# Using Sentinel-2-Based Metrics to Characterize the Spatial Heterogeneity of FLEX Sun-Induced Chlorophyll Fluorescence on Sub-Pixel Scale

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## Abstract

**:**

_{760}and SIF

_{687}, respectively) and to correlate it with the spatial heterogeneity of selected S2 derivatives. We used HyPlant airborne imagery acquired over an agricultural area in Braccagni (Italy) to emulate S2-like top-of-the-canopy reflectance and SIF imagery at different spatial resolutions (i.e., 300, 20, and 5 m). The ensemble decision trees method characterized FLEX intrapixel heterogeneity best (R

^{2}> 0.9 for all predictors with respect to SIF

_{760}and SIF

_{687}). Nevertheless, the standard deviation and spatial heterogeneity coefficient using k-means clustering scene classification also provided acceptable results. In particular, the near-infrared reflectance of terrestrial vegetation (NIRv) index accounted for most of the spatial heterogeneity of SIF

_{760}in all applied methods (R

^{2}= 0.76 with the standard deviation method; R

^{2}= 0.63 with the spatial heterogeneity coefficient method using a scene classification map with 15 classes). The models developed for SIF

_{687}did not perform as well as those for SIF

_{760}, possibly due to the uncertainties in fluorescence retrieval at 687 nm and the low signal-to-noise ratio in the red spectral region. Our study shows the potential of the proposed methods to be implemented as part of the FLEX ground segment processing chain to quantify the intrapixel heterogeneity of a FLEX pixel and/or as a quality flag to determine the reliability of the retrieved fluorescence.

## 1. Introduction

^{2}= 0.38) with stomatal conductance compared to ground measurements, due to the effects of different vegetation fractional cover. Moreover, Tagliabue et al. [27] showed that in mixed forests, spatial heterogeneity plays a crucial role in controlling the relationship between far-red SIF and GPP. Moncholi-Estornell et al. [28] showed that normalizing the SIF signal emitted from the top of the canopy by the fractional cover of sunlit vegetation improves the estimation of the effective fluorescence flux, reducing the error from 36% to 18% (red fluorescence) and from 24% to 6% (far-red fluorescence), respectively. These studies show how an inaccurate characterization of the spatial heterogeneity of a fluorescence pixel can lead to errors in the estimation of the fluorescence signal. Therefore, in this paper we will focus on characterizing the spatial heterogeneity of a SIF pixel.

## 2. Materials and Methods

#### 2.1. Study Area

^{2}rural area located in Braccagni, central Italy (42.82°N; 11.07°E) (Figure 1). The scene was mostly agricultural and encompassed different summer crops (i.e., tomato, corn, sorghum), which are irrigated during June-September (FlexSense final report—ESA contract no. 4000125402/18/NL/NA). According to the Urban Atlas 2018 land-use map (European Union, Copernicus Land Monitoring Service 2018, European Environment Agency (EEA)), arable lands dominate the site (~82%), followed by pastures (~7%), isolated structures (2.50%), industrial, commercial, private units (~1%), sports and leisure facilities (~1%), and other roads and lands associated with fast roads (~1%). Permanent crops (e.g., vineyards, orchards), water, forests, green urban areas, and discontinuous urban fabric each represent less than 1% of the site.

#### 2.2. Airborne Data

_{2}A (SIF

_{760}) and O

_{2}B (SIF

_{687}) absorption bands [36,37]. The spectral fitting method (SFM), developed by Cogliati et al. [38] and later adapted to airborne data [39], was used to retrieve SIF at 760 and 687 nm. The recorded HyPlant images cover an area of approximately 14 km

^{2}and were acquired heading in the northern direction from 350 m above ground level at 11:40 local time. The image data of both sensors were processed and georectified according to the HyPlant processing chain presented in Siegman et al. [37].

#### 2.3. Data Processing Description and Heterogeneity Methods Evaluation

#### 2.4. Data Preparation

- -
- From the FLUO sensor (4.5 × 4.5 m), SIF in the O
_{2}A (SIF_{760}) and O_{2}B (SIF_{687}) bands was spatially aggregated in the software SAGA ([40], version 2.3.2) using the nearest neighbor algorithm to downscale it from 4.5 m to 5 m (SIF_{760,5}and SIF_{687,5}). SIF was not aggregated to 20 m because we used the SIF image data as a reference, and therefore decreasing the resolution to 20 m would result in a loss of information needed for the characterization analysis. We did not exclude negative SIF values inherent to SIF retrieval uncertainty. Although they lack physical meaning (negative SIF is physically not possible), removing them would arbitrarily bias the resampled data. Therefore, retrieval uncertainty contributes unavoidably to the spatial heterogeneity of SIF. - -
- Top-of-canopy reflectance data from the DUAL module of HyPlant (626 bands in total) were first spatially aggregated from 4.5 m to 20 m to mimic S2 pixels. We, again, used the software SAGA and information about the S2 grid to perform this task [40] (version 2.3.2). Spatial resampling was performed using the mean (cell area weighted) downscaling method. The output image was then processed in R using the hsdar package [41] for spectral convolution. This resulted in 13 synthetic S2 spectral reflectance bands at 20 m spatial resolution (S2-R
_{20}), which later were used to retrieve the biophysical traits (S2-BT_{20}) and vegetation indices (S2-VI_{20}) used to characterize SIF spatial heterogeneity (Table 1 and Table 2).

