## 4 Discussion  
### The Ability of the Three LUE Models to Simulate GPP  
At the half-hourly temporal scale, TL-LUEn and TL-LUE performed better than MOD17 for three types of forests (MF, BF, and NF), GRASS and SHRUB and their differences between these vegetation types are significant. With the increase of temporal scales, the improvement of TL-LUEn and TL-LUE over MOD17 gradually became less distinct. The changes in the ability of TL-LUEn, TL-LUE, and MOD17 to simulate GPP with vegetation types and temporal scales are, at least in part, related to the different structure of various vegetation types and the different response of canopy GPP to incident PAR described by three models. It was found that scaling up in time tended to linearize the relationship between CO\({}_{2}\) flux and PAR [99]. Observations also showed that changes in canopy GPP with incident PAR are nonlinear at the half-hourly scale and become approximately linear at the daily and 8-day scales [29]. GPP simulated by MOD17 always linearly increase with incident PAR while the increase of GPP with incident PAR is nonlinear in both TL-LUEn and TL-LUE. The non-linearity of TL-LUEn and TL-LUE can be modified through changing parameters _cm_, \(\beta\), _cmsu_, and _cmsh_. For example, if _cmsu_ equals _cmsh_ in the TL-LUE model, the response of simulated canopy GPP to incident PAR would be close to linear. This is the reason why the improvement of TL-LUEn and TL-LUE over MOD17 is much smaller at the 8-day scale than at the half-hourly temporal scale. The better performance of TL-LUEn and TL-LUE models over MOD17 changed with vegetation types, most significantly for forests, then for SHRUB, GRASS. [PERSON] _et al_. [113] pointed out that the canopy CO\({}_{2}\) exchange rates of crops is a quasi-linear function of absorbed PAR. In contrast, forestsand sparse vegetation often show a markedly nonlinear response of canopy CO\({}_{2}\) exchange rates to absorbed PAR [99, 113, 114]. TL-LUEn and TL-LUE are able to capture both the nonlinear and linear responses of GPP to incident PAR while MOD17 is only able to describe the linear change of canopy GPP with incident PAR. Therefore, TL-LUEn and TL-LUE outperform MOD17 for forests, shrub and grass sites. The higher performance is the most significant for forests at the half-hourly scale. The linear response of GPP to PAR in MOD17 led to the underestimation/overestimation of GPP under conditions of low/high incident PAR, which has been confirmed by [PERSON] _et al._[22] and [PERSON] _et al._[23]. TL-LUEn and TL-LUE were, at least partially, able to correct this weakness. Figures 6-8 show the RMSE of simulated GPP as a function of incident PAR at three different temporal scales. Under medium PAR conditions, TL-LUEn, TL-LUE, and MOD17 performed similarly. The improvement of TL-LUEn and TL-LUE over MOD17 mainly occurred under low or high incident PAR conditions. Figure 6: The RMSE of modeled GPP against tower-derived GPP within different photosynthetically active radiation (PAR) classes for six different vegetation types: **(a)** BF, **(b)** CROP, **(c)** GRASS, **(d)** MF, **(e)** NF and **(f)** SHRUB, at the half-hourly scale. The ratio of diffuse to direct PAR changed with clearness index. Under conditions of low clearness index, canopy LUE is high [23] owing to more diffuse PAR being absorbed by shaded leaves with high LUE. MOD17 did not differentiate the different effects of diffuse and direct PAR on GPP and tended to underestimate/overestimate GPP under low/high clearness index conditions (Figure 9). In TL-LUEn and TL-LUE, incident PAR is first decomposed into diffuse and direct components according to clearness index. Under conditions of low clearness index, increased diffuse PAR will be mainly absorbed by shaded leaves, which have high LUE. Thus, GPP simulated by TL-LUEn and TL-LUE is higher than that simulated by MOD17 (Figure 9). In contrast, when clearness index is high, increased direct PAR will be mostly absorbed by sunlit leaves, which have low LUE.