The spectral re ectance of vegetative canopies is determined by plant functional and structural properties (Ollinger, 2011). Plant function, which includes eco-physiological processes such as photosynthesis, is linked to foliar biochemical traits (e.g., pigments, proteins). In turn, the optical properties of foliar biochemistry shape spectral re ectance (Gates et al., 1965). Plant canopy structurethe three-dimensional (3D) orientation, density, and vertical distribution of stems and leavesalso affects spectral re ectance across the entire solar domain, particularly enhancing scattering across the near-infrared (NIR) wavelengths (Sellers, 1987;Sellers, 1985), and also affecting the relative contributions of sunlit and shaded vegetation and soil background (Asner, 1998;Myneni and Ross, 1991). Plants have converged on a range of evolutionarily viable combinations of function and structure (Grime, 1977;Mooney and Gulmon, 1979), which create detectable differences in canopy re ectance among individuals and species. The effects on re ectance can be direct, such as varying levels of chlorophyll among species, or they can be indirect. For example, differences in nitrogen content and photosynthetic capacity will affect NIR albedo, primarily as a result of the in uence of foliar nitrogen on canopy structure (Knyazikhin et al., 2013;Townsend et al., 2013). Recent advances in remote sensing have provided new ways to measure canopy function and structure. Methods to retrieve solar-induced chlorophyll uorescence (SIF) have provided a tool to directly measure photosynthetic physiology (Frankenberg et al., 2011;Li et al., 2018;Sun et al., 2017;Yang et al., 2015). Similarly, developments in terrestrial laser scanning (TLS) have allowed canopy structure to be measured in ways previously not possible (Calders et al., 2020;Disney, 2019;Stovall et al., 2021). These tools allow us to connect spectral re ectance to canopy function and structure in a manner that can inform ecological theory.
SIF is an emission of red and far-red photons (640 nm -850 nm) originating from the excitation of chlorophyll a from absorbed sunlight. In principle, remote sensing observations of SIF (SIF obs ) at the canopy scale can be de ned when only rst-order scattering is considered as: SIF obs,(λ,Ω) = PAR × ( i 0,green × (1 -ω PAR )
where PAR is photosynthetically active radiation, i 0,green is the canopy directional interceptance of green components with chlorophyll (Zeng et al., 2022), ω PAR is the single scattering albedo for PAR (transmittance + re ectance). The i 0,green × (1 -ω PAR ) term comprises FPAR chl , the fraction of PAR absorbed by chlorophyll and PAR × FPAR chl = APAR.
ϕ F,λ is the quantum yield of steady-state uorescence at a given wavelength (λ), and f esc (λ,Ω) is the photon escape probability at the viewing angle of the sensor (Ω). f esc (λ,Ω) acts as a scaling factor, ranging from 0 to 1, on the total SIF emission. From Eq. 1, canopy observations of SIF are affected by 1) steady-state biochemistry in the form of canopy chlorophyll content; 2) photosynthetic physiology in the form of ϕ F,λ ; 3) canopy structure, which is represented as i 0 and f esc (λ,Ω) in Eq. 1. From Eq. 1, it becomes evident that to isolate ϕ F,λ from SIF obs,FR , the effects of canopy structure (i 0 and f esc (λ,Ω) ) must accounted for. These effects include the leaf area index (LAI), leaf angle distribution (LAD), and foliar clumping.
Early studies showed empirical relationships between SIF and gross primary productivity (GPP) across scales, from local (Yang et al., 2015) to regional and global (Frankenberg et al., 2011;Li et al., 2018;Sun et al., 2017). Additional studies showed that the relationship between SIF and GPP is more attributable to the APAR and structural terms in Eq.1 than ϕ F (Dechant et al., 2020;Wieneke et al., 2018;Yang et al., 2018a). In order to use SIF as a photosynthetic proxy, ϕ F must be connected to the quantum yield of photochemistry (ϕ P ), which controls the electron supply for the light-independent reactions of photosynthesis (Frankenberg and Berry, 2018;Magney et al., 2020;van der Tol et al., 2014). This is not a straightforward endeavor, as ϕ F competes with ϕ P and non-photochemical quenching (NPQ) for excitation energy from APAR. The competition among these processes is complex and dynamic, operating at timescales of milliseconds to minutes (Sun et al., 2023a). Moreover, the relationship between ϕ F and ϕ P exhibits non-linearity that is affected by light intensity and environmental stress (Gu et al., 2019;Magney et al., 2020;Porcar-Castell et al., 2014;Sun et al., 2023b;van der Tol et al., 2014). Under light-saturating conditions ϕ F and ϕ P are linearly related, but this linearity can be disrupted due to sudden adjustments in photosynthesis (Helm et al., 2020;Marrs et al., 2020;Wu et al., 2022). Interestingly, the same sensitivity to changes in photosynthetic physiology that decouples ϕ F and ϕ P enables SIF measurements to be used to detect stress responses of vegetation (Damm et al., 2022;Martini et al., 2022;Sun et al., 2023b;Wang et al., 2022). SIF and ϕ F also covary with foliar biochemical properties related to photosynthesis (Sun et al., 2023b, Sun et al., 2023a;Zhang et al., 2014). Nitrogen treatment experiments have shown differences in SIF in crops and natural systems (Ač et al., 2015;Jia et al., 2021;Migliavacca et al., 2017).
SIF and ϕ F,λ are correlated with chlorophyll content at the leaf scale (Tubuxin et al., 2015), while canopy scale observations covary with pigment pools (Kim et al., 2021;Pierrat et al., 2022) using the chlorophyll:carotenoid index (CCI, Gamon et al., 2016), an optical proxy for chlorophyll (Wong et al., 2020).
Optical proxies of canopy structure have also been important for SIF and inferring photosynthetic productivity. NIR wavelengths have long been known to be sensitive to canopy structure, dating back to formative studies on NDVI and its precursors (Colwell, 1974;Jordan, 1969;Tucker, 1979). It was recognized that NDVI could be used to estimate FPAR, a key parameter in light-use ef ciency models of GPP (Running et al., 2004). In principle NIR V is a better proxy for FPAR than NDVI (Sellers, 1987), but non-vegetative components are often an appreciable fraction of total scene NIR re ectance (NIR T ), particularly at the coarse resolutions of satellite imagery. Recently, Badgley et al. (2017) showed that NIR V can be approximated as the product of NDVI and NIR T , with NDVI representing the proportion of NIR re ectance attributable to vegetation. This approach for approximating NIR V has been found to be a stronger predictor of GPP than NDVI or SIF across vegetation types and across spatial scales (Badgley et al., 2019;Baldocchi et al., 2020;Dechant et al., 2022, Dechant et al., 2020). Importantly, NIR V shares a physical basis with far-red SIF which allows f esc (λ,Ω) to be approximated (Zeng et al., 2019). Additional modeling and eld-based analyses showed that ϕ F can be derived using the radiance equivalent of NIR V (NIR V R, Zeng et al., 2022).
