Leaf Inclination Distribution Function Research Articles

Leaf properties estimation enhancement over heterogeneous vegetation by correcting for terrestrial laser scanning beam divergence effect

The need for an accurate description of forest structure is increased as it is a key for monitoring carbon storage, energy, and mass exchange, and different ecosystem functions. The leaf area index (LAI), the leaf area density (ul), and the leaf inclination distribution function (LIDF) are regarded as important and critical keys allowing the characterization of the forest structure. The dependency between these properties and the heterogeneity of the forest makes their estimation challenging and delicate. In this context, despite the expanding body of works reporting forest structure properties retrieval using infinitesimal footprint size terrestrial LiDAR system (TLS) data, there seem to be few works evaluating the influence of the TLS beam divergence effect (i.e. its size increase with distance from the sensor), on the estimation accuracy, even though the influence is not negligible. In this study, we aim to jointly estimate LAI/ul and LIDF using non-infinitesimal footprint size TLS data based on forward/inverse radiative transfer (RT) modeling. Our approach assumes a uniform distribution of azimuth angles enabling us to attain valuable insights into inclination angles and leaf area density while simplifying our computational efforts. The forward modeling allows an understanding of the interaction between vegetation structure properties and TLS light beams, while the inversion allows retrieving the properties given the TLS data. The inversion technique is based on the maximum likelihood estimator (MLE). Our problem turns out to be a non-linear and high-dimensional cost function to be optimized. To tackle this complexity, the global optimization technique, the shuffled complex evolution (SCE-UA), is adapted to find the globally optimal solution. Our developed approach is validated with simulated and actual forest TLS point clouds acquired from Estonian Pine, Birch, and Spruce stands. Our findings using simulated data prove that our estimates are in agreement with the actual ul and LIDF values with (MAEul∈0.00120.0043) and (RMSEul∈0.01370.0224). In the actual case, RMSELAI for Pine, Birch and Spruce stands are 0.1066, 0.014, and 0.070, respectively. In all cases, our approach outperforms state-of-the-art techniques.

Joint Estimation of Leaf Area Density and Leaf Angle Distribution Using TLS Point Cloud for Forest Stands

The foliage density $(u_l)$ and the leaf angle distribution (LAD) are important properties that impact radiation transmission, interception, absorption and, therefore, photosynthesis. Their estimation in a forested scene is a challenging task due to their interdependence in addition to the large variability in the forest structure and the heterogeneity of the vegetation. In this work, we propose to jointly estimate both of them using terrestrial laser scanner (TLS) point cloud for different forest stands. Our approach is based on direct/inverse radiative transfer modeling. The direct model was developed to simulate TLS shots within a vegetation scene having known foliage properties (i.e., $u_l$ and LAD) resulting in a 3-D point cloud of the observed scene. Then, the inverse model was developed to jointly estimate $u_l$ and LAD decomposing the 3-D point cloud into voxels. The problem turns out to a high-dimensional cost function to optimize. To do it, the shuffled complex evolution method has been adopted. Our approach is validated with results derived from several simulated homogeneous and heterogeneous vegetation canopies as well as from actual TLS point cloud acquired from Estonian Birch, Pine, and Spruce stands. Our findings revealed that our estimates were considerably close to the actual $u_l$ and leaf inclination distribution function (LIDF) values with ( $\text{Biais}_{u_l} \in [0.001 \; 0.006]$ , $\text{RMSE}_{u_l} \in [0.019 \; 0.045]$ , $\text{RMSE}_{\text{LIDF}} \in [ 0.019 \; 0.038]$ ) for homogeneous dataset and ( $\text{Biais}_{u_l} \in [0.001 \; 0.045]$ , $\text{RMSE}_{u_l} \in [0.023 \; 0.078]$ , $\text{RMSE}_{\text{LIDF}} \in [ 0.011 \; 0.018]$ ) for heterogeneous dataset with different tree crown geometries (i.e., conical and elliptical). In the actual case (Birch, Pine, and Spruce stands), our approach with the traditional and novel techniques, $\text{RMSE}_{\text{LAI}}$ are 0.526 and 0.105, respectively. The results outperform those of the baseline technique (i.e., assuming spherical LAD) with $\text{RMSE}_{\text{LAI}}=2.651$ .

