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Physically based models simulating the spectral transmittance of solar radiation through forest canopies are useful tools for examining the connections between the shortwave radiation environment and the productivity and biodiversity of the forest floor. We report a comprehensive evaluation of two approaches simulating forest canopy spectral transmittance.The approaches were (i) three‐dimensional radiative transfer modelling in canopies composed of individual trees filled with turbid media and (ii) photon recollision probability theory (p‐theory), and were implemented using DART‐FT and PARAS models, respectively. The simulations were evaluated against mean and standard deviation of canopy transmittance spectra measured under clear‐sky conditions in forest plots across central and Northern Europe.In general, both models agreed well with the in situ measurements. They performed equally in conifer forests, while PARAS had a slightly lower accuracy than DART‐FT in broadleaved forests.We conclude that both approaches produce realistic simulations of canopy spectral transmittance at the spatial scale tested in this study, and that p‐theory constitutes a computationally efficient and easy‐to‐parameterize alternative to three‐dimensional radiative transfer. [ABSTRACT FROM AUTHOR]

Abstract Physically based models simulating the spectral transmittance of solar radiation through forest canopies are useful tools for examining the connections between the shortwave radiation environment and the productivity and biodiversity of the forest floor. We report a comprehensive evaluation of two approaches simulating forest canopy spectral transmittance. The approaches were (i) three‐dimensional radiative transfer modelling in canopies composed of individual trees filled with turbid media and (ii) photon recollision probability theory (p‐theory), and were implemented using DART‐FT and PARAS models, respectively. The simulations were evaluated against mean and standard deviation of canopy transmittance spectra measured under clear‐sky conditions in forest plots across central and Northern Europe. In general, both models agreed well with the in situ measurements. They performed equally in conifer forests, while PARAS had a slightly lower accuracy than DART‐FT in broadleaved forests. We conclude that both approaches produce realistic simulations of canopy spectral transmittance at the spatial scale tested in this study, and that p‐theory constitutes a computationally efficient and easy‐to‐parameterize alternative to three‐dimensional radiative transfer.

The past two decades have witnessed the widespread application of the spectral invariant theory (p -theory) in modeling the shortwave radiation absorbed or scattered by vegetation. The basic principle of this theory is that the canopy reflectance is solely determined by the optical properties of leaves and the photon recollision probability p. As one of the spectral invariants, p serves as a critical bond between the spectral characteristics of the canopy at any wavelength and the reflectance, transmittance, or absorptance of the vegetation canopy, and is intimately associated with the solution of the radiative transfer equation. Currently, estimation of p -value is predominantly accomplished through canopy structural parameters, such as the spherically averaged silhouette to total area ratio (STAR ¯) or Leaf Area Index (LAI). In this work, we provide an approach to estimate canopy photon recollision probability directly from Airborne Laser Scanning (ALS) data. We showed that the recollision probability can be interpreted as the interceptions of virtual rays emitted from sampling points within tree crowns described with turbid media, which avoided detailed reconstruction of leaf structures. The approach was evaluated with both virtual experiments as well as field measurements. The virtual experiments employed the Large-scalE remote Sensing data and image Simulation model (LESS) to simulate virtual ALS scanning data based on three RAdiation transfer Model Intercomparison (RAMI) actual canopies, with each divided into 25 segments, for which the p -values could be obtained through LESS. Our findings showed that p -values can be accurately estimated from ALS point clouds. Specifically, it exhibited great consistency with RMSE% less than 5% for broadleaved forest scenes, 25% for mixed forest scenes, and less than 10% for coniferous forest scenes in virtual experiments, respectively, and less than 25% compared to field measurements. This study displays the potential of ALS as a promising tool for forest structure characterization and short-wave radiation modeling in forest ecosystems. • Provided a new approach for estimation of canopy-level photon recollision probability p from ALS. • Calculated canopy-level p for forests of different types and varying levels of heterogeneity. • A 3D RT model based on computer simulations was used to evaluate the new approach. • Canopy-level p can be accurately estimated from ALS point clouds. [ABSTRACT FROM AUTHOR]

Clumping index (CI) is a measure of foliage aggregation relative to a random distribution of leaves in space. The CI can help with estimating fractions of sunlit and shaded leaves for a given leaf area index (LAI) value. Both the CI and LAI can be obtained from global Earth Observation data from sensors such as the Moderate Resolution Imaging Spectrometer (MODIS). Here, the synergy between a MODIS-based CI and a MODIS LAI product is examined using the theory of spectral invariants, also referred to as photon recollision probability (‘ p -theory’), along with raw LAI-2000/2200 Plant Canopy Analyzer data from 75 sites distributed across a range of plant functional types. The p- theory describes the probability ( p -value) that a photon, having intercepted an element in the canopy, will recollide with another canopy element rather than escape the canopy. We show that empirically-based CI maps can be integrated with the MODIS LAI product. Our results indicate that it is feasible to derive approximate p -values for any location solely from Earth Observation data. This approximation is relevant for future applications of the photon recollision probability concept for global and local monitoring of vegetation using Earth Observation data. [ABSTRACT FROM AUTHOR]

