A new vegetation index combination for leaf carotenoid-to-chlorophyll ratio: minimizing the effect of their correlation

ABSTRACT The ratio of leaf carotenoid to chlorophyll (Car/Chl) is an indicator of vegetation photosynthesis, development and responses to stress. However, the correlation between Car and Chl, and their overlapping absorption in the visible spectral domain pose a challenge for optical remote sensing of their ratio. This study aims to investigate combinations of vegetation indices (VIs) to minimize the influence of Car-Chl correlation, thus being more sensitive to the variability in the ratio across vegetation species and sites. VIs sensitive to Car and Chl variability were combined into four candidates of combinations, using a simulated dataset from the PROSPECT model. The VI combinations were then tested using six simulated datasets with different Car-Chl correlations, and evaluated against four independent datasets. The ratio of the carotenoid triangle ratio index (CTRI) with the red-edge chlorophyll index (CIred-edge) was found least influenced by the Car-Chl correlation and demonstrated a superior ability for estimating Car/Chl variability. Compared with published VIs and two machine learning algorithms, CTRI/CIred-edge also showed the optimal performance in the four field datasets. This new VI combination could be useful to provide insights in spatiotemporal variability in the leaf Car/Chl ratio, applicable for assessing vegetation physiology, phenology, and response to environmental stress. Trial registration: Clinical Trials Registry India identifier: CTRI/..


Introduction
The pigments in plant leaves include among other things chlorophylls (Chl) and carotenoids (Car), which play significant parts in plant physiological processes and vegetation functions (Croft and Chen 2018;Miraglio et al. 2019;Sun et al. 2019;Sonobe et al. 2020).Chlorophyll is the primary pigment of plant photosynthesis as it converts absorbed radiation energy into stored chemical energy by collecting sun light (Croft et al. 2015;Sun et al. 2019;Croft et al. 2020;Spafford et al. 2021).Carotenoids, on the other hand, plays an auxiliary role in plant photosynthesis through transferring the absorbed radiation energy to Chl (Hernández-Clemente, Navarro-Cerrillo, and Zarco-Tejada 2012).Remote sensing is a non-destructive method applicable at large-scales and has been widely applied for estimating leaf biochemical and biophysical properties.However, remote sensing of the Car/Chl ratio have received much less attention than Chl or Car alone as many studies assumed that Chl and Car are highly correlated, causing the ratio Car/Chl to be a fixed value (Danner et al. 2019;Li et al. 2020).
Under normal growing conditions, both Car and Chl are low in the beginning of the growing season, and high at the peak of the growing season.This means that under these conditions, the ratio of the two is static, and a fixed value can be assumed.However, at high temperatures, nutrient stress or leaf senescence, Car tends to decline more slowly than Chl, leading to deviation from such a static fixed value (Zhou et al. 2019;Gitelson 2020;Zhong et al. 2020).The ratio between Car and Chl has also been reported to differ between plant species (Merzlyak et al. 1999;Zhou et al. 2019;Ivanov et al. 2020).Therefore, accurate remote sensing methods for estimating Car/Chl ratio could be a great tool to monitor vegetation physiology, phenology and impact of environmental stress on plants.
Remote sensing of the Car/Chl ratio face two main challenges: the first is the overlapping contribution of Car and Chl as well as Car and anthocyanins (Anth) in the spectral range of 400-550 nm, which makes it difficult to separate Car from Chl and Anth in a quantification based on spectral properties, and hence affecting the accuracy of Car/Chl estimation (Hernández-Clemente, Navarro-Cerrillo, and Zarco-Tejada 2012; Kong et al. 2016;Féret et al. 2017).The second challenge is the strong covariation between Car and Chl: with increasing correlation between Car and Chl, the variation of their ratio becomes smaller, making the dynamics less likely to be reflected based on spectral properties.Hence, for improving our ability in remote sensing of the Car/Chl ratio, we need to find a VI combination able to separate the variability in dynamics of Car and Chl.
In the past years, several VIs have been proposed for estimating the Car/Chl ratio.Penuelas, Baret, and Filella (1995) constructed a structural insensitive pigment index (SIPI) which minimized the effect of leaf surface and mesophyll structure on the estimation of Car/Chla.Filella et al. (2009) demonstrated that the photochemical index (PRI) can accurately capture long-term changes of Car/ Chl.Gitelson (2020) proposed to use the leaf absorption coefficient to retrieve Car/Chl.Gamon et al. (2016) demonstrated that the chlorophyll/carotenoid index (CCI) could be an indicator of Car/Chl.However, these published VIs were based on experimental datasets of few plant species and were thereby limited in generalizability (Féret et al. 2011;Zhou et al. 2017;Sonobe et al. 2020).
Radiative transfer models (RTM) have a rigorous physical foundation and can be used to evaluate the sensitivity of VIs to leaf biochemical properties (Liang et al. 2015;Féret et al. 2017).Zhou et al. (2019) proposed CARI/CI red-edge for estimating the Car/Chl ratio allowing improved generalization ability, but their relationship was considerably affected by the correlation between Car and Chl (hereafter referred to as the Car-Chl correlation) (Esteban et al. 2015;Gitelson 2020).
An optimal VI should be sensitive to the parameter of interest, while being insensitive to other disturbing factors (Verstraete and Pinty 1996;Li and Wang 2001;Liang et al. 2015Liang et al. , 2016)).This study aims to propose a new VI combination less affected by the Car-Chl correlation and thereby being more robust for estimating the variability in the Car/Chl ratio.The following steps were implemented: (i) constructing candidate VI combinations in the form of Car indices divided by Chl indices; (ii) analyzing the sensitivity of these VI combinations to the Car-Chl correlation using simulated datasets derived from PROSPECT-D; (iii) validating the VI combination least sensitive to the correlation using four datasets of field observations; (iv) comparing the performance of the proposed VI combination for Car/Chl retrieval against seven previous-proposed VIs and two machine learning algorithms using the four datasets of field observations.

