A Vegetation Index to Estimate Terrestrial Gross Primary Production Capacity for the Global Change Observation Mission-Climate (GCOM-C)/Second-Generation Global Imager (SGLI) Satellite Sensor

To estimate global gross primary production (GPP), which is an important parameter for studies of vegetation productivity and the carbon cycle, satellite data are useful. In 2014, the Japan Aerospace Exploration Agency (JAXA) plans to launch the Global Change Observation Mission-Climate (GCOM-C) satellite carrying the second-generation global imager (SGLI). The data obtained will be used to estimate global GPP. The rate of photosynthesis depends on photosynthesis reduction and photosynthetic capacity, which is the maximum photosynthetic velocity at light saturation under adequate environmental conditions. Photosynthesis reduction is influenced by weather conditions, and photosynthetic capacity is influenced by chlorophyll and RuBisCo content. To develop the GPP estimation algorithm, we focus on photosynthetic capacity because chlorophyll content can be detected by optical sensors. We hypothesized that the maximum rate of low-stress GPP (called “GPP capacity”) is mainly dependent on the chlorophyll content that can be detected by a vegetation index (VI). The objective of this study was to select an appropriate VI with which to estimate global GPP capacity with the GCOM-C/SGLI. We analyzed reflectance data to select the VI that has the best linear correlation with chlorophyll content at the leaf scale and with GPP capacity at canopy and satellite scales. At the satellite scale, flux data of seven dominant plant functional types and reflectance data obtained by the Moderate-resolution Imaging Spectroradiometer (MODIS) were used because SGLI data were not available. The results indicated that the green chlorophyll index, CIgreen(ρNIR/ρgreen-1), had a strong linear correlation with chlorophyll content at the leaf scale (R2 = 0.87, p < 0.001) and with GPP capacity at the canopy (R2 = 0.78, p < 0.001) and satellite scales (R2 = 0.72, p < 0.01). Therefore, CIgreen is a robust and suitable vegetation index for estimating global GPP capacity.


