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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Combining geometric-optical and spectral invariants theories for modeling canopy fluorescence anisotropy

The spectral invariants theory ( p -theory) has received much attention in the field of quantitative remote sensing over the past few decades and has been adopted for modeling of canopy solar-induced chlorophyll fluorescence (SIF). However, the spectral invariant properties (SIP) in simple analytical formulae have not been applied for modeling canopy fluorescence anisotropy primarily because they are parameterized in terms of leaf total scattering, which precludes the differentiation between forward and backward leaf SIF emissions. In this study, we have developed the canopy-SIP SIF model by combining geometric-optical (GO) theory to account for asymmetric leaf SIF forward and backward emissions at the first-order scattering and by modeling multiple scattering based on the p-theory, thus avoiding the dependence on radiative transfer models. The applicability of the model simulations especially over 3D heterogeneous canopies was improved by incorporating canopy structure through multi-angular clumping index, and by modeling single scattering from the four components of the scene in view according to the GO approach. The results show good consistency with both the state-of-the-art SIF models and multi-angular field SIF observations over grass and chickpea canopies. Further, the coefficient of determination (R²) between the simulated SIF and field measurements was 0.75 (red) and 0.74 (far-red) for chickpea, and 0.65 (both red and far-red) for grass. The average relative error was approximately 3% for 1D homogeneous scenes when comparing the canopy-SIP SIF model simulations to the SCOPE model simulations, and around 4% for the 3D heterogeneous scene when comparing to the LESS model simulations. The results indicate that the proposed approach for separating asymmetric leaf SIF emissions is a robust way to keep a balance between satisfactory simulation accuracy and efficiency. Model simulations suggest that neglecting the leaf SIF asymmetry can lead to an underestimation of canopy red SIF by 6.3% to 42.6% for various leaf biochemical and canopy structural parameters. This study presents a simple but efficient analytical approach for canopy fluorescence modeling, with potential for large-scale canopy fluorescence simulations.

3D heterogeneous structure↗
NASA NTRS2018

An Interplay between Photons, Canopy Structure, and Recollision Probability: A Review of the Spectral Invariants Theory of 3D Canopy Radiative Transfer Processes

Earth observations collected by remote sensors provide unique information to our ever-growing knowledge of the terrestrial biosphere. Yet, retrieving information from remote sensing data requires sophisticated processing and demands a better understanding of the underlying physics. This paper reviews research efforts that lead to the developments of the stochastic radiative transfer equation (RTE) and the spectral invariants theory. The former simplifies the characteristics of canopy structures with a pair-correlation function so that the 3D information can be succinctly packed into a 1D equation. The latter indicates that the interactions between photons and canopy elements converge to certain invariant patterns quantifiable by a few wavelength independent parameters, which satisfy the law of energy conservation. By revealing the connections between plant structural characteristics and photon recollision probability, these developments significantly advance our understanding of the transportation of radiation within vegetation canopies. They enable a novel physically-based algorithm to simulate the “hot-spot” phenomenon of canopy bidirectional reflectance while conserving energy, a challenge known to the classic radiative transfer models. Therefore, these theoretical developments have a far-reaching influence in optical remote sensing of the biosphere.

vegetation remote sensing; stochastic radiative tr↗
DOE OSTI2025

Characterizing leaf-scale fluorescence with spectral invariants

Sun-induced chlorophyll fluorescence (SIF) is increasingly recognized as a non-destructive probe for tracking terrestrial photosynthesis. Emerging developments in spectral invariants theory provide an innovative and efficient approach for representing SIF radiative transfer processes at the canopy scale. However, modeling leaf-scale fluorescence based on the spectral invariants properties (SIP) remains underexplored. In this study, the spectral invariants theory is employed for the first time to model the leaf-scale total, backward and forward fluorescence (leaf-SIP SIF). The leaf-SIP SIF model separates the leaf-scale radiative transfer process into two distinct components: the wavelength-dependent one associated with leaf biochemical properties, and the wavelength-independent component linked to leaf structural characteristics. The leaf structure-related effects are characterized by two spectrally invariant parameters: the photon recollision probability (p) and the scattering asymmetry parameter (q), which are parameterized using the directly measurable leaf dry matter. Evaluation against field measurements shows that the proposed leaf-SIP SIF model has a good performance, with coefficient of determination (R 2 ) of 0.89, 0.89, 0.90 and root mean squared errors (RMSE) of 1.28, 0.69, 0.74 Wm -2 µm -1 sr -1 , respectively for the total, backward, and forward fluorescence (660–800 nm). The leaf-SIP SIF model with a more concise formulation demonstrates comparable performance with the widely used Fluspect model. Further, the leaf-SIP SIF model provides a simple and efficient approach for simulating leaf-scale fluorescence, with the potential to be integrated into a unified SIP-based model framework for simulating the radiative transfer processes across the soil-leaf-canopy-atmosphere continuum.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2007