When considering the spatial patterns of canopy re ectance and SIF, it is important to recognize that plants are biological organisms that have been shaped by evolutionary and ecological principles (Field, 1991;Gamon et al., 2019;Ollinger, 2011). Plants coordinate canopy function and structure to maximize whole-plant carbon gain given the biotic and abiotic environments in which they are growing (Givnish, 2020;Hirose, 2005;Horn, 1971;Monsi and Saeki, 1953). Foliar resources such as nitrogen and other elements are distributed based on the spatial arrangement of leaves through the canopy (Ellsworth and Reich, 1993;Niinemets, 2010;Yang et al., 2023). This distribution leads to a coordination between function and structure that modulates photosynthetic capacity and leaf chlorophyll content (Croft et al., 2017;Kattge et al., 2009). The result of this coordination has important implications for vegetation re ectance, derived spectral indices, and SIF. For example, NDVI is affected by NIR scattering from canopy structure and by leaf chlorophyll content (Gamon et al., 1995;Gitelson and Merzlyak, 1997). Since the arrangement of canopy structure also affects leaf chlorophyll content, NDVI and other vegetation indices can be viewed as indicators of different functional-structural con gurations that evolution has selected for across individuals and species. These biophysical linkages also extend to SIF. Canopy structure directly affects i 0,green and f esc (λ,Ω) in Eq. 1. The coordination between function and structure indirectly affects (1ω PAR ) and ϕ F via the in uence chlorophyll and foliar nitrogen (Kof et al., 2015;Migliavacca et al., 2017;Verrelst et al., 2016).
Given the connections between canopy function and structure, one might expect that remotely sensed observations of pigments and photosynthetic physiology covary with canopy structure. Studies investigating these covariations have been lacking, largely due to the dif culty in measuring canopy structure. TLS instrument quality and data processing has improved dramatically in the last decade (Calders et al., 2020;Disney, 2019), allowing accurate and rapid estimates of LAD and LAI (Jupp et al., 2009;Stovall et al., 2021;Vicari et al., 2019). In particular, leaf angle and LAD is an understudied component of canopy structure that is essential for plant ecophysiology (Close and Beadle, 2006;Hirtreiter and Potts, 2012) and is known to affect remote sensing observations (McNeil et al., 2023;Yang et al., 2023). However, no empirical studies have examined the relationship between LAD and remote sensing data. Additionally, there are few studies examining the spatial patterns in SIF and re ectance at the canopy or landscape scale (Maguire et al., 2021;Zeng et al., 2022). These questions require high spatial resolution data that can only be obtained from a xed-wing aircraft or uncrewed aerial system (UAS). Most canopy-scale studies of SIF rely on tower-based observation systems, which have a high temporal resolution but only measure either one canopy, or multiple canopies, typically with inconsistencies in viewing zenith angle (Dechant et al., 2020;Kimm et al., 2021;Pierrat et al., 2022, Pierrat et al., 2021). In this study, we combine a novel UAS-based system with concurrent TLS data and foliar sampling to answer the question, "Does canopy structure covary with re ectance indices, SIF, and ϕ F,λ , across individual tree canopies?" We hypothesize that LAD and LAI will be correlated with remotely sensed variables of NIR V , re ectance indices, SIF, and ϕ F,λ . We examine these relationships across two datasets collected under contrasting phenological stages; one dataset collected during the peak growing season, and another collected during autumn leaf senescence when nutrients are being remobilized and reallocated to other tissues in preparation for winter dormancy.
Our study site was Milton Air eld (37.9941 • N, -78.3976 • W, Fig. 1) -an abandoned air eld now used by radio-controlled aircraft hobbyists with adjacent regenerated stands of deciduous broadleaf (DBF) and evergreen needleleaf (ENF) trees. We developed a novel UAS called FluoSpecAir (Fig. 2, Section 2.2) to measure spatiotemporal patterns in SIF and VNIR re ectance (400 nm -850 nm) across individual tree canopies at Milton Air eld on clear-sky days. For this study, we collected two datasetsone collected at the onset of foliar senescence in 2020, and another during the peak growing season of 2021. We refer to these datasets as "foliar senescence" and "peak growing season" respectively. For each dataset, we supplemented FluoSpecAir ights with 3D structural data from a subset of canopies using terrestrial laser scanning (Section 2.3) and foliar sampling (Section 2.4).
The foliar senescence dataset was collected on three separate weeks, spaced approximately 14 days apart. Measurements began on DOY 251, 267, and 282, respectively. FluoSpecAir was own at four separate time intervals: 7:00-8:00, 11:00-12:00, 12:00-13:00, and 15:00-16:00 EST. Each ight ew predetermined waypoints that covered individual canopies of American sycamore, black cherry, red maple, and tulip poplar from the DBF stand, and canopies of eastern white pine from the ENF stand (Fig. 1, Table 1). Flights were repeated across 2-3 days to ensure suf cient spatiotemporal coverage and good data quality. Following the completion of ights, a subset of canopies targeted by FluoSpecAir were scanned using TLS. We collected foliar samples for the ights pertaining to DOY 267 and 282.
The peak growing season dataset was collected on four separate weeks (DOY 133,148,188,and 217). FluoSpecAir ights were made hourly from 7:00-16:00 EST, with another repeat day of ights. The peak growing season dataset was collected from a different but nearby set of waypoints with some canopy overlap, including black cherry, eastern white pine, red maple, and tulip poplar (Table 1). FluoSpecAir suffered a malfunction on the week pertaining to DOY 148, and thus, we were only able to make two ights at 7:00 and 8:00. For each week of FluoSpecAir ights, we scanned a subset of canopies using TLS. Foliar traits were sampled on days following DOY 148 and 188.
The UAS used in FluoSpecAir is a DJI Matrice 600 Pro (M600 Pro) with a D-RTK real-time kinematics mobile GNSS station, and a Zenmuse X2 camera. Autonomous ight and data acquisition were controlled using an onboard Raspberry Pi 3 Model B connected to the A3 ight controller on the M600 Pro. Using the DJI Onboard SDK (version 3.9), we developed an autonomous ight script that 1) centered on coordinates for each canopy, with the UAS positioned 15 m above the canopy and the aircraft "nose" always oriented north; 2) made measurements of downwelling irradiance and upwelling radiance at nadir; 3) initiated video capture from the Zenmuse X2 camera for the entirety of the upwelling radiance measurement. Coordinates for each canopy were selected by manually ying the M600 Pro over individual canopies. Using the Zenmuse X2 video feed, we recorded the coordinates from the RTK antenna onboard the M600 Pro when the ber eld of 1. Light blue circles indicate deciduous broadleaf forest (DBF) canopies and light yellow triangles represent evergreen needleleaf forest (ENF) canopies. The takeoff and landing location of FluoSpecAir is outlined in black. (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.) view (FOV) was covering the targeted canopy (see the following paragraphs for details). Using RTK positioning for FluoSpecAir measurements is criticalwe compared the accuracies of the RTK antennas and standard A3 antennas on the M600 Pro against 10 surveyed points and noted X/Y/Z accuracies of ≤5 cm using RTK, while A3 accuracy was ≥1 m (data not shown). For time and safety considerations, the take-off and landing of the M600 Pro were performed manually by the M600 Pro pilot.
FluoSpecAir uses a modi ed FluoSpec2 (Yang et al., 2018b) dualspectrometer system consisting of an Ocean Insight (Dunedin, Florida, United States) QEPro spectrometer, which measures wavelengths between 730 nm -785 nm (100 μm slit, 0.31 nm full-width half maximum (FWHM)), and an Ocean Insight Flame spectrometer, which measures between 340 nm -1040 nm (25 μm slit, 3.28 nm FWHM at 546 nm).