Introduction
Terrestrial ecosystems are major sinks in the global carbon cycle, sequestering carbon and slowing the increase in CO 2 concentration in the atmosphere [1].The amount of carbon removed from the atmosphere by vegetation via photosynthesis is the gross primary production (GPP).To understand vegetation activity, highly accurate estimation of GPP is important, and satellite remote sensing offers an efficient approach to estimate GPP globally.The Japan Aerospace Exploration Agency (JAXA) plans to launch the Global Change Observation Mission-Climate (GCOM-C) satellite carrying the second-generation global imager (SGLI) sensor in 2014 [2].The SGLI sensor will observe seven spectral bands from the visible to the near infrared (NIR) with a spatial resolution 250 m for land area observations.The obtained data are planned to be used to estimate global GPP.
Many studies have estimated GPP based on the concept of the light-use efficiency (LUE) model [3] using satellite data [1,[4][5][6].In LUE models, GPP is calculated as the product of the maximum LUE (LUE max ), the reduction of LUE max due to environmental stress [7][8][9], the photosynthetically active radiation (PAR), and the fraction of PAR absorbed by the plant canopy (FPAR).LUE max , the stress factor, and leaf area index (LAI) estimations are crucial to the LUE model.The LUE concept has been applied to diagnostic models for estimating GPP, such as the Biosphere Model Integrating Ecophysiological and Mechanistic Approaches Using Satellite Data (BEAMS) [10], as well as machine-learning techniques in conjunction with remote sensing data and flux tower data [11,12].Another approach includes process-based models such as the Boreal Ecosystem Productivity Simulator (BEPS) [13], the two-leaf process-based BEPS model [14], and the Breathing Earth System Simulator (BESS) [15].The two-leaf process-based BEPS model is an hourly process-based diagnostic model that computes canopy-level GPP as the sum of sunlit and shaded leaf groups [14].The BESS model couples atmospheric and land processes including leaf photosynthesis, stomatal conductance, and transpiration of the sunlit and shaded portions of vegetation and soil [15].However, the BESS model includes a major source of uncertainty that originates from satellite-derived LAI [15].Zhang et al. [13] demonstrated that process-based models that separate sunlit and shaded leaves perform better than the LUE model, in which LUE max does not vary spatially and temporally.However, process-based models are more complex and require many parameters, whereas LUE models have the advantage of simplicity.
GPP is affected by seasonal changes in the maximum velocity of carboxylation (V cmax ) [16][17][18][19].The plant physiological parameter of V cmax is estimated using satellite-derived LAI.Therefore, it is worthwhile to directly extract the ecophysiological and physiochemical properties of vegetation from satellite data.To accomplish this, many vegetation indices (VIs) have been developed, such as those related to the chlorophyll content of a leaf or the canopy.One VI uses NIR and green reflectance to estimate the chlorophyll content of a rice canopy [20].The photochemical reflectance index (PRI = [R 531 −R 570 ]/[R 531 +R 570 ]) [21] and the green ratio index (GRI = R 830 /R 550 ) [22]) are used to estimate photosynthetic efficiency and capacity.VIs for estimating chlorophyll include the chlorophyll index, CI = R 880 /R red-edge or green − 1 [23][24][25][26][27][28]; the chlorophyll content index, CCI = D 720 /D 700 (where D x is the first derivative of reflectance at wavelength x [29]); the red-edge position index (REP) [30]; the medium imaging spectrometer (MERIS) terrestrial chlorophyll index (MTCI) [31], which incorporates the REP index; the Transformed Chlorophyll Absorption in Reflectance Index/Optimized Soil-Adjusted Vegetation Index (TCARI [32]/OSAVI [33,34]) [32], which is sensitive to crop chlorophyll concentration and is used to minimize soil background effects; and the modified chlorophyll absorption ratio index (MCARI [35]/OSAVI) [36]).The CI red-edge , CCI, PRI, GRI, TCARO/OSAVI, and MCARI/OSAVI are calculated from hyperspectral satellite sensor data such as those obtained by the Project for On-Board Autonomy (PROBA) satellite carrying a Compact High Resolution Imaging Spectrometer (CHRIS) and by the Earth-Observing 1 (EO-1) satellite carrying the Hyperion imaging spectrometer.These indices cannot be calculated from data retrieved by multispectral satellite sensors such as SGLI and MODIS.
Gitelson et al. [26,37] showed that total canopy chlorophyll content in crops is closely related to midday GPP, and Wu et al. [38] demonstrated the green CI exhibits a linear relationship with chlorophyll content; incident LUE (GPP/PAR) in the morning, which is related to total chlorophyll in the canopy [38][39][40]; and seasonal changes of incident LUE [4].Using the chlorophyll index and incoming PAR, GPP was successfully estimated from LANDSAT data for crops [41] using MODIS data for deciduous and evergreen forest sites [42].This GPP estimation method assumed a linear relationship between incoming PAR and GPP.
Another global GPP estimation model that uses light-response curves has also been applied to VIs to estimate maximum photosynthesis under light saturation (P max ) [43][44][45].These studies have suggested that the VI should be linear to maintain sensitivity over as wide a range of P max as possible and to facilitate scaling and extrapolations across regional and global resolutions.The model, however, did not include weather conditions and used only a single shape of the light-response curve representing temperate vegetation in Japan.Ide et al. [46] analyzed the light-response curve by including weather conditions in a larch forest in Japan.They determined daily P max and the initial slope from seasonal and short-term variations.The seasonal variations in P max and initial slope were correlated with the ratio VI (RVI) or enhanced VI (EVI).These two research approaches estimated GPP using the light-response curve to examine the relationship between GPP and the VI.However, for global GPP estimation, the relationship between P max and VI should be determined more widely in other main biomes.
To estimate global GPP, photosynthesis of a single leaf is key.The leaf photosynthetic rate depends on photosynthetic capacity and photosynthesis reduction.Photosynthetic capacity is influenced by chlorophyll and RuBisCo (ribulose-1, 5-bisphosphate carboxylase/oxygenase) content [47].Photosynthesis reduction is affected by microclimatic factors (i.e., air temperature and vapor pressure deficit) and stomatal opening and closing.The chlorophyll pigment absorbs light energy and converts it to chemical energy, and RuBisCo is an enzyme involved in the first major step of carbon fixation [48].Chlorophyll pigment has the greatest chemical influence on a leaf's spectral properties [49] and can be detected by an optical sensor [50].However, photosynthesis reduction, which fluctuates in the short term (from seconds to minutes), is difficult to detect by an optical sensor alone and may require different techniques.Therefore, we focused on leaf chlorophyll content to estimate leaf photosynthetic capacity.
At the canopy scale, photosynthetic capacity is the integration of single-leaf chlorophyll content and the total leaf area [51].Recent research has suggested that it is better to consider leaf angle distribution in the analysis of canopy photosynthesis [16].We considered canopy photosynthetic capacity as the integration of leaf photosynthetic capacity for the effective leaf area exposed to light.The effective leaf area varies due to canopy structure and leaf angle distribution.We hypothesized that the maximum canopy photosynthesis rate in low-stress conditions is mainly dependent on the total leaf chlorophyll content of the effective leaf area.The objective of this study was to select an appropriate VI to estimate global GPP capacity (photosynthetic capacity) based on the light-response curve concept using GCOM-C/SGLI data (note that SGLI data are not yet available).

VI for Estimating the Maximum Rate of Low-Stress GPP
We defined the GPP under low-stress conditions as GPP capacity.The light-response curve under low-stress conditions using a rectangular hyperbolic function is described as: where GPP capacity (mg•CO 2 •m −2 •s −1 ) is the low-stress GPP, P max_capacity (mg•CO 2 •m −2 •s −1 ) is the maximum GPP capacity under light saturation, α slope is a photosynthetic quantum efficiency representing the initial slope of the light-response curve, and PAR (µmol•m −2 •s −1 ) is photosynthetically active radiation (Figure 1).To apply satellite data for estimating GPP capacity using Equation (1), α slope and P max_capacity should be determined.Leaf physiological research has revealed that the initial slope of the light-response curve depends on the efficiency of light conversion into fixed carbon [52] and the chlorophyll concentration.Furthermore, analysis of flux data has shown that the initial slope of a light-response curve derived from a non-rectangular hyperbolic function changes under different weather conditions; however, the initial slope and P max both exhibit a linear relationship with the same VI [46], suggesting that the initial slope and P max are linearly correlated.On the other hand, other studies have reported that P max is related to the amount of chloroplasts [53,54].From these findings, we in order to reduce the number of parameters, we assume that α slope is a constant for each plant functional type.In addition, we assume that P max_capacity is related to the amount of chlorophyll.From this perspective, we examined the method and VI for estimating P max_capacity from satellite data.
First, we examined spectral reflectance to select potential candidate VIs that show linear correlations with chlorophyll content from a set of VIs.Second, we studied the relationship between candidate VIs and P max_capacity of canopy light-response curves under low-stress conditions.Finally, the selected VI was validated.
is the maximum GPP capacity under light saturation, and α slope is photosynthetic quantum efficiency representing the initial slope of the light-response curve.

