2.1.

Leaf Sampling in the Study Area

Leaves from ten unique plants, including Prunus padus L., Swida alba Opiz, Acer saccharum Marsh, Armeniaca vulgaris Lam., Populus L., Epipremnum aureum, Schefflera microphylla Merr, Pachira aquatica, Juglans, and Citrus limon (L.) Burm. F. were collected from the Garden of Northeast Normal University, Changchun, Jilin, China. A total of 277 samples of 10 unique plant species were collected, as shown in Fig. 1. The basic statistics for the calibration dataset is shown in Table 2. All samples were collected by the most reliable and accurate method for reflectance. Before measurement, the samples were kept hydrated in a dark environment with high humidity and a low temperature, and all of the samples were mature leaves.^35–38 As in other studies, we only selected fresh leaves with a consistent color with no obvious signs of illness.^39,40

Fig. 1

(a)–(j) Leaf samples from various plant types were used in this research.

To detect spectrum reflection, we utilized the Northeast Normal University Laboratory Goniospectrometer System (NENULGS).⁴¹ An Analytical Spectral Devices FieldSpec4 and a goniometer was included in NENULGS, which was comprehensively discussed in the article.⁴¹ Several research studies have used NENULGS to analyze various leaf characteristics^42–44 precisely. The reflectance measurement was followed by a fresh weight measurement, which was afterward air-dried to a stable weight. The samples were dried in the oven for 36 hrs at 80°C, and their dry weight was calculated.³⁸ While the measurements were being taken, the leaf sample was placed on an object stage entirely covered with dark black tape. Because the black backdrop has a wavelength-independent reflectance factor of less than 0.05, it does not affect leaf reflection. The reflected radiance (dLSample) from the leaf sample surface is normalized by the reflected radiance (dLReference) from the reference surface (Spectralon) in the same viewing geometry to give the bidirectional reflectance factor (BRF)⁴⁵

2.2.

Definition of Water Equation Used

Several techniques, which include EWT, PWC, and GWC, were used to assess the water condition of leaves. EWT is the term used to describe how much water is present and how much energy is absorbed per unit of leaf area.^28,46 PWC relates to the dry weight ratio, and GWC determines the weight of the fresh and dry leaves.

Below is the correspondence for EWT, PWC, and GWC

2.3.

Choosing the Optimal Index by Iteration Method

We implemented the Datt type of index (combination of three different bands), which has been popularly used recently.⁴⁷ For EWT, PWC, and GWC, using MATLAB code to assess the best index in this study using a 5-nm wavelength interval with iteration method on the calibration datasets. The iteration process was programmed in such a way that those wavelength combinations with higher $R^2$ come out from the large amount of data, which has been taken during leaf sample reflection measurement. The equation is defined as

2.4.

Published leaf Water Indices

Different hyperspectral indices depend on the double difference ratio of three individual wavelengths within a specific spectrum and have been taken into account to figure out plant water content on the calibration dataset. For this analysis, ten previously published indices were chosen to test their effectiveness regarding how they respond to the data from the leaf dehydration experiment used in this work. The selected indices are listed in Table 1.

Table 1

Published water indices for determining the water status of leaves.

2.5.

Leaf Reflection Factors: Spectral Properties and Distribution

The spectral reflectance factors with multiple indicators at the nadir view zenith angle are shown in Fig. 2. The considerable absorption of leaf water at wavelengths greater than 1250 nm resulted in the spectral BRF of leaves being constrained as the different water indices shown in the nadir direction in NIR and SWIR wavelengths.³⁸ Various spectral indices are associated with these spectral properties to measure the water content. When the reflectance factor is considered, it can be used to understand the reflection attribute of leaves from various species.

Fig. 2

(a)–(d) Leaves BRF at nadir direction with variables EWT, GWC, and PWC.

3.1.

Statistical Analysis

A collection of 277 leaf samples from 10 different species was analyzed to determine the best hyperspectral index for calculating leaf water content. To assist in finding unique indices, several statistical tests were performed on data sets. The best indices were then chosen, and their robustness was verified and validated. First, some basic statistics were applied to the calibration dataset, as shown in Tables 2 and 3. Equations (2)–(5) have been used to calculate the results in Table 2.

Table 2

The statistics provided below were utilized to calculate the EWT, GWC, and PWC of the samples used.

Table 3

Summary statistics for calibration data (n=277).

