Deriving a light use efficiency estimation algorithm using in situ hyperspectral and eddy covariance measurements for a maize canopy in Northeast China

Abstract We estimated the light use efficiency (LUE) via vegetation canopy chlorophyll content (CCC canopy) based on in situ measurements of spectral reflectance, biophysical characteristics, ecosystem CO 2 fluxes and micrometeorological factors over a maize canopy in Northeast China. The results showed that among the common chlorophyll‐related vegetation indices (VIs), CCC canopy had the most obviously exponential relationships with the red edge position (REP) (R 2 = .97, p < .001) and normalized difference vegetation index (NDVI) (R 2 = .91, p < .001). In a comparison of the indicating performances of NDVI, ratio vegetation index (RVI), wide dynamic range vegetation index (WDRVI), and 2‐band enhanced vegetation index (EVI2) when estimating CCC canopy using all of the possible combinations of two separate wavelengths in the range 400−1300 nm, EVI2 [1214, 1259] and EVI2 [726, 1248] were better indicators, with R 2 values of .92 and .90 (p < .001). Remotely monitoring LUE through estimating CCC canopy derived from field spectrometry data provided accurate prediction of midday gross primary productivity (GPP) in a rainfed maize agro‐ecosystem (R 2 = .95, p < .001). This study provides a new paradigm for monitoring vegetation GPP based on the combination of LUE models with plant physiological properties.


| INTRODUCTION
The accurate assessment of vegetation gross primary productivity (GPP) is of great importance for regional and global studies of terrestrial ecosystem carbon budgets (Gitelson et al., 2006;Wu, Niu, & Gao, 2012), and it also plays a significant role in dynamic responses of terrestrial ecosystem carbon cycling to global climate change (Fang, Yu, & Qi, 2015;Fang & Zhang, 2013;Shen & Fang, 2014). The eddy covariance (EC) technique provides long-term continuous and frequent observations of CO 2 flux at the ecosystem level (e.g., Baldocchi, 2003). Remote sensing techniques conduct consistent and systematic monitoring of vegetation structure and function at the regional and site levels (Ide, Nakaji, & Oguma, 2010;Lawley et al., 2016;Running, Thornton, Nemani, & Glassy, 2000). How to effectively relate CO 2 flux observations with remote sensing techniques at the site level and ultimately to implement repetitive observations of CO 2 flux over extensive spatial areas are becoming critical challenges for assessing global carbon budgets and monitoring ecosystem dynamical processes. The key for addressing these questions lies in the development of remote sensing-based ecosystem process models at broad spatial scales that can be effectively and quantitatively parameterized and validated by CO 2 fluxes at site level.
Currently, the accurate estimations of the fraction of absorbed photosynthetically active radiation (fAPAR) and the light use efficiency (LUE) are two large sources of model uncertainties for LUE models (Inoue, Peñuelas, Miyata, & Mano, 2008;. On the one hand, studies showed that the sensitivity of the normalized difference vegetation index (NDVI) to variations in fAPAR usually decreases when fAPAR exceeds 0.7 for moderate-to-high vegetation density , moreover, the relationship of NDVI-fAPAR was also influenced by plant phenology (e.g., Jenkins et al., 2007;Running et al., 2000). On the other hand, studies have demonstrated that LUE was not a prescribed constant during the whole growing season (e.g., Jarvis & Leverenz, 1983) and was not only related to the absorbed photosynthetically active radiation (APAR) by green vegetation but also affected by the soil water content (SWC), nutrient conditions, ratio of direct to diffuse radiation, canopy age, and site history (Alton, North, & Los, 2007;DeLucia, Drake, Thomas, & Gonzalez-Meler, 2007). Thus, studies on how to effectively improve the accuracy of remote estimation models for fAPAR and LUE were especially essential. Involving remote estimation of fAPAR, corresponding research has been conducted (Zhang, Zhou, & Nilsson, 2015). So in this study, we will focus on the parameter LUE and its quantitative algorithms. Studies indicated that the variation in foliar chlorophyll content was well correlated with temporal changes in LUE (Dawson, North, Plummer, & Curran, 2003;, and it was also found that foliar chlorophyll content was a good proxy for leaf photosynthetic capacity (Croft et al., 2017). In addition, studies have shown that spectral vegetation indices (VIs) closely related to chlorophyll were used to estimate GPP, such as the photochemical reflectance index (PRI), which is strongly related to the photosynthetic radiation use efficiency of plant leaves (Gamon, Serrano, & Surfus, 1997;Peñuelas, Filella, & Gamon, 1995). However, its applicability at the canopy or ecosystem scales is still not well known (Ide et al., 2010;Nakaji et al., 2008;Rossini et al., 2010). Therefore, to estimate the ecosystem LUE using remote sensingbased models, we made seasonal measurements of the spectral reflectance, ecosystem CO 2 fluxes, ecophysiological characteristics, and micrometeorological variables over a maize cropland. This study aims to estimate LUE for a maize canopy through exploring the relationships between the spectral VIs and photosynthetic-efficiency or capacityvariable canopy chlorophyll content (CCC canopy ). The specific objectives were to (1) construct quantitative algorithms for CCC canopy considering the saturation of VIs with increasing green plants; and (2) test whether the estimation models for CCC canopy derived from field spectrometry can be effectively validated by EC fluxes data; and (3) ultimately assess the performance of hyperspectral remote sensing information for assessing CCC canopy . This study will provide theoretical bases for constructing ecosystem productivity models driven by full remote sensing information.

