Exploring the spatial relationship between airborne-derived red and far-red sun-induced fluorescence and process-based GPP estimates in a forest ecosystem

Abstract

Terrestrial gross primary productivity (GPP) plays an essential role in the global carbon cycle, but the quantification of the spatial and temporal variations in photosynthesis is still largely uncertain. Our work aimed to investigate the potential of remote sensing to provide new insights into plant photosynthesis at a fine spatial resolution. This goal was achieved by exploiting high-resolution images acquired with the FLuorescence EXplorer (FLEX) airborne demonstrator HyPlant. The sensor was flown over a mixed forest, and the images collected were elaborated to obtain two independent indicators of plant photosynthesis. First, maps of sun-induced chlorophyll fluorescence (F), a novel indicator of plant photosynthetic activity, were successfully obtained at both the red and far-red peaks (r² = 0.89 and p < 0.01, r² = 0.77 and p < 0.01, respectively, compared to top-of-canopy ground-based measurements acquired synchronously with the overflight) over the forested study area. Second, maps of GPP and absorbed photosynthetically active radiation (APAR) were derived using a customised version of the coupled biophysical model Breathing Earth System Simulator (BESS). The model was driven with airborne-derived maps of key forest traits (i.e., leaf chlorophyll content (LCC) and leaf area index (LAI)) and meteorological data providing a high-resolution snapshot of the variables of interest across the study site. The LCC and LAI were accurately estimated (RMSE = 5.66 μg cm⁻² and RMSE = 0.51 m²m⁻², respectively) through an optimised Look-Up-Table-based inversion of the PROSPECT-4-INFORM radiative transfer model, ensuring the accurate representation of the spatial variation of these determinants of the ecosystem’s functionality. The spatial relationships between the measured F and modelled BESS outputs were then analysed to interpret the variability of ecosystem functioning at a regional scale. The results showed that far-red F is significantly correlated with the GPP (r² = 0.46, p < 0.001) and APAR (r² = 0.43, p < 0.001) in the spatial domain and that this relationship is nonlinear. Conversely, no statistically significant relationships were found between the red F and the GPP or APAR (p > 0.05). The spatial relationships found at high resolution provide valuable insight into the critical role of spatial heterogeneity in controlling the relationship between the far-red F and the GPP, indicating the need to consider this heterogeneity at a coarser resolution.

1. Introduction

Photosynthesis is the primary process supporting life on Earth. Terrestrial plants exchange CO₂ with the atmosphere through this process, thereby playing a major role in the global carbon cycle (Beer et al., 2010; Heimann and Reichstein, 2008). Global change is altering the carbon uptake and release, with consequences for the functioning of the Earth's system (Ciais et al., 2013; Zhu et al., 2016). The effects of the global change on the Earth's system indicate a need to quantify the exact magnitude of these processes, which is still largely unknown (Schimel et al., 2015; Heimann and Reichstein, 2008).

Recent advances in remote sensing (RS) of sun-induced chlorophyll fluorescence (F) have disclosed unprecedented opportunities for the large-scale monitoring of terrestrial vegetation. F is a faint electromagnetic signal emitted by the core of the photosynthetic machinery to dissipate the excess of absorbed solar radiation (Papageorgiou and Govindjee, 2004). Photochemistry competes with heat dissipation and F emission for the absorbed radiation. Therefore, measurements of energy de-excitation pathways (i.e., fluorescence and heat dissipation) are expected to provide an indirect assessment of photochemical efficiency (Baker, 2008). This link constitutes the rationale behind the use of F to infer the actual functional status of the photosynthetic machinery. The chlorophyll fluorescence spectrum emitted by plants is characterised by two peaks centred in the red (685 nm) and far-red (740 nm) spectral regions. Fluorescence emanates from both photosystem II and photosystem I. However, red fluorescence and far-red fluorescence receive different contributions from the two photosystems; thus, the investigation of both fluorescence peaks is expected to provide valuable information about the photosynthetic performances.

Although solid evidence exists of the relationship between fluorescence and photosynthesis at the subcellular to leaf scales because of the considerable efforts undertaken using active fluorescence techniques (Baker, 2008; Porcar-Castell et al., 2014; Genty et al., 1989), the relationship between passive fluorescence and photosynthesis at the canopy scale is still unclear, and the underlying mechanisms need to be fully understood. Lately, various studies have shown strong empirical linear relationships (even though they are biome dependent in some cases) between F and gross primary productivity (GPP), which represents the carbon fixation by terrestrial plants via photosynthesis, (e.g., Sun et al., 2017; Li et al., 2018; Yang et al., 2015; Frankenberg et al., 2011; Guanter et al., 2012), but several knowledge gaps still exist. Most of these studies were based on the exploitation of space-based retrievals of F from high-spectral-resolution spectrometers onboard satellites deployed for atmospheric studies (e.g., Global Ozone Monitoring Experiment 2 (Munro et al., 2016); TANSO Fourier Transform Spectrometer (Hamazaki et al., 2004) and Orbiting Carbon Observatory-2 (Frankenberg et al., 2015)). However, their coarse spatial resolution (2 to 80 km) and, in some cases, their sparse spatial sampling, strongly limited the investigation of the spatial variability of F and GPP. The recent availability of high-resolution airborne sensors (e.g., Frankenberg et al., 2018; Colombo et al., 2018; Wieneke et al., 2016; Middleton et al., 2017; Sun et al., 2017) has created new possibilities for exploring this link at fine spatial scales.

The quantification of terrestrial GPP with data-driven or processbased models (e.g., Tramontana et al., 2016; Jung et al., 2011; Beer et al., 2010; Ryu et al., 2011; van der Tol et al., 2009; Knorr, 2000) is still uncertain. These uncertainties can come from the structure of the model employed (Knutti and Sedláček, 2013), the quality of the meteorological forcings and from the accuracy of the input parameters (Jung et al., 2007; Friedlingstein et al., 2014; Houborg et al., 2015a).

Incorporating accurate spatially and temporally resolved plant trait-related information into the models might bridge this gap. As a matter of fact, variability in plant traits (e.g., leaf chlorophyll content (LCC) and leaf area index (LAI)) constitutes a determinant of the ecosystem functionality that must be taken into account to better constrain the flux estimation (Butler et al., 2017; van Bodegom et al., 2014; van Bodegom et al., 2012). Regardless of its importance, this aspect was mostly neglected in previous studies because of the lack of adequate spatio-temporal data. The increasing availability of RS observations might overcome this limitation, as RS is capable of providing plant trait information at suitable temporal and spatial scales (Schimel et al., 2015; Homolova et al., 2013).

The retrieval of plant traits from RS observations advanced significantly in recent decades because of the considerable efforts made in the development and testing of multiple retrieval methods (for a review, see Verrelst et al., 2015a, 2018). Among the retrieval algorithms, the inversion of physically based radiative transfer models (RTMs) is generally considered the most reliable approach (Atzberger et al., 2015; Dorigo et al., 2007). RTMs exploit physical laws to describe the interactions between the incident solar radiation and the vegetation medium. Because it is established on a physical relationship between a measured radiometric signal and plant traits, the inversion of these models constitutes an accurate, robust and generic approach for plant trait retrievals (Verrelst et al., 2015b; Atzberger et al., 2015; Houborg et al., 2015a; Dorigo et al., 2007).

Regardless of the progress made, the retrieval of plant traits remains challenging. Their quantitative estimation is hampered by the influence of various confounding factors (Wang et al., 2018; Zarco-Tejada et al., 2004). In physically based frameworks, the main challenge is represented by the regularisation of the undetermined and ill-posed nature of the inverse problem (Houborg et al., 2015a). Multiple combinations of plant traits might yield analogous simulated spectra, resulting in non-unique solutions. Furthermore, the uncertainties affecting both the model and the data may be a source of large inaccuracies in the modelled reflectance (Houborg et al., 2015a; Combal et al., 2002; Baret and Buis, 2008). Hence, adequate model parameterisation and regularisation strategies are critical for mitigating the drawbacks of ill-posedness and for obtaining trustworthy results (Verrelst et al., 2014, 2015b; Houborg et al., 2015b; Combal et al., 2002). Several studies have recognised the importance i) of using prior information to reduce the variability of the input parameters (e.g., Meroni et al., 2004; Malenovský et al., 2006; Baret and Buis, 2008; Darvishzadeh et al., 2008), ii) of adding noise to the simulated spectra to account for uncertainties in the model and the data (e.g., Kötz et al., 2005; Richter et al., 2009) and iii) of using multiple solutions to regularise the inversion (e.g., Combal et al., 2002; Kötz et al., 2005; Atzberger and Richter, 2012). Conversely, the impact of using alternative cost functions to match simulated and measured reflectance has been poorly investigated (Rivera et al., 2013; Verrelst et al., 2014).

In this framework, this work aimed to investigate the potential of RS to provide new insights into actual plant photosynthesis. High-resolution airborne hyperspectral images acquired with the HyPlant sensor (Rascher et al., 2015) over a mixed forest were used to provide two independent indicators of plant photosynthesis: red and far-red F on the one hand and GPP on the other. This comprehensive high-resolution analysis was made possible by the characteristics of the HyPlant sensor, deployed as an airborne demonstrator of the forthcoming FLuorescence EXplorer (FLEX) satellite (Drusch et al., 2017): the sensor was in fact specifically designed to simultaneously acquire sub-nanometric spectral information in the 650–800 nm spectral region and hyperspectral information between 400 and 2500 nm, providing the means to retrieve F as well as obtain hyperspectral reflectance.

