Terrestrial ecosystems are major sinks in the global carbon cycle, sequestering carbon and slowing the increase in CO₂ 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 [1,4–6]. In LUE models, GPP is calculated as the product of the maximum LUE (LUE_max), the reduction of LUE_max due to environmental stress [7–9], 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 (Vcmax) [16–19]. 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 = [R₅₃₁−R₅₇₀]/[R₅₃₁+R₅₇₀]) [21] and the green ratio index (GRI = R₈₃₀/R₅₅₀) [22]) are used to estimate photosynthetic efficiency and capacity. VIs for estimating chlorophyll include the chlorophyll index, CI = R₈₈₀/R_{red-edge or green} − 1 [23–28]; the chlorophyll content index, CCI = D₇₂₀/D₇₀₀ (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 [38–40]; 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) [43–45]. 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).

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 [72–74]. 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 [46,76–78] 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 [79–82]. 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 (R² > 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·CO₂·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·CO₂·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 JPFJY and TH-SKR (P_{max_capacity2000} = 0.001 × CI_green + 0.006; R² = 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].

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.