Exploring the potential of transmittance vegetation indices for leaf functional traits retrieval

ABSTRACT

Leaf functional traits are key indicators of plant functions useful for inferring complex plant processes, including their responses to environmental changes. Vegetation indices (VIs) composed of a few reflectance wavelengths hold the advantages of being relatively simple and effective and have been widely used within remote sensing to estimate leaf traits. However, the difference between the reflectance from the upper and lower part of the leaf suggests that leaf reflectance mainly provides one-sided information, constraining its ability to estimate leaf functional traits. Leaf transmittance, on the other hand, gives information about the whole leaf and has more potential to be sensitive to changes in leaf biochemistry. As transmittance-based VI is rare, this study aims to propose new transmittance-based VIs for accurate estimations of leaf traits. Three forms, i.e. the normalized difference VI, the simple ratio VI, and the difference VI were employed, and wavelength selection for transmittance-based and reflectance-based VIs were conducted, respectively. The applicability of these VIs for estimating four leaf functional traits (leaf chlorophyll (C_ab), leaf carotenoids (C_ar), equivalent water thickness (EWT), and leaf mass per area (LMA)) were evaluated. Cross-validation using three datasets of field observations and sensitivity analysis showed that the VIs constructed using transmittance were relatively less affected by interferences from other leaf parameters, improving the estimation accuracy of C_ar, EWT, and LMA compared to their optimal reflectance counterparts (RMSE reduced by 2% to 15%, and MAE reduced by 7% to 20% for the pooled dataset). Our study revealed that the normalized difference VI based on transmittance showed considerable sensitivity to C_ar, EWT, and LMA, whereas the difference VI based on reflectance was effective in indicating C_ab. The proposed transmittance-based VIs will aid remote monitoring of leaf traits and thereby plant adaptations and acclimation to changes in environmental conditions.

KEYWORDS:

• Leaf transmittance
• remote sensing
• wavelength selection
• sensitivity analysis

1. Introduction

Leaf functional traits are measurable and effective indicators that can characterize plant demographic rates, fitness, and photosynthetic capacity (Homolova et al. 2013; Reich, Wright, and Lusk 2007; Violle et al. 2007; Westoby 1998). Plant adaptations and acclimation to different environmental conditions are reflected in these traits (Reich, Wright, and Lusk 2007). Consequently, accurate predictions of functional traits are important for understanding the survival mechanism of plants and diagnosing plant stress (Asner and Martin 2016; Diaz et al. 2016).

Leaf Chlorophyll content (C_ab) and leaf carotenoids content (C_ar) are important photosynthetic pigments that ensure the conversion of solar radiation into chemical energy during photosynthesis (Blackburn 2007; Croft et al. 2017). For a list of used acronyms, see Table S1 in supplementary. Leaf equivalent water thickness (EWT) and leaf mass per area (LMA) are two leaf traits highly related to leaf tissue density (Spafford et al. 2021). The trait EWT is also a commonly used indicator to describe plant transpiration and respiration (Yamasaki and Dillenburg 1999; Zhang et al. 2018), and it is also the abiotic factor with the highest impact on vegetation growth (Asner et al. 2014; Nilsen and Orcutt 1996). Leaf mass per area (LMA) is the ratio between leaf dry mass and leaf area and it is a key biophysical variable describing plant strategies under the background of rapid climate change (Asner et al. 2011; Féret et al. 2019). Considering the importance of these traits on plant functions, they were the main target variables in this study.

In recent decades, remote sensing technology with the advantages of being fast, large scale, and nondestructive has been widely used to estimate leaf traits (Fig. S1) (Qu, Li, and Zhang 2021; Weiss, Jacob, and Duveiller 2020; Zhang et al. 2021). Vegetation indices (VI), as a simple empirical method, have been very popular in vegetation remote sensing because of its simplicity, ease of application, and high accuracy (Ali et al. 2017). Based on some designed transformation formulas of single or multiple specific spectral wavelengths, VIs can maximize their sensitivity to leaf traits while minimizing sensitivity to disturbing factors such as structural parameters and other traits with similar light absorption (Camps-Valls et al. 2021; le Maire, François, and Dufrêne 2004; Li et al. 2021; Zhou et al. 2017). Examples of published VIs applicable for leaf trait monitoring include the red-edge VIs for pigments (Magney, Eitel, and Vierling 2017), the normalized difference water index (Zhang et al. 2018) and the normalized dry matter index (Wang et al. 2011) for EWT and LMA, respectively. Additionally, VIs can be easily integrated with sensors mounted on different platforms owing to their small demand for wavelengths of observation (Wan et al. 2021), which explains part of their popularity.

Conventional VIs used to indicate vegetation traits are usually based on leaf or canopy reflectance, as the reflectance is relatively easy to obtain through traditional remote sensing technology (Féret et al. 2011; le Maire, François, and Dufrêne 2004; Sharifi 2020). Although some traits (e.g. C_ab, EWT) have been reported with good estimation results through reflectance-based VIs (Ali et al. 2017; Féret et al. 2011; Kira, Linker, and Gitelson 2015; Main et al. 2011), the information provided by leaf reflectance is limited. For example, capturing LMA using reflectance-based VIs is remarkably difficult (Le Maire et al. 2008).

Both leaf transmittance and reflectance are related to leaf structure and component distribution (Sun et al. 2018), yet the extent to which they reflect the attenuation of light in leaves is different. Baránková, Lazár, and Nauš (2016) revealed that the visible and short-wave infrared light reflected from the upper surface of the leaf passes through a longer distance and is easier to be absorbed than light reflected from the lower surface, whereas leaf transmittance is almost the same from both surfaces for most species (Spafford et al. 2021). This indicates that leaf transmittance has a larger potential of containing information about the whole leaf than leaf reflectance. In addition, differences between leaf transmittance and reflectance vary among plant species depending on leaf structures. Plant species in different taxonomic groups show large differences in leaf structure. For example, dicotyledons have net-veined leaves, while monocots have parallel veined leaves (Helliker and Ehleringer 2000; Liu, An, and Lin 2021), oilseed rape and citrus leaves consist mainly of epidermis, palisades, and spongy mesophyll, while rice has almost no palisades and spongy mesophyll (Wan et al. 2021). All these factors affect the potential of leaf transmittance and reflectance to estimate leaf traits to some extent.

