E ﬀ ects of the Temporal Aggregation and Meteorological Conditions on the Parameter Robustness of OCO-2 SIF-Based and LUE-Based GPP Models for Croplands

: Global retrieval of solar-induced chlorophyll ﬂuorescence (SIF) using remote sensing by means of satellites has been developed rapidly in recent years. Exploring how SIF could improve the characterization of photosynthesis and its role in the land surface carbon cycle has gradually become a very important and active area. However, compared with other gross primary production (GPP) models, the robustness of the parameterization of the SIF model under di ﬀ erent circumstances has rarely been investigated. In this study, we examined and compared the e ﬀ ects of temporal aggregation and meteorological conditions on the stability of model parameters for the SIF model ( ε / SIF yield ), the one-leaf light-use e ﬃ ciency (SL-LUE) model ( ε max ), and the two-leaf LUE (TL-LUE) model ( ε msu and ε msh ). The three models were parameterized based on a maize–wheat rotation eddy-covariance ﬂux tower data in Yucheng, Shandong Province, China by using the Metropolis–Hasting algorithm. The results showed that the values of the ε / SIF yield and ε max were similarly robust and considerably more stable than ε msu and ε msh for all temporal aggregation levels. Under di ﬀ erent meteorological conditions, all the parameters showed a certain degree of ﬂuctuation and were most a ﬀ ected at the mid-day scale, followed by the monthly scale and ﬁnally at the daily scale. Nonetheless, the averaged coe ﬃ cient of variation ( CV ) of ε / SIF yield was relatively small (15.0%) and was obviously lower than ε max ( CV = 27.0%), ε msu ( CV = 43.2%), and ε msh ( CV = 53.1%). Furthermore, the SIF model’s performance for estimating GPP was better than that of the SL-LUE model and was comparable to that of the TL-LUE model. This study indicates that, compared with the LUE-based models, the SIF-based model without climate-dependence is a good predictor of GPP and its parameter is more likely to converge for di ﬀ erent temporal aggregation levels and under varying environmental restrictions in croplands. We suggest that more ﬂux tower data should be used for further validation of parameter convergence in other vegetation types. models for each timescale, and (iii) evaluate the estimation performances of the SIF-based and LUE-based GPP models from mid-day to monthly timescales using an independent dataset. This study provides the ﬁrst assessment of the e ﬀ ects of viewing the zenith angle in OCO-2 Glint mode on the magnitude of SIF values and the GPP–SIF relationship, and for the ﬁrst time compares and addresses the inﬂuence of multi-aspect on the SIF-based and LUE-based models (both one-leaf (SL)-LUE and two-leaf (TL)-LUE models). We aim at providing a for the CN-YuC site over the 2015 growth period of summer maize. There are only six data points on Glint mode and seven data points on Nadir mode for both satellite overpassing and tower observing at the same time. The missing observations from 17 August 2015 to 1 September 2015 were due to an equipment failure.

better understanding of the different capabilities or limitations of the SIF-based and LUE-based models for the estimation of GPP.

Experimental Site Description
The experiments were conducted at Yucheng Comprehensive Ecological Station (CN-YuC; 36.95 • N, 116.63 • E), which is located in the southwest of Yucheng County, Shandong Province, with a mean altitude of 28 m. This area is the hinterland of Huang-Huai-Hai Plain, and the landform type is the alluvial plain of the Yellow River. The soil is an alluvial deposit of the Yellow River and mainly consists of eutric cambisols and solonchaks. The surface soil is rich in sandy loam. CN-YuC is an agricultural experimental station for maize-wheat rotation. The growing period of the wheat begins in mid-November and continues until the beginning of June in the following year, and maize is sowed immediately after harvesting the winter wheat and reaped in the middle of October. The average annual rainfall in this area is 590 mm, about 70% of which falls between June and August, the growing period of summer maize.

Flux Tower Data Processing
At the site described above, an EC system was installed on one of the towers (40.0167 • N, 116.3833 • E) to measure the carbon dioxide (CO 2 ) exchange between the land surface and the atmosphere from September 2014 to April 2017. The EC system comprises a three-dimensional (3D) sonic anemometer (CSAT3, Campbell Scientific, USA) that measured 3D wind velocity, two temperature and relative humidity probes (HMP155A-L15) that collected the temperature and relative humidity, and a closed-path gas analyzer (Models 911-0010, Los Gatos, USA) for monitoring of the H 2 O/CO 2 /CH 4 density, etc. The installation height of the EC sensor was 21.6 m. The EC measurements were sampled at a frequency of 10 Hertz, and the turbulence data were stored using data loggers (CR3000, Campbell Scientific, USA) and processed every 30 minutes. A mini weather station was also installed beside the tower to record data on the air temperature, precipitation, radiation, wind speed/direction, and relative humidity every second.
The tower carbon flux data from January 2015 to December 2016 (a total of 2 years) were used in this study. EddyPro software (https://www.licor.com/env/products/eddy_covariance/eddypro.html) was used to correct the raw EC data conventionally, including coordinate rotation, Webb-Pearman-Leuning (WPL) correction, and frequency response calibration, etc. In addition, the half-hourly flux data were u* (friction wind speed) filtered and storage calculated by the u* threshold, gap-filled, and flux partitioned using the REddyProcWeb online processing tool (https://www.bgc-jena.mpg.de/bgi/ index.php/Services/REddyProcWeb). The ReddyProc tool used the nighttime net ecosystem exchange (NEE night ) as nighttime respiration, and the model of NEE night and air temperature at nighttime was determined using nonlinear optimization. After that, daytime respiration (R d ) was estimated using the daytime temperature. Finally, GPP was calculated as the difference between the daytime NEE and R d . The GPP in the output data files derived from the ReddyProc tool included the original and gap-filled results. The percentage of high quality gap-filled GPP data in the calibrated and validated years was 44% and 54%, respectively. Therefore, the original data and the most reliable 44% gap-filled GPP data in the calibrated year were used for the parameter estimations of LUE-based and SIF-based models. All the gap-filled GPP data in the validated year (including 54% of the most reliable data) were used for model validation in this study.

