Enhancing Transpiration Estimates: A Novel Approach Using SIF Partitioning and the TL-LUE Model

Abstract

Accurate evapotranspiration (ET) estimation is crucial for understanding ecosystem dynamics and managing water resources. Existing methodologies, including traditional techniques like the Penman–Monteith model, remote sensing approaches utilizing Solar-Induced Fluorescence (SIF), and machine learning algorithms, have demonstrated varying levels of effectiveness in ET estimation. However, these methods often face significant challenges, such as reliance on empirical coefficients, inadequate representation of canopy dynamics, and limitations due to cloud cover and sensor constraints. These issues can lead to inaccuracies in capturing ET’s spatial and temporal variability, highlighting the need for improved estimation techniques. This study introduces a novel approach to enhance ET estimation by integrating SIF partitioning with Photosynthetically Active Radiation (PAR) and leaf area index (LAI) data, utilizing the TL-LUE model (Two-Leaf Light Use Efficiency). Partitioning SIF data into sunlit and shaded components allows for a more detailed representation of the canopy’s functional dynamics, significantly improving ET modelling. Our analysis reveals significant advancements in ET modelling through SIF partitioning. At Xiaotangshan Station, the correlation between modelled ET and SIFsu is 0.71, while the correlation between modelled ET and SIFsh is 0.65. The overall correlation (R²) between the modelled ET and the combined SIF partitioning (SIF(P)) is 0.69, indicating a strong positive relationship at Xiaotangshan Station. The correlations between SIFsh and SIFsu with modelled ET show notable patterns, with R² values of 0.89 and 0.88 at Heihe Daman, respectively. These findings highlight the effectiveness of SIF partitioning in capturing canopy dynamics and its impact on ET estimation. Comparing modelled ET with observed ET and the Penman–Monteith model (PM model) demonstrates substantial improvements. R² values for modelled ET against observed ET were 0.68, 0.76, and 0.88 across HuaiLai, Shangqiu, and Yunxiao Stations. Modelled ET correlations to the PM model were 0.75, 0.73, and 0.90, respectively, at three stations. These results underscore the model’s capability to enhance ET estimations by integrating physiological and remote sensing data. This innovative SIF-partitioning approach offers a more nuanced perspective on canopy photosynthesis, providing a more accurate and comprehensive method for understanding and managing ecosystem water dynamics across diverse environments.

1. Introduction

Evapotranspiration is a critical component of the water and energy balances [1,2]. Accurately estimating ET is essential for understanding global terrestrial water flux and land–atmosphere interactions [3]. Reliable ET estimates are vital for linking water and carbon exchange, enhancing plant water use efficiency estimations, and refining projections of the global carbon cycle [3]. While traditional ET estimation methods, such as the Penman–Monteith and Priestley–Taylor models, are widely used for their simplicity and reasonable accuracy across various conditions [4], these models often depend on empirical coefficients and assumptions that may not be valid across diverse ecosystems and climatic settings. Early methods, such as the Thornthwaite approach, relied on empirical techniques using temperature and latitude to estimate potential ET [1]. While traditional methods like the Penman–Monteith equation and the Thornthwaite model have been used for their simplicity and ease of application, they often fail to capture spatial and temporal variations accurately. With technological advancements, remote sensing-based methods have emerged, leveraging satellite data to provide more comprehensive and spatially explicit ET estimates. Techniques such as SEBAL and METRIC (Mapping Evapotranspiration at High Resolution with Internalized Calibration) have improved ET estimation by integrating thermal and multispectral imagery to calculate energy balance components [5,6,7]. Machine learning techniques have facilitated the extraction of intricate patterns from large-scale datasets, leading to more robust ET models that can account for complex interactions between environmental variables [8].

Recent advancements in ET estimation methods have been driven by integrating machine learning techniques, remote sensing high-resolution data, and a deeper understanding of biophysical processes [9]. Combining ET estimation with hydrological models and data assimilation techniques has enhanced water resource management and drought monitoring capabilities. Integrating SIF observations with ecohydrological models better captures the complex interactions between vegetation dynamics and water fluxes across various spatial and temporal scales [10]. The ET estimation across different geographical and temporal scales necessitates a deep understanding of the relationships between SIF, stomatal conductance, photosynthesis, and ET. This complexity hampers the development of a universal model for ET variation and prediction across diverse global bioclimates [11]. Therefore, a more mechanistic understanding of SIF in sunlit and shaded leaves and stomatal conductance is essential for refining ET models at the ecosystem level. ET estimation methods have significantly evolved over the years due to technological advancements, data availability, and scientific understanding.

Remote sensing methods offer extensive spatial and temporal coverage, including Moderate Resolution Imaging Spectroradiometer (MODIS) (https://ladsweb.modaps.eosdis.nasa.gov/missions-and-measurements/modis/ (accessed on 20 January 2024)) products and satellite-based Solar-Induced Chlorophyll Fluorescence (SIF) platforms. However, both are limited by challenges such as cloud cover and sensor constraints, which affect the performance of all-optical remote sensing technologies [12,13,14]. These challenges highlight the need for advanced techniques to ensure accurate and consistent ET estimates across diverse landscapes [15]. Recent advancements in ET estimation involve the use of SIF and Gross Primary Productivity (GPP) [16,17]. SIF, a proxy for photosynthetic activity, enhances ET accuracy by providing insights into vegetation health and stress levels. The TL-LUE model utilizes SIF data to partition ET into its components, offering a more nuanced understanding of plant water use. Integrating SIF and GPP data represents a promising direction for improving the accuracy and spatial resolution of ET estimates, especially in complex landscapes and varying climatic conditions [18,19]. This approach aligns with ongoing research, including efforts involving the TL-LUE model, to better understand and predict ET dynamics across diverse ecosystems.

