Improving Soybean Gross Primary Productivity Modeling Using Solar-Induced Chlorophyll Fluorescence and the Photochemical Reflectance Index by Accounting for the Clearness Index

Abstract

Solar-induced chlorophyll fluorescence (SIF) has been widely utilized to track the dynamics of gross primary productivity (GPP). It has been shown that the photochemical reflectance index (PRI), which may be utilized as an indicator of non-photochemical quenching (NPQ), improves SIF-based GPP estimation. However, the influence of weather conditions on GPP estimation using SIF and PRI has not been well explored. In this study, using an open-access dataset, we examined the impact of the clearness index (CI), which is associated with the proportional intensity of solar incident radiation and can represent weather conditions, on soybean GPP estimation using SIF and PRI. The midday PRI (xanthophyll de-epoxidation state) minus the early morning PRI (xanthophyll epoxidation state) yielded the corrected PRI (ΔPRI), which described the amplitude of xanthophyll pigment interconversion during the day. The observed canopy SIF at 760 nm (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}$) was downscaled to the broadband photosystem-level SIF for photosystem II (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$). Our results show that GPP can be accurately estimated using a multi-linear model with ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI. The ratio of GPP measured using the eddy covariance (EC) method (${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$) to GPP estimated using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI exhibited a non-linear correlation with the CI along both the half-hourly (R² = 0.21) and daily scales (R² = 0.25). The GPP estimates using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI were significantly improved by the addition of the CI (for the half-hourly data, R² improved from 0.64 to 0.71 and the RMSE decreased from 8.28 to 7.42 $\mathsf{\mu }$mol•m⁻²•s⁻¹; for the daily data, R² improved from 0.71 to 0.81 and the RMSE decreased from 6.69 to 5.34 $\mathsf{\mu }$mol•m⁻²•s⁻¹). This was confirmed by the validation results. In addition, the GPP estimated using the Random Forest method was also largely improved by considering the influences of the CI. Therefore, our findings demonstrate that GPP can be well estimated using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI, and it can be significantly enhanced by accounting for the CI. These results will be beneficial to vegetation GPP estimation using different remote sensing platforms, especially under various weather conditions.

1. Introduction

The largest terrestrial carbon flux is produced by photosynthesis in vegetation, which is crucial for controlling the carbon cycle and mitigating climate change [1]. Vegetation photosynthesis plays an important role in achieving energy conversion in nature and maintaining the carbon–oxygen balance in the atmosphere. The carbon assimilated by vegetation is generally characterized by gross primary productivity (GPP). Numerous researchers have explored how to monitor GPP at various spatiotemporal scales [2,3,4,5,6]. However, the accurate estimation of GPP remains a challenge, especially under changeable environmental conditions.

To estimate GPP at in situ or regional scales, the eddy covariance (EC) technique, vegetation indices, physical process models (e.g., TEM, BEPS, and Biome-BGC), and light use efficiency (LUE) models (e.g., MODIS-LUE, VPM, and EC-LUE) have been suggested [7,8,9,10,11]. The flux measured using the EC method can only represent ground GPP in a limited spatial region. Due to the fact that vegetation indices (VIs) are generally representative of vegetation greenness, Vis-based statistical models only track some dynamics of photosynthesis and clearly lack consideration of the influence of climate conditions on the growth of plants. Compared to the Vis-based statistical models, the LUE model has better mechanisms, fewer parameters, and better spatiotemporal scalability, making it widely used at the regional scale. However, the main parameters of these models are generally based on empirical relationships, which pose many uncertainties. In addition, this model focuses on the vegetation–soil–atmosphere continuum as the research object, with better mechanistic properties, but there are many complex parameters, which leads to relatively few applications at a large scale [9].

Therefore, a predicted model with photosynthetic process information and simple parameters is important for tracking the dynamic variations in GPP at large scales, especially under different environmental conditions. It has been established that the energy dissipation pathway known as solar-induced chlorophyll fluorescence (SIF), which is directly related to light reactions, is the superior way to monitor GPP dynamics, particularly under stressful conditions [5,12,13]. SIF and GPP have an inherent theoretical foundation for coupling since absorbed photosynthetically active radiation (APAR) drives both SIF and GPP. In reality, the fundamental mechanism for SIF-based GPP estimation is intimately linked to the linear electron transfer rate (ETR), which is coupled with carboxylation processes [11,14]. Many studies have demonstrated that SIF is closely related to GPP and can be used to track the dynamic changes in GPP in response to stress conditions, even for evergreen forests with an almost invariant canopy structure [12]. However, the linkage between SIF and GPP is not set in stone, and it can be influenced by a complex canopy structure, growth stages, and environmental conditions.

With a complex canopy structure, the emitted SIF is scattered and reabsorbed by leaves until it is intercepted by sensors [15]. Because of the limited field of view (FOV) of sensors, hemispherical SIF emission can only be captured in the observation direction [15]. The observed SIF is only a small part of the total SIF and contains information from both photosystem I (PSI) and photosystem II (PSII) [16,17,18,19,20]. To obtain more findings about the physiological linkage between SIF and GPP, the impacts of the observed angle, the canopy structure, and the contribution of PSI SIF should be eliminated from the observed canopy SIF to obtain the total SIF at the full band (Figure 1) [20,21].

