We used TanSat version 2 Level 1B (L1B) nadir-mode Earth observation data in the retrieval process. The measurements covered the period from March 2017 to February 2018. Polarized radiance in the O2-A band with a spectral resolution of 0.044 nm was provided in the L1B data, and two micro-windows near 757 nm (758.3–759.2 nm) and 771 nm (769.6–770.3 nm) were chosen to retrieve top-of-atmosphere (TOA) SIF while avoiding the contamination from strong lines of atmospheric gas absorption. The retrieval was independent for each micro-window as shown in Fig. 1. To avoid duplication of information, we use the SIF product at 757 nm as the example in the analysis.

Filling-in on solar lines by chlorophyll fluorescence in the O2-A band can be detected in the hyperspectral measurements from TanSat. This effect on spectral radiance is different from the impact of atmospheric and surface processes, e.g., scattering and absorption. For example, scattering by aerosols and clouds does not change the relative depth of clear solar lines, unlike the SIF emission signal. We applied the differential optical absorption spectroscopy (DOAS) technique to IAPCAS/SIF algorithm for TanSat measurement (Frankenberg, 2014; Sun et al., 2018).

The TOA spectral radiance LTOAλ at wavelength λ can be represented as follows: 1LTOAλ=Itλ⋅μ0⋅ρ0λ+ρsλ⋅T↓λ⋅T↑λπ+FTOAλ, where Itλ is the incident solar irradiance at the TOA, μ0 is the cosine of the solar zenith angle (SZA), ρ0λ is atmospheric path reflectance, ρsλ is surface reflectance, and T↓λ and T↑λ are the total atmospheric transmittances along the light path in the downstream and upstream directions, respectively. FTOAλ is the SIF radiance at TOA.

The first term on the right of Eq. (1) represents the transmission process of solar radiance. In the micro-windows used in SIF retrieval, gas absorption is very weak and smooth, and hence, the atmosphere term μ0⋅ρ0λ+ρsλ⋅T↓λ⋅T↑λπ can be simplified to a low-order polynomial ∑i=0nai⋅λi that varies with λ (Joiner et al., 2013; Sun et al., 2018); this is always valid as long as the spectrum fitting range is out of sharp atmospheric absorptions. Then Eq. (1) could be represented as 2LTOAλFTOAλ,a=Itλ⋅∑i=0nai⋅λi+FTOAλ, where 〈〉 denote the convolution with the instrumental spectral response function (ISRF) from the line-by-line spectra, and the coefficient vector a determines the wavelength dependence polynomial for the atmosphere term.

To facilitate the extraction of SIF signals, the radiance is normalized to the continuum level radiance and the relative contribution of SIF to the continuum level radiance Fsrel is defined. In the micro-window, SIF was regarded as a constant signal due to its small changes. When the spectral radiance measurement was converted to logarithmic space, the forward model was expressed as 3fFsrel,b=log⁡It+Fsrel+∑i=0nbi⋅λi, where It is a normalized disk-integrated solar transmission model. The vector b consists of the polynomial coefficients bi and we used a second-order polynomial (i=0, 1, 2) in the retrieval.

Although the atmospheric gas absorption was very weak in the micro-window, the weak absorption and the far-wing effects (O2 lines) can still change spectral features, which induces errors in spectrum fitting. In other physics-based retrievals, the surface pressure data of the European Centre for Medium-Range Weather Forecasts (ECMWF) together with topographic data are usually used as the true surface pressure to simulate the atmospheric transmission in the range of the O2-A band. However, there is still a difference between the true surface pressure and the model surface pressure, so we introduced a factor here to reduce the influence of the inaccurate surface pressure. In the IAPCAS/SIF algorithm, we use the ECMWF interim surface pressure (0.75∘ × 0.75∘) to estimate O2 absorption first and then modify the absorption feature by a scale factor. The scale factor is obtained simultaneously in SIF retrieval to reduce the error induced by the uncertainty in surface pressure. As described by Yang et al. (2020), there is also a continuum feature in TanSat L1B data that needs to be considered for the high-quality fitting of the O2-A band. However, in this study, this continuum feature was not corrected, as the impact of such a smooth continuum variation in the micro-window is weak and the polynomial continuum model is capable of compensating for most of this effect.