We explored the possibility for i) obtaining high resolution ground-validated maps of both red and far-red F from airborne ultra-fine spectral resolution imagery using the spectral fitting method (SFM) (Cogliati et al., 2015); ii) obtaining high resolution ground-validated maps of key forest traits (i.e., LCC and LAI) from airborne hyperspectral imagery through an optimised RTM inversion; iii) obtaining high resolution maps of GPP, absorbed photosynthetically active radiation (APAR) and light use efficiency (LUE) through a modelling approach based on the use of the aforementioned airborne-derived spatially resolved traits to drive a process-based ecophysiological model–the Breathing Earth System Simulator (BESS) (Ryu et al., 2011; Jiang and Ryu, 2016)–with the ultimate goal of iv) exploring the spatial relationship between measured F and modelled BESS outputs at high resolution to facilitate the interpretation of the variability of ecosystem functioning at a regional scale.

2. Material and methods

2.1. Study site

The study was conducted on a mid-latitude plain mixed forest (Hardt Forest) located in France (47° 48′29″ N, 7°26′53″ E; Mulhouse; Alsace). The analysis focused on an area of ~90 ha in the northern part of the forest, corresponding to a subset of the total area covered by the airborne overpasses (Fig. 1).

Fig. 1.

a) Location of the Hardt Forest in Alsace, France; b) the Hardt Forest and location of the HyPlant flightline used in this study (RGB true colour composite); c) zoom of the HyPlant image and location of the sites where top-of-canopy spectral measurements were collected (purple dots). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The climate of the region is temperate, with an average temperature of 22 °C in summer and of 4 °C in winter. The mean annual rainfall is 680 mm distributed throughout the year, with a prevalence between May and August.

The forest covers ~13,000 ha and is relatively managed, with stands of at least 500 m size characterised by relatively large variability in forest age. The dominant canopy layer is characterised by the presence of European hornbeam (Carpinus betulus L.), pedunculate and sessile oak (Quercus robur L., Quercus petraea (Matt.) Liebl.), field maple (Acer campestre L.), small-leaved linden (Tilia cordata Mill.), Scots pine (Pinus sylvestris L.) and European larch (Larix decidua Mill.). The forest species composition of the area was mapped in a previous work (Tagliabue et al., 2016) using a semi-automatic classification approach that was validated against field observations. On average, the fraction between deciduous and coniferous species was determined as ~90% and ~10%, respectively.

2.2. Field spectral measurements and plant traits data collection

A field campaign aiming at nearly simultaneously collecting spectral measurements, plant traits and ancillary meteorological data was conducted in the summer of 2013.

Top-of-canopy high resolution radiance measurements were acquired on June 16–17 and July 2, 2013, around midday (10:00–15:00 solar time) under clear-sky conditions using portable spectroradiometers operating in the visible and near-infrared regions. The system included three different instruments (HR4000, HR4000, QE65000; Ocean Optics, Dunedin, USA) characterised by different spectral ranges and resolutions: the first covering the spectral range 350–1050 nm with a full width at half maximum (FWHM) of 1 nm for reflectance and vegetation indices computation, and the second (spectral range 700–800 nm, FWHM = 0.1 nm) and third (spectral range 657–740 nm, FWHM = 0.25 nm) specifically designed for the retrieval of sun-induced chlorophyll fluorescence at the O₂-A and O₂—-B absorption bands, respectively.

The system was housed in a thermally regulated Peltier box (model NT-16; Magapor, Zaragoza, Spain) and manually operated from the top of a mobile hydraulic platform to measure top-of-canopy reflectance and fluorescence corresponding to seven selected targets: six of the measurement cycles targeted representative forest species, whereas one measurement cycle targeted the meadow. The measurements were acquired from the nadir using bare optical fibres, with an angular field of view of 25°, mounted at the end of a 2.5 m long arm held at a height of 3.7–5 m above the canopy, corresponding to a sampling area of 1.7–2.3 m diameter. The arm was manually rotated horizontally to allow the alternative observation of the vegetated target to measure the upwelling radiance and of a levelled, calibrated, white reference panel (Spectralon; Labsphere, North Sutton, USA) to measure the incident solar radiation. Once the arm was extended over the vegetated targets, measurements corresponding to three different spots were acquired to capture the variability of the tree crowns.

The spectral data were acquired through the 3S software (Meroni and Colombo, 2009). Each measurement of the vegetated target was sandwiched between two measurements of the white reference panel and the dark current of the instruments was collected at the beginning of each measurement cycle. The data collected were processed with a dedicated IDL (ITT Visual Information Solutions, Boulder, USA) application described in Meroni et al. (2011). The F was estimated at the O₂—-B and O₂-A bands by exploiting the spectral fitting method described in Meroni et al. (2010) and Cogliati et al. (2015).

Field measurements were acquired to correspond with sampling sites representative of an area of 20 × 20 m, hereafter referred to as elementary sampling units (ESUs). The ESUs were selected by forest experts along the forest tracks at approximately 50 m distance from the path. The centre of each ESU was tracked with a high-precision Trimble Geo-XT GPS (Trimble, Sunnyvale, USA). The LCC was estimated from leaves collected from different forest species located in 12 ESUs. In each ESU, at least 10 leaves were sampled for each dominant species in the main canopy layer (n ≈ 250). The samples were collected from sunlit leaves sampled by shooting with guns at the top branches and were immediately placed in plastic bags that were then sealed and stored at –80 °C until the laboratory biochemical analysis. Leaf chlorophyll a and b contents were extracted using hydroxide carbonate magnesium buffered with acetone. Absorbance was measured at 645, 662 and 710 nm using a UVIKON XL spectrophotometer (BioTek Instruments, Winooski, USA), and chlorophyll a and b were quantified using the extinction coefficients derived by Lichtenthaler and Buschmann (2001). The LCC was then computed as the sum of the chlorophyll a and b. The LAI was estimated by means of digital hemispherical photos acquired within 14 ESUs using a Sigma camera (Sigma Corporation, Ronkonkoma, USA) equipped with a fisheye lens. The images–seven looking upward per plot-were processed with the CAN-EYE software (https://www4.paca.inra.fr/can-eye/CAN-EYE-Home/Welcome) to estimate the LAI. The clumping effect was considered by multiplying the effective LAI by the clumping index (Chen and Black, 1992), which was computed using the logarithm gap fraction averaging method (Lang and Yueqin, 1986).

2.3. Airborne hyperspectral images acquisition and pre-processing

The airborne data were acquired using the hyperspectral imaging sensor HyPlant (Rascher et al., 2015). HyPlant is made up of the following two modules: i) the Dual Channel Imager (DUAL), which is a hyperspectral imaging spectrometer with 624 spectral channels covering the visible, near-infrared and shortwave infrared (VIS-NIR-SWIR) spectral regions (370–2500 nm) at a full-width at half maximum (FWHM) of 4.0 nm (VIS-NIR) -13.3 nm (SWIR); and ii) the Fluorescence Imager (FLUO), which is a hyperspectral imaging spectrometer with 1024 spectral channels providing contiguous spectral information in the wavelength range 670–780 nm with a FWHM of ~0.25 nm. Both the DUAL and the FLUO sensors are line-imaging push-broom scanners with an angular field of view of 32.3°.

HyPlant was flown over the study site on board a Cessna Grand Caravan C208B on June 16, 2013, at approximately solar noon - 12:30 ± 1 Central European Summer Time (CEST) - under clear sky conditions. The flight was conducted heading 195° at an average altitude of 600 m above the ground level, resulting in a pixel size of 1 m. The acquisition of the image used in this study started at 11:55 CEST and was completed in approximately 157 s.

The pre-processing of the airborne data was performed using the CaliGeo software (Specim Ltd., Oulu, Finland). HyPlant raw data were corrected for dark current, radiometrically calibrated and geo-rectified using the information recorded by the HyPlant position and attitude sensor as input. The DUAL data were then atmospherically corrected using the ATCOR-4 atmospheric radiative transfer code to obtain top-of-canopy radiance and reflectance.

2.4. HyPlant data product generation

2.4.1. Sun-induced chlorophyll fluorescence retrieval

The images collected by the FLUO module were processed with a dedicated processing chain specifically developed to retrieve F from HyPlant observations. The SFM retrieval approach, originally developed for FLEX (Cogliati et al., 2015), was adapted to HyPlant ultrafine resolution data at both the O₂—-B and O₂-A absorption bands to derive red and far-red F maps (Cogliati et al., 2018). This approach allowed decoupling of the F and surface reflected radiance spectra from the upward radiance spectra detected by the HyPlant FLUO module. The rationale behind the SFM relies on mathematical functions to model canopy reflectance and fluorescence spectra at the different wavelengths. The exploitation of the full set of spectral bands provided by the HyPlant sensor reduces the overall impact of instrumental noise and allows the estimation of a higher number of model parameters describing the fluorescence/reflectance spectra. The SFM method was implemented and tested for processing HyPlant images collected during the campaign, following the surface-atmosphere coupled RT scheme proposed in Verhoef et al. (2018) and adapted to airborne observations. In fact, the reflectance and fluorescence spectral function parameters were directly estimated comparing forward RT model simulations with HyPlant radiance spectra at-sensor level. The forward RT model used for processing HyPlant images was limited to estimating surface parameters (i.e., reflectance and fluorescence), whereas the atmospheric variables were kept constant at pre-defined values. The atmospheric transfer functions (i.e., path radiance, spherical albedo and upward/downward transmittance) used in the forward RT model were computed by MODTRAN5. The atmospheric model input parameters were derived from sun photometer measurements collected simultaneously to Hy-Plant observations. The retrieval algorithm included a preliminary characterisation of instrumental signal distortions such as spectral-shift and bandwidth on image column base (i.e., sensor across-track). The red and far-red F at the O₂—-B and O₂-A bands, respectively, were estimated by analysing each O₂ absorption band independently. The output of the SFM consists of two distinct images, in which the red (684–697 nm) and far-red (750–777 nm) F spectra (with a spectral sampling interval resampled to 1 nm in order to reduce the output data volume) are provided in physical units (mW m^–2sr^–1 nm^–1). For further analysis, the F values at 687 nm (F₆₈₇) and 760 nm (F₇₆₀) were used in this study.