The two-leaf light use efficiency (TL-LUE) model estimates Gross Primary Productivity (GPP) by separately considering sunlit and shaded leaves, which helps accurately determine the photosynthetic activity. This model also connects to evapotranspiration (ET) as the stomatal conductance regulating CO₂ uptake for GPP controls water vapor release, linking photosynthesis and transpiration processes. Efficient energy use by sunlit leaves drives both GPP and ET, making the TL-LUE model valuable for understanding plant-water relations and managing water resources [20,21,22,23]. SIF, as a direct indicator of photosynthetic activity, provides a more mechanistic understanding of plant water use and physiological processes [24,25,26]. Incorporating Gross Primary Production (GPP) into this framework further improves ET estimates by linking carbon assimilation with water fluxes [27].

The effectiveness of SIF in determining ET is improved by distinguishing between sunlit and shaded leaves and integrating these components [16]. Incorporating SIF data into ET models provides valuable insights into plant responses to environmental stressors like drought and heat waves, improving our understanding of ecosystem resilience. These mechanistic methods offer a robust theoretical foundation for calculating ecosystem transpiration using satellite-derived SIF data [16]. SIF emissions may offer more accurate predictions of stand-level transpiration compared to conventional process-based models, particularly when examining extended records of SIF measurements [20]. Despite being critical for global climate and hydrology, global-scale transpiration estimations remain imprecise due to limited in situ measurements and the challenges associated with directly measuring transpiration. SIF retrievals present a promising alternative for inferring transpiration over extensive areas, given that transpiration is influenced by stomatal conductance (gs) and the anticipated relationship between gs and SIF emission [28]. Partitioning SIF into sunlit and shaded leaves could further enhance ecosystem transpiration estimates. The relationship between SIF from sunlit and shaded leaves and transpiration is complex and influenced by multiple factors.

Despite advancements in using sun-induced chlorophyll fluorescence (SIF) for estimating transpiration, the precise relationship between SIF emissions from sunlit and shaded leaves and transpiration rates remains poorly understood [29,30]. The lack of mechanistic insights into how sunlit and shaded SIF emissions influence transpiration limits the accuracy and reliability of ET estimation models based on SIF partitioning. Gaining a deeper understanding of the complex interactions between environmental factors, leaf physiology, and SIF emissions is crucial for enhancing SIF-based transpiration models [12,13]. By partitioning SIF into shaded and sunlit components, the TL-LUE model can more accurately estimate ET by accounting for the distinct responses of these leaf types to varying environmental conditions.

The main objective of this study is to enhance the reliability of evapotranspiration (ET) estimation by integrating the Solar-Induced Fluorescence (SIF) partitioning method with the TL-LUE model. Specifically, this research aims to: (1) Develop Partitioning Algorithms: Design algorithms to effectively partition SIF into sunlit (SIFsu) and shaded (SIFsh) components, considering factors such as solar radiation, leaf structure, and physiological processes. (2) Quantify SIF-Transpiration Relationships: Investigate the relationship between SIF emissions from sunlit and shaded leaves and transpiration rates to quantify the influence of SIF on transpiration. (3) Validate Estimates: Validate the transpiration estimates derived from SIF partitioning against ground-based measurements and other established ET estimation methods.

2. Materials and Methods

2.1. Datasets and Collection

Central to our investigation are datasets collected from five distinct stations (https://chinaspec.nju.edu.cn/EN/DATADOWNLOAD/DataDownload/index.html) accessed on 20 January 2024: Yunxiao Station, Xiaotangshan Station, Huailai Station, Heihe Daman Station [31], and Shangqiu Agricultural Station [32,33] (see

Table 1. Summary of Station Data Used (available at https://chinaspec.nju.edu.cn/EN/DATADOWNLOAD/DataDownload/index.html (accessed on 20 January 2024)).

Subordinate System	Site Name	DoY (2018)	Longitude	Latitude
Mangrove Wetland Ecosystem	Yunxiao Station	1–287	117.500°E	23.917°N
Cropland Ecosystem	Xiaotangshan Station	124–163, 204–271	116.443°E	40.179°N
Cropland Ecosystem	Huailai Station	188–216, 247–261, 297–362	115.783°E	40.349°N
Cropland Ecosystem	Shangqiu Agricultural Station	166–268	115.575°E	34.587°N
Cropland Ecosystem	Heihe Daman Station	128–255	100.407°E	38.858°N

Note: DoY: Days of the Year.

). These datasets form the basis of our analysis. The datasets from all stations are somewhat limited, with daily measurements primarily restricted to PAR and SIF, and more comprehensive data are available only from the Heihe and Xiaotangshan Stations. We utilized grid data encompassing air temperature and LAI to supplement these datasets. By extracting values based on the longitude and latitude of each station, we approximated the specific environmental conditions at each location. Additional data sources include air temperature, surface downwelling longwave radiation, surface downwelling shortwave radiation (available at https://cds.climate.copernicus.eu/datasets) accessed on 1 January 2024, relative humidity (accessible at https://www.psl.noaa.gov/data/gridded/data.ncep.html), LAI (from https://aims2.llnl.gov/search) accessed on 1 January 2024, CMIP6 model data produced by NCC, clumping index (Ω) [34], and albedo [35]. By integrating station-specific data with these grid-based environmental parameters, our study aims to refine transpiration estimation methodologies and enhance the predictive capabilities of the TL-LUE model. Utilizing diverse datasets and innovative modeling techniques, we seek to advance our understanding of transpiration processes and improve the accuracy of ecosystem water flux assessments across various ecological settings.

