Characterizing leaf-scale fluorescence with spectral invariants

The monitoring of photosynthetic activity stands as a central objective for the upcoming generation of satellite missions. Two promising avenues, Sun-Induced Chlorophyll Fluorescence (SIF) and Photochemical Reflectance Index (PRI), have emerged for remotely sensing leaf physiology, thereby advancing our comprehension of plant–climate interactions. Over the past few decades, substantial progress has been made in measurement techniques, retrieval algorithms, and modeling biochemical and radiative transfer processes related to SIF and PRI. However, it is essential to acknowledge that SIF and PRI observations are subject to influences such as canopy structure, soil background, and sun-observer geometry, in addition to leaf physiological status. Consequently, the key challenges in SIF and PRI remote sensing involve downscaling canopy SIF and PRI to leaf-level values and decoupling structural and physiological information.   Drawing a comparison between the radiative transfer processes involved in SIF and reflectance, a physical relationship between reflectance and scattering of far-red SIF has been established, giving rise to the R2F (Reflectance-to-Fluorescence) theory. Based on this theory, a Fluorescence Correction Vegetation Index (FCVI) has been formulated. The R2F theory and FCVI index have been successfully applied to interpret SIF observations across various scenarios, offering a theoretical foundation for the conversion of SIF across different scales—from canopy to leaf and photosynthetic systems.   Furthermore, an analysis of the radiative transfer processes determining PRI signals reveals that the deviation between canopy- and leaf-level PRI primarily stems from the soil background. Both canopy structure and sun-observer geometry indirectly affect canopy PRI by altering the contribution of soil to canopy reflectance. The structural and angular variation in canopy PRI can be elucidated by considering the soil background. In order to mitigate the effects of soil background, as well as associated structural and angular effects, a soil-adjusted canopy PRI (SacPRI) is proposed. This adjustment involves subtracting the soil contribution, estimated using red reflectance, from the original canopy reflectance. Field and numerical experiments confirm that compared with the raw canopy PRI, SacPRI more closely aligns with the PRI observed in sunlit leaves.   In summary, the proposed R2F relationship and the soil-adjusted canopy PRI offer valuable tools for enhancing the accuracy of photosynthesis monitoring through SIF and PRI, enabling more robust assessments across various scales and environmental conditions.

Numerous studies have demonstrated the ability of hyper-spectral data to discriminate crop types, however most methods rely on empirical data and are therefore site specific. In this brief proceeding we provide a physically based approach for separation of crop types using multiangle hyperspectral data. We use the radiative transfer theory of spectral invariants which allows for the parameterization of the canopy reflectance into two spectrally invariant and structurally varying parameters-recollision and escape probabilities. The spectral invariant parameters are retrieved from the CHRIS/PROBA multiangle hyperspectral sensor. We present the spectral invariant parameters in spectral invariant space. The horizontal axis provides information about macro scale features such as plant shape and size as well as ground cover. The vertical axis provides information about microscale features such as leaf density as well as portion of sunlit to shaded leaves. These features allow for the natural separation of crops. In addition we illustrate the potential for further separation of crop types based on angular information. Results suggest that multiangle information is important for canopies with similar structural features in the nadir direction.

A radiative transfer model for solar induced fluorescence using spectral invariants theory

Abstract. Data from satellite, aircraft, drone, and ground-based measurements have already shown that canopy-scale sun-induced chlorophyll fluorescence (SIF) is tightly related to photosynthesis, which is linked to vegetation carbon assimilation. However, our ability to effectively use those findings are hindered by confounding factors, including canopy structure, fluctuations in solar radiation, and sun–canopy geometry that highly affect the SIF signal. Thus, disentangling these factors has become paramount in order to use SIF for monitoring vegetation functioning at the canopy scale and beyond. Active chlorophyll fluorescence measurements (FyieldLIF), which directly measures the apparent fluorescence yield, have been widely used to detect physiological variation of the vegetation at the leaf scale. Recently, the measurement of FyieldLIF has become feasible at the canopy scale, opening up new opportunities to decouple structural, biophysical, and physiological components of SIF at the canopy scale. In this study, based on top-of-canopy measurements above a mature deciduous forest, reflectance (R), SIF, SIF normalized by incoming photosynthetically active radiation (SIFy), FyieldLIF, and the ratio between SIFy and FyieldLIF (named Φk) were used to investigate the effects of canopy structure and shadows on the diurnal and seasonal dynamics of SIF. Further, random forest (RF) models were also used to not only predict FyieldLIF and Φk, but also provide an interpretation framework by considering additional variables, including the R in the blue, red, green, red-edge, and near-infrared bands; SIF; SIFy; and solar zenith angle (SZA) and solar azimuth angle (SAA). Results revealed that the SIF signal is highly affected by the canopy structure and sun–canopy geometry effects compared to FyieldLIF. This was evidenced by the weak correlations obtained between SIFy and FyieldLIF at the diurnal timescale. Furthermore, the daily mean SIF‾y captured the seasonal dynamics of daily mean F‾yieldLIF and explained 58 % of its variability. The findings also revealed that reflectance in the near-infrared (R-NIR) and the NIRv (the product of R-NIR and normalized difference vegetation index (NDVI)) are good proxies of Φk at the diurnal timescale, while their correlations with Φk decrease at the seasonal timescale. With FyieldLIF and Φk as outputs and the abovementioned variables as predictors, this study also showed that the RF models can explain between 86 % and 90 % of FyieldLIF, as well as 60 % and 70 % of Φk variations under clear-sky conditions. In addition, the predictor importance estimates for FyieldLIF RF models revealed that R at 410, 665, 740, and 830 nm; SIF; SIFy; SZA; and SAA emerged as the most useful and influential factors for predicting FyieldLIF, while R at 410, 665, 705, and 740 nm; SZA; and SAA are crucial for predicting Φk. This study highlighted the complexity of interpreting diurnal and seasonal dynamics of SIF in forest canopies. These dynamics are highly dependent on the complex interactions between the structure of the canopy, the vegetation biochemical properties, the illumination angles (SZA and SAA), and the light conditions (ratio of diffuse to direct solar radiation). However, such measurements are necessary to better separate the variability in SIF attributable to radiation and measurement conditions from the subtler variability attributable to plant physiological processes.

