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Detection of relationship between two time series is so important in environmental and hydrological studies. Several parametric and non-parametric approaches can be applied to detect relationships. These techniques are usually sensitive to stationarity assumptions. In this research, a new copula- based method is introduced to detect the relationship between two cylostationary time series with fractional Brownian motion (fBm) errors. The numerical studies verify the performance of the introduced approach.

Floods are one of the most frequent and destructive natural events which lead to lots of human and financial losses with damage to the houses, farms, roads, and other buildings. Intensity-duration-frequency (IDF) curves are the main and practical tools that have been used for flood control studies including the design of the water structures. In many cases, there is not any measuring device at the desired place or their information are not useful if there is any available. In this case, it is not possible to extract these curves through the conventional methods. Regionalizing the IDF curves is a method that has solved the issues mentioned in the common methods. In this research, the regionalized IDF curves are extracted in Khozestan province, Iran using 21 rain gauge stations through L-moments and neural gas networks. Clustering is one of the most effective steps and a prerequisite for regional frequency analysis (RFA) that divides the region and existing stations into hydrologically homogenous regions. In this study, clustering is done using two new models named neural gas (NG) and growing neural gas (GNG) network. Comparing the regional IDF curves with single site curves, it was found that neural gas network models had a more accurate performance and higher efficiency so that they had the lowest estimate error amount among other models. Also, due to the acceptable difference between regional and single site curves, the efficiency of L-Moments in RFA was evaluated as appropriate.

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