Some researchers have employed various methods for calculating net radiation [36]. In this study, we explore the methodologies proposed by Yaojie Liu et al. (2022) [37] for computing net radiation (Rn) and vapor pressure deficit (VPD) in environmental research. Their approach for VPD calculation utilizes Tetens’s formula, which relates VPD to saturation vapor pressure (esat) and relative humidity (RH) at a given air temperature (T_air). This method provides valuable insights into atmospheric moisture conditions, allowing researchers to derive VPD from RH and T_air data. Eddy covariance data provide direct measurements of the exchange of gases, such as water vapor and carbon dioxide, between the land surface and the atmosphere. This method is crucial for validating ET models as it offers high temporal resolution data on ecosystem fluxes, enhancing our understanding of water and carbon cycles. However, obtaining eddy covariance data can be challenging due to the need for specialized equipment, extensive fieldwork, and complex data processing.

The necessary data for running the model were collected from five stations, with constants sourced from various articles. However, these stations only provided data for 2018, and all datasets are limited in scope.

2.2. The SIF-Partitioning Method and the Two-Leaf Light Use Efficiency (TL-LUE) Model

Light use efficiency (LUE) models are extensively used to understand climate change impacts on carbon flux dynamics to predict terrestrial GPP at global, regional, and local scales. According to LUE models, GPP is determined by factors such as maximum LUE, the fraction of PAR absorbed by plants (FPAR), incoming PAR, and environmentally stressed variables (e.g., water availability, carbon dioxide, and temperature) [38]. Canopies are composed of leaves exposed to varying amounts of direct and diffuse solar radiation, combining sunny and shaded areas. The leaves also vary in structural, morpho-anatomical, and physiological characteristics, such as chloroplasts’ number, shape, and size [39].

2.2.1. The SIF-PAR Partitioning Method

Since the fluorescence emission efficiency and yield are closely correlated, leaf fluorescence can be obtained by multiplying APAR and ΦF [40]. This study calculated fluorescence emissions for the sunlit and the shaded leaf [41]. A weighted summation of the fluorescence emitted by both shaded and sunlit leaves was then used to define the canopy-averaged leaf-level fluorescence.

Thus, SIF can be partitioned into:

$$SIFsu=APARsu · \Phi Fsu$$

(1)

$$SIFsh=APARsh · \Phi Fsh$$

(2)

where sh and su represent the shaded and sunlit leaves, respectively.

Here, ${\mathsf{\varphi }}_{\mathrm{F}},\mathrm{i}\mathrm{s} \mathrm{f}\mathrm{l}\mathrm{u}\mathrm{o}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{c}\mathrm{e}\mathrm{n}\mathrm{c}\mathrm{e} \mathrm{q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{u}\mathrm{m} \mathrm{y}\mathrm{i}\mathrm{e}\mathrm{l}\mathrm{d}$ [41,42]. The relationship between the fluorescence yield of the steady state (ΦF), the rate of electron transport, and the photosynthetic rate was established using an analysis of the numerical utilizing the exchange of the leaf-level gas measurements and the related data of the active fluorescence under different environmental conditions. The fluorescence emissions efficiency (ε) can be produced by the model at the leaf level by utilizing the photochemical yield (ΦP), as ε is directly proportional to ΦF [43].

2.2.2. The Two-Leaf Light Use Efficiency (TL-LUE) Model

The MOD17 algorithm is the basis for developing the TL-LUE model [44]. This model estimates the Gross Primary Production (GPP) for each leaf group in the canopy, dividing it into sunlit and shaded sections [41,45]. Given the direct relationship between GPP and SIF, the transpiration model can be constructed using the SIF-to-GPP connection. Subsequently, SIF can be computed by multiplying the absorbed PAR (APAR) by the fluorescence yield (ΦF). $APARsh$ and $APARsu$ are the absorbed PAR by shaded and sunlit leaves [44,46,47], where $\alpha$, albedo is associated with vegetation types, and PARdif and the PARdir are the diffuse and the direct components of the incoming PAR, respectively, that are partitioned according to the clearness index. $PARdif,u$, PAR diffuse under canopy and can also be calculated [48,49,50]. The diffuse and direct PAR have been partitioned [44,48] with calibrated parameters using diffuse and total incoming radiation daily data measured at Nanjing, Ganzhou, Shanghai, and Nanchang, China. The LAIsh (leaf area index for shaded leaf) and LAIsu (leaf area index for sunlit leaf) in the above equations can be computed as [51].

2.3. Deriving a Mechanistic Solution Correlating Transpiration with SIF Partitioning

Plants need to consume water from the soil and CO₂ from the atmosphere for photosynthesis to nurture. This is accomplished by CO₂ absorption through the stomatal pore, where water is also discharged. Water absorption by the roots and transportation through the xylem is driven by water transpiration. CO₂ is absorbed when the stomata are open, and water transpires simultaneously. Little CO₂ is absorbed when the stomata are closed, which lowers transpiration. In unfavorable environmental conditions, vegetation can control how much water is lost by sacrificing CO₂ uptake by opening and closing their stomata [52].

The SIF-to-GPP link is the foundation of the transpiration model.

$$GPP=f(SIF,\dots )$$

(3)

Fick’s law can be used to model GPP at the leaf level from the physiological standpoint of the plant [53].

$$GPP=gc(Ca-Ci)$$

(4)

where gc (mol/m²/s) is the conductance of canopy to CO₂, and $Ca$ and $Ci$ are the concentrations of ambient and intercellular CO₂ (ppm), respectively.

