# Modeling and Predicting Carbon and Water Fluxes Using Data-Driven Techniques in a Forest Ecosystem
## 4 Discussion
[71] used the regression tree model to predict the NEE using two different types of remote sensing data and obtained satisfactory results with \(R^{2}\) = 0.70 for Landsat data and \(R^{2}\) = 0.68 for MODIS data during 2005-2006. By comparing with these results, on the whole, our proposed models achieved higher accuracy with the average value of \(R^{2}\) =0.77 in 2009. In conclusion, our presently proposed models and aforementioned regression tree method have great potential for estimating carbon fluxes, and can be considered as alternative tools to scale up eddy covariance-measured carbon flux data to regional or global scale across different vegetation types. Furthermore, the seasonal and inter-annual variability in each flux caused by the environmental forcing variables can be satisfactorily captured (Figures 3 and 4). It is noteworthy to point out that appreciable underestimations of the peaks during the growing season and annual total carbon and water fluxes by most of the used models occurred both in the validation and testing periods. In addition, although all the applied models can adequately reproduce each flux for the entire year (2009), substantial differences existed among different seasons, which is consistent with the finding reported by [PERSON] et al. [70]. In general, our used models provided the worst estimates in winter (December, January and February), while produced satisfactory estimates in both summer and fall seasons. For example, according to our estimates, for GPP, a mean value of \(R^{2}\) = 0.15, RMSE = 0.13 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\), and MAE = 0.11 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\) was obtained by the six models in winter, compared with 0.95, 0.51 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\), and 0.32 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\) in fall. The reasons for these discrepancies may be due to the errors induced by the eddy covariance-measured NEE [72], the partitioning approach of NEE into GPP and \(R\)[73; 74], and the gap-filling methods for missing flux data [69]. Moreover, the annual average values of \(T_{a}\), \(T_{s}\) and \(R_{h}\) in both 2008 and 2009 were lower compared with the 4-year means during 2004-2007. For example, in 2009, the annual average values of \(T_{a}\) and \(T_{s}\) were lower by 2.84 and 0.52 \({}^{\circ}\)C, respectively, while the annual average value of \(R_{n}\) was higher by 0.57 mol\(\cdot\)m\({}^{-2}\). These non-stationary features in environmental variables may lead to a potential impediment in reproducing the carbon and water fluxes. According to the modeling performance of various carbon fluxes among all the examined approaches in this work, the ANN model provided the optimal estimates for GPP and NEE, while the ANFIS model achieved the best for \(R\), indicating that no single model consistently outperforms others for all the carbon flux estimation. For this reason, it is extremely essential to compare the estimates using a variety of data-driven modeling methods to forecast the carbon fluxes. In contrast, for all the carbon fluxes and ET prediction, the GMDH model consistently produced the worst modeling results. This may be caused in part by its inherent limitations such as selection of input arguments, reduction of complexity, multi-collinearity and over-fitting [75; 76]. Taken as a whole, according to the estimates using our proposed techniques, it was found that the performance differences among all the models were comparatively slight for GPP, \(R\) and ET fluxes, while considerable differences were found for NEE.