Spectral Measurements and Processing
An automated multi-angle spectrometer system named AMSPEC II [45] was installed on the same EC flux tower at a height of 32 m during the growing period of summer maize. It was used to measure continuous multi-angle remote sensing observations of top-of-canopy radiance and reflectance. The AMSPEC II comprises tower observation and a computer control modules. The tower part consists of a spectrometer (Unispec-DC, PP System, Amesbury, MA, USA), a pan-tilt unit (D-46, FLIR Commercial Systems, Inc), and a high-resolution digital camera (NetCam SC SD500BN). The Unispec-DC features 256 consecutive bands ranging from 350 to 1200 nm with a spectral resolution of 3 nm and a full-width half maximum (FWHM) spectral response of 10 nm. To enable sampling under various sky conditions, the Unispec-DC is equipped with two channels for measuring solar irradiance (upward probe) and vegetation radiance (downward probe) synchronously with a frequency of 5 s all day. Its instantaneous field of view (IFOV) is 20 • and it can collect the canopy spectral information around the tower with a viewing azimuth range of 0 to 330 • and zenith angle of 43 to 78 • using the pan-tilt unit. A complete horizontal and vertical rotation of the pan-tilt unit takes 15 minutes with a 10 • angular spacing. More detailed information about this system can be found in [45].
The spectral data during the growing period of summer maize (from June to October 2015) collected above were used in this study. The missing observations from 17 August 2015 to 1 September 2015 were due to an instrument failure. The discrepancies in light sensitivity were corrected using a cross-calibration method using the reflectance of a standardized reference whiteboard [42] and dark current (dc) was rectified by the relationship between the dc measured when blocking off the light from both probe channels and the sensor's temperature measured by the internal thermometer of Unispec-DC [45]. In addition, by comparing the reflected spectral curves, it was found that the anomaly values originated from the areas of non-vegetated areas near the tower and distant background observations. They were eliminated by removing the measurements in a range of the viewing azimuth (174-226 • ) and viewing zenith (>64 • ). Finally, multi-angle measurements included complete information on vegetation characteristics from different observation directions, which could cause directional impacts on the intrinsic spectrum compared with Nadir observations [45]. Therefore, the RossThick-LiSparse (RTLS) bidirectional reflectance distribution function (BRDF) model was further used to rectify vegetation indices to normalize the data into uniform sun-sensor geometry and minimize the directional effects. The BRDF model, which comprises RossThick volumetric and LiSparse geometric kernels, depicts the reflectance as the linear superimposition of multiple basic BRDF shapes [46]. Its specific formulation is given in [47].

SIF and Vegetation Index Retrieval from Ground Data
The three Fraunhofer line discrimination (3FLD) algorithm [48] was used to retrieve far-red SIF for the O 2 -A band near 760 nm in this study. Wand et al. [49] suggests that the SIF can be accurately extracted in the O 2 -A band near 760 nm rather than the O 2 -B band near 687 nm when the spectral resolution is 3.3 nm. Compared with the FLD [50] and the improved FLD (iFLD) algorithm [51], 3FLD can get more accurate SIF values [52] and is more robust than the iFLD, which appears to be highly sensitive to noise [53,54]. In this approach, three spectral channels are required for each absorption line, and the changes of fluorescence and reflectance in and out of the absorption line within a very narrow band are hypothesized to be linear. The radiance at a single outer channel is expressed as the weighted mean calculated from the two sides of the absorption valley (at the left and right wavelengths close to the absorption band). The weight factors (w) of the two outer channels are as follows [48]: where λ is the wavelength, and the subscripts, left and right, represent the shorter and longer wavebands close to the Fraunhofer lines, respectively. The subscript, in, indicates the wavelength of the absorption band. The SIF can then be determined by [48]: where I is the solar irradiance, and L is the canopy radiance. The 760 nm was used as the absorption band and then the left and right wavelengths were looped through to determine the optimal shorter and longer channels. Finally, 757 and 772 nm were taken as the left and right wavelengths, respectively, which are close to those in [55]. The normalized difference vegetation index (NDVI) and Vogelmann red edge index (VOG) were used in this study to compare SIF values over the growing stages of summer maize in 2015. The NDVI is retrieved from the reflectance difference of red and near-infrared bands and is calculated as [56]: The VOG can be derived based on the simple reflectance ratio of the red edge portion (680-750 nm) [57]. The equation is: where R xxx in Equations (3) and (4) denotes the reflectance at wavelength xxx in nm.

OCO-2 SIF Data and Processing
OCO-2 is a sun-synchronous satellite that has a 16-day repeat cycle, and its local overpass time is at 13:30. The OCO-2 SIF data are retrieved from three grating spectrometers using the O 2 -A band (FWHM of around 0.042 nm) based on the Fraunhofer line infilling at 757 and 771 nm [8], similar to the methods employed for GOSAT SIF retrievals [7]. Each spectrometer measures eight independent cross-track spectra, with each spectra having a spatial resolution of approximately 1.29 × 2.25 km 2 at Nadir, which together cover a maximum range~10 km wide full swath [11]. In the repeat cycles of measurements, OCO-2 switches between Nadir and Glint observation modes, and Target viewing mode is opened when the satellite overpass the ground validation sites, acquiring thousands of observations with different viewing zenith angles (VZA). The Nadir mode follows the same ground track to provide a relatively reliable dataset for the detection of variations over time, while certain varying east-west offsets of the ground tracks exist in the Glint mode's repeat cycles. It was pointed out in [11] that, over land, Glint measurements are likely to underestimate SIF values compared with those by Nadir, given that a more shaded fraction of the canopy may be measured (denoted as a vegetation dark-spot). Therefore, compared with the Glint mode, the Nadir mode's SIF measurements generally provide a more consistent dataset over land, and the effects of viewing geometries of the Glint mode should be taken into consideration when combining them together [1,8,11].
The OCO-2 v8 product (v.B8100r) that stores the daily lite files in netcdf (network common data form) was used in this study. The SIF Lite files only include the soundings that passing the initial quality standard thresholds and contain a significant SIF calibration program which uses non-fluorescent surfaces, including oceans and deserts [7,8]. Unless otherwise specified, the mean values of SIF at 757 nm and 771 nm were used in this study, and the SIF value at 771 nm was multiplied by a factor of 1.5. Sun et al. [11] suggests that the fundamental for averaging the two wavebands is to reduce the retrieval error (by about 1.4 times) through doubling the number of soundings and to improve the robustness of the data analysis, considering the retrievals of the two micro-windows are influenced by different uncertainties.
Finally, the averaged OCO-2 SIF data on Glint mode were used to examine the influence of different observation geometry on the SIF values and the relationship between SIF and GPP, and then the data with those on Nadir mode were combined in the SIF-based model for comparison with the LUE-based models. The land cover of the Huang-Huai-Hai Plain where the flux tower is located is known to be one of the three largest croplands in China. Therefore, the SIF data retrieval radius from the flux tower was broadened to 150 km [36] to increase the number of available soundings over the study period. Additionally, only those SIF data with a cropland proportion greater than 80% were used to establish the GPP-SIF function. For the comparison of the SIF model and the LUE-based models at different temporal aggregation levels, the daily correction factor provided in the SIF Lite files was applied to convert the mid-day SIF to daily SIF, and then to aggregate to a monthly average.