The maps were finally validated by comparing the airborne with the ground-based retrievals obtained from top-of-canopy spectral measurements collected over seven vegetated targets. The ground targets were precisely identified on the image with the help of RGB images acquired with a drone, and statistics were extracted from regions of interest of 3 × 3 pixels for comparison against the ground-based measurements. Given the limited number of ground validation sites, we further investigated the retrieval performances by comparing the SFM results against the ones obtained using another retrieval method. We selected the Singular Vector Decomposition (SVD) method developed by Guanter et al. (2012, 2013), which had already been successfully used, e.g., in Rossini et al. (2015), Colombo et al. (2018) and Middleton et al. (2017), to retrieve F from the HyPlant observations. The SVD is a data-driven approach based on the representation of the measured at-sensor radiance as a linear combination of the reflected surface radiance plus the F emission. The reflected surface radiance is formulated as a linear combination of orthogonal spectral vectors obtained from the singular vector decomposition of a set of fluorescence-free spectra from non-fluorescent targets. In this study, the method was applied to a broad fitting window including both solar Fraunhofer lines and atmospheric (i.e., oxygen and water vapour) absorption features. Regions of interest of 3 × 3 pixels were extracted from 30 tree crowns selected randomly across the study area. The F values retrieved at 687 nm and 760 nm using the SFM were compared against the ones retrieved at 690 nm and 740 nm, respectively, using the SVD. Since SVD-based farred F was extracted at 740 nm, we multiplied it by 0.582 to ensure the comparability with SFM-based F₇₆₀, as suggested by Joiner et al. (2013).

The fluorescence yields (Fy₆₈₇ and Fy₇₆₀) were calculated as the ratio between F₆₈₇ and F₇₆₀ and the APAR (μmol photon m^–2 s^–1) for each pixel of the image. The APAR was obtained as output of the BESS model. BESS uses a two-stream approach for the radiative transfer of the PAR radiation, which is used to estimate the BESS-APAR. The details of the calculation can be found in Ryu et al. (2011). Before the calculation, the F₆₈₇ and F₇₆₀ radiances were converted to μmol m⁻² s⁻¹ sr⁻¹ nm⁻¹ using a wavelength-dependent coefficient. The resulting Fy₆₈₇ and Fy₇₆₀ maps refer to emissions at 687 and 760 nm, respectively, and are thus expressed as sr⁻¹ nm⁻¹.

2.4.2. Plant trait retrieval

To obtain accurate high-resolution maps of key plant traits from HyPlant DUAL imagery, a physically based approach was chosen. A systematic evaluation of the RTM parameterisation and the Look-Up-Table (LUT)-based inversion strategy was conducted to propose a reproducible approach that could yield accurate and reliable plant trait retrievals in forest ecosystems, providing information that could be used for different purposes. In this case, the inversion strategy was optimised for the retrieval of the LCC and LAI, two key traits for use in subsequent modelling with BESS.

Among the variety of existing RTMs, the canopy level INvertible FOrest Reflectance Model (INFORM) (Atzberger, 2000; Schlerf and Atzberger, 2006) coupled with the leaf level PROSPECT-4 model (Jacquemoud and Baret, 1990; Feret et al., 2008) was chosen in this study because of its suitability in simulating forest canopy reflectance while preserving a relative simplicity. INFORM is a hybrid model combining the strengths of the turbid-medium and geometric-optical radiative transfer models. It couples the SAILH model (Verhoef, 1984; Kuusk, 1991) that simulates the radiative transfer within the turbid-medium canopy layer with the FLIM model (Rosema et al., 1992) to account for geometric aspects such as the leaf clumping inside the tree crowns and the crown geometry. The model simulates the forest reflectance in the spectral range 400–2500 nm as a function of several leaf-level (i.e., leaf chlorophyll content, leaf dry matter content, leaf water content and leaf structural parameter) as well as canopy-level (i.e., LAI of the single trees, LAI of the understory, average leaf angle, tree height, crown diameter and stem density) input parameters, in addition to other parameters that describe the sun-sensor geometries and irradiance conditions (i.e., sun zenith angle, observer zenith angle, relative azimuth angle and fraction of diffuse radiation).

Global sensitivity analysis (GSA) (Saltelli et al., 2010; Verrelst et al., 2015c) was conducted in order to examine the response of the model to the variation of each of its input parameters. This approach allows parameters to be identified that are less influential on the modelled reflectance. These parameters thereafter are set to fixed values to reduce the number of unknown variables, thereby maximising the predictive power of the model. The ranges of the input parameters used to perform the GSA are reported in Table 1.

Table 1. Range and distribution of the parameters used to perform a global sensitivity analysis of the PROSPECT-4-INFORM radiative transfer model. (*μ = mean, σ = standard deviation).

	Variable	Unit	Range	Distribution
Prospect-4	LCC	Leaf chlorophyll content	μg cm−2	10–70	Gaussian (*μ = 40, σ = 25)
	Cw	Leaf water content	g cm−2	0.001–0.05	Sobol
	Cm	Dry matter content	g cm−2	0.001–0.05	Sobol
	N	Leaf structural parameter	–	1.3–1.8	Sobol
Inform	LAI	Leaf area index	m2 m−2	1–10	Gaussian (μ = 4, σ = 2)
	LAIu	Leaf area index of understory	m2 m−2	0.5–3	Sobol
	sd	Stem density	trees ha−1	200–400	Sobol
	cd	Crown diameter	m	5–15	Sobol
	h	Tree height	m	10–40	Sobol
	ALA	Average leaf angle	deg	30–50	Sobol

A total of 2000 simulations were run, with each parameter varying according to all the possible variability in the study site. The GSA results were used to improve the parameterisation of the RTM; the less influential parameters on the modelled reflectance were set to constant values, whereas the other input parameters were varied within ranges defined according to prior knowledge of the study site. The range and distribution of the RTM input parameters used for the generation of the LUT are shown in Table 2.

Table 2. Range and distribution of the input parameters of the PROSPECT-4-INFORM model used for the generation of the LUT. (*μ = mean, σ = standard deviation).

Variable	Unit	Range	Distribution
Prospect-4	LCC	Leaf chlorophyll content	μg cm−2	10–70	Gaussian (*μ = 40, σ = 25)
	Cw	Leaf water content	g cm−2	0.006–0.015	Sobol
	Cm	Dry matter content	g cm−2	0.003–0.015	Sobol
	N	Leaf structural parameter	–	1.5	–
Inform	LAI	Leaf area index	m2 m−2	1.5–8	Gaussian (μ = 4, σ = 2)
	LAIu	Leaf area index of understory	m2 m−2	0.5–2.5	Sobol
	sd	Stem density	trees ha−1	200–400	Sobol
	cd	Crown diameter	m	3–9	Sobol
	h	Tree height	m	20	-
	ALA	Average leaf angle	deg	45	-
	θs	Sun zenith angle	deg	31	-
	θo	Observer zenith angle	deg	0	-
	Φ	Azimuth angle	deg	128	-
	skyl	Fraction of diffuse radiation	-	0.1	-

The model was then run in forward mode to generate a LUT of 30,000 simulated reflectance spectra obtained by all the possible combinations between the input parameters.

The inversion strategy was optimised by testing the effect of three regularisation options on the retrieval performances: i) the use of different cost functions, ii) the addition of Gaussian noise to the simulated spectra; and iii) the use of multiple solutions of the inversion.

Multiple cost functions introduced in Leonenko et al. (2013) and exploited in Rivera et al. (2013) were tested to identify the ones that minimise the mismatch between measured and simulated spectra. The cost functions belong to different fields of mathematics and statistics and can be grouped into three broad families: information measures, M-estimates and minimum contrast estimates.

All these metrics are used to minimise the distance D[M,S] between two functions M = (m(λ₁), m(λ₂)m(λ_n)) and S = (s(λ₁), s(λ₂), …, s(λ_n), which represent the shape of the measured (M) and simulated (S) reflectance spectra at the wavelengthλn, but different metrics describe D in distinctive ways.

With the information measures (e.g., Kullback Leibler divergence, Pearson χ-square, harmonique Toussaint measure), M and S are considered as probability distributions, and their divergence is measured. M-estimates (e.g., least square estimator) are maximum likelihoodbased distances based on the search of the minima of sums of M and S functions. They are the most widely used and are generally considered robust estimators, but they can give sub-optimal results when their assumptions are violated (e.g., errors not normally distributed). With minimum contrast estimates (e.g., contrast function), M and S are described as spectral density functions to be minimised. The list and mathematical formulation of the metrics selected in this study is reported in Table 3. For a more detailed description of the cost function families and of each estimator refer to Leonenko et al. (2013). Gaussian noise ranging from 0 to 10% (with step 1%) was added to the simulated reflectance spectra to consider the uncertainties affecting the model and the measured data, and 0 to 20 (with step 1) solutions of the best matching modelled spectra were averaged to mitigate the effect of ill-posedness.

Table 3.

Selected cost functions (CF) for the description of the distance D[M,S] between measured (M = (m(λ₁), m(λ₂), …, m(λ_n))) and simulated (S = (s(λ₁), s(λ₂), …, s(λ_n))) reflectance spectra. The CFs are grouped in three broad families: information measures, M-estimates and minimum contrast estimates.