**Table 1.**Summary of the Sentinel-2-based vegetation indices used to determine SIF spatial heterogeneity within the 300 × 300 m resolution FLEX pixels. Sentinel-2 central wavelength: B1 (443 nm), B2 (490 nm), B3 (560 nm), B4 (665 nm), B5 (705 nm), B6 (740 nm), B7 (783 nm), B8 (842 nm), B8a (865 nm), B9 (940 nm), B10 (1375 nm), B11 (1610 nm) and B12 (2190 nm).

Vegetation Index (VI) | General/Sentinel-2 Formula | Description |
---|---|---|

Normalized difference vegetation index (NDVI) | NDVI = (NIR − RED)/(NIR + RED) NDVI = ((B8A − B4)/(B8A + B4)) | Indicator of green vegetation [42]. |

Near-infrared reflectance of terrestrial vegetation (NIRv) | NIRv = NIR×((NIR − RED)/(NIR + RED)) NIRv = B8A×((B8A − B4)/(B8A + B4)) | Proportion of pixel reflectance due to vegetation in the pixel; strongly correlated with SIF [21,43,44]. |

Chlorophyll red-edge (ChlRE) | ChlRE = ([760:800]/[690:720]) – 1 ChlRE = B7/B5-1 | Estimates chlorophyll content in leaves [45]. |

Enhanced vegetation Index (EVI) | EVI = 2.5×(NIR − RED)/((NIR + 6 × RED − 7.5 × BLUE) + 1) EVI = 2.5×(B8A − B4)/(B8A + 6 × B4 − 7.5 × B2) + 1) | Indicator of green vegetation similar to NDVI, but corrects for some atmospheric conditions and is more sensitive to dense vegetation [46,47]. |

Moisture content (MSI) | MSI = SWIR/NIR MSI = B11/B08A | Indicator of leaf water content—higher values indicate high water stress with less water content and vice-versa [48,49]. |

**Table 2.**Summary of the Sentinel-2-based biophysical traits used to determine sun-induced fluorescence spatial heterogeneity within FLEX pixels of 300 × 300 m resolution. Biophysical traits were retrieved using the Sentinel-2 ToolBox Biophysical processor [50].

Biophysical Trait (BT) | Description |
---|---|

Fraction of Absorbed Photosynthetically Active Radiation (fAPAR) | Fraction of the down-welling photosynthetically active radiation that is absorbed by the canopy [51]. |

Leaf Area Index (LAI) | Quantifies the amount of leaf material in a canopy. It is the ratio of one-sided leaf area per unit ground area [52,53]. |

Fraction of green Vegetation Cover (fCover) | Quantifies the fraction of ground covered by green vegetation [54]. |

Leaf Chlorophyll Content (LCC) | Leaf chlorophyll content (µg of chlorophyll per cm^{2} of leaf area) was computed from the retrieved canopy chlorophyll content (CCC), dividing it to the retrieved LAI [55]. |

#### 2.5. Predictor Selection

_{687,20}and SIF

_{760,20}images (aggregated to 20 m only for predictor selection) with S2 predictors (spectral reflectance bands, vegetation indices and biophysical traits, 20 m resolution). The images were normalized, scaled between 0 and 1 in accordance with min-max values, and SSIM was computed for all 300 × 300 m pixels (FLEX pixels based on Sentinel-3 grid with assigned pixel ID-s). Tukey’s test was then used to compare the means of the SSIM values for the predictors (S2-R

_{20}, S2-BT

_{20}, and S2-VI

_{20}) and SIF (SIF

_{687,20}, SIF

_{760,20}). Values around 0 mean that there is no similarity between the SIF and the S2 predictor patterns, while values towards ±1 indicate high similarity. S2 bands B1, B2, B3, B4, B5, B10, B11 and B12 were not similar to SIF

_{687,20}and SIF

_{760,20}(Figure 3) and were not used for further analysis, meaning that all the visible and SWIR bands were removed, leaving only NIR and red-edge bands. It is worth noting that SIF

_{687,20}itself was not so similar to SIF

_{687,20}, nor to any S2-BT

_{20}or S2-VI

_{20}product.

#### 2.6. Methods to Characterize Sun-Induced Chlorophyll Fluorescence Heterogeneity

^{2}). Other goodness-of-fit metrics (e.g., coefficient of determination, root-mean-square error, and bias) would not produce meaningful comparisons for this task due to differences in the units of SIF (W m

^{−2}sr

^{−1}µm

^{−1}) and predictors (unitless for vegetations indices, fAPAR, fCover; m

^{2}m

^{−2}for LAI; sr

^{−1}for reflectance bands; µmol m

^{−2}for LCC). Due to the squared nature of the spatial heterogeneity coefficient (variance is a square of the standard deviation, see Table A1) it was unsquared using natural logarithm transformation to avoid heteroscedasticity while applying the linear regression.

#### 2.7. Outliers’ Distribution

## 3. Results

#### 3.1. Field Site Characterization

#### Spatial Analysis

^{−2}um

^{−1}sr

^{−1}for SIF

_{760,5}and from −0.13 to 0.2 W m

^{−2}um

^{−1}sr

^{−1}for SIF

_{687}(Figure 5a). Higher SIF

_{760,5}values were observed in the northern and central parts of the image, which correspond to green pasture and forested areas, respectively (Figure 4a).

