## 5 Conclusions  
The use of two state-of-the-art machine learning techniques (ELM and ANFIS) was undertaken in this investigation as a major contribution to the study of carbon flux estimation in terrestrial ecosystems. This contribution is expected to exert a considerable effect upon elucidating the biophysical mechanisms that dominate the exchanges of carbon dioxide between the land surface and atmosphere. More specifically, in this study, four modeling techniques were used and compared for estimating daily carbon fluxes in five different types of ecosystems. Moreover, the effects of internal algorithms on each method were also appraised based on four performance indices (\(R2\), IA, RMSE, and MAE). Our results demonstrated that machine learning models were able to effectively quantify the nonlinear processes that control the variation of carbon fluxes, especially for GPP and \(R\), between the land surface and atmosphere, using the limited climatic factors. The estimates from the novel ELM and ANFIS models were highly satisfactory. Their estimates were comparable to those of the conventional ANN and SVM models. On the whole, although the ANN method performed the best for each flux at the five sites, the ELM and ANFIS methods should be strongly recommended mainly due to their robustness and flexibility. In addition, in practical terms, the ELM and ANFIS approaches, in comparison with traditional ANN and SVM methods, require fewer parameters to be selected and optimized. In particular, for the ELM method, the computational time was substantially reduced. Moreover, it was found that the generalization ability of each method was dependent upon their respective internal parameters considered in this study. Specifically, the most widely utilized Levenberg-Marquardt algorithm in the ANN method was not the universally optimal choice for any of the carbon fluxes at the study sites. The ELM models with the sine and sigmoid transfer functions provided similar modeling accuracy and were consistently superior to the ELM model with the hard limit function. Among the three kernel functions for the SVM method, the RBF kernel function generated the most accurate estimates and substantially outperformed the polynomial and sigmoid functions. When the grid partitioning algorithm was used to generate the FISs, the modeling performance of the ANFIS approach appreciably differed among the different membership functions. In addition, the subtractive clustering and fuzzy c-means algorithms in the ANFIS method generally achieved similar estimates and performed substantially better than the grid partitioning algorithm. Among the five sites, considerable differences were found in the estimated accuracy of each flux. In general, the models performed the best in forest ecosystems for the three fluxes, including those of the CA-Oas and CA-Obs sites, and provided the worst estimates of both GPP and \(R\) in cropland ecosystem fluxes and of NEE in the grassland ecosystem. Our findings show that the two newly proposed ELM and ANFIS methods can be considered as desirable complements to conventional machine learning methods for characterizing land-atmospherecarbon fluxes. However, it is likely that these intelligent approaches will be criticized, predominantly owing to the lack of clarity regarding the intrinsic mechanisms of well-trained models. This criticism reduces, to some extent, their reliability and then hinders their applications and popularity. Therefore, in theory, more efforts should be made to uncover the hidden and useful knowledge from these black boxes in future work. Furthermore, another alternative solution can be considered: machine learning methods can be utilized in conjunction with physically based models through correction in the latter models. This combination is inspired by the fact that machine learning techniques and physically based methods can complement each other.