CF family	CF	Formula
M-estimates	RMSE	$\text{D}[\text{M},\text{S}]=\sqrt{\frac{{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}{({\text{m(λ}}_{\text{i}}\text{)–s}({\text{λ}}_{\text{i}}))}^2}}{\text{n}}}$
	Geman-McClure	$\text{D}[\text{M},\text{S}]={\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\frac{{(\text{m}({\text{λ}}_{\text{i}})-\text{s}({\text{λ}}_{\text{i}}))}^2}{(1+{({\text{m(λ}}_{\text{i}}\text{)–s}({\text{λ}}_{\text{i}}))}^2)}}$
Information measures	Kullback-Leibler	$\text{D[M,S]}\text{=}{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\text{m}({\text{λ}}_{\text{i}})\text{ln}\left(\frac{\text{m}({\text{λ}}_{\text{i}})}{\text{s}({\text{λ}}_{\text{i}})}\right)}$
	Jeffreys-Kullback-Leibler	$\text{D[M,S]}\text{=}{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}}{\text{ λ}}_{\text{n}}(\text{m}({\text{λ}}_{\text{i}})-\text{s}({\text{λ}}_{\text{i}}))(\text{ln}(\text{m}({\text{λ}}_{\text{i}}))-\text{ln}(\text{s}({\text{λ}}_{\text{i}})))$
	Neyman χ-square	$\text{D[M,S]}={\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\frac{{(\text{m}({\text{λ}}_{\text{i}})-\text{s}({\text{λ}}_{\text{i}}))}^2}{\text{s}({\text{λ}}_{\text{i}})}}$
	K-divergence Lin	$\text{D[M,S]}\text{=}{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\text{m}({\text{λ}}_{\text{i}})\text{ln}\left(\frac{\text{2m}({\text{λ}}_{\text{i}})}{\text{m}({\text{λ}}_{\text{i}})\text{+}\text{s}({\text{λ}}_{\text{i}})}\right)}$
	L-divergence Lin	$\text{D[M,S]}\text{=}{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\text{m}\left({\text{λ}}_{\text{i}}\right)\ln (\text{m}\left({\text{λ}}_{\text{i}}\right)+\text{s}\left({\text{λ}}_{\text{i}}\right)\ln (\text{s}\left({\text{λ}}_{\text{i}}\right)-\left(\text{m}\left({\text{λ}}_{\text{i}}\right)+\text{s}\left({\text{λ}}_{\text{i}}\right)\right)\ln \left(\frac{\text{m}\left({\text{λ}}_{\text{i}}\right)+\text{s}\left({\text{λ}}_{\text{i}}\right)}{2}\right)}$
	Harmonique Toussaint	$\text{D[M,S]}\text{=}{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\left(\text{m}\left({\text{λ}}_{\text{i}}\right)-\frac{\text{2m}\left({\text{λ}}_{\text{i}}\right)\text{s}\left({\text{λ}}_{\text{i}}\right)}{\text{m}\left({\text{λ}}_{\text{i}}\right)\text{+}\text{s}\left({\text{λ}}_{\text{i}}\right)}\right)}$
	Negative exponential disparity	$\text{D[M,S]}\text{=}{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\text{s}\left({\lambda }_{\text{i}}\right)\left(\exp \left(-\frac{\text{m}\left({\lambda }_{\text{i}}\right)-\text{s}\left({\lambda }_{\text{i}}\right)}{\text{s}\left({\lambda }_{\text{i}}\right)}\right)-1\right)}$
	Bhattacharyya divergence	$\text{D[M,S]}\text{=}-\log \left(1+{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{\text{λn}}\sqrt{\text{m}\left({\lambda }_{\text{i}}\right)\text{s}\left({\lambda }_{\text{i}}\right)}}-\frac{1}{2}\left(\text{m}\left({\lambda }_{\text{i}}\right)+\text{s}\left({\lambda }_{\text{i}}\right)\right)\right)$
	Shannon	$\text{D[M,S]}=-{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\frac{\left(\text{m}\left({\lambda }_{\text{i}}\right)+\text{s}\left({\lambda }_{\text{i}}\right)\right)}{2}}\log \frac{\left(\text{m}\left({\lambda }_i\right)+s\left({\lambda }_i\right)\right)}{2}+\frac{1}{2}\left({\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\text{m}\left({\lambda }_{\text{i}}\right)\log \left(\text{m}\left({\lambda }_{\text{i}}\right)\right)}+{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\text{s}\left({\lambda }_{\text{i}}\right)\log \left(\text{s}\left({\lambda }_{\text{i}}\right)\right)}\right)$
Minimum contrast estimation	K(x) = (log(x))2	$\text{D}[\text{M},\text{S}]={\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}{\text{λ}}_{\text{n}}{{\text{(log(m(λ}}_{\text{i}}\text{))}-{\text{log(s(λ}}_{\text{i}}\text{)))}}^{\text{2}}}$
	K(x) = log(x) + 1/x	$\text{D}[\text{M},\text{S}]={\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\left(\log \frac{\text{s}\left({\lambda }_{\text{i}}\right)}{\text{m}\left({\lambda }_{\text{i}}\right)}+\frac{\text{m}\left({\lambda }_{\text{i}}\right)}{\text{s}\left({\lambda }_{\text{i}}\right)}\right)-1}$
	K(x) = −log(x) + x	$\text{D}[\text{M},\text{S}]={\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\left(–\log \frac{\text{s}\left({\text{λ}}_{\text{i}}\right)}{\text{m}\left({\text{λ}}_{\text{i}}\right)}+\frac{\text{s}\left({\text{λ}}_{\text{i}}\right)}{\text{m}\left({\text{λ}}_{\text{i}}\right)}\right)-1}$
	K(x) = x(log(x))-x	$\text{D}[\text{M},\text{S}]=1+{\displaystyle {\sum }_{{\text{λ}}_{\text{i}}\text{=1}}^{{\text{λ}}_{\text{n}}}\frac{\text{s}\left({\text{λ}}_{\text{i}}\right)}{\text{m}\left({\text{λ}}_{\text{i}}\right)}\left(\log \frac{\text{s}\left({\text{λ}}_{\text{i}}\right)}{\text{m}\left({\text{λ}}_{\text{i}}\right)}-1\right)}$

The retrieval workflow was performed within ARTMO v. 3.23 (Automated Radiative Transfer Models Operator; http://ipl.uv.es/artmo/) (Verrelst et al., 2011; Rivera et al., 2013), a graphic user interface software package running in MATLAB including a suite of leaf and canopy RTMs. ARTMO streamlines the model configuration, running and output storage, thus facilitating the handling and processing of high dimensional spectral data.

The standard fitting statistics, such as coefficient of determination (r²), root mean square error (RMSE), relative RMSE (rRMSE) (i.e., RMSE/mean of measured values), bias (i.e., mean of estimated values – mean of observed values) and relative bias (rbias) (i.e., bias/mean of estimated values) between measured and simulated LCC and LAI, were computed to evaluate the performances of the different RTM inversion strategies tested. The leave-one-out cross-validated statistics (r_CV²; RMSE_CV) were also computed to compare the prediction performance of the different model implementations.

2.4.3. BESS parameterisation strategy and GPP, APAR and LUE estimation

The Breathing Earth System Simulator (BESS) (Ryu et al., 2011; Jiang and Ryu, 2016) was used to derive a snapshot of instantaneous GPP over the study area at the time of the HyPlant overflight.

BESS is a biophysical model developed to monitor carbon and water fluxes using multisource remotely sensed data at moderate spatial resolution (1–5 km). The model couples a 1-dimensional atmospheric radiative transfer module to compute direct and diffuse radiation in the PAR and NIR spectral regions (Kobayashi and Iwabuchi, 2008; Ryu et al., 2018); a two-leaf and two-stream canopy radiative transfer model to compute the PAR and NIR radiation absorbed by sunlit and shaded leaves, respectively (de Pury and Farquhar, 1997; Ryu et al., 2011); and an integrated carbon assimilation-stomatal conductance-energy balance model (Ball, 1988; Paw and Gao, 1988) to compute GPP and ET. In its original configuration, BESS uses as input MODIS atmosphere (e.g., cloud optical thickness, aerosol optical thickness, water vapour and ozone) and land products (e.g., LAI, land cover, and albedo in PAR and NIR spectral regions) as well as other satellite data (e.g., OCO-2-NOAA data to derive CO₂ concentration maps; Shuttle Radar Topography Mission (SRTM) data to take into account the effect of altitude on incoming radiation).

For this study, BESS was customised to ingest HyPlant high-resolution (1 m) products and atmospheric constraints obtained from meteorological data collected in the field, outputting a BESS-GPP map at the time of HyPlant's overflight at high spatial resolution.

