## 1 Introduction
Sunlit leaves receive both direct and diffuse radiation while shaded leaves mainly interact with diffuse beams. Under clear skies, solar irradiance is high and dominated by direct beams. Sunlit leaves are easily light saturated, and photosynthesis can even decrease with increasing radiation because of elevated temperature and enhanced photorespiration [13]. Consequently, the overall LUE of sunlit leaves is normally low [23]. In contrast, a large number of shaded leaves are only exposed to diffuse radiation, which is normally much lower than the radiation saturation point. Therefore, the photosynthesis of shaded leaves is typically light-limited. Under cloudy conditions, solar irradiance is dominated by diffuse sunlight, allowing shaded leaves to capture a large fraction of the solar irradiance. Even though the total incident radiation may be lower than that on clear days, the apparent improvement of the LUE for shaded leaves could lead to the enhanced LUE for the whole canopy [15, 19]. More and more process models now calculate photosynthesis for sunlit and shade leaves separately [24, 25, 26]. However, this strategy has not been adopted by LUE models. To remedy this limitation, [PERSON] _et al._[23] recently developed a two-leaf LUE model on the basis of the MOD17 model. This new model considered differences in radiation absorption and in LUE of sunlit and shaded leaves. Validation at 6 ChinaFLUX sites demonstrated the improvement of the two-leaf LUE models over the MOD17 model in simulating GPP, especially at forest sites, with a R\({}^{2}\) value increasing about 0.1 and a root mean square error (RMSE) value decreasing about 0.64 g C m\({}^{-2}\) day\({}^{-1}\) on average. In the two-leaf LUE model developed by [PERSON] _et al._[23], GPP of sunlit and shaded leaves increases linearly with APAR. However, many studies have shown a nonlinear increase of photosynthesis of sunlit leaves with increasing APAR because of light saturation of photosynthesis, especially at short temporal scales (minutes to hours) [15, 27, 28, 29, 30, 31]. Recently, [PERSON] _et al._[6] developed a two-leaf temperature and vegetation type dependent rectangular hyperbolic model, which links quantum yield (\(\alpha\)) and maximum photosynthetic rate (\(P_{m}\)) with the maximum carboxylation rate at 25 \({}^{\circ}\)C. The model is able to simulate GPP as accurately as a process-based model. Previously, linear LUE models have been mostly used to calculate GPP at daily, 8-day, and even longer temporal scales [7, 8, 9, 10, 32, 33]. Recently, this type of models is used to calculate GPP at short temporal scales. For example, Carbon Tracker, a system to optimize terrestrial carbon flux, uses the Carnegie-Ames Stanford Approach (CASA) biogeochemical model to calculate GPP every three hours as the prior carbon flux [34]. Such application of linear LUE models might induce biases in simulated GPP since observations have indicated the nonlinear response of canopy GPP to incoming PAR at short temporal scales [15, 27, 28, 29, 30, 31]. Therefore, the assessment of applicability of different types of LUE models in simulating GPP at different temporal scales is of great significance to improving the simulation of GPP using remote sensing data. In this study, the ability of nonlinear two-leaf LUE, linear two-leaf LUE, and MOD17 to simulate GPP at half-hourly, daily, and 8-day temporal scales were verified using GPP derived from net ecosystem productivity (NEP) measured at globally distributed 58 sites as benchmarks. The main goals of this study are: (1) to compare the performance of the MOD17, linear and nonlinear two-leaf LUE models at three different temporal scales (half-hourly, daily and 8-day); (2) to analyze the possible causes for the different performances of three LUE models. For simplicity, the MOD17, linear two-leaf LUE, and nonlinear two-leaf LUE models will be referred to hereinafter as MOD17, TL-LUE, and TL-LUEn, respectively.