Physical Interpretation of the Correlation Between Multi-Angle Spectral Data and Canopy Height

Recent empirical studies have shown that multi-angle spectral data can be useful for predicting canopy height, but the physical reason for this correlation was not understood. We follow the concept of canopy spectral invariants, specifically escape probability, to gain insight into the observed correlation. Airborne Multi-Angle Imaging Spectrometer (AirMISR) and airborne Laser Vegetation Imaging Sensor (LVIS) data acquired during a NASA Terrestrial Ecology Program aircraft campaign underlie our analysis. Two multivariate linear regression models were developed to estimate LVIS height measures from 28 AirMISR multi-angle spectral reflectances and from the spectrally invariant escape probability at 7 AirMISR view angles. Both models achieved nearly the same accuracy, suggesting that canopy spectral invariant theory can explain the observed correlation. We hypothesize that the escape probability is sensitive to the aspect ratio (crown diameter to crown height). The multi-angle spectral data alone therefore may not provide enough information to retrieve canopy height globally

Schull, M. A.↗
NASA NTRS2012

Generating Global Leaf Area Index from Landsat: Algorithm Formulation and Demonstration

This paper summarizes the implementation of a physically based algorithm for the retrieval of vegetation green Leaf Area Index (LAI) from Landsat surface reflectance data. The algorithm is based on the canopy spectral invariants theory and provides a computationally efficient way of parameterizing the Bidirectional Reflectance Factor (BRF) as a function of spatial resolution and wavelength. LAI retrievals from the application of this algorithm to aggregated Landsat surface reflectances are consistent with those of MODIS for homogeneous sites represented by different herbaceous and forest cover types. Example results illustrating the physics and performance of the algorithm suggest three key factors that influence the LAI retrieval process: 1) the atmospheric correction procedures to estimate surface reflectances; 2) the proximity of Landsatobserved surface reflectance and corresponding reflectances as characterized by the model simulation; and 3) the quality of the input land cover type in accurately delineating pure vegetated components as opposed to mixed pixels. Accounting for these factors, a pilot implementation of the LAI retrieval algorithm was demonstrated for the state of California utilizing the Global Land Survey (GLS) 2005 Landsat data archive. In a separate exercise, the performance of the LAI algorithm over California was evaluated by using the short-wave infrared band in addition to the red and near-infrared bands. Results show that the algorithm, while ingesting the short-wave infrared band, has the ability to delineate open canopies with understory effects and may provide useful information compared to a more traditional two-band retrieval. Future research will involve implementation of this algorithm at continental scales and a validation exercise will be performed in evaluating the accuracy of the 30-m LAI products at several field sites. ©

Landsat↗
NASA NTRS2020

Fluorescence Correction Vegetation Index (FCVI): A physically based reflectance index to separate physiological and non-physiological information in far-red sun-induced chlorophyll fluorescence

Sun-induced chlorophyll fluorescence (SIF) has been used to track vegetation photosynthetic activity for improving estimation of gross primary productivity (GPP) and detecting plant stress. There are both physical and physiological controls of SIF measured at the surface and retrieved from remote sensing including satellite observations. In order to accurately use SIF for monitoring of plant physiology, the effects of physically-based radiation processes related to leaf and canopy structure, notably photosynthetically active radiation (PAR) absorption and SIF scattering and re-absorption, must be characterized. In this study, we investigate both PAR absorption and SIF scattering processes and find that although it is difficult to quantify their effects individually by using just reflectance, the combined effects of the two processes can be well approximated by a reflectance index. This index, referred to as FCVI (Fluorescence Correction Vegetation Index), is defined as the difference between near-infrared (NIR) and broad-band visible (VIS, 400–700 nm) reflectance acquired under identical sun-canopy-observer geometry of the SIF measurements. The development of the index was based on the physical connection between reflectance and far-red SIF, which was revealed by using the spectral invariant theory. The utility of FCVI to correct far-red SIF for PAR absorption and scattering effects, thus improving the link to photosynthesis, was tested with data from: (i) a field experiment for a growing season; and (ii) a numerical experiment which included a number of scenarios generated by a radiative transfer model. For both the observations and simulations, the FCVI provided a promising estimate of the impact of the physically-based radiation processes on far-red SIF of moderately dense canopies (i.e., FCVI ≥ 0.18). Normalizing the TOC far-red SIF by both the incident PAR (iPAR) and the FCVI provided a good estimate of the far-red fluorescence emission efficiency of the canopies examined. This approach enhances our ability to generalize retrievals for vegetation processes as they change through natural growth phases and seasons. Taken together, far-red SIF and FCVI may enable the assessment of the light partitioning of vegetation canopies, an essential step to facilitate the use of far-red SIF for tracking physiological processes.

