The Solar-Induced Chlorophyll Fluorescence Imaging Spectrometer (SIFIS) Onboard the First Terrestrial Ecosystem Carbon Inventory Satellite (TECIS-1): Specifications and Prospects

The global monitoring of solar-induced chlorophyll fluorescence (SIF) using satellite-based observations provides a new way of monitoring the status of terrestrial vegetation photosynthesis on a global scale. Several global SIF products that make use of atmospheric satellite data have been successfully developed in recent decades. The Terrestrial Ecosystem Carbon Inventory Satellite (TECIS-1), the first Chinese terrestrial ecosystem carbon inventory satellite, which is due to be launched in 2021, will carry an imaging spectrometer specifically designed for SIF monitoring. Here, we use an extensive set of simulated data derived from the MODerate resolution atmospheric TRANsmission 5 (MODTRAN 5) and Soil Canopy Observation Photosynthesis and Energy (SCOPE) models to evaluate and optimize the specifications of the SIF Imaging Spectrometer (SIFIS) onboard TECIS for accurate SIF retrievals. The wide spectral range of 670−780 nm was recommended to obtain the SIF at both the red and far-red bands. The results illustrate that the combination of a spectral resolution (SR) of 0.1 nm and a signal-to-noise ratio (SNR) of 127 performs better than an SR of 0.3 nm and SNR of 322 or an SR of 0.5 nm and SNR of 472 nm. The resulting SIF retrievals have a root-mean-squared (RMS) diff* value of 0.15 mW m−2 sr−1 nm−1 at the far-red band and 0.43 mW m−2 sr−1 nm−1 at the red band. This compares with 0.20 and 0.26 mW m−2 sr−1 nm−1 at the far-red band and 0.62 and 1.30 mW m−2 sr−1 nm−1 at the red band for the other two configurations described above. Given an SR of 0.3 nm, the increase in the SNR can also improve the SIF retrieval at both bands. If the SNR is improved to 450, the RMS diff* will be 0.17 mW m−2 sr−1 nm−1 at the far-red band and 0.47 mW m−2 sr−1 nm−1 at the red band. Therefore, the SIFIS onboard TECIS-1 will provide another set of observations dedicated to monitoring SIF at the global scale, which will benefit investigations of terrestrial vegetation photosynthesis from space.

. Technical characteristics of current satellites/instruments with the ability to provide global solar-induced chlorophyll fluorescence (SIF) retrievals as well as the planned Terrestrial Ecosystem Carbon Inventory Satellite (TECIS-1) and FLuorescence EXplorer (FLEX).  The satellite will operate in a sun-synchronous orbit at a height of 506 km and have a 10:30 AM local time in the descending mode. It will be launched in 2021 with a designed lifetime of 8 years. The SIFIS includes the optical mechanical main body, signal processor unit, and power unit. A calibration unit is mounted in the main body for absolute calibration in orbit, as shown in Figure 2. The SIFIS aims to have a sub-nanometer SR of 0.3 nm and SNR of greater than 300. It is well known that the characteristics of the SNR and SR of a spectrometer are mutually limited by the defined binning scheme of pixels according to

Satellite
where refers to the number of noise electrons, which includes the readout noise, dark noise, and shot noise. K is the number of combined pixels and is the number of electrons in the measured signal, which is related to the SR. Based on the current performance of the instrument and Equation (1), a graph of the relationship between the SR and SNR can be calculated, as shown in Figure 3. Specifically, the specification of SNR can achieve approximately 322 at a given SR of 0.3 nm. However, up to now, The satellite will operate in a sun-synchronous orbit at a height of 506 km and have a 10:30 AM local time in the descending mode. It will be launched in 2021 with a designed lifetime of 8 years. The SIFIS includes the optical mechanical main body, signal processor unit, and power unit. A calibration unit is mounted in the main body for absolute calibration in orbit, as shown in Figure 2.

The TECIS-1 Satellite and SIF Payload
The Terrestrial Ecosystem Carbon Monitoring Satellite (TECIS-1) is intended to evaluate forest biomass, measure atmospheric aerosol content, and detect photosynthetic fluorescence. These measurements will contribute to efforts to combat global warming. The satellite is designed to carry 4 payloads: Multi-Beam LIDAR, Directional Multi-Spectral Camera, Directional Polarization Camera, and Chlorophyll Fluorescence Hyper-Spectral Monitor (SIFIS), as shown in Figure 1. The satellite will operate in a sun-synchronous orbit at a height of 506 km and have a 10:30 AM local time in the descending mode. It will be launched in 2021 with a designed lifetime of 8 years. The SIFIS includes the optical mechanical main body, signal processor unit, and power unit. A calibration unit is mounted in the main body for absolute calibration in orbit, as shown in Figure 2. The SIFIS aims to have a sub-nanometer SR of 0.3 nm and SNR of greater than 300. It is well known that the characteristics of the SNR and SR of a spectrometer are mutually limited by the defined binning scheme of pixels according to where refers to the number of noise electrons, which includes the readout noise, dark noise, and shot noise. K is the number of combined pixels and is the number of electrons in the measured signal, which is related to the SR. Based on the current performance of the instrument and Equation (1), a graph of the relationship between the SR and SNR can be calculated, as shown in Figure 3. Specifically, the specification of SNR can achieve approximately 322 at a given SR of 0.3 nm. However, up to now, The SIFIS aims to have a sub-nanometer SR of 0.3 nm and SNR of greater than 300. It is well known that the characteristics of the SNR and SR of a spectrometer are mutually limited by the defined binning scheme of pixels according to Sensors 2020, 20, 815 5 of 21 where N e refers to the number of noise electrons, which includes the readout noise, dark noise, and shot noise. K is the number of combined pixels and S e is the number of electrons in the measured signal, which is related to the SR. Based on the current performance of the instrument and Equation (1), a graph of the relationship between the SR and SNR can be calculated, as shown in Figure 3. Specifically, the specification of SNR can achieve approximately 322 at a given SR of 0.3 nm. However, up to now, the specifications for the SNR under an SR of 0.3 nm are still in the optimization process. The SNR of the spectrometer can be improved through merging the imaging pixels or decreasing the electronic noise (from 0.4 to 0.2 mV), which can be obtained by increasing the power filtering or decreasing the operating temperature of the CCD (from 15°C to 5°C). In addition, according to the information provided by the instrument manufacturer, an SNR greater than 450 can be achieved in the future.
Sensors 2020, 20, x FOR PEER REVIEW 5 of 22 the specifications for the SNR under an SR of 0.3 nm are still in the optimization process. The SNR of the spectrometer can be improved through merging the imaging pixels or decreasing the electronic noise (from 0.4 to 0.2 mV), which can be obtained by increasing the power filtering or decreasing the operating temperature of the CCD (from 15 ℃ to 5 ℃). In addition, according to the information provided by the instrument manufacturer, an SNR greater than 450 can be achieved in the future.

