Improved Methods for Retrieval of Chlorophyll Fluorescence from Satellite Observation in the Far-Red Band Using Singular Value Decomposition Algorithm

Abstract

Solar-induced chlorophyll fluorescence (SIF) is highly correlated with photosynthesis and can be used for estimating gross primary productivity (GPP) and monitoring vegetation stress. The far-red band of the solar Fraunhofer lines (FLs) is close to the strongest SIF emission peak and is unaffected by chlorophyll absorption, making it suitable for SIF intensity retrieval. In this study, we propose a retrieval window for far-red SIF, significantly enhancing the sensitivity of data-driven methods to SIF signals near 757 nm. This window introduces a weak O₂ absorption band based on the FLs window, allowing for better separation of SIF signals from satellite spectra by altering the shape of specific singular vectors. Additionally, a frequency shift correction algorithm based on standard non-shifted reference spectra is proposed to discuss and eliminate the influence of the Doppler effect. SIF intensity retrieval was achieved using data from the GOSAT satellite, and the retrieved SIF was validated using GPP, enhanced vegetation index (EVI) from the MODIS platform, and published GOSAT SIF products. The validation results indicate that the SIF products provided in this study exhibit higher fitting goodness with GPP and EVI at high spatiotemporal resolutions, with improvements ranging from 55% to 129%. At low spatiotemporal resolutions, the SIF product provided in this study shows higher consistency with EVI and GPP spatially.

1. Introduction

Sun-induced chlorophyll fluorescence (SIF) can serve as a dynamic indicator of photosynthetic activity [1], and it is used for estimating gross primary productivity (GPP) and monitoring vegetation stress [2,3,4]. SIF is emitted in the red and near-infrared regions (640–850 nm), which include multiple atmospheric absorption bands and Fraunhofer lines (FLs). Compared to atmospheric absorption bands, SIF retrievals in FLs do not require accurate estimates of atmospheric transmittance spectra and are minimally affected by aerosol scattering [5,6,7]. This provides significant advantages in SIF retrieval accuracy. The insensitivity to elastic aerosol scattering results in more relaxed cloud filtering thresholds for FLs [8,9,10], leading to more effective SIF retrievals and clearer intensity distribution images [11].

The FLs near 757 nm in the far-red region are close to the strongest SIF emission peak and are not affected by chlorophyll absorption, resulting in a good correlation between SIF retrievals in this band and photosynthetic activity [12]. The data-driven method avoids explicit modeling of complex radiative transfer, making it suitable for SIF retrievals based on high-spectral-resolution instruments (in FLs) or gas absorption bands [5,6,7,13], and it is widely used in satellite-based SIF retrievals [14]. These methods are particularly useful for hyperspectral instruments or wider fitting windows in SIF inversion. This method treats satellite spectra as a combination of non-SIF radiation spectra and top-of-atmosphere (TOA) SIF spectra, represented by a linear combination of singular vectors and state vectors of steady-state fluorescence (Fs).

When using data-driven methods for SIF retrieval in the 757 nm FLs, the SIF spectrum can sometimes be confused with the slope features of satellite spectra during the inversion process, leading to overfitting issues [13]. The forward model in data-driven methods is generated using non-SIF satellite spectra, so the Doppler effect-induced spectral shifts between satellite spectra should be considered. Random Doppler shifts increase the redundancy of information in non-SIF spectra, hindering the extraction of their features. And spectral shifts between the forward model and satellite spectra directly impact SIF signal retrieval. To our knowledge, no studies have discussed the correction and impact of the Doppler effect in data-driven methods.

The GOSAT satellite, with its excellent spectral resolution, includes numerous far-red FLs in its FTS-1 band, providing ample opportunities for improving retrieval windows. In this study, we propose a retrieval window to address the overfitting issue in data-driven methods, enabling better decoupling of far-red FLs SIF signals from singular vectors. Additionally, we propose a spectral shift correction algorithm based on standard reference spectra to eliminate spectral shifts between satellite spectra and discuss the Doppler effect’s impact on SIF retrieval. We performed SIF retrieval in the aforementioned window using the Doppler shift-corrected GOSAT spectra, generated the corresponding SIF product, and validated it. The structure of this paper is as follows. Section 2 presents the retrieval window, spectral shift correction algorithm, forward model, and strategies for generating and selecting singular vectors. It also introduces the data used and the evaluation methods for retrieval results. Section 3 validates the retrieval results using vegetation indices (VI), GPP, and contemporaneous Caltech GOSAT SIF products. Section 4 discusses the validation results and the impact of the Doppler effect. Finally, Section 5 concludes the paper.

2. Materials and Methods

2.1. Data Overview

2.1.1. GOSAT Level 1b Radiance Data

The GOSAT satellite, launched on 23 January 2009, operates on a sun-synchronous, descending orbit, ensuring an overpass time of 13:00 LT at the Equator. Each sounding is acquired by the satellite with a footprint of approximately 10.5 km × 10.5 km. Onboard the satellite is the Thermal and Near-infrared Sensor—Fourier Transform Spectrometer (TANSO-FTS), equipped with four bands. Specifically, the FTS-1 band spans the wavelength range of 757 to 775 nm, falling within the frequency range of SIF emission. The spectral resolution of FTS-1 is 0.025 nm, with a sampling interval of 0.012 nm [15].