Although leaf transmittance takes more effort to measure than leaf reflectance, in recent years, the potential of transmittance-based approaches for indicating leaf traits has been revealed. One study found that employing leaf transmittance spectra to estimate C_ar and LMA through PROSPECT model inversion exhibited better performance than using reflectance spectra (Sun et al. 2018). In addition, Asner et al. (2011) suggested that accurate estimates of C_ab and C_ar can be achieved using leaf transmittance spectra measured with a field spectrometer. Bergstrasser et al. (2015) showed an improved estimate of C_ab using both leaf transmittance and reflectance from hyperspectral images. However, there is still need for research on establishing the optimal transmittance-based VIs for estimating leaf functional traits compared with traditional reflectance-based VIs.

The main objective of this study was to establish the optimal transmittance VIs for estimating C_ab, C_ar, EWT, and LMA, and investigate their performance against their reflectance counterparts. These traits were selected because of their importance for functioning of the plants, and their applicability for monitoring plant adaptations and acclimation to changes in environmental conditions. In addition to the above, these traits are explicitly considered in the vegetation radiative transfer model of PROSPECT, and the verification data sources of these four traits are relatively richer. First, a sensitivity analysis of reflectance and transmittance to leaf trait variability was performed. Second, a database of field measurements was used to determine the optimal wavelength combinations of three types of VIs based on transmittance or reflectance for each leaf functional trait. Three-fold cross-validation was subsequently used to evaluate the performance of linear regression models using these VIs for estimating the leaf functional traits. A sensitivity analysis of the optimal VIs was performed to evaluate the VI’s ability of resisting interference from other factors, such as structural parameters and other traits with similar light absorption. Finally, the general applicability of these optimal VIs was investigated using simulated datasets.

2. Material and methods

2.1. PROSPECT-D model and sensitivity analysis of reflectance and transmittance to leaf traits

PROSPECT (Jacquemoud and Baret 1990) is a broadleaf radiation transfer model based on the generalized plate model (Allen, Gausman, and Richardson 1970; Allen et al. 1969) and has been widely used in leaf optical modeling for its simplicity and robustness. In the PROSPECT model, the radiative transfer process at leaf-level is simulated with mathematical functions using leaf structure parameter N, refractive index, leaf traits (C_ab, EWT, and LMA), and their specific absorption spectra. Among these, the variable N is an imaginary parameter for the PROSPECT model to consider the leaf internal structure. Running the PROSPECT model forward generates leaf directional-hemispherical reflectance and transmittance in the spectral region of 400–2500 nm, with a resolution of 1 nm. The inversion procedure is performed by iteratively identifying the minimum cost function value between the measured and simulated spectra. The PROSPECT-D version was used in this study (Féret et al. 2017), with additional consideration for the effects of C_ar, anthocyanins (C_ant) and brown pigment compared to the original PROSPECT version. The PROSPECT-D model has been programmed in an open-source package (http://teledetection.ipgp.jussieu.fr/prosail/), including both python and MATLAB versions. There are other radiative transfer models such as LIBERTY (Dawson, Curran, and Plummer 1998) and the Dorsiventral Leaf Model (Stuckens et al. 2009), but we used PROSPECT-D given the focus of fresh broad leaves in this study.

When performing a global sensitivity analysis, it is necessary to take into consideration the interactions between model input variables (Cannavó 2012). Thus, we conducted a Sobol’s global sensitivity analysis (Cannavó 2012; Sobol′ 2001) with the PROSEPCT-D model simulations to study the differences in the response of transmittance and reflectance to leaf traits. The Sobol’s sensitivity analysis contains two sets of indices: the first-order indices describe the independent influence of each parameter, whereas the second-order indices consider the interactive influence between the different parameters. The sum of the first- and second-order indices for each wavelength is 1, and the value of each index thereby indicates the contribution of that specific parameter/parameter interaction to the total sensitivity. For the simulated leaf spectral characteristics to represent as large a degree of plant species and leaf growing stages as possible, wide ranges of the input parameters of the PROSPECT-D model were used following (Féret et al. 2011; Sun et al. 2019). Gaussian distributions of the input parameters were assumed. The input variables used for the PROSPECT-D simulations are shown in Table 1.

Table 1. Input parameters of PROSPECT-D model for leaf optical properties modeling.

Parameters	Min	Max	Mean	SD	Reference
N	1	3.5	1.6	0.3	Sun et al. (2019)
Cab (μg/cm^2)	0	110	32.81	18.87	Sun et al. (2019)
Car (μg/cm^2)	0	30	8.51	3.92	Sun et al. (2019)
Cant (μg/cm^2)	0	40	8.8	7.1	Sun et al. (2019)
EWT (g/cm^2)	0	0.07	0.0115	0.007	Sun et al. (2019); Féret et al. (2011)
LMA (g/cm^2)	0.001	0.04	0.01	0.07	Sun et al. (2019); Féret et al. (2011)

2.2. Experimental datasets

Three datasets of field measurements from various ecoregions covering 1005 fresh leaves of more than 100 species were used in this study. These data represent foliage information of heterogeneous sites and climate conditions (see further in Supplementary). The ANGERS leaf database was established in 2003 in Angers, France (Feret et al. 2008), containing 276 leaves from 43 herbaceous and woody species, including measured leaf optical and biochemical properties. The Leaf Optical Properties Experiment (LOPEX) dataset was collected by the Joint Research Center of the European Commission at Ispra in Italy in 1993 (Hosgood et al. 1995). This dataset includes optical and biochemical measurements of 330 leaves of 46 different species. The five samples of dried corn leaves in the LOPEX dataset were discarded given that we focused on fresh leaves.

The NJU dataset was collected by Nanjing University from four field campaigns in Nanjing (Jiangsu, China) between 2014 and 2015 (Qiu et al. 2018). This dataset is composed of four smaller parts collected under different sampling conditions, covering trees and herbs. Two parts included measurements from the entire growing season of top canopy leaves of sweetgum (Liquidambar), oak (Quercus), and maize (Zea mays) collected in 2014, involving samples from leaf out to leaf fall. One part was collected in the summer of 2015, and the final part was collected in a broadleaved evergreen forest in May and July of 2015. The NJU dataset includes 404 leaves from 12 species over annual and perennial plants. A more detailed description can be found in the supplementary and in Qiu et al. (2018).

In these datasets, leaf directional-hemispheric transmittance and reflectance were measured with a spectroradiometer equipped with an integrating sphere. For each sample, measurements were made in five different areas to quantify small but non-negligible interleaf variation. The scan time for each sample was about 4 min. The spectral measurement range was from 400 to 2500 nm, and the spectral sampling interval was 1 to 2 nm from 400 to 1000 nm, and 2 to 5 nm from 1000 to 2500 nm. The final spectral interval was resampled to 1 nm.