Leaf Area Index Data
The Moderate Resolution Imaging Spectroradiometer (MODIS) MOD15A2 leaf area index (LAI) product was used to drive the LUE models. This dataset is an 8-day composite with a 1 km spatial resolution and was downloaded from the website (https://ladsweb.modaps.eosdis.nasa.gov/search/ order/4/MOD15A2H/). MOD15A2 LAI data from a 2-year period-from 1 January 2015 to 31 December 2016-were used. The projection of these data is sinusoidal, and the MODIS Reprojection Tools (MRT) was used to reproject them into a Universal Transverse Mercator/ World Geodetic System 1984 (UTM/WGS 84) projection. The resulting LAI time series was further smoothed using the locally adjusted cubic-spline capping (LACC) method [58] to remove unrealistically short-term abrupt changes in the LAI caused by contamination of the measurements by clouds.

Analysis
We first examined the effects of VZA at Glint mode on the SIF values and their relationship with tower GPP. We further compared the consistency of Glint and Nadir SIF observations with the tower SIF, which was retrieved from the spectrum measurements during the growing period of summer maize on a daily timescale. Then, we optimized the parameters of the SIF model, the SL-LUE model, and the TL-LUE model with different temporal aggregation levels to examine the stability of their key parameters. SL-LUE was developed based on the concept of radiation transformation efficiency [59] and can be defined as: where ε max means the maximum LUE (gC MJ −1 ), depending on different plant functional types, and ε max × APAR is the potential GPP. g(T a ) and f (VPD) are efficiencies and range from 0 to 1. They represent the adjusting scalars of the minimum air temperature (T a ) and vapor pressure deficit (VPD), which are used to constrain ε max to the real LUE value. They can be expressed as: where VPD max , VPD min , T max , and T min are biome-dependent parameters [11,27]. SIF can be likewise calculated as: where SIF yield is the LUE for SIF, and f esc denotes the proportion of SIF photons that escapes from the canopy in the viewing angle of the satellite sensor [19]. By combining Equations (5) and (8), a linear GPP-SIF model can be theoretically expressed as: where f esc ≈ 1 can be set when far-red SIF data are used from cropland and grassland [54] because these land types have a lower leaf absorptance in the far-red waveband, a higher LAI, and a simpler canopy structure compared with other ecosystems [19,60]. The TL-LUE model divides GPP into two components, sunlit and shaded leaves, by combining the algorithm of the SL-LUE model and the new generation of the dynamic land model (DLM) [32]: where ε msu and ε msh represent the maximum LUE of sunlit and shaded leaves, respectively. APAR su and APAR sh denote the PAR absorbed by sunlit and shaded leaves. They are calculated as: where α is the canopy albedo related to a given vegetation type and was set to 0.23 for cropland in this study [11]; PAR dif and PAR dir are the diffuse and direct components of incoming PAR, respectively. PAR dif,u is the diffuse PAR under the canopy and was calculated according to [61], (PAR dif − PAR dif,u )/LAI, which represents the diffuse PAR per unit leaf area within the canopy; C quantifies the contribution of multiple scattering of the total PAR to the diffuse irradiance per unit leaf area within the canopy; β is the mean leaf-sun angle and was set at 60 • for a canopy with a spherical leaf-angle distribution [61]; and θ is the solar zenith angle. More detailed information about the SL-LUE model and the TL-LUE model is in [5]. LAI su and LAI sh are the LAI of sunlit and shaded leaves. They are computed as [28,61]: where θ is the solar zenith angle; LAI is the leaf area index; Ω represents the vegetation clumping index according to different vegetation types and was set to 0.9 for cropland in this study [62].
The key parameters of the three models (ε/SIF yield , ε max , ε msu , and ε msh ) were optimized by applying a Bayesian approach that combines the Bayesian theory with the Markov chain Monte Carlo (MCMC) estimator using the 2015 training dataset.
Additionally, to evaluate the extent to which the model is affected by the integrated meteorological conditions independent of temporal aggregation, we calculated the meteorological condition index (ECI) by combining APAR, air temperature, and VPD [3]. We first took the normalized transformation of the three variables based on the maximum-minimum observations throughout the season. A minimum that accounted for 95% of the minimum observation was used for each variable to get a positive transformed value of the observed minimum. Taking APAR as an example, the scaled APAR at the time that OCO-2 passes over can be expressed as follows: where APAR denotes the APAR observations when OCO-2 overpasses from the mid-day timescale to the monthly timescale (corresponding to the superscript "i"), and APAR min and APAR max are the Remote Sens. 2019, 11, 1328 9 of 27 minimum and maximum APAR acquired during the transit of OCO-2 throughout the season's different temporal aggregation levels, respectively. In [3], it is suggested that whole canopies are prone to experiencing exposure to excess light when the ECI is greater than 0.8 compared with when the ECI is lower. Therefore, we used 0.8 as a threshold value at which the ECI values were fitted to these models separately. Finally, GPP estimations derived from the 2016 testing dataset were used to validate the SIF-based model with that of the LUE-based models for mid-day, daily, and monthly timescales, respectively.

Accuracy Assessment of Models
The fluctuations in the parameters were quantified using the coefficient of variation (CV) [63]. For example, the CV of ε max can be defined as: The capability of different model simulations was evaluated through statistical analyses at different temporal aggregation levels for each estimation-observation pair, for which the degree of mismatch was assessed by the coefficient of determination (R 2 ), bias, the root-mean-square error (RMSE), and the relative/normalized RMSE (RRMSE) [64,65]: where the subscripts, sim and obs, represent the simulations and observations of GPP, and the subscripts, obs max and obs min , mean the maximum and minimum GPP observations, respectively.