Simulated Experiment
In order to assess the retrieval characteristics under different combinations of SIFIS instrument specifications, we carried out an extensive set of simulations by combing the Soil Canopy Observation Photosynthesis and Energy (SCOPE) and Moderate resolution atmospheric TRANsmission (MODTRAN) models to generate high-spectral-resolution radiance spectra at the top of the atmosphere (TOA). SCOPE [47], a vertically integrated radiative transfer and energy balance model, is widely used to simulate the canopy radiative transfer process, especially to generate the leaf and top-of-canopy (TOC) reflectance and SIF spectra. In this study, the SCOPE model (version 1.70) was employed to simulate the canopy SIF and reflectance spectra based on a look-up-table (LUT) method combining different parameters that affect the SIF simulations. The main input parameters to the SCOPE model used in this study are listed in Table 2; all other input parameters were set to their default values. This gave 60 pairs of canopy reflectance and simulated SIF values according to the combinations in Table 2, as shown in Figure 4. The spectral shape of the SIF spectra, including two peaks at the vegetation canopy level, is clearly shown in Figure 4.

Simulated Experiment
In order to assess the retrieval characteristics under different combinations of SIFIS instrument specifications, we carried out an extensive set of simulations by combing the Soil Canopy Observation Photosynthesis and Energy (SCOPE) and Moderate resolution atmospheric TRANsmission (MODTRAN) models to generate high-spectral-resolution radiance spectra at the top of the atmosphere (TOA). SCOPE [47], a vertically integrated radiative transfer and energy balance model, is widely used to simulate the canopy radiative transfer process, especially to generate the leaf and top-of-canopy (TOC) reflectance and SIF spectra. In this study, the SCOPE model (version 1.70) was employed to simulate the canopy SIF and reflectance spectra based on a look-up-table (LUT) method combining different parameters that affect the SIF simulations. The main input parameters to the SCOPE model used in this study are listed in Table 2; all other input parameters were set to their default values. This gave 60 pairs of canopy reflectance and simulated SIF values according to the combinations in Table 2, as shown in Figure 4. The spectral shape of the SIF spectra, including two peaks at the vegetation canopy level, is clearly shown in Figure 4.  MODTRAN [48,49] is an atmospheric radiative transfer model that has a high spectral resolution of about 0.005 nm. In this study, MODTRAN 5 was used to simulate the radiation and upward atmospheric transmittance used in simulating TOA radiances in the spectral range from 600 to 800 nm. The solar irradiance data also included in this model consisted of the standard Kurucz solar data [50]. The MODTRAN 5 input parameters are listed in Table 3; there was a total of 4608 combinations. The radiance at the TOA received by the sensor instrument over the fluorescent vegetation surface can be represented as [51,52] where 0 and are the atmospheric path radiance and solar radiation arriving at the surface, respectively, is the surface reflectance, is the atmospheric spherical albedo, SIF is the TOC SIF signal, and ↑ is the upward atmospheric transmittance. Similarly, the TOA radiance over nonfluorescent surfaces can be calculated by leaving out the SIF term in Equation (2).
In this paper, the principal component analysis (PCA) [53] data-driven SIF retrieval method was used to evaluate the SIF retrieval performance using the simulated dataset. For this data-driven method, SIF is regarded as an additive signal; thus, the TOA radiance can be represented as the sum of the fluorescent component and non-fluorescent component, as shown in Equation (2). Detailed descriptions for this method can be found in Section 2.3. Thus, in order to make use of this method, two separate datasets are needed simultaneously. One of these, denoted as the training dataset, should not include the SIF contributions used for deriving the principal components; and the other, denoted as the test dataset, should contain the SIF signals used to assess the retrieval results under different settings. A schematic of the process for producing the simulated datasets is shown in Figure 5. First, three groups MODTRAN [48,49] is an atmospheric radiative transfer model that has a high spectral resolution of about 0.005 nm. In this study, MODTRAN 5 was used to simulate the radiation and upward atmospheric transmittance used in simulating TOA radiances in the spectral range from 600 to 800 nm. The solar irradiance data also included in this model consisted of the standard Kurucz solar data [50]. The MODTRAN 5 input parameters are listed in Table 3; there was a total of 4608 combinations. The radiance at the TOA received by the sensor instrument over the fluorescent vegetation surface can be represented as [51,52] where L 0 and L TOC are the atmospheric path radiance and solar radiation arriving at the surface, respectively, ρ s is the surface reflectance, S is the atmospheric spherical albedo, SIF is the TOC SIF signal, and T ↑ is the upward atmospheric transmittance. Similarly, the TOA radiance over non-fluorescent surfaces can be calculated by leaving out the SIF term in Equation (2). In this paper, the principal component analysis (PCA) [53] data-driven SIF retrieval method was used to evaluate the SIF retrieval performance using the simulated dataset. For this data-driven method, SIF is regarded as an additive signal; thus, the TOA radiance can be represented as the sum of the fluorescent component and non-fluorescent component, as shown in Equation (2). Detailed descriptions for this method can be found in Section 2.3. Thus, in order to make use of this method, two separate datasets are needed simultaneously. One of these, denoted as the training dataset, should not include the SIF contributions used for deriving the principal components; and the other, denoted as the test dataset, should contain the SIF signals used to assess the retrieval results under Sensors 2020, 20, 815 7 of 21 different settings. A schematic of the process for producing the simulated datasets is shown in Figure 5. First, three groups of TOA radiance spectra can be obtained, thus giving three reflectance values that can be used as input parameters for the MODTRAN model. Next, the relevant atmospheric radiation transfer parameters (L 0 , L TOC , and S) used in simulating the training and test datasets can be calculated using