Ferdowsi University of MashhadWater and Soil2008-475729320150823Estimation of Weighted Skew Coefficient for Design Flood Approximation (Case Study: West Azerbayjan, Islamic Republic of Iran)Estimation of Weighted Skew Coefficient for Design Flood Approximation (Case Study: West Azerbayjan, Islamic Republic of Iran)5785893810110.22067/jsw.v0i0.31707FAJ. BehmaneshUrmia University0000-0001-5856-9951M. Hesami AfsharUrmia UniversityJournal Article20140129Introduction: The frequency of floods is one of the characteristics of river flow statistics so thatanalyzing it has an important role to assess the hydrological and economical water resources projects. For determining flood frequency, the estimation of accurate skewness coefficient of annual peak discharges is required. Estimation of population skew for different regions will be improved when it is computed from the weighted average of the sample skew and an unbiased generalized skew estimate. There are different ways to develop a generalized skewness coefficient. The goal of this study is to analyze the methods for generating unbiased generalized skew coefficient and select the best method for creating the weighted generalized skewness coefficient.
Materials and Methods: In the present study, to calculate weighted generalized skewness coefficient, initially the hurst index is calculated to analyze the adequacy of time series length. The case study of the present research (West Azerbaijan, Iran) has three basins containing different hydrologic regions. These three basins are: the Aras River, Urmia Lake and Zab River basins. Therefore, various hydrologic regions, with the help of provincial border and the borders between sub-basins, are combined to form three larger hydrologic regions.After the formation of three larger hydrologic regions, the homogeneity of skewness variance of annual peak discharge of hydrometric stations within each three hydrological groups are tested using theleuven statistical parameter. Also the Dunnett test is applied to identify areas whichare significantly differentiated with other hydrologic regions. To develop the generalized skewness coefficient of 67 hydrometric stations with different statistical periods (16 to 62 years), three methods containing statewide map of skewness in West Azerbaijan, skewness map with including three hydrologic regions, and weighted average of skewness for the three hydrologic regions were used. Finally, after calculating the errors of three methods of generalized skewness development using Mean Square Error (MSE) coefficient, a weighted technique is used to calculate the weighted generalized skewness using sample skewness and the best generalized skewness (the one which has the least error) and their corresponding errors.
Results and Discussion: The results showed that most parts of the province have negative skewness values. The Hurst test results showed that the hurst coefficient is greater than 0.5 for all 67 hydrometric stations and lengthening of time series for the analysis is not required. Also, the results of the leuven statistical parameter showed that the homogeneous assumption is true for hydrological groups. Therefore, there is no reason for the variance heterogeneity. Moreover, the results of the Dunnett test stated that statistically, skewness means within the hydrological groups are not different. An error analysis showed that the Zab river basin had the least error amongthe studied basins. Among the methods studied for developing the skewness map, the division of the province into three hydrologic regions hada higher accuracy (MSE of Generalized skew coefficient = 0.55) than the other methods. However, this difference was very marginal. According to skewness maps, it can be seen that by considering hydrologic regions, the errors can be reduced in all three hydrologic regions. As the MSE in areas A and B is lower than the provincial level and in the region C, the error rate is close to zero. However, it should be noted that the number of hydrometric stations in region C, are much lower than other parts of the study area and this can be one of the reasons for error reduction in this area.
Conclusions: Considering that the aim of this study was to evaluate the accuracy of the generalized skewness estimating methods in the calculation of weighted generalized skewness coefficients, it has been seen that a regional approach, in addition to reducing the error rate, the fracture lines on the skewness map of the annual peak discharges can be reduced. Unlike the regional approach, the averaging method has shown worse results in all three regions.We may conclude that the sample skewness coefficient alone can bring better results than the averaging approach. Also, by comparing errors in areas A, B, and C, it can be concluded that with increment in area of hydrologic regions and inadequate spatial distribution of hydrometric stations, the error rate increases.Introduction: The frequency of floods is one of the characteristics of river flow statistics so thatanalyzing it has an important role to assess the hydrological and economical water resources projects. For determining flood frequency, the estimation of accurate skewness coefficient of annual peak discharges is required. Estimation of population skew for different regions will be improved when it is computed from the weighted average of the sample skew and an unbiased generalized skew estimate. There are different ways to develop a generalized skewness coefficient. The goal of this study is to analyze the methods for generating unbiased generalized skew coefficient and select the best method for creating the weighted generalized skewness coefficient.
Materials and Methods: In the present study, to calculate weighted generalized skewness coefficient, initially the hurst index is calculated to analyze the adequacy of time series length. The case study of the present research (West Azerbaijan, Iran) has three basins containing different hydrologic regions. These three basins are: the Aras River, Urmia Lake and Zab River basins. Therefore, various hydrologic regions, with the help of provincial border and the borders between sub-basins, are combined to form three larger hydrologic regions.After the formation of three larger hydrologic regions, the homogeneity of skewness variance of annual peak discharge of hydrometric stations within each three hydrological groups are tested using theleuven statistical parameter. Also the Dunnett test is applied to identify areas whichare significantly differentiated with other hydrologic regions. To develop the generalized skewness coefficient of 67 hydrometric stations with different statistical periods (16 to 62 years), three methods containing statewide map of skewness in West Azerbaijan, skewness map with including three hydrologic regions, and weighted average of skewness for the three hydrologic regions were used. Finally, after calculating the errors of three methods of generalized skewness development using Mean Square Error (MSE) coefficient, a weighted technique is used to calculate the weighted generalized skewness using sample skewness and the best generalized skewness (the one which has the least error) and their corresponding errors.
Results and Discussion: The results showed that most parts of the province have negative skewness values. The Hurst test results showed that the hurst coefficient is greater than 0.5 for all 67 hydrometric stations and lengthening of time series for the analysis is not required. Also, the results of the leuven statistical parameter showed that the homogeneous assumption is true for hydrological groups. Therefore, there is no reason for the variance heterogeneity. Moreover, the results of the Dunnett test stated that statistically, skewness means within the hydrological groups are not different. An error analysis showed that the Zab river basin had the least error amongthe studied basins. Among the methods studied for developing the skewness map, the division of the province into three hydrologic regions hada higher accuracy (MSE of Generalized skew coefficient = 0.55) than the other methods. However, this difference was very marginal. According to skewness maps, it can be seen that by considering hydrologic regions, the errors can be reduced in all three hydrologic regions. As the MSE in areas A and B is lower than the provincial level and in the region C, the error rate is close to zero. However, it should be noted that the number of hydrometric stations in region C, are much lower than other parts of the study area and this can be one of the reasons for error reduction in this area.
Conclusions: Considering that the aim of this study was to evaluate the accuracy of the generalized skewness estimating methods in the calculation of weighted generalized skewness coefficients, it has been seen that a regional approach, in addition to reducing the error rate, the fracture lines on the skewness map of the annual peak discharges can be reduced. Unlike the regional approach, the averaging method has shown worse results in all three regions.We may conclude that the sample skewness coefficient alone can bring better results than the averaging approach. Also, by comparing errors in areas A, B, and C, it can be concluded that with increment in area of hydrologic regions and inadequate spatial distribution of hydrometric stations, the error rate increases.https://jsw.um.ac.ir/article_38101_30dfdf47505985ef70cc0d627bb1bf5a.pdf