Effects of Viewing Zenith Angle in OCO-2 Glint Mode on SIF Observations
We intended to combine SIF values from Glint and Nadir observation modes to increase the number of available SIF observations, but the SIF retrievals on Glint mode were measured at different VZAs over time, which may affect the magnitude of SIF values and the relationship between SIF and GPP. Consequently, we first extracted the mid-day SIF data in Glint mode from a circular region with a radius of 150 km centering on the flux tower for the period from January 2015 to December 2016 (Table 1, sorted by ascending VZAs). The mid-day SIF averages of all soundings without VZA restriction and those with varying spacings of VZAs were further compared to explore how the VZA affected the SIF values, as well as the relationship between SIF and GPP ( Figure 1). The VZA was separated into three intervals [1] (VZA ≤ 20 • ; 20 • < VZA ≤ 40 • ; and VZA > 40 • ) and these three intervals accounted for 27.1%, 36.0%, and 36.9% of the soundings, respectively. The sensitivity analysis showed that differences of the SIF values only existed in the threshold value, which had few soundings (1 and 8), resulting in large uncertainties (bold in Table 1, green oval in Figure 1a). Accordingly, the differences were negligible between the averaged SIF retrievals with and without VZA restrictions ( Figure 1a). In addition, we also found that the viewing geometries in Glint mode varied with seasons.   The consistency of tower GPP with the OCO-2 SIF on Glint and Nadir modes, the tower derived SIF and vegetation index, retrieved from the spectral measurements in the 2015 growing period of summer maize at the CN-YuC site, was further examined (Figure 2a). Maize photosynthesis began in the middle of June, with GPP rising rapidly, and ended in mid-October, with GPP close to zero The consistency of tower GPP with the OCO-2 SIF on Glint and Nadir modes, the tower derived SIF and vegetation index, retrieved from the spectral measurements in the 2015 growing period of summer maize at the CN-YuC site, was further examined (Figure 2a). Maize photosynthesis began in the middle of June, with GPP rising rapidly, and ended in mid-October, with GPP close to zero (Figure 2a). Overall, the discontinuous OCO-2 SIF, tower derived SIF, NDVI, and VOG can reasonably capture seasonally photosynthetic dynamics. They all first increased and then decreased throughout the growing season of summer maize, consistent with the tower calculation of GPP. Compared with NDVI and VOG, the tower SIF especially captured better fluctuation details for the early ("green-up"), elongation, and later (senescence) phases (Figure 2a, Orange dotted box). In addition, Figure 2b further shows the relationship of the OCO-2 SIF values obtained from Glint and Nadir modes and the tower derived SIF. Compared with SIF glint , SIF nadir tended to overestimate the field SIF, with the higher slope of 1.21. However, both SIF nadir and SIF glint showed a strong linear relationship with tower derived SIF. The R 2 values were consistently higher than 0.70. These analyses suggest again that it may be reasonable to combine data from Glint and Nadir observation modes to increase the number of available observations for further comparison of the GPP-SIF and GPP-LUE models.

Comparison of Parameter Stability of the SIF and LUE Models across Multiple Temporal Aggregation Levels
We optimized the key parameters ( yield ε SIF , max ε , msu ε , and msh ε ) of the SIF model, SL-LUE model, and TL-LUE model on mid-day, daily, and monthly timescales, respectively, to explore the stability of these parameters ( Figure 3, Table 2). In general, the goodness of fit in these three models was better on the daily and monthly timescales than on the mid-day timescale, which is consistent with the results reported by [37] and [1]. Across all temporal aggregation levels, the TL-LUE model was better than the SIF model and the SL-LUE model at capturing and explaining the seasonal fluctuations of GPP. The corresponding R 2 were 0.70, 0.90, and 0.93 for the mid-day, daily, and monthly timescales, respectively, slightly higher than those of the SIF model by 4.3%, 7.8%, and 4.3%, and much higher than those of the SL-LUE model by 27.1%, 10%, and 14.0%. However, it is noteworthy that the posterior estimations of yield ε SIF in the SIF model and max ε in the SL-LUE model was relatively convergent across all temporal aggregation levels ( Table 2). The CV of yield ε SIF and max ε were 6.1% and 4.1%, which were on average 13.5% (±0.97%) and 34.3% (±1.28%) lower than those of msu ε and msh ε . These analyses indicate the existence of both a robust GPP-SIF linear relationship and a good ability to capture seasonal variation in GPP across multiple temporal aggregation levels in the SIF-based model, compared with LUE-based models.

Comparison of Parameter Stability of the SIF and LUE Models across Multiple Temporal Aggregation Levels
We optimized the key parameters (ε/SIF yield , ε max , ε msu , and ε msh ) of the SIF model, SL-LUE model, and TL-LUE model on mid-day, daily, and monthly timescales, respectively, to explore the stability of these parameters ( Figure 3, Table 2). In general, the goodness of fit in these three models was better on the daily and monthly timescales than on the mid-day timescale, which is consistent with the results reported by [37] and [1]. Across all temporal aggregation levels, the TL-LUE model was better than the SIF model and the SL-LUE model at capturing and explaining the seasonal fluctuations of GPP. The corresponding R 2 were 0.70, 0.90, and 0.93 for the mid-day, daily, and monthly timescales, respectively, slightly higher than those of the SIF model by 4.3%, 7.8%, and 4.3%, and much higher than those of the SL-LUE model by 27.1%, 10%, and 14.0%. However, it is noteworthy that the posterior estimations of ε/SIF yield in the SIF model and ε max in the SL-LUE model was relatively convergent across all temporal aggregation levels ( Table 2). The CV of ε/SIF yield and ε max were 6.1% and 4.1%, which were on average 13.5% (±0.97%) and 34.3% (±1.28%) lower than those of ε msu and ε msh . These analyses indicate the existence of both a robust GPP-SIF linear relationship and a good ability to capture seasonal variation in GPP across multiple temporal aggregation levels in the SIF-based model, compared with LUE-based models.
in the SL-LUE model, ε msu (gC MJ −1 ) and ε msh (gC MJ −1 ) in the TL-LUE model, and the coefficient of variation (CV, equal to 100% × standard deviation divided by the mean) of these optimizing parameters from mid-day to monthly timescales in 2015. All correlations were statistically significant (p < 0.001).

