Estimation of the Joint Frequency of Peak Flow Discharge-Suspended Load of Zarinehrood Basin Using Two-Dimensional Analysis

Document Type : Research Article

Authors

• M. Nazeri Tahroudi ¹
• Y. Ramezani ¹
• C. De Michele ²
• R. Mirabbasi Najafabadi ³

¹ University of Birjand

² Milan

³ Shahrekord University

https://doi.org/10.22067/jsw.v34i2.81812

Abstract

 
Introduction: The erosion, sediment transport, and estimation problems in the streamflow are the most complicated and essential subjects in the river engineering studies. It is important to model and predict these parameters correctly to determine the effective life of the hydraulic structures and drainage networks. On the other hand, river flow discharge is considered as one of the main components of water resources, which affects sediments. The increasing need of urban and rural communities for limited resources on the one hand, and issues related to climate change and atmospheric precipitation over the past few years, more and more attention is paid to the attitude of surface flows. The phenomena of erosion, sediment transport, and estimation of sediment load in the rivers due to its damages are one of the most critical and complex issues of river engineering. The primary goal of the frequency analysis is to relate extreme events to their frequency using probability distributions. In the frequency analysis of meteorological and hydrological events, the observed data would be analyzed for a long time at a basin. In these analysis, the assumption of independence and stationarity is considered. In fact, the basic assumption is that the studied data are spatially and temporally independent. The main issue is identifying actual distribution across different exiting distributions when using the frequency distribution to estimate the magnitude of the event. There is no appropriate general distribution for all types of rainfall regimes, river flows, etc. On the other hand, in order to analyze the frequency of a similar case, there is no agreement on the use of a particular distribution function. The experience gained so far in the field of statistical analysis of hydrological data shows that some data are more consistent with some specific statistical distributions.
Materials and Methods: In this study, the frequency analysis of total sediment load of the Zarinehrood basin was investigated in the south-east of Lake Urmia with consideration of the peak flow discharge at the Chalekhmaz hydrometric station during the statistical period of 1992-2016 using copula functions. At first, the correlation of these data was investigated using Kendall Tau correlation statistics, and the correlation coefficient was calculated as 0.75. In this study, Ali-Mikhail-Haq, Clayton, Frank, Galambos, Gumbel-Hougaard, Plackett, and Farlie-Gumbel-Morgenstern copula functions were used. In the conventional method of estimating the return period of extreme values, different statistical distributions are fitted on the studied data. After fitting the statistical distributions on the data series, the accuracy of each distribution is evaluated by one of the goodness of fit tests, such as the Kolmogorov-Smirnov test. After statistically controlling the goodness of fit test and determining the acceptable distributions, the root means square error (RMSE) and the Nash-Sutcliffe criterion are calculated to select the best fit model. Each of the fitting distributions that have the highest Nash-Sutcliffe (NS) criteria, and the lowest RMSE is chosen as an appropriate distribution.
Results and Discussion: With the fitting of 65 different distribution functions into the series, the Weibull distribution for total sediment load values and generalized Pareto distribution for peak flow discharge values were selected based on the evaluation criteria as appropriate marginal distributions. The results of the evaluation of the accuracy and efficiency of copula functions were studied by using root mean square error, Nash-Sutcliffe, BIAS, and AIC statistics. In this regard, the results were compared with the experimental copula functions. Finally, the Galambos copula was selected from the candidate copulas as superior copula function. The conditional and joint return period of the total sediment load based copula was proposed with a probability of 10 to 90 percent.
In univariate mode, the lowest probability of exceedance is 50%. In a bivariate mode, this possibility is presented more accurately. With a possibility of exceedance of 50%, it can be observed that the total sediment load at Chalekhmaz station during the studied period is about 400 tons per day. This is about 56% higher than its univariate mode, which is the average long-term of the total sediment load is closer to the Chalekhmaz station.
Conclusion: By comparing the bivariate analysis and its return period with univariate mode, the results indicated that more accurate calculation. Also the results showed the estimation of total sediment load is closer to the total sediment load of the Chalekhmaz station in bivariate analysis mode.  Also, the results showed that in univariate mode, estimation of total sediment load at Chalekhmaz station was less than its actual value during the two-year return period. Regarding the results, the generated return curves can be used as the type curves for the management of water resources in the basin.