Peiqi Yang↗
NASA NTRS2020

Reduction of structural impacts and distinction of photosynthetic pathways in a global estimation of GPP from space-borne solar-induced chlorophyll fluorescence

Quantifying global photosynthesis remains a challenge due to a lack of accurate remote sensing proxies. Solar-induced chlorophyll fluorescence (SIF) has been shown to be a good indicator of photosynthetic activity across various spatial scales. However, a global and spatially challenging estimate of terrestrial gross primary production (GPP) based on satellite SIF remains unresolved due to the confounding effects of species-specific physical and physiological traits and external factors, such as canopy structure or photosynthetic pathway (C3orC4). Here we analyze an ensemble of far-red SIF data from OCO-2 satellite and ground observations at multiple sites, using the spectral invariant theory to reduce the effects of canopy structure and to retrieve a structure-corrected total canopy SIF emission (SIF total). We find that the relationships between observed canopy-leavingSIF and ecosystem GPP vary significantly among biomes. In contrast, the relationships between SIF total and GPP converge around two unique models, one for C3and one for C4plants. We show that the two single empirical models can be used to globally scale satellite SIF observations to terrestrial GPP. We obtain an independent estimate of global terrestrial GPP of 129.56 ± 6.54 PgC/year for the 2015–2017 period, which is consistent with the state-of-the-art data- and process-oriented models. The new GPP product shows improved sensitivity to previously undetected ‘hotspots’ of productivity, being able to resolve the double-peak in GPP due to rotational cropping systems. We suggest that the direct scheme to estimate GPP presented here, which is based on satelliteSIF, may open up new possibilities to resolve the dynamics of global terrestrial GPP across space and time.

scale satellite SIF observations to terrestrial GP↗
NASA NTRS2008

Generating Vegetation Leaf Area Index Earth System Data Record from Multiple Sensors: Theory - Part 1

The generation of multi-decade long Earth System Data Records (ESDRs) of Leaf Area Index (LAI) and Fraction of Photosynthetically Active Radiation absorbed by vegetation (FPAR) from remote sensing measurements of multiple sensors is key to monitoring long-term changes in vegetation due to natural and anthropogenic influences. Challenges in developing such ESDRs include problems in remote sensing science (modeling of variability in global vegetation, scaling, atmospheric correction) and sensor hardware (differences in spatial resolution, spectral bands, calibration, and information content). In this paper, we develop a physically based approach for deriving LAI and FPAR products from the Advanced Very High Resolution Radiometer (AVHRR) data that are of comparable quality to the Moderate resolution Imaging Spectroradiometer (MODIS) LAI and FPAR products, thus realizing the objective of producing a long (multi-decadal) time series of these products. The approach is based on the radiative transfer theory of canopy spectral invariants which facilitates parameterization of the canopy spectral bidirectional reflectance factor (BRF). The methodology permits decoupling of the structural and radiometric components and obeys the energy conservation law. The approach is applicable to any optical sensor, however, it requires selection of sensor-specific values of configurable parameters, namely, the single scattering albedo and data uncertainty. According to the theory of spectral invariants, the single scattering albedo is a function of the spatial scale, and thus, accounts for the variation in BRF with sensor spatial resolution. Likewise, the single scattering albedo accounts for the variation in spectral BRF with sensor bandwidths. The second adjustable parameter is data uncertainty, which accounts for varying information content of the remote sensing measurements, i.e., Normalized Difference Vegetation Index (NDVI, low information content), vs. spectral BRF (higher information content). Implementation of this approach indicates good consistency in LAI values retrieved from NDVI (AVHRRmode) and spectral BRF (MODIS-mode). Specific details of the implementation and evaluation of the derived products are detailed in the second part of this two-paper series.