Likewise, it is possible to model transpiration (T) in the dense vegetation:

$$T=gw\cdot D$$

(5)

where gw (mol/m²/s) is the water vapor canopy conductance that is connected to $gc (mol m-2 s-1)$ as $gw=1.6gc$, D is the fraction atmospheric water vapor deficit expressed by the molar ratio $\left(\frac{VPD}{Pa}\right)$ (Pa is the atmospheric pressure with slight temporal variation; we used a constant of $100 kPa$ for $Pa$ [30]) and T is the transpiration and uses the unit of latent heat.

$$g_w=1.6\ast g_c$$

(6)

Thus, by substitution

$$T=1.6\ast g_c\ast D$$

(7)

From Equations (3), (4) and (7), the following ratio is derived:

$$\frac{f\left(SIF,\dots \right)}{T}=\frac{gc\left(Ca-Ci\right)}{ 1.6\ast g_c\ast D}$$

(8)

Combining the above equations, transpiration can be calculated by eliminating the canopy conductance [30].

And, to ensure that the unit conversion from mmol/m²/s to W/m² in the above equation is correct, a unit conversion coefficient (40.8) is added, and based on the equation adopted from [30], the transpiration equation can be,

$$T_{su}=\frac{40.8 \ast 1.6\ast \left(SIFsu\right)\ast VPD}{ca\left(1-\frac{ci\left(su\right)}{ca}\right)}$$

(9)

$$T_{sh}=\frac{40.8\ast 1.6\ast \left(SIFsh\right)\ast VPD}{ca\left(1-\frac{ci\left(sh\right)}{ca}\right)}$$

(10)

The ratio of Ci/Ca needs to be extracted [53]. And it can be calculated based on [30] and the Ball–Berry Model [53,54].

$$\frac{{Ci}_{su}}{ca}=0.96-0.0194\ast D+3.282\ast {10}^{-4}\ast D^2$$

(11)

where D is the vapor pressure deficit.

The soil evaporation (Es) model is then implemented and included [30].

Therefore, by combining the transpiration equation and the evaporation equation and by applying the conversion factor of 40.7 to ensure that the unit is in (W/M²), the total evapotranspiration from sunlit and shaded leaf (ETsu and ETsh, respectively) is expressed as follows ($ET=T+Es$):

$$ET(su)=\frac{40.7 \ast 1.6\ast \left(SIFsu\right)\ast D}{ca\left(1-\frac{ci\left(su\right)}{ca}\right)}+1.35RH\frac{\Delta {Ae}^{-kRnLAIsu}}{\Delta +\gamma }$$

(12)

$$ET(sh)=\frac{40.7\ast 1.6\ast \left(SIFsh\right)\ast D}{ca\left(1-\frac{ci\left(sh\right)}{ca}\right)}+1.35RH\frac{\Delta {Ae}^{-kRnLAIsh}}{\Delta +\gamma }$$

(13)

The calculations have been carried out by integrating the partitioned SIF into the equations.

2.4. Model Performance Evaluation

2.4.1. Performance Metrics: R² and RMSE

Regression analysis is a statistical technique to examine the relationships between two or more variables [55]. This method is particularly effective to analyze continuous model outputs. In the context of model evaluation, regression analysis can determine the relationship between the outputs of two models by fitting a regression model to the data. This approach allows us to quantify the strength and nature of the relationship between the model outputs and assess how well one model predicts the other.

Model performance evaluation is crucial for determining the accuracy and reliability of predictive models. Two widely used performance metrics are the coefficient of determination (R²) and the root mean square error (RMSE). R² measures the proportion of variance in the dependent variable that is predictable from the independent variables. The equation gives:

$$R^2=1-{\displaystyle \frac{{\sum }_{i=1}^n{(yi,observed-yi,calculated)}^2}{{\sum }_{i=1}^n{(yi,observed-y,Obs mean)}^2}}$$

(14)

where $yi,observed$ is the observed value, $yi,calculated$ is the calculated value, and $y,Obs mean$ is the mean of the observed values. An R² value nearer to 1 better fits the model to the observed data.

RMSE, on the other hand, quantifies the average magnitude of the errors between predicted and observed values, providing insight into the model’s predictive accuracy. Lower RMSE values indicate better model performance. These metrics complement each other, with R² providing a normalized measure of fit and RMSE offering a scale-dependent measure of prediction error. Together, they provide a comprehensive assessment of model performance [56,57].

2.4.2. Based on Satellite Global Terrestrial Evapotranspiration Data from the National Tibetan Plateau Datacenter

Terrestrial evapotranspiration (ET) is a crucial nexus in the global surface energy exchange and water cycle, and spatial and temporal continuous ET estimates are of great significance for related studies. The Datacenter provides the dataset for National Tibetan Plateau (https://cstr.cn/18406.11.Atmos.tpdc.272728) (http://data.tpdc.ac.cn) accessed on 1 February 2024. This dataset uses an improved ecohydrological model (SiTHv2) to estimate global daily terrestrial evapotranspiration [58]. The forcing data mainly include (1) net radiation, (2) temperature, (3) precipitation, (4) air pressure, (5) the leaf area index, and (6) land cover.

2.4.3. Model Intercomparing: Based on the Penman–Monteith Equations (PM Model) and SIF-Based ET (SIF-ET)

Using surface energy balance and mass transfer, the original Penman–Monteith equation estimates the potential evapotranspiration rate by considering crop physiological traits and meteorological data. The research effectively incorporates Solar-Induced Fluorescence (SIF) data into a semi-empirical ET-SIF model, assessing its applicability across diverse ecosystems [30]. This approach balances simplicity and accuracy in estimating evapotranspiration, offering a valuable benchmark for comparison with our model. The movement resistance of water vapor between the soil surface and leaf stomata is known as surface resistance, and this equation also takes into consideration the diffusion of the resistance of the vertical movement of the water vapor from the leaf to the surrounding air, known as aerodynamic resistance [59].

