## 1 Introduction
VIs for estimating chlorophyll include the chlorophyll index, CI = R\({}_{880}\)/R\({}_{\mathrm{red-edge~{}or~{}green}}-1\)[23, 24, 25, 26, 27, 28]; the chlorophyll content index, CCI = D\({}_{720}\)/D\({}_{700}\) (where D\({}_{\mathrm{x}}\) 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\({}_{\mathrm{red-edge}}\), 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. [PERSON] _et al._[26, 37] showed that total canopy chlorophyll content in crops is closely related to midday GPP, and [PERSON] _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\({}_{\text{max}}\)) [43, 44, 45]. These studies have suggested that the VI should be linear to maintain sensitivity over as wide a range of P\({}_{\text{max}}\) 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. [PERSON] _et al._[46] analyzed the light-response curve by including weather conditions in a larch forest in Japan. They determined daily P\({}_{\text{max}}\) and the initial slope from seasonal and short-term variations. The seasonal variations in P\({}_{\text{max}}\) 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\({}_{\text{max}}\) 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.