Fiber optics for measuring downwelling irradiance and upwelling radiance were connected to a rotating prism, which selectively directs incoming light from either ber to a BF19Y2LS02 bifurcated ber (Thorlabs Inc., Newton, NJ, USA) connected to the two spectrometers. The downwelling irradiance ber used an Ocean Insight CC-3 cosine corrector and was calibrated for irradiance using an Ocean Insight HL-3 light source. The upwelling radiance ber used a Gershun tube kit (Ocean Insight) to restrict the eld of view to 6 • , and was calibrated for radiance using a Labsphere 8 in. HELIOS integrating sphere (15.24 cm) (Labsphere, North Sutton, New Hampshire, United States). The QEPro had a thermoelectric cooler which kept the detector temperature stable around -10 • C. For correcting the dark signal on the QEPro we used the method by Yang et al. (2018aYang et al. ( , 2018b)), which creates a lookup table of dark current spectra across temperature values and integration times, and assumes dark current is linearly correlated with integration time at a given temperature. The Flame instrument lacked a TEC cooler and thus could not be temperature stabilized. To account for the dark current, we made measurements of dark spectra using the Flame before and after each ight, and averaged both values for the dark spectra. We assumed that the temperature of the Flame spectrometer stayed constant before, during, and after each ight. Inspection of pre-ight and post-ight dark spectra showed no noticeable differences between the two, providing some basis for this assumption.
The downwelling radiance ber was mounted on a bracket in order to maintain a xed position relative to the Zenmuse X2 camera and gimbalthis enabled alignment of the ber FOV with the video output from the camera. Projecting the ber FOV onto the video output was achieved by shining a light through the ber in a dark room while recording video feed from the camera. As a result, for every recorded video of upwelling radiance data collection, we were able to accurately identify if measurements were made from the targeted canopies for this study. With each measurement taken at a distance of 15 m above each canopy, the spot size was approximately 2 m 2 for all canopies.
We used the QEPro data to retrieve far-red SIF (SIF obs,FR ) in mW m -2 sr -1 nm -1 in the O 2 -A band using the spectral tting method (Meroni et al., 2010). We used a tting window of 759.5 nm -761.5 nm (Chang et al., 2020) with linear functions. In our retrieval of SIF, we did not account for any atmospheric attenuation of the SIF signal based on the distance from each target to the sensor. We measured this effect to be minimal based on an experimental ight where we examined how SIF obs, FR changed as a function of height against a non-uorescence target of asphalt pavement (Fig. S2). We used re ectance from the Flame to calculate NDVI and CCI using the equations: The red circle overlays the ber optic FOV with respect to the Zenmuse X2 camera. We ensured that FluoSpecAir was positioned over all targeted canopies by checking each recorded video feed (see Fig. S1 for examples). Panel C) Daily pattern of SIF obs,FR (mW m -2 sr -1 nm -1 ) and NIR V R (W m -2 sr -1 nm -1 ) for the canopy shown on the day of ight. (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.)
The list of canopies measured with FluoSpecAir in this study. The ID eld is a unique eld-assigned identi er for a given individual. DOY coverage signi es when FluoSpecAir data is available for a canopy.
T Signi es TLS scan of canopy on DOY. ID Species Common name PFT DOY coverage 1 Acer rubrum Red maple DBF 251, 267, 282 3 Platanus occidentalis American sycamore DBF 251, 267, 282 4 Acer rubrum Red maple DBF 133 T , 148, 217 T , 251, 267, 282 7 Acer rubrum Red maple DBF 267 T , 282 T 8 Liriodendron tulipifera Tulip poplar DBF 133 T , 148, 188 T , 217 T , 267 T , 282 T 10 Liriodendron tulipifera Tulip poplar DBF 133 T , 148, 188 T , 217 T , 267 T , 282 T 11 Prunus serotina Black cherry DBF 133 T , 188 T , 217 T , 251, 267 T , 282 T 12 Prunus serotina Black cherry DBF 133, 148, 188, 251, 267 13 Prunus serotina Black cherry DBF 267, 282 14 Acer rubrum Red maple DBF 133 T , 148, 188 T , 217 T , 251, 267 T , 282 T 15 Liriodendron tulipifera Tulip poplar DBF 251, 267 T , 282 T 16 Pinus strobus Eastern white pine ENF 133, 148, 188 T , 217 T , 251, 282 T 17 Pinus strobus Eastern white pine ENF 251, 267 T , 282 T 18 Pinus strobus Eastern white pine ENF 251, 267 T , 282 T 19 Pinus strobus Eastern white pine ENF 251 20 Pinus virginiana Virginia pine ENF 133, 188 T , 217 T 21 Liriodendron tulipifera Tulip poplar DBF 133 T , 148, 188 T , 217 T 22 Acer rubrum Red maple DBF 133 T , 148, 188 T , 217 T 26 Pinus strobus Eastern white pine ENF 188 T , 217 T 30 Pinus resinosa Red pine ENF 217
Where r represents re ectance at a wavelength in nm. Additionally, we calculated NIR V and NIR V R as:
Where L 780 is radiance at 780 nm. For radiance and re ectance at 780 nm, we used data from the QEPro.
Data were quality controlled and ltered out based on 1) whether upwelling radiance measurements occurred over the targeted canopy and were free of shadows based on the video feed (see Fig. S1 for examples); 2) whether there were clear and stable sky conditions based on the video feed and irradiance values; 3) spectral shape (was there a peak in green re ectance, red edge, and NIR plateau, indicating a vegetative spectral signature) and magnitude of NIR re ectance (0.2 ≤ NIR re ectance ≤0.6); 4) SIF obs,FR values <0 mW m -2 sr -1 nm -1 . We made no corrections for any potential roll and pitch effects on upwelling or downwelling measurements. These effects were observed to be minimal based on observing the video feed from each measurement.
We estimated ϕ F,FR using the conceptual approach by Zeng et al.
(2022), who showed that SIF obs,FR NIRVR is proportional to ϕ F,FR . NIR V R and SIF obs,FR are known to be strongly correlated with each otherthe reason for this being they share a physical basis that can be seen when comparing Eq. 1 to the following equation:
NIR V R and SIF obs,FR are dependent on incoming solar radiation (PAR for SIF, incoming solar radiation in the NIR (S NIR ) for NIR V ), canopy interceptance, and f esc (λ,Ω) . One key difference is that NIR V R is affected by the single scattering albedo for NIR wavelengths (ω NIR ), whereas for SIF,
(1ω PAR ) is the absorbance in the visible domain. Although f esc (λ,Ω) depends upon wavelength, NIR photons absorb and scatter similarly to farred photons from SIF, particularly at wavelengths ≥750 nm. Thus, f esc (λ,Ω) should functionally be similar for both. This approach is contingent on NIR V R and SIF obs,FR being measured from the same eld of view, otherwise mismatches in Ω and/or the ratio of diffuse radiation will introduce uncertainty into the estimation of ϕ F,FR . Additionally, an implicit assumption is that the ratio between (1ω PAR ) and ω N is constant within and across taxa, and throughout time. We explain how all variables in Eqs. 1 and 6 are calculated in Section 2.5.
In this study, we made 3D scans using a Faro Focus 120 (Faro Technologies, Lake Mary, FL, USA) for all measurement weeks, with the exception of one week (week 31) in the peak growing season where we used a Leica RTC 360 (Leica Geosystems, St. Gallen, CH) TLS. The difference in data collected by each instrument has not been reported in the literature, nor was it possible to do so for this study. We note that the Leica TLS collected approximately ve times as many points per second than the Faro TLS, creating denser and more detailed point clouds. FluoSpecAir canopies were scanned from multiple positions to create a 360 • reconstruction. In some instances, a 360 • reconstruction was not possible due to occlusion from surrounding canopies. Scans were made along a track that was designed to maximize coverage of FluoSpecAir canopies from each scan position. We staked a grid of 14.7 cm diameter reference balls to co-register individual TLS scans to one another. On average, each individual scan shared six reference balls with any other scan, and no scans shared fewer than four reference balls. Registration of TLS scans was performed using the instrument's respective software packagefor the Focus 3D we used Faro SCENE and for the Leica RTC 360, we used Register 360. Reported alignment error averaged around 5 mm for registered scans. Individual trees from registered point clouds were then manually extracted.