Sun-induced chlorophyll fluorescence (SIF) observations are strongly affected by canopy structure. Modelling the radiative transfer of SIF provides an approach to quantifying the canopy structure effects and a better estimation of photosynthesis from SIF. The spectral invariant approach allows for the separation of reflectance into spectrally dependent parameters and spectrally independent parameters. We extend the spectral invariant theory to model the radiative transfer of SIF. The spectral invariant approach gives similar simulations of SIF emission and scattering of far-red SIF as the SCOPE model does. This work can help to disentangle the part of SIF signal that is dependent on the structure from that which is dependent on physiology.

Detecting sun-induced chlorophyll fluorescence (SIF) offers a new approach for remote sensing photosynthesis. However, to analyse the response characteristics of SIF under different stress states, a long-term time-series comparative observation of vegetation under different stress states must be carried out at the canopy scale, such that the similarities and differences in SIF change law can be summarized under different time scales. A continuous comparative observation system for vegetation canopy SIF is designed in this study. The system, which is based on a high-resolution spectrometer and an optical multiplexer, can achieve comparative observation of multiple targets. To simultaneously measure the commonly used vegetation index and SIF in the O2-A and O2-B atmospheric absorption bands, the following parameters are used: a spectral range of 475.9 to 862.2 nm, a spectral resolution of approximately 0.9 nm, a spectral sampling interval of approximately 0.4 nm, and the signal-to-noise ratio (SNR) can be as high as 1000:1. To obtain data for both the upward radiance of the vegetation canopy and downward irradiance data with a high SNR in relatively short time intervals, the single-step integration time optimization algorithm is proposed. To optimize the extraction accuracy of SIF, the FluorMOD model is used to simulate sets of data according to the spectral resolution, spectral sampling interval and SNR of the spectrometer in this continuous observation system. These data sets are used to determine the best parameters of Fraunhofer Line Depth (FLD), Three FLD (3FLD) and the spectral fitting method (SFM), and 3FLD and SFM are confirmed to be suitable for extracting SIF from the spectral measurements. This system has been used to observe the SIF values in O2-A and O2-B absorption bands and some commonly used vegetation index from sweet potato and bare land, the result of which shows: (1) the daily variation trend of SIF value of sweet potato leaves is basically same as that of photosynthetically active radiation (PAR); and (2) the bare land is a non-fluorescent emitter, the SIF of which is significantly smaller than that of sweet potato; and (3) analysis result based on the measured data is basically same as that based on simulated data. The above results verified the reliability of the SIF extracted from the measured data and the feasibility of comparatively observing the SIF value and the commonly used vegetation index of multiple vegetation canopy with this continuous observation system. This approach is beneficial for comprehensively analysing the stress response characteristics of vegetation canopies.

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.

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 value of leaf area index (LAI). Both the CI and LAI can be obtained from global Earth Observing (EO) systems such as the Moderate Resolution Imaging Spectrometer (MODIS). Here, the compatibility between CI and LAI products derived from EO data is examined independently using the theory of spectral invariants, also referred to as photon recollision probability theory (i.e. ‘ $p$ -theory’), along with raw LAI-2000/2200 Plant Canopy Analyzer data from 75 sites distributed across a range of plant functional types (PFTs). 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. Our results indicate that the integration of empirically-based CI maps with the MODIS LAI product is feasible, providing a potential means to improve the accuracy of LAI EO data products. Given the strong results for the large range of PFTs explored here, we demonstrate the capacity to obtain p-values for any location solely from EO data. This is relevant for future applications of the photon recollision probability concept for global and local monitoring of vegetation using EO data.