Four HyPlant-derived spatially resolved products were used to feed BESS: two broadband reflectance maps and two key plant trait maps. Broadband reflectance was calculated from the DUAL hyperspectral reflectance cube as a weighted average after a regular spectral resampling (1 nm spectral interval) in the VIS (400–700 nm) and NIR (841–876 nm) spectral regions, respectively. The maximum carboxylation rate normalised to 25 °C (Vcmax₂₅) and the LAI were derived from the RTM inversion. Whereas the LAI is a direct output of the RTM, the Vcmax₂₅ was empirically inferred from the LCC using a linear relationship for broadleaved forest species found by Croft et al. (2017). This study found a strong linear relationship (r² = 0.78, p < 0.001) between the two variables across three growing seasons by considering four different deciduous tree species and demonstrated that LCC can be a reliable proxy for modelling Vcmax. The Vcmax₂₅ map was then derived from the LCC map obtained as output of the RTM inversion according to Eq. (1) (Croft et al., 2017):

$${\text{Vcmax}}_{25}=1.3\times \text{LCC}+3.72$$ (1)

Additionally, atmospheric forcings such as air temperature, pressure, column water vapour, relative humidity and aerosol optical thickness were obtained from punctual measurements acquired with a Microtops II sun photometer (Solar Light Company, Glenside, USA). The incident solar irradiance during the overpass was collected in the spectral region 350–2500 nm with a calibrated FieldSpec 4 (ASD Inc., Longmont, USA) measuring over a levelled white Spectralon (Labsphere, North Sutton, USA).

2.5. HyPlant data product comparison

The outputs obtained from HyPlant DUAL and FLUO images (e.g., GPP, F687, F₇₆₀) were compared by fitting regression models between pairs of variables. The statistical analysis was performed in R (R Core Team, 2019) and aimed at testing different models to find the best fit. The independency of observations condition required for regression analysis is not met in case of spatial-autocorrelation in the data, which means the clusters of data points present numerical similarity because of their spatial proximity (Haining, 1980). The spatial dependency implicates that part of the information within the dataset is repeated and therefore redundant. To detect a possible violation of the independency assumption, an analysis of the semi-variograms of the images was performed. Based on the results of this analysis, all air-borne-derived products were aggregated at tree crown level for the spatial comparison instead of performing a pixel by pixel comparison. The tree crowns were extracted through an image segmentation performed using the segmentation tool implemented in the ENVI software (Exelis, Boulder, USA). After segmenting the image, an inner buffer of two pixels (i.e., 2 m) was applied to each polygon in a GIS environment (ArcGIS, Esri, Redlands, USA) to exclude the shaded edges of the tree crowns. The pixels at the sunlit core of each tree crown were then averaged to obtain a single value per crown. In addition to overcoming the issues related to the spatial dependency, this approach allowed reducing random noise in the data and mitigating the slight geometric mismatch between the images recorded from the HyPlant DUAL and FLUO modules.

3. Results

3.1. HyPlant data products

3.1.1. Red and far-red sun-induced chlorophyll fluorescence maps

The high-spatial resolution F₆₈₇ and F₇₆₀ maps obtained over the forest using the SFM implemented for the processing of HyPlant imagery are shown in Fig. 2.

Fig. 2. F₆₈₇ (a) and F₇₆₀ (b) maps obtained from HyPlant hyperspectral radiance using the spectral fitting method.

Overall, the magnitude of F₇₆₀ ranged from 0 to 3mWm⁻² sr⁻¹ nm⁻¹, with a frequency peak at approximately 1.5 mWm⁻² sr⁻¹ nm⁻¹, whereas F₆₈₇ ranged from 0 to 2.5 mWm⁻² sr⁻¹ nm⁻¹, with values at approximately 0.8 mWm⁻² sr⁻¹ nm⁻¹ occurring most frequently. These values were consistent throughout the image and coherent with the ones usually observed on forested areas by ground-based measurements. The spatial patterns were meaningful for both F687 and F760: higher fluorescence was observed in the sunlit part of the canopy, lower fluorescence was observed in the inter-crown gaps, and non-fluorescent targets such as bare soil and asphalt exhibited near-zero values. On the other hand, the F687 was characterised by a higher noise in the retrieval which resulted in a remarkable ‘salt-and-pepper’ effect on the map. A validation of the airborne-based F retrievals using the SFM approach was carried out through a consistency check against the ground-based retrievals obtained from top-of-canopy measurements collected over seven vegetated targets (Fig. 3).

Fig. 3.

Comparison between ground-based and airborne F₆₈₇ (a) and F₇₆₀ (b) retrievals that corresponded with seven selected vegetated targets. The solid line corresponds to the linear model fitted between the paired variables. The dotted line represents the 1:1 line. The horizontal error bars indicate the spatio-temporal variability (standard error) of the ground-based F signal measured over the vegetated target within a time window of approximately 30 min close to the airborne overpasses. The vertical error bars indicate the spatial variability (standard error) of the airborne-based F signal within an area of 3 × 3 pixels.

The comparison showed consistency between airborne and ground F measured both in the red and far-red regions of the spectrum for the different canopies. The linear models fitted between the airborne and ground-based observations were statistically significant (p < 0.05) and showed the effectiveness of the SFM in F687 (r² = 0.89; RMSE = 0.4mWm⁻² sr⁻¹nm⁻¹) and F₇₆₀ (r² = 0.77; RMSE = 0.41 mWm⁻²sr⁻¹ nm⁻¹) retrievals. In terms of absolute values, a systematic overestimation of the F687 measured from HyPlant compared to the ground references was recorded (bias = 0.39 mW m⁻² sr⁻¹ nm⁻¹; rbias = 48%). This effect was smaller for the F₇₆₀ retrieval (bias = 0.26 mWm⁻² sr⁻¹ nm⁻¹; rbias = 17%).

The comparison between SFM and SVD retrievals showed consistent results between the two approaches for both F₇₆₀ (r² = 0.94, p < 0.001; bias = 0.12mWm⁻² sr⁻¹ nm⁻¹; rbias = 9%) and F₆₈₇ (r² = 0.72, p < 0.001; bias = -0.31 mWm⁻² sr⁻¹ nm⁻¹; rbias = –30%).

3.1.2. Plant trait maps

The results of the GSA performed on the coupled PROSPECT-4-INFORM model are shown in Fig. 4. For each input parameter of the RTM, the total order sensitivity index (SI) obtained was expressed as a percentage as a function of the wavelength. The analysis revealed a small influence of the leaf structural parameter, tree height and average leaf angle across the entire spectrum. These parameters were therefore set to constant values to allow the maximisation of the variability of the other input variables.

Fig. 4.

Results of the GSA of the coupled PROSPECT-4-INFORM radiative transfer model. The total order sensitivity index is expressed in % for each input parameter as a function of the wavelength. The acronyms in the legend correspond to leaf structural parameter (N), leaf chlorophyll content (LCC), leaf water content (Cw), leaf dry matter content (Cm), leaf area index (LAI), leaf area index of the understory (LAIu), average leaf angle (ALA), stem density (sd), tree height (h) and crown diameter (cd).

The LCC and LAI maps at high spatial resolution obtained as output of the RTM-based retrieval from HyPlant DUAL imagery are shown in Fig. 5.

Fig. 5. LCC (a) and LAI (b) high-resolution maps obtained from HyPlant DUAL data through LUT-based inversion of the coupled PROSPECT-4-INFORM RTM using the optimal inversion strategy.

Strong correlations were found between measured and predicted values of the LCC and LAI (Table 4, Fig. 6), demonstrating that the inversion of the INFORM model constrained with various regularisation techniques yields accurate retrievals of plant traits in forest ecosystems.

Table 4. Summary of statistics in fitting (r², RMSE, rRMSE, bias and rbias) and crossvalidation (r_CV², RMSE_CV) of the comparison between the measured and estimated LCC and LAI values.

Plant trait	r2	rCV2	RMSE	RMSECV	rRMSE	bias	rbias
LCC	0.65	0.58	5.66 (μg cm−2)	3.96 (μg cm−2)	15 (%)	2.61 (μg cm−2)	7 (%)
LAI	0.72	0.47	0.51 (m2 m−2)	0.57 (m2 m−2)	14 (%)	0.04 (m2 m−2)	1 (%)

Fig. 6.

Comparison between ground-based measurements and HyPlant estimates of the LCC (a) and LAI (b). The solid line corresponds to the linear model fitted between the paired variables. The dotted line represents the 1:1 line. Error bars indicate the standard errors of ground- and airborne-based LCC and LAI estimates.

The LCC was most accurately retrieved using a logarithmic minimum contrast cost function based on the minimisation of the distance (contrast) between a parametric model and a non-parametric spectral density (Leonenko et al., 2013). The best fit (r² = 0.65, p < 0.001; n = 21) was obtained using the mean of the ten best solutions and no addition of random noise to the simulations. The use of a divergence measure cost function formalised by Kullback and Leibler (1951), which was based on the minimisation of the distance between two probability distributions, showed the best performances when retrieving the LAI. As for the retrieval of the LCC, the best results were obtained using the ten best solutions and no addition of random noise (r² = 0.72, p < 0.001; n = 14). The summary statistics in fitting and cross-validation of the linear regressions between the measured and estimated LCC and LAI are reported in Table 4. The scatterplots showing the measured LCC and LAI values against the predicted ones are reported in Fig. 6.

Overall, the estimated LCC and LAI showed value distributions within the ranges expected based on the field measurements. The LCC and LAI maps showed some similarities, but they were not totally correlated (r² = 0.5, p < 0.001). Based on the species distribution in the study area obtained from the classification performed in Tagliabue et al. (2016) using APEX airborne data, the field maple and smallleaved linden were the species characterised by the highest LCC values, even though the differences compared to the other species were not significant. LAI showed a larger inter-species variability, with the highest value for small-leaved linden and the lowest for Scots pine. In general, the LCC did not differ significantly in regeneration and mature stands, while LAI was higher in the regeneration stands.

3.1.3. GPP, APAR and LUE maps

The incorporation of spatialised maps of key plant traits into the process-based BESS model allowed to obtain spatial maps of GPP, APAR and LUE at high spatial resolution (Fig. 7).

Fig. 7.

GPP (a), APAR (b) and LUE (c) maps obtained from the BESS model driven with airborne-derived high-resolution maps.