Although the total SIF is directly linked to photosynthesis, the relationship between SIF and GPP remains uncertain. The SIF–GPP relationship might be decoupled under mild stress conditions [22], and SIF shows less sensitivity in response to stress than GPP does. Environmental variables, such as air temperature, soil moisture, and light intensity, have an influence on the SIF–GPP relationship. Despite the fact that APAR drives both SIF and GPP, some studies found that there is a stronger relationship between the APAR and SIF than between the APAR and GPP and that the ratio of GPP to SIF decreases with light intensity. These findings may be related to the differences between light and dark reactions or the irregularly varied proportion of energy allocated to SIF and photosynthesis [23,24]. Despite the fact that SIF can monitor the downregulation of GPP in response to drought conditions at both the leaf and canopy levels, a water deficit also affects the link between SIF and GPP. Likewise, the SIF–GPP relationship is also somewhat impacted by photochemical activities and the kinetics of enzymes involved in dark processes, which are both affected by temperature [25]. Additionally, the SIF–GPP relationship can be altered by the dynamic energy distribution among three energy dissipation pathways in response to various temperature conditions. Therefore, SIF, a single energy dissipation pathway, is insufficient to effectively account for the dynamic fluctuations in GPP under stress.

As chlorophyll molecules become excited as a result of APAR, three processes—photochemical quenching (PQ), non-radiative decay or non-photochemical quenching (NPQ), and fluorescence—can be used to dissipate the excitation energy [26]. The three energy dissipation pathways compete with one another and display various patterns in response to the constantly changing external environment. As one of three pathways for consuming the solar energy absorbed by leaves, NPQ may distribute the energy between fluorescence and PQ [27]. The capacity of vegetation to digest APAR via photochemistry is often reduced by biotic circumstances, but NPQ normally occurs, which could potentially change the link between SIF and GPP [28]. However, it is currently unknown how SIF and GPP correlate with one another under various environmental circumstances and how NPQ mediates this relationship.

As another energy dissipation pathway, NPQ is important for SIF-based GPP estimation models. It is critical to quantify the contributions of NPQ to absorbed energy under stressful conditions as the response of SIF to stress is not unique, and NPQ co-occurs during fluorescence processes [11]. The downregulation of photosynthetic efficiency at diurnal timescales is often correlated with the degree of epoxidation in the xanthophyll pigments, which increases under stress in leaves [13]. Under stress, xanthophyll de-epoxidation typically causes a rise in NPQ activity. However, NPQ is generally difficult to obtain at the canopy scale, which limits its application in GPP estimation based on SIF. Numerous investigators have discovered that the photochemical reflectance index (PRI), defined as the normalized difference index utilizing narrow band reflectance at 531 and 570 nm [29], often exhibits a negative connection with NPQ, which might describe the epoxidation status of xanthophyll pigments [30]. The variations in PRI can accurately represent the changes in NPQ generated by the xanthophyll cycle in response to the external environment because of sluggish adjustments in the pigment pools at diurnal timescales.

Under the premise that some NPQ information is provided by the PRI, it makes sense to study the influence of PRI on SIF-based GPP estimation. Ma et al. [31] found that the PRI is sensitive to the soil water content and can be used to improve SIF-based GPP estimation. Wang et al. [27] used MODIS PRI, OCO-2 SIF observations, and contemporaneous flux data from EC locations to evaluate the value of PRI for SIF-based GPP estimation. Using tower-based observations, Kovac et al. [32] improved the carbon flux estimates in deciduous and evergreen forests by combing the normalized difference vegetation index (NDVI), the PRI, and the quantum yield of SIF. In addition, at seasonal timescales, changes in the structural factors (such as the leaf area index) and foliar pigment concentration can also contribute to the differences in PRI [33]. Some studies have reported that the seasonal-corrected PRI can be a good indicator of the dynamics of photosynthetic status under various environmental conditions and can be used to improve GPP estimation [13,29,34]. By eliminating the effects of foliar pigments and the LAI, the highly temporally resolved ground-based PRI can be an indicator of light use efficiency in various environmental conditions [28,29,34,35]. In addition, Magney et al. [34] used the delta PRI (ΔPRI) derived from the midday PRI (xanthophyll de-epoxidation state) and the early morning PRI (xanthophyll epoxidation state) and found that the highly temporally and spatially resolved ΔPRI could be used to track plants’ responses to changing environmental conditions.

Although the combination of SIF and PRI can quantify GPP based on ground, airborne, or satellite observations [27,31,32,36], the potential impacts of weather conditions on GPP estimation using ‘corrected’ SIF and the ‘corrected’ PRI have yet to be investigated with tower-based measurements. In this study, we examined the impacts of weather conditions on GPP estimation using ${SIF}_{TOT\_FULL\_PSII}$ (the broadband photosystem-level SIF for photosystem II) and ΔPRI (formed of the early morning and midday PRI) and explored the usefulness of combining weather conditions to improve soybean GPP estimation. The specific issues addressed in detail included the following:

(1)

How successful is GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI?

(2)

How do the weather conditions affect GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI?

(3)

Is it possible to improve GPP estimation accuracy using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI by considering the weather conditions?