The high spectral resolution of GOSAT, coupled with its suitability for SIF retrieval, provides an ideal operational space for refining the retrieval window. With a revisit period of 3 days, GOSAT facilitates global coverage in a relatively short timeframe. The high-precision SIF products obtained through GOSAT are valuable for conducting data analyses at high temporal resolutions.

2.1.2. Remote Sensing Products Utilized

Doughty et al. [16] provided the Caltech SIF product covering the period from April 2009 to June 2020. In this study, we specifically utilized the SIF data for the entire year of 2019. The Caltech SIF dataset includes instantaneous and daily mean SIF values for three spectral bands, corresponding to wavelengths of 757 nm, 771 nm, and 740 nm, respectively. To maintain consistency, we adopted the same naming convention.

For comparison with the Caltech SIF product, we applied a quality screening strategy similar to that outlined by Doughty et al. [16]. The quality factor for retrieval results was generated based on the criteria presented in

Table 1. Criteria of quality flags, with best and good for the GOSAT SIF product. Soundings that do not meet either set of criteria are flagged as having failed (2).

Quality_Flag = 0 (Best)	Quality_Flag = 1 (Good)
28 ≤ continuum radiance at 757 nm ≤ 195 (W·m−2·sr−1·µm−1)	28 ≤ continuum radiance at 757 nm ≤ 195 (W·m−2·sr−1·µm−1)
χ2 at 755 nm ≤ 2.0	2.0 < χ2 at 755 nm ≤ 3.0
χ2 at 770 nm ≤ 2.0	2.0 < χ2 at 770 nm ≤ 3.0
0.85 ≤ O2 ratio ≤ 1.5	0.85 ≤ O2 ratio ≤ 1.5
0.5 ≤ CO2 ratio ≤ 4	0.5 ≤ CO2 ratio ≤ 4
θSZA ≤ 80°	θSZA ≤ 80°
Land fraction = 100%	80% ≤ Land fraction < 100%

.

The criteria include continuum radiation levels to filter scenes with extreme brightness, a χ² threshold to exclude poorly modeled spectra, O₂ and CO₂ thresholds to eliminate cloudy scenarios, and a solar zenith angle (θSZA) threshold to restrict retrievals during extreme solar zenith angles. Both the “best” and “good” quality combinations were used for comparison, and the resulting SIF intensity maps were generated.

We validated our retrieval results and the Caltech SIF product using Terra MODIS MOD17A2HGF Version 6.1 GPP at a resolution of 500 m and Terra MODIS MOD13C2 Version 6.1 VI (EVI and NDVI) at a spatial resolution of 0.05°. The GPP product is a cumulative 8-day composite based on the radiation use efficiency concept, using an equal-area sinusoidal projection. We projected it into 0.1° and 2° spatial resolutions for monthly and annual GPP comparisons with the retrieval results and Caltech SIF product. The VI is a monthly gridded product with latitude and longitude coordinates, and monthly and annual products at both spatial resolutions can be directly obtained by averaging. Considering the influence of sub-pixel heterogeneity on vegetation index retrievals, only results from uniform surfaces were retained when generating SIF products at 0.1° and 2° spatial resolutions [11].

2.2. Retrieval Methodology

2.2.1. The Forward Model

The top-of-atmosphere (TOA) radiance spectrum, denoted as ${\mathrm{L}}_{\mathrm{TOA}}$, acquired by the satellite from nadir over a Lambertian reflecting surface, neglecting atmospheric bidirectional reflectance effects [17], can be expressed as

$${\mathrm{L}}_{\mathrm{TOA}}{=\mathrm{E}}_0\cdot {\cos \mathsf{\theta }}_{\mathrm{SZA}}{(\mathsf{\rho }}_0{+\mathrm{T}}_{\downarrow \uparrow }{\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{s}}}{\mathsf{\pi }}})+\mathrm{Fs}\cdot {\mathrm{T}}_{\uparrow }$$

(1)

where ${\mathrm{E}}_0$ represents extraterrestrial solar irradiance, ${\mathsf{\theta }}_{\mathrm{SZA}}$ is the solar zenith angle, ${\mathsf{\rho }}_0$ is the atmospheric path reflectance, ${\mathsf{\rho }}_{\mathrm{s}}$ is the surface reflectance, T denotes atmospheric transmittance with arrows indicating the direction of light propagation, and Fs represents the canopy solar-induced fluorescence (SIF) emission.

The ${\mathrm{L}}_{\mathrm{TOA}}$ can be considered as a superposition of non-SIF contributions and SIF emissions. In the forward model, the non-SIF contribution typically includes an n-order polynomial to characterize slow-varying components such as land surface reflectance spectra [5,18,19]. However, due to the smoothness of land surface reflectance spectra within the retrieval window proposed in this study and the inability to eliminate the slope features of reflectance spectra in the singular vectors through slope normalization of non-SIF spectral sets, we directly perform Singular Value Decomposition (SVD) on the non-SIF spectral set to obtain singular vectors that contain information about land surface reflectance and weak atmospheric absorption.