Datasets observed in the field
Four independent datasets based on field observations involving different vegetation species, sites and growing stages have been used in this study (See further in Supplementary S1 in Table A1).They included in total 1398 leaf samples belonging to more than 100 woody and herbaceous vegetation species.The first dataset DOGWOOD-2 was collected at Mead Nebraska (USA), including 51 leaves of the Siberian dogwood (Gitelson, Keydan, and Merzlyak 2006).The second one, BM, was obtained in Nanjing, China in the summer of 2015, containing 53 fresh leaf samples from eight different species (Qiu et al. 2018).The third dataset IFGG contained 38 herbaceous species of 734 leaf samples collected from botanical garden of the Karlsruhe Institute of Technology (KIT) from May to November (Kattenborn, Schiefer, and Schmidtlein 2017).The last dataset CABO included 560 fresh leaves from 68 woody and herbaceous species of the Canadian Airborne Biodiversity Observatory (CABO) (Kothari et al. 2022).Datasets DOGWOOD-2 (see https://www.researchgate.net/publication/319213426_Foliar_reflectance_and_biochemistry_5_data_sets),IFGG and CABO are available online (https://ecosis.org/).
Leaf reflectance spectra in dataset DOGWOOD-2 were collected by an Ocean Optics USB2000 radiometer.Leaf reflectance spectra in dataset BM were measured by an ASD FieldSpec spectroradiometer with the spectral sampling interval of 1.4 nm in the spectral domain from 400 nm to 1000 and 2 nm in the spectral domain from 1000 nm to 2500 nm.Leaf reflectance spectra in datasets IFGG and CABO were acquired by an ASD FieldSpec3 and FieldSpec4 respectively.A more detailed description on leaf reflectance spectra measurements with spectroradiometer can be found in Supplementary S2 spectral measurements.Reflectance measurements were calibrated against a white Spectralon 99% reflectance standard and corrected for stray light (Kothari et al. 2022).Further, all spectral reflectance spectra were resampled to 1 nm interval.The pigment estimation protocols were generally similar among the four experimental datasets.Following hyperspectral measurements, leaf disks were immediately sampled using a cork bore and subsequently ground in a chilled mortar with organic solvents to extract pigments.The pigment content determination of pigments was then performed with spectrophotometers following the Lightenthaler (1987) method and equations.Note that the pigments of dataset IFGG were derived by means of a look-up table, and the estimation accuracy of pigments of the look-up table was validated by lab spectroscopy methods as mentioned above with 20 samples leaves.For details on the protocols used in conducting the experiments see (Gitelson, Keydan, and Merzlyak 2006;Kattenborn et al. 2018;Qiu et al. 2018;Kothari et al. 2022).The main characteristics of the four datasets are provided in Table 1.
The Car-Chl correlation in the four datasets ranges from nearly uncorrelated in DOGWOOD-2 (Pearson correlation coefficient; R = 0.12) to highly correlated in datasets IFGG and CABO (R = 0.89), with that of BM lying in the middle (R = 0.71, Figure 1).Thus, the four datasets were used to assess the sensitivity of the constructed VI combinations (section 2.2) to Car/Chl and Car-Chl correlation.