an algebraic method based on Equation (2). Seven different non-fluorescent surface reflectance spectra corresponding to snow and bare soil surfaces, derived from the ENVI (Environment for Visualizing Images) spectral library [54], were used to derive the training dataset. Then, 60 pairs of canopy reflectance and SIF spectra derived using the SCOPE model were used to derive the test dataset. In addition, the training and test TOA radiance spectra with an original spectral resolution of 0.005 nm were calculated by combining the surface reflectance or TOC SIF and reflectance with the atmospheric parameters according to Equation (2). Eventually, a total of 32,256 training samples and 276,480 test samples were produced, respectively. Then, the high-spectral-resolution TOA spectra were convolved to lower-resolution spectra using a Gaussian filter with a full-width at half-maximum (FWHM) of 0.3 nm. An example of a group of simulated spectra with an SR of 0.3 nm is displayed in Figure 6: This includes spectra of TOA radiance over vegetated surfaces, incident radiance reaching the vegetation top-of-canopy (TOC), TOA SIF, and TOC SIF. Both the oxygen and solar absorption features can be clearly seen in Figure 6. of TOA radiance spectra can be obtained, thus giving three reflectance values that can be used as input parameters for the MODTRAN model. Next, the relevant atmospheric radiation transfer parameters ( 0 , , and ) used in simulating the training and test datasets can be calculated using an algebraic method based on Equation (2). Seven different non-fluorescent surface reflectance spectra corresponding to snow and bare soil surfaces, derived from the ENVI (Environment for Visualizing Images) spectral library [54], were used to derive the training dataset. Then, 60 pairs of canopy reflectance and SIF spectra derived using the SCOPE model were used to derive the test dataset. In addition, the training and test TOA radiance spectra with an original spectral resolution of 0.005 nm were calculated by combining the surface reflectance or TOC SIF and reflectance with the atmospheric parameters according to Equation (2). Eventually, a total of 32,256 training samples and 276,480 test samples were produced, respectively. Then, the high-spectral-resolution TOA spectra were convolved to lower-resolution spectra using a Gaussian filter with a full-width at half-maximum (FWHM) of 0.3 nm. An example of a group of simulated spectra with an SR of 0.3 nm is displayed in Figure 6: This includes spectra of TOA radiance over vegetated surfaces, incident radiance reaching the vegetation top-of-canopy (TOC), TOA SIF, and TOC SIF. Both the oxygen and solar absorption features can be clearly seen in Figure 6.  In this paper, except for the simulated spectra dataset with an SR of 0.3 nm and SNR of 322, preconfigured for the SIFIS currently, similar simulation experiments with different combinations of SR and SNR are also needed to investigate the prospects of these configurations for SIF retrieval. In addition, we assumed that the noise followed a Gaussian distribution and was independent of  of TOA radiance spectra can be obtained, thus giving three reflectance values that can be used as input parameters for the MODTRAN model. Next, the relevant atmospheric radiation transfer parameters ( 0 , , and ) used in simulating the training and test datasets can be calculated using an algebraic method based on Equation (2). Seven different non-fluorescent surface reflectance spectra corresponding to snow and bare soil surfaces, derived from the ENVI (Environment for Visualizing Images) spectral library [54], were used to derive the training dataset. Then, 60 pairs of canopy reflectance and SIF spectra derived using the SCOPE model were used to derive the test dataset. In addition, the training and test TOA radiance spectra with an original spectral resolution of 0.005 nm were calculated by combining the surface reflectance or TOC SIF and reflectance with the atmospheric parameters according to Equation (2). Eventually, a total of 32,256 training samples and 276,480 test samples were produced, respectively. Then, the high-spectral-resolution TOA spectra were convolved to lower-resolution spectra using a Gaussian filter with a full-width at half-maximum (FWHM) of 0.3 nm. An example of a group of simulated spectra with an SR of 0.3 nm is displayed in Figure 6: This includes spectra of TOA radiance over vegetated surfaces, incident radiance reaching the vegetation top-of-canopy (TOC), TOA SIF, and TOC SIF. Both the oxygen and solar absorption features can be clearly seen in Figure 6.  In this paper, except for the simulated spectra dataset with an SR of 0.3 nm and SNR of 322, preconfigured for the SIFIS currently, similar simulation experiments with different combinations of SR and SNR are also needed to investigate the prospects of these configurations for SIF retrieval. In addition, we assumed that the noise followed a Gaussian distribution and was independent of of SR and SNR are also needed to investigate the prospects of these configurations for SIF retrieval. In addition, we assumed that the noise followed a Gaussian distribution and was independent of radiance level. Thus, according to different evaluating purposes, four different simulation experiments were conducted based on the above training and test simulated datasets, which have an original spectral resolution of 0.005 nm, as shown in Table 4. First, in order to investigate the performance of SIF retrieval using simulated TOA spectra based on the current instrument level, as shown in Figure 3, one experiment denoted as Exp I in Table 4 was conducted to simulate three groups of simulations, including simulated spectra combining an SR of 0.3 nm and SNR of 322, an SR of 0.1 nm and SNR of 127, and an SR of 0.5 nm and SNR of 472. Secondly, one experiment that contains five groups of simulations, denoted as Exp II in Table 4, was conducted to investigate the effects of SR on the SIF retrievals under two given SNR cases, noise-free and SNR of 322. Thirdly, as an SNR of 450 at a given SR of 0.3 nm will be potentially achieved, one simulated dataset with this combination was included in Exp III, which was employed to investigate the SIF retrieval performance under this optimized specification in the future. Lastly, in order to investigate the effects of the SNR on the retrieval precision at given SRs, Exp IV included two different datasets with different noise added to simulations for a given SR of 0.1 and 0.3 nm. Detailed information of these simulation experiments is shown in Table 4.

