxLAD model using terrestrial laser scan (TLS) field survey data. Using voxel sizes ranging from 0.5 m to 5 m, overall LAI estimation showed linear fitting coefficient bias and for 1 and 2 m voxel sizes, and vertical LAD distribution showed strong correlation with and for 0.5 and 1m voxel sizes. For every forest stand, upper-canopy LAD had a low variance for voxel sizes of ≤ . Application of PVlad to the G-LiHT and other similar ALS data archives enables the development of fine-resolution LAI map products, including voxelization of LAD for ecosystem science and radiative transfer simulations of remote sensing imagery or surface energy balance.

Tiangang Yin↗