Simulated datasets
PROSPECT is a generalized plate model that considers a leaf as a series of absorbing layers separated by N-1 air spaces (variable N is an imaginary parameter that considers the leaf structure) (Jacquemoud and Baret 1990).With a strict physical basis to account for the light propagation within a leaf, it could simulate the leaf directional-hemispheric reflectance and transmittance from 400 and 2500 nm with input leaf biochemical and structural parameters (Jacquemoud and Baret 1990).Several versions of this model have been derived (Jacquemoud and Baret 1990;Féret et al. 2008Féret et al. , 2017Féret et al. , 2021)).Among them, one of the latest version, PROSPECT-D, was used to generate the synthetic datasets, which uses leaf Chl, Car, Anth, brown pigments, equivalent water thickness (EWT), dry matter (LMA) contents and the leaf structure parameter (N) as input parameters (Féret et al. 2017).
In this study, seven simulated datasets were generated by the PROSPECT-D model: Dataset A and Datasets 1-6 (2000 samples in each dataset).Dataset A was used to construct VI combinations, and the Car-Chl correlation in Dataset A was set to be the same as Sun et al. (2019) of 0.86.Datasets 1-6 were used to analyze the sensitivity of the relationships between the VI combinations and Car/ Chl to the Car-Chl correlation, with the Car-Chl correlations increasing sequentially from being comparatively uncorrelated to highly correlated (Datasets 1-6, R = 0.10, 0.40, 0.55, 0.75, 0.85, and 0.95).
According to the sensitivity analysis of the PROSPECT model (Spafford et al. 2021), the values of EWT and LMA can be set to static because their contributions to leaf reflectance in the visible and near-infrared domain were minimal.Féret et al. (2011) found that the contents of leaf Car and Chl can be fitted with a normal distribution, thus in this study combinations of Chl, Car, Anth and the structural parameter were randomly generated through multivariate normal distribution of 'mvnrnd' function in Matlab based on Table 2 (Sun et al. 2019).Subsequently, leaf reflectance spectra of the six simulated datasets were derived by running the PROSPECT-D model in the forward mode.Gaussian noises with a standard deviation of 4% of the reflectance amplitude were added to the simulated reflectance of each wavelength to take into account measurement inaccuracies (Féret et al. 2011;Locherer et al. 2015).Table 3 summarized the basic statistics about the Car/Chl ratio of the simulated datasets.

Construction of candidate VI combinations
In this study, 16 published VIs for Car and Chl estimation respectively were adopted, including the index forms of normalized difference indices, simple ratio indices, red-edge and green band-based indices, reciprocal spectral indices and modified indices (Table 4).Before constructing VI combinations for estimating the Car/Chl ratio, the ability of these indices to detect Car or Chl variability respectively was first investigated in correlation analysis using synthetic Dataset A. The VIs with R > 0.90 towards Chl and VIs with R > 0.60 towards Car were respectively selected.For the selected VIs, VI combinations for estimating the Car/Chl ratio were constructed by dividing indices detecting Car variability by indices detecting Chl variability.

Sensitivity analysis of VI combinations
The sensitivity of the constructed candidate VI combinations to the Car-Chl correlation was analyzed using the six simulated datasets with different Car-Chl correlations (Datasets 1-6).The relationship between a VI combination and Car/Chl was fitted by linear regression, and if the relationship was relatively robust across the six simulated datasets with varying Car-Chl correlation, the VI combination was considered less sensitive to the Car-Chl correlation, and thus the optimal VI combination was proposed.However, simulated datasets could not represent the actual circumstances of experimental datasets, therefore this study also used four datasets observed in the field with different Car-Chl correlations to further demonstrate the applicability of the proposed VI combination to estimate Car/Chl.