The Penman–Monteith equation for estimating the potential evapotranspiration rate is expressed as [60]:

$$\lambda ET={\displaystyle \frac{∆\left(Rn-G\right)+\rho aCp\left(\frac{e_s-e_a}{r_a}\right)}{∆+\gamma (1+\frac{r_s}{r_a})}}$$

(15)

where $ET$ is the evapotranspiration rate (W/m²), $\lambda$ is the latent heat of vaporization, Δ is the slope of the saturation vapor pressure curve (kPa/°C), Rn is the net radiation (W/m²) [37] (https://cds.climate.copernicus.eu/) accessed on 1 January 2024, G is the soil heat flux (W/m²), ρa is the air density (kg/m³), Cp is the specific heat of air at constant pressure (J/kg/°C), $es-ea$ is the vapor pressure deficit (kPa), $\gamma$ is the psychrometric constant (kPa/°C), $ra$ is the aerodynamic resistance (s/m), and $rs$ is the surface resistance to evaporation (s/m).

By ensuring that each term in the equation has units of W/m², the resulting evapotranspiration rate, ET, is also expressed in W/m².

And G can be calculated as follows [36]:

$$G=0.4\ast e(-0.5LAI)\ast Rn$$

(16)

LAI represents the leaf area index in m²/m². $rs$ can be calculated as:

$$rs=\frac{rl}{lAI\times 0.5}$$

(17)

where $rl$ represents the leaf resistance. $rl$ can be approximated as a function of Rn as:

$$rl=23.21\exp (\frac{1021.06}{Rn+365.71})$$

(18)

2.5. Computational Analysis

The research analysis for this study was conducted using a combination of programming languages, primarily Fortran CODE: BLOCK and Python 3.12 V on VS code. These languages were chosen for their versatility and efficiency in handling complex mathematical calculations and large datasets [61]. The calculations encompassed various aspects of data processing, including but not limited to parsing and manipulation of raw data, implementation of mathematical algorithms for model simulations, and generation of statistical outputs for analysis. Leveraging the capabilities of Fortran CODE: BLOCK and Python 3.12 V, we were able to streamline the computational workflow and ensure that the accuracy and reliability of the results obtained.

The codes utilized in this research endeavor are available upon request, providing transparency and reproducibility to the scientific community. These codes encapsulate the methodologies and algorithms employed in the data analysis, enabling researchers to replicate and validate this study’s findings. Moreover, the availability of the codes fosters collaboration and knowledge exchange among peers, facilitating further advancements in the field. Researchers interested in accessing the codes for additional scrutiny or extension of this study are encouraged to reach out, as we remain committed to promoting open science and sharing our research resources to improve scientific inquiry.

In this study, ET represents the satellite global terrestrial evapotranspiration Data provided by the Center for National Tibetan Plateau, while the Penman–Monteith model and Model ET represent our improvement from SIF-Partitioned ET. This study introduces a novel approach to ET estimation by integrating SIF partitioning with PAR and LAI data. By partitioning SIF into sunlit and shaded components, the model provides a more detailed characterization of photosynthetic activity and light interception within the canopy. The approach incorporates algorithms to estimate ET based on the combined influence of SIFsu and SIFsh, accounting for variations in light availability and canopy structure. In this study, all ET is expressed in W/m².

3. Results

3.1. Evaluation of SIF Partitioning and Its Impact on Evapotranspiration Estimates

Long-term observations of tower-based SIF are crucial for understanding ecosystem-specific periodic dynamics of photosynthetic activity, including Gross Primary Production (GPP). Of the five stations from which PAR and SIF data were collected [32,33], only Xiaotangshan Station and Heihe Daman Station [38] have accessible SIF measurements. A tower-based automated SIF measurement system (SIFSpec) was developed to obtain synchronous SIF observations and flux measurements across terrestrial ecosystems. This system confirms the growing satellite SIF product numbers with in situ measurements [31]. The outputs of the SIF-partitioning approach were equated with the measured SIF data from these two stations. The linear regression analysis showed a strong correlation, with R² values of 0.62 for Xiaotangshan Station and 0.98 for Heihe Daman Station (see Figure 1 and Figure 2). These findings suggest that the SIF-partitioning approach using PAR is a promising method for modelling ET with the TL-LUE model.

Furthermore, the partitioned SIF data used in this study, referred to as SIF(P), which include both sunlit (SIFsu) and shaded (SIFsh) components, showed higher correlations. This suggests that partitioned SIF captures different aspects of environmental processes, aligning with findings from Yuan et al. (2015) [62], which emphasize the robust performance of the Penman–Monteith model and the contextual nature of SIF data. The correlation matrix heatmap for Xiaotangshan Station illustrates the significant benefits of partitioning Sun-Induced Fluorescence (SIF) to enhance the accuracy of Model ET. By separating SIF into sunlit and shaded components, the correlation between Model ET and the combined SIF partition (SIF(P)) is 0.69, reflecting a strong positive relationship. This partitioning approach offers a more nuanced understanding of canopy photosynthesis by accounting separately for the contributions of shaded and sunlit leaves. The individual correlations of SIFsu and SIFsh with Model ET are 0.71 and 0.65, respectively, highlighting the importance of both components in capturing variations in light use efficiency and transpiration rates (see Figure 1).