We applied the TLSLeAF algorithm (Stovall et al., 2021) to create 10 cm 3 voxels of leaf inclination angles (θ L ) from the tree point clouds. Using the mean θ L for each voxel, we quanti ed LAD using; 1) a beta distribution (Goel and Strebel, 1984) parameterized by ν and μ; 2) the leaf inclination distribution function LIDF (Verhoef, 1997) which is parameterized by LIDFa and LIDFbthese are parameters used in radiative transfer models (RTMs) of canopies such as SCOPE (van der Tol et al., 2009); 3) the mean and standard deviation of θ L of all voxels. We used a voxel-based method (Hosoi and Omasa, 2006) to calculate vertical pro les of leaf area voxel density (LAVD). The contact frequency for each vertical slice was calculated using points classi ed as vegetation from the TLSLeAF output. We then multiplied the contact frequency by a correction factor of 1.1 that accounts for leaf inclination angle to calculate the leaf area voxel density (Li et al., 2017). We used the same voxel resolution for LAD and LAVD calculations (10 cm 3 as recommended by TLSLeAF). We computed the LAI by summing LAVD across all vertical bins.
We calculated LAD parameters as a function of the cumulative vertical LAVD to account for differences in vertical foliage density (Fig. 3). Representing the top of the canopy as 0 %, we calculated the canopy height where a speci ed cumulative LAVD is found. Next, we selected all angle voxels greater than or equal to the calculated height, and calculated the corresponding beta distribution and LIDF parameters, and the mean and standard deviation of angle voxels. Optimal LIDF parameters were calculated by applying a numerical minimization to an algorithm provided by Verhoef (1997), which generates the cumulative leaf inclination distribution for any combination of LIDFa and LIDFb. We used the lm t package in Python 3.8 to apply a least-squares minimization using the trust region re ective method. LIDFa and LIDFb were constrained such that |LIDFa| + |LIDFb| ≤ 1 (Verhoef, 1997). The optimization was performed on the probability density of observed leaf angles using one-degree bins. We calculated the probability density from the algorithm provided by Verhoef (1997) by taking the difference in cumulative distribution between inclination intervals θ 1 and θ 2 , where the interval was one degree.
We collected a limited set of foliar samples for the foliar senescence and peak growing season datasets. Foliar samples were collected on ights corresponding to DOY 148, 188, 267, and 282. Sun-exposed, top of canopy, foliar samples were collected from canopies using a modular pole pruner. We selected 1-5 non-chlorotic leaves per canopy. Foliar sampling occurred in the morning and midday; upon obtaining samples, they were immediately placed into plastic bags and stored in a dark cooler with ice. In the afternoon, samples were returned to the laboratory where they were measured for the projected area using a LI-3000C (LiCor Biosciences, Lincoln, NE, USA) leaf area meter. Foliar samples were then measured for spectral re ectancefor the foliar senescence dataset we used an ASD FieldSpec 3 (ASD Inc., Boulder, CO, USA) and the peak growing season dataset used an SVC HR-1024i (Spectra Vista Corp, Poughkeepsie, NY, USA). The leaf re ectance was measured by each instrument using a plant contact probe with an external light source. For ENF species, fresh spectra were measured by arranging needles together in a singular mat with no open spaces between needles. We measured re ectance spectra at ve positions for each leaf, and averaged all scans. Following projected area and re ectance measurements, foliar samples were oven-dried at 60 • C for 48 h to measure the dry mass and calculate LMA.
Spectral re ectance from 400 nm -950 nm was inverted using PROSPECT-D (Féret et al., 2017) to retrieve estimates of chlorophyll a + b (leaf chlorophyll content) and leaf carotenoid content. PROSPECT-D was inverted using a numerical minimization, with a least-squares curve t with a trust region re ective algorithm using the lm t package. We estimated the mesophyll thickness, the chlorophyll a + b content, the carotenoid content, the anthocyanin content, brown pigments, and water thickness, parameters. We used the leaf LMA as the dry mass parameter. We calculated leaf ω PAR averaging re ectance + transmittance from 400 nm -700 nm. Leaf ω NIR was calculated by averaging re ectance + transmittance from 777 nm -783 nm.
We examined the spatial distributions of canopy NDVI, canopy NIR V , canopy CCI, SIF obs,FR, and SIF obs,FR NIRVR , ν, and μ, across all individuals, and how they varied diurnally, across the foliar senescence and peak growing season datasets. We used the Tukey-Kramer approach to compare how distributions of each variable changed for DBF species within and across each dataset. We did not make statistical comparisons of ENF distributions because of limited observations. We then analyzed the relationships of SIF obs,FR and SIF obs,FR NIRVR with canopy NDVI, canopy NIR V , and canopy CCI. For each dataset, we show the relationships among variables for each week of FluoSpecAir measurements. We used all data from all ights and averaged observations from multiple days on an hourly basis. Additionally, we examined if the relationships among variables vary diurnally by averaging observations for certain times of the day. Speci cally, we examined relationships during the morning (7:00-9:00), midday (11:00-13:00), and afternoon (14:00-16:00).
We used linear mixed effects models to understand the spatiotemporal relationship of cumulative LAVD and LAD with our remote sensing observations. We chose this method because a simple linear regression analysis would violate the assumption of independence. The foliar senescence and peak growing season datasets consist of repeat canopy observations across different weeks, thus our analysis needed to account for effect of each canopy at different points in time. We used the model structure:
Where y is the outcome variable (canopy NDVI, canopy CCI, SIF obs, FR , or SIF obs,FR NIRVR ), Х is the predictor variable vector (cumulative LAVD, ν, μ, LIDFa, and LIDFb), β is the xed-effects regression coef cients, Ζ is the design matrix for the random effect (tree ID), μ is the vector for the random effects (the random complement to the xed β), and ε is the model residuals not explained by the model Хβ + Ζμ. We constructed models for the foliar senescence and peak growing season datasets, using canopies that had concurrent FluoSpecAir and TLS observations (Table 1). The outcome variables were calculated as the mean daily value using all hourly data for each canopy and week. Linear mixed effects models were generated in R using the lme4 package. We report the marginal R 2 (R 2 m ), which is the proportion of total variance explained by the xed effect, and the conditional R 2 (R 2 c ), which is the proportion of variance explained by both xed and random effects (Nakagawa et al., 2017). Model evaluation and calculation of R 2 m and R 2 C was done using the mlmtools package in R.
We present the model relationships using 10 % of the cumulative LAVD (LAVD 10% ). We report these variables with the percentage subscripted, such that ν 10% and μ 10% would represent ν and μ at 10 % of the cumulative LAVD. This percentage was chosen based on an analysis to determine what portion of the canopy is most relevant to our remote sensing data. Using the same model structure described in the previous paragraph, we built models using 1 % increments of the cumulative LAVD, starting from 1 % and ending at 100 %. The highest R 2 c values for models using μ were found approximately between 10%-20 % of the cumulative LAVD, while R 2 c values for ν typically reached their maximum between 50 % -70 % (Fig. S3).
We performed an exploratory analysis to provide greater contextual meaning to beta distribution parameters ν and μ. Using the underlying equations for ν and μ (Eq. A1 -A3), we showed how the mean and variance affect the shape of the beta distribution. We developed a more intuitive equation for explaining μ. To test the generality of our ndings, we compared our results to 100 randomly generated beta distributions, constraining the range of ν and μ in our simulated data to the range of our observational data.