Selection of Vegetation Indices (VIs)
At leaf and canopy scales, we resampled spectral reflectance for the following spectral bands of GCOM-C/SGLI: blue ( blue  ; 438-448 nm), green ( green  ; 520-540 nm), red ( red  ; 663.5-683.5 nm), and NIR ( IR N  ; 858.5-878.5 nm), as summarized in Table 1.At the satellite scale, we used data from the MODIS sensor on board the TERRA satellite (MOD09A1.005;8-day land-surface reflectance).The wavelengths of TERRA/MODIS are summarized in Table 1.We used MODIS sensor data in this study because MODIS is the most similar sensor to SGLI in that both have a short repeat cycle (2-4 days), wide swath (>2,000 km), high radiance resolution, moderate spatial resolution (1 km/250 m), and spectrally similar bands.Gitelson et al. [50] suggested that chlorophyll concentration can be derived using reflectance at 550 nm (ρ green ) and 675 nm (ρ red ).For low chlorophyll concentrations, the reflectance sensitivity is higher at the maximum absorption located around 675 nm (ρ red ).At medium to high concentrations, reflectance sensitivity is higher at 550 nm (ρ green ).Thus, we selected several VIs that may relate to chlorophyll content.Moreover, it better to select the VI which has the best linear relationship with chlorophyll content to estimate GPP at the global scale.Because the uncertainty involved in aggregating remote sensing data from smaller to larger spatial scales (up-scaling) is related both to non-linearity in the response function and to heterogeneity within a site.When the response is non-linear, conventional averaging of reflected radiation gives a biased estimate of photosynthesis [49].Spectral reflectance data were used to calculate VIs as illustrated in the following Equations ( 2) to ( 8): (1) The NDVI [55] is the most widely used index for many vegetation applications.However, the NDVI has a saturation problem with very dense vegetation.
NIR red (2) The enhanced VI (EVI) [56] is an improved VI that accounts for the effects of residual atmospheric contamination and soil background.The EVI reduces the saturation problem in various canopies.
(3) The modified NDVI (mNDVI) [57] was developed to eliminate the effects of surface reflectance by incorporating the blue band.This VI is more strongly correlated with total chlorophyll and eliminates the effect of surface reflectance.
NIR red (4) The green and red ratio VI (GRVI) [58] was proposed as an index to monitor the photosynthetically active biomass of plant canopies.The GRVI is calculated from the visible green and red reflectance.
green red (5) The simple ratio index (SR) [59] is probably the first index and is the most commonly used to derive LAI for a forest canopy.
(6) The green NDVI (GNDVI) [50] is a better VI at a higher LAI and is good at detecting chlorophyll.
The GNDVI can detect a wider range of chlorophyll compared to the NDVI.
(7) The green chlorophyll index (CI green ) [25] is sensitive to a wide range of chlorophyll variation.CI green can estimate canopy chlorophyll content under a wide range of canopy conditions.

Data Sets
To investigate relationships between VIs and photosynthesis capacity, data at three scales were used: leaf, canopy, and satellite scales.

Leaf-Scale Data Set
Data sets of the chlorophyll content (μg•cm −2 ) of 19 sampled leaves (minimum chlorophyll content of 0.88 μg•cm −2 , maximum of 50.76 μg•cm −2 , average of 16.08 μg•cm −2 , standard deviation of 14.56 μg•cm −2 ) were used, and reflectance data with a spectral range of 350 to 2,500 nm, were obtained from Furumi et al. [60] for 20 types of leaves measured in various states (fresh green, yellowish green, yellow, red, and dead leaves).