Ganguly, Sangram↗
NASA NTRS2011

Canopy Spectral Invariants: Application to Classification of Forest Types from Hyperspectral Data - Part 2

Many studies have been conducted to demonstrate the ability of hyperspectral data to discriminate plant dominant species. Most of them have employed the use of empirically based techniques, which are site specific, requires some initial training based on characteristics of known leaf and/or canopy spectra and therefore may not be extendable to operational use or adapted to changing or unknown land cover. In this paper we propose a physically based approach for separation of dominant forest type using hyperspectral data. The radiative transfer theory of canopy spectral invariants underlies the approach, which facilitates parameterization of the canopy reflectance in terms of the leaf spectral scattering and two spectrally invariant and structurally varying variables - recollision and directional escape probabilities. The methodology is based on the idea of retrieving spectrally invariant parameters from hyperspectral data first, and then relating their values to structural characteristics of three-dimensional canopy structure. Theoretical and empirical analyses of ground and airborne data acquired by Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over two sites in New England, USA, suggest that the canopy spectral invariants convey information about canopy structure at both the macro- and micro-scales. The total escape probability (one minus recollision probability) varies as a power function with the exponent related to the number of nested hierarchical levels present in the pixel. Its base is a geometrical mean of the local total escape probabilities and accounts for the cumulative effect of canopy structure over a wide range of scales. The ratio of the directional to the total escape probability becomes independent of the number of hierarchical levels and is a function of the canopy structure at the macro-scale such as tree spatial distribution, crown shape and size, within-crown foliage density and ground cover. These properties allow for the natural separation of dominant forest classes based on the location of points on the total escape probability vs the ratio log-log plane.

Schull, M. A.↗
NASA NTRS2017

The Spectral Invariant Approximation Within Canopy Radiative Transfer to Support the Use of the EPIC/DSCOVR Oxygen B-band for Monitoring Vegetation

EPIC (Earth Polychromatic Imaging Camera) is a 10-channel spectroradiometer onboard DSCOVR (Deep Space Climate Observatory) spacecraft. In addition to the near-infrared (NIR, 780 nm) and the 'red' (680 nm) channels, EPIC also has the O2 A-band (764+/-0.2 nm) and B-band (687.75+/-0.2 nm). The EPIC Normalized Difference Vegetation Index (NDVI) is defined as the difference between NIR and 'red' channels normalized to their sum. However, the use of the O2 B-band instead of the 'red' channel mitigates the effect of atmosphere on remote sensing of surface reflectance because O2 reduces contribution from the radiation scattered by the atmosphere. Applying the radiative transfer theory and the spectral invariant approximation to EPIC observations, the paper provides supportive arguments for using the O2 band instead of the red channel for monitoring vegetation dynamics. Our results suggest that the use of the O2 B-band enhances the sensitivity of the top-of-atmosphere NDVI to the presence of vegetation.

Alexander Marshak↗
NASA NTRS2008

Differential Cross Section Kinematics for 3-dimensional Transport Codes

In support of the development of 3-dimensional transport codes, this paper derives the relevant relativistic particle kinematic theory. Formulas are given for invariant, spectral and angular distributions in both the lab (spacecraft) and center of momentum frames, for collisions involving 2, 3 and n - body final states.

Norbury, John W.↗
NASA NTRS1990

Cascade model for fluvial geomorphology

Erosional landscapes are generally scale invariant and fractal. Spectral studies provide quantitative confirmation of this statement. Linear theories of erosion will not generate scale-invariant topography. In order to explain the fractal behavior of landscapes a modified Fourier series has been introduced that is the basis for a renormalization approach. A nonlinear dynamical model has been introduced for the decay of the modified Fourier series coefficients that yield a fractal spectra. It is argued that a physical basis for this approach is that a fractal (or nearly fractal) distribution of storms (floods) continually renews erosional features on all scales.