_{687,5}had higher values at the southern image boundary that were not observed at the northern boundary (Figure 5a). The patterns of vegetation indices and biophysical trait maps (Figure 5b,c) are consistent with those of SIF, with higher values of NIRv, NDVI, EVI, fAPAR, fCover, LAI, and low values of ChlRE, MSI and LCC in the same areas of the image. For example, the circular shape area in the middle of the image was a 1 km diameter irrigated corn crop and was highlighted in these maps. For MSI, a measure of vegetation water content, higher values indicate lower water content. Finally, the S2 reflectance bands B6, B7, B8, B8A and B9 all followed a mutually similar distribution (Figure 5d).

_{760,20}and SIF

_{687,20}showed a normal distribution, with SIF

_{760,20}having a higher frequency of lower values than SIF

_{687,20}(Figure 6a). When analyzing the distribution of Vis, a similar normal distribution pattern was observed for ChlRE and MSI, whereas the peaks for EVI, NDVI and NIRv (Figure 6b) distributions were skewed towards lower values. Distributions of biophysical traits fAPAR, fCover, and LAI (Figure 6c) also had higher frequency of lower values, but the skew is much more pronounced compared to the Vis. All S2 reflectance band distributions were slightly skewed to the left with a higher frequency of higher values (Figure 6d).

#### 3.2. Models’ Performances

#### 3.2.1. Evaluation

_{760,300}R

^{2}> 0.8 and SIF

_{687,300}R

^{2}> 0.6). Interestingly, when the spatial heterogeneity coefficient method was implemented with 15 classes (Figure 7d) instead of 5 (Figure 7e), the R

^{2}decreased to ~0.5 for SIF

_{760,300}and between 0.1–0.2 for SIF

_{687,300}. The standard deviation method (Figure 7b), despite its simple implementation, casted R

^{2}> 0.6 for SIF

_{760,300}and R

^{2}> 0.1–0.4 for SIF

_{687,300}when NIRv, fCover, LAI and B7 were used as predictors, showing similar results to the spatial heterogeneity coefficient SCL-15 approach. Finally, the Local Moran’s I (Figure 7c) and normalized entropy (Figure 7f) methods achieved the worst results, with SIF

_{760,300}R

^{2}< 0.3 and SIF

_{687,300}R

^{2}< 0.1. It is worth noting that the spatial heterogeneity was better predicted for SIF

_{760,300}than for SIF

_{687,300}.

_{760}spatial heterogeneity. Furthermore, fAPAR presented slightly better results than fCover for SIF

_{687}for ensemble decision trees and for spatial heterogeneity coefficient SCL-15 methods.

#### 3.2.2. Outliers’ Spatial Distribution

_{760,300}(Figure 8a), SIF

_{687,300}(Figure 8b), and the sum of both (Figure 8c). Outliers were more often located in the scene borders. However, this was not related to the absence of the missing (‘NaN’) high-resolution values, which was prevented by cropping the pixels on the edge of the image in the preprocessing steps.

_{760,5}, SIF

_{687,5}, NIRv

_{20}, fAPAR

_{20}, B7

_{20}and the scene classification maps with 5 and 15 classes (Figure 9). For pixel ID 166, its spatial distribution is shown for SIF (Figure 9a,b), as well as for NIRv (Figure 9c), fAPAR (Figure 9d) and B7 (Figure 9e).

_{760,5}and SIF

_{6875,5}values (Figure 9h,i), where approximately half of the pixels have SIF values greater than 0.2 W m

^{−2}sr

^{−1}um

^{−1}and the other half have SIF values close to zero or negative. Notably, SIF

_{687,5}shows higher values than SIF

_{760,5}for both pixels. Regarding the spatial distribution of NIRv (Figure 9j) and fAPAR (Figure 9k) for pixel ID 124, a homogeneous distribution across pixels was observed. Interestingly, the spatial distribution of B7 (Figure 9l) follows the pattern of SIF.

#### 3.2.3. Best-Performing Models

_{687,300}did not perform as well and are not included in this section but are included in Appendix C (Figure A1, Figure A2 and Figure A3).

_{760,5}reference data (Figure 10a,d,g) and predictor NIRv (Figure 10b,e,h) for all three selected methods. Lower values indicate low heterogeneity and higher values indicate high heterogeneity. There is a significant linear relationship between the reference and predictor SIF spatial characterization for standard deviation (R

^{2}= 0.76, p < 0.001, Figure 10c), ensemble decision trees (R

^{2}= 0.93, p < 0.001, Figure 10f) and spatial heterogeneity coefficient (R

^{2}= 0.63, p < 0.001, Figure 10i).

_{760,5}and NIRv,

_{20}values with eight land cover classes (Figure 11a–c). At pixel ID 82, higher values were observed grouped in the lower right part of the pixel for SIF

_{760,5}and NIRv,

_{20}maps. The scene classification map had nine different classes, with the lower part of the image fully following the SIF and NIR patterns, while the upper parts were less visually aligned. A less heterogeneous pixel, ID 192, was also observed in the northern edge of the image with homogeneous SIF

_{760,5}and NIRv,

_{20}maps (Figure 11d,e), which had low values. The scene classification map had five different classes, one of which dominated the image (orange color). In the left part of the pixel, a contrasting edge can be seen on the SCL map, which is not as pronounced on the SIF

_{760,5}and NIRv

_{20}maps.

## 4. Discussion

_{760,300}and SIF

_{687,300}with the different S2 bands, VIs and BTs considered in this study, which significantly improved the model performance. However, caution should be exercised when extrapolating these results to other studies, such as vegetation dynamics monitoring. When downscaling SIF from 300 × 300 to 20 × 20 m, we assume the same fluorescence response at each 20 × 20 sub-pixel englobed in a FLEX pixel, which is rather unexpected due to the dynamic response of fluorescence and consequently could lead to a misinterpretation of the vegetation status.