Data-Driven SIF Retrieval Method
Similar to Equation (2), assuming Lambertian reflectance over the fluorescent surface, the radiance at the TOA received by the sensor can also be represented as a superposition of the radiation reflected by the vegetation surface and the SIF signals [31], displayed as follows: where I sol is the solar irradiance at the TOA level, µ 0 is the cosine of the solar zenith angle, ρ 0 is the atmospheric path reflectance, and T ↓↑ is the two-way atmospheric transmittance, i.e., the product of the downward and upward atmospheric transmittance. The main challenge is to separate the SIF from the radiance reflected by the surface, which is more than 100 times the intensity of the SIF signal [28]. As stated in previous work, the spectrally smooth components, including contributions from the surface reflectance (ρ s ) and the atmospheric scattering effects (ρ 0 and S), can be modeled using a low-order polynomial, which is a function of the wavelength; the spectrally oscillating component, which is mainly due to the atmospheric absorption effect (T ↓ and T ↑ ), can be reconstructed using a statistical approach [25,26,31]. Principal component analysis (PCA) is a statistical procedure that uses an orthogonal transformation to convert a set of observations of possibly correlated variables into a set of values of linearly uncorrelated variables called principal components, and is widely Sensors 2020, 20, 815 9 of 21 used in the decomposition and reconstruction of signals [14,15]. In recent years, it has been used to replace the full-physics method to model the atmospheric absorption characteristics for satellite SIF retrievals [25,26,31].
Assuming that the SIF is Gaussian-like within the fitting window, a normalized and fixed spectral function h f can be formulated: where λ 0 is the wavelength of the SIF peak emission within the fitting window and the value of σ h depends on the spectral fitting window selected for SIF retrieval. In order to simplify the non-linear problem, the effective upward transmittance, T e ↑ [25], shown in Equation (5), is also used to replace T ↑ in the forward model.
where T e ↓↑ is the effective two-way atmospheric transmittance derived from the training dataset by normalizing the solar irradiance radiance spectra with respect to the low-order polynomials, θ o denotes the solar zenith angle (SZA), and θ v is the viewing zenith angle (VZA). Although there is a difference between T e ↑ and T ↑ over vegetated surfaces because of the in-filling of the SIF, this difference is negligible according to the results of the assessment conducted by Köhler, Guanter, and Joiner [28]. Thus, the final forward model derived from Equation (3) can be simplified to where α i and β j are coefficients of the polynomial and the principal components, respectively, F s is the SIF at the required wavelength, λ is the wavelength, n p is the order of polynomial, and n pc is the number of principal components selected. Based on this simplified forward model (Equation (6)) and the selected PCs, two different fitted TOA spectra can be calculated to demonstrate the suitability of the PCA method. One includes the SIF signal during the fitting process and the other does not take SIF into account.
In this study, we chose two retrieval fitting windows ranging from 735 to 758 nm and 682 to 692 nm to retrieve the SIF signals at the far-red and red band, respectively. Depending on the width and complexity of the fitting windows, we normalize the spectra with respect to 2-order and 3-order polynomial fits at wavelengths that are not significantly affected by atmospheric absorption. As for the reference SIF spectral shape, σ h was set to 21 and 9.5 for the far-red and red bands, respectively. The selection of the threshold used in this study was based on the experience acquired in previous studies [30] and was intended to be a compromise between dealing with the overfitting problem and guaranteeing the goodness of fit at the same time. Compared to the red band fitting window, the far-red band window is less complicated as it is mostly affected by the weak water absorption without any atmospheric absorption. The red band fitting window is affected by oxygen absorption, and there is a much deeper absorption depth in the O 2 -B band (centered at about 687 nm), as shown in Figure 7 and Figure 12.