Partitioning SIF data into sunlit and shaded components enables a detailed representation of the canopy’s functional dynamics [63], significantly improving ET modelling. This novel approach provides a more accurate and comprehensive method for estimating evapotranspiration, enhancing the predictive capabilities of hydrological models and contributing to a deeper understanding of ecosystem processes. Analyzing correlations between various parameters and Model ET offers valuable insights into the complex interactions that govern evapotranspiration processes.

The strong correlation between Photosynthetically Active Radiation (PAR) and Model ET underscores the crucial role of PAR in driving evapotranspiration. PAR significantly influences ET by enhancing photosynthetic activity and subsequent plant water use [64]. Similarly, the correlation between PAR and SIF(P) demonstrates the effectiveness of SIF partitioning in capturing radiation-driven photosynthetic processes, further validating its use in ET estimation. Net radiation (Rn), which provides the energy required for both sensible and latent heat fluxes, directly affects ET rates. This relationship is supported by Zhang et al. (2016) [65], who highlighted the importance of net radiation in controlling ET variations across different landscapes.

The correlation between Rn and the Penman–Monteith model (PM model) (R² = 0.78, see Figure 2) indicates that the PM model effectively incorporates energy balance components into its ET estimations, and the finding aligns with Allen et al. (1998) [66]. The strong correlations observed between SIF(P) and Model ET, as well as between observed SIF (SIF Obs) and Model ET (see Figure 1 and Figure 2), highlight the potential of solar-induced chlorophyll fluorescence (SIF) as an effective proxy for transpiration. These findings align with Magney et al. (2029) [67], who emphasized the utility of SIF in capturing diurnal and seasonal variations in plant water use. The slightly higher correlation of partitioned SIF(P) with Model ET compared to observed SIF suggests that the partitioning method improves ET estimation accuracy by differentiating contributions from various canopy layers.

At both Xiaotangshan and Heihe Daman Stations, strong correlations were between the Model ET and both the Penman–Monteith (PM) model and the observed ET, demonstrating the effectiveness of these models in capturing ET patterns (see Figure 1 and Figure 2). The consistency in performance is supported by similar standard deviations, indicating reliable replication of ET dynamics. These results underscore the importance of integrating multiple parameters, such as PAR, net radiation, and the SIF-partitioning method, for precise ET estimation. The improved model effectively captures the interplay between radiation, energy balance, and plant physiological responses. Compared to other research findings, this novel approach using SIF partitioning and the TL-LUE model is reliable for enhancing transpiration estimates, offering valuable insights into water use dynamics across diverse ecosystems. In general, SIF/PAR estimations efficiently capture the timing of phenological changes and the impact of environmental stress on the transpiration of natural ecosystems. They appropriately depict this variability without the need for complicated parameterizations [68].

At XiaoTangshan Station, the correlation between Model ET and ET is lower (0.52), indicating a more moderate alignment between the partitioned SIF-based ET and satellite data. SIF-ET and ET show a relatively similar correlation (0.51), suggesting that both methods are equally effective in this station, though not as strongly as in Heihe Daman (Figure 2). The correlation between Model ET and SIF-ET is strong at 0.98, which again underscores the accuracy of the partitioning process in reflecting SIF variations, even if it does not fully match the satellite ET data.

The heatmap correlation results from Heihe Daman Station (Figure 2) vividly illustrate the transformative benefits of partitioning Solar-Induced Fluorescence (SIF) into its sunlit (SIFsu) and shaded (SIFsh) components for enhancing Model ET. The exceptionally high correlation coefficients—0.88 between Model ET and SIF(P), 0.89 with SIFsh, and 0.88 with SIFsu—underscore the effectiveness of SIF partitioning in capturing intricate vegetation photosynthetic dynamics. This approach allows for a more precise differentiation between sunlit and shaded canopy photosynthesis, thereby enriching the model’s sensitivity to subtle physiological variations within the plant canopy. As a result, this refined method significantly improves evapotranspiration (ET) estimates, advancing current modelling capabilities.

By integrating partitioned SIF data, we radically enhance ET model estimation, leading to more reliable predictions and deeper insights for hydrological, ecological, and agricultural research. The revised Penman equation, which includes adjustments for the advection effect and water availability, has proven effective in estimating ET in the middle reach of the Heihe River Basin, showing a high correlation and low RMSE compared to eddy covariance measurements. Further integration of the SIF-partitioning approach can enhance ET estimation by providing more accurate insights into canopy photosynthesis dynamics [69].

At Heihe Daman Station, the correlation between Model ET and ET is moderate at 0.62, suggesting a reasonable level of agreement between the partitioned SIF-based ET and terrestrial satellite data. The relationship between SIF-ET and ET is more substantial, with a correlation of 0.88, indicating that normal SIF aligns more closely with terrestrial satellite ET. Interestingly, the correlation between Model ET and SIF-ET is also solid (0.9), suggesting that the SIF-partitioning method effectively captures the variations in SIF to estimate ET, though there remains a gap when compared to ET.

Eddy covariance measurements from stations such as Heihe Daman and Xiaotangshan are crucial for understanding ecosystem dynamics. These stations offer essential data on Photosynthetically Active Radiation (PAR), Solar-Induced Fluorescence (SIF), and evapotranspiration (ET), which are vital for evaluating vegetation productivity, carbon uptake, and water balance in alpine ecosystems.