_{760,5}showed a significant linear correlation with the NIRv index (R

^{2}= 0.76, p-value < 0.001) (Figure 10c), suggesting that it was successful in capturing the spatial heterogeneity of the fluorescence emitted at 760 nm in this study. Regarding SIF

_{687}, only the standard deviations of S2-B6, S2-B7 (both red-edge) and S2-B8 (NIR) were able to explain the ~40% of SIF

_{687}spatial heterogeneity. A similar approach was implemented in Rossini et al. [1], in which they used the absolute deviation from the mean between ground SIF

_{760}observations and medium-resolution SIF

_{760}pixels (300 m) to determine the optimal sampling strategy (i.e., number of sampling points) to characterize a FLEX-based pixel over an agricultural area. They concluded that between 3 and 13.5 sampling points are required to characterize the average SIF value of a monoculture field at a FLEX-based pixel resolution.

_{760,5}and the VI, BT and S2 reflectance band images in the study, but a higher variability is observed when looking at the SIF

_{687,5}map (Figure 5a). We hypothesize that this could be due to the higher retrieval uncertainty at SIF

_{687,5}when SIF is retrieved in pixels with high intrapixel heterogeneity, i.e., low vegetation fractional cover [24], as well as for the lower signal-to-noise ratio of the HyPlant instrument [69,70], which alters the measured spectral reflected radiance shape and increases the fluorescence retrieval uncertainty. Interestingly, the pixels identified as outliers support the hypothesis just described, for example, pixels ID166 and ID124 present low NDVI and LAI values (Figure 5), suggesting low fractional cover and consequently making the retrieval more prone to cast bias.

_{760}consistently performed better than those with SIF

_{687}. While canopy SIF

_{687}is dominated by chlorophyll re-absorption within the leaves and canopy, the SIF

_{760}signal is primarily affected by scattering owing to leaf and canopy structural properties as well as solar-and-observation angle [71,72,73]. In this study, S2-based images were used to estimate different VI and BT, but due to the S2 configuration, only structure-related VI and BT could be retrieved (i.e., NIRv, fAPAR, fCover, LAI), which explains why the proposed model better characterizes the spatial heterogeneity of SIF

_{760}, but fails to characterize the weaker—and most dynamic—fluorescence emission at 687 nm [22,74]. Furthermore, the characterization of SIF intrapixel heterogeneity analyzes a single scene at a single point in time, so it is expected that the static vegetation structure traits will drive the field variability. In a time series analysis, however, the changes in environmental conditions (i.e., PAR, water and nutrient availability) would instead be captured by the dynamic vegetation traits, such as APAR and/or NPQ [75].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Table A1.**Detailed explanations for each method used for expressing heterogeneity and the range of heterogeneity values.

Method Name | Heterogeneity Values |
---|---|

Local Moran’s I | Range from 0 to 1, where 0 corresponds to low heterogeneity and 1 to high heterogeneity |

We quantified the fluorescence heterogeneity at FLEX resolution as the fraction of pixels belonging to a single-pixel cluster or not assigned to any cluster. For each 300 × 300 m pixel, we independently clustered S2-R_{20} and SIF_{λ,5} using the Local Moran’s I method [57] implemented in the function Moran_Local() from the ESDA (Exploratory Spatial Data Analysis) package from the PySAL Python library [76]. The approach classifies pixels into four classes: diamond (a single high value among low values), doughnuts (a single low value among high values), hotspot (a high value among high values), and cold spot (a low value among low values); the first two are single-pixels classes. The classification is conducted based on the spatial autocorrelation Moran’s I metric whose statistical significance is defined using permutations (bootstrap). In this way, the pixels that were not significantly assigned to any of the former categories constituted a new “heterogeneous” class. FLEX pixel heterogeneity was then computed as the fraction of diamond, doughnut, and non-significant pixels within each 300 × 300 m FLEX pixel. | |

Spatial heterogeneity coefficient | High values determine higher heterogeneity and lower values lower heterogeneity. The lowest possible value is 0, when all pixels belong to one class (homogeneous). The highest value is limited by the range of the values and the number of land cover types, 0.0053 W^{2} m^{−4} um^{−2} sr^{−2} for SIF760, 0.55 m^{4} m^{−4} for LAI |

Heterogeneity was quantified as a function of land-use cover variability within each FLEX 300 m pixel, using the spatial heterogeneity coefficient described in [31]. Formula for spatial heterogeneity coefficient (C _{sh}): | |

${\mathrm{C}}_{\mathrm{sh}}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}}{\mathrm{p}}_{\mathrm{i}}\times {\mathrm{E}}_{\mathrm{i}}\times {\mathsf{\sigma}}_{\mathrm{i}}^{2}$ $=-{\sum}_{\mathrm{i}=1}^{\mathrm{N}}{\mathrm{p}}_{\mathrm{i}}^{2}\mathrm{ln}({\mathrm{p}}_{\mathrm{i}})\frac{{\sum}_{\mathrm{m}=1}^{{\mathrm{n}}_{\mathrm{i}}}({\mathrm{x}}_{\mathrm{m}}-\mathsf{\mu}{)}^{2}}{{\mathrm{n}}_{\mathrm{i}}}$ | |