2.4
The evaluation of the optimal VI combination

Comparison with previous VIs
To evaluate the performance of the proposed VI combination in estimating the Car/Chl ratio, seven previously published VIs (Table 5) for estimating the Car/Chl ratio were adopted and their performance was compared with the proposed VI using the four datasets of field observations.Linear regressions were fitted between each VI and Car/Chl, and five-fold cross-validation was applied to estimate the accuracy of the regression models.The VI of PRI was adopted both for Car estimation in section 2.2 to construct candidate VI combinations and for Car/Chl estimation here.PRI can indicate part of Car changes as it was initially developed to track the changes in the levels of xanthophylls (Table 4).PRI measures the relative reflectance between the two bands of 531 and 570 nm.As the band of 531 nm is affected by both Chl and Car absorbance while the band of 570 nm is only affected by Chl according to Sims and Gamon (2002), PRI can also be used for Car/Chl estimation.

Comparison with two machine learning (ML) algorithms
The effectiveness of the proposed VI combination was also proved by comparing with machine learning (ML) models.Support vector machine (SVM) is a non-parametric modeling technique based on the principle of structural risk minimization, which was found to be effective to solve hyperspectral task (Liang et al. 2016;Chen et al. 2021).Principal component analysis (PCA) is a classic mathematical method for extracting features (Maćkiewicz and Ratajczak 1993).In this study, we used SVM model and PCA coupled with multivariable linear regression model as comparison.(Gitelson, Keydan, and Merzlyak 2006)

Evaluation indicators
The coefficients of determination (R²) of the inversion models (SVM, PCA and linear regressions of VIs) and root mean square error (RMSE) were used to evaluate the performance of the model: where y ′ j and y j represent the estimated and measured Car/Chl for sample j respectively.y is the mean value of y j , and n is the number of samples.
Further, regression receiver operating characteristic (RROC) curves have been considered for evaluating the performance of inversion models.RROC curve is a two-dimensional space representing the sum of over-estimation against the sum of under-estimation, plotted on the X-and Y-axis, respectively.The closer the RROC curve of the inversion model is from the RROC heaven (point of (0,0) in RROC space), the better the performance of the inversion model is.The area over the RROC curve (AOC) was also employed as the evaluation indicator of inversion models in this study.The lower the AOC the better accuracy of the model.
where s represent the population variance of errors between estimated and measured Car/Chl, and n is the number of samples.

Construction of candidate VI combinations
In general, the relationships between Chl and its relevant VIs were better than those of Car (Figure 2).To guarantee the sensitivity towards Car/Chl, only VIs related to Chl with R above 0.90 and VIs related to Car with R above 0.60 were respectively considered in a candidate VI combination.For Chl, SR exhibited the highest correlation (R = 0.99), followed by CI red-edge , ND705 and OSAVI2 which also showed strong correlations.For Car, CTRI was selected among the investigated VIs as it showed the highest relationship with Car (R > 0.60).Hence, we constructed four candidate VI combinations to predict Car/Chl by dividing CTRI selected for Car with the four selected Chl indices (Table 6).

Analysis of simulated datasets
The performance of the four VI combinations was all affected by the changes of Car-Chl correlation to different extents, and the higher the Car-Chl correlation, the less sensitive each index was in general to Car/Chl (Figures 3 and 4).However, the combination of CTRI/CI red-edge exhibited more consistent good relationships with Car/Chl variability (with the highest R 2 and the lowest RMSE with respect to each simulated dataset) and was least affected by the changes of Car-Chl correlation in comparison with the other three VI combinations (Figures 3 and 4).
For the other three candidate VI combinations, the worst relationship with Car/Chl ratio was observed for CTRI/SR, with the lowest R² and the highest RMSE over all simulated datasets.The changes of Car-Chl correlation had a great influence on CTRI/SR ∼ Car/Chl relationship, as the RMSE of CTRI/SR varied greatly in the six simulated datasets, from 0.157 in Dataset 1 to 0.094 in Dataset 5 (Figure 3(b)).In comparison, the VI combinations of CTRI/ND, CTRI/CI red-edge and CTRI/OSAVI2 were less sensitive to Car-Chl correlation, with CTRI/ CI red-edge being the most insensitive combination.

Analysis of field datasets
With the increase of Car-Chl correlation (R) from 0.12 in DOGWOOD-2 to 0.89 in CABO, the sensitivity of all VI combinations to Car/ Chl deteriorated (Figure 5(a)), which was consistent with the results of the simulated datasets in Figure 3.In comparison with the other VI combinations, the proposed CTRI/CI red-edge exhibited the least sensitivity to Car-Chl correlation due to the minimal variation in R 2 and RMSE over four experimental datasets (Figures 5 and 6).Further, the proposed CTRI/CI red-edge exhibited robust sensitivity to Car/Chl ratio across four experimental datasets.The CTRI/SR was considerably affected by the Car-Chl correlation and showed worst sensitivity to Car/ Chl, also consistent with the results using simulated datasets.The performance of CTRI/ND and CTRI/OSAVI2 was similar.

