In order to optimize the management of groundwater resources, accurate estimates of groundwater level (GWL) fluctuations are required. In recent years, the use of artificial intelligence methods based on data mining theory has increasingly attracted attention. The goal of this research is to evaluate and compare the performance of adaptive network-based fuzzy inference system (ANFIS) and Wavelet-ANFIS models based on FCM for simulation/prediction of monthly GWL in the Maragheh plain in northwestern Iran. A 22-year dataset (1996–2018) including hydrological parameters such as monthly precipitation (P) and GWL from 25 observation wells was used as models input data. To improve the prediction accuracy of hybrid Wavelet-ANFIS model, different mother wavelets and different numbers of clusters and decomposition levels were investigated. The new hybrid model with Sym4-mother wavelet, two clusters and a decomposition level equal to 3 showed the best performance. The maximum values of R2 in the training and testing phases were 0.997 and 0.994, respectively, and the best RMSE values were 0.05 and 0.08 m, respectively. By comparing the results of the ANFIS and hybrid Wavelet-ANFIS models, it can be deduced that a hybrid model is an acceptable method in modeling of GWL because it employs both the wavelet transform and FCM clustering technique.
In this study, a new approach for rainfall spatial interpolation in the Luxembourgian case study is introduced. The method used here is based on a Fuzzy C-Means (FCM) clustering method. In a typical FCM procedure, there are a lot of available data and each data point belongs to a cluster, with a membership degree [0 1]. On the other hand, in our methodology, the center of clusters is determined first and then random data are generated around cluster centers. Therefore, this approach is called inverse FCM (i-FCM). In order to calibrate and validate the new spatial interpolation method, seven rain gauges in Luxembourg, Germany and France (three for calibration and four for validation) with more than 10 years of measured data were used and consequently, the rainfall for ungauged locations was estimated. The results show that the i-FCM method can be applied with acceptable accuracy in validation rain gauges with values for R2 and RMSE of (0.94–0.98) and (9–14 mm), respectively, on a monthly time scale and (0.86–0.89) and (1.67–2 mm) on a daily time scale. In the following, the maximum daily rainfall return periods (10, 25, 50 and 100 years) were calculated using a two-parameter Weibull distribution. Finally, the LISFLOOD FP flood model was used to generate flood hazard maps in Dudelange, Luxembourg with the aim to demonstrate a practical application of the estimated local rainfall return periods in an urban area.
The development of precise and simple spatial interpolation methods to estimate rainfall data in ungauged locations provides not only better understating and new insights into the predictive hydrological models but also improves the accuracy of these models. In this Scientific Briefing a new approach for rainfall spatial interpolation in Luxembourgian case study has been introduced. The method used here is based on a Fuzzy C-Means (FCM) clustering method. In the normal FCM procedure, there are a lot of available data and each data point belongs to a cluster, with a membership degree [0 1], i.e. the data points clustered in an iterative process, whereas in our methodology the center of clusters has been determined first and then random data will be generated around cluster centers. Therefore, this approach is called inverse FCM (i-FCM) from here on. In order to calibrate and validate the new spatial interpolation method four rain gauges in Luxembourg (3 for calibration and one for validation) with 10 years of measured data were used and consequently the rainfall for ungauged locations were estimated. The results show that the i-FCM method can be applied with acceptable accuracy in validation rain gauge with values for R2 and RMSE of 0.92 and 12 mm, respectively, on monthly time scale and 0.84 and 1.8 mm on daily time scale.
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