| Experimental site
The experimental site was located at Jinzhou Agricultural Ecosystem Research Station (41°8′53′'N, 121°12′6′'E, 23 m a.s.l.), the Institute of Atmospheric Environment, Chinese Meteorological Administration, Shenyang. It belongs to a temperate continental monsoon climate zone, with mean annual air temperature of 9°C and mean annual precipitation of 690 mm for the past 40 years. The rainfed maize is the main crop type in this area. The maize hybrid was Nong Hua 101, and it was sown in early May and harvested in late September. The maize was planted about 23 cm apart in rows and the distance of about 57 cm between rows at this experimental site. The fields are under till management and N fertilizer is around 300 kg N/ha (Han et al., 2007). The soil is a typical brown soil, which is composed of sand of 45%, silt of 40%, and clay of 15%. The pH value of the soil was 6.3, a soil organic matter content ranged from 0.6 to 0.9%, and total N was 0.069% (Han et al., 2007;Li, Zhou, & Wang, 2010;Zhang et al., 2015).

| Field measurements
An ASD (Analytical Spectral Devices, Boulder, CO, USA) FieldSpec3 spectroradiometer with a wavelength range of 350-2500 nm was used to collect canopy spectral reflectance data biweekly from late May to late September during the whole growing season in 2011 (nine measurement campaigns). The area-coefficient method (CMA, 1993) was used to measure leaf area index (LAI). A more detailed description of spectral reflectance and LAI measurements are given as Zhang et al. (2015).
Total CCC canopy is an important biophysical characteristic parameter at the canopy level Ustin et al., 1998) and is the product of LAI and the leaf chlorophyll content (LCC) . LCC was measured by a SPAD-502 meter (Minolta Corporation, NJ, USA) with the same observation dates as the spectral reflectance measurements in nine campaigns. Gitelson et al. (2005) (Markwell, Osterman, & Mitchell, 1995). LI-COR Inc., Lincoln, NE, USA) at the height of 3.5 m, and SWC (EasyAG sensors; Campbell Scientific Inc.) at depths of 10, 20, 30, and 40 cm were also measured in the 2011 growing season (Zhang & Zhou, 2014). They were installed in an undisturbed rainfed maize field occupying 43 ha with adequate fetches in all directions and uniform enough to meet requirements for EC measurements of carbon fluxes (Li et al., 2010).