Additionally, the regression approach expands to both linear and nonlinear regression. The procedures described were applied to all possible wavelength combinations, and an iterative approach resulted in a wavelength interval of 5 nm.^28,38 The parameters of published indices were selected using the maximum coefficient of determination ($R^2$), and the least root mean square error (RMSE). The principal objective was to identify indices with minimum RMSE and the highest $R^2$ values.

3.2.

Outcome of the Published Indices

Selected published indices performance in this study was analyzed individually to assess variation in EWT, PWC, and GWC. These published indices, which include $(R_{860}-R_{1640})/(R_{860}+R_{1640})$, $(R_{850}-R_{2218})/(R_{850}-R_{1928})$, $(R_{850}-R_{1788})/(R_{850}-R_{1928})$, $(R_{1600}/R_{820})$ and $(R_{858}-R_{1640})/(R_{858}+R_{1640})$, have good results in terms of EWT with calibration data sets, and no other indicator have a good result with the calibration dataset. The detail for each indicator and the corresponding results has been given in Table 4.

Table 4

The evaluation of published water indices for EWT, PWC, and GWC using calibration dataset.

3.3.

Newly Identified Leaf Water Status Index

Calibration dataset for EWT, PWC, and GWC was examined using an iteration process for 5-nm interval for linear [Eq. (7)] and nonlinear [Eq. (8)] regression approaches. The regions with the highest $R^2$ [Eq. (9)] and lowest RMSE value were finally selected based on reflectance spectra. In general, particular bands were strongly correlated with EWT, PWC, ${\mathrm{GWC}}_{\mathrm{D}}$, and ${\mathrm{GWC}}_{\mathrm{F}}$, as shown in Tables 5 and 6. The approach used in this was linear and nonlinear regression, respectively. Overall, the newly identified indices have a notable correlation with EWT, whereas PWC and GWC were not as good as EWT.

Table 5

Evaluation of four types of indices using a linear regression approach.

Table 6

Using a nonlinear regression technique, four different types of indices are evaluated.

3.4.

Regression Analysis

Linear and nonlinear regressions were executed to develop models, determine the coefficient of determination between different wavelength ranges and water indices, and compare the model’s efficiency

The results for both linear and nonlinear models are shown in Figs. 3 and 4. By looking at the coefficient of determination, we can easily analyze the indices.

Fig. 3

Utilizing calibration data, linear regression models were used to calculate the coefficient of determination of the selected wavelength and WI (EWT, ${\mathrm{GWC}}_{\mathrm{F}}$, ${\mathrm{GWC}}_{\mathrm{D}}$, and PWC).

Fig. 4

Nonlinear regression models were used to obtain the coefficient of determination of the selected wavelength and WI using calibration data (EWT, ${\mathrm{GWC}}_{\mathrm{F}}$, ${\mathrm{GWC}}_{\mathrm{D}}$, and PWC).

3.5.

Validation Datasets from Different Sources

The leaf optical properties experiment (LOPEX) of the European Commission’s Joint Research Center includes 330 leaf samples from 45 diverse plants.⁵² An experiment conducted at the INRA (National Institute for Agricultural Research) in Angers, France in June 2003, where a dataset associating visible/infrared spectra of vegetation elements with physical measurements and biochemical analyses was constructed. Reflectance and transmittance measurements of 275 leaf samples from 43 different species were collected along with associated biochemical and physical measurements.^28,53

Additional data from the LOPEX and ANGERS databases were considered to validate the indices provided in this work and determine their generalizability and reliability. As for both the databases reflectance curves with median spectrum have been measured, as shown in Fig. 5. First, EWT, GWC, and PWC were calculated and further expanded to assess $R^2$ and RMSE for the proposed spectral indices (Table 7).

Fig. 5

Reflectance spectrum from validation dataset (a) ANGERS and (b) LOPEX. The median spectrum is shown by the dashed red line.

Table 7

Validation datasets to calculate EWT, GWC, and PWC.

In the LOPEX dataset, the proposed index exhibits better results in terms of EWT having a strong coefficient of determination with the lowest RMSE ($\mathrm{g}/{\mathrm{cm}}^2$), as shown in Fig. 6.

Fig. 6

The validation of results of both linear and nonlinear indices of EWT, ${\mathrm{GWC}}_{\mathrm{F}}$, ${\mathrm{GWC}}_{\mathrm{D}}$, and PWC. Based on using the LOPEX database, RMSE is computed based on these models; $R^2$ is the determination coefficient, where panels (a) and (b) refer to linear and nonlinear regression indices, respectively.

