The aim of this study is to construct a down-scaling inversion strategy for retrieving the CWC, which integrates the modified spectral down-scaling model and the LWC inversion model. This integration is intended to alleviate the influence of canopy structure and soil background, with the ultimate goal of accurately estimating the CWC. The primary objective of down-scaling is to convert canopy-level reflectance spectra to leaf-level reflectance spectra, enabling more accurate estimation of the LWC and subsequently the CWC. The process involves several key steps, as detailed below: (1) Spectral Down-scaling: The canopy spectra are decomposed into leaf reflectance spectra by applying the down-scaling model, which accounts for the structural and optical properties of the canopy. Using our modified spectral down-scaling model, we convert the canopy reflectance spectra (measured at the 30 m × 30 m spatial resolution) to leaf reflectance spectra. (2) LWC Estimation: The EWT of the leaves was retrieved from the down-scaled leaf reflectance spectra using a leaf-scale EWT inversion model, which has been calibrated with PROSPECT simulated data. This step ensures that the water content at the leaf level is accurately estimated. (3) Calculation of the CWC: The estimated leaf EWT values are then combined with the LAI estimates at each site to calculate the overall CWC. This integration step translates the leaf-level EWT back to the canopy level, ensuring coherence with the initial spatial resolution of the satellite data. This dual-level approach (canopy to leaf and back to canopy) enhances the reliability and applicability of the retrieved water content data.
2.4.1. Coupled Down-Scaling Inversion Strategy
The workflow of the coupled down-scaling inversion strategy is illustrated in
Figure 2. The specific steps involved in the process are as follows: (1) To preprocess the remote sensing image, including atmospheric correction, geometric correction, pixel classification, and masking of non-vegetation pixels, using Environment for Visualizing Images (ENVI) software (Version 5.3); (2) To retrieve LAI using an algorithm developed by Wu et al. [
26]. This algorithm based on empirical relationships was calibrated using observations and the Modified Simple Ratio (MSR
705) derived from the same Hyperion image [
26]; (3) To determine soil reflectance. Since the study area primarily consists of gray soil and red soil, with gray soil being the predominant type, the reflectance of gray soil, as recorded in the soil spectral database, was utilized to represent the background reflectance of the study area; (4) To develop a modified spectral down-scaling model on the basis of the 4-Scale GO model [
29] to estimate leaf reflectance using hyperspectral images from the satellite at the canopy level; (5) To retrieve the leaf-level mean water content through the application of the leaf-level Similarity Water Index (SWI)-based inversion model, utilizing the estimated leaf-level reflectance; (6) To calculate the canopy-level water content by multiplying the retrieved leaf water content with canopy LAI, as shown in Equation (3):
where
is the mean LWC at the pixel scale (g/cm
2),
EWTcanopy is the CWC at the pixel scale (g/m
2), and 10
4 is the unit conversion factor.
The estimated values from the coupled model were compared with the satellite-ground synchronous measurements obtained from site sampling. The comparison of estimated and actual leaf and canopy EWT was conducted using the nRMSE and the adjusted R2 ().
The nRMSE is calculated by the following Equation (4):
where EWT
max and EWT
min are the maximum and minimum EWT, respectively.
2.4.2. Four-Scale Geometric Optical (GO) Model
Chen and Leblanc’s [
29] 4-Scale GO model assumed that canopy reflectance is a linear combination of four components/fractions: sunlit leaves, sunlit background, shaded leaves, and shaded background [
29,
30], as shown in Equation (5):
where
is the canopy reflectance observed from satellites,
and PT represent the reflectance of and the probability of viewing sunlit leaves,
and ZT represent the reflectance of and the probability of viewing shaded leaves,
and PG represent the reflectance of and the probability of viewing sunlit backgrounds,
and ZG represent the reflectance of and the probability of viewing shaded backgrounds, respectively.
Therefore, the forward modeling process from the leaf spectrum to the canopy spectrum is divided into two steps. First, a simulated observation scene is established based on the input vegetation canopy structure parameters and observation geometric parameters, etc., and the probabilities of viewing these four components (PT, ZT, PG, and ZG) in the simulated scene are calculated. The structural effects were determined by the spatial distribution of tree groups, the geometry of tree crowns, tree branching, and scattering elements. Structural and angular variations in multiple scattering processes are simulated using a multiple scattering scheme that is based on the viewing factors of the four canopy components [
31]. The canopy structural parameters were provided by field measurements at our study sites. The observation geometric parameters were determined from the Hyperion image.
Then, canopy reflectance spectra were simulated based on the input optical properties of leaf and forest backgrounds and the four canopy components of the observation scene [
29,
30]. The optical properties of leaf and forest backgrounds have been provided by field and laboratory measurements at our study sites.
Table A2 in
Appendix A lists the structural and other parameters incorporated in the 4-Scale GO model for the study sites. The corresponding canopy reflectance and probabilities of viewing sunlit and shaded fractions were estimated for each observation scene in the output.
2.4.3. Modified Spectral Down-Scaling Model
A modified spectral down-scaling model was proposed to invert the leaf reflectance spectrum using the canopy reflectance spectrum based on the 4-Scale GO model. In order to invert the leaf reflectance spectrum from the canopy reflectance spectrum, Zhang et al. [
24] introduced a multiple scattering factor M and proposed a spectral down-scaling model based on the 4-Scale GO model, as expressed in Equation (6):
where
is the individual leaf reflectivity, which is approximately equal to the reflectivity of sunlit foliage, while the former contains multiple scattering;
,
,
PT, and
PG have the same variable interpretation as in Equation (5). Multiple scattering factor M includes contributions from two shaded components and multiple scattering components.
