Simple analytical formula for calculating average photon recollision probability in vegetation canopies

The concept of recollision probability originates from the theory of canopy spectral invariants (‘p-theory’) but is a simplification that involves several heuristic assumptions. Nonetheless, the concept has been shown to be a useful tool for incorporating the effects of 3D structure on canopy absorptive and reflective properties in forest reflectance models. A method is presented by which an average value of the canopy recollision probability (pˆ) can be calculated from canopy gap fraction data, which are provided for example by the LAI-2000 plant canopy analyzer or can be extracted from fisheye photographs. The new method was used to calculate the average recollision probabilities (pˆ values) of uniform leaf and shoot canopies, showing good agreement with results from Monte Carlo simulations. Strengths of the method presented here are the explicitly formulated relationship between recollision probability and canopy structure, and its direct applicability in canopy RT studies.     

On the relationship of canopy LAI and photon recollision probability in boreal forests

The theory of spectral invariants, or ‘p-theory’, states that the canopy scattering coefficient at any wavelength can be related to the leaf scattering coefficient at the same wavelength through a spectrally invariant canopy structural parameter — the photon recollision probability p. The p-theory has recently gained interest in the vegetation reflectance modeling community as an efficient tool for characterizing scattering in clumped foliage structures. In this short communication paper, we report empirical data of the relationship of canopy leaf area index (LAI), diffuse non-interceptance and photon recollision probability for 1032 coniferous and broadleaved forest plots measured in Finland. Our results indicate that the relationship of canopy LAI and diffuse non-interceptance is near-universal in boreal stands i.e. it does not depend on stand age, tree species or growth conditions. This allows improving parameterizations used by canopy reflectance models which utilize the photon recollision probability concept. Our results also suggest that establishing species-specific p-LAI functions for northern European forests requires more research on the influence of micro- and macroscale foliage grouping on photon recollision probability.     

A simple parameterization of canopy reflectance using photon recollision probability

Information on the fractions of incident radiation reflected, transmitted and absorbed by a plant canopy is crucial in remote sensing of vegetation and modeling of canopy microclimate. Photon recollision probability p allows to calculate easily the spectral behavior of canopy scattering, i.e. the sum of canopy reflectance and transmittance. However, to divide the scattered radiation into reflected and transmitted fluxes, additional models are needed. In this paper, we present a simple formula to estimate the fraction of radiation scattered upwards by a canopy. The new method is semi-empirical, makes use of the concept of photon recollision probability, and is derived from an analysis of modeling results. Although a physical interpretation is given for the single additional parameter needed in the formula, the scattering asymmetry parameter q, the method is not strictly based on the radiative transfer equation. Our results indicate that the method is accurate for low to moderate leaf area index (LAI) values, and provides a reasonable approximation even at LAI = 8. In addition, we present a method to compute p using numerical radiative transfer models.     

Application of photon recollision probability in coniferous canopy reflectance simulations

A new semi-physical forest reflectance model, PARAS, is presented in the paper. PARAS is a simple parameterization model for taking into account the effect of within-shoot scattering on coniferous canopy reflectance. Multiple scattering at the small scale represented by a shoot is a conifer-specific characteristic which causes the spectral signature of coniferous forests to differ from that of broadleaved forests. This has for long led to problems in remote sensing of canopy structural variables in coniferous dominated regions. The PARAS model uses a relationship between photon recollision probability and leaf area index (LAI) for simulating forest reflectance. The recollision probability is a measurable, wavelength independent variable which is defined as the probability with which a photon scattered in the canopy interacts with a phytoelement again. In this study, we present application results using PARAS in simulating reflectance of coniferous forests for approximately 800 Scots pine and Norway spruce dominated stands. The results of this study clearly indicate that a major improvement in simulating canopy reflectance in near-infrared (NIR) is achieved by simply accounting for the within-shoot scattering. In other words, the low NIR reflectance observed in coniferous areas is mainly due to within-shoot scattering. In the red wavelength the effect of within-shoot scattering was not pronounced due to the high level of needle absorption in the red range. To conclude the paper, further application possibilities of the presented parameterization model are discussed.     

