## 1 Introduction  
Efforts to mitigate climate change require the stabilization of atmospheric CO\({}_{2}\) concentrations [1], which is significantly regulated by exchanges of carbon between terrestrial ecosystems and the atmosphere. Terrestrial gross primary productivity (GPP) is the largest component of the global carbon flux [2] and about 120 Pg C year\({}^{-1}\) globally, considerably larger than the carbon annually emitted by human activities (about 9 Pg C year\({}^{-1}\)) [3]. Consequently, even a small change in GPP is likely to have a significant impact on atmospheric CO\({}_{2}\) concentration. Thus, accurately simulating terrestrial GPP is of great significance to quantifying the global carbon cycle and predicting the future trajectories of the atmospheric CO\({}_{2}\) concentration. Two approaches have been widely employed to investigate the spatial and temporal variability in GPP using remotely sensed data: (i) remote sensing driven process-based models, and (ii) light use efficiency (LUE) models [4]. The former is based on the mechanistic description of the photosynthetic biochemical processes and scales the Farquhar instantaneous leaf-level biochemical model [5] to the canopy level using big-leaf, two-leaf, and multilayer scaling approaches. A number of process-based models have been successfully applied to quantify spatial-temporal variations of GPP at regional and global scales using remotely sensed vegetation parameters, such as leaf area index (LAI) and land cover types, as inputs. However, the application of these process-based models is limited by the complexity and uncertainty of their parameterization [6]. In contrast, LUE models, such as CASA [7], MOD17 [8], EC-LUE [9], and VPM [10], were developed according to the LUE argument of [PERSON] [11, 12] that productivity is linearly related to the amount of absorbed photosynthetically active radiation (APAR). A fundamental assumption underlying LUE models is that plant canopies behave like a big single-leaf and their LUE is independent of the directional nature of solar radiation and vegetation structure [13]. Many studies have indicated that both GPP and LUE vary with both quantity and quality of incoming solar radiation. [PERSON] _et al._[14] detected a 20% increase in Harvard Forest photosynthesis after the 1991 Pinatubo eruption owing to the increase of diffuse radiation caused by volcanic aerosols. Flux site data indicated that canopy LUE was enhanced under diffuse sunlight in comparison with that under direct radiation [13, 15, 16]. [PERSON] _et al._[17] estimated an increase of 110% in crop LUE under diffuse radiation. [PERSON] _et al._[18] conducted a study for three forest sites (two broadleaf and one needleleaf) and found that the canopy LUE was enhanced by 6-33% under diffuse radiation. [PERSON] [19] indicated that the enhancement of canopy LUE due to diffuse radiation varied with vegetation types, most significantly for tundra shrubs. [PERSON] _et al._[20] found that a single-leaf LUE model performed very well for a 56-year-old Douglas-fr stand when, instead of using total incident photosynthetically active radiation (PAR), they used the sum of incident diffuse PAR and a relatively small fixed fraction (22%) of incident direct PAR. Recently, [PERSON] _et al._[21] reported that canopy LUE generally decreased with increasing sky clearness index, which is the ratio of solar radiation observed on the ground to radiation received at the top of the atmosphere, over 5 ChinaFLUX sites, including a temperate forest, a subtropical forest, a tropical rain forest, and two grassland sites. Therefore, the assumption that LUE is independent of the quality of radiation and GPP linearly increases with absorbed photosynthetic radiation would induce underestimation/overestimation of GPP in cloudy/clear skies [22, 23]. Conceptually, a canopy is composed of clumps of sunlit and shaded leaves exposed to different levels of irradiance and showing variable LUE.