Metrics Used for Accuracy Assessment
In this paper, the simulated SIF spectra over the red and far-red fitting windows for 60 simulated vegetation canopy conditions are averaged and selected as true red and far-red band SIF values. In order to evaluate the performance of the SIF retrievals using simulated spectra with different combinations of SR and SNR, statistical parameters were used. Here, the commonly used parameters including the root-mean-squared difference (RMS diff), correlation coefficient (r), standard deviation (σ), bias between the retrieved and true SIF, and the slope and intercept of the linear fit were calculated and averaged for all atmospheric and geometrical conditions (a total of 4608 scenarios). In particular, systematic errors will inevitably be produced using the data-based retrieval method. Thus, in order to separate the influence of systematic effects due to the adopted method from those due to the different specifications, the corrected RMS difference (RMS diff*), which was based on comparisons between the true SIF values and the corrected SIF retrievals (SIF corr ) without any systematic effects, was also calculated. Making use of the statistical parameters for the linear fit between the true SIF and retrieved SIF (SIF retrieved ), the corrected retrieved SIF values were calculated using 3. Results

Performance of the PCA Data-Driven Approach for Fitting the TOA Radiance
Based on the cumulative variance explained by the principal components (PCs) derived from the simulated spectra of non-vegetated surfaces, the number of PCs used to reconstruct the SIF-free spectrum was determined by a threshold of 99.95% [32]. In the end, 8 far-red PCs and 10 red PCs were selected in the retrieval process. Figure 7a,b show the four leading PCs for the far-red and red fitting windows, respectively, which were computed using noise-free simulated data with SRs of 0.1, 0.3, and 0.5 nm. The explained variances for each PC of three simulations with SRs of 0.1, 0.3, and 0.5 nm are also displayed in each subplot, and they vary slightly for different SRs. The spectral variance in the far-red fitting window is mainly due to absorption by water vapor, as shown in Figure 7a, while it is due to the larger O 2 -B absorption band, as well as the Fraunhofer lines, in the red window, as shown in Figure 7b. For each fitting window, the spectral shapes of the PCs for the data simulated with the three different SRs are similar. The obvious difference is that much more detailed spectral information can be obtained by the simulated data with the higher SR of 0.1 nm. However, it should be noted that the first PC can capture almost all of the spectral variance for all of the simulations using the three different SRs.
Two different fitted TOA radiance spectra, SIF contributions included and not included, were obtained by making use of the simplified forward model and the selected PCs. Then, residual spectra between the measured TOA radiance and fitted radiance were averaged for a total of 276,480 simulated TOA radiances. Figure 8a,c,e show the averaged spectral residuals over the far-red band, and Figure 8b,d,f show those over the red band. It can be seen that the spectral residuals are much smaller when the SIF is included, particularly at the absorption lines. In addition, the spectral residuals for the case with low SR and high SNR (as shown in Figure 8a,b) are smaller than for other cases at the red and far-red windows, which indicates that the magnitude of the residuals is primarily dependent on the SR. Further comparisons between the spectral residuals for different SRs showed that the range of the averaged residual is larger for lower SRs, and the spectral residual for an SR of 0.1 nm and SNR of 127 (Figure 8a,b) is about 1.59 times that for an SR of 0.3 nm and SNR of 322 (Figure 8c,d). However, compared to the absolute radiance (usually greater than 100 mW m −2 sr −1 nm −1 ) and SIF (greater than 1 mW m −2 sr −1 nm −1 for a dense canopy and the simulated SIF magnitude shown in Figure 4), the magnitude of the residuals is almost negligible (the average absolute value is <0.02 and <0.003 mW m −2 sr −1 nm −1 at far-red and red band, respectively). The spectral residuals for different SRs vary from −0.15 to 0.10 mW m −2 sr −1 nm −1 at the far-red fitting window, and from −0.01 to 0.01 mW m −2 sr −1 nm −1 at the red fitting window. The above results show that the PCA method can be successfully used to reconstruct the shape of the spectra for SIF-free surfaces, which also implies that SIF signals can be discriminated from satellite-based TOA radiance using this data-driven method.

Performance of the PCA Data-Driven Approach for SIF Retrieval
In order to display the performance of the SIF retrieval using the simulated spectra covering both the far-red and red fitting windows, the retrieved SIF values were plotted against the true values at both the far-red and red bands for two sets of noise-free simulations with SRs of 0.1, 0.3, and 0.5 nm. The results of this are shown in Figure 9. From Figure 9a,c,e, it can be concluded that the retrieval accuracy and precision obtained using the noise-free simulated data with SRs of 0.1, 0.3, and 0.5 nm at the far-red band decrease slightly with low SRs, with RMS diff* values of 0.03, 0.07, and 0.12 mW m −2 s −1 nm −1 , respectively. In addition, the differences between the results obtained using three different SRs are negligible in terms of the statistical parameters RMS diff and RMS diff*. As for the red band, Figure 9f shows that the retrieved SIF values for the SRs of 0.5 nm are much worse than those for the simulations with SRs of 0.1 and 0.3 nm, as shown in Figure 9b,d, respectively; however, the retrieval errors are still all less than 20%. Thus, both far-red and red SIF signals can be successfully obtained using satellite-based observations covering both the above spectral ranges if the SNR is adequate.

Performance of the PCA Data-Driven Approach for SIF Retrieval
In order to display the performance of the SIF retrieval using the simulated spectra covering both the far-red and red fitting windows, the retrieved SIF values were plotted against the true values at both the far-red and red bands for two sets of noise-free simulations with SRs of 0.1, 0.3, and 0.5 nm. The results of this are shown in Figure 9. From Figure 9a,c,e, it can be concluded that the retrieval accuracy and precision obtained using the noise-free simulated data with SRs of 0.1, 0.3, and 0.5 nm at the far-red band decrease slightly with low SRs, with RMS diff* values of 0.03, 0.07, and 0.12 mW m −2 s −1 nm −1 , respectively. In addition, the differences between the results obtained using three different SRs are negligible in terms of the statistical parameters RMS diff and RMS diff*. As for the red band, Figure 9f shows that the retrieved SIF values for the SRs of 0.5 nm are much worse than those for the simulations with SRs of 0.1 and 0.3 nm, as shown in Figure 9b,d, respectively; however, the retrieval errors are still all less than 20%. Thus, both far-red and red SIF signals can be successfully obtained using satellite-based observations covering both the above spectral ranges if the SNR is adequate.