As a check on the assumption that SIF obs,FR NIRVR is proportional to ϕ F,FR , we rearranged Eq. 1 and Eq. 6 to the following: Fig. 3. A visualization of how LAD parameters were calculated using our point cloud data. In this example, we used ID 10 from DOY 217 (Table 1). For an isolated tree (left panel), we calculated the vertical LAVD pro le using all co-registered point cloud data. In this example, we show the height of the tree at which corresponds to 5 %, 10 %, 25 %, 50 %, and 100 %, of the cumulative LAVD (m 2 m -3 ). The probability density function using the beta and LIDF distributions, and the observed distribution, for each cumulative LAVD is shown on the right panels.
We used our eld observations to examine the potential in uence of the rst two terms in eq. 3 on SIF obs,FR NIRV R . S nir was calculated as incoming irradiance at 780 nm from the QEPro, while foliar samples were used to calculate 1-ωPAR ωNIR . ω PAR was calculated by averaging re ectance + transmittance from 400 nm -700 nm. ω NIR was calculated by averaging across wavelengths 777 nm -783 nm. PAR SNIR was approximated by averaging all daily values of PAR/S nir for individual plant canopies with concurrent foliar measurements of ω PAR and ω NIR during a sampling week.
Finally, we analyzed relationships between leaf chlorophyll content and remote sensing variables and canopy structural parameters. Due to limited foliar sampling during the peak growing season dataset, we show relationships from data collected on DOY 188. For the foliar senescence dataset, we show relationships from data collected on DOY 267. When examining relationships between leaf chlorophyll content and our structural metrics, we used whole-canopy values (e.g. LAVD 100% , ν 100% and μ 100% ). Whole-canopy values are more representative of coordination between leaf chlorophyll content and canopy structure, as they re ect the patterns of resource allocation made at the level of the individual.
Canopy NDVI, canopy CCI, SIF obs,FR, and SIF obs,FR NIRVR , were larger in the peak growing season than during foliar senescence for DBF canopies (Fig. 4). Canopy NIR V , LAVD 10% and beta distribution parameters ν 10% and μ 10% did not differ as much between the two datasets (Fig. 4). We note that for SIF obs,FR, and SIF obs,FR NIRVR , the last week of ights for the peak growing season dataset tended to show no differences against observations from the foliar senescence dataset (Fig. 4d -4e). LAVD 10% and ν 10% values were slightly higher during the peak growing season, but not large enough to differ signi cantly from measurements made during foliar senescence, except for DOY 217 (Fig. 4f, h). We observed no differences in the mean or standard deviation of leaf angle (mean 10% , sd 10% , Fig. S4f -S4g), though peak growing season distributions had comparatively more canopies with a higher mean leaf angle. TLS observations for this week were made using the Leica RTC 360, which as mentioned, collected 5× as many points compared to the Faro Focus TLS used on all other weeks.
During the peak growing season, canopy NDVI was constant among DBF species, with a mean value of 0.88 for ights on DOY 133,148, and 217. Canopy NDVI was larger on DOY 188, with a mean value of 0.91 (Fig. 4a). Canopy NIR V peaked on DOY 148 and declined the following weeks, with DOY 217 showing the lowest mean canopy NIR V . Canopy CCI declined throughout the peak growing season for DBF species, with a lower mean value for DOY 217 compared to DOY 133, though we note that DOY 133 exhibited larger variation (Fig. 4c). Similarly, SIF obs,FR and SIF obs,FR NIRVR declined across the peak growing season (Fig. 4c -4d), although we observed an increase in both for DOY 148. We observed decreases in canopy NDVI among DBF species during foliar senescence (Fig. 4a). Mean canopy NDVI declined by approximately 9 % from DOY 251 (canopy NDVI = 0.87) to DOY 282 (canopy NDVI = 0.79). Canopy NIR V , canopy CCI, SIF obs,FR , and SIF obs,FR NIRVR did not change across the sampling period for DBF species (Fig. 4b -4e), though the distributions changed, particularly when comparing DOY 251 and DOY 282. Given the limited number of ENF canopies for both datasets, we opted not to make any statistical or qualitative comparisons with either dataset.
During the peak growing season, spatial variation in SIF obs,FR was more strongly related to canopy CCI than canopy NDVI (Fig. 5). We observed signi cant relationships between SIF obs,FR and NIR V , though they were mostly weaker compared to canopy NDVI or canopy CCI. With respect to SIF obs,FR NIRVR ; canopy NDVI had a stronger relationship with SIF obs,FR NIRVR than canopy CCI, while no relationship with canopy NIR V was observed. These patterns were consistent across the morning, midday, and afternoon (Fig. S5). The R 2 values of spatial relationships at individual times were larger compared to Fig. 5, which pools all data across all times. The R 2 of spatial relationships declined as the peak growing season progressedthis is particularly noticeable when examining relationships of canopy NDVI and canopy CCI with SIF obs,FR NIRVR . We observed no signi cant relationships across canopy NDVI, and canopy CCI, with SIF obs,FR or SIF obs,FR NIRVR across the foliar senescence dataset (Fig. 6). Canopy NIR V was signi cantly correlated with SIF obs,FR on DOY 251. Similarly, we observed minimal correlations between variables when looking at data across individual times of day. Of note, midday observations, which minimize solar angle issues, showed only one signi cant correlation between canopy NDVI and SIF obs,FR NIRVR on DOY 282 (Fig. S6).
For full results of our exploratory analysis on interpreting beta distribution parameters, we refer readers to Appendix A. However, we identi ed several important points about ν and μ. First, ν and μ are inversely related to variancelower values indicate greater variability in leaf angle while higher values indicate low variability. Furthermore, when the mean leaf angle is greater than 45 • , as is the case for all canopies in this study (Table S1), ν and μ have speci c interpretations; 1) ν is mainly affected by the variance in leaf angle (Fig. A1); 2) μ is sensitive to both the mean and variance of leaf angle (Fig. A1), and is conceptualized as the variance in leaf angle when controlling for the effects of mean angle on the variance (Fig. A4) -as leaf angles are constrained from 0 • to 90 • , mathematically, variation in angle must be relatively lower the closer distribution mean is to either extreme. Another noteworthy point arising from the calculation of ν and μ is that when the mean leaf angle is greater than 45 • , ν will be larger than μ, with the opposite being true at mean leaf angles lower than 45 • .
In the peak growing season, we observed a negative relationship between beta distribution parameters and remote sensing variables, indicating that canopies with greater variation in leaf angle had larger canopy NDVI, CCI, SIF obs,FR , and SIF obs,FR NIRVR (Fig. 7). We did not nd any signi cant models between LAVD and our remote sensing variables, or for models using beta distribution LAD parameters and canopy NIR V .
Linear mixed models using ν 10% or μ 10% produced similar a R 2 c , but differed considerably in their values of R 2 m , which is the proportion of variance explained by the xed (i.e. ν 10% or μ 10% ) effect only. Models using μ 10% had a larger R 2 m and a smaller difference between R 2 c and R 2 m , compared to ν 10% . Canopy NDVI and SIF
obs,FR NIRVR had the strongest relationships with ν 10% and μ 10% , with R 2 c ≥ 0.75. The xed effect of μ 10% accounted for 80 % and 73 % of the variation in canopy NDVI and SIF obs,FR
NIRVR . No signi cant models were generated using LIDFa 10% as a predictor variable, while LIDFb 10% was positively related to canopy NDVI and SIF obs,FR NIRVR . R 2 c values for LIDFb 10% were lower compared to ν 10% and μ 10% , while R 2 m values were in-between ν 10% and μ 10% . No signi cant models were found using LAVD 10% , though we note that one ENF canopy (red pine, ID 30) had a large LAVD 10% while its LAD parameters were consistent with other ENF canopies.