The effect that the canopy structure and the viewing geometry have on the intensity and the spatial distribution of passively measured sun-induced chlorophyll fluorescence at canopy scale is still not well understood. These uncertainties constrain the potential use of fluorescence to quantify photosynthesis at this level. Using a novel technique, we evaluated the diurnal changes in the spatial distribution of sun-induced fluorescence at 760 nm (F760) within the canopy as a consequence of the spatial disposition of the leaves and the viewing angle of the sensor. High resolution spectral and stereo images of a full sugar beet canopy were recorded simultaneously in the field to estimate maps of F760 and the surface angle distribution, respectively. A dedicated algorithm was used to align both maps in the post-processing and its accuracy was evaluated using a sensitivity test. The relative angle between sun and the leaf surfaces primarily determined the amount of incident Photosynthetic Active Radiation (PAR), which in turn was reflected in different values of F760, with the highest values occurring in leaf surfaces that are perpendicularly oriented to the sun. The viewing angle of the sensor also had an impact in the intensity of the recorded F760. Higher viewing angles generally resulted in higher values of F760. We attribute these changes to a direct effect of the vegetation directional reflectance response on fluorescence retrieval. Consequently, at leaf surface level, the spatio-temporal variations of F760 were mainly explained by the sun–leaf–sensor geometry rather than directionality of the fluorescence emission. At canopy scale, the diurnal patterns of F760 observed on the top-of-canopy were attributed to the complex interplay between the light penetration into the canopy as a function of the display of the various leaves and the fluorescence emission of each leaf which is modulated by the exposure of the individual leaf patch to the incoming light and the functional status of photosynthesis. We expect that forward modeling can help derive analytical simplified skeleton assumptions to scale canopy measurements to the leaf functional properties.

A TIR forest reflectance and transmittance (FRT) model for directional temperatures with structural and thermal stratification

A physical model for simulating crop albedo based on the law of energy conservation and spectral invariants was developed. The idea referred to the primary PARAS albedo model for forest. The developed model concerned two key problems for crop monitoring, one is the anisotropy of soil reflectance and the other is the clumping effect of crop leaves at canopy scale, which contributed to the improvement of the model accuracy. The comparison between the model results and those simulated using a Monte Carlo method shows that the calculated clumping index, soil absorptance and canopy albedo all have high accuracy, indicating that the model is able to reflect the interaction mechanism between radiation and the canopy-soil system.

Extension of radiative transfer code MOMO, matrix-operator model to the thermal infrared – Clear air validation by comparison to RTTOV and application to CALIPSO-IIR

Time evolution of large classical systems.- Ergodic properties of infinite systems.- Time evolution and ergodic properties of harmonic systems.- The laser: A reversible quantum dynamical system with irreversible classical macroscopic motion.- What does it mean for a mechanical system to be isomorphic to the Bernoulli flow?.- The Geodesic flow on surfaces of negative curvature.- Lectures on the billiard.- Spectral invariants and smooth ergodic theory.- Nonlinear wave equations.- Integrable systems of nonlinear evolution equations.- Discrete and periodic illustrations of some aspects of the inverse method.- Finitely many mass points on the line under the influence of an exponential potential -- an integrable system.- On traveling wave solutions of nonlinear diffusion equations.- The existence of heteroclinic orbits, and applications.- Hadamard's generalization of hyperbolicity, with applications to the hopf bifurcation problem.- Hyperbolic sets and shift automorhpisms.- Triple collision in Newtonian gravitational systems.- Solutions of the collinear four body problem which become unbounded in finite time.- On optimal estimates for the solutions of linear partial differential equations of first order with constant coefficients on the torus.

Imaging and non-imaging spectroscopy employed in the field and from aircraft is frequently used to assess biochemical, structural, and functional plant traits, as well as their dynamics in an environmental matrix. With the increasing availability of high-resolution spectroradiometers, it has become feasible to measure fine spectral features, such as those needed to estimate sun-induced chlorophyll fluorescence (F), which is a signal related to the photosynthetic process of plants. The measurement of F requires highly accurate and precise radiance measurements in combination with very sophisticated measurement protocols. Additionally, because F has a highly dynamic nature (compared with other vegetation information derived from spectral data) and low signal intensity, several environmental, physiological, and experimental aspects have to be considered during signal acquisition and are key for its reliable interpretation. The European Cooperation in Science and Technology (COST) Action ES1309 OPTIMISE has produced three articles addressing the main challenges in the field of F measurements. In this paper, which is the second of three, we review approaches that are available to measure F from the leaf to the canopy scale using ground-based and airborne platforms. We put specific emphasis on instrumental aspects, measurement setups, protocols, quality checks, and data processing strategies. Furthermore, we review existing techniques that account for atmospheric influences on F retrieval, address spatial scaling effects, and assess quality checks and the metadata and ancillary data required to reliably interpret retrieved F signals.

High spatiotemporal resolution vegetation FAPAR estimation from Sentinel-2 based on the spectral invariant theory