As the proposed retrieval window introduces only a narrow portion of atmospheric absorption lines and Fs is only influenced by the upward atmospheric transmittance ${\mathrm{T}}_{\uparrow }$, and accurate estimation of unidirectional atmospheric transmittance faces certain challenges [20], we neglect the atmospheric impact on the SIF spectral shape. The forward model is represented as the direct summation of non-SIF contributions and the TOA SIF spectrum.

$${\mathrm{F}(\mathsf{\omega },\mathrm{F}}_{\mathrm{s}})={\displaystyle \sum }_{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{v}}}{\mathsf{\omega }}_{\mathrm{i}}{\mathrm{Sv}}_{\mathrm{i}}{+\mathrm{F}}_{\mathrm{s}}^{\mathrm{TOA}}{\mathrm{V}}_{\mathrm{Fs}}$$

(2)

where ${\mathsf{\omega }}_{\mathrm{i}}$ and ${\mathrm{F}}_{\mathrm{s}}^{\mathrm{TOA}}$ represent the weights of the singular vectors ${\mathrm{Sv}}_{\mathrm{i}}$ in the reconstructed spectrum and the intensity information of the TOA SIF spectrum, respectively. Considering that within the inversion window, the shape of the vegetation canopy’s SIF spectrum does not change when transmitted to the top of the atmosphere, we used the state vector ${\mathrm{V}}_{\mathrm{Fs}}$ of the canopy steady-state fluorescence ${\mathrm{F}}_{\mathrm{s}}$ to characterize the shape of the TOA SIF spectrum.Its slight shape error compared to the actual SIF spectrum has little impact on the retrieval results [17,21,22]. Utilizing the least-squares method to minimize the residual between the forward model and the satellite spectrum allows the inversion of ω and ${\mathrm{F}}_{\mathrm{s}}^{\mathrm{TOA}}$, thereby retrieving the intensity information of the SIF signal.

2.2.2. The Singular Vectors in Forward Model

In the SIF retrieval process within the FLs band using data-driven methods, the construction of the forward model typically involves utilizing the singular vectors derived from a set of spectra devoid of SIF emissions. For the GOSAT satellite, bare soil areas can be distinguished from surfaces such as vegetation, water, clouds, and snow by using the ratio of apparent reflectance from three FTS bands [13,23]. Building upon this, we further refined the selection of SIF-free spectra using MODIS GPP products [24], thus extending the temporal coverage of the SIF-free spectrum dataset to encompass the entire year. Specifically, GPP products within an 8-day interval were projected and gridded at a resolution of 0.2°. Regions with GPP approximately equal to zero were selected to represent bare soil areas, ensuring observations devoid of Fs. Additionally, SIF-free spectra were acquired exclusively from high-gain mode, with spectral radiance constrained within the range of [1.5–8]∙10⁻⁷ W⁻¹·m⁻²·sr⁻¹·cm⁻¹, and scenes with solar zenith angle (SZA) greater than 70° were excluded to reduce uncertainty. The non-SIF spectral collection also includes observations over snowy areas to increase the range of radiance in the spectral set and to add slope characteristics similar to those of satellite spectra over vegetation canopies.

We selected the top 5 singular vectors corresponding to the largest singular values from the SIF-free spectrum dataset for constructing the forward model. Among these vectors, the first one encompasses the primary spectral shape information, the second one is used to fit the intensity difference on either side of the Fraunhofer lines caused by sensor discretization, the third one primarily fits the spectral slope, the fourth one reflects the instrumental line shape (ILS) widening the spectral bands, and the fifth one is mainly employed to fit the higher variability in atmospheric absorption bands. To validate the effectiveness of this set of singular vectors, we exhaustively tested all combinations involving the top 10 singular vectors for SIF retrieval. The results indicate that employing the first 5 singular vectors yields the highest correlation with the Enhanced Vegetation Index (EVI) and maintains the lowest zero-level offset.

2.2.3. The State Vectors of Fs in Forward Model

In this study, the Fs state vector is generated using the Soil Canopy Observation, Photochemistry, and Energy fluxes (SCOPE v2.1) model. SCOPE is a vertical (1D) integrated radiative transfer and energy balance model [25]. The model calculates SIF spectra at the scale of chlorophyll molecules, leaves, and canopies. Here, we use the SCOPE to generate SIF spectra set at the canopy scale. Principal Component Analysis (PCA) is applied to extract the far-red spectral bands from these spectra. Given the simplicity and stability of the SIF spectral shape within the specified retrieval window [26], this study employs the first principal component, accounting for over 99% of the corresponding variance, as the state vector of SIF to represent the SIF spectra.

2.3. Selection of Retrieval Window

The SIF retrieval in this study is conducted near the FLs around 757 nm in the far-red band. The satellite spectra in the far-red FLs band exhibit prominent slope characteristics due to vegetation canopy reflectance effects. Through SVD of the non-SIF radiance spectra, these characteristics are extracted and concentrated in the third singular vector, Sv3. Despite the significant difference in slope between singular vector Sv3 and the SIF spectrum, Sv3 itself cannot fit the SIF spectrum, but it enhances the fitting capability of singular vectors to the SIF spectrum within the forward model. Inversion results indicate that there is an order of magnitude difference between the coefficients of Sv3 and the Fs state vector, compensating for the significant difference in slope between them. The intensity difference caused by the coefficients can be compensated for by other singular vectors.