Simple parameterizations of the radiation budget of uniform broadleaved and coniferous canopies

Simulations of the different components of the spectral radiation budget of structurally simple leaf and shoot canopies with varying canopy leaf area index (LAI) were performed. The aims were (1) to test a proposed parameterization of the budget using two spectrally invariant canopy structural parameters (p and p_t) governing canopy absorption and transmittance, respectively, and (2) to incorporate the effect of within-shoot scattering in the parameterization for shoot canopies. Results showed that canopy spectral absorption and scattering were well described by a single parameter, the canopy p value or ‘recollision probability’, which was closely related to LAI. The relationship between p and LAI was however different in leaf and shoot canopy: e.g., at the same LAI the recollision probability was larger in the shoot canopy. It was shown that the p value of the shoot canopy could be decomposed into the p value of an individual shoot (p_sh) and the p value of the leaf canopy with the same effective LAI (LAI_e). The canopy p value allows calculation of canopy absorption and scattering at any given wavelength from the leaf (or needle) scattering coefficient at the same wavelength. To calculate canopy reflectance, separation of the downward and upward scattered parts is needed in addition. The proposed parameter p_t worked rather well in the leaf canopy at moderate values of LAI, but not in the coniferous shoot canopy nor at high values of LAI. However, the simulated fraction of upward scattered radiation increased in a straightforward manner with LAI, and was not particularly sensitive to the leaf (or needle) scattering coefficient. Judged by this ‘smooth’ behavior, the existence of another kind of simple parameterization for this separation remains an interesting possibility.     

Radiative transfer modelling of discontinuous tree canopies at microwave frequencies

Abstract

Development of a first-order radiative transfer model for predicting backscatter from tree canopies has been underway at the University of Michigan Radiation Laboratory for some time. This model is known as the Michigan Microwave Canopy Scattering (MIMICS) model. The first-generation model, MIMICS I, was developed for canopies with continuous (closed) crown layers and its validity has been verified in several modelling analyses. This article presents the second-generation MIMICS model (MIMICS II) which accounts for canopies with discontinuous (open) crown layer geometries. MIMICS II models open crown layers by treating the location, size and shape of the individual tree crowns as random variables. The backscattering coefficients for the canopy are then determined by introducing statistics derived from these parameters into the radiative transfer solution.

Application of the radiative transfer equations to the discontinuous canopy geometry is presented. The application of random variables defining the crown geometry and the incorporation of these variables into the radiative transfer solution is discussed. The resulting model is a robust fully polarimetric solution that is applicable over a wide variety of canopy architectures. Model simulations are compared to results generated with the continuous canopy model. The effect of the open crown geometry is found to be most significant at shallow incidence angles and at high frequencies for trees with well-developed crowns. Under these conditions, the gaps in the crown layer give rise to a notable increase in crown layer transmissivity which allows the radar to see through to the lower layers of the canopy more easily thereby directly affecting the backscatter contribution of the trunks and ground.     

The effect of clumping on canopy scattering and its directional properties: a model simulation using spectral invariants

The spectral invariants theory predicts that the bidirectional reflectance factor (BRF) of a vegetation canopy can be expressed in terms of the canopy interceptance (i₀), the recollision probability (p), and the directional escape probability (ρ). These spectral invariant parameters together form a novel canopy structural parameter – the directional area scattering factor (DASF). The DASF can be retrieved from remotely sensed hyperspectral imagery and has been found to be useful, e.g. for the separation of tree species. The spectral invariants theory, however, does not provide an interpretation of which specific canopy structural properties are captured by the DASF. In this study, we examined the possible link between the DASF and the canopy clumping index (β). A simple model was designed to simulate the effect of β on canopy first order scattering, which was assumed to govern the directional behaviour of the DASF. The model is based on a modified spectral invariants approach, where the assumption of constant p is relaxed so that the first order recollision probability (p₁) and single scattering are calculated separately, and canopy BRF is expressed as the sum of the first and multiple order components. Simulations were performed on model canopies, where radiation penetration is described using a traditional statistical approach but allowing non-random foliage distributions caused by clumping. The results indicated a strong dependency between the modelled DASF and the canopy clumping index.     