The state vector includes the relative SIF signal Fsrel, a wavenumber shift, the scale factor for the O2 column absorption, and coefficients of the polynomial. The continuum level radiance Icont within the fitting window is calculated using the radiance outside the absorption features in the micro-window and is then used for the actual SIF signal calculation thus, F=Fsrel⋅Icont.

In the IAPCAS/SIF algorithm, we used an OEM for state vector optimization in the retrieval process. Compared to the IAPCAS XCO2 retrieval, the IAPCAS/SIF retrieval employs a state vector with fewer elements and a much simpler forward model, so there is no need to perform complex radiative transfer calculations. Considering the low complexity of SIF retrieval, the Gauss–Newton method was applied to find the optimal solution.

A systematic error remains in the raw SIF retrieval output if no bias correction is performed; similar results have been reported in GOSAT and OCO-2 SIF retrieval studies (Frankenberg et al., 2011a, b; Sun et al., 2018). This is because the SIF signal is weak (e.g., typically 1 %–2 % of the continuum level radiance), which means that even a small issue in the measurement, such as a zero-offset caused by radiometric calibration error, could induce significant bias. Unfortunately, the lack of knowledge on in-flight instrument performance makes it difficult to perform a direct systematic bias correction in the measured spectrum.

The bias was considered to be related to the continuum level radiance in the previous works. To get the relationship between the continuum level radiance and the bias, we calculated the mean bias for continuum level radiance at the interval of 5 W m-2 µm-1 sr-1 from all non-fluorescence measurements, and then a piecewise linear function fit was applied to describe the relationship between the continuum level radiance and the biases.

The non-fluorescence soundings that were used in the bias estimation were based on the dataset “sounding_landCover” in TanSat L1B data. This dataset depends on the MODIS land cover product and provides a scheme consisting of 17 land cover classifications defined by the International Geosphere-Biosphere Programme. The measurements marked as “snow and ice,” “barren,” and “sparsely vegetated” were chosen to estimate the bias. Calibrations compensated for most of the instrument degradations, but this alone was not perfect. To reduce the impact of the remaining minor discrepancies, we built the bias correction function daily to obtain bias for each sounding via interpolation of the continuum level radiance (K. Sun et al., 2017; Sun et al., 2018).

The bias curves shown in Fig. 2 differ significantly between TanSat and OCO-2. This is mostly due to the differences in instrument performance and radiometric calibration. In general, the TanSat bias curves exhibited two peaks at radiance levels of approximately 40 and 125 W m-2 µm-1 sr-1, separately, and most biases were larger than 0.015. For OCO-2, the curves dropped sharply at low radiance levels, reaching a valley at a radiance level of approximately 40 W m-2 µm-1 sr-1, and then increased slowly with the radiance level.