Effects of varying solar-view geometry and canopy structure on solar-induced chlorophyll fluorescence and PRI

The increasing amount of continuous time series of solar-induced fluorescence (SIF) and vegetation indices (e.g. Photochemical Reflectance Index, PRI) acquired with high temporal (sub-minute) frequencies is foreseen to allow tracking of the structural and physiological changes of vegetation in a variety of ecosystems. Coupled with observations of CO2, water, and energy fluxes from eddy covariance flux towers, these measurements can bring new insights into the remote monitoring of ecosystem functioning. However, continuously changing solar-view geometry imposes directional effects on diurnal cycles of the fluorescence radiance in the observation direction (F) and PRI, controlled by structural and biochemical vegetation properties. An improved understanding of these variations can potentially help to disentangle directional responses of vegetation from physiological ones in the continuous long-term optical measurements and, therefore, allow to deconvolve the physiological information relevant to ecosystem functioning. Moreover, this will also be useful for better interpreting and validating F and PRI satellite products (e.g., from the upcoming ESA FLEX mission).Many previous studies focused on the characterization of reflectance directionality, but only a handful of studies investigated directional effects on F and vegetation indices related to plant physiology. The aim of this study is to contribute to the understanding of red (F687) and far-red (F760) fluorescence and PRI anisotropy based on field spectroscopy data and simulations with the Soil-Canopy Observation of Photochemistry and Energy fluxes (SCOPE) model. We present an extensive dataset of multi-angular measurements of F and PRI collected at canopy level with a high-resolution instrument (FloX, JB Hyperspectral Devices UG, Germany) over different ecosystems: Mediterranean grassland, alfalfa, chickpea and rice.We found, that F760 and F687 directional responses of horizontally homogeneous canopies are characterized by higher values in the backscatter direction with a maximum in the hotspot and lower values in the forward scatter direction. The PRI exhibited similar response due to its sensitivity to sunlit-shaded canopy fractions.As confirmed by radiative transfer forward simulations, we show that in the field measurements leaf inclination distribution function controls the shape of F and PRI anisotropic response (bowl-like/dome-like shapes), while leaf area index and the ratio of leaf width to canopy height affect the magnitude and the width of the hotspot. Finally, we discuss the implications of off-nadir viewing geometry for continuous ground measurements. F observations under oblique viewing angles showed up to 67 % difference compared to nadir observations, therefore, we suggest maintaining nadir viewing geometry for continuous measurements of F and vegetation indices. Alternatively, a correction scheme should be developed and tested against multi-angular measurements to properly account for anisotropy of canopy F and PRI observations. The quantitative characterization of these effects in varying illumination geometries for different canopies that was performed in this study will also be useful for the validation of remote sensing F and PRI products at different spatial and temporal scales.

Comparison of terrestrial LiDAR and digital hemispherical photography for estimating leaf angle distribution in European broadleaf beech forests

Leaf inclination plays a crucial role in regulating the radiation, carbon and water fluxes in plant canopies. Accurate measurement of the probability density function of leaf inclination (i.e., the leaf angle distribution or leaf inclination distribution function (LIDF)), is very important for modelling photosynthesis as well as measuring leaf area index. In spite of its importance, in situ measurement of LIDF is very challenging. Both digital hemispherical photography (DHP) and terrestrial LiDAR (TLS) have been used to measure LIDF. However, the consistency and relative accuracy of these two techniques has never been evaluated.In this research, we aimed to evaluate which in situ technique, either DHP or TLS, could measure LIDF more accurately, with respect to both field-based and synthetic datasets. The field-based datasets were collected from 36 natural European beech stands covering a range of forest structures. The synthetic datasets were generated from 44 virtual forest scenes using TLS and DHP simulators. Due to the inability of differing leaf and woody materials in DHP, the average plant inclination angle (θ¯) from DHP and TLS was selected for LIDF comparison. The average inclination angle (θ¯) was retrieved from TLS point clouds using a geometric method, and from DHP using three gap fraction inversion methods including the NC method (Norman and Campbell, 1989), as well as the CAN-EYE and Hemisfer software.Results from the field-based datasets showed a significant difference and inconsistency between the average inclination angle (θ¯) retrieved from TLS and DHP (respectively θ¯∈(40°, 58°) from TLS, (15°, 86°) from DHP NC, (36°, 78°) from DHP CAN-EYE, (0°, 67°) from DHP Hemisfer). Results from the synthetic datasets demonstrated that the accuracy of θ¯ from TLS was considerably higher than that obtained from DHP (R2: 0.90 > 0.74; RMSE: 5.38° < 13.30°).This study demonstrated that the LIDF estimated from TLS and DHP were not coherent. Based on the experimental results as well as deduction from theoretical arguments, we recommended using TLS when measuring leaf inclination in broadleaf forests, especially for stands with a heterogeneous structure.