| Data analysis
The net ecosystem CO 2 exchange (NEE) data were determined by the EC method as the mean covariance between fluctuations in vertical wind speed (ϖ′) and the carbon dioxide concentration (c′) on a half-hourly basis (Equation 4) (Baldocchi, 2008), and data processing and quality control procedure were conducted. To obtain complete time-series of half-hour CO 2 fluxes data, the gap-filling method of Reichstein et al. (2005) was used to fill NEE data. We used Equation (5) to estimate daytime ecosystem respiration (R eco ) and Equation (6) to partition NEE into GPP (GPP = 0 during the night) and R eco . NEE is positive when CO 2 is emitted from the ecosystem into the atmosphere, where GPP and R eco are both positive (Reichstein et al., 2005).
where R ref is the ecosystem respiration at the reference temperature 10°C (mg CO 2 m −2 s −1 ), E 0 is the activation energy parameter (J/mol), T is soil temperature (°C, 0.05 m depth), T 0 = 273.15 K, and a 91-day window that can reflect the seasonal dynamics of ecosystem R eco was applied to parameterize R ref and E 0 (Lloyd & Taylor, 1994). To match simultaneous spectral measurements over a maize canopy, the daily mean midday GPP values measured between 11 and 14 h were used in this study.
Eleven common chlorophyll-related VIs were calculated in this study (Table 1). Additionally, the red edge position (REP) was used, which is particularly sensitive to green vegetation information, and was determined as the wavelength inflection point between 680 and 750 nm (i.e., the point of maximum slope) (Dawson & Curran, 1998).
Four widely used VIs, that is, the NDVI, ratio vegetation index (RVI), wide dynamic range vegetation index (WDRVI), and 2-band enhanced vegetation index (EVI2) ( Table 1), were used to select the optimal CCC canopy indicators using all of the possible combinations of two separate wavelengths in the range of 400-1300 nm along with 12 chlorophyll-related VIs to explore the relationships between VIs and CCC canopy . Considering the saturation effects of VIs with an increasing CCC canopy , linear and exponential regression models were employed.

| Validation of the models
According to LUE principles (Monteith, 1972(Monteith, , 1977, ecosystem GPP can be accurately estimated using the product of fAPAR and LUE following Equation (7):
Considering LUE was closely related to ecosystem chlorophyll (Gitelson et al., 2006;, thus, Equation (7)   LAI, CCC canopy showed a notable single-peak seasonal trend, which rapidly increased at the vegetative stage and gradually decreased after its peak value, occurring at the period from late July to early August ( Figure 1c).

| Relationships between chlorophyll-related VIs and CCC canopy
Based on the relationships between VIs and CCC canopy , VIs were classified into two categories.  (Figure 2e−l). The best linear relationship exhibited between EVI and CCC canopy , with an R 2 value of .70 (p < .01, Figure 2e).
The worst relationships occurred between PRI and CCC canopy , with an R 2 value of .38 (p = .08, Figure 2f), and SR and CCC canopy , with an R 2 value of .39 (p = .074, Figure 2g); the other R 2 values were approximately .50 (Figure 2h−l). To some degree, the latter could overcome the saturation effects, but the explained variances of CCC canopy by the linear relationships were still very limited.
Photochemical reflectance index can detect epoxidation and de-epoxidation changes in xanthophyll relevant to heat dissipation and can be used to indicate rapid changes of the photosynthetic efficiency of photosystem II and LUE of plant leaves (Gamon et al., 1997;Peñuelas et al., 1995). However, at the canopy scale, the sensitivity of PRI to the variation in CCC canopy did not perform well in this study. In addition, studies also showed that CCI could indicate changes of the chlorophyll content by the shifting of the red edge (Ide et al., 2010;Sims et al., 2006). In particular, CI green [(R NIR / R green ) − 1] and CI red edge [(R NIR /R red edge ) − 1] could effectively reflect (8) GPP = PAR × fAPAR ×α×CCC canopy , F I G U R E 1 Seasonal variations of the environmental variables, canopy chlorophyll content (CCC canopy , g m −2 ), and leaf area index (LAI). (a) Photosynthetically active radiation (PAR, μmol m −2 s −1 ) and the mean daily temperature (T air , °C), and (b) soil water content (SWC, %), relative humidity (RH, %), and vapor press deficit (VPD, kPa) from micrometeorological measurements, as well as (c) CCC canopy and LAI the variation of CCC canopy and explain more than 92% of the Chl variation . However, they could not be used as better proxies in this study because the effects of the canopy structure, spatial distribution of the chlorophyll content, LAI, and soil background decreased the reflectance signatures of Chl at the canopy level.  Figure 3 shows a contour map of R 2 between the CCC canopy and the commonly utilized VIs, NDVI, RVI, WDRVI, and EVI2 using all of the possible combinations of two separate wavelengths in the range 400−1300 nm according to linear and exponential relationships. The Compared with NDVI, WDRVI, to some extent, showed a similar linear relationship with CCC canopy , but it was not better than NDVI for the exponential R 2 value (Figure 3e,f). Among the four VIs used in this study, EVI2 was the best indicator of CCC canopy because the R 2 values of the exponential relationships between CCC canopy and EVI2 [667,675], CCC canopy and EVI2 [498,675] reached .94 and .89 (Figure 3h), respectively. Actually, good linear relationships also existed between CCC canopy and EVI2 [1214,1259] and CCC canopy and EVI2 [726,1248], with R 2 values of .92 and .90, which effectively overcame the saturation effects ( Figure 4). EVI2 proved to be suitable for accurate estimations of CCC canopy , and they were very sensitive to the CCC canopy variations in this study.

