# Enhancing Solar-Induced Fluorescence Interpretation: Quantifying Fractional Sunlit Vegetation Cover Using Linear Spectral Unmixing

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## Abstract

**:**

_{sunlit}) was used to estimate the (dominant) green APAR flux, and this was combined with the integral of the spectrally resolved fluorescence to calculate the FQE. The results of this study demonstrated that under no-stress conditions and independently of the FVC, similar FQE values were observed when SIF was properly normalised by the green APAR flux. The results obtained showed that the reflectance spectra retrieved using a linear unmixing method had a maximum RMSE of less than 0.03 along the spectrum. The FVC

_{sunlit}evaluation showed an RMSE of 14% with an R

^{2}of 0.84. Moreover, the FQE values obtained at the top of the canopy (TOC) were found statistically comparable to the reference values at the leaf level. These results support further efforts to improve the interpretation of fluorescence based on field spectroscopy and the further upscaling to imaging spectroscopy at airborne and satellite levels.

## 1. Introduction

_{sunlit}), which is necessary to calculate the effective APAR flux at the canopy level [9,34] (RQ I) to obtain the FQE from remote sensing techniques (RQ II).

## 2. Materials and Methods

#### 2.1. Plant Material and Experimental Setup

#### 2.2. Multisensor Setup and Transect Sampling Protocol

_{sunlit}.

#### 2.3. Leaf Fluorescence

#### 2.4. Sunlit Fractional Vegetation Cover Based on MAIA Multispectral Reflectance Images

_{total}) and the reference sunlit fractional vegetation cover (MAIA FVC

_{sunlit}) to validate the FVC

_{total}and FVC

_{sunlit}products derived from the Piccolo hyperspectral point spectroradiometer (Section 2.5).

_{total}. Based on the MAIA FVC

_{total}and a reflectance band 7 threshold, a second mask was created to discriminate between sunlit and shaded leaves, resulting in the reference MAIA FVC

_{sunlit}and MAIA FVC

_{shaded.}For further details see [36].

#### 2.5. Development of Piccolo FVC_{sunlit} Obtained from the TOC Surface Reflectance

#### 2.5.1. Surface Reflectance Unmixing Concept

#### 2.5.2. Extraction of Surface Reflectance Endmembers

_{total}= 0% (n = 26) (Figure 4, ${R}_{soil}$). The pure ${R}_{veg,shaded}$ endmember was obtained by shielding a vegetation area, MAIA FVC

_{total}= 100% (n = 1), from direct sunlight with a panel at the side. Regarding ${R}_{veg,sunlit}$, since it is not possible to measure a spectrum of 100% sunlit vegetation, the strategy was to obtain it indirectly from a TOC total (mixed) vegetation canopy (i.e., sunlit + shaded) and to correct it for the shaded contribution based on the previously obtained ${R}_{veg,shaded}$ endmember. Furthermore, it must be considered that both the sunlit and total vegetation endmembers are composed of a direct and a diffuse illumination component, while the shaded endmember is composed only of the diffuse component [41]. For simplicity, the potted plants were assumed to have a constant vertical structure (i.e., canopy height, leaf density, and leaf area index). A constant ratio between diffuse and direct components was assumed for the sunlit canopies, and a single diffuse component for the shaded canopies.

- ${R}_{veg,total}$ is the reflectance spectrum of all the Piccolo measurements where MAIA FVC
_{total}is higher than 95% (n = 16); - ${w}_{veg,sunlit}$ and ${w}_{veg,shaded}$ are the weight values of sunlit and shaded fractions obtained from the corresponding MAIA reference images, MAIA FVC
_{sunlit,}and MAIA FVC_{shaded}, respectively; Section 2.4 (n = 16); - ${R}_{veg,shaded}$is the shaded endmember reflectance spectrum previously defined (n = 1).