Only data that passed quality control were used in further applications. There were two data quality control processes for the SIF products: pre-screening and post-screening. Pre-screening focused mainly on cloud screening; only cloud-free measurements were used in SIF retrieval. A surface pressure difference (SPD), defined as 4ΔP0=Pretrieval-PECMWF, was used to evaluate cloud contamination along with a χ2 test: 5χ2=∑ysim-yobs2ynoise2, where ysim, yobs, and ynoise represent the model fitting spectrum, observation spectrum, and spectrum noise, respectively. Pretrieval is the apparent surface pressure obtained from O2-A band surface pressure retrieval, assuming a Rayleigh scattering atmosphere. PECMWF is the surface pressure data from the ECMWF interim (0.75∘ × 0.75∘) reanalysis data product (Dee et al., 2011), which is interpolated to the sounding location and corrected for elevation differences with the Shuttle Radar Topography Mission Global 30 Arc-Second Elevation digital elevation model (https://doi.org/10.5067/MEaSUREs/SRTM/SRTMGL30.002, NASA JPL, 2013). A “cloud-free” measurement was required to simultaneously satisfy an SPD of less than 20 hPa and a χ2 value of less than 80. Here, post-screening was applied to filter out “bad” retrievals; this screening process involved the following steps: (1) SIF retrievals with reduced χ2χred2 values ranging from 0.7 to 1.3 were considered “good” fitting, (2) continuum level radiance outside the range of 15–200 W m-2 µm-1 sr-1 was screened out to avoid scenes too bright or too dark, and (3) soundings with the SZA higher than 60∘ were also filtered out.

Before applied to TanSat retrievals, we tested the IAPCAS/SIF algorithm on the OCO-2 L1B data first (OCO2_L1B_Science.8r) and then compared the retrieval results with the OCO-2 L2 Lite SIF product (OCO2_Level 2_Lite_SIF.8r) retrieved by the Iterative Maximum A Posteriori-Differential Optical Absorption Spectroscopy (IMAP-DOAS) algorithm (Frankenberg, 2014). The Lite product provides the SIF value for each sounding and hence the SIF comparison could be performed on the sounding scale for each month.

Table 1 displays the relationship of OCO-2 SIF values between the IAPCAS/SIF and IMAP-DOAS in a 757 nm micro-window for each month. Overall, the two SIF products were in good agreement. The linear fitting of the two SIF products suggests that they are highly correlated, as indicated by the strong linear relationship with R2 mostly larger than 0.85 and the root mean square error (RMSE) of about 0.2 W m-2 µm-1 sr-1. Good consistency between the two SIF products implies the reliability of the IAPCAS/SIF algorithm; thus, it was further applied to TanSat SIF retrieval. However, there was still a small bias in the comparisons, which was due, most likely, to the impact of differences in the bias correction method, retrieval algorithm, and fitting window.

The comparison between TanSat and OCO-2 SIF measurements is a useful and powerful method for further verification of the IAPCAS/SIF algorithm. The reason for adopting OCO-2 data is that OCO-2 and TanSat have similar observation modes, including scanning method, transit time, spatial resolution, spectral resolution, and spectral range. The similarities mean that the SIF product from the two satellite missions can be directly compared. Directly comparing OCO-2 and TanSat SIF measurements could provide information on joint data application at the sounding scale for further studies. However, an identical sounding overlap only slightly exists because the two satellites often have different nadir tracks on the ground, which is induced by the different temporal and spatial intervals of the two satellite missions. Fortunately, the ground tracks of the two satellites were relatively close from 17 to 23 April 2017. A couple of overlapping orbits were found in the measurements obtained from Africa with the orbit number of 1733 from TanSat and 14890a from OCO-2 (Fig. 3). In the comparison, the OCO2_Level 2_Lite_SIF.8r product was used to present the SIF emission over the study area. These overlapping measurements encompassed multiple land cover types, in which the SIF varied within an acceptable time difference (< 5 min).

Overall, measurements from the two satellites indicated SIF variation with land cover type. The SIF emission over evergreen broadleaf forests was larger than that over savannas, and grasslands exhibited the lowest SIF emission in April (Fig. 3a, b). The mean SIF emission over evergreen broadleaf forests was approximately 0.9–1.1 W m-2 µm-1 sr-1, whereas those over savannas and grasslands were 0.5–0.7 W m-2 µm-1 sr-1 and less than 0.1 W m-2 µm-1 sr-1, respectively (Fig. 3c, d). Furthermore, we also found a significant difference in the SIF emission intensity over tropical savannas, which was observed by both satellites (Fig. 3c, d).