Canopy Reflectance Modeling of Aquatic Vegetation for Algorithm Development: Global Sensitivity Analysis

Optical remote sensing of aquatic vegetation in shallow water is an essential aid to ecosystem protection, but it is difficult because the spectral characteristics of the vegetation are sensitive to external features such as water background effects, atmospheric effects, and the structural properties of the canopy. A global sensitivity analysis of an aquatic vegetation radiative transfer model provides invaluable background for algorithm development for use in optical remote sensing. Here, we use the extended Fourier Amplitude Sensitivity Test (EFAST) method for the modelling. Four different cases were identified by subdividing the ranges of water depth and leaf area index (LAI) involved. The results indicate that the reflectance of emergent vegetation is affected mainly by the concentrations of chlorophyll a + b in leaves (Cab), leaf inclination distribution function parameter (LIDFa) and LAI. The parameter LAI is influential in sparse vegetation cases whereas Cab and LIDFa are influential in dense vegetation cases. Canopy reflectance for submerged vegetation is dominated by water parameters. Relatively, LAI and Cab are highly sensitive vegetation parameters. The analysis is extended to vegetation index as well, which takes the Sentinel-2A as the reference sensor. It shows that NDAVI (Normalized Difference Aquatic Vegetation Index) is suitable for retrieving LAI in all cases except deep-sparse for emergent vegetation, whereas NDVI (Normalized Difference Vegetation Index) would be better in the deep-sparse case. NDVI, NDAVI and WAVI (Water Adjusted Vegetation Index), respectively, are suitable for retrieving Cab, Car and LIDFa in dense cases. For submerged vegetation, the sensitivity of LAI to NDAVI is relatively high only in the shallow-sparse case. The adjustment factor L in SAVI and WAVI fails to suppress the sensitivity to water constituent parameters. The sensitivity of LAI and Cab to NDVI in deep cases is relatively higher than that to the other indices, which may provide clues for the construction of inversion algorithms in macrophyte remote sensing in the aquatic environment using spectral signatures in the visible and near infrared regions.

Integrating satellite optical and thermal infrared observations for improving daily ecosystem functioning estimations during a drought episode

Satellite optical and thermal infrared (TIR) spectra are linked to vegetation properties and, therefore, carry valuable information needed for estimating vegetation functioning as expressed in canopy photosynthesis [gross primary production (GPP)] and evapotranspiration (ET). The joint effort is required to fully exploit this satellite spectral information and to demonstrate its capability to reveal ecosystem functioning in various environmental conditions. We investigated the relationship between Landsat (TM5 and ETM7) optical/thermal data and canopy daily functioning of annual C3 grasses at a Fluxnet site (US-Var) during a prolonged drought episode. By using the ‘Soil-Canopy Observation of Photosynthesis and Energy fluxes’ (SCOPE) model, reference GPP and ET were simulated via locally measured weather data, and then actual GPP and ET were simulated twice: first using the vegetation properties retrieved only from the optical bands, and second using information from both the optical and thermal bands. The outputs of last two simulations were compared to flux tower measurements. For the first simulation, we used the MODTRAN atmospheric model and the optical radiative transfer (RT) routine in SCOPE, RTMo, to perform atmospheric correction and retrieve vegetation properties [notably Leaf Area Index (LAI), leaf chlorophyll content (Cab), leaf water content (Cw), leaf dry matter content (Cdm), the leaf inclination distribution function (LIDF) and the senescent material content (Cs)] by model inversion through optimization. We used the optical bands of 20 Landsat images covering the period from January to August 2004. The model inversion performance was assessed by R2 (0.86) and RMSE (0.13) between the retrieved and ground-measured LAI. All the retrieved vegetation properties were linearly interpolated over time and were used, together with locally measured weather variables, to simulate GPP and ET at half-hourly time steps with SCOPE. For the second simulation, we additionally used TIR information to retrieve the maximum carboxylation capacity (Vcmax), the Ball-Berry stomatal conductance parameter (m) and soil surface and boundary resistances (rss and rbs) by inversion of the energy balance and thermal radiative transfer routines of SCOPE, RTMt, through separate look-up tables. The comparison between simulations and measurements shows that most drought effects on ET, GPP and transpiration are “visible” in the Landsat optical bands. However, the accurate simulation of soil evaporation requires TIR information. The results from this study indicate that the integration of optical and TIR information has a great potential to capture the drought effects on the grass canopy in terms of reductions in daily GPP and ET.