The measurement protocol for pigments is roughly the same for all three datasets. Leaf disks were ground in a chilled mortar with organic solvents such as 100% acetone and methanol, and the calculation of pigments was done according to Litchtenthaler (1987). The EWT and LMA were estimated by measuring the fresh weight and the area of the leaf disks, and then the dry weight of the disks after drying in an oven at 65°C for at least 48 hours until the weight was constant. The spectral range used in this study was restricted between 400 and 2200 nm, given that the signal-to-noise ratio above 2200 nm is low (Qiu et al. 2018). Moreover, as a biased relationship between photosynthetic pigments (C_ab, C_ar) and optical properties has been reported for LOPEX (Feret et al. 2008; Qiu et al. 2018), this dataset was not used in the assessment of C_ab and C_ar. Table 2 shows information about the measurements of the experimental datasets.

Table 2. Summary of main characteristics of three datasets.

Dataset	ANGERS	LOPEX	NJU
Number of leaves	276	325	404
Number of species	43	46	12
Spectrometer	ASD FieldSpec	Perkin Elmer Lambda 19	ASD FieldSpec
Spectral domain	400–2500 nm	400–2500 nm	400–2500 nm
Spectral sampling	1–2 nm (400–1000 nm) 4–5 nm (1000–2500 nm)	1.4 nm (400–1000 nm) 2 nm (1000–2500 nm)	1.4 nm (400–1000 nm) 2 nm (1000–2500 nm)
Leaf traits	Cab, Car, EWT, LMA	EWT, LMA	Cab, Car, EWT, LMA
Reference	(Feret et al. 2008)	(Hosgood et al. 1995)	(Qiu et al. 2018)
Ecoregion	Temperate marine climate	Subtropical marine climate	Humid subtropical climate
Growth habit	Tree, shrub, vine, forb	Tree, shrub, vine, forb	Tree, shrub, forb

2.3. Vegetation indices (VIs) for estimating leaf traits

2.3.1. Investigated VI types

To explore the potential of transmittance to establish VIs for estimating leaf traits, three types of VIs with two wavelengths, the normalized difference (ND) VI, the simple ratio (SR) VI, and the difference (D) VI were selected for subsequent analysis (Table 3). These VI types were adopted due to their widespread use and good performance (Ali et al. 2017; Mutanga and Skidmore 2010). VI of ND type was reported to achieve good results in the quantification of many leaf traits (Le Maire et al. 2008). While SR and D are simple in structure, their ability to accurately estimate leaf traits has still been reported (Féret et al. 2011; Wang and Li 2012). Except from being sensitive to the target parameter, most VIs are also designed to be insensitive to specific disturbing factors. For example, D is suitable for eliminating the influence of additive changes in leaf spectral characteristics, while SR and ND can deal with proportional variations (Le Maire et al. 2008). Figure 1 presents the process flow diagram showing the method adopted in this study.

Figure 1. Process flow diagram explaining the study scheme.

Table 3. The vegetation index formats used in this study. B1 and B2 represent the leaf transmittance or reflectance of two wavelengths.

Index name	Index ID	Formula
Normalized difference vegetation index	ND	$\frac{B1-B2}{B1+B2}$
Simple ratio vegetation index	SR	$\frac{B1}{B2}$
Difference vegetation index	D	$\mathrm{B}1-\mathrm{B}2$

2.3.2. Wavelength selection of transmittance and reflectance-based VIs

To determine the optimal wavelength combination of each VI type based on transmittance or reflectance, the method of exhaustive search according to Togeiro de Alckmin et al. (2021), Mutanga and Skidmore (2010) and Tagesson et al. (2015) was adopted with correlation analysis toward the target plant trait and VI combination based on all the experimental datasets. In this process, as leaf pigments (C_ab and C_ar) mainly absorb the visible light and that EWT and LMA negligibly affect leaf optical properties below 900 nm (Sun et al. 2019), we conducted wavelength selection for C_ab and C_ar in the spectral range of 400–900 nm, while EWT and LMA were in the range of 900–2200 nm. The performance of all possible wavelength combinations in the relevant spectral domain was investigated and the establishment of the VIs based on transmittance or reflectance follows the same procedure. The coefficient of determination (R²) was used to describe the linear correlation between VIs and leaf traits, and the VI combination that achieved the highest R² was the optimal VI selected.

After determining the optimal wavelength combination for the given types of VI based on transmittance or reflectance, the performance of ordinary least square linear regression models to estimate leaf traits was analyzed. The performance was investigated using three-fold cross validation, with two-thirds of the data used for training and one-third for validation where the training and validation data were randomly separated from each experimental dataset. The statistical indicators included to evaluate the performance were R², root mean square error (RMSE), normalized root mean square error (NRMSE), and mean absolute error (MAE):

(1) ${\mathrm{R}}^2=1-\frac{{\sum }_{i=1}^n{\left({y{ }^{\mathrm{\prime }}}_i-y_i\right)}^2}{{\sum }_{i=1}^n{\left({y{ }^{\mathrm{\prime }}}_i-\bar{y}\right)}^2}$(1)

(2) $\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{{\sum }_{i=1}^n{\left({y{ }^{\mathrm{\prime }}}_i-y_i\right)}^2}{n}}$(2)

(3) $\mathrm{N}\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}\left(\mathrm{\%}\right)=\frac{RMSE}{y_{max}-y_{min}}\cdot 100$(3)

(4) $\mathrm{M}\mathrm{A}\mathrm{E}=\hspace{0.17em}\frac{{\sum }_{i=1}^n\left|y{ }_i^{\prime }-y_i\right|}{n}$(4)

where ${y_i}^{\prime }$and $y_i$ are the estimated and measured leaf trait values, respectively; $y_{max}$ and $y_{min}$ are the maximum and minimum values of $y_i$, respectively; $n$ is the number of measurements, and $i$ is the serial number of the measured leaf trait content.

To study the effectiveness of the proposed optimal VIs for estimations of leaf traits, a global sensitivity analysis of the optimal VIs was conducted following the same method as described in section 2.1. Instead of analyzing the contribution of the input parameters of the PROSPECT-D model to the variability of the reflectance and transmittance spectrum, we analyzed the sensitivity to the variability of the optimal VIs. With this analysis, the sensitivity of VIs to target parameters and its ability to resist other confounding parameters can be directly observed, facilitating the evaluation of the comprehensive ability of VIs for estimating leaf traits.