Canopy-Scale Data Set
Eddy covariance (EC) flux data and canopy spectral reflectance of broadleaf deciduous trees at a site in Takayama, Japan, were used.The EC flux data for 2003 and 2004 were used to calculate P max_capacity from the light-response curve.These data were downloaded from AsiaFlux (http://asiaflux.yonsei.kr/)and included the net ecosystem exchange air temperature (T air ; °C), relative humidity (Rh; %), soil temperature (T soil ; °C), vapor pressure deficit (VPD; kPa), and precipitation (PPT; mm).Precipitation data were provided by the Institute for Basin Ecosystem Studies, Gifu University, Japan.Respiration, NEE, and GPP data were provided by the National Institute for Environmental Studies (NIES).The data had a time interval of 30 min.
For canopy reflectance, data measured by a hemispherical spectroradiometer (HSSR; MS-700, EKO Instruments Co., Ltd.) in 2004 were used.The HSSR had a spectral range of 350 to 1,050 nm and spectral interval of 3.3 nm.The data were downloaded from the PEN website (http://www.pheno-eye.org/)[61].Seven EC flux tower sites were selected from Bonan, 1996 [62].These sites correspond to seven of dominant plant functional types.We selected study sites on the basis of online availability and accessibility of necessary parameters.Details of each site are summarized in Table 2.The study sites were representative of C3 grass, arctic (CA-Let); needleleaf deciduous trees (JP-TMK); broadleaf deciduous trees, temperate (JP-TKY); crop-paddy fields (JP-Mase); needleleaf evergreen trees, temperate (JP-FJY); C3 grass (US-Dk1); and broadleaf evergreen trees, tropical (TH-SKR).
All of the EC flux data were used to calculate P max_capacity using the light-response curve.The EC flux datasets were downloaded from the FluxNet project (http://daac.ornl.gov/FLUXNET/fluxnet.shtml) for the JP-Mase site, from AmeriFlux (http://public.ornl.gov/ameriflux)for the US-Dk1 site, from FluxNet Canada (http://www.fluxnet-canada.ca)for the CA-Let site, and from AsiaFlux (http://asiaflux.yonsei.kr/)for the JP-TMK and TH-SKR sites.For the JP-FJY site, original measurement data were downloaded from the Forestry and Forest Products Research Institute (FFPRI) [63].Additionally, we used the level-2 product or original measurement data of AmeriFlux data to reduce errors that may arise in the gap-filling process.The downloaded data were the same parameters as those used for the canopy scale for JP-TKY.The time interval of the data was 30 min.
All data for the year 2003 were used.To examine relationships between VIs and P max_capacity , 8-day composited level-3 global reflectance data from TERRA/MODIS (MOD09A1.005)with 500-m resolution were used.The datasets were downloaded from the Oak Ridge National Laboratory Distributed Active Archive Center (ORNL DAAC; http://daac.ornl.gov/MODIS/),which provides subsets of MODIS Land Products for any tower site in the global FluxNet network by area (from one pixel up to 201 × 201 km) and time period.From the subsets, one center pixel corresponding to the flux tower location was used.

Data Processing
Data processing included two main parts: the reflectance data process for calculating the VI and the photosynthetic capacity calculation processes.At the leaf scale, we analyzed the relationship between SGLI band reflectance and chlorophyll content.At the canopy scale, we analyzed the relationship between SGLI band reflectance and P max_capacity .At the satellite scale, we analyzed the relationship between MOD09A1 and P max_capacity .P max_capacity was calculated from EC flux data by fitting the light-response curve.

Reflectance Data Process
At the leaf and canopy scales, the reflectance was averaged over the wavelength interval of the SGLI sensor (Table 1) to calculate VIs.At the canopy scale, HSSR data between 10:20 a.m. and 10:40 a.m.(Terra overpass time) were averaged for 16-day periods.At the satellite scale, values of band reflectance and quality assurance (QA) descriptions of the surface reflectance data were extracted from the MOD09A1.005data [64].Only data with 'no cloud shadow' and 'clear' cloud-state flags were used; data flagged as 'cloudy,' 'mixed,' and 'not set, assumed clear' were excluded.We then averaged 8-day data to 16-day periods under the following conditions.If the cloud-state flag was 'clear' in both 8-day periods, we used their average value.If 'not clear' appeared in only one dataset, we selected the 8-day period with the clear-state flag.If 'not clear' appear in both datasets, we discarded both datasets.

Photosynthetic Capacity Calculation Processes EC Flux Data Process for Selection of Low-Stress Data
To identify criteria for selecting low-stress conditions, we investigated the diurnal change in net ecosystem production (NEP) by averaging half-hourly NEP over a 16-day period.We used a 16-day period to avoid strong confounding seasonal effects, to have a period long enough to provide sufficient data [65], and to decrease the number of spectral peaks and gaps captured in various types of ecosystem fluxes [66].To find low-stress conditions, we then examined the VPD which is an important cause of the midday depression of net photosynthesis [67].Therefore, we used half-hourly VPD averaged over 16-day periods to select low-stress conditions.The VPD threshold was determined when the midday depression of photosynthesis occurred in the diurnal NEP curve.Photosynthesis and midday depression [68] are shown in Figure 2, which categorizes pattern in the diurnal variation in photosynthesis into three types: (1) a single diurnal peak, which means that no stress occurs; (2) two diurnal peaks, which normally occur in nature; and (3) one peak with severe midday depression, which occurs mostly in drought areas.We used these three patterns to observe midday depression phenomena in the diurnal NEP curve.

P max_capacity Calculation
To draw the light-response curve, GPP capacity data were plotted against PAR.GPP data are typically provided by the FluxNet project.When GPP data were not provided by a flux tower, we calculated GPP as a sum of NEP and ecosystem respiration (Rec).Rec was estimated using nighttime NEP as a function of air temperature.Appendix describes the Rec estimation in detail.P max_capacity and α slope were calculated from the light-response curve by fitting half-hourly GPP capacity data (not averaged) for each 16-day period to PAR.First, GPP capacity values were fitted to the light-response curve (Equation ( 1)) using the least-squares method as a function of PAR.Then, P max_capacity and α slope were determined.GPP capacity values were fitted again as a function of PAR to determine P max_capacity using α slope averaged from each 16-day photosynthesis period over the growing season.The photosynthesis periods used were those for which NEP in daytime was greater than zero.