Comparison of Parameter Sensitivity of the SIF and LUE Models under Multiple Meteorological Conditions
The sensitivity of environmental factors in the SIF and LUE models was further independently analyzed at mid-day, daily, and monthly timescales. The ECI well summarized the information contained in the three environmental variables (APAR, air temperature, VPD) ( Figure 4) and provided an objective and simple criterion to describe the extent of meteorological conditions experienced by the vegetation and photosynthetic devices. Across all temporal aggregations, we found that ECIs higher than 0.8 occurred in the later growth phase of wheat, the early growth stage of maize, and over the whole growth phase of summer maize from early July to early October (Figure 4). The high ECI values of wheat were mainly due to high air temperature and VPD, with high VPD occurring at the beginning of the growing phase of summer maize. This might be due to the lack of sprinkler irrigation during this period with high temperature, leading to higher VPD values, because the irrigation in the CN-YuC site is mainly used during the growth period of wheat. The high ECI values of the maize were mostly due to exposure to an environment with high light and high air temperature. This could be explained by the precipitation being concentrated between June and August, thus keeping sufficient water vapor content in the air. Therefore, the corresponding VPD values were lower even though the temperature was high during this period.   The whole canopies are prone to experiencing exposure to excess light when the ECI is greater than 0.8 compared with when the ECI is lower. Figure 5 and Table 3 further show the fluctuations of parameters in the SIF and LUE models under a range of different meteorological conditions using 0.8 as a threshold value of ECI values to fit separately. Overall, the relationship remained linear without significant nonlinearity, though there is one point at which large ECI values deviated from the linear relationship on the mid-day timescale (the left panel of Figure 5a,d), which agrees with the results reported by [3]. However, all curves showed a slight change in the direction of their slopes with different values of air temperature, APAR, and VPD at individual timescales. For all three models, we noted that the posterior estimations of their parameters had the smallest CV values on the daily timescale, while larger fluctuations occurred on both the mid-day and monthly timescales. A detailed comparison is shown in Table 3. The values of ε/SIF yield were relatively constant, with CV values ranging from 5.7% at the daily timescale to 22.5% at the monthly timescale, about one-half of the ε max CVs and one-quarter of the ε msu and ε msh CVs. These results thus enhance the confidence of using SIF to simulate ecosystem-scale GPP under varying meteorological conditions.

Validation of LUE-Based and SIF-Based Models
The estimation performances of the LUE models and the linear SIF model were finally evaluated using the testing dataset from the year 2016 at the CN-YuC site. Maize photosynthesis started around mid-June with a rapid rise in GPP and ended in mid-October with GPP approaching zero, while wheat photosynthesis started around late February after the overwintering period and ended in mid-June. In general, GPP SL-LUE , GPP TL-LUE , and GPP SIF captured the seasonal variations and magnitude of tower GPP well, except for some underestimation for the growth stage of maize on the mid-day timescale (Figure 6a). By contrast, the SIF model and the TL-LUE model could better describe the trajectory of the whole growing period of summer maize and winter wheat, and especially better described the fluctuation details for the early ("green-up") and late (senescence) phases compared with SL-LUE (Figure 6a-c).
As a result, the SIF model and TL-LUE model had higher values of R 2 and lower values of RMSE than the SL-LUE model across all temporal aggregation levels ( Figure 6; Table 4), which is consistent with the fitted coefficient of determination using the training dataset in Table 2. The averaged changing trajectory of GPP explained by the SIF model and TL-LUE model was 77% and 83%, respectively. The averaged R 2 values were better than that of the SL-LUE model by 15.5% and 23.9%, and the corresponding average RRMSE values decreased by 2.9% and 2.9%, respectively (Table 4). Although the averaged biases of the SL-LUE model were lower than the biases of the SIF and TL-LUE models, its fluctuations in bias values were much greater. The small biases of the SL-LUE model might be due to bias items with opposite signs that cancel each other. Overall, the model performance in predicting GPP was ranked in three tiers as: TL-LUE > SIF model > SL-LUE. Moreover, the cross-validation and prediction results show that the SIF model and the TL-LUE model both have good stability and powerful prediction ability. These results indicate that the performance of the SIF models was comparable to the LUE models and actually better than the SL-LUE model, even though the SIF models were completely based on SIF and did not contain any ancillary data (e.g., temperature, radiation, VPD).

Effects of Viewing Zenith Angle in OCO-2 Glint Mode
The robustness of the GPP-SIF relationships is affected by the quality of SIF retrievals, the accuracy of the carbon fluxes, as well as the homogeneity of the studied ecosystems. Because of OCO-2's high discrete coverage, the SIF data in this study were obtained within a radius of 150 km centered at the flux tower to increase the number of soundings. Although only the SIF data with a cropland fraction greater than 80% were used to establish the SIF-GPP function (Table 1), this could also cause a footprint mismatch between the OCO-2 SIF and tower observations to some extent.
On the other hand, Sun et al. [11] has suggested that the effects of VZAs should be considered when using OCO-2 Glint or Target modes. We found that there is little difference between SIF values with and without VZA restriction except for two threshold values (Figure 1a), while the slope of the GPP-SIF relationship with VZA ranging between 20° and 40° exhibited slightly higher values than those with other VZAs (Figure 1b). The circumstances are not exactly the same as the directional effect on the SIF emission in Target mode that was reported by [1]. Li et al. [1] showed that the