The map of instantaneous GPP showed values ranging from 0 μmol CO₂ m⁻² s⁻¹ for bare soil to ~30μmol CO₂ m⁻² s⁻¹ for dense vegetation. The regeneration areas, where trees were planted with higher density and both LCC and LAI were higher, were clearly distinguishable in the image due to their larger CO₂ assimilation. In the mature stands, the crown-shadow patterns were more evident and the GPP values were generally lower, although with a noticeable variability across the image. Notably, because of the nature of the model and the available input data, the obtained modelled GPP was primarily driven by the LAI and Vcmax₂₅ (r² = 0.94 and r² = 0.68 respectively, p < 0.001). However, the LAI and Vcmax₂₅ were only weakly related (r² = 0.5, p < 0.001).

APAR varied from 0 to ~1900 μmol photon m⁻² s⁻¹ and showed consistent patterns with GPP (r² = 0.82, p < 0.001) despite having a lower variability for high APAR values. The LUE, obtained as ratio between modelled GPP and APAR, ranged from 0 to ~0.018 μmol CO₂ μmol photon⁻¹ and appeared strongly related to both the GPP (r² = 0.76, p < 0.001) and APAR maps (r² = 0.8, p < 0.001).

3.2. Linking measured F and modelled BESS-GPP, -APAR and -LUE

The analysis of the semi-variograms of the images obtained from HyPlant revealed the presence of a clear spatial autocorrelation in the data. This effect exists within a range from 0 to 10–15 m, as it can be gathered from the range (i.e., the distance expressed in m at which the semi-variogram levels) of the semi-variogram function shown in Fig. 8. This distance corresponds to the average diameter of the tree crowns, indicating a high similarity among pixels of the same crown. For this reason, the spatial relationships between the airborne-derived outputs shown hereafter refer to the data aggregated at the tree crown level.

Fig. 8.

Semi-variogram functions of the F₇₆₀ (a) and GPP (b) images expressed as a function of the distance (m). The red dashed lines represent the range of the semi-variogram functions. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

The spatial relationships between the F₆₈₇ and F₇₆₀ retrieved from HyPlant ultrafine spectral resolution radiance data and the GPP, APAR and LUE obtained as outputs of the BESS model driven with airborne-derived data are shown in Fig. 9. In the scatterplots, each data point is the average of all the sunlit pixels of the same tree crown.

Fig. 9.

Relationships at the tree crown level between: (a) F₆₈₇ and GPP, (b) F₆₈₇ and APAR, (c) F₆₈₇ and Vcmax₂₅, (d) Fy₆₈₇ and LUE, (e) F₇₆₀ and GPP, (f) F₇₆₀ and APAR, (g) F₇₆₀ and Vcmax and (h) Fy₇₆₀ and LUE. The colour scale represents the point density. The solid curves correspond to a logarithmic model fitted between the paired variables.

Different regression models were tested between the paired variables. Overall, the best fit was found when using a logarithmic model that allowed the nonlinearity of the relationships to be described. A positive logarithmic relationship was found between the F760 and GPP (r² = 0.46, p < 0.001), the F₇₆₀ and APAR (r² = 0.43, p < 0.001) and between the F₇₆₀ and Vcmax₂₅ (r² = 0.17, p < 0.001). Conversely, no significant relationship was found between the F₆₈₇ and GPP, the F₆₈₇ and APAR or the F₆₈₇ and Vcmax₂₅ (p > 0.05). The analysis of the logarithmic regressions between the LUE and the red and far-red F yields revealed the opposite nature of the two relationships: the Fy₇₆₀ showed a positive correlation with LUE (r² = 0.19, p < 0.001), whereas the Fy₆₈₇ and LUE were found to be negatively correlated (r² = 0.25, p < 0.001) (Fig. 9 d, h).

4. Discussion

The quantitative estimation of vegetation traits is required in a variety of ecological applications. Regardless of the considerable advances achieved through the development and testing of a wide range of retrieval methods at the leaf and the canopy level (Verrelst et al., 2015a), the quantification of these traits from remotely sensed data remains challenging. The inference of these traits is in fact concealed by confounding factors related to the canopy (e.g., canopy structure, background influence and illumination effects), the atmosphere (Malenovský et al., 2013; Houborg et al., 2015b) and the sun-sensors geometries, which might introduce large inaccuracies into the retrieved traits. The inversion of physically based RTMs is generally recognised as a reliable and accurate approach (Atzberger et al., 2015; Dorigo et al., 2007). However, the use of regularisation strategies is critical to mitigate the drawbacks of ill-posedness and to obtain trustworthy results (Verrelst et al., 2014; Combal et al., 2002). In this study, the LCC was accurately estimated with an r² of 0.65 and RMSE of 5.66 μg cm⁻² (refer to Table 3 for the complete summary of statistics) by inverting the canopy-level INFORM model coupled with the leaf-level PROSPECT-4 model. Previous studies conducted in similar contexts showed estimation accuracies ranging from ~4.5 to ~13.5 μg cm⁻² depending on the inversion strategy, sensor configuration and study site characteristics. Darvishzadeh et al. (2019) yielded an accuracy of 8.6 μg cm⁻² (r² = 0.39) in spruce stands by inverting the INFORM model with Sentinel-2 satellite data; Croft et al. (2013) obtained an accuracy of 6.42 μg cm⁻² (r² = 0.62) by inverting the PROSPECT-4Scale model (Chen and Leblanc, 1997) in a mixed forest site using MERIS satellite data; this accuracy degraded to 10.45 μg cm⁻² (r² = 0.41) when the model was inverted with CASI airborne hyper-spectral data. Croft et al. (2015) further achieved an accuracy of 7.05-13.40 μg cm⁻² (r² = 0.79-0.38) using the same model in a followup study. Inverting the PROSPECT-DART model (Gastellu-Etchegorry et al., 1996) in coniferous sites, Hernández-Clemente et al. (2014) and Malenovský et al. (2013) obtained LCC estimates with an RMSE of 5.03 μg cm⁻² (r² = 0.54) and of 2.27–12.30 μg cm⁻² (r² = 0.72-0.41), respectively. Notably, none of the aforementioned studies tested the use of regularisation options to constrain the model inversion apart from the use of prior information to restrict the variability of the model input parameters. In this study, the LAI was estimated using the same LUT-parameterisation as for LCC of the coupled PROSPECT-4-INFORM model, with an r² of 0.72 and RMSE of 0.5m²m⁻² (refer to Table 3 for the complete summary of statistics) being obtained in comparison to the ground measurements. Similar results were obtained when the INFORM model was inverted in broadleaved as well as coniferous forests by Wang et al. (2018) (RMSE = 0.43 m² m⁻²; r² = 0.63), Yang et al. (2011) (RMSE = 0.41 m²m⁻²; r² = 0.74), Atzberger (2000) (r² = 0.57) and Schlerf and Atzberger (2006) (RMSE = 0.58 m² m⁻²; r² = 0.73). The latter authors achieved lower accuracies (RMSE = 0.74–0.94 m² m⁻²; r² = 0.51–0.57) using the same model applied on multi-directional CHRIS-PROBA satellite data (Schlerf and Atzberger, 2012). Similar results were achieved using different RTMs; for example, Omari et al. (2013) inverted the PROFLAIR model (White et al., 2001) in a broadleaf-dominated forest and obtained an estimation accuracy of 0.47 m² m⁻² (r² = 0.59) and Banskota et al. (2015) used DART to estimate LAI in a deciduous forest with an accuracy of 0.5–0.74 m² m⁻² (r² = 0.6–0.64). Overall, the LAI estimation accuracy reported in the literature ranges between ~0.4 and ~0.9 m² m⁻². A systematic assessment of the different strategies for minimising the ill-posedness of the inversion has not been performed in studies conducted in forest ecosystems yet. However, based on previous works, the use of even few regularisation options (e.g., prior information about the input parameters, multiple best solutions of the inversion and ecological rules to exclude unrealistic solutions) usually leads to more accurate LAI retrievals. In this study, the coupled PROSPECT-4-INFORM model was successfully inverted, thereby providing reliable LCC and LAI spatia-lised maps in a mixed forest site. In addition to the representativeness of the model, which provides a fair compromise between realism and simplicity, the parameterisation of the model to generate the LUT and the recourse to the regularisation options were found to be advisable to obtain accurate retrievals, as highlighted in analogous studies conducted on crops (Verrelst et al., 2015b). The prior knowledge about the variability of the model input parameters allowed the exclusion of unlikely combinations that constitute a source of error and unnecessarily increase the LUT size. Likewise, the global sensitivity analysis allowed an optimised model parameterisation: redundant information in the LUT due to multiple combinations carrying the same information was avoided, whereas the variability of the most sensitive model parameters was maximised.