2.4. Generalization analysis of the optimal VIs

To evaluate the robustness and generalization ability of the selected optimal VIs, a generalization analysis was conducted by examining the correlation between VIs and leaf traits using both in-situ and simulated datasets. Although three independent experimental datasets were used, these data do not cover all plant species and growth conditions. By incorporating a wide range of leaf traits and leaf structure parameter in the PROSPECT-D model, we can simulate reflectance and transmittance for different plant species and growing stages that help to assess the generalization capability of the VIs. First, 100,000 combinations of PROSPECT-D model input parameters were randomly generated based on Table 1 and assuming Gaussian distributions. Then, the PROSEPCT-D model was used to simulate the spectral properties of leaves with these parameter combinations, and a large synthetic database of 100,000 simulations of leaf optical properties was subsequently generated. Finally, the relationships between the optimal VIs and the four leaf traits were analyzed with Pearson correlations for both the experimental and synthetic datasets. The consistency of correlation between VIs and leaf traits in both experimental and synthetic datasets represents their generalization ability.

3. Results

This section is divided into four subsections. The first subsection mainly describes differences in the sensitivity of reflectance and transmittance to leaf functional traits in the wavelength range of 400 to 2500 nm. The second subsection focuses on determining the optimal wavelength combination of transmittance-based and reflectance-based VIs and comparing the performance of the VIs for leaf functional traits estimation against actual measurements. The third subsection simulates the sensitivity of the optimal VIs to the leaf traits using the PROSPECT-D model. Finally, the fourth subsection presents the evaluation of the generalization ability of the optimal VIs.

3.1. Sensitivity analysis of leaf transmittance and reflectance to leaf traits

The sensitivity analysis of the PROSPECT-D model simulations shows that the different responses of leaf transmittance and reflectance to leaf parameters (N, C_ab, C_ar, C_ant, EWT, and LMA) mainly exist at wavelengths below 800 nm and above 1200 nm (Figure 2). In the blue (400–500 nm) and red (600–700 nm) domains, leaf transmittance was more sensitive to C_ab than reflectance, while the reflectance was more sensitive to C_ab than transmittance in the domain of the red edge (700–800 nm). For C_ar, transmittance has a higher sensitivity compared to reflectance in the blue domain. Furthermore, transmittance was more sensitive to EWT and LMA variations than reflectance at the shortwave infrared region (1000–2500 nm). To conclude, almost all leaf functional traits were more sensitive to transmittance than reflectance in most spectral domains, and the VIs constructed with transmittance should thereby be superior for estimating the leaf traits C_ab, C_ar, EWT, and LMA.

Figure 2. Difference in contribution to the sensitivity to the specific leaf traits between reflectance and transmittance for the input parameters (N: Structural parameter, C_ab: chlorophyll, C_ar: carotenoids, C_ant: anthocyanin, EWT: equivalent water thickness, and LMA: leaf mass per area) based on PROSPECT-D model simulations. A positive contribution means that the contribution of the components in reflectance is higher than that in transmittance, while a negative value is the opposite.

3.2. Optimal transmittance and reflectance-based VIs for retrieval of leaf traits

3.2.1. Vis for estimating leaf chlorophyll content

The correlation map between C_ab and VIs was constructed by testing all the possible wavelength combinations between 400 and 900 nm using transmittance and reflectance from the combination of the ANGERS and NJU datasets (Figure 3). The correlation matrices showed some areas of high R² values between C_ab and VIs. For example, VIs composed of a combination of red-edge (700–750 nm) and near-infrared (700–900 nm) wavelengths showed high correlation with C_ab, irrespective of the VI type used. Given that the spectral areas with high correlation were relatively large, the corresponding VIs are expected to be easily and effectively applied to sensors also with broad bands. Most VIs constructed with transmittance were more sensitive to C_ab than those constructed with reflectance, except for the reflectance-based D-type VI using a combination of red edge (732 nm) and near-infrared (770 nm) wavelengths, which obtained the highest R² value (0.87).

Figure 3. The coefficient of determination (R²) based on the correlation between leaf chlorophyll content (C_ab) and normalized difference (ND) VIs (a, b), simple ratio (SR) VIs (c, d), and difference (D)-type VIs (e, f) VIs constructed by all possible wavelength combinations of B1 (400–900 nm) and B2 (400–900 nm) based on reflectance (left) or transmittance (right). The combination representing the highest R² is marked with a black star, and their respective R² value and wavelengths are noted in the figure.

The results of the analysis of the performance of the linear regression model using the optimal VIs based on transmittance or reflectance as input for estimating C_ab are shown in Table 4. The results are consistent with the findings of the correlation analysis in Figure 3, and the linear regression model using the D-type VI constructed with reflectance captured the highest accuracy (RMSE = 7.36 μg/cm², MAE = 5.52 μg/cm²). For ND and SR, the transmittance-based VIs achieved higher accuracy compared with their reflectance-based counterparts (Table 4).

Table 4. Accuracy of the linear regression models using the three optimal normalized differences (ND), simple ratio (SR), and difference (D) VIs constructed by transmittance or reflectance as input for estimating C_ab. POOLED is a combined ANGERS and NJU dataset. The best results (highest R², lowest RMSE, NRMSE, and MAE) from the listed VIs using pooled dataset are in bold.

Input Vegetation Index	Experimental Dataset	R^2		RMSE (μg/cm^2)		NRMSE (%)		MAE (μg/cm^2)
		R	T	R	T	R	T	R	T
ND	ANGERS	0.91	0.95	8.02	5.41	8.01	5.41	6.25	3.99
	NJU	0.72	0.72	8.58	9.41	11.08	12.15	7.04	7.30
	POOLED	0.84	0.85	8.36	8.04	8.36	8.04	6.72	5.95
SR	ANGERS	0.91	0.95	8.15	5.41	8.14	5.41	6.32	4.02
	NJU	0.72	0.72	8.60	9.35	11.10	12.07	7.06	7.26
	POOLED	0.84	0.85	8.42	8.00	8.42	8.00	6.76	5.95
D	ANGERS	0.93	0.79	6.13	11.73	6.14	11.70	4.44	8.90
	NJU	0.75	0.70	8.08	9.36	10.43	12.08	6.26	7.25
	POOLED	0.87	0.78	7.36	10.40	7.36	10.38	5.52	7.92

3.2.2. Vis for estimating leaf carotenoids content

The R² map between C_ar and VIs was constructed by correlating all the possible wavelength combinations in 400–900 nm using transmittance and reflectance from the pooled ANGERS and NJU datasets against C_ar (Figure 4). For the three types of VIs, the transmittance-based VIs showed larger regions with high R² compared to the maps against reflectance. The transmittance-based ND and SR VIs achieved higher R²-values than their reflectance counterparts, whereas the reflectance-based D-type VIs were better than the transmittance counterparts. The transmittance-based ND constructed with the wavelengths of 576 nm and 711 nm achieved the highest R² (0.68). In addition, the R² maps from the correlation analysis between C_ar and the different VIs types were similar to the maps of C_ab (Figure 3), but the R² values were lower.