Validation of the VI
To test the potential of the selected VI to estimate P max_capacity in a different year, we used the empirical relationship between the selected VI and P max_capacity of year 2003.The selected VI was calculated from MOD09A1 for the CA-Let, JPTMK, JP-Mase, and TH-SKR sites in 2002 and the JP-TKY and JP-FJY sites in 2004.We then compared estimated P max_capacity and observed P max_capacity .

Leaf Scale: Relationship between VIs and Chlorophyll Content
The relationship between the reflectance at each SGLI spectral band and chlorophyll content is illustrated in Figure 3. ρ blue was stable at all chlorophyll contents, and ρ NIR was not sensitive to the chlorophyll content.ρ red and ρ green exhibited negative relationship with chlorophyll content.However, when chlorophyll content was more than 25 μg•cm −2 , ρ red remained constant.On the other hand, ρ green exhibited a strong negative relationship with chlorophyll content across a wide range from 0.3 to 50 μg•cm −2 .The seven VIs calculated from Equations ( 2) through ( 8) are shown in Figure 4. mNDVI and NDVI saturated when chlorophyll content was higher than 10 μg•cm −2 , and EVI and GNDVI saturated when chlorophyll content was higher than 20 μg•cm −2 and 35 μg•cm −2 , respectively.EVI, NDVI, GNDVI, and SR were strongly positively correlated with chlorophyll content, with coefficients of determination (R 2 ) of 0.66, 0.68, 0.83, and 0.74, respectively (P < 0.001).GRVI and mNDVI were more weakly correlated with chlorophyll content, with R 2 values of 0.32 (P < 0.05) and 0.58 (P < 0.001), respectively.In contrast, CI green had the strongest linear correlation with chlorophyll content (R 2 = 0.87; P < 0.001).Therefore, CI green , EVI, NDVI, GNDVI, and SR were selected as candidate VIs for the canopy-and satellite-scale analyses.

GPP capacity Selection Criteria
For GPP capacity selection, diurnal NEP and VPD averaged over 16-day periods were examined.The results are shown in Figure 5 for the CA-Let 5(a,b), TH-SKR 5(c,d), and JP-FJY 5(e,f) sites.In Figure 5(a), the midday depression followed Pattern 2 (Figure 2) around 14:00 (local time), as shown by the arrow.In Figure 5(b), VPD at the time of the midday depression was around 2 kPa, as shown by the arrow.Figure 5(c) shows a midday depression for TH-SKR at around noon, indicating Pattern 2 diurnal variation (Figure 2).In Figure 5(d), VPD at the time of the midday depression was around 2 kPa.VPD values for all Japanese sites were less than 2 kPa (Figure 5(f)).Therefore, daytime GPP (PAR > 0) and VPD < 2 kPa (VPD threshold) were applied as GPP capacity selection criteria for each study site.

P max_capacity of the Light-Response Curve from EC Flux Data
To determine P max_capacity and α slope , the relationships between GPP capacity and PAR were examined for broadleaf deciduous temperate trees at JP-TKY in 2003 and 2004, as shown in Figure 6, which illustrates the light-response curve of GPP capacity .The lines represent the fitting curves of each 16-day period with α slope averaged over the growing season.In many cases, the fitted P max_capacity saturated in regions of unrealistically high PAR, such as 2,500 μmol•m −2 •s −1 .Thus, we fixed maximum PAR at 2,000 μmol•m −2 •s −1 and defined the maximum GPP capacity when PAR = 2,000 μmol•m −2 •s −1 as P max_capacity2000 .

Relationship of VIs and P max_capacity2000
The relationships between the five candidate VIs (CI green , EVI, NDVI, GNDVI, and SR) and P max_capacity2000 at the canopy scale are shown in Figure 7.All five indices exhibited strong correlations with P max_capacity2000, with R 2 values of 0.78, 0.62, 0.64, 0.63, and 0.69, respectively (all P < 0.001).EVI, NDVI, GNDVI, and SR became clearly saturated when P max_capacity2000 was more than about 0.4 mg•CO 2 •m −2 •s −1 , whereas CI green did not saturate.The strongest linear correlation occurred for CI green .We obtained the following empirical equation for the relationship between CI green and P max_capacity2000 (mg•CO 2 •m −2 •s −1 ): P max_capacity2000 = 0.13 × CI green − 0.13. Figure 8 presents the relationships between the five candidate VIs (CI green , EVI, NDVI, GNDVI, and SR) and P max_capacity2000 at the satellite scale.EVI, NDVI, GNDVI, and SR exhibited strong correlations with P max_capacity2000 , with R 2 values of 0.63 (P < 0.05), 0.64 (P < 0.05), 0.69 (P < 0.01), and 0.59 (P < 0.05), respectively.However, the strongest linear correlation occurred for CI green (R 2 = 0.72, P < 0.01).Thus, compared to EVI, NDVI, GNDVI, and SR, CI green was the best VI for estimating P max_capacity2000 .We obtained the following empirical equation for the relationship between CI green and P max_capacity2000 (mg•CO 2 •m −2 •s −1 ): P max_capacity2000 = 0.15 × CI green − 0.37.