The above Fig. 6 shows the result for EWT $(R_{1910}-R_{1340})/(R_{1910}-R_{1125})$ and $(R_{1930}-R_{1425})/(R_{1930}-R_{1360})$, ${\mathrm{GWC}}_{\mathrm{F}}$ $(R_{1400}-R_{1835})/(R_{1400}-R_{1505})$ and $(R_{1395}-R_{1825})/(R_{1395}+R_{1515})$, ${\mathrm{GWC}}_{\mathrm{D}}$ $(R_{1400}-R_{1835})/(R_{1400}-R_{1505})$ and $(R_{1515}-R_{1825})/(R_{1515}-R_{1395})$ and PWC $(R_{1495}-R_{1400})/(R_{1495}-R_{1830})$, and $(R_{1500}-R_{1400})/(R_{1500}-R_{1830})$.

While in the ANGERS dataset, the indicators were individually compared to the proposed indices. The results were encouraging for EWT, which had the highest $R^2$ and minimum RMSE values, as shown in Fig. 7.

Fig. 7

The validation of results of the EWT, GWC, and PWC based on using the ANGERS database. RMSE is calculated based on these models and $R^2$ is the determination coefficient. Panels (a) and (b) refer to linear and nonlinear regression indices, respectively.

The Fig. 7 presented the result for EWT $(R_{1910}-R_{1340})/(R_{1910}-R_{1125})$ and $(R_{1930}-R_{1425})/(R_{1930}-R_{1360})$, ${\mathrm{GWC}}_{\mathrm{D}}$ $(R_{1400}-R_{1835})/(R_{1400}-R_{1505})$ and $(R_{1515}-R_{1825})/(R_{1515}-R_{1395})$ and PWC $(R_{1495}-R_{1400})/(R_{1495}-R_{1830})$, and $(R_{1500}-R_{1400})/(R_{1500}-R_{1830})$.

So generally, it is concluded that both the databases, i.e., LOPEX and ANGERS have good correlations with the suggested indices (linear and nonlinear), specifically with EWT. While for the other two indices, such as GWC and PWC, LAI is not involved in measuring water content.

3.6.

Best Indicators for Defining the Status of Leaf Water

Ratio of modified difference, normalized difference index, double difference (R1 − R2/R1 − R3), and simple ratios (SR) are the most commonly used criteria for evaluating leaf water indices. These criteria typically disrupt standard water-absorbing indices, such as water index (WI), normalized differential water index (NDWI), and water index using a simple ratio (SRWI), because they vary and use different wavelengths. Our findings also show that the combination of the $(R1\text{-}R2)$ and $(R1\text{-}R3)$ bands significantly impacts the status of leaf water. In this study, the linear regression model $(R_{1910}-R_{1340})/(R_{1910}-R_{1125})$ having $R^2=0.9692$ and $\mathrm{RMSE}=0.0017(\mathrm{g}/{\mathrm{cm}}^2)$ while the nonlinear regression model $(R_{1930}-R_{1425})/(R_{1930}-R_{1360})$ having $R^2=0.9596$ and $\mathrm{RMSE}=0.0019({\mathrm{g}/\mathrm{cm}}^2)$ shows good results as compared to the already published indices. Therefore, the recommended indices are more dependable and persistent in calculating leaf water content for the plants species used in this study.

The results have been further verified by LOPEX and ANGERS datasets; as we can see in Fig. 7, both the suggested indices have performed well in terms of $R^2$ and RMSE, which further strengthens the results on the proposed linear and nonlinear indices. Figure 7 indicates that EWT, with LOPEX and ANGERS, has come up with better results than the other water indicators, such as GWT and PWC.⁵⁴ Both, the indices have shown reliable results with calibration data set, but to make these indices more generalized and could be used for any type of plant leaf that’s why we have to check the accuracy and the reliability of the proposed indices with already published and worldwide used databases, such as LOPEX and ANGERS and while looking at the results, as shown in Fig. 7, we can see that the indices proposed in this study are reliable and accurate.

4.1.

Stability of the Index Suggested

The proposed EWT linear and nonlinear indices were tested with odd combinations until 57 nm in both a forward and backward manner within the calibration dataset. The combination of the proposed indices has been made with the difference of odd numbers (to take the average), such as 5, 9, and 13 nm, until 57 nm and they showed stability and a strong determination coefficient on both aspects, indicating their correctness and dependability as shown in Fig. 8. Theoretically, a valid and reliable index should be assessed for calibration on numerous datasets with varying random percentages and to keep high stability under different wavelength resolution.^38,55 Newly proposed indices have the potential to be expanded to enormous sizes and would satisfy future applications due to their intensity and dependability.³⁸

Fig. 8

From calibration dataset: suggested bandwidth index for EWT with reliable stability showing both (a) linear and (b) nonlinear indices.