Effects of Viewing Zenith Angle in OCO-2 Glint Mode
The robustness of the GPP-SIF relationships is affected by the quality of SIF retrievals, the accuracy of the carbon fluxes, as well as the homogeneity of the studied ecosystems. Because of OCO-2's high discrete coverage, the SIF data in this study were obtained within a radius of 150 km centered at the flux tower to increase the number of soundings. Although only the SIF data with a cropland fraction greater than 80% were used to establish the SIF-GPP function (Table 1), this could also cause a footprint mismatch between the OCO-2 SIF and tower observations to some extent.
On the other hand, Sun et al. [11] has suggested that the effects of VZAs should be considered when using OCO-2 Glint or Target modes. We found that there is little difference between SIF values with and without VZA restriction except for two threshold values (Figure 1a), while the slope of the GPP-SIF relationship with VZA ranging between 20 • and 40 • exhibited slightly higher values than those with other VZAs (Figure 1b). The circumstances are not exactly the same as the directional effect on the SIF emission in Target mode that was reported by [1]. Li et al. [1] showed that the averaged SIF values and GPP-SIF relationship were almost unaffected when VZA was less than 40 • , while the averaged SIF with VZA greater than 40 • exhibited slightly higher values than those with all VZAs and the resulting GPP-SIF relationships were slightly different from those with smaller VZAs. This might be due to the VZA changes in different ways between the Target mode and Glint mode. In the Target mode, a great amount of measurements at different VZA values was acquired when the satellite focused on the ground sites during the overpass time. However, the viewing geometry of the Glint mode changed as the position of the land dark-spot varies over the season from east to west. That is, the average SIF with 20 • < VZA ≤ 40 • occurred in the growing season of winter wheat, while the SIF with 0 • < VZA ≤ 20 • appeared at the ripening stage of winter wheat and the early stage of summer maize, and the SIF with VZA > 40 • appeared at the seedling stage of winter wheat. The corresponding SIF values with VZA ≤ 40 • exhibited slightly higher values compared with those VZA > 40 • (Figure 1a), and consequently, the GPP-SIF function had certain deviations with the SIF soundings with high VZA values (Figure 1b). The slope of the GPP-SIF is inconsistent between VZA ≤ 20 • and 20 • < VZA ≤ 40 • , which had similar SIF values, which may be mainly because of the different cropland types (C3 winter wheat-fix and reduce inorganic CO 2 into organic compounds using only the C3 pathway in photosynthesis and C4 summer maize) in this study site. Therefore, the difference in the slopes of the GPP and SIF functions in this study may partly be attributable to the combining of the SIF Glint and Nadir mode observations and cropland types. There is still much to learn, and further validations with more flux sites are still needed to address the specific effects of VZAs in Glint mode on SIF values and on the relationship between SIF and GPP at different spatial scales and other ecosystems, as well as the mechanism between them.

Temporal Scaling Effect on the SIF-Based and LUE-Based Models
There was no evidence of obvious nonlinearity or changes in the slope (ε/SIF yield ) direction of the SIF-based model across the mid-day to monthly timescales ( Figure 3; Table 2), which is consistent with previous results [13,37,66]. Guanter et al. [13] points out that the responses of GPP to light at the ecosystem-scale display low saturation levels when considering the mid-day (half-hourly) data and become further linearized with increasing spatial or temporal aggregation. Similar results were demonstrated in [37], and the GPP-SIF relationship remained consistent from mid-day to monthly timescales for both the maize and landscape ecosystem ( Table 5). The linear correlation between GPP and SIF tends to converge across different timescales and may primarily depend on the fact that SIF is only emitted from photosystems and is closely linked to the fraction of PAR absorbed by the chlorophyll in all leaves of the canopy ( f PAR chl ) [38,67]. Zhang et al. [38] derived an estimation of the f PAR chl , which defined by SIF/cos(SZA) from 127 flux tower sites, and found that the light use efficiency (ε) showed a spatial-temporal convergence using chlorophyll-absorbed light (PAR chl ) to fix carbon dioxide. Moreover, both theoretical and experimental investigations have suggested that the two terms (ε and SIF yield ) in the SIF model covary and the ratio of one to the other tends to be constant under high light intensities [67,68]. In this case, it is possible to conserve the GPP-SIF relationship across space and time. By comparison, the values of the ε max in the SL-LUE model were similarly robust as ε/SIF yield and considerably more stable than ε msu and ε msh in the TL-LUE for all temporal aggregation levels. As for the SL-LUE model, at the site scale, the photoresponse of an unstressed canopy is generally more linear for the variation in light absorption, along with canopy depth [69], and the slope of this photosynthesis-APAR relationship is the ε max . The ε max value at the satellite overpass time (e.g., mid-day) is close to that of the daily average [70,71], and the relative similarity between the mid-day and daily ε max values also appears on the annual scale. As for the TL-LUE model, two possibilities exist for the large fluctuations of ε msu and ε msh . First, the diffuse and direct radiation were partitioned using the exponential model with default parameters [72], which would result in uncertainty in the estimates of sunlit and shaded GPP. Additionally, it should be noted that any deviation of the parameter may also be related to biases in the GPP simulations [11]. The second possibility to consider is that no unique solution for ε msu and ε msh occurs at different spatial or temporal scales. The boundary conditions of ε msu and ε msh were set according to their observations and previous research results to separate their contribution, but lacked the specific constraint functions between them for the current study. Although previous studies (e.g., [5,28,31]) have shown that a linearly relationship exists between either ε max and ε msu or ε max and ε msh based on a number of statistical results, but is not clear yet, thus there is no unified equation of them in LUE models so far. These analyses suggest that the existence of both robust parameters and a good ability to capture seasonal variation in GPP may be in the SIF model, compared with the SL-LUE model, which has a robust argument, but poorer performance, and the TL-LUE model, which has unstable arguments, but better performance.