To avoid overfitting singular vectors to SIF spectra, we have improved the traditional retrieval window. The enhanced retrieval window introduces the edge portion of the O₂ absorption line, which occupies less than one-tenth of the entire retrieval window, thereby having minimal impact on Fs affected only by atmospheric absorption in the observation direction. Furthermore, benefiting from SVD’s feature extraction of the non-SIF radiance spectra, the introduction of the O₂ absorption band can significantly alter the morphological characteristics of specific singular vectors. As shown in Figure 1, Sv3 contains two distinct slope features, caused by O₂ absorption and surface reflection, respectively. These markedly different slope features effectively restrict the fitting of singular vectors to SIF spectra with a single slope characteristic, thereby achieving better decoupling between Fs and singular vectors.

In the narrow retrieval window, the complexity of the SIF spectrum is low, making it prone to overfitting. Although using a larger window for SIF retrieval helps in decoupling Fs from singular vectors, it results in the loss of the advantage of high Fs intensity in the far-red band, thus not improving the retrieval results. By introducing the O₂ absorption band, better decoupling of Fs can be achieved while retaining the intensity advantage. However, the introduction of the O₂ absorption band complicates the SIF inversion, requiring a reconsideration of the construction of the forward model and the selection of singular vectors.

2.4. Frequency Shift Correction Algorithm

In order to correct for frequency shifts in satellite spectra, a reference spectrum devoid of frequency shifts relative to the Earth’s surface is employed. This reference spectrum is defined as the product of the solar irradiance spectrum and the standard atmospheric transmittance spectrum:

$${\mathrm{I}}^{\mathrm{ref}}\left(\mathsf{\nu }\right)=\mathrm{E}\left(\mathsf{\nu }\right)\exp \left[-\left({\displaystyle \frac{1}{{\cos \mathsf{\theta }}_{\mathrm{SZA}}}}+{\displaystyle \frac{1}{{\cos \mathsf{\theta }}_{\mathrm{ZA}}}}\right)\tau \left(\nu \right)\right]$$

(3)

where ${\mathrm{I}}^{\mathrm{ref}}\left(\nu \right)$ represents the radiance spectrum at the top of the atmosphere (TOA), Eis the solar radiance spectrum, τ is the atmospheric optical thickness, and ${\mathsf{\theta }}_{\mathrm{SZA}}$ and ${\mathsf{\theta }}_{\mathrm{ZA}}$ represent the solar zenith angle and satellite zenith angle, respectively. Convolution of ${\mathrm{I}}^{\mathrm{ref}}$ with the GOSAT satellite’s instrumental line shape (ILS) yields the reference spectrum:

$${\mathrm{S}}_{\mathrm{P}/\mathrm{S}}^{\mathrm{ref}}\left(\mathrm{i}\right)={\displaystyle \sum }_{{\mathrm{j}=-\mathrm{N}}_{\mathrm{W}}}^{{\mathrm{N}}_{\mathrm{W}}}{\mathrm{ILS}}_{\mathrm{P}/\mathrm{S}}\left(-\mathrm{j}\mathsf{\delta }\mathsf{\nu }\right){\mathrm{I}}^{\mathrm{ref}}\left({\mathsf{\nu }}_{\mathrm{i}}+\mathrm{j}\mathsf{\delta }\mathsf{\nu }\right)\mathsf{\delta }\mathsf{\nu }$$

(4)

where P and S represent two polarization directions, ${\mathrm{S}}_{\mathrm{P}/\mathrm{S}}^{\mathrm{ref}}\left(\mathrm{i}\right)$ denotes the intensity at the i-th sampling point of the reference spectrum, δν is the convolution step size (usually set to 0.01 cm⁻¹), and N_W δν represents the convolution half-width, set to 20 cm in this study.

To determine the actual wavenumber axis of the satellite spectrum, a lookup table consisting of n wavenumber axes with certain frequency shifts is constructed. The wavenumber axis corresponding to the reference spectrum is interpolated in the lookup table to build the corresponding reference spectrum matrix ${\mathrm{M}}_{\mathrm{P}/\mathrm{S}}^{\mathrm{ref}}$. The correlation between the satellite spectrum and each reference spectrum in ${\mathrm{M}}_{\mathrm{P}/\mathrm{S}}^{\mathrm{ref}}$ is then calculated using Equation (5), where ${\mathrm{V}}_{\mathrm{correlation}}$ is a row vector of length n representing the magnitudes of the correlations between the satellite and reference spectra, and $\mathrm{Sounding}$ represents the satellite spectrum, a column vector of length 1755.

$${\mathrm{V}}_{\mathrm{correlation}}{{=\mathrm{Sounding}}_{\mathrm{P}}}^{\mathrm{T}}{\times \mathrm{M}}_{\mathrm{P}}^{\mathrm{ref}}{{+\mathrm{Sounding}}_{\mathrm{S}}}^{\mathrm{T}}{\times \mathrm{M}}_{\mathrm{S}}^{\mathrm{ref}}$$

(5)

According to the actual wavenumber axis of the satellite spectrum obtained, the satellite spectrum is interpolated in the SIF retrieval window, effectively eliminating frequency shifts between satellite spectra. The effectiveness of the wavenumber correction is illustrated in Figure 2.