Hyperspectral remote sensing data carry information on the leaf area index (LAI) of forests, and thus in principle, LAI can be estimated based on the data by inverting a forest reflectance model. However, LAI is usually not the only unknown in a reflectance model; especially, the leaf spectral albedo and understory reflectance are also not known. If the uncertainties of these parameters are not accounted for, the inversion of a forest reflectance model can lead to biased estimates for LAI. In this paper, we study the effects of reflectance model uncertainties on LAI estimates, and further, investigate whether the LAI estimates could recover from these uncertainties with the aid of Bayesian inference. In the proposed approach, the unknown leaf albedo and understory reflectance are estimated simultaneously with LAI from hyperspectral remote sensing data. The feasibility of the approach is tested with numerical simulation studies. The results show that in the presence of unknown parameters, the Bayesian LAI estimates which account for the model uncertainties outperform the conventional estimates that are based on biased model parameters. Moreover, the results demonstrate that the Bayesian inference can also provide feasible measures for the uncertainty of the estimated LAI. [ABSTRACT FROM AUTHOR]

Empirical and theoretical evidence has shown that the scattering and absorptance of a homogeneous leaf canopy with black soil can be modeled using simple algebraic combinations of two spectrally invariant parameters (the recollision probability and the canopy interceptance) and one spectrally dependent quantity (the single scattering albedo of an average phytoelement). This study generalizes such results for vegetation canopies composed of one or more types of phytoelements and with a reflective background surface also composed of one or more materials, all of which are treated as endmembers of a nonlinear spectral mixture. The conservative radiation field of a canopy is represented by a finite state Markov chain, such that for a vegetation-surface medium composed of m endmembers, the model is thereby parameterized in terms of an m -length vector of endmember interceptances and an m th-order square matrix containing probabilities of photon recollision amongst the endmembers. Comparisons of some instances of the model with radiative transfer based approximations showed how the latter may overestimate canopy reflectance and transmittance. The two-endmembers model was also compared with Monte Carlo simulations for spherically-oriented leaf canopies with reflective soil. Results indicated that the analytical model accurately describes the radiation field for a wide range of soil reflectance and LAI values. Simulations also showed that while the zenith angle of the illumination source has a small influence on the recollision probabilities, the LAI value mainly determines these through distinct functional relationships. The application of the model to estimate the canopy radiation field of two coniferous species located on the Mexico City Conservation Land is also demonstrated using airborne hyperspectral measurements. [ABSTRACT FROM AUTHOR]

The fraction of absorbed Photosynthetically Active Radiation (fPAR, 400–700 nm) can be retrieved from satellite measurements and is used to estimate and monitor ecosystem productivity and vegetation phenology. Although fPAR depends primarily on the Leaf Area Index (LAI), it is also influenced by the incoming radiation field and thus varies diurnally and seasonally. The overall aim of this study was to compare different ground and satellite-based fPAR estimates. The field data consisted of nearly 1000 plots located in the southern boreal forest zone in Finland. For all plots, data on canopy transmittance and forest inventory variables were available. We compared two different approaches to estimate fPAR and studied which satellite-based vegetation indices are best correlated with the instantaneous ground reference fPAR. Finally, a canopy fPAR model was used to assess some underlying assumptions of the satellite-based fPAR products: the similarity between instantaneous (at the time of satellite overpass) and daily-integrated fPAR. Results showed that allometric estimates of LAI and Beer’s law are not sufficient to estimate fPAR in a boreal forest, because canopy openness strongly influences the relationship between canopy LAI and fPAR. We found that vegetation indices calculated from Landsat were only moderately correlated (maximum R 2 = 0.34) with the ground-based fPAR. Our study showed that the absolute difference between fPAR at the moment of the satellite overpass and daily integrated fPAR exceeds the 0.05 fPAR-units limit set by Global Climate Observing Systems −network in northern latitudes during the peak growing season. Thus, at high latitudes covered by boreal forests, the satellite-based fPAR systematically underestimates the daily integrated black sky fPAR. [ABSTRACT FROM AUTHOR]