Because the footprint sizes of the two satellites are different, it is difficult to make a direct footprint-to-footprint comparison. Therefore, we made the comparison between the two satellite measurements based on a small-area average. Each small area spans a degree in latitude and continues along the track. The small-area-averaged SIF comparison is shown in Fig. 3e. The results indicate good agreement, with an R2 of 0.94 and an RMSE of 0.096 W m-2 µm-1 sr-1. Additional ground-based SIF measurement setups (Guanter et al., 2007; Liu et al., 2019; van der Tol et al., 2016; X. Yang et al., 2015; Yu et al., 2019) should allow for direct evaluation of satellite retrieval accuracy in the future.

Figure 4 shows the global SIF comparison between IAPCAS/SIF retrieved from OCO-2 and TanSat; this comparison is only performed at 1∘ × 1∘ spatial resolution. In general, the difference in SIF globally is mostly less than 0.3 W m-2 µm-1 sr-1 for all seasons, and on average, the smallest difference appears in fall. There are regional biases observed in North Africa, southern Africa, South America, and Europe in all seasons except fall. This is mainly caused by the differences in instrument performance between TanSat and OCO-2, such as the instrument spectral response and the signal-to-noise ratio. The instrument performance difference is represented by the different structural characteristics of the bias curves. The bias correction compensates for most of the bias caused by instrument performance; however, small biases could remain. Furthermore, the hundreds of kilometers of distance between the OCO-2 and TanSat footprints, for example, over different vegetation regions, will also cause some measurement discrepancies. The global distribution of the two satellites was also compared with the official OCO-2 SIF data on the global scale; the results show that the difference between the retrieved SIF maps and the official map is less than 0.2 W m-2 µm-1 sr-1, indicating that the retrieved SIF data from OCO-2 and TanSat both have good SIF characterization capabilities on a global scale. The uncertainty σ of each sounding was estimated to validate SIF reliability and is provided in the product. σ is derived from the retrieval error covariance matrix, Se=KTS0-1K-1, where K is the Jacobian matrix from the forward model fitting and S0 is the measurement error covariance matrix that is calculated from the instrument spectrum noise. In general, σ ranges from 0.1 to 0.6 W m-2 µm-1 sr-1 for both TanSat and OCO-2 measurements in the 757 nm fitting window, which is of a similar magnitude and data range as those of previous studies (Du et al., 2018; Frankenberg et al., 2014). Meanwhile, the standard error of the mean SIF in each grid σmeas was estimated to represent the gridded retrieval error and natural variability, which is calculated from TanSat SIF values with σmeas=SDn and SD=∑i=1nSIFi-SIF‾2n, where SD represents the standard deviation of the grid cell with n soundings, SIFi is the retrieved SIF values of each sounding, and SIF‾ is the mean SIF value for all measurements in the grid. As depicted in the right column of Fig. 4, the σmeas of each grid cell is much lower than the precision of a single sounding. The σmeas for South America is larger than that for any other region on the globe (Fig. 4i–l). This is similar to that of OCO-2 SIF retrieval and caused by fewer effective measurements due to the South Atlantic Anomaly (Sun et al., 2018). The difference in SIF emission values between the two satellites indicates that the synergistic use of two satellite SIF products still requires analysis of the impact of instrument differences, although the two satellite SIF products share the same spatiotemporal pattern on a global scale.

The SIF emission intensity reflects the growth status of vegetation, and hence the overall global vegetation status can be represented by global SIF maps for each season. TanSat SIF over a whole year's cycle, from March 2017 to February 2018, is represented seasonally as a 1∘ × 1∘ grid spatially. The seasonal variation in SIF emission is clear in the Northern Hemisphere, i.e., it increases from spring to summer and then decreases (Sun et al., 2018).