3.2. Validation of SIF Partitioning-Based Evapotranspiration Estimation

3.2.1. Based on the Satellite Et Data of the National Tibetan Plateau Data Center (ET)

The comparison between the SIF-partitioned ET model and satellite-derived evapotranspiration (ET) data from the National Tibetan Plateau Data Center provides valuable insights into the model’s performance in capturing temporal and spatial variations in ET across diverse landscapes. By correlating the model outputs with satellite ET data, we can evaluate the accuracy and reliability of the SIF-partitioned ET model and assess how well it aligns with observed satellite-derived ET values. This comparison helps quantify the strength and nature of the relationship between model estimates and observed satellite data, offering validation of the model’s effectiveness at regional or global scales [70,71,72].

Analysis of the correlation between Model ET and observed ET across the HuaiLai, Shangqiu, and Yunxiao Stations shows a positive trend, with increasing R² values indicating improved model accuracy. Specifically, the R² values for HuaiLai, Shangqiu, and Yunxiao are 0.68, 0.76, and 0.88, respectively. These results suggest that the Model ET aligns more closely with observed ET at Yunxiao, where the model performs most accurately, while the lower R² value at HuaiLai indicates potential areas for improvement. Overall, the increasing R² values across the stations demonstrate the model’s enhanced reliability and accuracy in estimating ET as its correlation with observed data strengthens (Figure 3).

3.2.2. Comparison of Modeled ET and Penman–Monteith Equation

The Penman model has long been a staple in hydrological and agricultural studies for estimating evapotranspiration (ET), as demonstrated by research [5,66]. However, developments in remote sensing and ecosystem modelling have directed the development of alternative approaches, such as SIF partitioning-based methods, which promise improvements in spatial resolution and accuracy. Zhang et al. (2020) [69] illustrated the benefits of integrating Solar-Induced Fluorescence (SIF) data with PAR and LAI to enhance ET estimates, emphasizing the importance of incorporating physiological processes into ET models.

Correlation analysis between Model ET and the Penman–Monteith (PM) model reveals a compelling trend across HuaiLai, Shangqiu, and Yunxiao Stations, with R² values of 0.75, 0.73, and 0.90, respectively (Figure 4). This indicates that Model ET aligns closely with the PM model and shows increasing efficacy in replicating ET measurements from HuaiLai to Yunxiao. The exceptionally high R² value at Yunxiao underscores the model’s superior performance in this region, suggesting that Model ET offers a more refined and accurate representation of ET compared to the PM model. The consistent correlation across all stations highlights the robustness of Model ET, demonstrating its potential as a valuable tool for ET estimation in diverse settings.

3.2.3. Comparison of ET and Penman–Monteith Equation

Figure 5 illustrates the correlation between Evapotranspiration (ET) and the Penman–Monteith (PM) model across HuaiLai, Shangqiu, and Yunxiao. HuaiLai Station shows a strong positive correlation with an R² value of 0.74 and an RMSE of 10.46, indicating a high degree of agreement between Model ET and the PM model (Figure 5). Shangqiu Station exhibits a moderate positive correlation with an R² value of 0.46 and a higher RMSE of 17.78, suggesting lower predictive accuracy and more significant variability in the data. Yunxiao Station demonstrates the highest correlation, with an R² value of 0.75 and an RMSE of 8.34, highlighting the model’s robust performance at this location. The dashed lines represent the linear regression fits for each station, visually confirming the strength of these correlations and providing insights into the model’s effectiveness across different geographical areas.

4. Discussion

Recent research underscores the potential of Solar-Induced Fluorescence (SIF) as a valuable proxy for assessing vegetation productivity and stress, offering significant insights into evapotranspiration (ET) processes and demonstrating its utility in quantifying plant physiological responses to environmental factors [73,74]. One of the primary strengths of the SIF-partitioning method lies in its ability to capture the distinct contributions of sunlit and shaded leaves to overall photosynthesis and transpiration. In typical canopy environments, different light conditions exist within the canopy structure, where sunlit leaves receive direct sunlight and shaded leaves receive indirect light. The PM model traditionally assumes uniform light distribution and does not account for this heterogeneity, potentially oversimplifying the complex interactions that govern plant physiological processes. This SIF-partitioning approach builds on this foundation by distinguishing between sunlit (SIFsu) and shaded (SIFsh) leaf contributions to ET estimation, thereby enhancing accuracy and capturing diurnal variations [16]. Separating SIF into sunlit and shaded components provides a nuanced understanding of canopy photosynthesis and improves ET estimates by accurately representing light absorption and photosynthetic activity across different canopy layers [63].

This study innovatively improves transpiration (T) estimates by integrating SIF partitioning with the TL-LUE model, incorporating PAR and LAI. Traditional methods often struggle to capture the complex interactions between environmental variables and plant physiological processes, resulting in less reliable ET estimates. By leveraging the direct measurement capabilities of SIF, this research provides a more mechanistic understanding of plant water use. The TL-LUE model differentiates between sunlit and shaded leaves, accounting for the unique environmental response, thereby enhancing ET accuracy [46,75]. Integrating Gross Primary Productivity (GPP) into this framework further links carbon assimilation with water fluxes, offering a comprehensive view of ecosystem dynamics [25,27]. Utilizing PAR and LAI for partitioning SIF effectively captures variability in plant photosynthesis and transpiration rates, improving the precision and applicability of ET models across diverse ecosystems [30,37,60]. This novel approach advances our understanding of ET dynamics and has significant potential for improving water resource management and predictions of the impacts of climate change on the global water cycle. The PAR-based method demonstrated superior performance in scaling SIF from instantaneous to daily measurements, effectively tracking diurnal cycles on sunny and cloudy days. In contrast, the cosine-based method exhibited increased relative root mean square error (RRMSE) values under cloudy conditions, while the PAR-based method maintained consistent accuracy, with RRMSE values below 40% on sunny days and reliably capturing diurnal variations even on overcast days. This indicates that the PAR-based approach is more robust across varying weather conditions [76].