P max_capacity of the Light-Response Curve from EC Flux Data
The relationships of GPP capacity and PAR for various plant functional types are shown in Figure 9(a-f), which presents results for C3 grass arctic (CA-Let), needleleaf deciduous trees (JP-TMK), crop-paddy fields (JP-Mase), C3 grass (US-Dk1), needleleaf evergreen temperate trees (JP-FJY), and broadleaf evergreen tropical trees (TH-SKR).The lines are the fitting curves for each 16-day period.The highest rate of photosynthesis occurred in late June at JP-TMK, where the P max_capacity2000 was

Relationships of CI green and P max_capacity2000
Figure 10 presents the linear relationships between CI green and P max_capacity2000 for the seven plant functional types.For CA-Let, JP-TMK, JP-TKY, JP-Mase, and JP-FJY, the R 2 values of the CI green −P max_capacity2000 correlations were 0.81, 0.84, 0.67, 0.95, and 0.70, respectively.A linear correlation was not found for TH-SKR, as CI green and P max_capacity2000 changed very little.Additionally, a linear correlation was not observed for US-Dk1.The linear regression functions (y = ax ± b) for CA-Let, JP-TMK, JP-TKY, JP-Mase, and JP-FJY are summarized in Table 4. Differences in these empirical equations reveal the characteristics of each plant functional type.

Validation of CI green
To test the potential of CI green to estimate P max_capacity2000 in a different year, we used the empirical equations of year 2003 (Table 4) and CI green calculated from MOD09A1 for the CA-Let, JP-TMK, JP-Mase, and TH-SKR sites in 2002 and the JP-TKY and JP-FJY sites in 2004.Comparisons of estimated P max_capacity2000 and observed P max_capacity2000 with standard error bars are shown in Figure 11.Estimated P max_capacity2000 was obtained from the empirical equations in Table 4, and observed P max_capacity2000 was calculated from the flux data.Standard errors of estimated P max_capacity2000 were calculated from standard-error propagation of empirical relationships between CI green and P max_capacity2000 .Standard errors of observed P max_capacity2000 were calculated from standard-error propagation of least-square fitting of the light-response curves.The standard errors of the estimated P max_capacity2000 from linear regression were larger than those of observed P max_capacity2000 .Figure 11 shows that the observed P max_capacity2000 values for all plant functional types were within the standard error of the estimated P max_capacity2000 , especially in spring, when most of the plant functional types showed better matching.These results indicate that the CI green and empirical equations successfully estimated P max_capacity2000 for all plant functional types.For TH-SKR, only five periods are shown because most CI green data were affected by clouds.