Canopy spectral invariants for remote sensing and model applications

The concept of canopy spectral invariants expresses the observation that simple algebraic combinations of leaf and canopy spectral transmittance and reflectance become wavelength independent and determine a small set of canopy structure specific variables. This set includes the canopy interceptance, the recollision and the escape probabilities. These variables specify an accurate relationship between the spectral response of a vegetation canopy to the incident solar radiation at the leaf and the canopy scale and allow for a simple and accurate parameterization for the partitioning of the incoming radiation into canopy transmission, reflection and absorption at any wavelength in the solar spectrum. This paper presents a solid theoretical basis for spectral invariant relationships reported in literature with an emphasis on their accuracies in describing the shortwave radiative properties of the three-dimensional vegetation canopies. The analysis of data on leaf and canopy spectral transmittance and reflectance collected during the international field campaign in Flakaliden, Sweden, June 25-July 4, 2002 supports the proposed theory. The results presented here are essential to both modeling and remote sensing communities because they allow the separation of the structural and radiometric components of the measured/modeled signal. The canopy spectral invariants offer a simple and accurate parameterization for the shortwave radiation block in many global models of climate, hydrology, biogeochemistry, and ecology. In remote sensing applications, the information content of hyperspectral data can be fully exploited if the wavelength-independent variables can be retrieved, for they can be more directly related to structural characteristics of the three-dimensional vegetation canopy.     

Hyperspectral indices and model simulation for chlorophyll estimation in open-canopy tree crops

An investigation of the estimation of leaf biochemistry in open tree crop canopies using high-spatial hyperspectral remote sensing imagery is presented. Hyperspectral optical indices related to leaf chlorophyll content were used to test different radiative transfer modelling assumptions in open canopies where crown, soil and shadow components were separately targeted using 1 m spatial resolution ROSIS hyperspectral imagery. Methods for scaling-up of hyperspectral single-ratio indices such as R₇₅₀/R₇₁₀ and combined indices such as MCARI, TCARI and OSAVI were studied to investigate the effects of scene components on indices calculated from pure crown pixels and from aggregated soil, shadow and crown reflectance. Methods were tested on 1-m resolution hyperspectral ROSIS datasets acquired over two olive groves in southern Spain during the HySens 2002 campaign conducted by the German Aerospace Center (DLR). Leaf-level biochemical estimation using 1-m ROSIS data when targeting pure olive tree crowns employed PROSPECT-SAILH radiative transfer simulation. At lower spatial resolution, therefore with significant effects of soil and shadow scene components on the aggregated pixels, a canopy model to account for such scene components had to be used for a more appropriate estimation approach for leaf biochemical concentration. The linked models PROSPECT-SAILH-FLIM improved the estimates of chlorophyll concentration from these open tree canopies, demonstrating that crown-derived relationships between hyperspectral indices and biochemical constituents cannot be readily applied to hyperspectral imagery of lower spatial resolutions due to large soil and shadow effects. Predictive equations built on a MCARI/OSAVI scaled-up index through radiative transfer simulation minimized soil background variations in these open canopies, demonstrating superior performance compared to other single-ratio indices previously shown as good indicators of chlorophyll concentration in closed canopies. The MCARI/OSAVI index was demonstrated to be less affected than TCARI/OSAVI by soil background variations when calculated from the pure crown component even at the typically low LAI orchard and grove canopies.     

Estimation of canopy parameters for inhomogeneous vegetation canopies from reflectance data. II. Estimation of leaf area index and percentage of ground cover for row canopies

The canopy reflectance (CR) model for row-planted vegetation proposed earlier has been tested for soybean canopies in three different stages of growth and for corn canopies at early and full growth stages. The model fits the field-measured bidirectional CR data quite well. It is shown that, by inverting this model, one could estimate the leaf area index as well as the percentage of ground cover quite accurately from measured canopy reflectances.     

Coupling forest canopy and understory reflectance in the Arctic latitudes of Finland

The Arctic region is predicted to experience considerable climatic and environmental changes as the global atmospheric CO₂ increases. Growing awareness of the role of tundra and taiga ecosystems and their transition zone in the climate change process has resulted in a recent increase in remote sensing studies focusing on the Arctic latitudes. Remote sensing of biophysical properties of the canopy layer in the forested part of the region is often, however, challenged by the dominating role of the understory in the spectral signal. In this paper, we examine the influence of understory vegetation on forest reflectance in the Arctic region of Finland during no-snow conditions. The study is based on SPOT HRVIR images, field goniospectrometry, 300 ground reference plots and a physically-based forest reflectance model (PARAS). The results indicate that lichen-dominated forest site types can be distinguished from sites dominated by dwarf shrubs. The paper also contains results from applying an analytical method for calculating photon recollision probability from canopy transmittance data for forest stands, and then using it to simulate the reflectance of the same stands.     

