Radiance-based NIRv as a proxy for GPP of corn and soybean

Substantial uncertainty exists in daily and sub-daily gross primary production (GPP) estimation, which dampens accurate monitoring of the global carbon cycle. Here we find that near-infrared radiance of vegetation (NIRv,Rad), defined as the product of observed NIR radiance and normalized difference vegetation index, can accurately estimate corn and soybean GPP at daily and half-hourly time scales, benchmarked with multi-year tower-based GPP at three sites with different environmental and irrigation conditions. Overall, NIRv,Rad explains 84% and 78% variations of half-hourly GPP for corn and soybean, respectively, outperforming NIR reflectance of vegetation (NIRv,Ref), enhanced vegetation index (EVI), and far-red solar-induced fluorescence (SIF760). The strong linear relationship between NIRv,Rad and absorbed photosynthetically active radiation by green leaves (APARgreen), and that between APARgreen and GPP, explain the good NIRv,Rad-GPP relationship. The NIRv,Rad-GPP relationship is robust and consistent across sites. The scalability and simplicity of NIRv,Rad indicate a great potential to estimate daily or sub-daily GPP from high-resolution and/or long-term satellite remote sensing data.


Introduction
Monitoring and quantifying terrestrial photosynthesis from satellite remote sensing is crucial for understanding the global carbon cycle. Either process-based models (Jiang and Ryu 2016, Chen et al 2019) or more empirical models (Running et al 2004, Jung et al 2011 have been widely used for regional or global gross primary production (GPP) estimations. Process-based models employ complex model structure, while existing empirical models rely on various imposed functions. Uncertainties in climate forcing and model parametrization lead to largely diverged GPP estimation regarding the total amount and spatio-temporal patterns (Anav et al 2015. Particularly, GPP estimation at short time scales (e.g. sub-daily and daily) is still challenging (Bodesheim et al 2018, Wang et al 2019. Effective and parsimonious ways to estimate GPP with low dependence on climate forcing and model parameterization are highly required. Recent advances in satellite-based solar-induced fluorescence (SIF) monitoring capabilities may Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. provide a new opportunity for GPP estimation. Although SIF has been reported as a better proxy for photosynthesis at leaf (Baker 2008), landscape (Li et al 2018), and global (Guanter et al 2014) scales than traditional GPP proxies such as enhanced vegetation index (EVI) (Sims et al 2006), divergent SIF-GPP relationships have been obtained from ground-based observations ( A new vegetation index, near-infrared reflectance of vegetation (NIR v,Ref ), could open up a new opportunity to quantify GPP. NIR v,Ref , defined as the product of normalized difference vegetation index (NDVI) and NIR reflectance (NIR Ref ), is found accounting for canopy structure well and photosynthetic capacity to some extent (Badgley et al 2017). Without any other auxiliary information, NIR v,Ref has been reported to explain 68% of FLUXNET GPP variation at monthly to annual time scales . However, the relationship between NIR v,Ref and GPP at shorter time scales (sub-daily to daily) has not been investigated yet, and that relationship is expected to be poorer than at monthly scale, as NIR v,Ref has much smaller variations at short time scales. Considering that radiances can be used in studies with variable light (Badgley et al 2017), observed NIR Ref in NIR v can be replaced with observed NIR radiance (NIR Rad ) to derive a new proxy NIR v,Rad , which takes the incoming radiation into account (Zeng et al 2019) and has the potential to be a better proxy for GPP at short time scales. However, the relationship between NIR v,Rad and GPP has not been investigated and its potential awaits to be evaluated.
The objective of this study is to evaluate whether NIR v,Rad is a better proxy of GPP than NIR v,Ref and SIF for corn and soybean, two major crops in the US Corn Belt. For a comprehensive assessment of the relationships between GPP and those proxies, we integrated a range of field observations including hyperspectral radiance and reflectance, far-red SIF, GPP flux, and canopy light absorption at half-hourly interval over seven site-years. The overachieving questions that we aim to address are: How is NIR v,Rad 's ability to estimate GPP compared with other widely used recognized proxies (NIR v,Ref , EVI and SIF) for corn and soybean, and what factors may lead to a better performance of NIR v,Rad ?We propose the following three hypotheses. First, we hypothesize that the relationship between NIR v,Rad and GPP is the strongest compared to three other widely recognized proxies (NIR v,Ref , EVI and SIF), especially at short time scales. Second, we hypothesize that the strong relationship between NIR v,Rad and GPP can be explained by the fact that NIR v,Rad better accounts for photosynthetically active radiation (PAR) absorbed by green leaves (APAR green ). Third, we hypothesize that the relationship between NIR v,Rad and GPP for soybean (C3 crop) or corn (C4 crop) is site-independent. We suggest these features might make NIR v,Rad a better proxy for estimating GPP in the US Corn Belt than NIR v,Ref , EVI and SIF.