The solar irradiance spectrum database is provided by Toon [27]. This database offers a merged solar pseudo-transmittance spectrum, ranging from 600 to 33,300 cm⁻¹, by consolidating measurements derived from various methods. The pseudo-transmittance spectrum has a spectral resolution of 0.01 cm⁻¹, which can be directly used for convolution with ILS. For the accuracy of the reference spectrum, the solar radiation continuum of TSIS SIM was utilized in this study to convert the solar pseudo-transmittance spectrum into the solar irradiance spectrum.

2.5. Evaluation Methods

2.5.1. Generation of Daily Average SIF

Daily average SIF offers a more reasonable estimate of photosynthetic activity compared to instantaneous SIF, and our approach involves the computation of a daily correction factor. This paper utilizes daily average SIF to generate a global-scale composite SIF product for comparative validation. The calculation of this factor is dependent on various parameters such as overpass time and solar zenith angle (SZA), among others [28].

The conversion from instantaneous SIF ($\mathrm{SIF}\left({\mathrm{t}}_{\mathrm{m}}\right)$) to daily SIF ($\overline{\mathrm{SIF}}$) average is performed using the following equation:

$$\overline{\mathrm{SIF}}{=\mathrm{SIF}(\mathrm{t}}_{\mathrm{m}})\cdot {\sec \left(\mathsf{\theta }\right(\mathrm{t}}_{\mathrm{m}}\left)\right){{\displaystyle \int }}_{{\mathrm{t}=\mathrm{t}}_{\mathrm{m}}-12\mathrm{h}}^{{\mathrm{t}=\mathrm{t}}_{\mathrm{m}}+12\mathrm{h}}\cos \left(\mathsf{\theta }\right(\mathrm{t}\left)\right)\cdot \mathrm{H}\left(\cos \right(\mathsf{\theta }\left(\mathrm{t}\right)\left)\right)\mathrm{dt}$$

(6)

where ${\mathsf{\theta }(\mathrm{t}}_{\mathrm{m}})$ represents the measured solar zenith angle at time ${\mathrm{t}}_{\mathrm{m}}$, and the integral is computed in 10-minute time increments (dt). The Heaviside step function H is employed to eliminate negative values of ${\cos \left(\mathsf{\theta }\right(\mathrm{t}}_{\mathrm{m}}\left)\right)$.

2.5.2. Uncertainty Estimates

Measurement errors are considered the primary source of uncertainty in the retrieved SIF signal. The uncertainty associated with the data-driven retrieval of SIF can be estimated using the following equation:

$${\mathrm{S}}_{\mathrm{e}}{=\mathsf{\sigma }}_{\mathrm{m}}^2{{(\mathrm{J}}^{\mathrm{T}}\mathrm{J})}^{-1}$$

(7)

where ${\mathrm{S}}_{\mathrm{e}}$ represents the inversion error covariance matrix with dimensions (n_v + 1) × (n_v + 1), ${\mathsf{\sigma }}_{\mathrm{m}}^2$ denotes the measurement error, and J is a matrix composed of the first n_v singular vectors and the state vector of Fs. Equation (7) effectively illustrates the propagation of measurement errors into the Fs.

While a small portion of the uncertainty in our retrieval method is attributed to the introduction of atmospheric absorption bands rather than measurement errors, Equation (7) remains a robust tool for effectively estimating the majority of uncertainties in the retrieval results.

2.5.3. Production of Global SIF Composites

To facilitate the comparison of retrieval results, this study generated two types of SIF products and vegetation indices at two temporal resolutions (annual and monthly) and two spatial resolutions (2° and 0.1° grid cells). The 2° grid cells followed the established strategy for generating GOSAT composite SIF, while the 0.1° grid cells corresponded to GOSAT’s spatial resolution.

Monthly composite SIF was created by directly averaging daily SIF within each grid cell. For annual composite SIF, normalization of lighting conditions based on solar zenith angle (SZA) was applied to balance significant illumination differences between months for comparison with vegetation indices. Obvious outliers were filtered out using uncertainty values. The formula for calculating the uncertainty $\mathsf{\sigma } \overline{\mathrm{F}}$ of composite SIF is given by

$$\mathsf{\sigma } \overline{\mathrm{F}}=\sqrt{{\displaystyle \frac{1}{{{\displaystyle \sum }}_{\mathrm{i}=1}^{{\mathrm{n}}_{\mathrm{f}}}{(1/\mathsf{\sigma }}_{\mathrm{e},\mathrm{i}}^2)}}}$$

(8)

where ${\mathsf{\sigma }}_{\mathrm{e}}$ represents the uncertainty of individual retrieval results calculated through Equation (7), and ${\mathrm{n}}_{\mathrm{f}}$ is the number of retrieval results in the grid cell after quality screening. Guanter et al. [13] removed composite SIF with $\mathsf{\sigma }\overline{\mathrm{F} }$> 0.07 mW·m⁻²·sr⁻¹·nm⁻¹ for 2° grid cells. We scaled this threshold for screening composite SIF at other temporal and spatial resolutions.