Plant functional traits and canopy structure control the relationship between photosynthetic CO2 uptake and far-red sun-induced fluorescence in a Mediterranean grassland under different nutrient availability.

Sun-induced fluorescence (SIF) in the far-red region provides a new noninvasive measurement approach that has the potential to quantify dynamic changes in light-use efficiency and gross primary production (GPP). However, the mechanistic link between GPP and SIF is not completely understood. We analyzed the structural and functional factors controlling the emission of SIF at 760nm (F760 ) in a Mediterranean grassland manipulated with nutrient addition of nitrogen (N), phosphorous (P) or nitrogen-phosphorous (NP). Using the soil-canopy observation of photosynthesis and energy (SCOPE) model, we investigated how nutrient-induced changes in canopy structure (i.e. changes in plant forms abundance that influence leaf inclination distribution function, LIDF) and functional traits (e.g. N content in dry mass of leaves, N%, Chlorophyll a+b concentration (Cab) and maximum carboxylation capacity (Vcmax )) affected the observed linear relationship between F760 and GPP. We conclude that the addition of nutrients imposed a change in the abundance of different plant forms and biochemistry of the canopy that controls F760 . Changes in canopy structure mainly control the GPP-F760 relationship, with a secondary effect of Cab and Vcmax . In order to exploit F760 data to model GPP at the global/regional scale, canopy structural variability, biodiversity and functional traits are important factors that have to be considered.

Estimation of solar-induced fluorescence using the canopy reflectance index

This article presents a methodology to quantitatively extract the solar-induced fluorescence (SIF) using the canopy reflectance index. The sensitivity analysis was conducted with a spectral vegetation Fluorescence Model (FluorMOD), and the results demonstrate that Sun zenith angle (θ), fluorescence quantum efficiency (Fi), leaf inclination distribution function (LIDF), leaf temperature (T), leaf area index, and leaf chlorophyll a + b content (chl-a+b) had large effects on the fluorescence radiance at 761 nm (LF,761). Based on the results of the sensitivity analysis, the input parameters θ, Fi, LIDF, T, and chl-a+b varied within a certain range during the generation of the simulated data. Based on the simulated data, R740/R630, R685/R850, and R750/R710 were thought to be the best candidates to extract the fluorescence radiation. The quantitative relationships between the fluorescence retrieved by R740/R630, R685/R850, and R750/R710 and LF,761 were analysed and expressed as functions of θ, Fi, T, and reflectance index. The correlation coefficients (r) between the fluorescence retrieved using R685/R850, R740/R630, and R750/R710 and LF,761 are 0.94, 0.95, and 0.95, respectively, and the root mean square errors (RMSEs) were 0.32, 0.29, and 0.30 W m−2 μm−1 sr−1, respectively. Through comparison with FLD and 3FLD, the method presented in this article yielded better results, and could be used to estimate the fluorescence. This methodology provides new insights into the quantitative retrieval of SIF from the reflectance spectrum.