Direct retrieval of the shape of leaf spectral albedo from multiangular hyperspectral Earth observation data

Physically-based retrieval of vegetation canopy properties from remote sensing data presumes a knowledge of the spectral albedo of the basic scattering unit, i.e. leaf. In this paper, we present a novel method to directly retrieve the spectral dependence of leaf single-scattering albedo of a closed broadleaf forest canopy from multiangular hyperspectral satellite imagery. The new algorithm is based on separating the reflected signal into a linear (first-order) and non-linear (diffuse) reflectance component. A limitation of the proposed algorithm is that the leaf single-scattering albedo ω(λ) is retrieved with an accuracy of a structural parameter (called a₀) which, in turn, depends on canopy bidirectional gap probability, ratio of leaf reflectance to transmittance, and distribution of leaf normals. The structural parameter (a₀) was found to depend on tree-level structural parameters, such as tree height and volume of a single crown, but not the amount of leaf area.     

A method to account for shoot scale clumping in coniferous canopy reflectance models

The three-dimensional structure of a coniferous shoot gives rise to multiple scattering of light between the needles of the shoot, causing the shoot spectral reflectance to differ from that of a flat leaf. Forest reflectance models based on the radiative transfer equation handle shoot level clumping by correcting the radiation attenuation coefficient with a clumping index. The clumping index causes a reduction in the interception of radiation by the canopy at a fixed leaf area index (LAI). In this study, we show how within-shoot multiple scattering is related to shoot scale clumping and derive a similar, but wavelength dependent, correction to the scattering coefficient. The results provide a method for integrating shoot structure into current radiative transfer equation based forest reflectance models. The method was applied to explore the effect of shoot scale clumping on canopy spectral reflectance using simple model canopies with a homogeneous higher level structure. The clumping of needles into shoots caused a wavelength dependent reduction in canopy reflectance, as compared to that of a leaf canopy with similar interception. This is proposed to be one reason why coniferous and broad-leaved canopies occupy different regions in the spectral space and exhibit different dependency of spectral vegetation indices on LAI.     

双层植被结构冠层光谱特性的理论模拟

利用双层冠层反射率模型ACRM，模拟不同叶面积指数LAI、含水量Cw和结构参数N下，波长是820nm和1600nm冠层反射率的角度分布。结果说明，该模型能准确模拟出“热点”效应 |冠层反射率角度分布对LAI的敏感性小于LAI和Cw以及LAI和N的共同作用。其中LAI和Cw共同作用对波长1 600 nm反射率角度分布的影响非常显著，而LAI和N的共同作用在820 nm略微大于1 600 nm。另外，提取冠层含水量的土壤可调节水分指数SAWI受冠层结构的影响也较大。今后在模型选取中应该更好的考虑冠层结构影响。     

Modeling airborne laser scanning data for the spatial generation of critical forest parameters in fire behavior modeling

Methods for using airborne laser scanning (also called airborne LIDAR) to retrieve forest parameters that are critical for fire behavior modeling are presented. A model for the automatic extraction of forest information is demonstrated to provide spatial coverage of the study area, making it possible to produce 3-D inputs to improve fire behavior models.The Toposys I airborne laser system recorded the last return of each footprint (0.30-0.38 m) over a 2000 m by 190 m flight line. Raw data were transformed into height above the surface, eliminating the effect of terrain on vegetation height and allowing separation of ground surface and crown heights. Data were defined as ground elevation if heights were less than 0.6 m. A cluster analysis was used to discriminate crown base height, allowing identification of both tree and understory canopy heights. Tree height was defined as the 99 percentile of the tree crown height group, while crown base height was the 1 percentile of the tree crown height group. Tree cover (TC) was estimated from the fraction of total tree laser hits relative to the total number of laser hits. Surface canopy (SC) height was computed as the 99 percentile of the surface canopy group. Surface canopy cover is equal to the fraction of total surface canopy hits relative to the total number of hits, once the canopy height profile (CHP) was corrected. Crown bulk density (CBD) was obtained from foliage biomass (FB) estimate and crown volume (CV), using an empirical equation for foliage biomass. Crown volume was estimated as the crown area times the crown height after a correction for mean canopy cover.     

