Abstract
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.
Highlights
Changing hydrological conditions, as well as the increasing impervious areas due to increasing urban development, have caused fundamental changes in the surface water regimes [1]
The newly introduced i-Fuzzy C-Means (FCM) method was used as a spatial interpolation methodology to estimate rainfall data for an ungauged location (Figure 5)
A machine learning (ML) clustering method as an efficient, fast, accurate yet simple tool was introduced in this study, named inverse FCM (i-FCM) spatial interpolation
Summary
As well as the increasing impervious areas due to increasing urban development, have caused fundamental changes in the surface water regimes (e.g., flood events in recent years) [1]. With the development of improved statistical approaches, earth observation technologies and machine learning methods, the accuracy as well as the number of spatial interpolation methods have greatly increased [4,5]. In the authors’ opinion, not enough attention has been given to clustering methods and fuzzy logic for spatial interpolation of precipitation; this becomes even more important when thinking meticulously about the process of estimating rainfall data in certain point locations based on measured data around that location. Spatial interpolation is the process of organizing observed data into groups that are relatively similar, in order to fill the gaps between groups. This type of grouping shows the importance of similarity in interpolation
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