Study site
This study was conducted at three agricultural sites in the US Corn Belt. One rainfed site was located at the Energy Farm of University of Illinois at Urbana-Champaign (UIUC, 40. 0628°N, 88.1959°W). Another two sites were located at the Eastern Nebraska Research and Extension Center of University of Nebraska-Lincoln, with one irrigated (UNL irrigated, 41.1649°N, 96.4701°W) and one rainfed (UNL rainfed, 41.1797°N, 96.4397°W) site. The mean annual temperature and precipitation over the period of 1990-2018 were (11.5°C, 1036 mm) and (10.1°C, 770 mm) at UIUC (Willard Airport weather station) and two UNL sites (National Climate Data Center, Nebraska, Mead 6 S weather station), respectively. The UIUC site had a corn-corn-soybean rotation, whereas the two UNL sites were corn-soybean rotation. The growing season (from planting to harvesting) was generally May-October for both crops across all the three sites. During 2016-2018, a total of four and three site-year observations were made for corn and soybean, respectively. Detailed site and observation information are summarized in table 1.
where the average of 770-780 nm, 650-660 nm, and 460-470 nm were used for NIR, Red and Blue band, respectively. SIF at 760 nm (SIF 760 ) was retrieved from the SIF subsystem using the improved Fraunhofer Line Depth method (Alonso et al 2008, Cendrero-mateo et al 2019), which used the whole downwelling irradiance (E) and upwelling radiance (L) spectrum information from 745 to 780 nm to extract the SIF signal.
where a R and a F are correction factors to account for the non-linear variation of reflectance (R) and fluorescence (F) inside (λ in ) and outside (λ out ) the O 2 -A absorption band at wavelength λ, respectively. Detailed SIF data processing can be found in supplementary methods.
2.3. Eddy covariance (EC) system and derivation of GPP EC systems were installed to acquire net ecosystem exchange (NEE), and GPP was estimated based on standard night-time partitioning algorithms (Reichstein et al 2005). Each EC system consisted of a sonic anemometer (81000VRE, R.M. Young Inc., USA for the UIUC site; R3, Gill Instruments Inc., UK for the two UNL sites) and a CO 2 /H 2 O infrared gas analyzer (LI-7500 and LI-7200, LI-COR Inc., USA for the UIUC site and the two UNL sites, respectively). Raw 10 Hz Carbon fluxes data collected from EC systems were processed to derive half-hourly NEE. Detailed information on site instrumentation can be found in (Zeri et al 2011) for UIUC site, and in (Suyker and Verma 2012) for UNL sites. Detailed EC data processing can be found in supplementary methods.

Ancillary data
Downwelling and upwelling PAR were measured above and below canopy by multiple point or line quantum sensors (LI-COR Inc., USA), from which the fraction of absorbed PAR (FPAR) were derived at halfhourly interval. Leaf area index (LAI) were measured from destructive samples at an interval of 10-14 d, and green leaves were separated from yellow leaves to provide green area index (GAI) measurements. The ratio of GAI to LAI were linearly interpolated and halfhourly APAR green , light use efficiency of green leaves (LUE green ) (Gitelson and Gamon 2015) and fluorescence yield (LUE f ) were then calculated as: These data were only acquired at the two UNL sites.

