Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2016 | 25 | 3 |
Tytuł artykułu

Finding probability distributions for annual daily maximum rainfall in Pakistan using linear moments and variants

Treść / Zawartość
Warianty tytułu
Języki publikacji
In this study, at-site frequency analysis (AFA) of an annual daily maximum rainfall (ADMR) series was carried out using the method of linear moments (L-moments) and their variants such as trimmed linear moments (TL-moments) and higher order linear moments (LH-moments). The ADMR series we investigated was observed at 28 meteorological observatories across Pakistan as retrieved from the Pakistan Meteorological Department (PMD). The basic aim of the study was to fi nd best-fit (i.e., the most suitable) probability distribution among the class of various probability distributions. Initially different goodness-offit (GOF) measures such as the Kolmogorov-Smirnov test (KST), Anderson-Darling test (ADT), root mean square error (RMSE) and L-moments ratio diagram (LRD) were applied to determine not only the best-fit distributions but also the best linear estimation method for AFA. We observed that no single probability distribution could be declared as the best-fi t distribution for all the stations. Five distributions were found to be the most appropriate: generalized extreme value (GEV), three parameter lognormal (LN3), Pearson type III (P3), generalized logistic (GLO), and generalized pareto (GPA). The TL-moments method was also applied for parameter estimation to mitigate the effect of outliers on fi nal estimates. LH-moments were used for estimating the upper part of probability distributions and larger events in the data samples. LH moments alleviate the unwanted affects due to small sample values that may be obvious during estimation of events related to larger return periods. Using different GOF tests, we observed that the L-moments method was best for eight stations, TL-moments with trimming (1, 0), and LH-moments with level η =2, 3, 4 were best for six and 14 stations, respectively. A theoretical relationship between TL-moments and LH-moments was also revisited, which revealed that LH-moments are special cases of TL-moments when we are motivated to make trimming only from the lower side.
Słowa kluczowe
Opis fizyczny
  • Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
  • Department of Mathematics, University of Poonch Rawalakot, Pakistan
  • Mir Pur University of Science and Technology, AJK, Pakistan
  • Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan
  • 1. AHMAD I., MAHMOOD I., MALIK I.R., ARSHAD I.A., HAQ E., IQBAL Z. Probability analysis of monthly rainfall on seasonal monsoon in Pakistan. International Journal of Climatology, 34, 827, 2014.
  • 2. ADNAN S., KHAN A.H. Effective rainfall for irrigated agriculture plains of Pakistan. Pak J Meteorology. 6, 61. 2009.
  • 3. SHAMSHAD K.M. The Meteorology of Pakistan, First Edition, Royal Book Company Publishers. 1988.
  • 4. SHABRI A.B., DAUD Z.M., ARIFF N.M. Regional analysis of annual maximum rainfall using TL-moments method. Theor. Appl. Climatol, 104, 561, 2011.
  • 5. KYSELY J., PICEK J., HUTH R. Formation of homogeneous regions for regional frequency analysis of extreme precipitaion events in the Czech Republic. Studia Geophysica et Geodaetica, 51, 327, 2006.
  • 6. DURRANS S.R., KIRBY J.T. Regionalization of extreme precipitation estimates for the Alabama rainfall atlas. Journal of Hydrology, 295, 101, 2004.
  • 7. NOTO L.V., LA LOGGIA G. Use of L-moments approach for regional flood frequency analysis in Sicily, Italy. Water resources management, 23, 2207, 2009.
  • 8. RAHMAN A.S., RAHMAN A., ZAMAN M.A., HADDAD K., AHSAN A., IMTEAZ M. A study on selection of probability distributions for at-site flood frequency analysis in Australia. Natural hazards, 69, 1803, 2013.
  • 9. BOBEE B., CAVADIAS G., ASHKAR F., BERNIER J., RASMUSSEN P. Towards a systematic approach to comparing distributions used in flood frequency analysis. Journal of Hydrology, 142, 121, 1993.
  • 10. HOSKING R.M. L-Moments: Analysis and Estimation of Distributions using Linear Combinations of Order Statistics, Journal of Royal Statistical Society, 52, 105, 1990.
  • 11. ELAMIR E.A.H., SEHEULT A.H. Trimmed L-Moments, Computational Statistics & Data Analysis, 43, 299, 2003.
  • 12. WANG Q. J. Using Higher Probability Weighted Moments for Flood Frequency Analysis, Journal of Hydrology, 194, 95, 1997.
  • 13. HOSKING J.R.M., WALLIS J.R. Regional frequency analysis: An approach based on L-moments, Cambridge University Press, UK, 1997.
