# Effect of the Partitioning of Diffuse and Direct APAR on GPP Estimation
###### Abstract  
Accurate estimation of gross primary productivity (GPP) is necessary to better understand the interaction of global terrestrial ecosystems with climate change and human activities. Light use efficiency (LUE)-based GPP models are widely used for retrieving several GPP products with various temporal and spatial resolutions. However, most LUE-based models assume a clear-sky condition, and the influence of diffuse radiation on GPP estimations has not been well considered. In this paper, a diffuse and direct (DDA) absorbed photosynthetically active radiation (APAR)-based method is proposed for better estimation of half-hourly GPP, which partitions APAR under diffuse and direct radiation conditions. Firstly, energy balance residual (EBR) FAPAR, moderate resolution imaging spectroradiometer (MODIS) leaf area index (LAI) (MCD15A2H) and clumping index (CI) products, as well as solar radiation records supplied by FLUXNET2015 were used to calculate diffuse and direct APAR at a half-hourly scale. Then, an eddy covariance-LUE (EC-LUE) model and meteorological observations from FLUXNET2015 data sets were used for obtaining corresponding LUE values. A co-variation relationship between LUE and diffuse fraction was observed, and the LUE was higher under more diffuse radiation conditions. Finally, the DDA-based method was tested using the half-hourly FLUXNET GPP and compared with half-hourly GPP calculated using total APAR (GPP_TA). The results indicated that the half-hourly GPP estimated using the DDA-based method (GPP_DDA) was more accurate, giving higher R\({}^{2}\) values, lower RMSE and RMSE\({}^{*}\) values (R\({}^{2}\) varied from 0.565 to 0.682, RMSE ranged from 3.219 to 12.405 and RMSE\({}^{*}\) were within the range of 2.785 to 8.395) than the GPP_TA (R\({}^{2}\) varied from 0.558 to 0.653, RMSE ranged from 3.407 to 13.081 and RMSE\({}^{*}\) were within the range of 3.321 to 9.625) across FLUXNET sites within different vegetation types. This study explored the effects of partitioning the diffuse and direct APAR on half-hourly GPP estimations, which demonstrates a higher agreement with FLUXNET GPP than total APAR-based GPP. EC-LUE [9]. In the LUE-based models, GPP is calculated as the product of absorbed photosynthetically active radiation (APAR) and actual LUE attenuating from several meteorological stressed scalars. However, most LUE-based models hypothesize a clear-sky condition, which leads to an overestimation of GPP for all-sky conditions [10]. The MODIS GPP algorithm (MOD17) is commonly used in various studies, while the uncertainties originated from the model inputs, containing actual LUE attenuating from the maximum LUE by meteorological scalars, APAR obtaining from flux observations and remote sensing products cannot be ignored [11; 12; 13; 14; 15; 16; 17; 18; 19; 20]. Meanwhile, the calculation of GPP with a total incident radiation or a constant LUE value under a total-sky condition (both direct and diffuse conditions) often leads to an overestimation of GPP values absorbing the illumination without light saturation [21; 22; 23; 24]. In addition, [PERSON] et al. [25] pointed out that the MOD17 product results in an underestimation caused by the bias of the MODIS FAPAR product and an overestimation under higher illuminative conditions. Generally, GPP estimates under cloudy-sky conditions are commonly greater than clear-sky values. In addition, the existence of clouds may reduce the direct radiation while increasing the diffuse radiation. LUE displays a lower value for sunlit leaves because of the light saturation, while the shaded leaves receive little radiation under clear-sky conditions and absorb more diffuse radiation under cloudy-sky conditions [21; 26; 27]. As a result, LUE values for the whole canopy can be increased under cloudy-sky conditions [22; 28; 29]. Therefore, the bias derived from the diffuse radiation must be calibrated to accurately model LUE. On that basis, GPP can be estimated under different radiation conditions.