Newman, W. I.↗
DOE OSTI2025

Modular-Invariant Random Matrix Theory and AdS 3 Wormholes

We develop a nonperturbative definition of RMT 2 : a generalization of random matrix theory that is compatible with the symmetries of two-dimensional conformal field theory. Given any random matrix ensemble, its 𝑛-point spectral correlations admit a prescribed modular-invariant lift to RMT 2 , which moreover reduce to the original random matrix correlators in a near-extremal limit. Central to the prescription is a presentation of random matrix theory in Mellin space, which lifts to two dimensions via the SL⁡(2,ℤ) spectral decomposition employed in previous work. As a demonstration we perform the explicit RMT 2 lift of two-point correlations of the GUE Airy model. We propose that in AdS 3 pure gravity, semiclassical amplitudes for off-shell 𝑛-boundary torus wormholes with topology Σ 0,𝑛 × 𝑆 1 are given by the RMT 2 lift of JT gravity wormhole amplitudes. For the three-boundary case, we identify a gravity calculation which matches the RMT 2 result.

conformal field theory↗
DOE OSTI2025

Cosmological quasiparticles and the cosmological collider

The interplay between cosmology and strongly coupled dynamics can yield transient spectral features that vanish at late times, but which may leave behind phenomenological signatures in the spectrum of primordial fluctuations. Of particular interest are strongly coupled extensions of the standard model featuring approximate conformal invariance. In flat space, the spectral density for a scalar operator in a conformal field theory is characterized by a continuum with scaling law governed by the dimension of the operator, and is otherwise featureless. Anti–de Sitter/conformal field theory arguments suggest that for large 𝑁, in an inflationary background with Hubble rate 𝐻, this continuum is gapped. We demonstrate that there can be additional peak structures that become sharp and particlelike at phenomenologically interesting regions in parameter space, and we estimate their contribution to cosmological observables. We find phenomena that are potentially observable in future experiments that are unique to these models, including displaced oscillatory features in the squeezed limit of the bispectrum. These particles can be either fundamental, and localized to a UV brane, or composite at the Hubble scale, 𝐻, and bound to a horizon in the bulk of the 5D geometry. We comment on how stabilization of conformal symmetry breaking vacua can be correlated with these spectral features and their phenomenology.

conformal field theory↗
NASA NTRS2024

A new spectrally-invariant approach to the remote sensing of inhomogeneous clouds

Current operational satellite retrievals of cloud optical and microphysical properties go back to the Nakajima-King technique developed at the end of the 1980s. This technique is based on library calculations for plane-parallel homogeneous clouds. It often works well for overcast skies but leads to substantial errors for inhomogeneous and broken cloud fields where the plane-parallel-geometry assumption is no longer valid. The basic concept of a new technique was first introduced in nuclear physics to quantify the critical conditions of reactors. Based on the eigenvalues of the radiative transfer equation, their approach provides a powerful means to parameterize the structure of 3D media. This parameterization was later successfully applied to relate surface reflectance spectra to 3D canopy structure and is known as the spectrally-invariant approximation. The proposed approach adapts this technique to the remote sensing of cloud properties such as droplet single scattering albedo and the average number of scatterings (which are the fundamental parameters in radiative transfer theory), with an emphasis on quantifying the associated errors and uncertainties. This retrieval is free from the plane-parallel homogeneous cloud assumption.

clouds↗
NASA NTRS1995

A Simple Theory of Capillary-Gravity Wave Turbulence

Employing a recently proposed 'multi-wave interaction' theory, inertial spectra of capillary gravity waves are derived. This case is characterized by a rather high degree of nonlinearity and a complicated dispersion law. The absence of scale invariance makes this and some other problems of wave turbulence (e.g., nonlinear inertia gravity waves) intractable by small-perturbation techniques, even in the weak-turbulence limit. The analytical solution obtained in the present work for an arbitrary degree of nonlinearity is shown to be in reasonable agreement with experimental data. The theory explains the dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves, while the appropriate (long- and short-wave) limits yield power laws corresponding to the Zakharov-Filonenko and Phillips spectra.

Glazman, Roman E.↗
NASA NTRS1983

Riccati group invariants of linear hamiltonian systems

The action of the Riccati group on the Riccati differential equation is associated with the action of a subgroup of the symplectic group on a set of hamiltonian matrices. Within this framework various sets of canonical forms are developed for the matrix coefficients of the Riccati differential equation. The canonical forms presented are valid for arbitrary Kronecker indices, and it is shown that the Kronecker indices are invariants for this group action. These canonical forms are useful for studying problems arising in the areas of optimal decentralized control and the spectral theory of optimal control problems.

Garzia, M. R.↗