N—total number of land cover classes of each sub-pixel included in a pixel; x _{m}—m-th pixel value, which is included in the i-th land cover class;μ—mean value of the total sub-pixels that are included in one pixel; n _{i}—total number of sub-pixels included in the i-th type; p _{i}—fraction of the i-th land cover class in a pixel. One FLEX pixel could contain more than one land cover class; such a class is represented by sub-pixels (5 m for SIF and 20 m for S2 metrics). Heterogeneity combines class variance with information entropy. Class variance (${\mathsf{\sigma}}_{\mathrm{i}}^{2})$ is the difference in sub-pixels reflecting intraclass (difference in growth conditions for the same vegetation type, i.e., different canopy densities) and interclass (i.e., land cover class patchiness) heterogeneity. Information entropy (${\mathrm{E}}_{\mathrm{i}})$ or class frequency explains how much each land cover class (p _{i}) contributes to the pixels and is expressed as a fraction of a specific land cover class in a pixel multiplied by its natural logarithm. Two scene classification maps with 5 (SCL-5) and 15 classes (SCL-15) were produced using supervised and unsupervised approaches, respectively. Information from the Urban Atlas layer was used for creating a simpler SCL-5 (containing five classes defined as crops, pasture, water, forest, other) using semi-automatic classification plugin [60] on S2 bands in the QGIS environment (“QGIS Geographic Information System,” 2021) (Figure 4A)). Another SCL-15 map was produced using k-means clustering on the S2 dataset in SAGA with 15 clusters (the same number of land cover types for Braccagni image as in the Urban Atlas layer). Both maps were smoothed out with a 3 × 3 mode (majority) kernel. The spatial heterogeneity coefficient was calculated for every 300 m pixel using land cover frequencies and land cover class variances from scene classification maps. | |

Standard deviation | High values determine higher heterogeneity and lower values lower heterogeneity. The range depends on the range of the predictor, i.e., from 0.03 to 0.22 W m^{−2} um^{−1} sr^{−1} for SIF_{760}, 0.05 to 2.52 m^{2} m^{−2} for LAI. |

The standard deviation is a measure of how dispersed the data are in relation to their mean. Riera et al. [61] used the standard deviation of the NDVI as an expression of vegetation heterogeneity; moreover, Li and Rodell [62] used it as a measure of spatial variability of soil moisture. | |

Ensemble decision trees | High values determine higher heterogeneity and lower values lower heterogeneity. This method converted predictor values to SIF values; therefore, the range was always from 0.03 to 0.22 W m^{−2} um^{−1} sr^{−1} for SIF_{760} and from 0.05 to 0.11 W m^{−2} um^{−1} sr^{−1} for SIF_{687}. |

We assessed the capability of four different machine learning algorithms to predict SIF_{λ,20} as a function of SIF_{λ,300}, and R_{20}: eXtreme Gradient Boosting, Random Forests, support vector machines, and neural networks. The imagery was randomly split into training and validation subsets based on the finest resolution. For training models, 20% of the data (6800 samples) were used for computation economy. We used a k-fold (k = 5) cross-validation approach to assess each algorithm’s performance. Random Forests [58] was the most accurate algorithm. Thus, we made use of this approach to upscale SIF from the FLEX to the S2 spatial resolution. | |

Normalized Entropy | Normalized entropy ranging from 0 to 1, where 1 corresponds to low heterogeneity and 0 to higher heterogeneity. Probability values pi are expressed for sub-pixel locations i inside the FLEX pixel, and their values correspond to the sub-pixel values in S2 or F |

$\mathrm{E}={\sum}_{\mathrm{i}=0}^{\mathrm{N}}({p}_{i}\times {\mathrm{log}}_{2}({p}_{i}\left)\right)$ ${p}_{i}=\frac{{x}_{\mathrm{i}}}{{\sum}_{i=0}^{N}{x}_{i}},\mathrm{where}{x}_{i}-\mathrm{pixel}\mathrm{value}$ ${E}_{max}={E}_{uniform},\mathrm{where}{p}_{i}=\frac{1}{N}$ $\frac{E}{{E}_{max}}-\mathrm{heterogeneity}$ | |

Heterogeneity was quantified using the concept of entropy [64] that measures the average information content. Entropy is maximized when every sub-pixel within the 300 × 300 m FLEX pixel contains the same value (uniform probability distribution, no heterogeneity). Thus, within a 300 m pixel, the maximum possible entropy value for 225 20 m sub-pixels (S2 products) is 7.81 (all p_{i} = 1/225) and for 3600 5 m sub-pixels it is 11.81 (all p_{i} = 1/3600). For each pixel at FLEX resolution (SIF_{λ,300}), we calculated the entropy using each dataset SIF_{λ,5}, S2-VI_{20}, S2-BT_{20}, and S2-R_{20}. We normalized the entropy by the entropy of the uniform distribution (E_{ma}_{x} with N = sub-pixels in a FLEX pixel). This custom “normalized entropy” function was passed as an additional parameter to the python module rasterstats [77]. |

## Appendix B

Method Name | Heterogeneity Definition | Predictors | Heterogeneity Values |
---|---|---|---|

Cluster entropy | Uncovered sub-pixel information by aggregating patterns with a similar distribution. | S2-VI_{20} S2-BT _{20} S2-R _{20} | Uncovered sub-pixel information by aggregating patterns with a similar distribution. |