Data analysis
To test the first hypothesis, the relationships between GPP and its four proxies, NIR v,Ref , EVI, NIR v,Rad , and SIF 760 were investigated. All site-year data for each species were combined in this analysis. Investigations were conducted at three time scales (half-hourly, daily, and monthly). Because of uncertainties under low light conditions in the early morning and late afternoon, only data from 8:00 am to 6:00 pm (local standard time) were used. Therefore, daily data averaged from half-hourly data were daytime means in the strict sense. Only days with data gaps less than 25% were used. Monthly mean data were calculated for months with at least 10 days of available data. Linear regression of GPP-NIR v,Rad and GPP-SIF 760 were established with zero intercepts, considering the fact that there is no photosynthesis when radiation is zero. For linear regression of GPP-NIR v,Ref and GPP-EVI, the intercept term was employed because these two proxies do not reach zero.
To test the second hypothesis, the relationships between the four proxies and APAR green were also evaluated at the three time scales at the two UNL sites, where APAR green data were available. Similar to LUE green and LUE f , we divided NIR v,Rad by APAR green and then examined the relationship between LUE green and NIR v,Ref , EVI, LUE f , NIR v,Rad /APAR green at halfhourly, daily and monthly scales. Coefficient of determination (R 2 ) was used to quantify their relationships.
To test the third hypothesis, site-specific GPP-NIR v,Rad relationship was investigated separately for corn and soybean. Half-hourly data were used for this analysis. For each crop type and each site, the linear relationship between GPP and NIR v,Rad was established, and the slopes across sites were compared. Subsequently, linear models calibrated from one site were applied to the remaining two sites to predict GPP, i.e. NIR v,Rad -derived GPP. The NIR v,Rad -derived GPP was compared with EC-derived GPP. Root mean square error (RMSE) was used to evaluate the performance of the GPP prediction.

Relationship between GPP and its proxies
Overall, GPP, NIR v,Ref , EVI, NIR v,Rad and SIF 760 followed similar seasonal trajectories (figure 1). Peak GPP was higher for corn than for soybean. NIR v,Ref , EVI, and APAR green were similar between corn and soybean, but SIF 760 and NIR v,Rad were lower for corn than soybean. LUE green , LUE f and NIR v,Rad /APAR green displayed weak seasonal variation, especially after excluding the senescence period (e.g. from late September to October) when the derivations of FPAR green and subsequently LUE green were prone to uncertainties (Gitelson et al 2018).
NIR v,Ref -GPP relationship varied with time scales for both corn and soybean, and it tended to be stronger scaled with temporal aggregation (figure 2). From half-hourly to monthly, R 2 of NIR v,Ref -GPP increased from 0.37 to 0.80 for corn and from 0.48 to 0.83 for soybean. The EVI-GPP relationship also showed a similar time scale-dependent pattern. In contrast, both NIR v,Rad and SIF 760 showed more consistent performance at different time scales. R 2 differences of NIR v,Rad -GPP relationship between monthly scale and , APAR green (μmol m −2 s −1 ), LUE green (μmol CO 2 μmol absorbed photon −1 ), NIR v,Rad /APAR green (mW s nm −1 sr −1 μmol −1 ) and LUE f (mW s nm −1 sr −1 μmol −1 ) at 2017 UNL irrigated corn site (left column) and 2018 UNL irrigated soybean site (right column). All data are at half-hourly intervals from 8:00 am to 6:00 pm.
half-hourly scale were only 0.06 and 0.08 for corn and soybean, respectively.
Among the four GPP proxies, NIR v,Rad exhibited the strongest relationship with GPP at short time scales (half-hourly and daily) for both corn and soybean (figure 2), which confirmed our first hypothesis. Overall, NIR v,Rad explained 84%, 86% and 89% of the variation of corn GPP at half-hourly, daily and monthly scales, respectively. Slightly lower values were achieved for soybean GPP, with 78%, 79% and 86% of the variation explained at half-hourly, daily and monthly scales, respectively. In particular, at daily scale which is of concern for crop growth monitoring, NIR v,Rad better explained the variation of GPP compared to other three proxies. For corn, the portion of GPP variation explained by NIR v,Rad was 19%, 16% and 10% higher than NIR v,Ref , EVI and SIF 760 , respectively. For soybean, this portion was 10%, 9% and 9% higher than NIR v,Ref , EVI and SIF 760 , respectively.