2. Materials and Methods

2.1. Study Site

In this study, we used an open-access dataset from the Agroecosystem Sustainability Center, the Institute for Sustainability, Energy, and Environment, University of Illinois, at Urbana-Champaign, Urbana, IL, United States (https://daac.ornl.gov/cgi-bin/dsviewer.pl?ds_id=2136, accessed on 19 January 2024). The data were obtained from the US-Ne2 (41.1649°N, 96.4701°W) site in Lincoln, NE, USA (Figure 2), which is located in the US Corn Belt [37]. The site is one of three fields at the University of Nebraska Agricultural Research and Development Center near Mead, Nebraska. The terrain is flat and the soil is productive with organic matter. It is elevated at 362 m. It has a summertime average temperature of about 25 °C and experiences abundant rainfall (mean annual precipitation: 788.89 mm) [37]. It has an obvious climate with a fully humid summer, where there is at least one month colder than −3 °C; precipitation is generally the same throughout the year, and summers can be very hot. The site is used for corn–soybean rotation. Soybean is irrigated, with no fertilization controls. In general, soybean is typically sown in May and harvested in October. The measurements were continuously collected from 14 May 2018 to 19 October 2018 throughout the whole growing season [37].

2.2. Flux Measurements

The carbon flux data were obtained from FLUXNET, which represents a community of scientists who measure and study the exchange of carbon, water, and energy between ecosystems and the atmosphere. The carbon flux measured system continuously measured the carbon dioxide (CO₂) exchange between the atmosphere and soybean using the eddy covariance (EC) method. A CO₂/H₂O open-path infrared gas analyzer (IRGA) was used to collect CO₂ and water vapor turbulence data with a frequency of around 10 Hz. Then, latent heat (LE), soil heat flux beneath the canopy (G), sensible heat (H), Obukhov length (L), and friction velocity (u*) data were extracted. Net ecosystem exchange (NEE) was calculated using various preprocessing procedures (e.g., data quality control and gap filling). Using the ReddyProc-based online tool created by the Max Planck Institute for Biogeochemistry, partitioning algorithms were then utilized to partition NEE into ecosystem respiration and GPP (https://www.bgc-jena.mpg.de/REddyProc/, accessed on 10 January 2024) [38,39]. GPP measured using the EC method (${GPP}_{EC}$) was considered to be true. In addition, an automatic weather station (AWS) continually measured the meteorological variables, like photosynthetically active radiation (PAR), relative humidity (RH), and air temperature (Ta), among others [40]. More details about these measurements can be found in Suyker and Verma [40].

2.3. Spectral Observations

The spectral data were measured using the FluoSpec2 system, which consists of two subsystems: a hyperspectral observational system used for calculating vegetation indices and a directional–hemispherical system used for SIF retrieval [18,41]. The hyperspectral observational system has an HR2000+ spectrometer with a wavelength ranging from 350 to 1100 nm, which was used to calculate various vegetation indices. The directional–hemispherical system has a QEPRO spectrometer (Ocean Optics, Dunedin, FL, USA) with a wavelength ranging from 730 to 780 nm, which was used to retrieve canopy SIF data at the near-infrared band. A temperature-controlled box contained the spectrometer and shutter, and the ends of the fibers were placed in a tower 5 m above the ground within a 2.2-meter-diameter sample area on the ground. Some vegetation indices and the fPAR calculated from the red-edge normalized difference vegetation index (${\mathrm{N}\mathrm{D}\mathrm{V}\mathrm{I}}_{\mathrm{r}\mathrm{e}\mathrm{d}\mathrm{e}\mathrm{d}\mathrm{g}\mathrm{e}}$) were also provided alongside these open-access data. A more detailed description of the open-access dataset can be found in Wu et al. [37].

Upwelling radiance includes solar-induced chlorophyll fluorescence in addition to radiance reflected by foliage and the soil background. Because of the specific absorption by atmospheric molecules, the SIF emitted by leaves contributes significantly more to reflected radiance in the atmospheric absorption regions than the atmospheric window does [42]. Based on the presumption that fluorescence and reflectance in the retrieval bands obey a specific law of change, numerous methods for SIF retrieval have been proposed [43]. In this study, we used the SIF results retrieved using the spectral fitting approach (SFM), which assumes that fluorescence and reflectance exhibit a nonlinear pattern with the wavelength, which can better utilize the features in the fitting window [44]. In addition, according to Hu et al. [45], the observed spectral and flux data were processed into half-hourly and daily averaged data.

2.4. Downscaling from Canopy to Photosystem Levels

Due to scattering and reabsorption effects, SIF observed at the canopy scale represents only a small portion of the total SIF that chlorophyll molecules emit. In addition, canopy SIF contains contributions from both PSI and PSII photosynthetic activities. Therefore, to better understand the SIF–GPP relationship, PSI SIF and PSII SIF should be partitioned, and canopy-level SIF should be downscaled to photosystem-level SIF.

