Comparison efficiency of moments, L-moments and maximum likelihood methods in regional flood analysis

Document Type : Research Paper

Authors

1 Ph.D. of Watershed Management Engineering, Faculty of Natural Resources and Desert Studies, Yazd University, Yazd, Iran

2 Professor, Faculty of Natural Resources and Desert Studies, Yazd University, Yazd, Iran

10.29252/aridbiom.2021.16213.1838

Abstract

It is necessary to determine the appropriate probability distribution for fitting the flood data. There are several methods for estimating the parameters of probability distribution functions. In the present study, L-moments approach is used for flood frequency analysis in Gavkhouni Basin, Abarkouh- Sirjan Basin and Yazd- Ardakan Basin. Some stations were selected and their data were analyzed to find out peak discharge. Then, Hosking and Wallis homogeneity criterion were used to identify the homogeneous region. Examining the homogeneity criterion closely shows the discordant region. Eliminating and transferring some selected stations, leads to determining a homogeneous region of flood frequency. Parameters of the regional frequency distribution were evaluated using L-moment, moments, and maximum likelihood methods. The results of this analysis were compared using RMSE, R, and RRMSE statistics. The goodness of fit tests such as Chi-square, Kolmogorov-Smirnov were applied for checking the adequacy of fitting of probability distributions to the recorded data. The study reveals that the Pearson Type-3 distribution (using LMM) is better suited amongst the ten distributions used in estimating the peak flood. In general, the L-moment method estimated the peak flood for return periods of 10, 25, 50, and 100-year, and moments method at return periods of 2 and 5-year.