Environmental Restrictions on the SIF-Based and LUE-Based Models
The parameters of these three models all showed fluctuations to some extent under different ECI values of which contained the information of the air temperature, APAR, and VPD. However, the CV values of ε/SIF yield in the SIF model were relatively small under different ambient conditions in each independent temporal aggregation compared with those values in the SL-LUE and TL-LUE models ( Figure 5; Table 3). It was also found by [3] that the GPP-SIF relationship in grassland tended to remain linear at the canopy scale with different meteorological conditions. Physiological stress caused by excessive light is known to affect the photochemical yield and fluorescence [73,74]. For the SIF model, the values of ε/SIF yield showed the greatest change with a CV of 16.7% and 22.5% at the mid-day and monthly timescales, which is possibly attributable to the dramatic changes in the slope as the ECI values change (Figure 7a,c). Moreover, at the mid-day and daily timescales, the linear relationship between ε and SIF yield changed from a strong correlation (average R 2 value of 0.70) to a weak correlation (average R 2 value of 0.30) as the ECI values increased (Figure 7a,b). Therefore, the weakening of covariation between the ε and SIF yield is likely the cause of the small fluctuations in the slope in the SIF model. Furthermore, fluorescence, photochemical quenching (PQ), and non-photochemical quenching (NPQ) are mutually exclusive and competing pathways. Changes in the efficiency of one affects the efficiency of the other two pathways [75]. The stress-induced closing down of photochemical traps in photosystem-II increases the fluorescence yield as the lifespan of an excited electron lengthens, while stress-induced opening up of extra NPQ pathways causes the fluorescence to decrease [76]. Nevertheless, both the shutdown of photosynthetic reaction centers and the opening of NPQ pathways cause the photochemical yield to drop. The influences of an increasing NPQ on ε and SIF yield are not necessarily proportional [3]. That is, the nonlinear effects of NPQ on ε and SIF yield are complex, which may also be a reason for the distinct response of these models to the different meteorological conditions. excited electron lengthens, while stress-induced opening up of extra NPQ pathways causes the fluorescence to decrease [76]. Nevertheless, both the shutdown of photosynthetic reaction centers and the opening of NPQ pathways cause the photochemical yield to drop. The influences of an increasing NPQ on ε and yield SIF are not necessarily proportional [3]. That is, the nonlinear effects of NPQ on ε and yield SIF are complex, which may also be a reason for the distinct response of these models to the different meteorological conditions. Additionally, sunlit leaves receive both direct and diffuse radiation and should have higher temperatures than shaded leaves, resulting in greater temperature gradients between the surrounding air and sunlit leaves. A former study has suggested that the different temperatures of sunlit and shaded leaves should be considered in the parameter optimization procedure in the TL-LUE model [31]. Moreover, it is also noted that the differences in leaf temperature can also cause disparities in the VPD of sunlit and shaded leaves. In the LUE-based models, the application of the same VPD and air temperature scalars to the whole canopy may also be a source of uncertainty in the optimized parameters and estimated GPP [30]. Therefore, although we partitioned the efficiency ( ε ) term of the LUE-based models into fixed parts ( max ε , msu ε , and msh ε ) that depict the optimal efficiency and variable components that represent the effects of light, temperature, and water stress (e.g., VPD), the sensitivity of the LUE models to the ECI may be the main cause of the larger fluctuations in the parameter values.

Estimation Performances of the SIF-Based and LUE-Based Models
The performances of the three GPP models were highly consistent in their predictions of the magnitudes and seasonal dynamics of GPP, as validated using GPP observations ( Figure 6). The performance of the SIF model was better than that of the SL-LUE model and was only slightly poorer than that of the TL-LUE model. Similar to this study, previous research (see Table 6) indicates that the models performed better at the daily timescale compared to the mid-day and half-hour timescales. Furthermore, the goodness of fit in the process-based two-leaf model provides the best Figure 7. Relationship between SIF yield (SIF/APAR, SIF yield ) and light-use efficiency (ε) at the satellite overpass time throughout 2015 at the CN-YuC cropland site in northern China, where 0.8 is the threshold value at which ECI values are fit separately for the mid-day, daily, and monthly timescales, respectively. The whole canopies are prone to experiencing exposure to excess light when the ECI is greater than 0.8 compared with when the ECI is lower.
Additionally, sunlit leaves receive both direct and diffuse radiation and should have higher temperatures than shaded leaves, resulting in greater temperature gradients between the surrounding air and sunlit leaves. A former study has suggested that the different temperatures of sunlit and shaded leaves should be considered in the parameter optimization procedure in the TL-LUE model [31]. Moreover, it is also noted that the differences in leaf temperature can also cause disparities in the VPD of sunlit and shaded leaves. In the LUE-based models, the application of the same VPD and air temperature scalars to the whole canopy may also be a source of uncertainty in the optimized parameters and estimated GPP [30]. Therefore, although we partitioned the efficiency (ε) term of the LUE-based models into fixed parts (ε max , ε msu , and ε msh ) that depict the optimal efficiency and variable components that represent the effects of light, temperature, and water stress (e.g., VPD), the sensitivity of the LUE models to the ECI may be the main cause of the larger fluctuations in the parameter values.

Estimation Performances of the SIF-Based and LUE-Based Models
The performances of the three GPP models were highly consistent in their predictions of the magnitudes and seasonal dynamics of GPP, as validated using GPP observations ( Figure 6). The performance of the SIF model was better than that of the SL-LUE model and was only slightly poorer than that of the TL-LUE model. Similar to this study, previous research (see Table 6) indicates that the models performed better at the daily timescale compared to the mid-day and half-hour timescales. Furthermore, the goodness of fit in the process-based two-leaf model provides the best simulation, and the GOME-2 SIF linear model is also better than the big-leaf LUE model used in the MOD17A2 product. Wagle et al. [44] demonstrated that SIF is more relevant to the PAR absorbed by the photosynthetic parts of the maize canopy. That is, the components of PAR related with the SIF are mainly absorbed by vegetation chlorophyll, while the SL-LUE model in this study uses the PAR absorbed by the plant canopy ( f PAR canopy ) to estimate GPP. However, vegetation photosynthesis and chlorophyll fluorescence can only be driven by the PAR absorbed by photosynthetic parts, not by non-photosynthetic parts, such as branches, senescent foliage, and stems. This may be the reason that the SIF model has a better performance than the SL-LUE model. Nonetheless, previous studies have indicated that remote sensing SIF retrievals tend to represent the top layer of the vegetation canopy, which is primarily composed of sunlit leaves, thereby causing deviation between the SIF-based simulation and the tower observations [35,39]. Similar results were found when we analyzed the relationship between the SIF and LAI, the latter including the LAI of both sunlit and shaded leaves. The values of R 2 for the relationship between the SIF and the LAI of sunlit leaves were all greater than 0.85, while the values of R 2 ranged from 0.62 to 0.70 and from 0.53 to 0.65 for the relationships between SIF and the LAI of the whole canopy and between SIF and the LAI of shaded leaves across multiple temporal aggregation levels, respectively ( Figure 8). Although the f PAR canopy was also used in the TL-LUE model, it explicitly considers the difference in the LUE and APAR of sunlit and shaded leaves within the canopy. He et al. [28] illustrated that considering the entire canopy as a big extended leaf and ignoring the difference in the LUE and APAR of leaves can cause biased values of the simulated GPP. Consequently, the TL-LUE model can reduce the bias in GPP simulated by the SL-LUE model and the SIF model. On the other hand, the LUE-based models depend on a set of biome-specific parameters (ε max , ε msu , and ε msh ) and also require different inputs, such as air temperature, PAR, and water or soil moisture scalars, while the SIF-based models are completely based on SIF information without requiring any other ancillary variables. In this case, using SIF to estimate GPP may save computational resources and reduce the uncertainty in GPP estimates across spatial and temporal scales compared with the LUE-based algorithm. In summary, there is a compelling amount of data that supports the existence of a linear relationship between GPP and SIF for cropland that (1) is uniform for different temporal aggregation levels and under different meteorological conditions, and (2) contains adequate information for modeling ecosystem-level GPP. Additionally, whether our assessments are applicable to areas other than the cropland (maize-wheat rotation) used in this study is a problem that needs to be addressed in future research, and further studies are also needed to extend this analysis to other croplands, such as soybean, for cross-site comparisons.