According to Bacour et al. [46], the linear combination of PSI and PSII fluorescence radiance can be used to describe canopy SIF at 760 nm (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}$, mW/m²/nm/sr). The proportionate contribution of PSII SIF at the canopy level should be equal to that at the photosystem level. First, we excluded the effects of PSI SIF and calculated the contribution of PSII to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}$ [21]:

$${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}={\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}\times {\mathrm{f}}_{\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$$

(1)

$${\mathrm{f}}_{\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}={\displaystyle \frac{{\mathrm{m}}_2\times \epsilon }{{\mathrm{m}}_1+{\mathrm{m}}_2\times \epsilon }}$$

(2)

where ${\mathrm{f}}_{\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ (%) indicates the contributions of PSII fluorescence to the ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}$; ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ were obtained using a large number of SCOPE (Soil Canopy Observation, Photochemistry, and Energy fluxes) simulations and were equivalent to 0.00561 and 0.00917; $\epsilon$ represents the ratio of PSII steady-state fluorescence to minimum fluorescence, which has a maximum percentage of open PSII reaction centers [21].

Second, canopy-directional ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ should be divided from the escape probability at 760 nm (${\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{P}-\mathrm{C}}$) to obtain photosystem-level SIF (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$, mW/m²/nm):

$${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}={\displaystyle \frac{{\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}}{{\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{P}-\mathrm{C}}}}$$

(3)

According to Zeng et al. [15], the probability of SIF photons escaping from a leaf surface to the canopy’s top (${\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{L}-\mathrm{C}}$) can be described as

$${\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{L}-\mathrm{C}}\approx {\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{N}\mathrm{I}\mathrm{R}}\times \mathrm{N}\mathrm{D}\mathrm{V}\mathrm{I}}{\mathrm{f}\mathrm{P}\mathrm{A}\mathrm{R}}}$$

(4)

where ${\mathsf{\rho }}_{\mathrm{N}\mathrm{I}\mathrm{R}}$ represents reflectance at the near-infrared band (760 nm in this study); $\mathrm{f}\mathrm{P}\mathrm{A}\mathrm{R}$ indicates the percentage of absorbed photosynthetic active radiation.

The probability of SIF photons escaping from the chlorophyll molecules to the leaf surface (${\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{P}-\mathrm{L}}$) can be roughly predicted using the leaf albedo and has a value of 0.9 in the near-infrared region, which is rather stable [20]. Therefore, in the NIR band, ${\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{P}-\mathrm{C}}$ could be approximately calculated as follows:

$${\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{P}-\mathrm{C}}=0.9\times {\mathrm{f}}_{\mathrm{e}\mathrm{s}\mathrm{c}\_\mathrm{L}-\mathrm{C}}$$

(5)

Finally, total PSII SIF within the 640–850 nm spectral range (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$) could be estimated from ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$. According to Liu et al. [21], PSII SIF’s spectral shape is mostly stable, despite the complex process of SIF escaping throughout the leaf and canopy. Total PSII SIF at a specific wavelength (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\lambda }\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$) can be estimated from ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ by multiplying the first principal component (PC1) obtained from the relationship between ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\lambda }\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ (defined as the conversion ratio, ${\mathrm{f}}_{\mathrm{C}}(\mathsf{\lambda })$). Therefore, reconstructed broadband PSII SIF at the photosystem level (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$, $\mathsf{\mu }$mol•m⁻²•s⁻¹) can be expressed as follows:

$${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}={\sum }_{\mathsf{\lambda }=640}^{850}({\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_760\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}\times {\mathrm{f}}_{\mathrm{C}}(\mathsf{\lambda })\times {\displaystyle \frac{\mathsf{\lambda }\times {10}^6}{\mathrm{h}\times \mathrm{c}\times {\mathrm{N}}_{\mathrm{A}}\times {10}^3\times {10}^9}})$$

(6)

where $\mathsf{\lambda }$ denotes the wavelength (nm), c represents the speed of light (3 $\times$ 10⁸ m/s), NA indicates the Avogadro constant (6.02 $\times$ 10²³ mol⁻¹), and h represents the Planck constant (6.63 $\times$ 10⁻³⁴ j·s).

2.5. Correcting Seasonal Effects in PRI

Because reflectance at 531 nm is responsive to variations in the xanthophyll pigments’ epoxidation state, the PRI exploits the changes in reflectance at 531 nm and a reference wavelength at 570 nm to represent the dynamics of the epoxidation status of xanthophyll pigments [27,30,47].

However, the application of PRI to estimate instantaneous photosynthesis is limited by changes in the ratio of chlorophylls to carotenoids and the canopy structure. It has previously been discovered that at a 20° view zenith angle, the influence on canopy reflectance in the visible range is insignificant [31,34]. Therefore, in order to accurately quantify the “departure from steady/xanthophyll cycle deoxidation”, we calculated the ‘corrected’ $\mathsf{\Delta }PRI$ that took the seasonal variations in pigment composition into consideration [34]. At the diurnal timescale, the $\mathsf{\Delta }PRI$ could be expressed as follows:

$$\mathsf{\Delta }{\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{d}\mathrm{i}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{a}\mathrm{l}}={\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{t}}-{\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{o}}$$

(7)

where ${\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{o}}$ represents the light-acclimated PRI, which could be computed by taking the early morning PRI during the day (prior to xanthophyll de-epoxidation); ${\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{t}}$ represents the PRI at a particular time of day.