Keywords

• Chalekhmaz
• Copula function
• Galambos
• Lake Urmia
• Marginal distribution

20.1001.1.20084757.1399.34.2.7.7

References

1- Aas K., Czado C., Frigessi A., and Bakken H. 2009. Pair-copula constructions of multiple dependence. Insurance: Mathematics and Economics 44(2): 182-198.

2- Abdi A., Hassanzadeh Y., Talatahari S., Fakheri-Fard A., and Mirabbasi R. 2016. Regional bivariate modeling of droughts using L-comoments and copulas. Stochastic Environmental Research and Risk Assessment, DOI: 10.1007/s00477-016-1222-x.

3- Ahmadi F., Radmaneh F., Parham G.A., and Mirabbasi R. 2017. Comparison of the performance of power law and probability distributions in the frequency analysis of flood in Dez Basin, Iran. Natural Hazards 87(3): 1313-1331.

4- Ahmadi F., Radmanesh F., Parham G.A., and Mirabbasi Najaf Abadi R. 2017. Application of Archimedean and Extreme values Copula Functions for Multivariate Analysis of Low Flows in Dez Basin. Journal of Water and Soil 31(4): 1031-1045. (In Persian with English abstract)

5- Ayantobo O.O., Li Y., and Song S. 2019. Multivariate drought frequency analysis using four-variate symmetric and asymmetric Archimedean copula functions. Water Resources Management 33(1): 103-127.

6- Bedford T., and Cooke R.M. 2001. Probability density decomposition for conditionally dependent random variables modeled by vines. Annals of Mathematics and Artificial Intelligence 32(1-4): 245-268.

7- Besharat S., Khalili K., and Tahrudi M.N. 2014. Evaluation of SAM and Moments methods for estimation of log Pearson type III parameters (Case Study: daily flow of rivers in Lake Urmia basin). Journal of Applied Environmental and Biological Sciences 4(S1): 24-32.

8- Bevacqua E., Maraun D., Hobæk Haff I., Widmann M., and Vrac M. 2017. Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy). Hydrology and Earth System Sciences 21(6): 2701-2723.

9- Bezak,N., Rusjan S., Kramar Fijavž M., Mikoš M., and Šraj M. 2017. Estimation of suspended sediment loads using copula functions. Water 9(8): 1-23.

10- Brunner M.I., Furrer R., and Favre A.C. 2019. Modeling the spatial dependence of floods using the Fisher copula. Hydrology and Earth System Sciences 23(1): 107-124.

11- Cooke R.M., Kurowicka D., and Wilson K. 2015. Sampling, conditionalizing, counting, merging, searching regular vines. Journal of Multivariate Analysis 138: 4-18.

12- De Michele C., and Salvadori G. 2003. A generalized Pareto intensity‐duration model of storm rainfall exploiting 2‐copulas. Journal of Geophysical Research: Atmospheres 108(D2).

13- Gräler B., van den Berg M., Vandenberghe S., Petroselli A., Grimaldi S., De Baets B., and Verhoest N. 2013. Multivariate return periods in hydrology: a critical and practical review focusing on synthetic design hydrograph estimation. Hydrology and Earth System Sciences 17(4): 1281-1296.

14- Joe H. 1997. Multivariate models and multivariate dependence concepts. London: Chapman & Hall, 399 pp.

15- Kavianpour M., Seyedabadi M., and Moazami S. 2018. Spatial and temporal analysis of drought based on a combined index using copula. Environmental Earth Sciences 77(22):769.

16- Khalili K., Tahoudi M.N., Mirabbasi R., and Ahmadi F. 2016. Investigation of spatial and temporal variability of precipitation in Iran over the last half century. Stochastic Environmental Research and Risk Assessment 30(4): 1205-1221.

17- Khan F., Spöck G., and Pilz J. 2020. A novel approach for modelling pattern and spatial dependence structures between climate variables by combining mixture models with copula models. International Journal of Climatology 40(2): 1049-1066.

