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The existence of reliable rain-gauge networks is a necessity in managing water sources and the relevant environmental issues in any basin. The present study aimed to investigate the rain-gauge network and rank the rain-gauge stations in the Tazehkand sub-basin in the southwest of Lake Urmia, Iran, using the entropy–copula approach using the data obtained from six rain-gauge stations in the Siminehrood basin in Northwestern Iran between 1981 and 2019. The interaction effects of the stations were investigated using the copula simulation approach instead of the multivariate regression analysis. The R-vine was selected as the most convenient copula after investigating various vines using the statistics related to error investigation. Then, the interaction effects of the stations were investigated using the R-vine. The rainfall in each station was estimated by considering the rainfall of other stations. Moreover, the more prevalent multivariate regression analysis was implemented, and its results were compared with the results obtained from the vine simulation approach. The results of the comparison according to the NSE statistic showed that the vine simulation approach was above 90% across all stations. The estimates for the ITI and N(i) indices of each station using the entropy theory showed the shortage of stations in the investigated area. The stations were in average, above-average, and surplus modes according to the ITI index. The rating concerning the N(i) index indicated that the Dashband station was the most appropriate one in terms of communicating with other stations and conveniently covering the plain.

Groundwater is considered an essential water resource in arid and semi-arid regions such as Iran. This study used a copula-based approach to analyze the joint frequency of groundwater level and the duration of groundwater pumping with a constant discharge. In particular, this study examines the correlation between the pumping time and groundwater drawdown variables for two cases of 26.6 and 28.8 l/s constant discharges and a pumping time of 220 min. In addition, the Weibull probability distribution and Galambos copula were used for these two tests. To estimate the groundwater drawdown at different pumping times with different probabilities, the obtained typical curves by providing the contour curves of the cumulative groundwater drawdown probability and the pumping time in both tests were obtained. For example, for 150 min of pumping, the groundwater drawdown for pumping discharge of 26.64 and 28.8 l/s with a 60% probability is about 7.4 and 8 m, respectively. The results of the joint-occurrence frequency analysis in the study area showed that for each unit of increase in pumping discharge in the pumping well, a drawdown of 0.32 m is imaginable in the observation well. In the next step, the groundwater drawdown got analyzed in both tests simultaneously. Since the pumping time is the same, the effect of increasing the pumping discharge in the study area is observable in the joint-occurrence probability curve.

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