When examining relationships in the foliar senescence dataset, we did not observe any signi cant relationships (Fig. S7). However, models using μ 10% and LIDFb were trending signi cant (P ≤ 0.05) for canopy NDVI and SIF obs,FR NIRVR . Relationships with mean and SD leaf angle varied between the two datasets (Figs. S8, S9). In the peak growing season, models using SD 10% were trending signi cant for all remote sensing variables (Fig. S8). In the foliar senescence dataset, mean 10% was trending signi cant for canopy NDVI and NIR V (Fig. S9), with mean 10% being positively related to canopy NDVI and negatively related to NIR V .
Beta distribution parameter μ was highly related to LIDFb (R 2 ≥ 0.90, not shown), while the relationship between LIDFa and mean leaf angle was nearly a perfect line (R 2 ≥ 0.98 not shown).
PROSPECT-D inversions were able to accurately replicate our measurements of leaf re ectance spectra using a leaf clip (Fig. S10) from 400 nm -950 nm. When comparing the measured re ectance spectra to the simulated, we report a median root mean square error (RMSE) and standard error of 0.0086 ± 0.0004. During the peak growing season, leaf chlorophyll content ranged from 52 to 86 μg cm 2 with a median and standard deviation of 67 ± 9. During the foliar senescence dataset, leaf chlorophyll content ranged from 35 to 78 μg cm 2 with a median and standard deviation of 53 ± 13. When correlating leaf chlorophyll content to midday observations of SIF obs,FR NIRVR for a given sampling week, we found positive relationships between both variables for both datasets (Fig. 8). While we did not see signi cant relationships between leaf chlorophyll content and LAVD 100% and μ 100% (data not shown), we observe a negative relationship with ν 100% for both datasets (Fig. 9). Fig. 7. Spatial relationships between LAVD 10% (m 2 m -3 ), leaf angle distribution parameters from the beta distribution (ν 10%, μ 10% ), and LIDF distribution (LIDFa 10% , and LIDFb 10% ), and canopy NDVI, NIR V , CCI, SIF obs,FR (mW m -2 sr -1 nm -1 ), and SIFobs,FR NIRV R , for the peak growing season. We show the "between-group" associations from our linear mixed models, where each data point is the mean value for each canopy (n = 11) across all weeks of measurements (see Table 1). The error bars represent one standard deviation. The R 2 m (marginal R 2 ) and R 2 c (conditional R 2 ) for each signi cant linear-mixed model (Bonferroni adjusted P ≤ 0.002) are displayed in the upper left.
When we tested the assumption that SIFobs,FR NIRVR is proportional to ϕ F,FR , we did not see any apparent relationship between SIFobs,FR NIRVR , PAR SNIR , and 1-ωPAR ωNIR (Fig. S11). 1-ωPAR ωNIR exhibited little variation among DBF canopies in both datasets. There was a difference in 1-ωPAR ωNIR when comparing DBF vs ENF canopies in the foliar senesce dataset, with ENF canopies having a 1-ωPAR ωNIR around 0.9, while DBF species were around 1 (Fig. S11). No ENF canopies were sampled for the peak growing season dataset. PAR SNIR varied more within the foliar senescence dataset (Fig. S11) compared to the peak growing season data, but overall, variation in
PAR SNIR was low. Furthermore, for any given ight, all remote sensing observations are made within ~10 min each other, thus PAR SNIR should not vary signi cantly. As our analyses in Figs. 4-9 are separated by individual weeks, variation in PAR SNIR should will be minimal. Based on these results, we concluded that variability in SIF obs,FR
NIRVR is driven primarily by differences in ϕ F,FR across the peak growing season dataset.
Our results show that during the peak growing season, canopies exhibiting greater variation in leaf angle have a larger NDVI, CCI, SIF obs, FR , and SIF obs,FR NIRVR (Fig. 7), and they have higher leaf chlorophyll content (Fig. 9). We attribute this nding to the coordination between canopy function and structureassemblages of biochemical and structural traits are coordinated to facilitate a particular growth strategy (McNeil et al., 2023;Reich, 2014). We propose that increasing intra-canopy leaf angle variability enhances light interception in the visible wavelengths, allowing canopies to invest in greater concentrations of foliar pigments. The exact con gurations of leaf placement within a canopy that leads to increased variability in leaf angle and enhanced light interception are unknown, but this could be addressed in future studies using 3D radiative transfer models (Gastellu-Etchegorry et al., 2017). As we discuss further on in Section 4.2., the radiative transfer mechanisms driving the strong coupling between LAD and our remote sensing variables likely include factors beyond the relationship between LAD and leaf chlorophyll content. Furthermore, the relationships in Fig. 7 were strengthened by a separation between DBF and ENF canopies, particularly with respect to LAD parameters. ENF canopies are known to be biochemically and spectrally distinct from DBF canopiesconsistent with our understanding of plant strategies (Guillén-Escribà et al., 2021;Lusk et al., 2003;Serbin et al., 2014). Our data suggest that DBF and ENF canopies also differ in their LAD, although to what degree DBF and ENF species might overlap in their range of LAD values remains to be seen. However, given suf cient sample sizes for each, we would still expect comparable relationships within each PFT when comparing LAD with the same remote sensing variables.
Enhanced light interception increases whole-canopy photosynthesis, and the positive covariation of SIF obs,FR NIRVR with leaf chlorophyll and LAD may be indicative of these larger photosynthetic rates. Model simulations have shown that the uorescence yield increases with photosynthetic capacity under light-saturating conditions (Johnson and Berry, 2021). The model results in Johnson and Berry (2021) are also consistent with the positive correlation between leaf chlorophyll and SIF obs,FR NIRVR observed in our data (Fig. 8). Furthermore, leaf chlorophyll content is positively related to foliar nitrogen and photosynthetic capacity (Croft et al., 2017) in some DBF species, including red maple, which we measured in our study. Thus, an exciting implication is that our remote sensing data are capturing differences in whole-canopy photosynthesis among individual tree canopies, although we do not have measurements of leaf gas exchange or foliar nitrogen to con rm this.
One curiosity is that our data showed a stronger relationship between canopy NDVI and SIF obs,FR compared to canopy NIR V (Fig. 5). This is surprising, as empirical studies and RTM simulations have shown a strong relationship between SIF and NIR V (Badgley et al., 2017;Du et al., 2023;Zeng et al., 2019). The reasons for this discrepancy are unclear, but one possibility merits discussion. Prior studies showed a strong coupling between NIR V and SIF from coarse spatiotemporal resolutions (Badgley et al., 2017) or stationary tower observations from a xed FOV across ecosystems (Du et al., 2023), while our study examines relationships at a previously unstudied spatiotemporal scale of individual tree canopies at hourly intervals. This may suggest that scaling affects the relationship between NIR V and SIFa phenomenon that has been previously reported in Arctic Boreal vegetation using 30 m 2 airborne imagery (Maguire et al., 2021). Similar to Maguire et al. (2021), our results may indicate that spatial variability in canopy SIF obs,FR is driven more by leaf chlorophyll than canopy structure, as NDVI is sensitive to chlorophyll and canopy structure, while NIR V is primarily sensitive to canopy structure. The correlations of SIF obs,FR with leaf chlorophyll content (Fig. 8) and canopy CCI (Fig. 5) are consistent with this view as well. Our data can also contradict this hypothesis, as notably NIR V was more strongly coupled with SIF obs,FR than NDVI in our foliar senescence dataset on DOY 251, and perhaps suggests potential measurement uncertainties associated with our FluoSpecAir system. Future studies that explicitly address questions of scaling with remote sensing observations may be able to de nitively resolve this particular nding.