Utilizing variables such as Photosynthetically Active Radiation (PAR) and the leaf area index (LAI), rather than relying solely on direct SIF measurements, allows for a more precise differentiation of contributions from sunlit and shaded leaves, leading to enhanced ET modelling [76]. Despite its advantages, challenges like light conditions and canopy structure variability can introduce uncertainties in estimating SIFsu and SIFsh. Addressing these issues necessitates refining calibration techniques, developing advanced algorithms, and integrating additional data sources. Future advancements should incorporate high-resolution remote sensing data and machine learning to improve accuracy and adaptability further, thereby enhancing SIFsu/sh-based ET models.

The distinction between SIFsu/sh and total SIF lies in the detailed partitioning of fluorescence into sunlit (SIFsu) and shaded (SIFsh) components. Unlike traditional ET models, this approach provides a deeper understanding of canopy photosynthesis by separately accounting for contributions from sunlit and shaded leaves. Our results show that the SIF-partitioning method significantly improves ET estimation, as evidenced by solid correlations for SIFsu (0.71) and SIFsh (0.65) with Model ET, as seen in Figure 1. This innovative approach enhances ET modelling, improves the predictive capabilities of hydrological models, and contributes to a deeper understanding of ecosystem processes. SIF, a remote sensing-derived parameter, provides a direct and sensitive measure of photosynthetic activity, crucial for improving ET estimations, as highlighted by recent studies [77].

We compared ET estimates derived from our SIF-partitioning approach with Model ET data from the National Tibetan Plateau/Third Pole Environment Data Center. Linear regression analysis revealed that the correlations between model outputs and observed ET values were consistent with broader literature on ET estimation. For example, studies [20,30,78] demonstrated similar high correlations between SIF and ET in various ecosystems, reinforcing the reliability of SIF as an indicator of transpiration. Additionally, the moderate correlation between the Penman–Monteith (PM) model and Model ET (R² = 0.78) aligns with research by Fisher (2011) [79], validating the PM model’s performance under diverse climatic conditions. The ET data from the Tibetan Plateau (R² = 0.79) further underscores the model’s capability to replicate observed ET patterns in complex terrains.

Preliminary results indicate that incorporating sunlit and shaded SIF partitioning improves ET estimation. By accounting for differential fluorescence emissions from sunlit and shaded leaves, the model captures variations in canopy photosynthetic activity more effectively, resulting in more precise ET estimates. This partitioning allows for a more nuanced representation of light interception within the canopy, enhancing the model’s ability to account for variations in evapotranspiration rates across different environmental conditions and canopy structures. Furthermore, integrating sunlit and shaded SIF partitioning offers insights into the spatial and temporal dynamics of canopy-level processes, facilitating a comprehensive understanding of ecosystem functioning [80]. This method improves ET estimation reliability and enhances our ability to monitor and assess ecosystem health and productivity [50].

The comparative analysis of the Penman–Monteith model and the modified SIF-partitioning approach demonstrates the validity and effectiveness of both methods in estimating ET [23]. The strong correlation observed between the two methods at all stations highlights the robustness of the modified approach and its potential as an alternative to traditional ET estimation methods. These findings have implications for hydrological modelling, agricultural management, and ecosystem studies, emphasizing the importance of incorporating physiological processes and remote sensing data into ET estimation frameworks. Future research should further validate and refine this modified approach across different geographical regions and land cover types. Comparing our SIF-based method with the Penman–Monteith model underscores its robustness. The observed strong correlation highlights the effectiveness of integrating physiological processes and remote sensing data into ET estimation frameworks. This study aligns with similar research, such as [68,81], emphasizing the benefits of using remote sensing data and advanced models for accurate ET estimation. Future research should aim to validate and refine this method across diverse geographic regions and land cover types, exploring its applicability to other ecosystems. The promising results suggest that similar methodologies could enhance ET estimates in various contexts, benefiting water resource management and agricultural practices.

5. Conclusions

This study introduces an innovative method for estimating ET by integrating Sun-Induced Fluorescence (SIF) partitioning with Photosynthetically Active Radiation (PAR) and leaf area index (LAI) data through the two-leaf LUE (TL-LUE) model. Partitioning SIF into sunlit (SIFsu) and shaded (SIFsh) components provides a detailed view of vegetation photosynthetic activity, enhancing ET accuracy. The development of the SIF-partitioned approach ET Model represents a significant advancement in methodologies for estimating evapotranspiration (ET). The model’s ability to outperform traditional methods highlights its potential for broader application in ET estimation, particularly in diverse and complex landscapes. The proposed model underwent rigorous testing against the SIF-based ET (SIF-ET) model, the Penman–Monteith model (PM model) and the global terrestrial ET dataset from the National Tibetan Plateau Data Centre. Future studies should further validate and refine the model across diverse geographical regions and land cover types. The model improves evapotranspiration (ET) estimation accuracy, which is crucial for precise water resource management. By providing more reliable data, the model aids in optimizing irrigation planning and enhancing agricultural productivity. Also, its application supports climate adaptation strategies by enabling better water usage efficiency and management across diverse ecosystems. This improved ET estimation can lead to more effective water usage in agriculture, ensuring crops receive the right amount of water at the right time, which can boost yields and reduce waste. Furthermore, this method can help manage water resources more sustainably, particularly in regions facing water scarcity or variable climatic conditions. Ultimately, the model holds substantial potential for operational use in water resource management and agricultural planning, offering a powerful tool for achieving accurate and timely ET estimates crucial for sustainable water and agricultural management.