Performance of SIF Retrievals Using Simulations with Different SRs and SNRs
For comparison, scatter plots of retrieved versus true SIF values for the far-red and red bands for three different SNR and SR combinations are displayed in Figure 10. Similar to the comparisons in Figure 9 (free of noise), Figure 10a-f represent the comparison results for simulations with SRs of 0.1, 0.3, and 0.5 nm at both far-red and red bands, in which the corresponding noise was included. The RMS diff* for the far-red SIF retrievals using simulations with an SR of 0.1 nm and SNR of 127 (0.15 mW m −2 s −1 nm −1 ) is slightly less than for the simulations with an SR of 0.3 nm and SNR of 322 (0.20 mW m −2 s −1 nm −1 ) and SR of 0.5 nm and SNR of 472 (0.26 mW m −2 s −1 nm −1 ). However, as for the red band in Figure 10b,d,f, the retrieval accuracy noticeably decreases with the decrease in SR, and the retrieval of SIF with an RMS diff* of 1.30 mW m −2 s −1 nm −1 is too poor for the configuration with an SR of 0.5 nm and an SNR of 472. The value of RMS diff* for the SIF results is also much higher  In order to determine the best choice of SNR and SR, we conducted a further set of experiments using simulated datasets with different combinations of SNR and SR. The SIF values at both the far-red and red bands were again obtained using the fitting windows and retrieval method described above. Table 5 lists comprehensive results of the true and retrieved SIF values at both the far-red (line 1 to 9) and red bands (line 10 to 18). Statistical results for the comparisons using the simulations with different combinations of SR and SNR are also listed in Table 5. Lines 4, 5, and 6 show retrieval statistics for the far-red band based on three simulations: An SR of 0.1 nm and SNR of 127, an SR of 0.3 nm and SNR of 322, and an SR of 0.5 nm and SNR of 472. For the second case, the retrieval accuracy is rather low at the red band-the corrected RMS diff* is 0.62 mW m −2 s −1 nm −1 . Table 5. Statistical parameters for the comparisons between the retrieved and true fluorescence derived from the simulated dataset with different combinations of SNR and SR. The statistical parameters include the root-mean-squared difference (RMS diff), correlation coefficient (r), standard deviation (σ), bias between the retrieved and true fluorescence, slope and intercept of the linear fit, and the RMS difference after correction for systematic errors (RMS diff*). 'No' in the SNR column indicates that the simulated data do not include noise signals. The units used in columns with bold headings are mW m −2 sr −1 nm −1 . In addition, the bold rows represent the best statistical results for simulations with an SR of 0.1 nm and SNR of 127 and those with current specifications (SR of 0.3 nm and SNR of 322) of SIFIS at both far-red and red bands. It is inevitable that the retrieval precision (R 2 ) and accuracy (RMS diff and RMS diff*) will both increase for a higher SR and SNR. For the experiments without any noise, there is no obvious difference in retrieval performance between an SR of 0.1 and 0.3 nm at both the far-red and red bands, and both perform well. However, if the noise is included, the performance for an SR of 0.1 nm is noticeably better than for SRs of 0.3 and 0.5 nm at both bands. At the red band, in particular, there is a clear decrease in RMS diff and corrected RMS diff* for an increased SR. These improvements may be contributed to the deeper absorption lines and larger number of spectral samples used in the same fitting window when the SR is higher. However, the performance for the simulations with an SR of 0.3 nm is most likely to improve along with the simulations with an SR of 0.1 nm and SNR of 127 if the SNR is greater than 450.

Line
In order to clearly display the effects of the SNR on the retrieval precision, Figure 11 shows the variations in RMS diff* for the true and retrieved SIF values for different SNRs using the simulated data with SRs of 0.1 and 0.3 nm. The RMS diff* was calculated using the SIF retrievals after correction for the systematic retrieval errors. Thus, RMS diff* indicates the performance of simulated data for different SNRs at a given SR. It can clearly be seen that, at both far-red and red bands, the RMS diff* errors decrease significantly as the SNR increases for the simulations with SRs of 0.1 and 0.3 nm, which is consistent with the behavior displayed in previous studies [25,26,32]. The RMS diff* errors are clearly higher in the red band than in the far-red band. Thus, although the continuing increase in the SNR will lead to an improvement in SIF retrieval performance, according to the current specifications of the instrument, the RMS diff* based on simulations with an SR of 0.3 nm and SNR of 322 is larger than for simulations with an SR of 0.1 nm and SNR of 127, especially in the red band. This indicates that an SR of 0.1 nm is more likely to guarantee good SIF retrieval performance. However, if the SNR is improved to greater than 450, an SR of 0.3 nm will guarantee an RMS diff* almost as small as for an SR of 0.1 nm and SNR of 127.