At the seasonal timescale, the $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ could be calculated by deducting the ${\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{o}}$ for a given day from the minimum PRI, which reflected the maximal xanthophyll cycle de-epoxidation (${\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{d}}$, generally at midday):

$$\mathsf{\Delta }{\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}\mathrm{a}\mathrm{l}}={\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{m}\mathrm{i}\mathrm{d}}-{\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{o}}$$

(8)

2.6. Determining the Environmental Parameters

Several studies have proven that the clearness index (CI) is a significant meteorological parameter that can characterize the proportional intensity of solar incident radiation, which is associated with the ratio of direct to diffuse light [48,49]. The CI can be used to differentiate between weather conditions, such as sunny and cloudy days. A greater CI value indicates a sunnier day. To gain a deeper comprehension of how various incident light conditions affect GPP estimation using SIF and PRI, we calculated the CI based on the observed canopy PAR (${\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{T}\mathrm{O}\mathrm{C}}$, $\mathsf{\mu }$mol•m⁻²•s⁻¹) and the PAR above the atmosphere (${\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$, W/m²):

$$\mathrm{C}\mathrm{I}={\displaystyle \frac{{\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{T}\mathrm{O}\mathrm{C}}}{{\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{T}\mathrm{O}\mathrm{A}}}}$$

(9)

$${\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{T}\mathrm{O}\mathrm{A}}={\mathrm{S}}_0\times (1+0.033\times \cos (2\pi \times {\displaystyle \frac{\mathrm{D}\mathrm{O}\mathrm{Y}}{365}}))\times \mathrm{c}\mathrm{o}\mathrm{s} (\mathrm{S}\mathrm{Z}\mathrm{A})$$

(10)

where ${\mathrm{S}}_0$ represents the solar constant, which canopy be set to a value of 1367 W/m²; $\mathrm{D}\mathrm{O}\mathrm{Y}$ stands for the day of the year; and $\mathrm{S}\mathrm{Z}\mathrm{A}$ indicates the solar zenith angle. Finally, the unit of ${\mathrm{P}\mathrm{A}\mathrm{R}}_{\mathrm{T}\mathrm{O}\mathrm{A}}$ was converted from W/m² to $\mathsf{\mu }$mol•m⁻²•s⁻¹ by multiplying it by 4.6.

The vapor pressure deficit (VPD) was determined by Teten’s formula based on the air temperature and RH [50]. The VPD was used to indicate the dryness of the air. Other environmental parameters (e.g., PAR and Ta) could be obtained from the open-access dataset.

2.7. Modeling GPP Based on SIF and PRI

In order to assess the performance of GPP estimation based on canopy and ecosystem-level SIF using a linear model, we compared the GPP results estimated with ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}}$ (${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{C}}$) and the GPP results estimated with ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ (${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}}$).

Since obtaining the necessary parameters for the physical modeling of the GPP is challenging (e.g., FvCB and MLR), a statistical model was trained on the dataset to estimate GPP. According to Ma et al. [31] and Wang et al. [27], the inclusion of the PRI with SIF-based GPP estimation models enhances the GPP estimation accuracy, but they neglected to account for the seasonal effects of SIF and PRI in the canopy. In this study, we also used a multi-linear regression model to investigate GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$:

$${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}=\mathrm{f}\left({\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}},\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}\right)=\mathrm{a}{\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}+\mathrm{b}\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}+\mathrm{c}$$

(11)

where $\mathrm{a}$, $\mathrm{b}$, and c are parameters fitted using regression analysis. We used the observed canopy SIF and PRI to model GPP for comparison:

$${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_\mathrm{P}\mathrm{R}\mathrm{I}}=\mathrm{f}\left({\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760},\mathrm{P}\mathrm{R}\mathrm{I}\right)={\mathrm{a}}^{\prime }{\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}+{\mathrm{b}}^{\prime }\mathrm{P}\mathrm{R}\mathrm{I}+{\mathrm{c}}^{\prime }$$

(12)

where ${\mathrm{a}}^{\prime }$, ${\mathrm{b}}^{\prime },$ and ${\mathrm{c}}^{\prime }$ are parameters fitted using regression analysis. To better determine whether the CI has a great impact on the model, partial correlation analysis was carried out to examine the influence of environmental conditions (CI, PAR, Ta, and VPD) on the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}$.

In addition, since environmental conditions have complex effects on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$, we used Random Forest (RF) regression—one of the best machine learning models for predictive analytical approaches—to model the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}$:

$${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}}=\mathrm{f}\left(\mathrm{T}\mathrm{a},\mathrm{V}\mathrm{P}\mathrm{D}\right)\times {\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}$$

(13)

$${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}\_\mathrm{C}\mathrm{I}}=\mathrm{f}\left(\mathrm{C}\mathrm{I},\mathrm{T}\mathrm{a},\mathrm{V}\mathrm{P}\mathrm{D}\right)\times {\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}$$

(14)

where $\mathrm{f}\left(\mathrm{T}\mathrm{a},\mathrm{V}\mathrm{P}\mathrm{D}\right)$ represents the RF regression result, which describes the effects of Ta and VPD on the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}$; $\mathrm{f}\left(\mathrm{C}\mathrm{I},\mathrm{T}\mathrm{a},\mathrm{V}\mathrm{P}\mathrm{D}\right)$ denotes the RF regression result, which describes the effects of CI, Ta, and VPD on the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}$. Finally, we obtained the ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}}$ and ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}\_\mathrm{C}\mathrm{I}}$ by combining Equation (10) and the RF results. The overall research framework is shown in Figure 3. The different relationships of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}}$ and ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}\_\mathrm{C}\mathrm{I}}$ reveal the influences of the CI on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ and emphasize the importance of including the CI in GPP models based on SIF and the PRI.