Among the five input parameters of the spectral down-scaling model, canopy reflectance spectra are derived from satellite remote sensing images. Assuming that the background reflectance is known, the conversion of canopy reflectance spectra to single-leaf reflectance can be realized only by further calculating PT, PG, and M.
Theoretically, M can be calculated from the following Equation (7) [
24]:
In practical application,
M cannot be determined by the above equation because
is unknown. In order to solve this problem, Zhang et al. [
24] developed lookup tables (LUTs) based on the simulation results of the 4-Scale GO model to retrieve PT, PG, and M.
Given that canopy reflectance
and forest background reflectivity
can be measured remotely, it is necessary to estimate the PT, PG, and M parameters to invert the leaf reflectivity
. The 4-Scale GO model was used to develop two LUTs to account for different canopy structures and viewing angles. In order to simplify the process, two LUTs were designed based on observation geometric parameters (VZA, SZA, and PHI) as well as LAI to estimate the PT and PG components and M factor, respectively. However, we found that there is no one-to-one correspondence between the variables in the lookup tables (see
Section 3.1 and
Figure 3), which would lead to an ill-conditioned retrieval problem.
To address this ill-conditioned retrieval issue inherent in the original LUT method, we have modified the LUT approach to make it more efficient. An estimation model based on the normalized spectral angle index (NSAI), which shows significant potential for estimating PT and PG from canopy spectra observed by satellites at the pixel level, replaced the traditional LUTs for PT and PG, enabling direct acquisition of high-precision PT and PG values from satellite canopy reflectance (see reference [
25] and
Section 3.2). As shown in Equation (7), the M value is computable utilizing PT, PG, canopy reflectance, single-leaf reflectance, and background reflectance. Analysis revealed that with PT, PG, and background reflectance held constant, the conversion relationship between canopy and single-leaf reflectance is primarily related to LAI. Therefore, when PT and PG are estimated, the M lookup table of the original down-scaling model can be adapted to utilize PT, PG, and LAI as search parameters, creating a new lookup table for M. In the initial phase of calibration for the NSAI-based PT and PG estimation model and to compute M values across various retrieval combinations, we employed the 4-Scale GO model. This model simulated the Hyperion canopy reflectance of the study area, with the simulation’s precision validated (as detailed in
Table A3 in
Appendix A). Based on the Hyperion simulation dataset, we calibrated and validated the NSAI-based PT and PG estimation models and constructed a new lookup table for M using PT, PG, and LAI as the retrieval items. The modified spectral down-scaling model not only solves the problems that existed before, but makes it simpler.
2.4.4. PT and PG Prediction Model
PT and PG are pivotal variables in the modified spectral down-scaling model. Fang et al. [
25] introduced an effective method for estimating PT using the NSAI, which shows significant potential for estimating PT and PG. The NSAI was calculated based on a pixel-level canopy spectrum observed by satellites at the Red (645 nm), NIR (858 nm), and SWIR (1240 nm) wavelengths to estimate PT.
The efficacy of the NSAI-based PT model was corroborated using Hyperion data, revealing an nRMSE and an adjusted R
2 for an estimated PT of 14.9% and 0.744, respectively [
25]. Notably, the empirical NSAI-based PT model demonstrated strong transferability from simulated to in situ satellite data, underscoring its utility.
Theoretical analysis indicates that the NSAI is predominantly influenced by PT and PG. The relationship was further validated using the simulated data, and a strong correlation between these variables was observed (see
Figure A2 in
Appendix A). Building on this, the current study adopts the PT inversion model construction method described by Fang et al. [
25] to also develop a PG inversion model based on the NSAI, aiming to enhance the precision of the results. The derived PT and PG values, in conjunction with the LAI, facilitate the determination of the spectral multiple scattering factor M using a lookup table. These values are then applied in conjunction with M as inputs into Equation (6) to translate canopy reflectance into single-leaf reflectance, optimizing the inversion process.
2.4.5. Leaf-Level Water Content Prediction Model
Fang et al. [
32] introduced the spectral similarity water indices (SWIs) as a means to effectively estimate the LWC (EWT) by utilizing the Spectral Angle Cosine (SAC) of leaf reflectance spectra and the specific water absorption spectrum. In this study, the spectral intervals (970–1150 nm) have been chosen based on the spectral characteristics of Hyperion to calculate the SWI index using the following Equation (8):
where
r and
w are the vectors representing the reflectance spectra of the leaves and the specific water absorption spectrum, which are assumed to comprise reflectance components from the Hyperion bands within the spectral domain (970–1150 nm), with the number of bands denoted as L.
EWT can be predicted using the following Equation (9):
where
a and
b are the coefficients obtained by calibration.
In order to assess the retrieval performance of SWI-based EWT models on Hyperion remote sensing data, the measured reflectance of all samples was resampled to acquire Hyperion-equivalent spectra.
Moreover, the transferability of the SWIs-based EWT models from simulation to in situ data has also been tested using Hyperion-equivalent spectra simulated by the PROSPECT to calibrate the models and the measured data to test the models. For the comparison, the SWI indices and six commonly used spectral indices specifically designed to estimate vegetation water content were calculated using the Hyperion-equivalent spectra. These indices include the Maximum Difference Water Index (MDWI), NDWI, Normalized Difference Infrared Index (NDII), Moisture Stress Index (MSI), Shortwave Angle Slope Index (SASI), and SANI. The correlations between these indices and EWT were then analyzed.
The calibrated regression models were further applied to the Hyperion-equivalent spectra of all measured samples, and the measured LWC was used to verify the performance of the SWIs-based EWT models and the indices-based EWT models. The resultant and nRMSE values between the estimated and reference EWT were calculated.