Uncertainty in the SIF Retrieval Method
As shown in Figures 9 and 10, there is obvious systematic bias (about 18%-21% for far-red band and 27%-33% for red band) between the retrieved SIF and true SIF, which is inevitably produced by the data-driven retrieval algorithm. This bias can be contributed to two factors, the calculation of effective upward transmittance and the fitting bias of SIF spectral shape. The first factor is related to the difference between the true upward transmittance (T ↑ ) and the effective upward transmittance, T e ↑ , calculated based on Equation (5). T e ↑ is estimated from the effective two-way atmospheric transmittance (T e ↓↑ ), which is calculated using the apparent reflectance normalized by the low-order polynomials. In Figure 12, a schematic example of a comparison between the estimated T e ↓↑ and T e ↑ and the real T ↑ at both far-red and red bands is provided. It can be seen that T e ↑ is higher than T ↑ across the whole of the fitting windows. This is generally because the polynomial fit of the apparent reflectance assumes that the transmittance of the fitting window is approximately 1; this is quite different from the real situation, especially for the cases of high atmospheric optical thickness or larger solar or viewing angles. The ratio of T e ↑ to T ↑ is about 1.10 at the far-red band and about 1.13 at the red band. Therefore, the systemic underestimation of the retrieved SIF can be partly corrected using the ratio of T e ↑ /T ↑ determined from the simulated dataset.
the true upward transmittance ( ↑ ) and the effective upward transmittance, ↑ , calculated based on Equation (5). ↑ is estimated from the effective two-way atmospheric transmittance ( ↓↑ ), which is calculated using the apparent reflectance normalized by the low-order polynomials. In Figure 12, a schematic example of a comparison between the estimated ↓↑ and ↑ and the real ↑ at both far-red and red bands is provided. It can be seen that ↑ is higher than ↑ across the whole of the fitting windows. This is generally because the polynomial fit of the apparent reflectance assumes that the transmittance of the fitting window is approximately 1; this is quite different from the real situation, especially for the cases of high atmospheric optical thickness or larger solar or viewing angles. The ratio of ↑ to ↑ is about 1.10 at the far-red band and about 1.13 at the red band. Therefore, the systemic underestimation of the retrieved SIF can be partly corrected using the ratio of ↑ / ↑ determined from the simulated dataset. In order to quantitatively investigate the effects of the use of the effective upward transmittance to retrieve the SIF, an example showing a comparison between the SIF retrieved using the true upward transmittance derived from the simulated dataset and the effective upward transmittance calculated using Equation (3) is shown in Figure 13. It is clear that, for both the far-red and red bands, the SIF points retrieved using the true upward transmittance are much closer to the 1:1 line than those obtained using the effective upward transmittance. In addition, the results retrieved using the simulations with an SR 0.3 nm and SNR of 322 show that the use of the effective upward transmittance results in an underestimation of approximately 23% and 21% at the far-red and red bands, respectively. Furthermore, as ↑ is estimated from the training dataset and is directly applied when retrieving SIF signals using the test data, ↑ will also slightly differ from the real ↑ over vegetation surfaces, especially at the atmospheric absorption lines. This is due to the in-filling effect of SIF, which has been regarded as negligible in previous studies [25]. Thus, for both of these reasons, the estimation value of ↑ can be higher than the real ↑ , which, in turn, leads to an underestimation of the SIF.
There are still other factors to be considered when trying to reduce the uncertainty in the SIF retrieval. For example, though the Gaussian function is usually used to model the shape of the SIF spectrum, differences between the simulated shape and the real shape within the fitting windows, which are displayed in Figure 14, will produce large uncertainties in the retrieved values. The SIF emission peaks are also variable and depend on variations in the canopy structure and leaf biochemistry, especially in the case of the red SIF emission peak [55]. A wider fitting window increases the size of the differences between the Gaussian function and the real spectrum. Specifically, In order to quantitatively investigate the effects of the use of the effective upward transmittance to retrieve the SIF, an example showing a comparison between the SIF retrieved using the true upward transmittance derived from the simulated dataset and the effective upward transmittance calculated using Equation (3) is shown in Figure 13. It is clear that, for both the far-red and red bands, the SIF points retrieved using the true upward transmittance are much closer to the 1:1 line than those obtained using the effective upward transmittance. In addition, the results retrieved using the simulations with an SR 0.3 nm and SNR of 322 show that the use of the effective upward transmittance results in an underestimation of approximately 23% and 21% at the far-red and red bands, respectively. Furthermore, as T e ↑ is estimated from the training dataset and is directly applied when retrieving SIF signals using the test data, T e ↑ will also slightly differ from the real T ↑ over vegetation surfaces, especially at the atmospheric absorption lines. This is due to the in-filling effect of SIF, which has been regarded as negligible in previous studies [25]. Thus, for both of these reasons, the estimation value of T e ↑ can be higher than the real T ↑ , which, in turn, leads to an underestimation of the SIF.
There are still other factors to be considered when trying to reduce the uncertainty in the SIF retrieval. For example, though the Gaussian function is usually used to model the shape of the SIF spectrum, differences between the simulated shape and the real shape within the fitting windows, which are displayed in Figure 14, will produce large uncertainties in the retrieved values. The SIF emission peaks are also variable and depend on variations in the canopy structure and leaf biochemistry, especially in the case of the red SIF emission peak [55]. A wider fitting window increases the size of the differences between the Gaussian function and the real spectrum. Specifically, different combinations of the input parameters σ h and λ 0 will result in big differences in the retrieved SIF values [56]. Comparisons between the simulated SIF spectra and the SIF spectra fitted using the Gaussian function and the combinations used in this paper show that the differences are about 2% and 4% at the far-red and red bands, respectively. Here, we selected the optimal combinations of σ h and λ 0 to conduct the retrieval process. These combinations were based on the correlation between the simulated and true SIF spectra. In addition, the accuracy and precision of the retrieved values are also highly sensitive to the PCs and fitting windows that are selected. However, the sensitivity to these factors is not our focus of this paper, and the selections used were based on the retrieval results obtained during this study.
combinations of ℎ and 0 to conduct the retrieval process. These combinations were based on the correlation between the simulated and true SIF spectra. In addition, the accuracy and precision of the retrieved values are also highly sensitive to the PCs and fitting windows that are selected. However, the sensitivity to these factors is not our focus of this paper, and the selections used were based on the retrieval results obtained during this study. Figure 13. Comparisons between SIF retrievals using the true upward transmittance (a,c) and that using the effective upward transmittance (b,d) calculated by Equation (3) at both far-red (upper panels) and red bands (bottom panels). Similar to Figure 12, simulations with SR of 0.3 nm and SNR 322 are used. Figure 13. Comparisons between SIF retrievals using the true upward transmittance (a,c) and that using the effective upward transmittance (b,d) calculated by Equation (3) at both far-red (upper panels) and red bands (bottom panels). Similar to Figure 12, simulations with SR of 0.3 nm and SNR 322 are used.
combinations of ℎ and 0 to conduct the retrieval process. These combinations were based on the correlation between the simulated and true SIF spectra. In addition, the accuracy and precision of the retrieved values are also highly sensitive to the PCs and fitting windows that are selected. However, the sensitivity to these factors is not our focus of this paper, and the selections used were based on the retrieval results obtained during this study. Figure 13. Comparisons between SIF retrievals using the true upward transmittance (a,c) and that using the effective upward transmittance (b,d) calculated by Equation (3) at both far-red (upper panels) and red bands (bottom panels). Similar to Figure 12, simulations with SR of 0.3 nm and SNR 322 are used. Figure 14. True SIF spectrum at red (green) and far-red (red) fitting windows derived using the SCOPE model and the fixed spectral function (black) based on the Gaussian function. σ h was set as 21 and 9.5 and λ 0 was set as 740 and 692 nm for the far-red and red band, respectively.

