Approximating the complex nonlinear relationships that dominate the exchange of carbon dioxide fluxes between the biosphere and atmosphere is fundamentally important for addressing the issue of climate change. The progress of machine learning techniques has offered a number of useful tools for the scientific community aiming to gain new insights into the temporal and spatial variation of different carbon fluxes in terrestrial ecosystems. In this study, adaptive neuro-fuzzy inference system (ANFIS) and generalized regression neural network (GRNN) models were developed to predict the daily carbon fluxes in three boreal forest ecosystems based on eddy covariance (EC) measurements. Moreover, a comparison was made between the modeled values derived from these models and those of traditional artificial neural network (ANN) and support vector machine (SVM) models. These models were also compared with multiple linear regression (MLR). Several statistical indicators, including coefficient of determination (R²), Nash-Sutcliffe efficiency (NSE), bias error (Bias) and root mean square error (RMSE) were utilized to evaluate the performance of the applied models. The results showed that the developed machine learning models were able to account for the most variance in the carbon fluxes at both daily and hourly time scales in the three stands and they consistently and substantially outperformed the MLR model for both daily and hourly carbon flux estimates. It was demonstrated that the ANFIS and ANN models provided similar estimates in the testing period with an approximate value of R² = 0.93, NSE = 0.91, Bias = 0.11 g C m⁻² day⁻¹ and RMSE = 1.04 g C m⁻² day⁻¹ for daily gross primary productivity, 0.94, 0.82, 0.24 g C m⁻² day⁻¹ and 0.72 g C m⁻² day⁻¹ for daily ecosystem respiration, and 0.79, 0.75, 0.14 g C m⁻² day⁻¹ and 0.89 g C m⁻² day⁻¹ for daily net ecosystem exchange, and slightly outperformed the GRNN and SVM models. In practical terms, however, the newly developed models (ANFIS and GRNN) are more robust and flexible, and have less parameters needed for selection and optimization in comparison with traditional ANN and SVM models. Consequently, they can be used as valuable tools to estimate forest carbon fluxes and fill the missing carbon flux data during the long-term EC measurements.

Accurately estimating the carbon budgets in terrestrial ecosystems ranging from flux towers to regional or global scales is particularly crucial for diagnosing past and future climate change. This research investigated the feasibility of two comparatively advanced machine learning approaches, namely adaptive neuro-fuzzy inference system (ANFIS) and extreme learning machine (ELM), for reproducing terrestrial carbon fluxes in five different types of ecosystems. Traditional artificial neural network (ANN) and support vector machine (SVM) models were also utilized as reliable benchmarks to measure the generalization ability of these models according to the following statistical metrics: coefficient of determination (R²), index of agreement (IA), root mean square error (RMSE), and mean absolute error (MAE). In addition, we attempted to explore the responses of all methods to their corresponding intrinsic parameters in terms of the generalization performance. It was found that both the newly proposed ELM and ANFIS models achieved highly satisfactory estimates and were comparable to the ANN and SVM models. The modeling ability of each approach depended upon their respective internal parameters. For example, the SVM model with the radial basis kernel function produced the most accurate estimates and performed substantially better than the SVM models with the polynomial and sigmoid functions. Furthermore, a remarkable difference was found in the estimated accuracy among different carbon fluxes. Specifically, in the forest ecosystem (CA-Obs site), the optimal ANN model obtained slightly higher performance for gross primary productivity, with R² = 0.9622, IA = 0.9836, RMSE = 0.6548 g C m⁻² day⁻¹, and MAE = 0.4220 g C m⁻² day⁻¹, compared with, respectively, 0.9554, 0.9845, 0.4280 g C m⁻² day⁻¹, and 0.2944 g C m⁻² day⁻¹ for ecosystem respiration and 0.8292, 0.9306, 0.6165 g C m⁻² day⁻¹, and 0.4407 g C m⁻² day⁻¹ for net ecosystem exchange. According to the findings in this study, we concluded that the proposed ELM and ANFIS models can be effectively employed for estimating terrestrial carbon fluxes.

Remarkable progress has been made over the last decade toward characterizing the mechanisms that dominate the exchange of water vapor between the biosphere and the atmosphere. This is attributed partly to the considerable development of machine learning techniques that allow the scientific community to use these advanced tools for approximating the nonlinear processes affecting the variation of water vapor in terrestrial ecosystems. Three novel machine learning approaches, namely, group method of data handling, extreme learning machine (ELM), and adaptive neurofuzzy inference system (ANFIS), were developed to simulate and forecast the daily evapotranspiration (ET) at four different grassland sites based on the flux tower data using the eddy covariance method. These models were compared with the extensively utilized data-driven models, including artificial neural network, generalized regression neural network, and support vector machine (SVM). Moreover, the influences of internal functions on their corresponding models (SVM, ELM, and ANFIS) were investigated together. It was demonstrated that most developed models did good job of simulating and forecasting daily ET at the four sites. In addition to strengths of robustness and simplicity, the newly proposed methods achieved the estimates comparable to those of the conventional approaches and accordingly can be used as promising alternatives to traditional methods. It was further discovered that the generalization performance of the ELM, ANFIS, and SVM models strongly depended on their respective internal functions, especially for SVM.

Accurate estimation of carbon and water fluxes of forest ecosystems is of particular importance for addressing the problems originating from global environmental change, and providing helpful information about carbon and water content for analyzing and diagnosing past and future climate change. The main focus of the current work was to investigate the feasibility of four comparatively new methods, including generalized regression neural network, group method of data handling (GMDH), extreme learning machine and adaptive neuro-fuzzy inference system (ANFIS), for elucidating the carbon and water fluxes in a forest ecosystem. A comparison was made between these models and two widely used data-driven models, artificial neural network (ANN) and support vector machine (SVM). All the models were evaluated based on the following statistical indices: coefficient of determination, Nash-Sutcliffe efficiency, root mean square error and mean absolute error. Results indicated that the data-driven models are capable of accounting for most variance in each flux with the limited meteorological variables. The ANN model provided the best estimates for gross primary productivity (GPP) and net ecosystem exchange (NEE), while the ANFIS model achieved the best for ecosystem respiration (R), indicating that no single model was consistently superior to others for the carbon flux prediction. In addition, the GMDH model consistently produced somewhat worse results for all the carbon flux and evapotranspiration (ET) estimations. On the whole, among the carbon and water fluxes, all the models produced similar highly satisfactory accuracy for GPP, R and ET fluxes, and did a reasonable job of reproducing the eddy covariance NEE. Based on these findings, it was concluded that these advanced models are promising alternatives to ANN and SVM for estimating the terrestrial carbon and water fluxes.