In general, the SIF emission varied with latitude and the vegetation-covered areas near the Equator maintained a continuous SIF emission throughout the year. Large SIF emissions in the Northern Hemisphere, above 1.5 W m-2 µm-1 sr-1, mostly from the eastern USA, southeast China, and southern Asia in summer, were due to the large areas of cropland. There was also an obvious SIF emission of 1–1.2 W m-2 µm-1 sr-1 observed over central Europe and northeastern China during the summer. In these regions, croplands and deciduous forests contribute to SIF emissions. In the Southern Hemisphere, the strongest SIF emission occurred in the Amazon, with a level of approximately 1–2 W m-2 µm-1 sr-1 in DJF (Northern Hemisphere winter), where there is an evergreen broadleaf rainforest. Africa, which is covered by evergreen broadleaf rainforests and woody savannas, had an average SIF value of 0.7–1.5 W m-2 µm-1 sr-1 during the year.

The SIF–GPP relationship over different vegetation types was also investigated by comparing the annual mean satellite SIF measurements with the FLUXCOM GPP (Jung et al., 2020; Tramontana et al., 2016) dataset in a 1∘ × 1∘ grid over the globe. The FLUXCOM GPP dataset used in the study comprises monthly global gridded flux products with remote sensing and meteorological/climate forcing (RS+METEO) setups, which are derived from mean seasonal cycles according to MODIS data and daily meteorological information (Jung et al., 2020; Tramontana et al., 2016). In the correlation analysis, the high spatial resolution (0.5∘ × 0.5∘ ) of the FLUXCOM GPP was first resampled to 1∘ × 1∘ to keep the same spatiotemporal scale of SIF and GPP data. The satellite-measured SIF is an instantaneous emission signal that varies with incident solar radiance within the day. To reduce the differences caused by the observation time and SZA at different latitudes, we applied a daily adjustment factor to convert the instantaneous SIF emission into a daily mean SIF (Du et al., 2018; Frankenberg et al., 2011b; Sun et al., 2018). The daily adjustment factor d is calculated as follows: 6d=∫t=t0-12ht=t0+12hcos⁡(SZA(t))⋅dtcos⁡(SZA(t0)), where t0 is the observation time in fractional days and SZA(t) is a function of latitude, longitude, and time for calculating the SZA of the measurements. The annually averaged SIF is calculated from the daily mean SIF. To evaluate the relationship between SIF and GPP on the periodic scale of vegetation growth status, annually averaged data were used in the regression fitting analysis.

Figure 5 shows the linear fits for six vegetation types, including needle leaf forest, evergreen broadleaf forest, shrubland, savanna, grassland, and cropland. Recent studies have shown a strong linear correlation between SIF and GPP. The TanSat SIF and the OCO-2 official SIF data were used to estimate the SIF–GPP correlation. To make a direct comparison of the relationship between SIF and GPP among various vegetation types, we used non-offset linear fitting to indicate the correlation between satellite SIF and FLUXCOM GPP. For savanna and cropland, there were strong relationships between the mean SIF and GPP with an R value above 0.84. The fitting results show that the SIF products of the two satellites have similar capabilities in characterizing GPP, especially for the evergreen broadleaf forest, savanna, and cropland, with slopes of approximately 21, 18, and 13, respectively. For shrubland and grassland, the slope of OCO-2 SIF with GPP is higher than that of TanSat and has a worse correlation. For forests, OCO-2 SIF presents a better correlation with GPP, especially in the needle leaf forest. As a whole, for the same vegetation type, the SIF–GPP correlations for the two satellites are rather similar, indicating that the two satellite SIF products have similar capabilities in characterizing GPP. This shows the strong feasibility of the comprehensive application of different satellite SIF products. For different vegetation types, the SIF–GPP correlations were significantly different, indicating the different ability of SIF to characterize GPP of different vegetation. This represents that vegetation type is a key factor in determining the SIF–GPP relationship. The markedly different fitting slopes across various biomes suggest that the application of SIF in GPP estimation needs more detailed analysis despite the evidence of the strong linear relationship between them.