Determination of SR, SNR, Spectral Range, and Other Requirements for the SIFIS and the TECIS-1 Satellite
Through the statistical analysis of comparisons between the true and retrieved SIF values, it can be concluded that both the far-red and red SIF can be obtained successfully if the SIFIS is able to obtain measurements that cover the spectral range from the red to far-red band. In addition, due to the significant influence of water vapor and the lower SIF signals in the wavelength range from about 780 to 850 nm [46], we suggest that the spectral range for the SIFIS should be from 670 to 780 nm, which also covers the O 2 -A and O 2 -B bands. In addition, according to the above analysis, of the three simulations, the best is the combination of an SR of 0.1 nm and SNR of 127. Thus, based on the current specifications with an SR of 0.1 nm and SNR of 127 and SR of 0.3 nm and SNR of 322, the SR for the SIFIS should be set to 0.1 nm and the corresponding SNR should be greater than 127. However, the RMS diff* values of SIF retrievals at both the far-red (0.17 mW m −2 s −1 nm −1 ) and red (0.47 mW m −2 s −1 nm −1 ) bands using simulations with an SR of 0.3 nm and SNR of 450 are similar compared to using simulations with an SR of 0.1 nm and SNR of 127, with an RMS diff* value of 0.15 mW m −2 s −1 nm −1 at the far-red band and 0.43 mW m −2 s −1 nm −1 at the red band, as displayed in Table 5. As stated in Section 2.1, an SNR of 450 for an SR of 0.3 nm is likely to be achieved in the future. In addition, as suggested by the instrument manufacturer, it is easier to improve the SNR based on an SR of 0.3 nm than to improve the SR from 0.3 to 0.1 nm. Thus, if the SNR could be improved to 450, the retrieval performance for simulations with an SR of 0.3 nm would be as good as those with an SR of 0.1 nm and SNR of 127.
In terms of SIF retrieval, as well as the requirements for the spectrometer onboard TECIS-1, several other requirements should be considered, including temporal, spatial, and local time requirements. The SIF is an instantaneous signal and will have a highly dynamic variance depending on the illumination and effects of stress and environmental conditions. A high frequency of measurements and large coverage are needed to track the dynamic variations in SIF signals. In addition, a high spatial resolution is also needed in order to investigate the photosynthetic mechanisms in vegetation on a small land scale, especially so that validation with ground-based measurements can be carried out. However, due to production constraints, these requirements cannot be satisfied simultaneously. Considering the need for a high spatial resolution and global coverage, a spatial resolution of greater than 1 km is optimal for identifying vegetation canopy types at site scales. As for the global coverage, coverage over all land surfaces and main islands should be available [46]. The SIFIS gives only a coarse resolution of 2 km and a narrow swath of 30 km, which does not match well with the requirements for the global mapping of SIF.

Conclusions
TECIS-1 is the first Chinese scientific satellite designed for the comprehensive monitoring of terrestrial ecosystems. The SIFIS onboard TECIS-1 is also the first Chinese instrument specifically designed for SIF monitoring from space. In this paper, a wide spectral window ranging from 670 to 780 nm is recommended, which will enable SIF retrievals at both the far-red and red bands. In general, there is a trade-off between spectral resolution and SNR as well as the spatial-temporal resolution. In order to guarantee SIF retrieval accuracy and precision at both the far-red and red bands, it is concluded that the optimal combination is an SR of 0.1 nm and SNR of 127. With these specifications, SIF retrievals with RMS diff* values of 0.15 and 0.43 mW m −2 sr −1 nm −1 for the far-red and red band, respectively, can be obtained using the PCA retrieval algorithm. However, it is very hard to improve the SR from 0.3 to 0.1 nm. For an SR of 0.3 nm, RMS diff* can be improved to 0.17 mW m −2 sr −1 nm −1 at the far-red band and 0.47 mW m −2 sr −1 nm −1 at the red band if the SNR can also be improved to 450. In conclusion, the SIFIS onboard TECIS-1 will be the first Chinese instrument specifically designed for terrestrial vegetation SIF monitoring on a global scale.