Relationship between APAR green , LUE green and GPP proxies
Strong correlations were observed between APAR green and NIR v,Rad (figures 3(a) and (b)). The relationship between APAR green and GPP proxies (figure 3) followed similar time scale patterns as the relationship between GPP and GPP proxies (figure 2). NIR v,Rad showed the strongest correlation with APAR green at all time scales for both corn and soybean. Specifically, for corn, R 2 values of APAR green -NIR v,Rad were 0.94, 0.96 and 0.98 at half-hourly, daily and monthly scale, respectively ( figure 3(a)), and for soybean, they were   (d), respectively. All half-hourly data at the two UNL sites were used. No APAR green and LUE green data was available at the UIUC site. R 2 between LUE green and NIR v,Ref , EVI, and LUE f were almost zero at half-hourly and daily scale for corn (c). 0.85, 0.83 and 0.91, respectively ( figure 3(b)). SIF 760 also showed similar correlation with APAR green across the three time scales. In contrast, such relationship between APAR green and the two proxies without radiation information (NIR v,Ref and EVI) varied substantially with time scales, following the order of half-hourly<daily<monthly.
We further investigated the relationship between LUE green and NIR v,Ref , EVI, LUE f , NIR v,Rad /APAR green and LUE f . For corn, NIR v,Rad /APAR green had weak correlation with LUE green at half-hourly and daily scales, whereas NIR v,Ref , EVI, LUE f showed no correlation ( figure 3(c)). This was probably due to the small seasonal variability of corn LUE green in most of the growing season (figure 1). R 2 values of proxies-LUE green at halfhourly and daily scales were much higher for soybean than for corn ( figure 3(d)), and they all increased with time scales, i.e. half-hourly<daily<monthly.
The relationship between GPP and GPP proxies at two UNL sites showed similar time scale patterns (figure S1) as the pattern observed in figures 2(a) and (b) when all site data were used. The above results sufficiently proved that our second hypothesis is correct.

Relationship between NIR v,Rad and GPP at different sites
The slopes of NIR v,Rad -GPP relationship were significantly different between corn and soybean (figure S2). The overall slope was 0.582 (μmol s −1 mW −1 nm sr) for corn, almost two times of 0.312 (μmol s −1 mW −1 nm sr) for soybean. There was little variation in slopes of NIR v,Rad -GPP relationship for the same crop type across different sites. The cross-site standard deviations of slopes were 0.039 for corn and 0.041 for soybean, with coefficients of variation of 6.6% and 12.9% for corn and soybean, respectively.
The prediction performance of the NIR v,Rad -GPP linear model was relatively stable (table 2), largely confirming our third hypothesis. When the model was calibrated at one site and validated at each of the three sites, the RMSE values were in general within a relatively small range: 6.14<RMSE<10.96 for corn, and 4.40<RMSE<10.85 for soybean, respectively. Similar small ranges were also observed for R 2 (figure S3) and bias (figure S4), with 0.78<R 2 <0.91and −5.32<bias<4.32 for corn, and 0.69<R 2 <0.88 and −6.10<bias<5.97 for soybean, respectively. Furthermore, when models calibrated at different sites were applied to a specific site, the performance of those models were similar. This was indicated by small RMSE differences (~1 for corn and~2 for soybean) between different models within each column.