Global sensitivity analysis of the spectral radiance of a soil–vegetation system

We analyzed the sensitivity of Top-Of-Atmosphere (TOA) radiance and surface reflectance of a soil–vegetation system to input biophysical and biochemical parameters using the coupled Soil–Leaf-Canopy radiative transfer model SLC and MODTRAN. We applied variance-based global sensitivity analysis for different atmospheric conditions and observation configurations. Among 23 input parameters, crown coverage, leaf area index, leaf inclination distribution function and soil moisture were found to be the most influential parameters driving the output variance of the radiance between 400 and 2500nm with a few exceptions. Hapke's soil parameters and the canopy layer dissociation factor were recognized to have marginal influence on the output radiance. It is also found that a large portion of uncertainty in the output radiance is driven by the interaction effects among input parameters in the visible (~550nm), whereas the red-near infrared (~670nm), seems to have fewer interaction effects. The effect of solar/view direction is found to be significant on TOA radiance sensitivity to the input parameters. The results also confirmed that the sensitivities of surface reflectance are comparable to the TOA radiance sensitivities when the atmosphere is clear and visibility is high. Since coupled surface-atmosphere RT models can be computationally intensive, this work also introduces an improvement to the design and sampling of screening methods for efficient sensitivity analysis of computationally expensive models. The improvement is based on three elements: a) generating sample points by Sobol's sequence generator; b) variational analysis in the parameter space using the winding stairs method; c) use of mean and variance sensitivity measures. The results with 1200 model runs demonstrated high correlation (92%) with variance-based global sensitivity analysis using 49,152 model runs, in determining the most influential and non-influential parameters.

Modelling the spectral response of the desert tree Prosopis tamarugo to water stress

In this paper, we carried out a laboratory experiment to study changes in canopy reflectance of Tamarugo plants under controlled water stress. Tamarugo (Prosopis tamarugo Phil.) is an endemic and endangered tree species adapted to the hyper-arid conditions of the Atacama Desert, Northern Chile. Observed variation in reflectance during the day (due to leaf movements) as well as changes over the experimental period (due to water stress) were successfully modelled by using the Soil-Leaf-Canopy (SLC) radiative transfer model. Empirical canopy reflectance changes were mostly explained by the parameters leaf area index (LAI), leaf inclination distribution function (LIDF) and equivalent water thickness (EWT) as shown by the SLC simulations. Diurnal leaf movements observed in Tamarugo plants (as adaptation to decrease direct solar irradiation at the hottest time of the day) had an important effect on canopy reflectance and were explained by the LIDF parameter. The results suggest that remote sensing based assessment of this desert tree should consider LAI and canopy water content (CWC) as water stress indicators. Consequently, we tested fifteen different vegetation indices and spectral absorption features proposed in literature for detecting changes of LAI and CWC, considering the effect of LIDF variations. A sensitivity analysis was carried out using SLC simulations with a broad range of LAI, LIDF and EWT values. The Water Index was the most sensitive remote sensing feature for estimating CWC for values less than 0.036g/cm2, while the area under the curve for the spectral range 910–1070nm was most sensitive for values higher than 0.036g/cm2. The red-edge chlorophyll index (CIred-edge) performed the best for estimating LAI. Diurnal leaf movements had an effect on all remote sensing features tested, particularly on those for detecting changes in CWC.

Evaluation of a turbid medium model to simulate light interception by walnut trees (hybrid NG38×RA and Juglans regia) and sorghum canopies (Sorghum bicolor) at three spatial scales.

Light is one of the most important components to be included in functional-structural plant models that simulate the biophysical processes, such as photosynthesis, evapotranspiration and photomorphogenesis, involved in plant growth and development. In general, in these models, light is treated using a turbid medium approach in which radiation attenuation is described by the Beer-Lambert law. In the present study, we assessed the hypothesis of leaf random dispersion in the Beer-Lambert law at the whole-canopy, horizontal-layer and local scales. We compared two calculation methods of radiation attenuation: a 3D turbid medium model using the Beer-Lambert law and the other based on a projective method. The two models were compared by applying the calculations to two walnut trees and two sorghum canopies, which have contrasting structural characteristics. The structures of these canopies were measured in 3D to take into account the arrangement and orientation features of the plant elements. The assumptions made by the Beer-Lambert law allowed adequate simulation of light interception in a structure with little overlapping at the horizontal-layer and whole-canopy scales. At the local scale, discrepancies between the turbid medium model and the model based on a virtual plant were reduced with an adequate choice of structural parameters, such as the leaf inclination distribution function.