Figure 4. The coefficient of determination (R²) based on the correlation between leaf carotenoids (C_ar) and the normalized difference (ND) (a, b), the simple ratio (SR) (c, d), and the difference (D)-type VIs (e, f). VIs were constructed using all possible wavelength combinations of B1 (400–900 nm) and B2 (400–900 nm) based on reflectance (left) and transmittance (right). The combination representing the highest R² is marked with a black star, and their respective R² value and wavelengths are noted in the figure.

Subsequently, the performance of the linear regression models against optimal VIs for predicting C_ar was evaluated (6). In the evaluation against the pooled ANGERS and NJU datasets, ND and SR based on transmittance obtained higher accuracy than their reflectance counterparts, while the performance of the D-type VI based on reflectance was superior to the transmittance-based VI. For all regression models, the one using transmittance-based ND as input obtained the highest accuracy for estimating C_ar (RMSE = 2.64 μg/cm², MAE = 1.94 μg/cm²).

3.2.3. Vis for estimating leaf equivalent water thickness

The R² map based on the correlation between EWT and VIs (Figure 5) indicated very high R² for a broad range of wavelength combinations (red areas in Figure 5), both in the cases of transmittance and reflectance-based VIs. For ND and SR, the spectral regions of high R² were substantially larger than those for D-type VIs. The optimal VIs for estimating EWT showed larger R² for the transmittance-based VIs compared with their reflectance-based counterparts. The transmittance-based ND using the shortwave infrared wavelengths at 1474 and 1506 nm had the highest R² (0.90) Table 5.

Figure 5. The coefficient of determination (R²) based on the correlation between equivalent water thickness (EWT) and the normalized difference (ND) (a, b), the simple ratio (SR) (c, d), and the difference (D)-type VIs (e, f). VIs constructed by all possible wavelength combinations of B1 (900–2200 nm) and B2 (900–2200 nm) based on reflectance (left) or transmittance (right). The combination representing the highest R² is marked with a black star, and their respective R² value and wavelengths are noted in the figure.

Table 5. Accuracy of the linear regression models using the three optimal normalized differences (ND), simple ratio (SR), and difference (D) VIs constructed by transmittance or reflectance as input for estimating C_ar. POOLED is a pooled dataset of ANGERS and NJU. The best results (highest R², lowest RMSE, NRMSE, and MAE) from the listed VIs using pooled dataset are shown in bold.

Input Vegetation Index	Experimental Dataset	R^2		RMSE (μg/cm^2)		NRMSE (%)		MAE (μg/cm^2)
		R	T	R	T	R	T	R	T
ND	ANGERS	0.77	0.76	3.61	2.97	15.16	12.42	2.83	2.18
	NJU	0.50	0.72	2.71	2.34	21.72	18.71	2.22	1.78
	POOLED	0.61	0.69	3.12	2.64	13.14	11.08	2.47	1.94
SR	ANGERS	0.78	0.86	3.63	2.43	15.25	10.18	2.84	1.85
	NJU	0.50	0.56	2.73	2.97	21.88	23.71	2.24	2.37
	POOLED	0.61	0.66	3.14	2.77	13.22	11.68	2.49	2.16
D	ANGERS	0.82	0.69	2.70	3.81	11.32	15.97	2.13	3.02
	NJU	0.60	0.66	2.72	2.67	21.68	21.33	2.06	2.23
	POOLED	0.66	0.60	2.72	3.19	11.44	13.44	2.09	2.55

For most cases, the linear regression models using the optimal VIs based on transmittance as input showed higher accuracy for estimating EWT (lower RMSE and MAE) compared with their reflectance counterparts, except for the regression model using the D-type VI parameterized and evaluated against the LOPEX dataset (Table 6). When all datasets were combined (POOLED in Table 6), the regression model using transmittance-based ND achieved the highest accuracy of all (R² = 0.90, RMSE = 0.0018 g/cm², MAE = 0.0013 g/cm²). To conclude, compared with using reflectance, linear models constructed with transmittance-based VIs consistently allowed more accurate estimates of EWT, and the ND VI performed particularly well.

Table 6. Accuracy of the linear regression models using the three optimal normalized differences (ND), simple ratio (SR), and difference (D) VIs constructed with transmittance (T) or reflectance (R) as input for estimating equivalent water thickness (EWT). POOLED is a combination of the ANGERS, LOPEX, and NJU datasets. The best results (highest R², lowest RMSE, NRMSE, and MAE) from the listed VIs using pooled dataset are shown in bold.

Input Vegetation Index	Experimental Dataset	R^2		RMSE (g/cm^2)		NRMSE (%)		MAE (g/cm^2)
		R	T	R	T	R	T	R	T
ND	ANGERS	0.93	0.91	0.0016	0.0014	6.81	6.23	0.0011	0.0009
	LOPEX	0.93	0.94	0.0022	0.0020	5.28	4.62	0.0017	0.0014
	NJU	0.75	0.78	0.0024	0.0019	10.75	8.50	0.0016	0.0014
	POOLED	0.86	0.90	0.0021	0.0018	5.12	4.29	0.0015	0.0013
SR	ANGERS	0.92	0.90	0.0016	0.0015	7.09	6.54	0.0011	0.0010
	LOPEX	0.92	0.93	0.0020	0.0019	4.90	4.63	0.0014	0.0015
	NJU	0.76	0.76	0.0023	0.0020	10.35	9.02	0.0015	0.0015
	POOLED	0.87	0.89	0.0020	0.0019	4.94	4.45	0.0014	0.0013
D	ANGERS	0.87	0.90	0.0022	0.0015	9.76	6.82	0.0015	0.0011
	LOPEX	0.89	0.91	0.0023	0.0024	5.59	5.54	0.0016	0.0016
	NJU	0.68	0.64	0.0027	0.0025	12.13	11.33	0.0021	0.0019
	POOLED	0.82	0.85	0.0025	0.0023	5.89	5.35	0.0018	0.0016

3.2.4. Vis for estimating leaf mass per area

Most wavelength combinations used for creating the three VI types were ineffective for estimating LMA (blue regions), with only a few small spectral regions with high R²-values (Figure 6). An effective spectral domain can be found near 1200 nm in the reflectance-based VIs, but not for the transmittance-based VIs. For ND and SR, the spectral regions with the highest R²-values were similar for both the transmittance- and reflectance-based VIs (B1 of 1300–1400 nm, B2 of 1700–1800 nm). The transmittance-based SR using wavelengths between 1377 and 1720 nm obtained the highest R² of 0.81. Overall, the transmittance-based VI showed closer correlation with LMA than the reflectance-based VIs. There were missing values around 1900 nm in the R² map for transmittance (Figure 6). This is due to the strong absorption of the leaf at these wavelengths (Li et al. 2021), leading to a transmittance close to zero at these wavelengths (Figure 6b, d).

