## 3 Results
### Modeling of Hourly Carbon Fluxes  
To examine the modeling ability of machine learning methods at a finer time scale, we further use these approaches to estimate hourly carbon fluxes at the three sites. The results estimated by different models with four input variables in the testing period are shown in Table 9. It should be noted that the gap-filled hourly carbon flux data were not used for these estimates. The number of observed NEE data available in the testing period in Table 9 is 5865 (2009), 6233 (2008) and 6099 (2010) for CA-Obs, CA-Oas and CA-Gro, respectively. As a whole, the machine learning models accurately quantify hourly carbon fluxes at the three sites. They consistently and substantially outperform the MLR model for GPP and NEE estimates in terms of \(R^{2}\), NSE, Bias and RMSE, while for \(R\) estimates, the MLR model achieves satisfactory results comparable to those of machine learning models. Specifically, for the comparison among the three sites in the prediction of hourly GPP, the developed machine learning models offered the highest accuracy at CA-Obs site, followed by CA-Oas site. Regarding the estimates of hourly \(R\) among the three sites, according to the \(R^{2}\) indictor, the applied models perform the best at CA-Gro site, whereas they provide the worst statistical results with respect to NSE, Bias and RMSE indices. On the whole, these models generate the best \(R\) estimates in terms of NSE, Bias and RMSE. For NEE estimates, the machine learning models give similar results at both CA-Obs and CA-Oas sites, and slightly perform better than the models at CA-Gro site. Figure 6: Eddy covariance measured and model simulated daily net ecosystem exchange (NEE) in the whole period in the three boreal forest stands. (**a**) For CA-Obs stand using ANN model; (**b**) for CA-Oas stand using ANFIS model; and (**c**) for CA-Gro stand using GRNN model. As commonly known in the eddy covariance community, the requirement for turbulent atmospheric conditions limits the quality of data observed by the eddy covariance technique. Half-hourly NEE data are directly measured and may be rejected due to low turbulence conditions. The majority of missing NEE data occur during nighttime. Therefore, it is essential to provide some insights into the modeling ability of our proposed models for nighttime and daytime NEE data. In this study, the identification of nighttime and daytime was according to the values of photosynthetic photon flux density (PPFD). A positive PPFD implied daytime, while nighttime was defined by the periods of the day without light (the values of PPFD were equal to zero). The comparisons of different models with four input variables for predicting hourly NEE in the testing period for daytime and nighttime datasets at the three sites are summarized in Table 10. As can be seen from the Tables 9 and 10, the NEE estimates of each model for the daytime data at both CA-Obs and CA-Oas sites are similar to those for all the data (daytime + nighttime), and are considerably better than those for the nighttime data. In contrast, at CA-Gro site, all the models (except MLR) for the daytime and nighttime data give similar estimates according to the \(R^{2}\) performance index (Table 10), while in terms of the NSE index, the estimates from all the models for the daytime data are consistently superior to those for the nighttime data. As a case study, Figure 7 illustrates hourly NEE between eddy covariance measured and predicted by the ANFIS model in the testing period. The daily courses of hourly measured and predicted NEE flux for 7 days during the mid-growing season at the three sites are displayed in Figure 7a-c. It can be clearly seen that most of the modeled NEE values at the three sites well match the corresponding observed ones. In comparison with the estimates at both CA-Oas and CA-Gro sites, the simulated NEE values at CA-Obs site more closely match the corresponding measured ones.