#### 2.5.3. Unmixing Strategy

_{2}, a is the endmember weight and could vary from 0 to 1, X is an m × n matrix (wavelengths × number of endmembers) where X ∈ Rn, and Y ∈ Rm, and Y is the apparent reflectance for each wavelength (m)). Two different approaches were implemented, i.e., approach A, where only soil and mixed vegetation endmembers were considered, and approach B, where three endmembers corresponding to sunlit vegetation, shaded vegetation, and soil were considered. In both cases, the implemented Lawson–Hanson NNLS package in R [42] was used to solve for the contribution (weight and fitted value) of the different signal components. The sum of the estimated weights (${w}_{soil}+{w}_{veg,total}$ or ${w}_{soil}{+w}_{veg,sunlit}+$ ${w}_{veg,shaded})$should be equal to 1. However, in some scenarios, the sum of the weights resulted in values greater than 1. This was proposed to consider other elements present in the scene and the multiple scattering of vegetation, which mainly influences the shaded fraction of vegetation, in the unmixing process [25].

_{total}, Piccolo FVC

_{sunlit}, and Piccolo FVC

_{shaded}when referring to the total (i.e., mixed sunlit and shaded), sunlit, and shaded vegetation fractions, respectively. Finally, to validate the unmixing results, for both approaches A and B, the spectral-fitting-based FVC from the Piccolo measurements was compared with the image-based reference FVC of the MAIA measurements by means of the root-mean-square error (RMSE) between the two data pairs (i.e., for approach A: Piccolo FVC

_{total}vs. Maia FVC

_{total}and Piccolo FVC

_{total}vs. Maia FVC

_{sunlit}; for approach B: Piccolo FVC

_{total}vs. Maia FVC

_{total}, and Piccolo FVC

_{sunlit}vs. Maia FVC

_{sunlit}).

#### 2.6. TOC Fluorescence Retrieval

#### 2.7. Retrieval of Piccolo-Based Green APAR Flux of Sunlit Canopy Fraction and Fluorescence Quantum Efficiency

_{sunlit}previously retrieved:

_{leaf}) was assumed to be constant at 0.84 [9,44,45], and the PAR was spectrally integrated based on photon flux units obtained from the Piccolo’s downwelling radiance channel. The proposed method assumed that the sunlit fraction was the dominant surface triggering fluorescence emission, and that chlorophyll absorption was constant at the leaf level.

_{sunlit}of 1 (i.e., 100% FVC

_{sunlit}). The values obtained for each transect were compared with the results at the leaf level made within a time span of 20 min before and after each transect. The transects without leaf measurements in that time range were discarded for the comparison. Two tests were used to compare the pairwise variance of the data from the different scales. Fligner’s test was used to discriminate between different types of data variance. Either Student’s t-test (equal variances) or Welch’s t-test (unequal variances) was used to compare data pairs. All calculations were performed using the Python library Scipy version 1.1 (“PyPI ⋅ The Python Package Index”, 2021).

## 3. Results

#### 3.1. Surface Reflectance and Reference MAIA FVC

_{total}reference distribution shows, for the range 0–100%, at least 20 measurements for each 10% group, with peaks at both extremes, 0% and 100%, of approximately 45 measurements, and a broad peak of 50 measurements around an FVC

_{total}of 70%. For the values obtained for the MAIA FVC

_{sunlit}and FVC

_{shaded}classified fractions, the distribution of the number of measurements shows a higher number of measurements in the 0–10% range for the former and in the 10–20% range for the latter.

#### 3.2. TOC and Leaf Surface Fluorescence

_{total}(Figure 8A). While the fluorescence values around the 740 nm peak show a gradual increase with the MAIA FVC

_{total}, the fluorescence values at the 687-nm peak remain rather indifferent to the underlying FVC. Interestingly, when FVC

_{total}= 0–10% (i.e., pure soil), although no fluorescence signal should be obtained, values of the order of 1 mW m

^{−2}sr

^{−1}nm

^{−1}were obtained from the TOC measurements. In terms of magnitude, TOC fluorescence values of the first, rather constant, peak are similar to the leaf level (full surface) values, while the 740 nm peak at the TOC given a FVC

_{total}= 100% shows values up by a factor of two compared to the leaf value (Figure 8B).

