Abstract
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.