Leaf chlorophyll content is also a strong driver of SIF obs,FR NIRVR in our study. It was previously shown that when using NIR v × PAR (NIR V P), SIF obs,FR NIRVP and canopy CCI are tightly coupled seasonally in a boreal ENF forest (Kim et al., 2021). Surprisingly, in our data, we found that canopy NDVI had roughly comparable, or stronger, correlations with SIF obs,FR NIRVR compared to canopy CCI. This is a novel nding within our dataset, and could be related to canopy NDVI acting as a better indicator of photosynthetic capacity than CCI. In our data, the in uence of chlorophyll on NDVI, as well as the indirect effect of foliar nitrogen on NIR albedo (Knyazikhin et al., 2013;Townsend et al., 2013), could lead to the stronger relationship with SIF obs,FR NIRVR . However, we caution that additional eld studies are needed to verify the connections between canopy NDVI, SIF obs,FR NIRVR , and photosynthetic capacity.
Here, we distinguish the effects of LAD, and canopy structural traits more broadly, on remote sensing observations as both direct and indirect. The direct effects relate to how canopy structural traits impact radiative transfer properties such as i 0,green and f esc (λ,Ω) . The indirect effects of canopy structural traits are related to the coordination between function and structure. In our study, we found that within-canopy variability in leaf angle is more strongly related to our remote sensing observations than the mean leaf angle of the canopy (Fig. 7, Fig. S7 -S9). As we discussed in 4.1., this appears to be an indirect effect that is predicated on the relationship between LAD and leaf chlorophyll (Fig. 9). However, within-canopy variability in LAD should also affect i 0,green and f esc (λ,Ω) as well, and these factors are likely to be contributing to the strength of the relationships in Fig. 7. This can be reasoned by observing that the relationships between LAD and our remote sensing variables are considerably stronger compared to the relationships with leaf chlorophyll content, and the relationship between LAD and leaf chlorophyll content. Thus, changes in i 0,green and f esc (λ,Ω) as LAD changes, are likely contributing additional explanatory powerhowever this would need to be more thoroughly investigated using RTM simulation.
Our ndings are contrasted with RTM-based studies, which have illustrated the direct effects of mean leaf angle on canopy re ectance (Hase et al., 2022;Jacquemoud et al., 2009;Kattenborn et al., 2024;Zeng et al., 2019). Our results are not inconsistent with RTM simulations howeverwe observed a negative relationship between mean leaf angle and canopy NIR V (Fig. S9) that mirrors studies using RTM simulations (Kattenborn et al., 2024;Zeng et al., 2019). In other instances, relationships among remote sensing variables with mean leaf angle were not signi cant, but small sample sizes are limiting our power (Fig. S8). We also stress that our understanding of the direct effects of LAD on radiative transfer, particularly within complex canopies such as forests, is incomplete and limited, partly due to a lack of observational data. For example, no RTM-based studies have examined how canopy variability in leaf angle affects i 0,green × f esc (λ,Ω) , and resulting observations of re ectance and SIF. Thus, while it may be surprising that our dataset shows a much stronger relationship between parameters of leaf angle variability and remote sensing observations compared to the mean leaf angle, our ndings are within reason.
We also found the relationship between LAD and canopy NDVI to be appreciably stronger than the relationship between LAD and canopy CCI. This is likely because canopy CCI was designed to measure the relative concentrations of chlorophyll to carotenoids (Gamon et al., 2016). In-situ eld observations have shown positive relationships between totalchlorophylls and canopy CCI (Wong et al., 2020), but our own data did not corroborate this nding (Fig. 8). However, the relationship between chlorophyll and canopy CCI found by Wong et al. (2020) were species dependent. The limited number of individuals per species in our study may prevent a clearer relationship from being present in our dataset. Furthermore, given the consistent pattern between LAD, canopy NDVI, and canopy CCI, and canopy NDVI and canopy CCI with SIF and SIF obs,FR NIRVR , we believe it is still reasonable to assume larger CCI values correspond to a greater leaf chlorophyll content in our data.
While our peak growing season data showed coordination between function and structure, data collected during foliar senescence (2020) showed no signi cant relationships among our remote sensing variables (Fig. 6, Fig. S7). This result is not unexpected, as the main physiological function of plants during this time is remobilization and reallocation of nutrients in preparation for growth during the following spring rather than resource acquisition at that moment (Chapin, 1980;Killingbeck, 1996). This process is characterized by the breakdown of chlorophyll and leaf proteins (Christ and Hörtensteiner, 2014;Hörtensteiner and Feller, 2002;Kuai et al., 2018), resulting in the decline and eventual termination of photosynthetic processes, including leaf gas exchange and ϕ PSII (McConnaughay et al., 1996;Weng et al., 2005). These changes in leaf biochemistry affect spectral re ectance, which we observed in our FluoSpecAir data (Fig. 4.). The onset of senescence creating changes in leaf optical properties and photosynthesis likely explains why canopy CCI and canopy NDVI were not correlated with SIF obs,FR or SIF obs,FR NIRVR in the foliar senescence dataset (Fig. 6). We also attribute the lower values of SIF obs,FR observed in the foliar senescence dataset (Fig. 4d) to functional changes more than structural ones. The physiological breakdown of chlorophyll will reduce APAR, leading to lower values of SIF obs,FR.
Additionally, we observed lower values of SIF obs,FR NIRVR (Fig. 4e), indicating that ϕ F,λ was also lower during this time period, which would also contribute to lower values of SIF obs,FR . Canopy structural metrics however remained comparatively stable between the two datasets (Fig. 4f -4h, Fig. S4f, S4g), further pointing to functional changes driving the lower values in SIF obs,FR .
Despite the lack of relationships with SIF variables from either remote sensing indices or LAD, we still observed positive relationships between leaf chlorophyll content, SIF, and SIF obs,FR NIRVR (Fig. 8). Our foliar sampling preferentially selected non-chlorotic leaves and tissues for spectral measurements, as senescing leaves would have a signi cantly reduced SIF emission. As the canopy SIF emission would predominantly be from the remaining green vegetation, it is unsurprising to see correlations between leaf chlorophyll and SIF variables. From a statistical perspective, there is an even stronger decoupling between leaf chlorophyll and SIF obs,FR in the foliar senescence dataset. Compared to the peak growing season, leaf chlorophyll content had a larger range and was more variable, while SIF obs,FR was less variable with a smaller range. While the greater variability in leaf chlorophyll content should lead to stronger correlations, we nd a weaker R 2 with SIF obs,FRin part due to the smaller range and variability of SIF obs,FR .
NIRVR is a proxy for ϕ F,λ As indicated by Eq. 8, the constitutive components of SIF obs,FR NIRVR are related to the light environment ( PAR SNIR ), leaf albedo ( 1-ωPAR ωNIR ), and ϕ F,λ . As we observed no relationship between SIFobs,FR NIRVR and the light environment or leaf albedo terms (Fig. S11), our conclusion was that SIFobs,FR NIRVR ≈ ϕ F,FR . However, we were unable to make leaf-level measurements of ϕ F to compare against SIF obs,FR NIRVR , preventing us from making a de nitively validating the approach suggested by Zeng et al. (2022). There are also several assumptions and uncertainties using this method that merit discussion. First, this method is slightly sensitive to soil background brightness (Zeng et al., 2022), although we note that all FluoSpecAir measurements completely covered each tree canopyminimizing the contribution of soil background. Another noteworthy point is that the ENF and DBF leaves exhibited separation in the 1-ωPAR ωNIR term, suggesting that neither ω PAR or ω NIR should be assumed to be constant across plant functional types. Lastly, acknowledge the possibility that SIF obs,FR NIRVR could show no correlation with PAR SNIR , 1-ωPAR ωNIR , or ϕ F , while still showing a correlation between the product of the three.