Evaluation against VIs previously-proposed and ML
As ML has great potential to retrieve leaf biochemical parameters and several VIs have been previously proposed for Car/Chl estimation (Penuelas, Baret, and Filella 1995;Filella et al. 2009;Gamon et al. 2016;You et al. 2017;Zhou et al. 2019;Gitelson 2020;Sonobe et al. 2020), we compared the performance of the proposed CTRI/CI red-edge with seven published VIs as well as SVM and PCA through linear regression models and 5-fold cross-validation (Table 7).
For all field datasets, CTRI/CI red-edge achieved the highest accuracy of Car/Chl estimation, with both the highest R² and the lowest RMSE.CARI/CI red-edge and (α500/α700)−1 also had good estimation results in all experimental datasets, though inferior to that of CTRI/CI red-edge .Several of the previously published VIs, like RVI, CCI, PRI and α500-α660 did not present a consistent performance among different datasets.For example, CCI had a relatively good estimation of Car/Chl based on DOGWOOD-2 and BM dataset (R² = 0.61; R 2 = 0.43), but not for IFGG and CABO (R² = 0.17; R 2 = 0.03).The SIPI index showed poor results towards Car/Chl variability, with R² < 0.3 in all experimental datasets.For the two ML algorithms, SVM only had higher accuracy in dataset DOG-WOOD-2 with R 2 of 0.81 in comparison with previously-published VIs, but was inferior to the  Table 7. Performance of the proposed CTRI/CI red-edge , support vector machine (SVM) model, principal component analysis (PCA) and other seven published indices for the estimation of Car/Chl with linear models and 5-fold cross-validation, using four experimental datasets.proposed CTRI/CI red-edge .PCA showed poor results towards Car/Chl variability across all experimental datasets.Also, the RROC curve of CTRI/CI red-edge and points of CTRI/CI red-edge in RROC space were closer to (0,0) in comparison with other models, which indicated that CTRI/ CI red-edge was superior to other models (Figures 7 and 8, black lines and dots).To conclude, the proposed VI combination CARI/CI red-edge is a superior method for estimating Car/Chl compared with the previous VIs as well as the SVM and PCA.

Factors influencing Car-Chl correlation
Several factors influence the correlation between leaf Car and Chl, such as vegetation species, growth stages and environmental stresses (Gamon et al. 2016;Gitelson 2020).In a growing season, Car and Chl are both low in the beginning and high at the peak, which means that Car and Chl have high correlation.During leaf senescence, though both leaf Car and Chl contents decrease, the synthesis of Chl is prevented by an abscission layer that forms from the cells near the leaf stem and thereby declines more rapidly than Car, hence the covariance of the two changes (Gitelson and Merzlyak 1994a;Croft and Chen 2018).
Figure 7.The regression receiver operating characteristic (RROC) curve of inversion models (the total over-estimation and the total under-estimation were plotted on the X-and Y-axis respectively).The closer the RROC curve of the inversion model is from the RROC heaven (point of (0,0) in RROC space), the better the performance of the inversion model is.The smaller the area over the RROC curve (AOC, calculated in Table 7), the higher the accuracy of the model.In case of environmental stresses, the responses of leaf Car and Chl contents differ.Under low temperature, salinity and drought, the contents of leaf Car (such as violaxanthin, antheraxanthin and zeaxanthin significantly) increase, while Chl decreases in response to chilling and drought and highly increases under salinity (Esteban et al. 2015).This is related to the biochemical processes within a leaf.Under low temperature, for example, leaf Chl decreases with the decrease of enzyme activity, while leaf Car increases as the of xanthophyll cycle increases for energy dissipation of the excessive absorbed light from decreased photosynthetic rate (Demmig-Adams and Adams III 1996).These factors can also explain the different Car-Chl correlations of the four independent field datasets used in this study that varied from 0.12 to 0.89.