3. Results

3.1. Performance of GPP Estimation Using SIF and PRI

First, we explored the performance of GPP estimates based on SIF using a linear model. Compared to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}}$, ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ could quantify canopy photosynthesis more accurately for both half-hourly (R² = 0.61, RMSE = 8.67 $\mathsf{\mu }$mol•m⁻²•s⁻¹, Figure 4a,b) and daily (R² = 0.63, RMSE = 7.54 $\mathsf{\mu }$mol•m⁻²•s⁻¹, Figure 4e,f) data. This indicates that broadband photosystem-level PSII SIF can better track the dynamics of GPP.

We further analyzed the GPP estimates based on SIF and PRI using a multi-variable linear model. GPP was more accurately estimated using both SIF and the PRI than when using only SIF (Figure 4). Compared to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_\mathrm{P}\mathrm{R}\mathrm{I}}$ estimated by ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}$ and $\mathrm{P}\mathrm{R}\mathrm{I}$, ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_∆\mathrm{P}\mathrm{R}\mathrm{I}}$ estimated by ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ correlated better with the ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ for both half-hourly (R² = 0.63, RMSE = 8.47 $\mathsf{\mu }$mol•m⁻²•s⁻¹, Figure 4c,d) and daily (R² = 0.66, RMSE = 7.17 $\mathsf{\mu }$mol•m⁻²•s⁻¹, Figure 4g,h) data. This indicates that the corrected PRI ($\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$) and broadband photosystem-level PSII SIF (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$) can monitor dynamic changes in GPP better.

3.2. Effects of Weather Conditions on GPP Estimation Using PRI and SIF

To clarify the complex effects of the CI on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$, we first examined how the CI affected the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$. From Figure 5, we can see that the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ obviously decreased with an increasing CI for the half-hourly (r = −0.65, p < 0.01) and daily (r = −0.80, p < 0.01) data. However, the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}$ (the normalized $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$) showed an increased trend with an increasing CI for the half-hourly (r = 0.45, p < 0.01) and daily (r = 0.31, p < 0.01) data.

In addition, we investigated the connection between the CI and the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_∆\mathrm{P}\mathrm{R}\mathrm{I}}$ (Figure 6). The ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_∆\mathrm{P}\mathrm{R}\mathrm{I}}$ exhibited a non-linear correlation with the CI for both the half-hourly (R² = 0.21) and daily (R² = 0.25) scales.

Moreover, we performed partial correlation analysis to investigate the impacts of the CI on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ by controlling various environmental parameters and structural indicators (

Table 1. Correlation coefficients for the links between CI and the ratio of ${GPP}_{EC}$ to ${GPP}_{TOT\_∆PRI}$. NIRv refers to the near-infrared reflectance (NIR) of the vegetation portion, which is expressed as NIR multiplied by NDVI. The control variables are included in parenthesis, and the Pearson and partial correlation coefficients are provided.

Crops	Timescales	Pearson’s Coefficient of Correlation	Partial Correlation Coefficient
			Structure		Environment
			(NIRv)	(NDVI)	(PAR)	(Ta)	(VPD)
Soybean	Half-hourly	−0.10 **	−0.16 **	−0.17 **	−0.11 **	−0.08 **	−0.18 **
	Daily	−0.38 **	−0.55 **	−0.50 **	−0.47 **	−0.36 **	−0.07

** stands for the significance level of 0.01.

). It can be seen that the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}}$ exhibited a significant correlation with the CI by controlling the near-infrared reflectance (NIR) of the vegetation portion (NIRv), NDVI, PAR, Ta, and VPD. This indicates that the effects of the CI should be integrated into GPP estimation models based on ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$.

In addition, we also used an RF model to evaluate the effects of the CI on the modeling of GPP using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$. The different relationships between ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ and ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}}$ and ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}\_\mathrm{C}\mathrm{I}}$ revealed the influence of the CI on GPP estimation. When considering the effects of the CI, the GPP estimation accuracy was improved (R² increased from 0.72 to 0.77 and the RMSE decreased from 7.60 to 6.94 $\mathsf{\mu }$mol•m⁻²•s⁻¹, Figure 7a,b). Therefore, the effects of the CI should be considered in GPP estimation based on ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ for soybean.

3.3. Improving GPP Estimation Using SIF and PRI by Considering the CI

Finally, we investigated the accuracy of GPP estimation based on ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ when the effects of the CI were considered. A total of 70% of the tower-based observations was used to train the GPP estimation models, and the remaining 30% of the dataset was used to validate the models (

Table 2. The multi-variable linear GPP models based on the training dataset when considering the influences of CI or not. The impact of CI on the GPP models is represented by the function g(CI).