Consistent with the findings of Wang et al. (2018), who performed a sensitivity analysis of the PROSPECT-5-INFORM model, the leaf water content and leaf dry matter content showed a great influence on the modelled canopy reflectance (Fig. 4). In addition, a great contribution of the LCC to the variation of canopy reflectance was observed in the visible part of the spectrum, which was not considered in Wang et al. (2018). At the canopy level, the most affecting variables across the spectrum were LAI (understory and overstory) and crown diameter, whereas the stem density had a moderate influence on the output. This finding is not in complete agreement with the aforementioned study, but the authors suggested a mutual compensation between the three canopy structural parameters. Since the stem density did not vary much in our study site, this effect likely resulted from the larger influence of the LAI. Leaf structural parameters, canopy height and average leaf angle, which showed a negligible effect on the reflectance variation, were fixed to maximise the predictive power of the model. Regarding the LUT-based inversion strategy, various optimisation options were tested in this work, including the use of different cost functions to match measured and modelled spectra, the addition of Gaussian noise to the simulated data and the use of multiple solutions of the inversion. Our results showed a considerable impact of the choice of the cost function used to minimise the distance between the measured and simulated spectra on the retrieval of both the LCC and LAI. As observed by Verrelst et al. (2014) in a study focused on the LUT-based retrieval of the LCC and LAI in crops, we found that the use of the classical RMSE always led to sub-optimal results. The use of multiple best solutions also improved the estimates, but did not have as much impact as the choice of the cost function. The addition of random noise to the simulations did not affect the retrieval in our case. While clearly improving the retrieval results, the use of regularisation strategies does not completely solve the ill-posedness of the inversion. This ill-posedness, together with the underlying assumptions of the RTM and the possible underrepresentation of the ground data used for validation, could explain the portion of the variance (35% for LCC and 28% for LAI) which is not explained by the RTM inversion.

Beyond focusing on the retrieval of reflectance-based products, this work aimed at analysing the spatial variability of red and far-red sun-induced chlorophyll fluorescence across the study site, which constitutes a more direct proxy of the vegetation functional state (Wieneke et al., 2016). The F₆₈₇ and F₇₆₀ were estimated using the spectral fitting methods with an r² of 0.75 and 0.74 (p < 0.05), respectively, as assessed from the comparison against the ground-based measurements. The reliability of the SFM approach was further assessed through a comparison with F maps obtained with the Singular Vector Decomposition (SVD) method developed by Guanter et al. (2012, 2013), which had already been used, e.g., in Rossini et al. (2015), Colombo et al. (2018) and Middleton et al. (2017) to retrieve F from HyPlant observations. Compared to the SFM method that requires complex atmospheric modelling, the SVD does not include any physical formulation of atmospheric absorption or scattering effects. However, the SVD retrieval accuracy may suffer from the sub-optimal spectral and radiometric resolution of the HyPlant sensor to resolve the very narrow solar Fraunhofer lines. Additionally, the SVD method performs better when reference “non-vegetated” pixels can be used to constrain the retrieval. This is not trivial in areas as densely vegetated as the one investigated in this study. Conversely, the SFM approach has a physical nature that makes it totally independent from the observed scene, but it requires accurate modelling of the atmospheric influence in the O2 bands to obtain reliable F estimates. In particular, atmospheric absorption and scattering were identified as being the most critical factors determining F retrieval accuracies (Frankenberg et al., 2012; Guanter et al., 2010; Joiner et al., 2013). In this study, we used a physically based approach in which the atmospheric radiative transfer model used to derive the atmospheric functions required to retrieve F was accurately parameterized using ancillary information derived from sun-photometer measurements.

The retrievals based on the two methods yielded very similar results, indicating consistency between the two retrieval approaches. The SFM- and SVD-based retrievals showed a better agreement at 760 nm (r² = 0.94, p < 0.001) than at 687 nm (r² = 0.72, p < 0.001). Thus, even though we are aware of the fact that both of the retrieval methods might be affected by errors from different sources, we are confident that the consistency between the two approaches is a further indication of the robustness of the F estimates used in this work. The narrower shape of the O₂—-B band compared to the O₂-A and the overall lower signal that is detectable from above because of the reabsorption within the leaf and the canopy pose more challenges in the retrieval of F687, thereby resulting in a higher uncertainty in the retrieval. This is clearly visible in the full resolution maps obtained and is also confirmed by the comparison between SVD and SFM. The relationship is in fact more scattered, indicating a higher noise in the retrieval using both the retrieval approaches compared to the F760 retrieval. However, the aggregation of the data at crown level partly reduced this issue as a consequence of the random noise averaging.

In this study, the F estimated at crown level was then related to instantaneous carbon uptake, light absorption and light-use efficiency estimated at comparable spatial resolution using the BESS model. BESS is a process-based model, and its performance in predicting GPP has been comprehensively evaluated in Ryu et al. (2011), Jiang and Ryu (2016) and Whitley et al. (2016). Ryu et al. (2011) validated the model at the global scale against eddy covariance tower flux data from 33 FLUXNET sites covering a broad range of plant functional types. The strong linear relationship found with modelled GPP (r² = 0.86, relative bias: 5%) at annual composite provided experimental evidence of the model capacity to produce accurate GPP estimates. Further evaluation of the model was carried out in Jiang and Ryu (2016) by means of a comparison against a set of 113 FLUXNET sites distributed worldwide in the period 2000–2015. The results at both 8-daily and annual composites confirmed the reliability of the model in predicting GPP (r² = 0.67 and r² = 0.93, respectively, compared to flux measurements). In Whitley et al. (2016), BESS was benchmarked against a set of models of increasing complexity, showing consistent performances with other terrestrial biosphere models. With respect to the ordinary BESS implementation, the differences in our study mainly reside in the high-spatial resolution data used to feed the model and in the snapshot nature of the analysis. The unavailability of the eddy covariance tower data in the study site limited our possibility to directly compare Hy-Plant-BESS outputs with ground-based flux estimates, and, anyhow, a proper validation would not have been feasible even in case of their availability. The flux tower information is, in fact, a point measurement, which is valuable for monitoring the temporal variation of the carbon fluxes but is difficult to exploit when assessing the spatial variability of these fluxes. A proper ground validation of the simulated GPP spatial variability would have required an extensive spatial array of flux towers, which is extremely challenging to set-up in practice. For globally distributed FLUXNET sites and annual averages, BESS performed differently for the spatial variability: for the mixed forest, the performance was relatively good (r² = 0.47) and much better than the MODIS GPP product (r² = 0.04) (Jiang and Ryu, 2016). These results, however, neither represent the general performance of the BESS model itself for spatial variability, nor are they indicative of the spatial variability performance of the HyPlant-based GPP simulations. The reasons for the latter are twofold: first, the HyPlant-based results represent an instantaneous snapshot, whereas the global results of spatial variability of the BESS-GPP were based on annual averages; second, for the HyPlant-based results, the spatial variability in the simulated GPP was strongly driven by spatially explicit inputs for the LAI and Vcmax, whereas the global results were based on plant functional type-specific peak Vcmax values that are seasonally scaled with the LAI. We think the use of a spatially explicit Vcmax proxy, as well as a high-quality LAI map, predominantly determine the quality of the spatial variability (Madani et al., 2014).

Because of the highly detailed nature of this snapshot analysis and the data available, a more feasible option for checking the model performances was the comparison between modelled variables and proxies of these variables that can be remotely sensed. As shown in Fig. 10, the BESS-fAPAR (i.e., fraction of APAR, calculated as the ratio between BESS-APAR and incoming PAR) was found to be highly correlated to the VIs, which are well-known to be related to the fraction of absorbed PAR. The BESS-fAPAR showed the strongest correlation with VIs such as NDVI (Rouse et al., 1974) (r² = 0.86, p < 0.001) and NDVIre (Gitelson and Merzlyak, 1994) (r² = 0.86, p < 0.001), which are sensitive to the photosynthetic component of the canopy. Conversely, the correlation with VIs related to the totality of the canopy (i.e., including photosynthetic and non-photosynthetic components) such as NDSI (Inoue et al., 2008) was found to be lower (r² = 0.63, p < 0.001). This finding further supports the correct representation of the carbon fluxes by the model, since the modelled APAR that is used to estimate GPP is representative of the canopy component which is effectively involved in photosynthesis.

Fig. 10. Relationships at tree crown level between BESS derived fAPAR and VIs: BESS-fAPAR and NDVIre (a); and BESS-fAPAR and NDSI (b).

The soundness of the HyPlant-BESS results was determined by the accurate spatial representation of the LAI and Vcmax₂₅. These two variables constitute the two main drivers of BESS according to the sensitivity analysis performed in Ryu et al. (2011). However, we cannot exclude potential uncertainties in the BESS-GPP estimates related to the use of the LCC to empirically infer Vcmax₂₅.

The relationship between far-red F and GPP has been shown to be strong in several studies conducted at different spatio-temporal scales over different vegetation types. Multiple studies exploiting satellite data have shown a linear relationship between global scale monthly or annual averages of spaceborne F retrievals and data-driven upscalings of GPP from EC tower measurements (Frankenberg et al., 2011; Joiner et al., 2011; Guanter et al., 2014). However, different results were obtained in studies conducted at local and regional scales as well as from modelled data. Several authors found nonlinear and ecosystemspecific relationships (e.g., Damm et al., 2015; Zhang et al., 2016; Goulas et al., 2017), revealing that this link is more complex at finer spatial resolution. The distribution of the absorbing and scattering elements within the canopy determines the canopies to act as photon traps (Lewis and Disney, 2007; Knyazikhin et al., 2013). As a consequence, the escape probability of photons is a function of the complexity of the canopy architecture. These factors modulate the F signal detected by the sensor, which, in turn, might be nonlinearly correlated with GPP when the scale of observation allows appreciative effects.

