## 1 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 (\(\text{LUE}_{\text{max}}\)), the reduction of \(\text{LUE}_{\text{max}}\) due to environmental stress [7, 8, 9], the photosynthetically activeradiation (PAR), and the fraction of PAR absorbed by the plant canopy (FPAR). \(\mathrm{LUE_{max}}\), 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]. [PERSON] _et al._[13] demonstrated that process-based models that separate sunlit and shaded leaves perform better than the LUE model, in which \(\mathrm{LUE_{max}}\) 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\({}_{\mathrm{cmax}}\)) [16, 17, 18, 19]. The plant physiological parameter of V\({}_{\mathrm{cmax}}\) 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.