Crops	Timescale	Linear Model	R2	RMSE	p
Soybean	Half-hourly	$\begin{array}{c}{\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}=12.81\times {\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}+238.39\times \mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}+10.75\end{array}$	0.64	8.28	<0.01
		$\begin{array}{c}{\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}\_\mathrm{C}\mathrm{I}}=\mathrm{g}(\mathrm{C}\mathrm{I})\times {\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}\\ \mathrm{g}\left(\mathrm{C}\mathrm{I}\right)=-4.74 \ast {\mathrm{C}\mathrm{I}}^2+3.87 \ast \mathrm{C}\mathrm{I}+0.45\end{array}$	0.71	7.42	<0.01
	Daily	$\begin{array}{c}{\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}=14.08\times {\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}+191.80\times \mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}+9.33\end{array}$	0.71	6.69	<0.01
		$\begin{array}{c}{\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}\_\mathrm{C}\mathrm{I}}=\mathrm{g}(\mathrm{C}\mathrm{I})\times {\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}\\ \mathrm{g}\left(\mathrm{C}\mathrm{I}\right)=-4.01 \ast {\mathrm{C}\mathrm{I}}^2+2.83 \ast \mathrm{C}\mathrm{I}+0.71\end{array}$	0.81	5.34	<0.01

). The empirical statistical equations presented in Figure 6 were utilized to determine the g(CI) functions.

It is evident that taking the CI into account can improve GPP estimation based on ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$. For the half-hourly data, the R² values improved from 0.64 to 0.71 and the RMSE values decreased from 8.28 $\mathsf{\mu }$mol•m⁻²•s⁻¹ to 7.42 $\mathsf{\mu }$mol•m⁻²•s⁻¹; for the daily data, the R² values improved from 0.71 to 0.81 and the RMSE values decreased from 6.69 $\mathsf{\mu }$mol•m⁻²•s⁻¹ to 5.34 $\mathsf{\mu }$mol•m⁻²•s⁻¹. The remaining 30% of the dataset validated these findings (Figure 8). GPP estimation based on ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ could be improved when the influence of the CI was taken into account.

4. Discussion

4.1. Uncertainties in the GPP Estimates Made with SIF and PRI

In this study, we determined the performance of GPP estimation by using only SIF or using both SIF and the PRI. Compared to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}}$, ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ could quantify canopy photosynthesis more accurately for both the half-hourly and daily data (Figure 4). This indicates that broadband photosystem-level PSII SIF can better track the dynamics of GPP. In addition, GPP was estimated better using both SIF and the PRI than when using only SIF (Figure 4). These results agree with the previous studies based on leaf and satellite observations [27,51].

This study used the PRI as an indicator of NPQ to track dynamic changes, as per previous studies, especially at short timescales [47]. Although this study assessed the role of the PRI in SIF-based GPP estimation, the PRI is a good proxy for NPQ. Regulated NPQ is affected by the xanthophyll cycle, which can be detected by a canopy reflectance of 531 nm at short timescales [33,52]. However, the seasonal variations in the PRI were largely influenced by changes in the pigment pools (e.g., chlorophyll content), and the reliability of using the PRI to indicate NPQ needs to be further investigated. Magney et al. [12] reported that plant adaptation to winter not only corresponds to changes in the xanthophyl cycle but also to a variation in a variety of carotenoids (e.g., lutein and beta-carotene), which may play a photoprotective role for plants in response to low temperatures. In addition, canopy reflectance was influenced by the solar viewing geometry, the canopy structure, and the soil background, which further affected the calculation of the PRI and the linkage of PRI to NPQ.

Due to this, the change in heat dissipation (NPQ) can be described using the PRI; therefore, it is reasonable to combine the information from PRI and SIF to enhance GPP estimation. Numerous studies have shown that improvement in GPP estimation for various ecosystems can be achieved by combining SIF and the PRI [27,30,31,47]. Several studies have employed PRI measurements to monitor the diurnal variations in photosynthesis [28,30,34]. However, due to chlorophyll and carotenoid absorption, it is challenging to measure photosynthesis using the PRI across a season [53,54]. Therefore, it is important to eliminate the effects of varying concentrations of xanthophylls, chlorophylls, anthocyanins, and carotenes on photosynthesis using the PRI, especially for different canopy structures and crop growth stages [55]. Although some studies have reported that the seasonally corrected PRI can be a good indicator of photosynthetic status under various environmental conditions, the performance of GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI has not been properly explored [28,29,34,35]. In this study, we assessed the performance of GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI. Compared to the ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_\mathrm{P}\mathrm{R}\mathrm{I}}$ estimated using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{C}\_760}$ and $\mathrm{P}\mathrm{R}\mathrm{I}$, ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_∆\mathrm{P}\mathrm{R}\mathrm{I}}$ estimated using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ correlated better with ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ for both the half-hourly and daily data (Figure 4). This indicates that GPP was monitored better by using broadband photosystem-level PSII SIF (${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$) and the corrected PRI ($\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$). Nevertheless, the potential underlying mechanisms for linking ΔPRI to NPQ at the canopy scale must be explored.

