## 4 Groundwater Level Prediction Techniques
### Adaptive Neuro-Fuzzy Inference System (ANFIS)  
This is a hybrid technique that aims to utilize the advantage of a fuzzy inference system (FIS) with an adaptable neural network (AN). FIS is based on fuzzy logic and is good at capturing uncertainties and noise in data. [PERSON] [59] pioneered the use of fuzzy if-then rules with right membership functions (MPs) to construct input-output pairs and a neural network learning algorithm. The fuzzy inference system is further classified into two approaches, namely Mamdani and Sugeno. Linear MFs are used by the Sugeno approach while Mamdani uses fuzzy MFs. ANFIS consists of five layers. The structural representation of ANFIS is similar to the ANN model, except it has two input parameters, linear and non-linear, which makes it difficult to train. Input parameters are optimized simultaneously in the training process. [PERSON] et al. [60] applied three different algorithms for GWL prediction, namely, radial basis function neural network (RBFNN), ANFIS, and the grey self-memory (GSM) method. Evaluation reveals the superiority of ANFIS over the other applied algorithms based on the performance metrics result (i.e., NSE, RMSE, R\({}^{2}\), and MARE). [PERSON] and [PERSON] [61] trained the ANFIS algorithm with precipitation (P) and mean temperature (T\({}_{\text{mean}}\)) to predict GWL and reported the performance metrics RMSE as 0.1381 and MAPE as 37.869%. [PERSON] et al. [62] investigated the prediction accuracy of ANFIS, FNN, and SVM for monthly GWL simulation and concludes the superiority of ANFIS over other algorithms. Previous GWL, lake level, precipitation (P), and Tmean were used as input variables. [PERSON] et al. [63] investigated the performance of ANFIS, FFNN, and the cascade forward network (CFN) model to simulate monthly GWL at Langat Basin in Selangor state's south-eastern part. R and MSE were used as performance metrics. The ANFIS model outperformed FFNN and CFN with R = 0.94 and MSE = 0.005. [PERSON] et al. [64] analyzed the differences in the monthly GWL prediction of ANN and ANFIS in Bastam plain, Iran. The following input variables were used in the study: pumping rate, rainfall recharge, and irrigation returned flow. ANFIS performed significantly better than ANN and it was also found that high accuracy can be achieved by applying different structures. Sometimes, hydrological time series data can be highly non-stationary which makes it hard for models, such as ANN and ANFIS, to better understand the underlying seasonality and thus leads to inaccurate predictions. In this situation, some researchers, such as [PERSON] and [PERSON] [65] and [PERSON] et al. [66], applied the wavelet data decomposition technique to first pre-process the input data. Wavelet transform can decompose data at various resolution levels to obtain useful information and give insights about trends and irregularities in the data. Therefore, it has several applications in hydrological studies because of the non-stationary nature of the data. The performance of regular ANNs, ANFISs, and both coupled with the wavelet technique, i.e., WANN and WANFIS, was examined by [PERSON] et al. [67]. They conducted a study to simulate monthly GWL for two subbasins in Mashad, Iran. Precipitation (P), evaporation (E), temperature (T), and previous GWL were the input variables. ANN and ANFIS failed to cope with the noise in the data while the ones coupled with wavelet performed considerably better. However, the authors reported that wavelet transform does contribute more to the efficiency of ANFIS than ANN. Another study was performed by [PERSON] and [PERSON] [68] to analyze the impact of the wavelet pre-processing technique. They developed wavelet-ANN, multi-linear regression (wavelet-MLR), and support vector machine (wavelet-SVM) up to two decomposition levels, and their regular counterparts. GWL at previous lag was used as the only input variable to simulate GWL with a one-month lead. The results showed that data decomposition translates into the high prediction accuracy of the models.