Figure 6. The coefficient of determination (R²) based on the correlation between leaf mass per area (LMA) and the normalized difference (ND) (a, b), the simple ratio (SR) (c, d), and the difference (D)-type VIs (e, f). VIs constructed by all possible wavelength combinations of B1 (900–2200 nm) and B2 (900–2200 nm) based on reflectance (left) or transmittance (right). The combination representing the highest R² is marked with a black star, and their respective R² value and wavelengths are noted in the figure.

The estimates of LMA with the linear regression models using the different VI types based on transmittance and reflectance were evaluated (Table 7). For ND and SR, the linear regressions using transmittance VIs as input showed better performance (higher R², lower RMSE and MAE) compared to their reflectance counterparts. Linear regressions using the transmittance-based D-type VI were more accurate in estimating LMA for the LOPEX and NJU datasets. However, the poor estimates for ANGERS caused the model using transmittance-based D-type VI to perform worse overall compared to the one using the reflectance-based D-type VI. For each regression model, the ones using ND and SR as input made better LMA estimates than the ones using D-type VIs. In the evaluation against all data (the POOLED dataset of Table 7), the linear regression models using transmittance-based ND and SR were equally good and acquired the most accurate LMA estimations (R² = 0.81, RMSE = 0.0018 g/cm², MAE = 0.0013 g/cm²).

Table 7. Accuracy of the linear regression models using the three optimal normalized differences (ND), simple ratio (SR), and difference (D) VIs constructed with transmittance (T) or reflectance (R) as input for estimating leaf mass area (LMA). POOLED is a combination of the ANGERS, LOPEX, and NJU datasets. The best results (highest R², lowest RMSE, NRMSE, and MAE) from the listed VIs using pooled dataset are shown in bold.

Input Vegetation Index	Experimental Dataset	R^2		RMSE (g/cm^2)		NRMSE (%)		MAE (g/cm^2)
		R	T	R	T	R	T	R	T
ND	ANGERS	0.87	0.93	0.0020	0.0016	9.09	7.25	0.0016	0.0014
	LOPEX	0.70	0.76	0.0024	0.0019	20.07	16.29	0.0020	0.0014
	NJU	0.82	0.84	0.0020	0.0018	13.34	11.95	0.0014	0.0011
	POOLED	0.74	0.81	0.0021	0.0018	9.12	7.67	0.0017	0.0013
SR	ANGERS	0.89	0.92	0.0019	0.0017	8.48	7.53	0.0015	0.0014
	LOPEX	0.71	0.79	0.0023	0.0018	19.34	15.12	0.0019	0.0014
	NJU	0.81	0.83	0.0020	0.0018	13.54	12.17	0.0014	0.0011
	POOLED	0.75	0.81	0.0021	0.0018	8.86	7.67	0.0016	0.0013
D	ANGERS	0.78	0.77	0.0018	0.0029	8.26	12.77	0.0013	0.0023
	LOPEX	0.53	0.64	0.0022	0.0021	18.44	17.51	0.0017	0.0017
	NJU	0.74	0.82	0.0023	0.0021	15.73	14.31	0.0018	0.0016
	POOLED	0.73	0.71	0.0022	0.0024	9.56	10.28	0.0016	0.0018

3.3. Sensitivity of the optimal transmittance and reflectance VIs to interference

We compared the sensitivity of the optimal VI for each VI type in section 3.2 toward the target traits and interference factors using PROSPECT-D simulations (Figure 7). All VIs for estimating C_ab showed high sensitivity to C_ab except for D constructed using transmittance, which is also sensitive to N. Most VIs for estimating C_ar in Figure 7b reflects C_ar to a limited extent, while C_ab accounted for the major contribution. Only D based on transmittance showed certain sensitivity to C_ar. The VIs for estimating EWT based on transmittance and reflectance showed consistently good correlation to EWT, and the transmittance-based VIs showed slightly higher sensitivity to EWT than their reflectance counterparts (Figure 7c), which agrees with the results in section 3.2.3. The most striking improvements of transmittance-based VIs compared to reflectance-based ones were seen in LMA, and the contribution of LMA to the transmittance-based VIs was substantially larger than the reflectance-based VIs. In summary, almost all VIs for estimating C_ab performed well, while the VIs for C_ar barely showed sensitivity to C_ar. The transmittance-based VIs for estimating EWT and LMA showed higher sensitivity to the parameters of interest and little interference from other parameters compared with the optimal reflectance-based VIs.

Figure 7. The sensitivity of the optimal VIs (normalized difference (ND), simple ratio (SR), difference (D)) for leaf structure parameter (N) and leaf functional traits (C_ab: chlorophyll, C_ar: carotenoids, C_ant: anthocyanin, EWT: equivalent water thickness, and LMA: leaf mass per area) based on PROSPECT-D simulations. (a-d) correspond to the VIs towards estimating C_ab, C_ar, EWT and LMA respectively. The subscript indicates whether the optimal VI is based on reflectance (R) or transmittance (T).

3.4. Evaluation of the generalization ability of VIs based on reflectance and transmittance

In order to comprehensively investigate the generalization capability of the optimal VIs based on transmittance or reflectance proposed in this study, the relationships between these VIs and leaf traits were analyzed using the pooled experimental dataset and a simulated dataset (Figure 8). Almost all VIs showed good correlation with their target parameter using both experimental and simulated datasets, demonstrating good generalization capability, except for the VIs for estimating C_ar (D_R(754,756) and D_T(576,711)). Transmittance-based VIs are more closely correlated with C_ar, EWT, and LMA than reflectance-based VIs. In addition, the VI values of simulations were separated from the VI values of observations for the transmittance-based VIs toward C_ar (Figure 8d).

Figure 8. The relationships between the optimal reflectance (left) or transmittance-based (right) VIs of C_ab (a, b), C_ar (c, d), EWT (e, f), and LMA (g, h) and observations or simulations. The fitted lines and coefficients of determination (R²) correspond to the relationship between observations and VIs. Each density plot is composed of 100,000 PROSPECT-D simulations, and the dark to light colors represent high to low density of simulations, respectively. The subscripts represent the optimal VI constructed based on reflectance (R) or transmittance (T), and the numbers in parentheses indicate the two wavelengths constructing the optimal VIs.