Spectroscopy of canopy chemicals in humid tropical forests

Remote sensing of canopy chemistry could greatly advance the study and monitoring of functional processes and biological diversity in humid tropical forests. Imaging spectroscopy has contributed to canopy chemical remote sensing, but efforts to develop general, globally-applicable approaches have been limited by sparse and inconsistent field and laboratory data, and lacking analytical methods. We analyzed leaf hemispherical reflectance and transmittance spectra, along with a 21-chemical portfolio, taken from 6136 fully sunlit humid tropical forest canopies, and developed an up-scaling method using a combination of canopy radiative transfer, chemometric and high-frequency noise modeling. By integrating these steps, we found that the accuracy and precision of multi-chemical remote sensing of tropical forest canopies varies by leaf constituent and wavelength range. Under conditions of varying canopy structure and spectral noise, photosynthetic pigments, water, nitrogen, cellulose, lignin, phenols and leaf mass per area (LMA) are accurately estimated using visible-to-shortwave infrared spectroscopy (VSWIR; 400-2500 nm). Phosphorus and base cations are retrieved with lower yet significant accuracy. We also find that leaf chemical properties are estimated far more consistently, and with much higher precision and accuracy, using the VSWIR range rather than the more common and limited visible to near-infrared range (400-1050 nm; VNIR). While VNIR spectroscopy proved accurate for predicting foliar LMA, photosynthetic pigments and water, VSWIR spectra provided accurate estimates for three times the number of canopy traits. These global results proved to be independent of site conditions, taxonomic composition and phylogenetic history, and thus they should be broadly applicable to multi-chemical mapping of humid tropical forest canopies. The approach developed and tested here paves the way for studies of canopy chemical properties in humid tropical forests using the next generation of airborne and space-based high-fidelity imaging spectrometers.     

Effects of woody elements on simulated canopy reflectance: Implications for forest chlorophyll content retrieval

An important bio-indicator of actual plant health status, the foliar content of chlorophyll a and b (Cab), can be estimated using imaging spectroscopy. For forest canopies, however, the relationship between the spectral response and leaf chemistry is confounded by factors such as background (e.g. understory), canopy structure, and the presence of non-photosynthetic vegetation (NPV, e.g. woody elements)—particularly the appreciable amounts of standing and fallen dead wood found in older forests. We present a sensitivity analysis for the estimation of chlorophyll content in woody coniferous canopies using radiative transfer modeling, and use the modeled top-of-canopy reflectance data to analyze the contribution of woody elements, leaf area index (LAI), and crown cover (CC) to the retrieval of foliar Cab content. The radiative transfer model used comprises two linked submodels: one at leaf level (PROSPECT) and one at canopy level (FLIGHT). This generated bidirectional reflectance data according to the band settings of the Compact High Resolution Imaging Spectrometer (CHRIS) from which chlorophyll indices were calculated. Most of the chlorophyll indices outperformed single wavelengths in predicting Cab content at canopy level, with best results obtained by the Maccioni index ([R₇₈₀ − R₇₁₀] / [R₇₈₀ − R₆₈₀]). We demonstrate the performance of this index with respect to structural information on three distinct coniferous forest types (young, early mature and old-growth stands). The modeling results suggest that the spectral variation due to variation in canopy chlorophyll content is best captured for stands with medium dense canopies. However, the strength of the up-scaled Cab signal weakens with increasing crown NPV scattering elements, especially when crown cover exceeds 30%. LAI exerts the least perturbations. We conclude that the spectral influence of woody elements is an important variable that should be considered in radiative transfer approaches when retrieving foliar pigment estimates in heterogeneous stands, particularly if the stands are partly defoliated or long-lived.     

