# Modeling and Predicting Carbon and Water Fluxes Using Data-Driven Techniques in a Forest Ecosystem
## 4 Discussion
Specifically, in the prediction of NEE,the ANN model achieved the optimal estimate with the approximate value of \(R^{2}\) = 0.84, NSE = 0.78, RMSE = 0.63 g-C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\) and MAE = 0.44 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\), whereas GMDH model performed the worst with the approximate value of \(R^{2}\) = 0.67, NSE = 0.60, RMSE = 0.84 g-C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\) and MAE = 0.57 g\(\cdot\)C\(\cdot\)m\({}^{-2}\cdot\)Day\({}^{-1}\). Moreover, it is noteworthy that evaluating the difference in predicting the carbon fluxes at different time scales (e.g., daily, monthly and annual) should take into account the influences of random errors in half-hourly flux observations. [PERSON] et al. (2016) demonstrated that a total random error in NEE induced by both the eddy covariance measurements and gap filling is roughly 25 g-C\(\cdot\)m\({}^{-2}\cdot\)year\({}^{-1}\). In addition to random error, systematic errors can also add to the uncertainty of carbon flux estimates. Therefore, when ranking the performance of our proposed methods for NEE prediction, it seems difficult to find the sources of error in the estimates from these models. Furthermore, in comparison to other fluxes, the diurnal and seasonal variations of NEE in amplitude and phase are strongly affected by the complex interplay between photosynthesis and respiration. On the other hand, through comparing the estimates among the fluxes, the worst results occurred for NEE estimates. A potential explanation for the lower performance in NEE prediction could be attributed to the omission of some important variables such as soil properties and biomass pools for the establishment of our used models. Hence, it is essential to select effective driving variables as model inputs for the further improvement in the predictive ability of data-driven models, especially for NEE, in the future work. In view of the estimates of ET, all the models achieved almost consistent, high modeling accuracy, suggesting that machine learning techniques can be expected as powerful tools to simulate and predict ET. What's more, it should be acknowledged that in recent years, these modeling techniques have been triumphantly applied in numerous branches in hydrology for nonlinear time series analysis, such as reference ET ([PERSON], 2016; [PERSON], 2017) and evaporation prediction ([PERSON], 2016), rainfall ([PERSON], 2016) and runoff forecasting ([PERSON], 2016; [PERSON], 2016). Our applied models were trained via many attempts in order to determine the optimized internal structure, functions and parameters. And afterwards their corresponding best predictions were derived based on the cross-validation strategy, taking into account the common drawback of over-fitting. Despite all this, the uncertainty issue in estimated results remains a great challenge for further research. To a certain extent, the predictive error caused by such uncertainty could potentially undermine the credibility of the models, and may lead to some problems in the applications of interpolation and extrapolation. Unfortunately, the uncertainty issues existing in the output results are ignored by most studies of machine learning modeling techniques in practical applications. Therefore, to overcome the negative impacts brought by the uncertainty in time series prediction, the uncertainty issues of data-driven models, involving a range of sources such as input data, internal parameters as well as geometry, have been recently addressed by a number of studies ([PERSON], 2016). Reasonable uncertainty evaluation is needed to quantify the beneficial information related to confidence bounds and provide more rigorous and credible estimates for policy makers. Specifically, for addressing the uncertainty problem in time series prediction, a suite of algorithms, such as Markov chain Monte Carlo (MCMC) ([PERSON], 2016) and Bayesian model averaging (BMA) ([PERSON], 2016), have been integrated into either a single data-driven model or a set of ensemble models. For example, [PERSON] et al.