4. Discussion

4.1. Differences between transmittance and reflectance

Both leaf reflectance and transmittance contain information about leaf structure and biochemical constituents. In comparison, leaf reflectance is light reflected from one side of a leaf, while transmittance is light that went through a whole leaf, both with certain times of internal reflection and transmission within. Therefore, the differences between leaf transmittance and reflectance mainly derive from two aspects: i) leaf internal structure and structure of leaf upper and lower surfaces and ii) distribution of functional traits within a leaf.

First, from top to bottom, a leaf is usually composed of upper epidermis, mesophyll (including palisade parenchyma, bundle sheath parenchyma, vascular tissues, and spongy mesophyll), and lower epidermis (Jiang et al. 2021). Among the mesophyll tissues, the palisade tissue is close to the upper epidermis and has tightly arranged cells, while the spongy tissue is close to the lower epidermis with many stomata and cells arranged loosely (Jiang et al. 2021). The tightness of the cell arrangement is related to the degree of light scattering, with the looser structure having a higher light scattering (Stuckens et al. 2009; Woolley 1971). As leaf reflectance measured from the upper or lower faces mainly provides single-sided information of a leaf, the two can vary greatly because of different leaf surface structures (Wan et al. 2021). On the other hand, leaf transmittance measured from the two sides was reported to be very similar (Jiang et al. 2021), indicating that leaf transmittance may contain more thorough information about a leaf than reflectance.

Second, the distribution of light-absorbing materials in a leaf is heterogeneous, changing both vertically across a leaf and temporally with growth stages, thus affecting the potential of leaf transmittance and reflectance as indicators of functional traits. For example, with strong absorption of the visible light, C_ab is abundant in the palisade tissue which is near the upper side of leaves to promote photosynthesis (Govaerts et al. 1996), therefore leaf reflectance from the upper surface has larger potential in estimating C_ab. This explains the good estimation results of reflectance-based VI (D_R(732, 770)) toward C_ab (Table 4). Since EWT and LMA are relatively dispersed within a leaf instead of concentrated on one side (Govaerts et al. 1996), leaf transmittance has a stronger ability to indicate the two leaf traits than reflectance, which explains the accurate estimation of EWT and LMA from transmittance-based VI (ND_T(1467, 1540)).

4.2. Wavelength selection of transmittance-based and reflectance-based VIs

Previous studies mainly focused on the establishment and application of reflectance-based VIs; therefore, the wavelengths of transmittance and reflectance-based VIs selected in this paper were compared with published reflectance-based VIs. For VIs toward C_ab, the reflectance-based VIs in this study used red-edge wavelengths between 700 and 800 nm, consistent with Main et al. (2011) and Le Maire et al. (2008). This spectral domain was reported to contain the most sensitive wavelengths for C_ab (Gitelson and Solovchenko 2017; Li et al. 2020). Most of the transmittance-based VIs proposed in this paper have also adopted wavelengths in this spectral range. The exception is transmittance-based D that uses the wavelength of 412 nm, where transmittance is low due to the joint absorption of C_ab and C_ar (Sims and Gamon 2002). Sims and Gamon (2002) suggested a similar wavelength of 445 nm in modified ND and modified SR, with the aim of eliminating the surface effect by subtracting this wavelength from the red-edge wavelength.

For VIs of C_ar, the reflectance-based VIs proposed in this paper only used the wavelengths between 700 and 800 nm; this red-edge region has been employed in published VIs as well (Blackburn 1998; Hernández-Clemente, Navarro-Cerrillo, and Zarco-Tejada 2012). However, C_ar was reported to absorb little light in this region; given the strong correlation between C_ar and C_ab, the selection of these wavelengths is probably due to the strong absorption of C_ab (Féret et al. 2011). Compared to the reflectance-based VIs of C_ar, the transmittance-based ones involved wavelengths between 500 and 600 nm (green light) and 400 and 500 nm (blue-violet light) in ND and D. The range between 500 and 600 nm was revealed to be the maximum absorption peak of C_ar, especially around 520 nm (Hernández-Clemente, Navarro-Cerrillo, and Zarco-Tejada 2012; Zhou et al. 2017), with transmittance-based D in this paper using a wavelength of 524 nm. The spectral domain between 400 and 500 nm was also reported to be important for C_ar estimation as one of its absorption peaks (Blackburn 1998; Zhou et al. 2017).

For the VIs of EWT, the wavelengths in the reflectance-based and transmittance-based VIs in this paper were relatively close (around 1100–1600 nm). Ceccato et al. (2001) reported that EWT affects most of the spectral range of 900–2500 nm of leaf reflectance and transmittance. The results of this paper agree with many previous studies (Colombo et al. 2008; Klemas and Smart 1983; Zarco-Tejada, Rueda, and Ustin 2003), which found that the characteristic wavelengths for EWT were between 1200 and 1500 nm due to its extensive absorption domain.

For the VIs of LMA, we have identified highly consistent wavelength combinations near 1370 nm and 1720 nm, which were used by many transmittance and reflectance-based VIs. These wavelengths are very close to the combination of 1368 and 1722 nm used by Cheng et al. (2014). In addition, a combination of 1190 and 1288 nm was used in reflectance-based D. This may be due to the influence of EWT, as the relatively strong correlation between EWT and LMA may interfere with the wavelength selection of LMA (Féret et al. 2011). Figure 7 also shows that the transmittance-based D with the optimal performance has strong sensitivity to EWT.

As can be seen in Figure 8, the density of the simulated data for most biochemical traits coincides with the separated observations, except for leaf carotenoids (C_ar) in Figure 8d. This is mainly due to the fact that the specific absorption coefficient spectra of C_ar in the PROSPECT-D model do not cover the wavelengths selected for VIs closely related to C_ar in this study (Figure 8d). The best reflectance and transmittance-based VIs for C_ar in this study used wavelengths of 576 nm, 711 nm, 754 nm, and 756 nm, while the PROSPECT-D model sets specific absorption spectra of C_ar in the range of 400–560 nm. The leaf reflectance and transmittance of these wavelengths are thereby independent of the C_ar content in the simulated data.

4.3. Evaluation of the optimal VIs based on transmittance or reflectance

In this study, the performance of a VI was evaluated from two aspects: the estimation accuracy toward the target functional trait and the ability to resist interference from other parameters. First, our results showed that transmittance-based VIs outperformed those using reflectance for retrieving leaf C_ar, EWT, and LMA (Tables 5–7). The case with leaf C_ab was an exception, with reflectance-based D performing better than all transmittance-based VIs.

