## 2 Materials and Methods
### Machine Learning Methods  
#### 2.3.1 Adaptive Neuro-Fuzzy Inference System  
The ANFIS method has been widely acknowledged as a promising alternative tool to traditional ANN and SVM techniques in recent years, especially for predicting hydrological time series [50; 51; 52]. The popularity of the ANFIS modeling technique predominantly stems from its powerful generalization ability and robustness in terms of elucidating nonlinear processes by combining the advantages of both an adaptive ANN and a fuzzy inference system (FIS). In the present study, the most commonly used Sugeno FIS [53] was adopted to calculate the final network outputs from our developed ANFIS models. When a specific ANFIS model is trained, determining the related parameters is of particular importance for ensuring the model's generalization ability. The hybrid-learning algorithm is devoted to optimizing the premise parameters according to the gradient descent procedure and the consequent parameters according to the least squares algorithm.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Site** & **Latitude** & **Longitude** & **Elevation** & **MAT** & **TAP** & **Vegetation** & **Period** & **Reference** \\ \hline AT-Neu & 47.12 & 11.32 & 970 & 6.68 & 669 & GRA & 2004–2009 & [PERSON] et al. [43] \\ SE-Deg & 64.18 & 19.55 & 270 & 2.90 & 436 & WET & 2004–2009 & [PERSON] et al. [44] \\ US-Bo1 & 40.01 & \(-\)88.29 & 219 & 11.52 & 785 & CRO & 2001–2006 & Meyers and Hollinger [45] \\ CA-Oas & 53.63 & \(-\)106.20 & 601 & 1.82 & 343 & DRF & 2003–2008 & [PERSON] et al. [46] \\ CA-Oes & 53.99 & \(-\)105.12 & 629 & 1.00 & 373 & ENF & 2004–2009 & [PERSON] et al. [47] \\ \hline \end{tabular}
\end{table}
Table 1: Site characteristics used in this study. The mean annual temperature (MAT, \({}^{\circ}\)C) and total annual precipitation (TAP, mm year\({}^{-1}\)) are calculated according to the time period (Period). Vegetation types include grassland (GRA), wetland (WET), cropland (CRO), deciduous broadleaf forest (DBF), and evergreen needle leaf forest (ENF).  
In addition, it is worth noting that the applicability and generalization performance of ANFIS strongly relies on the methods of generating the FIS. Therefore, the present study aims to examine not only the effects of different membership functions under the grid partitioning method on the ability of developed ANFIS models, but also the impacts of different FIS identification algorithms, including fuzzy c-means clustering, grid partitioning, and subtractive clustering algorithms. For these purposes, the predictive ability of the ANFIS method was explored with respect to eight different membership functions under the grid partitioning method, including Gaussian curve (gaussmf), Gaussian combination (gauss2 mf), \(\pi\)-shaped (pimf), difference between two sigmoidal (dsigmf), trapezoidal-shaped (trapmf), product of two sigmoidal (psigmf), triangular-shaped (trimf), and generalized bell-shaped (gbellmf) algorithms. For the sake of convenience, the ANFIS models with the membership functions gaussmf, gauss2 mf, pimf, dsigmf, trapmf, psigmf, trimf, and gbellmf are hereinafter referred to as ANFIS1, ANFIS2, ANFIS3, ANFIS4, ANFIS5, ANFIS6, ANFIS7, and ANFIS8, respectively. Moreover, the ANFIS models with two other FIS identification methods, subtractive clustering and fuzzy c-means clustering, are abbreviated as ANFIS9 and ANFIS10, respectively.