3. Results

We validated the retrieval results and the Caltech SIF product at both annual and monthly scales using MODIS VI and GPP products. Considering that validation results at high spatiotemporal resolution can better reflect the differences between the two SIF products, the monthly scale validation was conducted only at a spatial resolution of 0.1° (similar to the footprint size of the GOSAT satellite). In addition to the 0.1° spatial resolution, the annual scale validation was also conducted at a spatial resolution of 2°, which is commonly used for validating GOSAT satellite SIF products and for generating intensity spatial distribution maps [13,29,30]. Vegetation indices (VI) include the Normalized Difference Vegetation Index (NDVI) and the Enhanced Vegetation Index (EVI). EVI reduces canopy background signals and atmospheric influences, enhancing vegetation monitoring capabilities. In this study, we primarily used this index to validate the SIF products.

3.1. Comparison with GPP and VI

The scatter plots for January 2019 in Figure 3, showing the relationship between the two SIF products and GPP and EVI at a 0.1° spatial resolution, highlight the differences between our retrieval results and the Caltech SIF product at high spatiotemporal resolutions. For higher goodness-of-fit (GOF) with VI, no normalization for illumination conditions was applied to the SIF products. The scatter plots revealed that our retrieval results had a slightly higher degree of dispersion, primarily due to the inclusion of the O₂ absorption band. Additionally, our retrieval results were more sensitive to variations in GPP and VI, leading to a significant advantage in GOF and higher intensity levels. Since high-vegetation areas typically correspond to stronger illumination, there should be a non-linear relationship between the SIF signal and VI. This non-linearity was evident in our retrieval results, while the scatter plot for Caltech SIF product and VI showed minimal slope differences between high- and low-vegetation areas.

To verify the stability of the GOF differences between the two SIF products at high spatiotemporal resolution, we conducted a linear fit of two SIF products with GPP and EVI at a 0.1° spatial resolution on a monthly scale from January 2018 to June 2020, and calculated the GOF. The GOF calculation results are presented in Figure 4 in the form of a line chart. Due to insufficient retrievals in December 2018, the fitting results for that month showed significant bias. Both SIF products exhibited similar temporal variation in their GOF with EVI and GPP. During the southern hemisphere summer, the global SIF intensity and its gradient were higher, resulting in a better fit. Since changes in EVI accumulate over time, the variation in the goodness-of-fit between the SIF products and EVI lagged behind and was smaller compared to GPP. Notably, during the southern hemisphere summer, the improvement and enhancement ratios of the fit between our retrieval results and both EVI and GPP were higher compared to the Caltech SIF products, indicating enhanced sensitivity of the data-driven method in our study.

We also present the Pearson correlation coefficients (p-values) of the two SIF products with GPP and VI at high spatiotemporal resolutions in Figure 5. The temporal trend of the p-values closely resembles that of GPP, indicating that our retrieval results consistently show a higher linear correlation with GPP and VI at high spatiotemporal resolutions. Compared to GOF, the differences in p-values between the two SIF products are smaller.

Figure 6 presents the annual-scale scatter plots of the two SIF products with GPP and EVI. When comparing with VI, SIF products were normalized for illumination conditions using the solar zenith angle to balance the significant differences in illumination across various months and regions. As the spatiotemporal resolution decreased, random noise in the composite SIF products was more effectively suppressed, leading to an improvement in goodness-of-fit and a reduction in the difference between the two SIF products’ fit.

Figure 7 shows the scatter plots and fitting results of the two SIF products with GPP and VI at the annual scale and 2° spatial resolution. At a 2° spatial resolution, the goodness-of-fit of the SIF products further improved. Our retrieval results maintained a noticeable advantage over the Caltech SIF product in terms of fit with GPP but showed lower fit levels with VI. The lower goodness-of-fit was mainly associated with outliers in low-vegetation areas, potentially due to VI product underestimating vegetation abundance in highly heterogeneous regions (such as cities and deserts). Similar outliers also appeared in the scatter plots for the Caltech SIF product, but their quantity and dispersion were lower due to its relatively lower sensitivity to the SIF signal. Due to the higher level of random noise in the monthly composite SIF product and the lack of normalization for seasonal factors, the relative dispersion and proportion of outliers in the scatter plot of the monthly SIF product and VI are lower, as shown in Figure 3.

3.2. Spatial Distribution of Remote Sensing Products

In this section, we present intensity maps of annual SIF, GPP, and EVI at spatial resolutions of 0.1° and 2° in Figure 8 and Figure 9, respectively. The SIF products at 0.1° grid cells are directly averaged results, while those at 2° grid cells are normalized for illumination conditions to enable comparison with EVI.

Considering the differences in intensity between the two SIF products, we assigned different color bars to them using the 3σ principle, resulting in higher color–intensity resolution in the Caltech SIF product’s intensity map. The differences between the two SIF maps at a 0.1° grid resolution are minimal. However, under this color bar, the Caltech SIF product cannot effectively distinguish between high SIF scenarios near the equator and other vegetation regions. In contrast, in the intensity map of our retrieval results, high-intensity levels of blue SIF can be observed near the equator, which is particularly noticeable in Southeast Asia.