#### 3.3. Surface Reflectance Spectral Unmixing

_{eff,surface}) was composed of the fitted effective soil and vegetation reflectance (R

_{eff,soil}, R

_{eff,veg,total}), while for the three-endmember case (approach B), it was composed of the fitted components R

_{eff,soil}, R

_{eff,veg,sunlit}, and R

_{eff,veg,shade}. Figure 9 shows several linear fitting examples of both approaches along a range of MAIA FVC

_{total}values. In general, the two-endmember unmixing approach slightly overestimated the fitted surface reflectance spectrum, especially in the region beyond the red edge. In contrast, the results from the three-endmember unmixing approach slightly underestimated the fitted reflectance surface spectrum.

#### 3.4. Validation of the Piccolo FVC_{sunlit} Obtained by Spectral Unmixing

_{total}and MAIA FVC

_{sunlit}reference products (Figure 11). Generally, for both unmixing approaches, the FVC

_{total}was underestimated; in contrast, the FVC

_{sunlit}fraction was overestimated in comparison with the reference values. The difference between Figure 11A,B in the FVC

_{total}ranges is due to the fact that no restrictions were applied to the unmixing NNLS weights, resulting in values greater than one when the FVC

_{sunlit}and FVC

_{shaded}fractions were summed to obtain FVC

_{total}.

_{total}(which integrated sunlit and shaded vegetation) and the MAIA FVC

_{total}was 0.11, with a coefficient of determination (R

^{2}) of 0.88. In addition, the RMSE obtained between Piccolo FVC

_{total}and the MAIA FVC

_{sunlit}was 0.21, with an R

^{2}of 0.86 (Figure 11A). For the three-endmember approach, the Piccolo FVC

_{total}(obtained by adding the unmixed sunlit and shaded weights) and the Piccolo FVC

_{sunlit}were compared with the MAIA FVC

_{total}and MAIA FVC

_{sunlit}, respectively. Compared to the two-endmember approach results, this strategy improved both the correlation factor and the estimated error, with an RMSE between Piccolo FVC

_{total}and MAIA FVC

_{total}of 0.13, (R

^{2}= 0.88) and an RMSE between Piccolo FVC

_{sunlit}and MAIA FVC

_{sunlit}of 0.14, (R

^{2}= 0.84) (Figure 11B).

#### 3.5. Fluorescence Quantum Efficiency

_{sunlit}(R

^{2}= 0.76, Figure 13A,B) compared to FVC

_{total}(R

^{2}= 0.58, Figure 13D,E). Interestingly, the relationship between FQE, calculated with Equation (7), and FVC shows that FQE remains in the range between 0.3 and 0.8% for FVC

_{sunlit}> 20% and FVC

_{total}> 30% (Figure 13C–F). Within this range, further analyses were carried out on the dataset. These are described below.

_{total}were discarded. Considering these points, TOC FQE values were pooled per transect (average of 18 samples per transect) and compared with the leaf FQE values (average of five samples per transect). From the t-test analysis (p-value = 0.05) of the eleven TOC FQE vs. leaf FQE pairs, only four cases showed statistical differences (25-Salvia 1, 25-Salvia 3, 26-Salvia 1, 28-Datura 1).

## 4. Discussion

_{total}from 0 to 100% (Figure 6 and Figure 7), having a peak at 70 measurements for 0–10% FVC

_{sunlit}and decreasing to 16 measurements for 80% FVC

_{sunlit}(Figure 6).

_{eff,soil}, R

_{eff,veg,total}, approach A) and a three-endmember (R

_{eff,soil}, R

_{eff,veg,sunlit}, and R

_{eff,veg,shade}, approach B) approach. When comparing the reference and fitted reflectance spectra, the results showed that decomposing the signal using three endmembers provided better results than with two endmembers, reducing the averaged spectral RMSE between the actual reflectance spectrum and the fitted spectrum from 0.03 to 0.01 (Figure 10). The largest difference in terms of RMSE was observed after the red edge, in the NIR range. This can be explained by the nonlinear behaviour of the canopy’s multiple scattering caused by the interaction of the light within the canopy [18]. Moreover, this is the reason why the three-endmembers provided better results than the two-endmember approach. The addition of a shaded vegetation endmember introduced a diffuse component into the fit. This improved the results of the spectral vegetation unmixing in the NIR range in [25].

_{sunlit}and FVC

_{shaded}provided values greater than one.