Discussion
Our results support all three hypotheses on the NIR v,Rad as a proxy for GPP of corn and soybean. At half-hourly and daily time scales, NIR v,Rad shows considerably higher correlations with GPP than NIR v,Ref and EVI, but they have similar performance at monthly scale (figure 2). At monthly scale, plants adjust their structure and functions to acclimate to environmental changes (Hikosaka and Hirose 1997, Yamori et al 2010). As a result, structure and function co-vary with environmental variables, and the reflectance itself is able to capture long-term variability of GPP. In contrast, dayto-day and diurnal variations are strongly affected by high-frequency changes of PAR due to varying solar angle and sky conditions (Peng and Gitelson 2011), which does not cause much changes in bi-directional reflectance (Kim et al 2019). Therefore, NIR v,Rad containing the information of PAR in addition to biophysical and biochemical information contained in reflectance-based vegetation indices better captures short-term variability of GPP. SIF 760 containing considerable PAR information (Miao et al 2018) also shows stronger relationship with GPP compared to NIR v,Ref and EVI at half-hourly scale for both species. Though there is a strong link between SIF and GPP at photosystem scale (Porcar-Castell et al 2014), SIF 760 does not show better correlation with GPP than NIR v,Rad . A possible reason is the larger uncertainty in SIF observations than reflectance (Meroni et al 2009), but more studies are needed to better understand the potential of SIF for estimating GPP.
The strong relationship between NIR v,Rad and GPP is mainly attributed to their strong links with APAR green (figures 3 and S5). A previous study has reported the linear relationship between daily GPP and APAR green for corn and soybean from 2001 through 2008 at the UNL sites (Gitelson et al 2015), and we further demonstrate Table 2. RMSE (μmol m 2 s −1 ) between tower-based GPP and GPP predicted by NIR v,Rad -GPP linear models. Each row refers to a model calibrated at a specific site, and each column refers to different models applied to a specific site.  3). This is due to a negative correlation between LUE f and LUE green at the earlymiddle growing season (figure S6). The difference between NIR v,Rad /APAR green -LUE green and LUE f -LUE green explains higher correlation of NIR v,Rad -GPP than SIF 760 -GPP even though NIR v,Rad and SIF 760 have similar correlation with APAR green (figure 3).
The strong relationship of NIR v,Rad -GPP may be further explained by the dominant role of canopy structure. Although LUE is usually considered as a function of leaf physiology which relates to heat and water stress (Running et al 2000, Xiao et al 2005, its concept is originally based on the functional convergence theory (Monteith 1972, 1977, Field 1991 hypothesizing that plants scale canopy leaf area and light harvesting by the availability of resources as a result of evolutionary processes in order to optimize their carbon fixation (Goetz et al 1999). Simulations by sophisticated radiative transfer model also indicate that LUE is a function of canopy structure (Medlyn 1998 The NIR v,Rad -GPP relationship for corn and soybean is site-independent in the US Corn Belt, and the slope of NIR v,Rad -GPP is significantly higher for corn than for soybean. The site-independence of NIR v,Rad -GPP relationship is revealed from the following two aspects: (1) the slopes between NIR v,Rad and GPP are similar among different sites, though some variations are observed ( figure 4); (2) the linear model built at one site can be applied to other sites without significantly losing accuracy (table 2). This is also consistent with a recent study which found a general NIR . This is reasonable, as C4 plants tend to have much higher GPP than C3 plants even though they have similar density/greenness. It is worth mentioning that observational factors could influence the generality of the NIR v,Rad -GPP relationship. The first one is that the hyperspectral data of this study cover different time periods across sites (table 1). It has been reported that even for a strong proxy-GPP relationship, slope can differ between vegetative and reproductive stages to some degree (Gitelson et al 2014). The second one is that Fluospec2 footprint covers less than 2% of EC footprint (Liu et al 2017b). Such mismatch between sensor footprints varies across sites and the spatial heterogeneity of underlying surface can further contribute to uncertainties of GPP prediction (Wang et al 2019). Further comprehensive studies are needed to address whether the NIR v,Rad -GPP relationship is robust.
The strong and robust NIR v,Rad -GPP relationship has a great implication as we can easily apply this relationship at satellite observations to scale up to globe for long-term record or at high resolution. NIR v,Rad is the product of field observed NIR Rad and NDVI. NIR v,Rad can be reformed as: where NIR irra is incoming radiation in NIR region and can be derived as the difference between incoming shortwave radiation and PAR, both of which are available from high-resolution satellite data (

Conclusion
We investigated the performance of radiance-based NIR v (NIR v,Rad ) in estimating GPP of corn and soybean based on field observations across multiple site-years. NIR v,Rad outperformed NIR v,Ref , EVI and SIF 760 for GPP estimation at short timescales (halfhourly and daily), mainly because NIR v,Rad strongly correlated with APAR green which determined GPP variation for both corn and soybean. The NIR v,Rad -GPP relationship showed robust performance across sites, indicating that the NIR v,Rad -based simple models have a great potential to estimate crop GPP at short timescales with high-resolution or long-term satellite remote sensing data.
Acknowledgments GW, KG, BP and HK, acknowledged the support from NASA New Investigator Award and NASA Terrestrial Ecology Program. GW, KG, CJ, SW, CB and CM were supported by the DOE Center for Advanced Bioenergy and Bioproducts Innovation (US Department of Energy, Office of Science, Office of Biological and Environmental Research under Award Number DESC0018420). XY is supported by the NASA Interdisciplinary Science (80NSSC17K0110) and NSF AGS (1837891). MC acknowledged the support from NASA Terrestrial Ecology Program and the Laboratory Directed Research & Development program of PNNL, US Department of Energy. MP Cendrero-Mateo is currently funded by Juan de la Cierva incorporación scholarship, n°IJC2018-038039-I, and FLEXL3L4 project (L3 and L4 advanced Products for the FLEX-S3 mission), n°RTI2018-098651-B-C51, Ministry of science, innovation, and universities, Spain. Any opinions, findings, and conclusions or recommendations expressed in this publication are those of the author(s) and do not necessarily reflect the views of the US Department of Energy. We thank Guofang Miao for the data collection and the Fluospec2 system maintenance at the three sites.

Data availability statement
The data that support the findings of this study are available from the corresponding author upon reasonable request.