A set of spatial patterns were extracted from S2-VI_{20}, S2-BT_{20} and S2-R_{single,20} by means of a clustering approach, aggregating patterns with a similar distribution. Analogously, patterns from SIF at 5 m pixel resolution are also extracted. This allows us to compare the uncovered sub-pixel information for both co-registered datasets. For this method, 300 × 300 m patches from SIF and S2 data were extracted, and considering that the SIF spatial resolution is 5 m, each patch contains 60 × 60 sub-pixels or 3600 pixels, whereas for FLEX patches are represented by 15 × 15 or 225 pixels. All the patches containing missing values were discarded, leaving a total of 110 patches for SIF and 114 patches for S2. Nevertheless, only 104 patches of S2 and SIF overlapped and were used for the comparison. We used the SIF _{760} and SIF_{687} as reference data and the S2 reflectance bands and its derived indices as predictors. A Gaussian mixture model (GMM) clustering algorithm [78] grouped the 300 m patches of F_{λ,5} into k = 3 clusters. S2-VI_{20}, S2-BT_{20} and S2-R_{single,20} were clustered into k = 4 groups as they showed higher heterogeneity than the patches of F_{λ,5}. Since cluster labeling was arbitrary, clusters were relabeled from 1 to 3, allowing for comparing Sentinel-2 and F_{λ,5} groups. The capability of the different S2 predictors to capture F_{λ,5} on FLEX scales (300 m) was evaluated using confusion matrices. | |||

Fuzzy approach | Model fluorescence (SIF_{760,20} and SIF_{687,20}) sub-pixels variance in a 300 × 300 FLEX pixel | S2-VI_{20} S2-BT _{20} S2-R _{20} | |

Fuzzy modelling allows for building flexible weighted maps from several variables [79], which can be used as a predictor of a third variable once combined. It is a two-step method where the original variables (VI_{20} or BT_{20}) are first transformed to the range [0, 1] using different “membership” functions. These are selected according to their expected or known relationship with the predicted variable (SIF_{λ} in this case). Then, the transformed variables (membership values) can be combined through various operators [80]. The combined values can then be used as predictors of the variable of interest. In this work, we applied fuzzy modelling to VI _{20} and BT_{20} separately to eventually predict SIF_{λ}. We selected the membership functions so that membership values positively correlated with SIF (Table A3). Membership values computed from VI _{20} or BT_{20} variables were combined using the fuzzy overlay operator GAMMA since it has been reported to offer a balance between over and underestimation of fluorescence radiance [80,81]. μ_γ (x) = 〖[μ_SUM (x)]〗^γ * 〖[μ_PRODUCT (x)]〗^(1 − γ) Then a linear model was fit using the integrated membership values as a predictor of SIF _{λ}: (F_λ) ̂ = b_0 + b_1 μ_γ (x) Fuzzy modelling was applied to 5 and 20 m spatial resolution data, and then these maps were gridded to 300 m pixels. Predicted and observed SIF _{λ} and their intrapixel variability were assessed. |

**Table A3.**Membership functions selected for each spectral index or vegetation parameter and the corresponding justifications according to the expected correlation with fluorescence radiance. Here, x stands for the input variable (predictor), µ for the transformed membership value, m for the mean, and s for the standard deviation. a and b are scaling factors of the mean and the standard deviation and were set to 1 in all the cases.

HyPlant Derived VIs | Membership Functions | Equations | Justifications | Representing Traits | References |
---|---|---|---|---|---|

NDVI | Fuzzy MS Large | $\mu \left(x\right)=1-\frac{bs}{x-am+bs}if$ $x>amotherwise\mu \left(x\right)=0$ | Positive correlation | Greenness Content | [82,83,84] |

Chl-Red edge | Red-edge position | [84] | |||

EVI | Fuzzy Linear | $\mu \left(x\right)=\left\{\frac{x-min}{max-min}\right\}$ | Weak correlation | Biomass | [84,85] |

MSI | Fuzzy MS Small | $\mu \left(x\right)=\frac{bs}{x-am+bs}if$ $x>amotherwise\mu \left(x\right)=1$ | Negative correlation | Canopy water stress | [84,86,87] |

## Appendix C

**Figure A1.**Heterogeneity maps (300 × 300 m) for the standard deviation method: (

**a**) Reference SIF

_{687,5}; (

**b**) Best predictor NIRv; (

**c**) Scatter plot with lowest (red circle) and highest (green circle) heterogeneity pixels highlighted; (

**d**) 5 m pixel with high heterogeneity for SIF

_{687,5}; (

**e**) 20 m pixel with high heterogeneity for NIRv; (

**f**) Scene classification with 15 classes for a pixel with high heterogeneity; (

**g**) 5 m pixel with low heterogeneity for SIF

_{687,5}; (

**h**) 20 m pixel with low heterogeneity for NIRv; (

**i**) Scene classification with 15 classes for a pixel with low heterogeneity.

**Figure A2.**Heterogeneity maps (300 × 300 m) for the ensemble decision trees method: (

**a**) Reference SIF687,5; (

**b**) Best predictor NIRv; (

**c**) Scatter plot with lowest (red circle) and highest (green circle) heterogeneity pixels highlighted; (

**d**) 5 m pixel with high heterogeneity for SIF

_{687,5}; (

**e**) 20 m pixel with high heterogeneity for NIRv; (

**f**) Scene classification with 15 classes for a pixel with high heterogeneity; (

**g**) 5 m pixel with low heterogeneity for SIF

_{687,5}; (

**h**) 20 m pixel with low heterogeneity for NIRv; (

**i**) Scene classification with 15 classes for a pixel with low heterogeneity.

**Figure A3.**Heterogeneity maps (300 × 300 m) for the spatial heterogeneity coefficient method: (

**a**) Reference SIF

_{687,5}; (

**b**) Best predictor NIRv; (

**c**) Scatter plot with lowest (red circle) and highest (green circle) heterogeneity pixels highlighted; (

**d**) 5 m pixel with high heterogeneity for SIF

_{687,5}; (

**e**) 20 m pixel with high heterogeneity for NIRv; (

**f**) Scene classification with 15 classes for a pixel with high heterogeneity; (

**g**) 5 m pixel with low heterogeneity for SIF

_{687,5}; (

**h**) 20 m pixel with low heterogeneity for NIRv; (

**i**) Scene classification with 15 classes for a pixel with low heterogeneity.

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**Figure 1.**Study area, Braccagni, Italy. Map of the area on the left was produced using Sentinel-2 RGB bands (B4-B3-B2).