18- Kurowicka D., and Cooke R.M. 2007. Sampling algorithms for generating joint uniform distributions using the vine-copula method. Computational Statistics & Data Analysis 51(6): 2889-2906.

19- Mirabbasi R., Anagnostou E.N., Fakheri-Fard A., Dinpashoh Y., and Eslamian S. 2013. Analysis of meteorological drought in northwest Iran using the Joint Deficit Index. Journal of Hydrology 492: 35-48.

20- Mirabbasi R., Fakheri-Fard A., and Dinpashoh Y. 2012. Bivariate drought frequency analysis using the copula method. Theoretical and Applied Climatology 108(1-2): 191-206.

21- Nash J.E., and Sutcliffe J.V. 1970. River flow forecasting through conceptual models part I—A discussion of principles. Journal of Hydrology 10(3): 282-290.

22- Nazeri Tahroudi M., Khalili K., Abbaszadeh Afshar M., Nazeri Tahroudi Z., Ahmadi F., and Motallebian M. 2016. Evaluation of the Univariate, Multivariate and Combined Time Series Models in order to Prediction and Estimation the Mean Annual Sediment Load. Quarterly journal of Environmental Erosion Research 6: 1(21):52-70. (In Persian with English abstract)

23- Nelsen R.B. 2006. An introduction to copulas. Springer, New York, 269p.

24- Nguyen-Huy T., Deo R.C., Mushtaq S., Kath J., and Khan S. 2019. Copula statistical models for analyzing stochastic dependencies of systemic drought risk and potential adaptation strategies. Stochastic Environmental Research and Risk Assessment 1-21.

25- Rahimi L., Dehghani A.A., Abdolhosseini, M., Ghorbani K. 2014. Flood frequency analysis using archimedean copula functions based on annual maximum series (Case Study: Arazkuseh hydrometric station in Golestan province). Iranian Journal of Irrigation and Drainage 2(8): 353-365.

26- Ramezani Y., Tahroudi M.N., and Ahmadi F. 2019. Analyzing the droughts in Iran and its eastern neighboring countries using copula functions. Quarterly Journal of the Hungarian Meteorological Service 123(4): 435-453.

27- Salvadori G., and De Michele C. 2004. Frequency analysis via copulas: Theoretical aspects and applications to hydrological events. Water Resources Research 40(12).

28- Salvadori G., and De Michele C. 2007. On the use of copulas in hydrology: theory and practice. Journal of Hydrologic Engineering 12(4): 369-380.

29- Sanikhani H., Mirabbasi Najaf Abadi R. and Dinpashoh Y. 2014. Modeling of temperature and rainfall of tabriz using copulas. Journal of Irrigation and Water Engineering 5(17): 123-134. (In Persian)

30- Shiau J.T. 2006. Fitting drought duration and severity with two-dimensional copulas. Water Resources Management 20(5): 795-815.

31- Sklar A. 1959. Fonctions de Repartition and Dimensions et Leurs-Marges. Publications de L’Institute de Statistique, Universite’ de Paris, Paris. 8: 229–231.

32- Tahroudi M.N., Ramezani Y., and Ahmadi F. 2019. Investigating the trend and time of precipitation and river flow rate changes in Lake Urmia basin, Iran. Arabian Journal of Geosciences 12(6): 219-239.

33- Vazifehkhah S., Tosunoglu F., and Kahya E. 2019. Bivariate risk analysis of the droughts using a nonparametric multivariate standardized drought index and copulas. Journal of Hydrology Engineering 24(5): 1-17.

34- Yue S., and Rasmussen P. 2002. Bivariate frequency analysis: discussion of some useful concepts in hydrological application. Hydrological Processes 16(14): 2881-2898.

35- Yue S., Ouarda T.B.M.J., and Bobee B. 2001. A review of bivariate gamma distributions for hydrological application. Journal of Hydrology 246(1): 1-18.

36- Zhang D., Yan M., and Tsopanakis A. 2018. Financial stress relationships among Euro area countries: an R-vine copula approach. The European Journal of Finance 24(17): 1587-1608.