The spectral invariants theory predicts that amount of radiation scattered by a canopy in a given wavelength is a simple function of the leaf albedo and a spectrally invariant parameter p. This study provides the first assessment of p parameter obtained from the Earth Reflector Type Index (ERTI) provided in Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) Vegetation Earth System Data Record (VESDR) product. Our results suggest that ERTI parameter can possibly deliver information about photon recollision probability, albeit with a risk of lower accuracy, even for conditions that differ from the original assumptions in the spectral invariants theory (non-reflecting soil, dense canopies). We verified the expected link between ERTI p parameter in the EPIC VESDR product, foliage clumping, and canopy cover with empirical data. Importantly, this was done with study sites in Australia that included types of forests that are still relatively unexplored with spectral invariants theory. Our findings contribute to understanding product uncertainty and spatial representativeness of the in situ measurements from the Terrestrial Ecosystem Research Network (TERN) SuperSites in Australia. • First validation of ERTI p parameter from the EPIC VESDR product with in situ data. • ERTI p parameter linked to foliage clumping, canopy cover. • Spatially representative TERN sites, data suitable for satellite products validation. [ABSTRACT FROM AUTHOR]

Nearly two decades ago, the idea of the ‘spectral invariants theory’ was put forth as a new tool to model the shortwave radiation absorbed or scattered by vegetation. The theory states that the amount of radiation absorbed by a canopy should to a great accuracy depend only on the wavelength and a wavelength-independent parameter describing canopy structure. The revolutionary idea behind this theory was that it would be possible to approximate vegetation canopy absorptance, transmittance and reflectance based on only the optical properties of foliage elements and the spectrally invariant parameter(s). This paper explains how this so-called spectral invariant is related to photon recollision probability and to canopy structural variables. Other spectral invariants were later introduced to quantify the directionality of canopy scattering. Moreover, the paper reviews the advances in the theoretical development of the photon recollision probability ( p ) concept and demonstrates some of its applications in global and local monitoring of vegetation using remote sensing data. [ABSTRACT FROM AUTHOR]

Abstract: A recent method based on the spectral invariants theory to retrieve physically-based information on forest properties from remotely sensed hyperspectral imagery was tested in a southern boreal setting in central Finland. An atmospherically corrected Hyperion image and ground measurements from 66 forest stands were used. First, the novel concept of transformed green leaf single scattering spectral albedos was tested against leaf (needle) albedo measurements on Scots pine, Norway spruce and Silver birch from the study area. We found the transformed Beaked hazel albedo applied in previous studies could be used as reference also for the boreal tree species. Second, we derived a newly suggested spectrally invariant variable, the directional area scattering factor (DASF), to estimate the broadleaf fraction of forest stands. Based on our results, DASF seems highly promising as a potential new hyperspectral satellite product for change monitoring of broadleaf fraction over different vegetation zones. Finally, we plotted our results in the spectral invariants space, and suggest a new interpretation for the reference-dependent structural parameter p R . We propose this parameter is an indicator of canopy cover and suffers less from saturation problems than vegetation indices. [Copyright &y& Elsevier]

Abstract: A simple approach for simulating forest albedo based on the spectral invariants theory was applied to produce the black-sky albedos of 644 boreal forest stands composed of Scots pine, Norway spruce and Silver birch. Results were compared to those simulated using a detailed forest radiative transfer model with input from an extensive forest inventory database. The model based on the spectral invariants produced similar ranges of albedo values for the stands of all species as the detailed model, indicating that despite its simplicity and limited input variables it is flexible enough when predicting the albedo of a forest. [Copyright &y& Elsevier]

We measured simultaneously the spectral albedo of ten Scots pine shoots and the needles constituting the shoots. Next, we used the spectral information to calculate the photochemical reflectance index (PRI) which allows to retrieve photosynthetic productivity from imaging spectroscopy data. We showed that PRI can be scaled from needle to shoot level using a strictly positive scaling factor. The scaling factor is a function of photon recollision probability and the harmonic mean of needle spectral albedos at the wavelengths used in the index. The method is applicable to other normalized difference indices, as demonstrated here using normalized difference vegetation index (NDVI). At shoot level, both PRI and NDVI depend on the angle between view and illumination directions. This anisotropy, however, is not a direct function of scattering angle. [ABSTRACT FROM PUBLISHER]

Abstract: Mutual shading of needles in coniferous shoots and small-scale variations in needle area density both within and between shoots violate conventional assumptions used in the definition of the elementary volume in radiative transfer models. In this paper, we test the hypothesis if it is possible to scale needle spectral albedo up to shoot spectral albedo using only one structural parameter: the spherically averaged shoot silhouette to total area ratio (STAR). To test the hypothesis, we measured both structural and spectral properties of ten Scots pine (Pinus sylvestris) shoots and their needles. Our results indicate that it is possible to upscale from needle to shoot spectral albedo using STAR. The upscaling model performed best in the VIS and SWIR regions, and for shoots with high STAR values. As STAR is linearly related to photon recollision probability, it is also possible to apply the upscaling model as integral part of radiative transfer models. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