Canopy bidirectional reflectance dependence on leaf orientation

Abstract

The bidirectional reflectance patterns of a complete (dense) canopy are examined as functions of canopy architecture, as specified by azimuth angle δ_e and zenith angle ψ for a leaf normal. The leaves are assumed to be opaque Lambertian reflectors, all with identical orientation and reflectance properties throughout the canopy, and randomly distributed with respect to the irradiation field and the viewing direction. Multiple reflections are not considered and irradiation is by direct beam only. Simple analytical expressions for the bidirectional reflectance factor are presented and analysed. The nadir reflectance (expressed as a fraction of the leaf reflectance) for canopies whose leaves face the sun, δ_e = 0, is bounded by cos ψ and 1/2; cos ψ. The nadir reflectance initially increases with increasing ψ, but then decreases when ψ reaches moderate to large values. For a δ_e = π canopy, on the other hand, the much lower nadir reflectance is bounded by ½ cos ψ and 0, and decreases with increasing ψ throughout the entire range of ψ (0 to ½π). The maximum bidirectional reflectance occurs at large viewing zenith angles (i.e. close to the horizon). The maximum reflectance is always higher for a δ_e = 0 canopy than for a δ_e = π canopy, but the differences become small when ψ approaches ½π. The bidirectional reflectance thus depends on the leaf azimuth as well as the zenith angle. Leaf-area azimuthal distributions should be considered when conducting model inversions to infer canopy characteristics and architecture.     

A spectral directional reflectance model of row crops

A computationally efficient reflectance model for row planted canopies is developed in this paper through separating the contributions of incident direct and diffuse radiation scattered by row canopies. The row model allows calculating the reflectance spectrum in any given direction for the optical spectral region. The performance of the model is evaluated through comparisons with field measurements of winter wheat as well as with an established 3D computer simulation model. Especially the systematic comparisons with the computer simulation model demonstrate that the model can adequately simulate the characteristic distribution of directional reflectance factors of row canopies, which is shown in the polar map of reflectance as a high or low value stripe approximately parallel to the row orientation, besides the hotspot effect. Physical mechanisms causing the dynamics were proposed and supported by comparison studies. The features of reflectance distributions of row canopies, which are distinctively different from those of homogeneous canopy, imply that it is problematic to use one-dimensional radiation transfer model to interpret radiation data and estimate the structural or spectral parameters of row canopies from reflectance measurements. Finally, further improvements needed for the current model are briefly discussed.     

Large area mapping of southwestern forest crown cover, canopy height, and biomass using the NASA Multiangle Imaging Spectro-Radiometer

A rapid canopy reflectance model inversion experiment was performed using multi-angle reflectance data from the NASA Multi-angle Imaging Spectro-Radiometer (MISR) on the Earth Observing System Terra satellite, with the goal of obtaining measures of forest fractional crown cover, mean canopy height, and aboveground woody biomass for large parts of south-eastern Arizona and southern New Mexico (> 200,000 km²). MISR red band bidirectional reflectance estimates in nine views mapped to a 250 m grid were used to adjust the Simple Geometric-optical Model (SGM). The soil-understory background signal was partly decoupled a priori by developing regression relationships with the nadir camera blue, green, and near-infrared reflectance data and the isotropic, geometric, and volume scattering kernel weights of the LiSparse–RossThin kernel-driven bidirectional reflectance distribution function (BRDF) model adjusted against MISR red band data. The SGM's mean crown radius and crown shape parameters were adjusted using the Praxis optimization algorithm, allowing retrieval of fractional crown cover and mean canopy height, and estimation of aboveground woody biomass by linear rescaling of the dot product of cover and height. Retrieved distributions of crown cover, mean canopy height, and aboveground woody biomass for forested areas showed good matches with maps from the United States Department of Agriculture (USDA) Forest Service, with R² values of 0.78, 0.69, and 0.81, and absolute mean errors of 0.10, 2.2 m, and 4.5 tons acre^- 1 (10.1 Mg ha^- 1), respectively, after filtering for high root mean square error (RMSE) on model fitting, the effects of topographic shading, and the removal of a small number of outliers. This is the first use of data from the MISR instrument to produce maps of crown cover, canopy height, and woody biomass over a large area by seeking to exploit the structural effects of canopies reflected in the observed anisotropy patterns in these explicitly multiangle data.