At a 2° spatial resolution, the SIF products were normalized for illumination to enable comparison with the EVI intensity maps. It is noteworthy that, although the goodness-of-fit (GOF) between the Caltech SIF and EVI is higher at this resolution, our retrieval results show a higher correlation with the EVI maps and a stronger ability to distinguish between different land features. This will be detailed in conjunction with Figure 9.

Figure 10 presents intensity maps of SIF and EVI for some typical regions. Considering the absence of scenes in the intensity map of EVI for 2° grid cells due to the selection of uniform land surfaces, we compare it with the intensity map of EVI for 0.1° grid cells. Clear boundaries exist between tropical rainforests, farmland, and bare mountains in South America, which can be observed distinctly in the intensity map of the retrieval results but relatively fuzzily in the Caltech SIF map. Both SIF products can distinguish high-vegetation areas in the southeastern United States from low-vegetation areas, but the color matching between our retrieval results and the EVI map is significantly higher. Most regions in Europe have high vegetation abundance, while the Iberian Peninsula is relatively barren. In contrast to the retrieval results, the differences between these two regions are not obvious in the intensity image of Caltech SIF. The color differences in the intensity map of the retrieval results for different vegetation types (tropical rainforest, grassland, desert) in Africa are more pronounced, achieving better differentiation of these terrains. The comparison with EVI in these regions reflects the stronger resolution capability of our retrieval results for different land surface types.

4. Discussion

By improving the retrieval window and correcting the frequency shift of satellite spectra, we achieved better separation of the SIF signal at the FLs band near 757 nm wavelength. The new retrieval window addresses the issue of overfitting of singular vectors, significantly enhancing the sensitivity of the data-driven method to Fs. Furthermore, the correction for the Doppler effect can further enhance the intensity of the retrieval results. In this paper, we illustrate this through the comparison of retrieval results and SVD results before and after the correction of satellite spectrum frequency shift. In addition to the higher correlation with GPP and VI, our retrieval results also exhibit a more reasonable intensity distribution, further demonstrating the improvement in sensitivity of the data-driven algorithm due to the enhanced methods.

4.1. Impact of Retrieval Window

Figure 11 presents the slope and goodness-of-fit (GOF) of the linear fit between the SIF retrieval results from the combined retrieval window (including O₂ absorption and FLs bands) and the FLs band alone with GPP/EVI. The fitting is performed on a monthly scale and at a 0.1° spatial resolution, encompassing the retrieval results for the entire year of 2019. The retrieval results from the combined window exhibit a slightly higher degree of dispersion compared to the linear fit results. Due to the lack of direct validation for SIF products, it is unclear whether this is caused by the introduction of a small amount of noise from the O₂ absorption bands or a true reflection of the SIF–GPP/EVI relationship. What is certain is that the inclusion of the O₂ absorption bands facilitates better decoupling of the SIF spectra from the singular vectors. As a result, the SIF products obtained from the combined retrieval window exhibit higher slopes relative to GPP/EVI, leading to a higher GOF.

4.2. Impact of Doppler Shift

To investigate the effect of the Doppler shift on the forward model, we compared the SVD results of the no-Doppler-shift spectral dataset before and after frequency shift correction. Since the differences between the two sets of singular vectors mainly reside in the seventh and eighth singular vectors, we adopted different strategies in Figure 12 to display the first eight singular vectors.

The frequency shift correction reduces the redundancy of information in the no-Doppler-shift spectral dataset, resulting in richer information contained in the first few singular vectors of the no-shift spectrum set. For instance, the second singular vector carries additional slope information of the satellite spectrum, and the prominence of peaks in the second to fourth singular vectors is significantly enhanced in correlation with the depth of the Fraunhofer lines. Overall, the differences in the first six singular vectors are minimal. The seventh and eighth singular vectors of the original spectral dataset exhibit strong high-frequency features, concentrated near the Fraunhofer lines, which are absent in the corresponding singular vectors of the no-shift spectral dataset. Therefore, we attribute the seventh and eighth singular vectors mainly to the Doppler effect. These two singular vectors are not suitable for constructing the forward model, and thus the Doppler effect cannot be corrected through singular vectors.

By correcting the Doppler shift in the satellite spectra, both the slope and the goodness-of-fit between the retrieval results and GPP and VI are further improved, as shown in Figure 13. This is because the frequency shift correction eliminates the frequency shift between the forward model and the satellite spectra, allowing the depths of the Fraunhofer lines to be fully utilized, thereby further enhancing the sensitivity of the data-driven method to the SIF signal.

4.3. Retrieval Evaluation

Through improvements in the retrieval window and Doppler shift correction of satellite spectra, our data-driven method achieved significantly improved sensitivity to Fs. From the same set of satellite spectra, we retrieved SIF products with higher intensity and credibility, as demonstrated by the monthly validation results at 0.1° grid cells. As the spatiotemporal resolution (especially spatial resolution) decreases, the differences in fit between the two SIF products also diminish. This is because averaging multiple retrieval results effectively reduces random noise following a normal distribution; specifically, the noise of the average of n retrieval results is expected to be ${\displaystyle \frac{1}{\sqrt{\mathrm{n}}}}$ times the noise of a single retrieval result, which weakens the advantage of our retrieval results in signal-to-noise ratio.