Discussion
At the leaf scale, the results show that CI green has a strong correlation with variation in leaf chlorophyll content from a wide range of species and leaf development stages (Figure 4).This result agrees with that of Gitelson et al. [50], who demonstrated a wide range of leaf greenness and found that the maximum sensitivity of the reflectance coincides with green absorption.The green wavelength range was also reported to be superior for determining chlorophyll content in eight crops [69].VI based on red reflectance (680 nm) was largely insensitive to variation in chlorophyll content.For most leaves, when light enters the upper surface of a leaf, blue light and red light are absorbed by chloroplasts near the irradiated surface, owing to strong absorption bands of chlorophyll in the blue and red regions of the spectrum.Because blue overlaps with the absorption of carotenoids, it is not generally used for estimation of chlorophyll content [57].The green band wavelength of SGLI ranges from 520 to 540 nm, and the spectral reflectance around 520 nm is determined not only by chlorophyll-a and chlorophyll-b absorption, but also by carotenoid absorption [24].However, the pigments contributing most to light absorption in the PAR region are those that are intimately involved in photosynthesis, namely, chlorophyll a and b and carotenoids [70].Moreover, during the growing season as the chlorophyll content in leaves increases, the spectral features of carotenoids diminish owing to the strong and overlapping absorption by chlorophyll [71].Therefore, the green band of SGLI can serve as a good representative wavelength for estimating leaf chlorophyll content.
Because leaf chlorophyll content increases toward the middle of a leaf [48] and because green light penetrates deeper into the leaf, green reflected light is decreased by chlorophyll content absorption.Thus, green reflected light is very effective for detecting chlorophyll content and can represent leaf photosynthesis.To select an appropriate VI for estimating chlorophyll content, we chose CI green because NIR is insensitive to chlorophyll content and the ratio between the insensitive and sensitive bands can minimize the variations in leaf-scattering properties [72].Furthermore, the reflectance of NIR and green wavelengths has a strong linear correlation with chlorophyll content [72][73][74].Therefore, CI green is suitable for estimating leaf chlorophyll content.
Yoder and Waring [75] found that the chlorophyll concentration of sun-exposed canopy was closely related to both leaf and canopy photosynthetic capacity in a Douglas fir canopy in a controlled environment.The correlation coefficient for sun-exposed canopy was higher than that for shaded canopy.Moreover, the NDVI calculated using a narrow green band (565-575 nm) was best correlated with photosynthesis potential under sunlight.Thus, it is possible to estimate the photosynthetic capacity of a sun-exposed canopy by integrating the leaf photosynthetic capacity.
At the canopy and satellite scales, P max_capacity2000 was used instead of the canopy chlorophyll content because chlorophyll content within a vegetation canopy is positively related to the productivity of that vegetation [31].To obtain P max_capacity from the light-response curve, some researchers have applied a non-rectangular hyperbolic equation [46,[76][77][78] with three main parameters: initial slope, P max , and convexity.A non-rectangular hyperbola yielded a better fit than a rectangular hyperbola equation with only two parameters (initial slope and P max ).However, we chose to use a rectangular hyperbola (Equation ( 1)) to obtain P max_capacity with constant α slope to simplify the methodology and minimize the number of parameters [79][80][81][82].Our results demonstrate the applicability of the rectangular hyperbola using constant α slope for calculating P max_capacity2000 for each plant functional type.
To estimate GPP at the global scale, we prefer the VI which has linear relation with chlorophyll content and P max_capacity2000 .If we use the VI which has exponential relation with chlorophyll content and P max_capacity2000 , it may cause big error in high chlorophyll content or P max_capacity2000 region.In big VI region, and with exponential form VI, small error of VI makes big error of chlorophyll content and P max_capacity2000 .Therefore, we selected VIs that had linear correlations with P max_capacity2000 .The CI green showed a strong linear correlation (R 2 > 0.67) with P max_capacity2000 for each of the plant functional types and did not have saturation problems in various plant-canopy structures.Linear correlations between remote sensing-obtained VI values and GPP from local flux measurements were found in North American vegetation [83], evergreen needle leaf forests [84], deciduous broadleaf forests [85], and Amazon rainforests [86].However, these studies did not use GPP in low-stress conditions and the linear regressions showed some scattered data [51].
In Figure 10, linear correlations were observed at every site except US-Dk1 and TH-SKR.US-Dk1 has a spatial resolution problem with MOD09.US-Dk1 covers approximately 480 × 305 m, which is less than the MOD09 1-km spatial resolution [87].Furthermore, the CI green range of 3.5-6.5 is relatively high for grassland, suggesting contamination by light reflected from surrounding evergreen and deciduous forests.Similarly, linear correlations were not found at TH-SKR, where CI green and large photosynthetic capacity changed less year-round.These results indicate that when canopy greenness is stable, other meteorological factors will play limiting roles for GPP [42].The maximum and minimum of P max_capacity2000 at TH-SKR in 2003 were 1.37 and 0.94 mg•CO 2 •m −2 •s −1 , respectively.These results are consistent with those of Aguilos et al. [88], who reported that maximum and minimum values of the saturation point of photosynthesis (GPP max ) at TH-SKR in 2003 were 1.54 and 0.82 mg•CO 2 •m −2 •s −1 , respectively.Tropical forests have the least seasonality in terms of carbon absorption, emission, and greenness [89].JP-FJY is generally classified as a needleleaf evergreen forest, but seasonal changes in leaves occur.Our results agree with those of Ohtani et al. [90], who found that the seasonal change in LAI at JP-FJY ranged from 3 to 5. Needle-fall and expansion mainly occurred in November and May, respectively.The LAI increased rapidly in early May, reached a maximum in midsummer, and then decreased from September to November.Moreover, for further global GPP estimation, we may use the same empirical linear equation for evergreen forest sites JP-FJY and TH-SKR (P max_capacity2000 = 0.001 × CI green + 0.006; R 2 = 0.44, P<0.01).P max_capacity2000 can be converted to the maximum incident LUE (GPP/PAR) as shown in Figure 10.Observed CI represents different growth states and is related to seasonal changes of incident LUE in a similar manner as for wheat [38].This method has good potential for estimating seasonal changes of maximum incident LUE from CI green .
Our P max_capacity2000 estimation concept is more similar to the greenness and radiation (GR) model [37,39,42] than to the LUE model.However, the framework for the estimation of GPP capacity differs from those of both the GR and LUE models.The GR and LUE models assume a linear relationship between GPP and incident PAR or PAR during an integral time such as 1 day or 1 month.Our GPP capacity estimation framework introduced a non-linear relationship between photosynthesis velocity and PAR.P max_capacity was the parameter of the photosynthesis response curve (Equation ( 1)) and was estimated from CI green .Using this parameter, the photosynthesis response curve was determined.Using the response curve and PAR data, the velocity of GPP capacity was estimated.For calculation of GPP during a particular time frame, integration of the velocity of GPP capacity is required.Our GPP capacity estimation framework is the differential form.
Moreover, our approach coincides with that of Gitelson et al. [41], who discussed that uncertainty in their crop GPP estimation model (GPP ∝ VI × PAR potential ) arose because of its failure to detect variation in GPP related to short-term (minutes to hours) changes in controlling factors that do not immediately affect crop chlorophyll content.And Hashimoto et al. [91] discussed that although annual mean LAI correlates well with annual GPP, seasonal LAI correlates poorly with seasonal GPP because it does not respond to short term stresses such as anomalous heat waves.Therefore, our approach using a VI to estimate GPP under the low-stress condition (GPP capacity ) is quite efficient.
In the present study, we applied a VI to estimate canopy chlorophyll content of the effective leaf area exposed to light.The next step is to refine the effective leaf area by incorporating plant structural characteristics, such as leaf angle orientation and sunlit/shaded leaf and foliar clumping, which are important to GPP estimation because they affect light interception by leaves and light penetration into the canopy [16,17,92] and produce bidirectional reflectance effects in the canopy.In future studies, variation in the slope of the linear correlation between CI green and P max_capacity2000 for each plant functional type should be compared with results from a radiative transfer model that can predict the radiative transfer of solar energy or changes in leaf physiology as canopy profiles adapt to sunlight [75].