| Relationships between VIs from the combinations of two separate wavelengths and CCC canopy
Usually, the chlorophylls have strong absorbance peaks in the red and blue regions of the spectrum. However, the blue peak is not used to estimate Chl because it overlaps with the absorbance of the carotenoids (Wu et al., 2009). In addition, maximal chlorophyll absorbance in the red region occurred at wavelengths from 660 to 680 nm; spectral reflectance at these wavelengths are prone to saturated light information, so they were nonsensitive, while reflectance near 550 nm in the green region and red edge region at 700 nm, where more Chl is required to saturate the absorption, showed greater sensitivity to a wide range of Chl (Wu et al., 2009). This study found that the sensitive

| Validation of the hyperspectral remote estimation of CCC canopy
Crop GPP was strongly related to CCC canopy , Chl per unit area to a large extent determined crop productivity, net photosynthesis, and light absorbance . Moreover, long-or medium-term changes in CCC canopy were closely related to crop phenology, canopy stresses, and photosynthetic capacity, thus it F I G U R E 4 Relationships of CCC canopy with the VIs (a) EVI2 [1214,1259] and (b) EVI2 [726,1248]. Figures 2 and 3 provide the definitions of acronyms.
F I G U R E 5 Comparisons of the estimated PAR (photosynthetically active radiation) * fAPAR green (the fraction of absorbed photosynthetically active radiation calibrated by green LAI) * CCC canopy using the VIs and gross primary productivity (GPP) derived from the eddy covariance observations. (a) CCC canopy estimated by NDVI, (b) CCC canopy estimated by REP, (c) CCC canopy estimated by EVI2 [1214,1259], and (d) CCC canopy estimated by EVI2 [726,1248]. Figures 2 and 3 provide the definitions of acronyms.
was an important physiological variable that strongly related with productivity at the community level (Gitelson et al., , 2006Ustin et al., 1998).
Half-hourly midday GPP between 11 and 14 h estimated and measured by an open-path EC, through in combination with the algorithms of fAPAR calibrated by green LAI (fAPAR green ) (Zhang et al., 2015) and PAR from meteorological observations were utilized to validate the remote estimation models for the CCC canopy . Studies derived from the same field measurements, including spectral measurements and crop canopy data from fAPAR observations, showed that NDVI was a good predictor of fAPAR green as Equation (9) (Zhang et al., 2015): Here we established CCC canopy algorithms based on hyperspectral data including NDVI and REP (Figure 2a

| CONCLUSIONS
This study investigated remote estimation of LUE through estimating CCC canopy based on field measurements of spectral reflectance, Chl, LAI, and ecosystem CO 2 fluxes as well as micrometeorological factors conducted during the entire growing season for a maize canopy.
Among the common chlorophyll-related VIs, REP and NDVI had better exponential relationships with CCC canopy , although there existed a certain saturation effect with increasing CCC canopy ; to some degree, EVI, PRI, SR and so on, could overcome the saturation effects, the explained variances of CCC canopy by the linear relationships were still very limited. Thus to select the most sensitive spectral information, when estimating CCC canopy using all of the possible combinations of two separate wavelengths in the range of 400-1300 nm, EVI2 [1214,1259] and EVI2 [726,1248] were proved to be the best indicators of CCC canopy . This study demonstrated that hyperspectral remote sensing information could effectively monitor the seasonal variations of CCC canopy . Although more researches are needed to validate the performance of spectral features for estimating CCC canopy , we believe that the selected sensitive indicating spectral information will be attractive for actual applications of satellite data at broader temporal and spatial scales.
This study further demonstrated that based on LUE principles, a CCC canopy algorithm derived from field spectrometry measurements through in combination with an algorithm of fAPAR green and PAR from meteorological observations could be used to monitor midday GPP in maize agricultural ecosystems. We optimized the parameterization of LUE using field spectrometry observation data sets, developed an ecophysiological based LUE model, and it showed a good performance.
However, considering limited observations in this study, more studies in the future are still necessary to validate this new conceptual model for monitoring vegetation GPP based on the combination of LUE models with plant physiological properties.