While TLS processing algorithms are rapidly advancing, it should be noted that no methods exist to estimate the clumping index of individual trees from TLS. Canopy clumping, which describes the spatial deviation of foliage with respect to a random distribution (Nilson, 1971), is a critical structural parameter and is essential for understanding canopy radiative transfer processes. Contemporary methods rely on using the entire TLS scan to derive a plot level estimate of clumping index (Ma et al., 2018;Schraik et al., 2023). While clumping index is known to vary by species, there is some limited evidence suggesting that clumping covaries vertically with leaf angle (Béland and Baldocchi, 2020). Thus, it's possible that our relationships between LAD and remote sensing observations include some effects of clumping index.
Our study is one of a handful of studies that have quanti ed the LAD of tree crowns from multiple species with TLS. Most studies that report LAD rely on a leveled digital photography method (Chianucci et al., 2018;Pisek et al., 2022;Raabe et al., 2015) which is more labor and time intensive, and cannot measure whole canopies. Despite these drawbacks, these approaches yield comparable results to TLS-derived methods (see Kattenborn et al., 2022;Pisek et al., 2022). When comparing LAD from our deciduous broadleaf species, we observed higher mean values of leaf angle, and lower standard deviations in leaf angle in Acer rubrum and Prunus serotina compared to other species in their respective genus (Table S1, Pisek et al., 2022). Values of ν are also larger in our data, while μ falls within reported ranges for comparable species. LAD reported in Pisek et al. (2022), the most comprehensive dataset available, predominantly comes from European trees. There are considerable differences in environment and latitude with our data collected in the mid-Atlantic region of the U.S. Thus, we would expect to observe differences in mean angle and beta parameters.
It is important to report a suite of parameters related to LAD as they are important for the remote sensing and forest structure communities.
Tabular data reporting means, standard deviation, ν, and μ, are relatively scarce and should be standard output for future studies that quantify LAD. These metrics are important because of their strong tie with remote sensing observations (Figs. 7, 8). Studies often assign observed LAD to a "best-t" theoretical LAD (e.g., plagiophile, Raabe et al., 2015), but variation in LAD falls along a gradient that has no clear boundaries between these types. We also suggest that, when possible, the vertical pro le of these values should be provided. Additionally, the choice of distribution parameters (i.e., beta distribution, LIDF, or mean and standard deviation) matters. RTMs such as SCOPE rely on LIDF, which is parameterized by LIDFa and LIDFb. However, the LIDF produces leaf angle distributions that are different compared to those based on beta distribution parameters. We observed this in our observational data (Fig. S12) and when replicating theoretical leaf angle distributions (e.g., spherical, plagiophile, etc., Fig. S13). When using the LIDF, the leaf angle distribution was overestimated at the tails, whereas the beta distribution underestimated the peak (Fig. S12). Furthermore, the beta distribution t to observational data better than the LIDF, with an average NRMSE of 6.4 % and 10.9 %, respectively. Given these points, including beta distributions as an alternative to LIDF parameters in RTMs would allow for LAD to be more realistically represented, potentially creating more accurate model output. LIDF parameters are still useful however, particularly as their meaning is more interpretable than beta distribution parameters (e.g. LIDFa is closely related to mean leaf angle).
We used a novel remote sensing platform to study the spatial variability in SIF and canopy re ectance across two phenological periods (foliar senescence in 2020, the peak growing season in 2021). These remote sensing measurements were combined with TLS and foliar sampling to examine how functional and structural attributes of plant canopies spatially covary. Our study is the rst to examine the empirical relationships between LAD, SIF, canopy re ectance indices, leaf chlorophyll content. Across the peak growing season, LAD parameters ν and μ were negatively related to canopy NDVI, CCI, SIF, SIFobs,FR NIRVR (Fig. 7, Fig. S3), and ν was negatively related to leaf chlorophyll content (Fig. 9).
Canopy NDVI and CCI were also positively related with SIF and SIF obs,FR NIRVR (Fig. 5). Our results highlight that canopies with greater variation in leaf angle have more chlorophyll and larger remote sensing values, as ν and μ are inversely related to variance in leaf angle (Fig. A1). These ndings are consistent with ecological principles regarding coordination between canopy function and structure. We hypothesize that greater intracanopy variation in leaf angle enhances light interception, driving a demand for greater allocation of foliar resources and enhancing wholecanopy photosynthesis. We also found that parameters from the beta distribution t to real world distributions of leaf angle better than LIDF parameters, which are commonly used in radiative transfer models. Our results illustrate the importance of direct versus indirect effects of canopy structure when interpreting spatial variability in canopy re ectance and SIF across a landscape.
The relationship between σ 2 and beta distribution parameters ν and μ at ve different mean values, starting from 45 • and increasing in increments of 10 • . The blue shaded region represents the range of σ 2 observed from our empirical data. Second column: The same plot as the rst column, but the range of σ 2 is constrained to the blue shaded region in the rst column. Third column: Scatterplots between σ 2 and ν and μ using empirical data from this study (blue dots), and simulated data (light gray triangles). (For interpretation of the references to colour in this gure legend, the reader is referred to the web version of this article.) First, we examined how σ 2 is related to ν and μ at ve different values of t (θ L = 45 • , 55 • ,65 • , 75 • , 85 • , rst two columns of Fig. A1.). While the overall curvature of the relationship between σ 2 and ν and μ is similar across different means, the relationship between σ 2 and μ is more affected by t, particularly in the range of our in-situ observations (shaded rectangle in the rst column, the middle column shows the relationship within the constraints of our observed data). As a result, our in-situ observations between σ 2 and ν show a strong relationship (top rightmost panel, blue circles), while σ 2 and μ show considerably more scatter (bottom rightmost panel, blue circles). To check these relationships, we simulated 100 random points constrained by the observed values of t and the concentration, and overlayed those points with our in-situ observations (rightmost panels, gray triangles). The patterns from our simulated data track with our in-situ data. As the relationship between σ 2 and μ is poor, simplifying the interpretation of μ as σ 2 is largely incorrect. From Eq. A3, the concentration is likely a stronger driver of variation in μ. However, when checking the relationship between the concentration and μ, considerable scatter was still apparent (not shown, r 2 = 0.59). Thus, we explored further formulations to explain μ while retaining parsimony. The concentration is the ratio between σ 2 0 and σ 2 ; conceptually it represents how much variation there is with respect to the maximum variance allowed for a given t. This a purely a mathematical construct based on the beta transformation which restricts values between 0 and 1. When t approaches 0 or 1 (θ L = 0 • and 90 • respectively) σ 2 0 decreases; variances larger than σ 2 0 would create values outside the bounds of 0 and 1. From Fig. A2, σ 2 is maximized at 45 • -an interesting question arises as to the extent to which actual maximum variation in leaf angle tracks with this statistical constraint. We note the lowest observed value of concentration in our data was 7.7. To visualize how variation in concentration affects leaf angle distribution at different levels of t, we simulated leaf angle distributions with the same ve t from before, while varying the concentration (from 2 to 30) at each value of t. Lower values of concentration increase the spread of t, and as θ L approaches 45 • , the spread of t becomes more uniform across all angles. As the interaction between t and the concentration can change the shape of leaf angle distribution in both directions, we examined whether normalizing concentration by t would provide a greater contextualization of μ. While the slope of the relationship changes by θ L (left panel), deviation in the slopes gets smaller as θ L moves further away from 45 • . This approximation tracks fairly well with our in-situ and simulated data (right panel)low values of μ describe canopies that have greater variation in leaf angle when adjusting for some effects of θ L . The effect of θ L isn't entirely removed, as the concentration contains the σ 2 0 term, which is governed by θ L .