Effect of Car-Chl correlation on Car/Chl estimation
Previous studies have shown that the changes of Car-Chl correlation hampers the estimation of Car/Chl ratio (Zhou et al. 2019).Considering that Car-Chl correlation variation is common because of different factors, we investigated the sensitivity of the four candidate VI combinations to Car-Chl correlation to improve the robustness for Car/Chl estimation.As displayed in Figures 3 and 5, the suggested VI combinations for Car/Chl estimation were differently influenced by Car-Chl correlations.Among the candidate VI combinations, the proposed combination of CTRI/CI red-edge demonstrated the closest relationship with Car/Chl as well as the least sensitivity to Car-Chl correlations based on simulated and field datasets.In addition, the performance of VI combinations in estimating Car/Chl using the synthetic datasets were significantly worse than that using the field datasets, probably due to that Anth was set higher in synthetic datasets than experimental datasets, affecting Car estimation accuracy (Figures 3 and 5).This can be proved by the result that the relationships between Chl and the related VIs were generally better than those between Car and the related VIs in Figure 2.

Comparison with previously-proposed VIs and ML algorithms
In the past decades, several VIs have been developed for Car/Chl, usually based on bands in the red, green and red-edge spectral regions (Hennessy, Clarke, and Lewis 2020).Compared with the seven published VIs and two ML algorithms in section 2.4, the estimation of Car/Chl through CTRI/CI red- edge was superior to all previously developed VIs, SVM and PCA in the four field datasets across vegetation species and sites (Table 7).These indicate that CTRI/CI red-edge is more robust and effective for Car/Chl estimation at foliar level.The spectral reflectance at 800 nm in CTRI index could eliminate the effects of light scattering caused by the leaf surface (Kong et al. 2016).Furthermore, the spectral reflectance at 531 nm in CTRI was initially proposed for xanthophyll pigments and thus sensitive to Car (Filella et al. 2009;Kong et al. 2016).In addition, a normalization in CTRI using the band of 550 nm, which is strongly correlated with Chl, may attenuate the effects of Chl in the estimation of Car.Therefore, CTRI/CI red-edge may hold more potential than other VIs to assess the Car/ Chl variability.
For the seven published VIs, SIPI exhibited the worst estimation results of Car/Chl in all datasets.This may be due to that SIPI was initially developed for Car/Chla estimation using a few limited field datasets (Penuelas, Baret, and Filella 1995).In addition, numerous studies have shown that the spectral reflectance at 500 nm, along with neighboring bands, has the strongest correlation with Car (Gitelson, Keydan, and Merzlyak 2006;Zhou et al. 2017).Hence, the absorption band at 445 nm in the SIPI which may not accurately capture the variation in Car.For RVI, CCI, PRI and α500-α660 all showed considerable instability across the four field datasets.RVI only had a relatively good estimation of Car/Chl in dataset IFGG of herbaceous species, but exhibited worst estimation results in the other datasets containing woody species.Further, Yang et al. (2010) found that RVI was good correlated with Car/Chl in Festuca arundinaceous species, which belonged to herbaceous.This might suggest that RVI may be more suitable for the estimation of Car/Chl of herbaceous species.
The performance of the two absorption coefficients of (α500/α700)−1 and α500-α660 were not as good as that shown in Gitelson (2020), which may be due to that (α500/α700)−1 and α500-α660 cannot stably capture the changes of Car/Chl across different plant species (Danner et al. 2021).PRI was originally developed to indicate changes in the xanthophyll cycle pigment changes.In fact, it was also widely used to retrieve Car and Car/Chl in previous studies (Sims and Gamon 2002;Filella et al. 2009;Kong et al. 2016).However, PRI showed worst performance for the estimation of Car/Chl in DOGWOOD-2 and CABO datasets.The discrepancy can be explained by the fact that the role of Car/Chl in driving PRI varies across different vegetation species, conditions and timescales (Song and Wang 2022;Gamon 2015).