_{total}and FVC

_{sunlit}, both the two-endmember and three-endmember approaches provided accurate results when comparing Piccolo FVC

_{total}and MAIA FVC

_{total}(R

^{2}= 0.88 and RMSE = 0.11–0.13). However, only the three-endmember approach was able to discriminate between FVC

_{total}and FVC

_{sunlit}, improving the estimation of FVC

_{sunlit}(RMSE = 0.14) compared to using the two-endmember approach’s FVC

_{total}used as an estimation of the sunlit fraction (RMSE = 0.21) (Figure 11). Nevertheless, the results obtained in this study are in the same order of magnitude as other works where more complex hyperspectral unmixing methods have been proposed [50,51,52].

_{sunlit}(R

^{2}= 0.76) is higher than when correlated with FVC

_{total}(R

^{2}= 0.58), corroborate the hypothesis that the measured TOC SIF is mainly emitted by sunlit leaves [16,17]. Hence, both ${\mathrm{J}}_{A,greensunlit}$ and the total calculated fluorescence flux (${\mathrm{J}}_{F,total}$) show a strong relationship with the FVC

_{sunlit}. The combination of these two terms allows us to decouple the changes in ${\mathrm{J}}_{F,total}$ dynamics driven only by the physiological component [9].

_{sunlit}below 20%, similar FQE values were obtained throughout the experiment regardless of the vegetation fractional cover (Figure 12C). These results support the hypothesis that under equal environmental conditions, and without any applied stress such as drought or nitrogen excess/deficit, similar FQE values should be obtained (Figure 13). An accurate estimation of FQE is essential for a quantitative interpretation of SIF and its role in early plant stress detection. Regarding the high FQE values obtained when FVC

_{sunlit}< 20%, these results could be explained by the positive (and overestimated) SIF values retrieved over samples where bare soil predominates in the measurement transect (Figure 8, red lines). In this study, unfortunately, these observations indicate an overestimation of the retrieved values obtained by the Specfit method in cases with a low FVC. These results are consistent with the findings in [43], where a decrease in performance is observed with a low LAI. These results do not alter the findings of the present study but suggest a revision of the proposed retrieval method when low FVC values are investigated. Consequently, measurements with FVC

_{total}lower than 20% were discarded for the comparison between TOC and leaf level measurements (Figure 14).

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**A**) Experimental setup. (

**B**) Platform with the instruments onboard; (

**C**,

**D**) exemplars of thorn apple and mealy sage, respectively.

**Figure 2.**Examples of soil, sunlit and shaded classification for four MAIA images, with different amounts of FVC for thorn apple (98%

**top left**, and 68%

**bottom left**) and mealy sage (99%

**top right**, 40%

**bottom right**).

**Figure 3.**Abstraction of vegetation signal components acquired by the Piccolo sensor used to obtain the sunlit and shaded vegetation reflectance endmembers.

**Figure 4.**Endmember spectra implemented for the unmixing. ${R}_{veg,total}$ is the reflectance spectrum of all the Piccolo measurements where MAIA FVC

_{total}is higher than 95% (n = 16). ${R}_{veg,shaded}$ is the shaded vegetation reflectance spectrum (n = 1). ${R}_{veg,sunlit}$ is the vegetation spectrum obtained indirectly from ${R}_{veg,total}$ corrected for the shaded contribution (${R}_{veg,shaded}$ endmember). The ${R}_{soil}$ spectrum was obtained from the average of pure soil surface measurements (n = 26). Both ${R}_{eff,veg,sunlit}$ and ${R}_{eff,veg,shaded}$ are the effective reflectance components of the sunlit and shaded vegetation fractions of the ${R}_{veg,total}$ spectrum.

**Figure 5.**Diagram summarising the methodology applied to obtain the top of the canopy’s fluorescence quantum efficiency (FQE) and its comparison to the leaf reference value. It represents the processing chain of the different products obtained from the FluoWat, Piccolo, and MAIA systems, as well as the processing chain to retrieve the necessary variables to obtain the FQE.

**Figure 6.**Histogram of the number of fractional vegetation cover (FVC) measurements obtained from the MAIA images for each type of vegetation fraction (sunlit, shaded, and total), showing the well-represented FVC distribution in the experimental setup.