Working at the scale of the individual tree crown, we found a statistically significant positive nonlinear relationship between the measured F₇₆₀ and modelled GPP (r² = 0.46, p < 0.001), confirming the previous findings and demonstrating that, even in a snapshot case, an empirical relationship between the spatial variation of the two variables exists. Our ground validation of the F retrievals showed that a positive bias existed in both the F₇₆₀ and F₆₈₇ (Fig. 3). We acknowledge that, in relative terms, the bias between airborne and ground-based retrievals is considerable. However, from the results, it seems more appropriate to consider the bias in absolute terms. In fact, we found a constant offset that led to linear regression lines almost parallel to the 1:1 line (Fig. 3). This means that a similar absolute bias in the magnitude of F₆₈₇ and F₇₆₀ leads to a higher relative bias for F₆₈₇, as the absolute F₆₈₇ is considerably smaller. Apart from that, biases of the same order (or even larger ones) were reported in previous studies for both the F₇₆₀ retrievals from the satellite and the F687 and F760 retrievals from the field spectrometers. In particular, the spectral resolution is known to strongly affect the airborne retrievals (e.g., Damm et al., 2014; Zarco-Tejada et al., 2016). We therefore think that the bias in our F retrievals is not exceptionally large. In addition, this study strongly focuses on the relationships between the F and GPP (Fig. 9 a, e), which are not affected by biases in the F magnitude. The same applies to a potential overall bias of the simulated GPP, which cannot be excluded without a flux tower in the study area. What matters for the analysis of the F-GPP relationship in terms of correlation is exclusively the spatial variability. The high r² values for the airborne F retrievals compared to the ground observations (Fig. 3) indicate that the spatial variability of F is well captured and the spatial variability of simulated GPP is expected to have a good performance based on the spatially explicit inputs for the LAI and, especially, Vcmax₂₅.

The pronounced scattering of the F-GPP relationship suggests other factors are affecting the relationship, and these factors are apparently masked when working at broader spatial and/or temporal scales. To understand whether this actually depends on the scale of the observation, the effect of spatial degradation was tested on our data by aggregating the HyPlant high-resolution images at increasing pixel sizes (i.e., 10 m, 20 m, 40 m and 80 m) (Fig. 11). In contrast with the results shown in Fig. 9, where the data were aggregated at the crown level, the spatial aggregation exercise shown in Fig. 11 provides insight to situations that could be potentially observed at the satellite scale, where the coarser spatial resolution does not allow working at the individual crown level anymore.

Fig. 11. Relationship between F₇₆₀ and BESS-GPP at increasing spatial aggregation: (a) 10 m, (b) 20 m, (c) 40 m and (d) 80 m. The solid lines correspond to the linear models fitted between the two variables. The equations of the regression lines are reported.

The clear progressive decrease of the scattering, along with the increase of the correlation (i.e., r² = 0.29 at 10 m resolution and r² = 0.52 at 80 m resolution), suggests that the averaging of the spatial heterogeneity effectively improves the relationship between F and GPP. The spatial scale also affects the slope and intercept of the regression models fitted: while the spatial resolution decreases, the slope increases, and the intercept decreases. In addition, the relationship tends to become more linear as the spatial resolution decreases, which is somewhat similar to what Zhang et al. (2016) and Damm et al. (2015) observed in the temporal dimension and might be explained by the reduction of the variability across the study site and by the changing impact of the confounding effects of canopy structure at a coarser spatial resolution. A similar correlation was observed between the F₇₆₀ and APAR (r² = 0.43, p < 0.001). The APAR has been shown to be the main driver of F760 temporal variability because of its large variation (Miao et al., 2018; Yang et al., 2015; Li et al., 2018; Koffi et al., 2015; Rossini et al., 2010; Yang et al., 2018). To disentangle such influence of the APAR in the relation between the F₇₆₀ and GPP, the relationship between the Fy₇₆₀ (F₇₆₀/APAR) and LUE (GPP/APAR) was examined, revealing a significant positive nonlinear correlation (r² = 0.19, p < 0.001) between the two variables. This result is consistent with the findings of Yang et al. (2015), Zhang et al. (2016) and Verma et al. (2017), supporting the hypothesis that the F₇₆₀ contains information not only on the APAR, but on both of the terms that constitute the equation GPP = APAR × LUE. Other studies conducted in the temporal domain found an opposite behaviour. For example, recent works conducted by Yang et al. (2018) in a rice paddy site and Miao et al. (2018) in a soybean field found that far-red F is a better proxy of the APAR than the GPP at high temporal resolution, suggesting a different meaning of the relationship between the F, GPP and APAR in the spatial and temporal domain. However, further investigation is needed to understand if these findings also hold for other sites and in particular for forest ecosystems. Notably, the F-APAR relationship (Fig. 9e) we found differs considerably from the saturating one reported in process-based simulations of time series (e.g., Zhang et al., 2016). We carefully verified that our results are correct for the spatial snapshot case and consistent with the time series results. We concluded that the difference between the latter two cases is caused by either the LAI (spatial snapshot) or the PAR (time series) as main drivers of the variability in the F, GPP and APAR.

Regarding the F emitted in the red region, some studies have suggested that it might be a more sensitive indicator of the plants’ photosynthetic activity due to the greater contribution of photosystem II in this region (Verrelst et al., 2015d; Baker, 2008; Porcar-Castell et al., 2014). Following this hypothesis, simulation studies conducted using the SCOPE model (van der Tol et al., 2009) showed that the relationship between the red F and GPP should be similar or even better than the one observed between the far-red F and GPP (Zhang et al., 2016; Verrelst et al., 2016). However, the few studies that have exploited real red F observations to validate this finding have shown contradictory results. Whereas Cheng et al. (2013) reported that the red F performed better than the far-red F in predicting the GPP, Goulas et al. (2017) and Liu et al. (2017) concluded that the far-red F is a better proxy of the GPP, especially when considering canopies with varying biochemical and structural composition. This is supported by the modelling results of Du et al. (2017) and Liu et al. (2018) that show a heavily scattered relationship between red F and APAR compared to the one between farred F and APAR because of the greater influence of the LCC and LAI variation. In our study, no significant correlation was found between the spatial variability of F687 and the GPP and APAR. Although we acknowledge that this result might be partly due to the higher uncertainty in the retrieval of F₆₈₇ (resulting in a significant impact of the random noise), we think that other factors predominantly mask this relationship. In particular, we believe that further investigation is needed to understand the role of the reabsorption within the leaf and the canopy in the observed F₆₈₇-GPP relationship.

However, interestingly, a statistically significant negative correlation emerged when both the red F and GPP were normalised by APAR (r² = 0.25, p < 0.001). To the best of our knowledge, whilst both positive and negative correlations were shown to be possible between the Fy₇₆₀ and LUE depending on the energy partitioning (Miao et al., 2018), no previous study investigated the relationship between the Fy687 and LUE. Hence, further studies need to be performed to interpret this finding. Again, a possible explanation could be related to the role of reabsorption within the canopy, which has a strong effect on the red F while having almost no effect on the far-red F.

The results of the spatial analysis conducted in this study pointed out the complex nature of the relationship between F₇₆₀ and GPP at high-spatial resolution. While the effective implications of our findings on the quantification of photosynthesis at large scales are hardly inferable (since the empirical nature of the relationships we found does not allow upscaling them), our results broadly demonstrated that the spatial heterogeneity controls the F₇₆₀-GPP relationship and needs to be considered to infer reliable estimates of the GPP when the F is known. In particular, the variation of the F₇₆₀-GPP relationship at increasing spatial aggregation in terms of correlation coefficient, as well as of the slope and intercept we observed, could explain why linear relationships are usually found at coarse spatial resolutions, suggesting that they can be affected by an unknown bias related to the scale of observation.

5. Conclusions

In this study, HyPlant airborne high-resolution images acquired over a mixed forest ecosystem were exploited to obtain and analyse the spatial intra- and inter-variability of different variables related to the biochemical, structural and functional state of the vegetation. First, the LCC and LAI, two key variables in vegetation-related studies, were estimated with accuracy of 5.66 μg cm⁻² and 0.51 m² m⁻², respectively, by inverting the coupled PROSPECT-4-INFORM radiative transfer model. The high accuracy of the two spatialised products and their consistent spatial patterns were made possible by an optimal parameterization and inversion strategy applied to the HyPlant hyperspectral data. Second, high-resolution maps of sun-induced chlorophyll fluorescence, an indicator of plants' photosynthetic activity, were obtained for the first time at both the red and far-red peaks over a forested area. The comparison against top-of-canopy measurements acquired at the same time of the overpass highlighted the accuracy of the estimates, demonstrating the reliability of the SFM retrievals (r² = 0.89 at O₂—-B band; r² = 0.77 at O₂-A). Third, the spatialised plant traits obtained through RTM inversion were successfully exploited to drive a customised version of the Breathing Earth System Simulator (BESS), which provided the GPP, APAR and LUE maps. These maps constitute an independent measure of the spatial variability of the instantaneous carbon fluxes and light absorption at the time of HyPlant overflight. BESS-GPP and APAR showed a nonlinear positive–albeit scattered–correlation with the F₇₆₀ (r² = 0.46 and r² = 0.43, respectively). In addition, a positive nonlinear correlation was found between the Fy₇₆₀ and LUE (r² = 0.19). This result showed that this relationship, usually observed in the temporal domain, can apply to the spatial domain at the scale of individual tree crowns. At the same time, this result revealed that the relationship between the F and GPP can be more complex at a more detailed scale, and suggests the consideration of the spatial variability in future studies. The BESS-GPP, -APAR and -LUE were also compared against F in the red region, showing more unexpected results. No significant correlation was, in fact, found between the F₆₈₇ and GPP or APAR, whereas a negative correlation was observed between the Fy₆₈₇ and LUE (r² = 0.25).

Collectively, our results provided insights into the critical role of the spatial heterogeneity in controlling the relationship between the far-red F and GPP, highlighting the importance of using high spatial resolution RS data to grasp the complexity of the terrestrial ecosystem dynamics. Furthermore, our results indicate the need to integrate different RS derived products to obtain a comprehensive picture of the vegetation-related processes. Further research in this direction constitutes a high priority for advancing the understanding of terrestrial ecosystem dynamics and prediction of their future responses to a changing climate.