Practical challenges and limitations
Though the proposed CTRI/CI red-edge is most sensitive to Car/Chl and least sensitive to Car-Chl correlation with respect to other candidates and previous published VIs, its performance was still unsatisfactory in dataset CABO with a high Car-Chl correlation (R² = 0.29, RMSE = 0.019).Since all VI combinations in this study were constructed based on existing VIs, future studies could consider building more efficient VIs for Car/Chl based on the characteristic bands selected by a vegetation radiative transfer model or consider different VI forms.
The PROSPECT model has been widely used in estimating leaf biochemical constituents and provided abundant simulation data for selecting VIs sensitive to Chl and Car in this study.Using simulated datasets to propose optimal VI combinations strengthens the generalization ability and provides solid physical foundation for the proposed index.However, the limitations of the model should be noticed.Plant leaves are regarded as several stacking homogeneous layers which is not always applicable as leaves of different species in varying environments can differ greatly in anatomy (Qiu et al. 2018).In addition, the model only considers carotenoids as a class of pigments, rather than as a series of individual pigments having individual spectral properties.Future studies could consider using some new radiative transfer models such as SCOPE (Van der Tol et al. 2009;Yang, Verhoef, and van der Tol 2017).
The performance of CTRI/CI red-edge upscaled to the canopy scale calls for follow-up studies.At the canopy level, the effects of canopy structure, soil background and atmospheric absorption on the VI need to be considered (Hernández-Clemente, Navarro-Cerrillo, and Zarco-Tejada 2012).The applicability of CTRI/CI red-edge needs to be tested using canopy datasets.In case that CTRI/ CI red-edge does not perform well at canopy level, the proposed method of constructing suitable VI combination in this study can still be conducted at the canopy level.A sensitivity analysis of the aforementioned disturbance factors on the new VI could be investigated through coupling PROSPECT with canopy models such as 4SAIL (Wan et al. 2021).In addition, though we applied the proposed VI combination on four datasets observed in the field, more field datasets with different Car-Chl correlations are needed to further validate the performance of CTRI/CI red-edge for Car/ Chl estimation, and these datasets should involve wider varieties of vegetation species, sites, and growing stages.

Conclusion
The ratio of Car to Chl is an effective indicator of vegetation physiological status.However, the applicability of existing VIs to predict foliar Car/Chl ratio is hindered by the changes of Car-Chl correlation.Thus, a new VI combination was proposed in this study by analyzing the effect of different Car-Chl correlations on the relationships between candidate VI combinations and Car/Chl using six simulated datasets and four independent field datasets with varying Car-Chl correlations.Results demonstrated that CTRI/CI red-edge exhibited the largest sensitivity to the target parameter Car/Chl and the least sensitivity to the changes of Car-Chl correlation than other candidate VI combinations.We also compared the performance of CTRI/CI red-edge with seven previously published VIs of Car/Chl and two ML algorithms by using four field datasets.Results showed that CTRI/CI red- edge also achieved higher accuracy and robustness in Car/Chl estimation than published VIs and ML algorithms.This study improves the understanding of the effect of Car-Chl correlation on Car/Chl estimation and the new VI of CTRI/CI red-edge holds great promises for monitoring the physiological status of vegetation across vegetation species and sites.

Figure 2 .
Figure 2. The Pearson correlation coefficient (R) for the relationship between VIs estimated using the synthetic Dataset A and (a) chlorophyll (Chl) as well as (b) carotenoid (Car).

Figure 3 .
Figure 3. Influence of Car-Chl correlations on the relationship between Car/Chl and VI combinations using simulated datasets.From Datasets 1-6, the Car-Chl correlation increased sequentially (the abscissa).The coefficient of determination (R 2 ) and root mean square root (RMSE) in the ordinates indicate the least squares fit of the relationships between a VI combination and leaf Car/Chl ratio.The more dramatic the color changes among datasets, the greater the effect of Car-Chl correlation on the index.

Figure 4 .
Figure 4. Relationships between Car/Chl and the optimal VI combination CTRI/CI red-edge from Dataset 1-6.Density of scatter points is depicted by colors ranging from blue (sparse) to red (dense).

Figure 5 .
Figure 5. Influence of Car-Chl correlations on Car/Chl ∼ VI combinations relationships using the four datasets of field observations.From DOGWOOD-2 to CABO, the Car-Chl correlation increased sequentially (the abscissa).The coefficient of determination (R 2 ) and root mean square root (RMSE) in the ordinates indicate the least squares fit of the relationships between VI combinations and Car/Chl.

Figure 6 .
Figure 6.Relationships between Car/Chl and the optimal VI combination CTRI/CI red-edge from the four datasets of field observations.

Table 1 .
Description of field datasets used in this study (Chl: leaf chlorophyll, Car: leaf carotenoid, Anth: leaf anthocyanins, Car/ Chl: the ratio of leaf chlorophyll and leaf carotenoid).

Table 2 .
Distribution of leaf biochemical traits for simulated datasets.

Table 3 .
Statistics of the ratio of Car to Chl content for the simulated datasets.

Table 5 .
Published vegetation (VI) indices for Car/Chl estimation used in this study.

Table 6 .
Candidate VI combinations constructed in this paper.