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. [Copyright &y& Elsevier]

Abstract: The photon recollision probability in vegetation canopies, defined as the probability that a photon, after having interacted with a canopy element, will interact again, is a useful tool in remote sensing and ecological applications, enabling to link canopy optical properties at different wavelength and to estimate radiation absorption. In this work, a method is presented to estimate the photon recollision probability for horizontally homogeneous leaf canopies with arbitrary leaf angle distribution as well as for discrete crown canopies. The estimation is based on analytical approximation of the first-order recollision probability. Using the analytical solution of the two-stream equations of radiative transfer and Monte Carlo modeling, the first-order photon recollision probability is shown to slightly underestimate the mean recollision probability. Also, an approximation formula for the mean recollision probability in a horizontally homogeneous canopy is presented as a function of leaf area index. The method to calculate photon recollision probability in discrete crown canopies requires only the knowledge of total and between-crown canopy transmittance and is thus independent of the geometric-optical model used. [Copyright &y& Elsevier]

Leaf optical spectra reflect the combination of leaf biochemical, morphological and physiological properties, and play an important role in many ecological and Earth system processes. Radiative transfer models are widely used to simulate leaf spectra by quantifying photon transfer processes of reflection, transmission and absorption within a plant leaf. Recent advances in spectral invariants theory offer a unique and efficient approach for modeling the canopy-scale radiative transfer processes, but remain underexplored for applications at the leaf scale. In this study, we developed a leaf-scale optical property model based on the spectrally invariant properties (leaf-SIP) of plant leaves. Similar to the canopy-scale model, the leaf-SIP model decouples leaf-scale radiative transfer process into two parts: wavelength-dependent contribution from leaf chemical components and wavelength-independent contribution from leaf structures, described by two spectrally invariant parameters (i.e., a photon recollision probability p and a scattering asymmetry parameter q). We implemented the leaf-SIP model by parameterizing p and q with a measurable leaf morphological trait, the leaf mass per area (LMA). We evaluated the performance of the leaf-SIP model with two in situ datasets (i.e., LOPEX and ANGERS) and the widely used PROSPECT leaf optical model. The results show that the leaf spectra simulated by the leaf-SIP model agreed well with in situ datasets and the simulations of the PROSPECT model, with a small root mean squared error (RMSE), bias, and high coefficients of determination (R 2 ) of 0.026, 0.035, 0.95 and 0.037, 0.049, 0.91 for leaf reflectance and leaf transmittance, respectively. Our results also show that the leaf-SIP model can be used with measured leaf spectra to accurately estimate several key leaf functional traits, such as the leaf chlorophyll content, equivalent water thickness, and LMA. The leaf-SIP model provides an efficient and physical way of accurately simulating leaf spectra and retrieving key leaf functional traits from hyperspectral measurements. • A leaf-scale radiative transfer model is proposed by spectral invariants theory. • Spectral invariants decouple the leaf structure and biochemical constituents. • Leaf spectrally invariant parameters can be described by leaf mass per area. • The SIP model is efficient in retrievals of leaf structural and biochemical traits. [ABSTRACT FROM AUTHOR]

Forests protection and restoration is increasingly acknowledged as a crucial bridge in the ongoing world's economy transition towards a low-fossil-fuel future, to help achieving the global emission reduction target, and thus avoiding the predicted devastating impacts of unmitigated climate change. The long-operational optical Earth-observing satellites, together with recent developments in optical satellite data quality and availability, as well as in computational power, have brought new, unprecedented capabilities in using the freely available satellite data for the urgent task of monitoring the world's forest cover. The findings of this dissertation show that, the current freely-available satellite data from the Landsat missions can be feasibly utilized for, firstly, large-area monitoring of forests canopy cover in the managed Northern European boreal forests, and secondly, deforestation monitoring in the tropical insular South East Asia at a sub-annual time scale. Further, the findings suggest that the detection of subtler forest degradation activities can be best performed by detecting the forest cover loss immediately as it happens. This in turn will soon be possible by harmonizing data from Landsat satellites and the newly-fully-operational Sentinel-2 satellites. Overall, this dissertation provides the physically sound, and thus more generalizable, future optimization pathways, for the task of continuous monitoring of forests canopy cover using freely-available satellite data, in both the boreal and tropical biomes. Such physical insights are especially valuable in guiding the developments and interpretations of data-driven, machine learning methods in satellite data mining that are presently proliferating with the ongoing big data and computing revolutions. [ABSTRACT FROM AUTHOR]