Keywords

References

[1]. Abida. H. & Ellouze. M. (2007). Probability distribution of flood flow in Tunisia. Hydrology and Earth System SciencesDiscussions. 4: 957-981.
[2]. Adamowski. K. (2000). Regional analysis of annual maximum and partial flood data by nonparametric and L-moments methods. Journal of Hydrology. 229: 219-231.
[3]. Afandizadeh. S., Ameri. M. & Mirabi Moghadaam. M. H. (2010). A new method for optimization of log likelihood function for the purpose of determining the coefficients of accident prediction models. Journal of Transportation Research. 7(3(24)):215-255 (in Farsi).
[4]. Ahmad. I., Fawad. M. & Mahmood. I. (2015). At-Site Flood Frequency Analysis of Annual Maximum Stream Flows in Pakistan Using Robust Estimation Methods. Polish Journal of Environmental Studies. 24(6): 1-9.
[5]. Alam. J., Muzzammil. M. & Khan. M. K. (2016). Regional flood frequency analysis: comparison of L-moment and conventional approaches for an Indian catchment. ISH Journal of Hydraulic Engineering. 22(3):1–7.
[6]. Bhuyan. A., Borah. M. & Kumar. R. (2010). Regional flood frequency analysis of north-bank of the river Brahmaputra by using LH-moments. Water Resources Management. 24(9): 1779-1790.
[7]. Burn. D. H. (1990). Evaluation of regional flood frequency analysis with a region of influence approach. Water Resource Research. 26(10): 2257-2265.
[8]. Cavadias, G. (1990). The canonical correlation approach to regional flood estimation. Regionalization in hydrology, 191, 171-178.
[9]. Dalrymple. T. (1960). Flood Frequency Analysis. US Geological Survey, Water Supply Paper, 1543 p.
[10]. Eslamian. S. S. & Chavoshi. S. (2003). Regional flood frequency analysis using L-Moments in central basins of Iran. Journal science and Technology Agricultural and Natural Resources. 7:1.1-17 (in Farsi).
[11]. Eslamian. S. S., Fathian. F. & Hasanzadeh. H. (2012). A comparative evaluation of L-moment method with maximum ‎likelihood parametric method and kernel functions of ‎nonparametric methods in five Iranian stations. Watershed Engineering and Management. 4(2): 63-72 (in Farsi).
[12]. Faucher. D.. Rasmussen. P. S. & Bobee. B. (2001). A distribution function based on bandwidth selection method for kernel quantile estimation. Journal of Hydrology. 250(1): 1-11.
[13]. Gholami. A. (2016). Comparison efficiency of linear moment method with common methods for estimation of annual maximum peak flood (case study: Sheikh Osman watershed in Oshna Vieh area). Journal of watershed management research. 7(13): 119-.127 (in Farsi).
[14]. Greenwod. J. A., Landwehr. J. M., Matalas. N. C. & Wallis. J. R. (1979). Probability Weighted Moments: definition and relation to parameters of several distributions expressible in inverse form. Water Resources Research. 15(5): 1049-1054.
[15]. Hailegeorgis. T. T. & Alfredsen. K. (2017). Regional flood frequency analysis and prediction in ungauged basins including estimation of major uncertainties for mid-Norway. Journal of Hydrology: Regional Studies. 9:104-126.
[16]. Hamed. K. & Rao. A. R. (1999). Flood frequency analysis. CRC press, 59p.
[17]. Hassanzadeh. Y. & Abdikordani. A. (2012). The four-parameter kappa distribution in prediction of standardized precipitation index. Irrigation Sciences and Engineering. 35(2):21-31 (in Farsi).
[18]. Hosking. J. R. M. (1986). The theory of probability weighted moments. Research Report RC12210, IBM Research Division, Yorktown Heights, NY, 10598p.
[19]. Hosking. J. R. M. (1990). L-moment: analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society. 52(2):105-124.
[20]. Hosking. J. R. M. & Wallis. J. R. (1997). Regional Flood Frequency Analysis: An approach based on L-moment. Cammbridge University Press, London, UK, 224p.
[21]. Izinyon. O. C. & Ajumuka. H. N. (2013). Probability distribution models for flood prediction in Upper Benue River Basin–Part II. Civil and Environmental Research. 3(2): 62-74.
[22]. Jingyi. Z. & Hall. M. J. (2004). Regional Flood Frequency Analysis for the Gan-Ming River Basin in China. Journal of Hydrology. 296:98-117.
[23]. Keshtkar. A., Salajegheh. A. & Najafi Hajivar. M. (2012). Flood flow frequency model selection using L-moment method in arid and semi arid regions of Iran. Desert. 17(1): 41-48.
[24]. Khalili. K., Nazeri. Tahrudi. M., Abbaszadeh Afshar. M. & Nazeri tahrudi. Z. (2014). Comparison of different peak flow frequency distribution functions (Case Study: Babolrood River). Journal of Middle East Applied Science andTechnology. 7(4): 174-179.
[25]. Khandi. S., Kachroo. H. & Gunasekara. R. K. (2002). Comparision of Annual Maximum Series and Partial Duration of Homogeneous Regions. Hydrological Science Journal. 45:437-447.