FluorMODgui V3.0: A graphic user interface for the spectral simulation of leaf and canopy chlorophyll fluorescence

The FluorMODgui Graphic User Interface (GUI) software package developed within the frame of the FluorMOD project Development of a Vegetation Fluorescence Canopy Model is presented in this manuscript. The FluorMOD project was launched in 2002 by the European Space Agency (ESA) to advance the science of vegetation fluorescence simulation through the development and integration of leaf and canopy fluorescence models based on physical methods. The design of airborne or space missions dedicated to the measurement of solar-induced chlorophyll fluorescence using remote-sensing instruments require physical methods for quantitative feasibility analysis and sensor specification studies. The FluorMODgui model developed as part of this project is designed to simulate the effects of chlorophyll fluorescence at leaf and canopy levels using atmospheric inputs, running the leaf model, FluorMODleaf, and the canopy model, FluorSAIL, independently, through a coupling scheme, and by a multiple iteration protocol to simulate changes in the viewing geometry and atmospheric characteristics. Inputs for the FluorMODleaf model are the number of leaf layers, chlorophyll a+ b content, water equivalent thickness, dry matter content, fluorescence quantum efficiency, temperature, species type, and stoichiometry. Inputs for the FluorSAIL canopy model are a MODTRAN-4 6-parameter spectra or measured direct horizontal irradiance and diffuse irradiance spectra, a soil reflectance spectrum, leaf reflectance & transmittance spectra and a excitation-fluorescence response matrix in upward and downward directions (all from FluorMODleaf), 2 PAR-dependent coefficients for the fluorescence response to light level, relative azimuth angle and viewing zenith angle, canopy leaf area index, leaf inclination distribution function, and a hot spot parameter. Outputs available in the 400–1000 nm spectral range from the graphical user interface, FluorMODgui, are the leaf spectral reflectance and transmittance, and the canopy reflectance, with and without fluorescence effects. In addition, solar and sky irradiance on the ground, radiance with and without fluorescence on the ground, and top-of-atmosphere (TOA) radiances for bare soil and surroundings same as target are also produced. The models and documentation regarding the FluorMOD project can be downloaded at http://www.ias.csic.es/fluormod.

Modeling hemispherical and directional radiative fluxes in regular-clumped canopies

A model of radiative transfer in regular-clumped canopies is presented. The canopy is approximated by an array of porous cylinders located at the vertices of equilateral triangles. The model is split into two submodels, each describing a different level of structure: 1) The macrostructure submodel is based on Brown and Pandolfo (1969), who applied geometrical optics theory to an array of opaque cylinders. This model is adapted for porous cylinders and is used to derive expressions for directional interception efficiency as a function of height, radius, spacing and porosity of the cylinders. 2) The microstructure submodel makes use of the average canopy transmittance theory, applied to a cylinder, to compute the porosity of the clumps as a function of the leaf area density, the leaf inclination distribution function, the dimensions of the cylinder (height and radius), and the transmittance of green leaves in the appropriate spectral band. It is shown that, in the case of erectophile plant stands, the daily porosity of the cylinder can be approximated by the porosity calculated using the extinction coefficient of diffuse radiation. Directional interception efficiency, geometric conditions (incidence/viewing), and landscape component reflectances are used to compute hemispherical (interception, absorption, and reflectance) and directional (reflectance) radiative fluxes from simple analytical formulae. This model is validated against a data set of biological, radiative (PAR region) and radiometric (SPOT channels) measurements, collected in Niger on pearl millet ( Pennisetum typhoides). The model fits the data quite well in terms of hourly and daily single-band or combined (NDVI) radiative fluxes. Close correspondence to measured fluxes, using few parameters, and the possibility of inversion makes the present model a valuable tool for the study of radiative transfer in discontinuous canopies.

Light scattering by leaf layers with application to canopy reflectance modeling: The SAIL model

The scattering and extinction coefficients of the SAIL canopy reflectance model are derived for the case of a fixed arbitrary leaf inclination angle and a random leaf azimuth distribution. The SAIL model includes the uniform model of G. H. Suits as a special case and its main characteristics are that canopy variables such as leaf area index and the leaf inclination distribution function are used as input parameters and that it provides more realistic angular profiles of the directional reflectance as a function of the view angle or the solar zenith angle.