4.2.

Leaf Properties Based on Individual Wavelength

We have checked the individual wavelength and their correlation coefficients. In the single band, the correlation coefficient is relatively low with the calibration dataset. But these individual bands play a crucial role in estimating leaf water content because they cover the sensitive region where water can be traced. The main theme of doing this is to show how they respond separately, and when it came to bands combination, they have shown good results. As a result, we used a technique that included specified steps to examine how each band of the indices related to reflectance, as shown in Fig. 9.

Fig. 9

Relationship between EWT and reflectance from calibration data set at (a) linear (bands): $R_{1125}$, $R_{1340}$, and $R_{1910}$ (nm) and (b) non-linear (bands): $R_{1360}$, $R_{1425}$, and $R_{1930}$ (nm). Power curves of the form best represented the relationships as $y=a{x}^{-b}$. Correlation coefficients ($r$) are shown.

The mean spectra of leaves for various EWT ranges are illustrated in Fig. 10. At 1350 to 1580 nm, leaves with high EWT and other indicators show comparatively low reflectance. The spectral region of the reflectance spectrum is primarily influenced by pigment absorption (mostly by chlorophyll molecules).^56,57 Increased relative reflectance at wavelengths between 1400–1580 nm resulted from the dehydration of leaves, affecting their optical characteristics. However, numerous published research documents erratic changes in leaf reflectance during dehydration, such as an overall rise, a decrease, and no significant fluctuations in reflectance.^56,58 After using the first derivative of relative reflectance, these outcomes were more obvious as shown in Fig. 10(b). The trend of the Pearson’s correlation coefficients (rP) in the relationship between the EWT and wavelength-dependent relative reflectance values shown in Fig. 10(c).^18,34 While Fig. 10(d) demonstrates how rP has changed over time in the relationship between the wavelength dependent first derivative of the relative reflectance values and EWT.

Fig. 10

(a) Reflectance spectral signatures, (b) first derivative for reflectance, (c) EWT correlation coefficient (rp) and reflectance spectra correlation, and (d) first derivative of reflectance.

As Fig. 11 demonstrates that the indices’ values are restricted to the ranges of 0.6 to 1.0 for LOPEX and 0.001 to 0.04 for ANGERS (horizontal axis). Leaf samples were utilized to evaluate the model. The relative RMSE was calculated in relation to the mean measured values. Overall, it is evident that the model’s predicted values and the measured values exhibit a strong linear positive connection. Most of the existing research on the association between the water content of leaves and their ability to reflect light (particularly EWT) is restricted to several unique species and specific wavelengths. However, in our study, we try not to keep ourselves to specific species; as a result, the method applies to any species for EWT calculation.

Fig. 11

The results of validation of EWT based on using the (a) LOPEX and (b) ANGERS databases. RMSE is computed based on the EWT model and $R^2$ is the coefficient of determination.

Due to changes in water indices and interior leaf structure, the spectral reflectance fluctuates slightly, mainly in the infrared and NIR. This study examines whether a water sensitivity index can accurately estimate the EWT of different plant species.

4.3.

Advantages of the Proposed Indices

Nowadays, most EWT indices are calculated using measurements of the reflectance factors of leaves obtained with an integrating sphere, a spectrometer equipped with a leaf clip, or a spectrometer positioned close to the nadir direction.⁵⁰ Although it has not received much attention from academics seeking to estimate EWT, the specular reflection off the leaf surface in these directions has little impact on spectral reflection measurements. In a variety of illumination-viewing geometries over a wide range of species, the newly suggested index can reduce the specular reflection brought on by the leaf surface. Compared to other existing indices in this study, this enables these indices to have the best relationship with EWT and the lowest sensitivity to reflectance variables.

The proposed indices also have the advantage of being adaptable to additional observed and simulated datasets containing reflected signals from other plant species in various geographic locations or regions under various measurement conditions. The reflectance factors of leaves take into account reflection values that are equivalent to those measured by leaf clip or integrating sphere, as well as reflectance factors that are dominated by specular reflection from the leaf surface, which result in the expected phenomena.