Suggestions for Remote Sensing SIF Applications in LUE-Based Modeling
Previous studies have demonstrated that remotely sensed SIF retrievals can not only offer another approach to explore the seasonal variations in the photosynthesis, but can also restrict the parameters in process-based models to improve GPP simulations [77]. On the one hand, the Soil-Canopy Observation, Photosynthesis and Energy balance (SCOPE) model provides a theoretical method for modeling canopy SIF and photosynthesis by constraining the estimates of the maximum carboxylation rate (Vcmax) by coupling the soil-vegetation-atmosphere-transfer (SVAT) model with radiation transmission models [77]. On the other hand, the SCOPE model can also combine the SIF data derived from satellites to infer GPP from the land surface process model or carbon cycle data assimilation system [78,79]. In addition to the advantages of SIF in process-based models, it is also Figure 8. Scatterplots of the solar-induced chlorophyll fluorescence (W m −2 µm −1 sr −1 ) and sunlit/shaded/total leaf area index (LAI su , LAI sh , LAI, m 2 /m 2 ) on the mid-day, daily, and monthly timescales, respectively.
In summary, there is a compelling amount of data that supports the existence of a linear relationship between GPP and SIF for cropland that (1) is uniform for different temporal aggregation levels and under different meteorological conditions, and (2) contains adequate information for modeling ecosystem-level GPP. Additionally, whether our assessments are applicable to areas other than the cropland (maize-wheat rotation) used in this study is a problem that needs to be addressed in future research, and further studies are also needed to extend this analysis to other croplands, such as soybean, for cross-site comparisons.

Suggestions for Remote Sensing SIF Applications in LUE-Based Modeling
Previous studies have demonstrated that remotely sensed SIF retrievals can not only offer another approach to explore the seasonal variations in the photosynthesis, but can also restrict the parameters in process-based models to improve GPP simulations [77]. On the one hand, the Soil-Canopy Observation, Photosynthesis and Energy balance (SCOPE) model provides a theoretical method for modeling canopy SIF and photosynthesis by constraining the estimates of the maximum carboxylation rate (Vc max ) by coupling the soil-vegetation-atmosphere-transfer (SVAT) model with radiation transmission models [77]. On the other hand, the SCOPE model can also combine the SIF data derived from satellites to infer GPP from the land surface process model or carbon cycle data assimilation system [78,79].
In addition to the advantages of SIF in process-based models, it is also beneficial to the development of LUE-based models. Verma et al. [3] report that the correlation between the observed and simulated LUE is improved slightly when the normalized PRI and SIF yield are combined as predictive factors in the framework of multiple linear regression. Many studies have also shown that SIF comprises not just the light absorption information, but also the LUE information [36]. Moreover, we found that the values of ε/SIF yield and ε max tend to converge across time in this study, which may provide a basis for combining the satellite products of PRI and SIF to track ecosystem LUE. Additionally, remote sensing SIF retrievals tend to represent the top layer of the vegetation canopy, primarily composed of sunlit leaves [35,39], which may provide information for further studies to determine the contribution of the sunlit leaves and the structural sensitivity of SIF signals escaping the canopy to refine SIF-based models. We also can assume that SIF observations can be used to constrain the maximum rates of sunlit leaves in the two-leaf LUE model to improve the robustness of their estimates in future studies.

Conclusions
In this study, the effects of temporal aggregation and meteorological conditions on the parameter robustness of OCO-2 SIF-based and LUE-based GPP models, as well as the models' estimation performances were examined and compared, respectively, at a maize-wheat rotation site in Yucheng, China. The main findings are as follows: (1) The values of ε/SIF yield in the SIF model and those of ε max in the SL-LUE model are similarly robust and both are considerably more stable than those of ε msu and ε msh in the TL-LUE model across all temporal aggregation levels. Under different meteorological conditions, all the parameters show a certain degree of fluctuation and are most affected at the mid-day scale, followed by the monthly scale and finally at the daily scale overall. Nonetheless, the averaged coefficient of variation of the ε/SIF yield was relatively small and obviously lower than those of ε max , ε msu , and ε msh . Therefore, compared with the LUE-based models, for different temporal aggregation levels and environmental restrictions in cropland, the SIF-based model is a good predictor of GPP and its parameter is more likely to converge. Moreover, the SIF models were completely based on SIF and did not contain any ancillary inputs, such as air temperature, PAR, and VPD. This study thus strongly supports the continuous effort to take advantage of SIF for improved monitoring of GPP.
(2) It is feasible to combine the OCO-2 SIF data of the Nadir observation mode with those of the Glint observation mode after fully considering the viewing zenith effects of the latter on the magnitude of SIF values and on the relationship between SIF and GPP. This enables the limitation of sparse data to be alleviated and better exploration of the link between the ground-observed GPP and remote-sensing-based SIF retrievals at the canopy scale to be achieved. Additionally, the OCO-2 SIF data are found to be more strongly correlated with the LAI of sunlit leaves. It indicates that SIF observations may be useful to constrain the maximum photosynthetic rates of sunlit leaves in the two-leaf LUE model, thus reducing the uncertainty of parameter estimates and improving the accuracy of GPP prediction in future studies.