**Figure 2.**Workflow diagram. (

**a**) HyPlant reflectance image (4.5 × 4.5 m) was aggregated to mimic S2 spectral and spatial resolution (13 bands and 20 × 20 m ~ S2-R

_{20}). At the same time, HyPlant fluorescence products were spatially aggregated to 5 × 5 m resolution (SIF

_{687,5}and SIF

_{760,5}) (see data preparation section). * For the ensemble decision trees method, SIF was additionally aggregated to 300 × 300 m. (

**b**) Synthetic S2-R

_{20}bands were used to obtain the biophysical traits (S2-BT

_{20}) and vegetation indices (S2-VI

_{20}), which were later used to characterize the spatial heterogeneity of SIF (Table 1 and Table 2). (

**c**) The Structural Similarity Index Measure (SSIM) was implemented to filter the input data (i.e., S2 bands, VIs, BT) used in the study. (

**d**) To determine the spatial heterogeneity of a FLEX pixel, a 300 × 300 m grid was applied to the S2 synthetic (S2-R

_{20}, S2-BT

_{20}and S2-VI

_{20}) and SIF (SIF

_{687,5}and SIF

_{760,5}) resampled images. Each FLEX pixel potentially contained 15 × 15 S2 pixels and 60 × 60 SIF 5 × 5 m pixels. (

**e**) Different heterogeneity methods (see methods to characterize sun-induced chlorophyll fluorescence heterogeneity section) were applied to the S2 and HyPlant SIF products using the 300 × 300 FLEX grid defined in step (

**d**). A FLEX heterogeneity product was obtained for each S2 predictor (S2-R

_{20}, S2-BT

_{20}and S2-VI

_{20}) and SIF reference data (SIF

_{687,5}and SIF

_{760,5}). (

**f**) Finally, we compared S2 vs. SIF heterogeneity products using linear regression (see models’ performance section).

**Figure 3.**Tukey’s test applied to the Structural Similarity Index Measure (SSIM) used to measure the similarity between two normalized images (SIF

_{760,20}, SIF

_{687,20}, and respective Sentinel-2 predictors). Dashed vertical lines indicate the similarity threshold of ±0.1 SSIM. Bands with SSIM values above this threshold for both SIF

_{760}and SIF

_{687}were used for further analysis.

**Figure 4.**Scene classification maps: (

**a**) Map produced using supervised classification with 5 classes; (

**b**) Map produced using k-means algorithm with 15 classes.

**Figure 5.**Dataset imagery: (

**a**) Sun-induced fluorescence with 5 × 5 m resolution; (

**b**) Vegetation indices maps from Sentinel-2 data NIRv, NDVI, EVI, ChlRE, MSI with 20 × 20 m resolution; (

**c**) Biophysical traits maps for LCC, fAPAR, fCover and LAI at 20 × 20 m resolution; (

**d**) Reflectance bands maps from Sentinel-2 data B6, B7, B8, B8A, B9 with 20 × 20 m resolution. Values in maps are shown as 2nd and 98th percentiles of the raster band values. Lower values are shown in blue, higher values in red.

**Figure 6.**(

**a**) Histogram of normalized values for sun-induced fluorescence; (

**b**) Vegetation indices; (

**c**) Biophysical traits; (

**d**) Reflectance bands. Notice that all the distributions (

**b**–

**d**) are skewed, compared to (

**a**).

**Figure 7.**Square of Pearson’s correlation coefficient between reference SIF

_{760}and SIF

_{687}heterogeneity and predictors’ heterogeneity: Sentinel-2 derived vegetation indices, biophysical traits, reflectance bands and their stacks using the following methods: (

**a**) Ensemble decision trees; (

**b**) Standard deviation; (

**c**) Local Moran’s I; (

**d**) Spatial heterogeneity coefficient using scene classification with 5 classes (SCL-5); (

**e**) Spatial heterogeneity coefficient using scene classification with 15 classes (SCL-15); (

**f**) Normalized entropy. *** p-value ≤ 0.001; ** p-value ≤ 0.01; * p-value ≤ 0.05, ns—p-value > 0.05.

**Figure 8.**The number of times a pixel (pixel ID shown as numbers next to pixels) was considered an outlier (top 6 RMSE) by ensemble decision trees, spatial heterogeneity coefficient with SCL-15 and standard deviation methods using the most important predictors from each category (i.e., NIRv—vegetation index category, fAPAR—biophysical trait category, B7—reflectance band category) for (

**a**) SIF

_{760,300}, (

**b**) SIF

_{687,300}and (

**c**) the sum of counts for both SIF

_{760,300}and SIF

_{687,300}. The maximum possible count for (

**a**,

**b**) is 9 (three models, three predictors), for (

**c**) 18.

**Figure 9.**Top two outlier pixels (ID 166 and 124) with input data for (

**a**,

**h**) SIF

_{760,5}; (

**b**,

**i**) SIF

_{687,5}; (

**c**,

**j**) NIRv; (

**d**,

**k**) fAPAR; (

**e**,

**l**) B7; (

**f**,

**m**) SCL-5 classes; (

**g**,

**n**) SCL-15 classes. SIF units are W m

^{−2}sr

^{−1}µm

^{−1}, NIRv and fAPAR are unitless; and B7 is in sr

^{−1}. Classes for SCL-5 are water (cyan), cropland (olive), pasture (green), and other (gray), as in Figure 4. Classes for SCL-15 are discrete values and represent spectral rather than land cover classes.