In terms of the ability to resist interferences, all transmittance and reflectance-based VIs for C_ab and EWT were hardly disturbed by other leaf parameters (Figure 7), which can be attributed to their dominant absorption characteristics in the visible light and near-infrared region, respectively (Féret et al. 2021; Sun et al. 2018). On the other hand, the VIs for estimating C_ar and LMA often show considerable sensitivity to another parameter simultaneously, due to their covariance with confounding parameters (Le Maire et al. 2008). The transmittance-based VIs for EWT resisted the influence of interference parameters more than their reflectance counterparts, due to the considerably higher sensitivity of transmittance to EWT than reflectance (Figure 2). Reflectance-based VIs of C_ab are less sensitive to confounding parameters than VIs based on transmittance, although the transmittance spectra are more sensitive to C_ab than reflectance in a larger spectral region. This is due to the fact that most of the selected wavelengths in VIs for C_ab exceeded 680 nm (Table S2), where reflectance was more sensitive to C_ab (Figure 2). For the VIs for estimating C_ar, Figure 7b shows that they are highly sensitive to C_ab, both in transmittance and reflectance-based ones. Leaf trait EWT and N are the main confounding factors for LMA estimation. Compared with the reflectance-based VIs, the transmittance-based VIs for LMA improved resistance to interference from EWT and N (Figure 7d). Although Spafford et al. (2021) reported that N affects short-wave infrared signals especially due to strong light scattering inside the foliage, this study shows that the effect of N on transmittance is relatively low (Figure 2).

4.4. Limitations and prospect of transmittance-based VIs

This study demonstrated the good performance of transmittance-based VIs in leaf traits estimation, especially in estimating EWT and LMA, yet several limitations remain. First, the robustness of the proposed VIs based on transmittance in estimating leaf functional traits needs further validation. Although extensive experimental datasets have been used when constructing the transmittance-based VIs, their species coverage is limited. The use of radiative transfer modeling may alleviate this problem, yet Le Maire et al. (2008)’s study showed that the performance of the optimal VIs established using simulations alone can be poor, especially for LMA estimation. Our results also provide evidence that simulated C_ar VIs based on leaf transmittance do not correspond well to actual measurements (Figure 8d). Le Maire et al. (2008) also suggested that the best way to find effective VIs is to use a large experimental database. Therefore, more in situ measurements or refinement of physical models may contribute to solving this problem.

Second, our results are valuable for improving the efficacy of some proximal measurement devices. For example, these VIs proposed in this study can be integrated on handheld instruments to achieve real-time, nondestructive, and high-precision measurements of leaf biochemical traits. Such handheld leaf meters include Minolta SPAD-502 (Konica-Minolta, Tokyo, Japan), Dualex 4 Scientific (FORCE-A, Orsay, France), CCM-200 (Opti-Sciences, Hudson, NH), CL-01 (Hansatech, King’s Lynn, UK), and TYS-3N (Zhejiang Top Instrument Co., China), etc., which are widely used in agroforestry to track the physiological state of leaves (Casa et al. 2014; Chang and Robison 2003; Donnelly et al. 2020). However, the significance of transmittance-based VI at the canopy scale is ambiguous. Fortunately, some studies have focused on the application of canopy transmittance, making it possible to further upscale our research. The canopy transmittance has long been measured by multiple commercial optical instruments, including LAI-2000 Plant Canopy Analyzer, AccuPAR, and Tracing Radiation and Architecture of Canopies (TRAC) (Jonckheere et al. 2004), and has been used in estimating the leaf area index and average leaf inclination angle (Garrigues et al. 2008; Lathrop and Pierce 1991). Specifically, the development of airborne scanning LiDAR yielded successful estimates of canopy transmittance (Essery et al. 2008; Parker, Lefsky, and Harding 2001; Todd, Csillag, and Atkinson 2003; Varhola et al. 2012). However, canopy transmittance is greatly affected by canopy structures such as leaf area index and gap fraction. Therefore, these confounding factors must be removed before applying canopy transmittance to estimate leaf biochemical parameters. Nevertheless, the upscaling of VIs is a task that needs to be explored in the future.

5. Conclusion

Considering the potential of leaf transmittance in reflecting changes in leaf biochemical traits over leaf reflectance, the present paper aims to propose transmittance-based VIs to improve the estimation of leaf traits including C_ab, C_ar, EWT, and LMA. We observed significant differences in the sensitivity of leaf transmittance and reflectance to leaf traits in the visible and short-wave infrared regions. The optimal reflectance and transmittance-based VIs (ND, SR, and D) were proposed through wavelength selection using three experimental datasets. Cross-validation results showed that the VIs established based on transmittance can effectively improve the estimation of C_ar, EWT, and LMA compared to their reflectance counterparts, although reflectance-based D provided the highest estimation accuracy of C_ab. The results of sensitivity analysis of VIs showed that VIs constructed by transmittance were more sensitive to EWT or LMA and less disturbed by other parameters compared with reflectance-based VIs. The optimal VI for C_ab is D_R (732,770) (RMSE = 7.36 μg/cm²), for C_ar is ND_T (576,711) (RMSE = 2.64 μg/cm²), for EWT is ND_T (1467,1540) (RMSE = 0.0018 g/cm²), and for LMA is SR_T (1377,1720) (RMSE = 0.0018 g/cm²), with the subscript representing the leaf transmittance (T) or reflectance (R) version. The findings of this study provide novel insights for determining the optimal VIs of leaf traits, and our proposed transmittance-based VIs showed good applicability and accuracy for traits estimation of fresh broad leaves.

Acknowledgements

This study was supported by the National Natural Science Foundation of China (42001314) and the Open Research Fund of the State Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University (Grant No. 20R02). Torbern Tagesson was additionally funded by the Swedish National Space Agency (SNSA 2021-00144) and FORMAS (Dnr. 2021-00644).

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The ANGERS and LOPEX datasets that support the findings of this study are openly available in OPTICLEAF database at http://opticleaf.ipgp.fr/index.php?page=database. The NJU dataset that supports the findings of this study is available from Feng Qiu with the permission of Nanjing University, Nanjing, China.

Supplementary material

Supplemental data for this article can be accessed online at https://doi.org/10.1080/15481603.2023.2168410

Additional information

Funding

The work was supported by the National Natural Science Foundation of China, the Open Research Fund of the State Laboratory of Information Engineering in Surveying, Mapping, and Remote Sensing, Wuhan University, the Swedish National Space Agency (SNSA 2021-00144), and FORMAS (Dnr. 2021-00644).