[26]. Khosravi. G., Majidi. A. & Nohegar. A. (2012). Determination of suitable probability distribution for annual mean and peak discharges estimation (case study: Minab river-barantin gage, Iran). International Journal of Probability Statictics. 1(5): 160-163.
[27]. Kjeldsen. T. R., Smithers. J. & Schulze. R. (2002). Regional flood frequency analysis in the KwaZulu-Natal province, South Africa, using the index-flood method. Journal of hydrology. 255(1-4): 194-211.
[28]. Kroll. C. N. & Vogel. R. M. (2002). Probability distribution of low stream flow series in the United States. Journal of Hydrologic Engineering. 7(2): 137-146.
[29]. Kumar. R. & Chatterjee. C. (2005). Regional flood frequency analysis using L-Moments for North Brahmaputra region of India. Journal of Hydrologic Engineering. 10: 1-7.
[30]. Langat. P. K., Kumar. L. & Koech. R. (2019). Identification of the Most Suitable Probability Distribution Models for Maximum, Minimum, and Mean Streamflow. Water. 11(4): 1-24.
[31]. Landwehr. J. M.. Matalas. N. C. & Wallis. J. R. (1979). Probability weighted moments compared with some traditional techniques in estimating Gumbel parameters and quantiles. Water Resources Research. 15(5): 1055-1064.
[32]. Leonardo. V. N. & Goffredo. L. L. (2008). Use of L-moments approach for regional flood frequency analysis in Sicily, Italy. WaterResources Management. 23: 2207-2229.
[33]. Li. M., Li. X. & Ao. T. (2019). Comparative Study of Regional Frequency Analysis and Traditional At-Site Hydrological Frequency Analysis. Water. 11(3): 1-19.
[34]. Mahdavi. M., Salajegheh. A., Keshtkar. A. R., Fahmi. H. & Sharifi. F. (2006). A Study of the Appropriate Probability Distributions for Annual Flow Series, Using L-Moment Method in Arid and Semi-arid Regions. Iranian journal of natural resources. 59(1): 74-87 (in Farsi).
[35]. Malekinezhad. H., Nachtnebel. Hp. & Klik. A. (2011). Comparing the index flood and multiple regression methods using L-moment. Journal of Physics and Chemistry of the Earth. 36: 54-60.
[36]. Mohammadi. M. (2008). Regional Flood Frequency Analysis using L-moments approach in some watersheds of Isfahan – Sirjan and Yazd - Ardakan basins. M.Sc. Thesis, Faculty of Natural Resources, Yazd University (in Farsi).
[37]. Mohammadi. M., Malekinezhad. H. & Afkhami. H. (2017a). Determination of Hydrological Homogeneous Regions using Canonical Correlation Analysis. Iranian Journal of Watershed Management Science and Engineering. 11(38): 11-24 (in Farsi).
[38]. Mohammadi. M., Malekinezhad. H. & Dastorani. M. T. (2017b). Comparing Regional Analysis methods of estimation of the peak flow in some watershed s of Isfahan- Sirjan and Yazd- Ardakan Basins. Iranian Journal of Natural Resources. 70(2): 515-529 (in Farsi).
[39]. Noori Gheidari. M. H. (2012). Identifying the Regional of Ungauged Station for Regional Flood Frequency Analysis Using Canonical Correlation Method. Journal of Water and Soil. 26: 943-952 (in Farsi).
[40]. Noto. L. V. & La Loggia. G. (2009). Use of L-moments approach for regional flood frequency analysis in Sicily, Italy. Water Resources Management. 23(11): 2207-2229.
[41]. Ourada. TBMJ. Girard. C., Cavadias. G. S. & Bobee. B. (2001). Regional flood frequency estimation with canonical correlation analysis. Journal of hydrology. 254:157-173.
[42]. ÖZTEKİN. T. (2005). Comparison of parameter estimation methods for the three-parameter generalized Pareto distribution. Turkish journal of agriculture and forestry. 29(6): 419-428.
[43]. Rao. A. R. & Srinivas. V. (2006). Regionalization of watersheds by hybrid-cluster analysis. Journal of Hydrology. 318(1-4): 37-56.
[44]. Saf. B. (2009). Regional flood frequency analysis using L-moments for the West Mediterranean region of Turkey. Water Resources Management.23(3): 531-551.
[45]. Sakarasubramaniam. A. & Srinivasan. K. (1999). Investigation and composition of sampling properties of L-Moment and conventional Moments. Journal of hydrology. 218:13–34.
[46]. Vivekanandan. N. (2015a). Flood frequency analysis using method of moments and L-moments of probability distributions. Cogent Engineering. 2(1): 1-10.
[47]. Vivekanandan. N. (2015b). Frequency analysis of annual maximum flood discharge using method of moments and maximum likelihood method of gamma and extreme value family of probability distributions. International Journal of Math Computer Science. 1(3): 141-146. [48]. Vogel. R. M., McMahon. T. A. & Chiew. FHS. (1993). Flood flow frequency model selection in Australia. Journal of hydrology. 146:421-449.
Journal of Arid Biome
Volume 10, Issue 2
March 2021
Pages 79-97

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