Conclusion
To accurately estimate the maximum rate of low-stress GPP (called "GPP capacity ") based on the light-response curve, an appropriate VI was selected.The green chlorophyll index, CI green (ρ NIR /ρ green -1), had a strong linear correlation with chlorophyll content at the leaf scale and with GPP capacity at the canopy and satellite scales.We demonstrated that CI green could capture seasonal changes and variation in photosynthesis patterns in six main plant functional types.Therefore, we consider CI green to be suitable for GPP capacity estimation globally, especially for GCOM-C/SGLI satellite data.Nevertheless, CI green should be validated further in different areas and with other plant functional types [93] to test its robustness and sensitivity over a global range of vegetation conditions.
For implementation of GPP capacity global estimation using GCOM-C/SGLI, we should first calculate CI green from satellite data and use the empirical linear equation from Table 4 to estimate the P max_capacity2000 (the maximum GPP capacity when PAR = 2,000 μmol•m −2 •s −1 ).The P max_capacity (the maximum GPP capacity under light saturation) in Equation (1) should be calculated using P max_capacity2000 , PAR of 2,000 μmol•m −2 •s −1 and α slope (photosynthetic quantum efficiency) in Table 3 for each plant functional type.Then, GPP capacity should be estimated with the PAR obtained by satellite using Equation (1).
Additionally, in the future, the global GPP capacity can be combined with vegetation stress maps to estimate global GPP.Stress maps may be calculated from environmental conditions such as the vapor pressure deficit, leaf water potential, and soil water content.We expect that our approach will be useful for improving the accuracy of global GPP estimations derived from satellite data.

Figure 1 .
Figure 1.Canopy light-response curve.Low-stress global gross primary production(GPP capacity ) (mg•CO 2 •m −2 •s −1 ) is the low-stress GPP, P max_capacity (mg•CO 2 •m −2 •s −1 )is the maximum GPP capacity under light saturation, and α slope is photosynthetic quantum efficiency representing the initial slope of the light-response curve.

Figure 2 .
Figure 2. Three patterns of diurnal variation in net ecosystem production for the photosynthesis.Pattern 1: a single diurnal peak, indicating that no stress occurs; Pattern 2: two diurnal peaks, which is a common occurrence in nature; and Pattern 3: one peak with severe midday depression, which occurs mostly in drought areas.

Figure 3 .
Figure 3. Relationship between the reflectance at each SGLI spectral band and the leaf chlorophyll content.

Figure 5 .
Figure 5.Diurnal variation in the mean half-hourly dataset over 16-day periods: (a) net ecosystem production (NEP), (b) vapor pressure deficit (VPD) at CA-Let, (c) NEP and (d) VPD at TH-SKR, and (e) NEP and (f) VPD at JP-FJY.Arrows indicate the timing of the midday depression.

Figure 6 .
Figure 6.Light-response curve of low-stress GPP (GPP capacity ) and PAR in broadleaf deciduous temperate trees (JP-TKY) in (a) 2003 and (b) 2004.Lines represent the least-squares fitting curve for each 16-day period.Dots in different colors indicate half-hourly data (no average) of each 16-day period of GPP capacity .

Figure 7 .
Figure 7.The best fit regression of the linear relationships between various VIs calculated from daily HSSR datasets and P max_capacity2000 of broadleaf deciduous temperate trees at JP-TKY 2004 at the canopy scale: (a) CI green , (b) EVI, (c) NDVI, (d) GNDVI, and (e) SR.

Figure 8 .
Figure 8.The best fit regression of the linear relationships between various VIs from 16-day-period MOD09A1 data and P max_capacity2000 of broadleaf deciduous temperate trees at JP-TKY 2004 at the satellite scale: (a) CI green , (b) EVI, (c) NDVI, (d) GNDVI, and (e) SR.

Figure 10 .
Figure 10.Relationships between CI green calculated from 16-day period MOD09A1 data and P max_capacity2000 and maximum light-use efficiency (LUE max ) for the seven plant functional types in 2003.

Table 2 .
Description of the study sites representing seven plant functional types.

Table 3 .
Summary of the growing season average P max_capacity2000 and initial slope, and the VPD threshold for the seven plant functional types.
* Averaged values (averaged over growing season), T soil = Soil temperature, T air = Air temperature, VPD = Vapor Pressure Deficit; ** Rec was not calculated because AmeriFlux provided GPP for this site.