**Figure 7.**Example of the Piccolo-measured surface reflectance (R

_{surface}) dataset obtained along a transect with different vegetation cover densities. This transect was measured from 10:30 to 11:05 UTC on 26 July, starting from full vegetation cover to full bare soil. The spectra are coloured based on the MAIA FVC

_{total}value obtained using the classification protocol described. The shaded areas indicate the (small) standard deviation of each measurement (n = 15).

**Figure 8.**(

**A**) Top of the canopy’s fluorescence spectra retrieved with the Specfit method for the same transect shown in Figure 7. (

**B**) Example of leaf fluorescence spectra measured with the FluoWat leaf clip for three leaves sampled within the time range of the TOC transect sampling. In plot (

**B**), the shaded areas represent the standard deviation.

**Figure 9.**Five examples of the measured and fitted surface reflectance (R

_{surface}) and its components using the 2-endmember (

**A**) or 3-endmember strategy (

**B**). The FVC

_{total}is from the MAIA reference values.

**Figure 10.**Absolute error of all 321 surface reflectance spectra (grey lines) and the RMSE (red line) between the measured and fitted top of canopy reflectance spectra for the 2-endmember (

**A**) and the 3-endmember (

**B**) fitting strategies.

**Figure 11.**Comparison of Piccolo spectral-based vegetation cover for the total and sunlit components with the MAIA reference products FVC

_{total}and FVC

_{sunlit}. For the 2-endmember strategy (

**A**), FVC

_{total}does not differentiate between sunlit and shaded vegetation, and for the 3-endmember strategy (

**B**), FVC

_{total}is the sum of unmixed sunlit and shaded weights.

**Figure 12.**Examples of top of the canopy measurements showing the photon flux received, absorbed, and emitted by the vegetation surface. The fractional vegetation cover decreasing (

**A**–

**D**), and the FQE are shown to analyse the differences. In the legend, the PAR, green APAR, and SIF are shown, each represented by a line. The coloured area below each line represents the integrated value used to calculate the FQE, with ${\mathrm{J}}_{A,greensunlit}$ (green area) and ${\mathrm{J}}_{F,total}$ (red area).

**Figure 13.**Correlation between green APAR, SIF, and FQE with the reference FVC

_{sunlit}(

**A**–

**C**) and FVC

_{total}(

**D**–

**F**).

**Figure 14.**Comparison between the FQE obtained at the TOC (Piccolo-based) and at the leaf level (FluoWat) for each transect. Due to the sampling strategy, the number of measurements at the canopy and leaf levels varies between transects. The average number of samples for TOC FQE values is 18 samples per transect. The average number of samples for the leaf FQE values is 5 samples. * indicates a pair with statistical differences (p-level = 0.05).

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## Share and Cite

**MDPI and ACS Style**

Moncholi-Estornell, A.; Cendrero-Mateo, M.P.; Antala, M.; Cogliati, S.; Moreno, J.; Van Wittenberghe, S.
Enhancing Solar-Induced Fluorescence Interpretation: Quantifying Fractional Sunlit Vegetation Cover Using Linear Spectral Unmixing. *Remote Sens.* **2023**, *15*, 4274.
https://doi.org/10.3390/rs15174274

**AMA Style**

Moncholi-Estornell A, Cendrero-Mateo MP, Antala M, Cogliati S, Moreno J, Van Wittenberghe S.
Enhancing Solar-Induced Fluorescence Interpretation: Quantifying Fractional Sunlit Vegetation Cover Using Linear Spectral Unmixing. *Remote Sensing*. 2023; 15(17):4274.
https://doi.org/10.3390/rs15174274

**Chicago/Turabian Style**

Moncholi-Estornell, Adrián, Maria Pilar Cendrero-Mateo, Michal Antala, Sergio Cogliati, José Moreno, and Shari Van Wittenberghe.
2023. "Enhancing Solar-Induced Fluorescence Interpretation: Quantifying Fractional Sunlit Vegetation Cover Using Linear Spectral Unmixing" *Remote Sensing* 15, no. 17: 4274.
https://doi.org/10.3390/rs15174274