4.2. Potential Influences of Weather Conditions on GPP Estimation Using PRI and SIF

Although combining SIF and PRI has been proven to be beneficial for quantifying GPP based on ground, airborne, or satellite observations [27,31,32,36], the potential impact of weather conditions on GPP estimation using SIF and PRI has yet to be investigated based on tower-based measurements. In this study, we examined the impacts of weather conditions on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ (broadband photosystem-level SIF for photosystem II) and ΔPRI (formed of early morning and midday PRIs) and explored the usefulness of combining weather conditions to improve soybean GPP estimation. The results showed that the CI can be used to improve GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI (Table 2, Figure 7). Using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI for GPP estimation can cause carbon assimilation in bright conditions, while the quantum yield of SIF stays comparatively stable [14]. In addition, ΔPRI is representative of NPQ and generally exhibited a downward trend under increasingly bright conditions [29,34]. Some studies have reported that the APAR is more related to SIF than GPP [11,18,56]. The “diffuse light fertilization effect” and interactions between other cloud-related environmental factors may cause the increased uptake of carbon under cloudy conditions [57,58,59,60].

In this study, we found that the ratio of GPP to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ obviously decreased with an increasing CI (r = −0.65 and $p$ < 0.01 for the half-hourly data, r = −0.80 and $p$ < 0.01 for the daily data, Figure 5), which agrees with previous studies [48]. However, the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}$ (the normalized $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$) showed an increased trend with an increasing CI for the half-hourly (r = 0.45, $p$ < 0.01) and daily (r = 0.31, $p$ < 0.01) data. This indicates that the effects of the CI on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$ are complex. The ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_∆\mathrm{P}\mathrm{R}\mathrm{I}}$ exhibited a non-linear correlation with the CI along both the half-hourly (R² = 0.21) and daily (R² = 0.25) scales. In addition, based on partial correlation analysis by controlling various environmental parameters and the structural indicators (Table 1), the impact of the CI on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI was significant. Therefore, the impact of the CI should be incorporated into GPP estimation models using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI. Nevertheless, the potential underlying mechanisms of linking ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI to GPP need to be explored in the future.

It should be noted that the CI is associated more with the proportional intensity of solar incident radiation [48,49]. The CI can be used to differentiate between weather conditions, such as sunny and cloudy days. However, the CI is a weather condition. The precipitation index (for example, the simple daily intensity index and the SDII) and light intensity can also be used to characterize weather conditions. Future research needs to investigate the impact of other conditions on GPP estimation based on SIF and PRI.

4.3. Limitations and Implications

In this study, we found that the effects of the CI should be considered in GPP multi-linear estimation models of soybean crops using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI. However, the results are only applicable to soybean crops. In addition, there are large uncertainties in estimating NPQ using the PRI [27,31]. The separation of sunlit/shaded areas and diffuse/direct beam radiation among multilayered canopy structures is also important for understanding how GPP relates to SIF and the PRI [18,61]. To comprehend the complicated dynamics of SIF and the PRI, more research is required.

In addition, we built a multiple linear regression model for GPP estimation with the assumption that the effects of PRI and SIF on GPP are linear. However, some studies have reported that SIF is non-linearly connected to GPP because of the saturation effects in dark reaction processes. This must be investigated in research on the performance of GPP estimation using other models. In this study, we also used an RF model to evaluate the effects of the CI on the modeling of GPP using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and $\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I}$. The different relationships between ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}\_\mathrm{C}\mathrm{I}}$ and the ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{R}\mathrm{F}}$ will reveal the influence of the CI on GPP estimation (Figure 8).

However, the results only show that the relationship of GPP to ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI are influenced by the CI. The influence of environmental stress on GPP estimation using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI should be further investigated from the leaf to the canopy. More leaf and canopy observation experiments should be carried out in the future [34]. The Fluorescence Explorer (FLEX) is the eighth Earth observation satellite to be commissioned, and it will be used in the future [62]. It can help us improve the understanding of the interaction between carbon dioxide, vegetation, and the atmosphere by obtaining contemporaneous PRI and SIF data. In addition, FLEX data will be in conjunction with data from the Copernicus Sentinel series of satellites, which utilize thermal and light sensors, to better understand how photosynthetic processes affect the water and carbon cycles. Overall, our results demonstrated that GPP can be accurately estimated using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI and significantly enhanced by taking the impact of the CI into account. These results will help increase the accuracy of GPP estimation under various weather conditions.

5. Conclusions

In this study, using tower-based observations, we found that GPP can be accurately estimated using a multi-linear model built with ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI. The ratio of ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{E}\mathrm{C}}$ to ${\mathrm{G}\mathrm{P}\mathrm{P}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathsf{\Delta }\mathrm{P}\mathrm{R}\mathrm{I} }$ exhibited a non-linear correlation with the CI. Whether based on a multiple-linear model or a Random Forest model, the GPP estimates using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI were significantly improved by considering the influence of the CI. Therefore, our results demonstrate that GPP can be well estimated using ${\mathrm{S}\mathrm{I}\mathrm{F}}_{\mathrm{T}\mathrm{O}\mathrm{T}\_\mathrm{F}\mathrm{U}\mathrm{L}\mathrm{L}\_\mathrm{P}\mathrm{S}\mathrm{I}\mathrm{I}}$ and ΔPRI, and taking into account the effects of the CI can increase the accuracy of GPP estimation. In order to develop a more accurate GPP estimation model, more leaf and canopy observation experiments should be carried out in the future. These findings will be beneficial to vegetation GPP estimation using different remote sensing platforms, especially under various weather conditions.