**Figure 10.**Heterogeneity maps (300 × 300 m) for standard deviation, ensemble decision trees and spatial heterogeneity coefficient SCL-15 methods; (

**a**,

**d**,

**g**) reference SIF

_{760}; (

**b**,

**e**,

**h**) best predictor NIRv; (

**c**,

**f**,

**i**) scatter plots with lowest (green circle) and highest (red circle) heterogeneity pixels highlighted.

**Figure 11.**Highest and lowest heterogeneity pixels from best-performing models (standard deviation, spatial heterogeneity coefficient using 15 classes, ensemble decision trees) with input data shown for (

**a**,

**d**) SIF

_{760,5}; (

**b**,

**e**) NIRv

_{20}; (

**c**,

**f**) scene classification map 15 classes.

**Table 3.**Summary of the different methods used to characterize SIF spatial heterogeneity within the FLEX spatial resolution (300 × 300 m). Predictors reported are single-band reflectance at 20 m (S2-R

_{20}); spectral vegetation indices at 20 m (S2-VI

_{20}); biophysical traits at 20 m (S2-BT

_{20}); or a combination of several of these (S2-R

_{multi20}/S2-VI

_{multi20}/S2-BT

_{multi20}).

Method Name | Heterogeneity Definition | Predictors | Reference |
---|---|---|---|

Local Moran’s I | The classification of sub-pixels is based on the spatial autocorrelation metric Moran’s I, whose statistical significance is defined by permutations (bootstrap). Heterogeneity is expressed as the fraction of sub-pixels belonging to the “no class” or “single pixel cluster class” over the total number of sub-pixels in a 300 × 300 FLEX pixel. | S2-VI_{20}S2-BT _{20}S2-R _{20} | [57] |

Spatial heterogeneity coefficient | Interclass and intraclass differences combined with their spatial distribution. Classes are generated using supervised and unsupervised approaches in the form of Scene Classification Maps (SCLs). | S2-VI_{20}S2-BT _{20}S2-R _{20} | [31] |

Standard deviation | Standard deviation over the total number of sub-pixels in a 300 × 300 FLEX pixel. | S2-VI_{20}S2-BT _{20}S2-R _{20} | / |

Ensemble decision trees | Four different machine learning algorithms to predict SIF_{λ,20} as a function of SIF_{λ,300}, and S2-VI_{20}, S2-BT_{20}, S2-R_{20}, S2-R_{multi20}, S2-VI_{multi20}, S2-BT_{multi20}: eXtreme Gradient Boosting, Random Forests, Support Vector Machines, and Neural Networks. The most accurate algorithm (Random Forest) was used to upscale SIF from FLEX to S2 spatial resolution. | S2-VI_{20}S2-BT _{20}S2-R _{20}S2-R _{multi20}S2-VI _{multi20}S2-BT _{multi20} | [58] |

Normalized Entropy | Heterogeneity was quantified using the concept of entropy that measures the average information content. The entropy was normalized by the entropy of the uniform distribution (Emax with N = sub-pixels in a FLEX pixel). | S2-VI_{20}S2-BT _{20}S2-R _{20} | [59] |

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## Share and Cite

**MDPI and ACS Style**

Jantol, N.; Prikaziuk, E.; Celesti, M.; Hernandez-Sequeira, I.; Tomelleri, E.; Pacheco-Labrador, J.; Van Wittenberghe, S.; Pla, F.; Bandopadhyay, S.; Koren, G.;
et al. Using Sentinel-2-Based Metrics to Characterize the Spatial Heterogeneity of FLEX Sun-Induced Chlorophyll Fluorescence on Sub-Pixel Scale. *Remote Sens.* **2023**, *15*, 4835.
https://doi.org/10.3390/rs15194835

**AMA Style**

Jantol N, Prikaziuk E, Celesti M, Hernandez-Sequeira I, Tomelleri E, Pacheco-Labrador J, Van Wittenberghe S, Pla F, Bandopadhyay S, Koren G,
et al. Using Sentinel-2-Based Metrics to Characterize the Spatial Heterogeneity of FLEX Sun-Induced Chlorophyll Fluorescence on Sub-Pixel Scale. *Remote Sensing*. 2023; 15(19):4835.
https://doi.org/10.3390/rs15194835

**Chicago/Turabian Style**

Jantol, Nela, Egor Prikaziuk, Marco Celesti, Itza Hernandez-Sequeira, Enrico Tomelleri, Javier Pacheco-Labrador, Shari Van Wittenberghe, Filiberto Pla, Subhajit Bandopadhyay, Gerbrand Koren,
and et al. 2023. "Using Sentinel-2-Based Metrics to Characterize the Spatial Heterogeneity of FLEX Sun-Induced Chlorophyll Fluorescence on Sub-Pixel Scale" *Remote Sensing* 15, no. 19: 4835.
https://doi.org/10.3390/rs15194835