At lower spatiotemporal resolutions, the limitations of our retrievals in scenarios with very low SIF intensities become more apparent. This is due to the increased variability in satellite spectra introduced by the inclusion of O₂ absorption bands, which slightly weakens the forward model’s ability to explain the TOA SIF spectra, potentially leading to a slight increase in noise levels in the retrieval results. Given that the nonlinear transformation NDVI has a higher weight in low-vegetation areas, the difference in GOF between the two SIF products and NDVI becomes more pronounced at lower spatiotemporal resolutions.

GOF can be easily affected by outliers and may not comprehensively reflect the relationship between SIF products, GPP, and VI. Therefore, we present intensity–frequency distribution images of the original retrieval results for both SIF products, as well as for GPP and EVI in Figure 14. The two SIF products show good consistency in terms of intensity range, indicating that the differences in grid-based products are only related to the intensity–frequency distribution of single retrieval results. Our retrieval results have a noticeably higher proportion in high-SIF areas, which aligns more closely with the intensity–frequency distribution images of EVI and GPP. This further demonstrates the enhanced sensitivity of our data-driven method.

The intensity–frequency curve of the Caltech SIF product is steep, making it prone to averaging SIF retrieval results of different intensity levels when generating composite products at certain spatiotemporal resolutions. This leads to a significant reduction in the intensity range and contrast of the composite SIF product. This explains the significant differences in intensity range between the two SIF products shown in Figure 8, Figure 9 and Figure 10, as well as the better differentiation of our retrieval results for different vegetation communities.

4.4. Outlook and Implications

Benefiting from the enhanced spectral resolution for FLs depth [31], the spectral sensitivity of the GOSAT satellite to Fs filling is heightened. However, the overfitting of singular vectors to the SIF spectrum has reduced the sensitivity of the data-driven approach to Fs. Addressing these issues through improvements in the retrieval window, combined with the Doppler shift correction of satellite spectra, has yielded retrieval results with higher intensity levels, further exploring the potential of high spectral resolution satellites in SIF retrieval.

SIF products can be utilized for monitoring vegetation drought and temperature stress [2,3,4]. This study significantly enhances the sensitivity of the data-driven approach to Fs, coupled with GOSAT’s shorter revisit period, enabling more timely and accurate alerts for vegetation environmental stress.

For other hyperspectral satellites, the key to the applicability of the retrieval window proposed in this study lies in two aspects. Firstly, the spectral resolution of the satellite payload should be sufficiently high to ensure the capture of spectral slope variations through narrow weak O₂ absorption bands. Secondly, the satellite spectrum should contain an adequate number of usable FLs to minimize the proportion of atmospheric absorption bands in the retrieval window, reducing the impact of O₂ absorption on the SIF spectrum.

5. Conclusions

We proposed a retrieval window for Fs retrieval near 757 nm, which avoids the overfitting of singular vectors to the SIF spectrum. By employing a Doppler shift correction algorithm based on standard reference spectra, we eliminated the Doppler shift between satellite spectra and discussed for the first time the impact of the Doppler effect on data-driven methods. The inversion window assigns two distinctly different slope characteristics to specific singular vectors by introducing weak O₂ absorption bands, thereby restricting the fit of singular vectors to the SIF spectrum in the forward model. A linear forward model was proposed for this window, which ignores the influence of atmospheric absorption on the SIF spectrum. The construction of the forward model utilized the first five physically meaningful singular vectors and was validated using EVI. A comparison of retrieval results before and after Doppler shift correction revealed that eliminating the Doppler shift between satellite spectra further enhances the sensitivity of data-driven methods to Fs.

The validation of the retrieval results was conducted using MODIS GPP and VI. Our retrieval results demonstrated higher goodness-of-fit and p-value with GPP and VI at high spatiotemporal resolutions. Specifically, at a 0.1° spatial resolution on a monthly scale, the goodness-of-fit generally improved by more than 55% compared to the Caltech SIF product.

The introduction of O₂ absorption bands brought about a slight noise increase while enhancing the sensitivity of the data-driven algorithm. Consequently, retrieval performance in low SIF regions was compromised. However, due to the more serious issue of Fs underestimation caused by low sensitivity, our retrieval results generally exhibited higher signal-to-noise ratios in most scenarios.

Due to the difficulty in balancing signal-to-noise ratio (SNR) and spectral resolution, SIF retrieval results from satellites equipped with high spectral resolution payloads, such as GOSAT, often have higher root m0thean square error (RMSE). However, these spectra have deeper Fraunhofer line depths, making them more sensitive to the filling effect caused by SIF signals. In this study, by optimizing window selection and correcting for Doppler shifts, we further explored the retrieval potential of high spectral resolution payloads for SIF signals, significantly improving the SNR of the retrieval results at high spatiotemporal resolutions. Combined with the short revisit cycle of the GOSAT satellite, this approach enables accurate monitoring of SIF signals at high temporal resolutions.