  • 14. MESHGI A., KHALILI D. Comprehensive evaluation of regional flood frequency analysis by L-and LH-moments. I. Are-visit to regional homogeneity. Stochastic Environmental Research and Risk Assessment, 23, 119, 2009a.
  • 15. MESHGI A., KHALILI D. Comprehensive evaluation of regional flood frequency analysis by L-and LH-moments. II. Development of LH-moments parameters for the generalized Pareto and generalized logistic distributions. Stochastic Environmental Research and Risk Assessment, 23, 137, 2009b.
  • 16. SHABRI A., ARIFF N. Frequency analysis of maximum daily rainfalls via l-moment approach. Sains Malaysiana, 38, 149, 2009.
  • 17. DEKA S., BORAH M., KAKATY S.C. Distribution of Annual Maximum Rainfall Series of North-East India. European Water (EW) Publications 27, 3, 2009.
  • 18. DAUD Z.M., KASSIM A.H.M., DESA M.N.M., NGUYEN V.T.V. Statistical analysis of at-site extreme rainfall processes in peninsular Malaysia. International Association of Hydrological Sciences. 274, 61, 2002.
  • 19. HAKTANIR T., COBANER M., KISI O. Frequency analyses of annual extreme rainfall series from 5 min to 24 h. Hydrological processes, 24, 3574, 2010.
  • 20. AL MAMOON A., JOERGENSEN N.E., RAHMAN A., QASEM H. Derivation of new design rainfall in Qatar using L-moment based index frequency approach. International Journal of Sustainable Built Environment. 3, 111, 2014.
  • 21. ABDUL-MONIEM I., SELIM Y.M. TL-moments and L-moments estimation for the generalized Pareto distribution. Applied Mathematical Sciences, 3, 43, 2009.
  • 22. AHMAD I., ABBAS A., ASLAM M., AHMAD I. Total Annual Rainfall Frequency Analysis in Pakistan using Methods of L-Moments and TL-Moments. Sci. Int. (Lahore), 27, 2331, 2015.
  • 23. MURSHED M.S., AM SEO Y., PARK J.S. LH-moment estimation of a four parameter kappa distribution with hydrologic applications. Stochastic Environmental Research and Risk Assessment, 28, 253, 2014.
  • 24. DURRANS S., TOMIC S. Comparison of Parametric tail Estimation for Low-Flow frequency Analysis. JAWRA Journal of the American Water Resources Association, 37 (5), 1203, 2001.
  • 25. ESLAMIAN S.S., GOHARI S.A., BIABANAKI M., MALEKIAN R. Estimation of monthly pan evaporation using artificial neural networks and support vector machines. J Appl Sci, 19, 3497, 2008.
  • 26. TOLIKAS K., GETTINBY G.D. Modelling the distribution of the extreme share returns in Singapore. Journal of Empirical Finance, 16, 54, 2009.
  • 27. MORGAN E.C., LACKNER M., VOGEL R.M., BAIS, L.G. Probability distributions for offshore wind speeds. Energy Conversion and Management, 52, 15, 2011.
  • 28. BÍLKOVA D. Robust parameter estimations using L-moments, TL-moments and the order statistics. American Journal of Applied Mathematics, 2, 36, 2014.
  • 29. ABDUL-MONIEM. L-moments and TL-moments estimation for the Ex-ponential distribution, Far East J.Theor. Stat, 23, 51, 2007.
  • 30. ABDUL-MONIEM, I. B.TL-moments and L-moments estimation for the Weibull distribution. Advances and Applications in Statistics, 15, 83, 2010.
  • 31. HOSKING J.R.M. Some theory and practical uses of trimmed L-moments. Journal of Statistical Planning and Inference. 137, 3024, 2007.
  • 32. ASQUITH W.H. L-moments and TL-moments of the generalized lambda distribution. Computational Statistics & Data Analysis. 51, 4484, 2007.
  • 33. SHABRI A. Comparisons of the LH Moments and the L Moments, Matematika, 18, 33, 2002.
  • 34. GAMAGE W., S.H.P., HEWA G.A., SUBHASHINI W.H.C., DANIELL T.M., KEMP D. Modelling the extreme floods of South Australian catchments, MODSIM, 3435, 2009.
  • 35. MURSHED M.S., PARKB B.J., JEONGA B.Y., PARK J.S. LH-Moments of some distributions useful in Hydrology, Communications of the Korean Statistical Society, 16, 647, 2009.
  • 36. DEKA S., BORAH M., KATATY S.C. Statistical Analysis of Annual Maximum Rainfall in North-East India: an approach of LH-moments, Theor Appl clim, 104, 111, 2011.
  • 37. JAN N.A.M. SHABRI A. Estimating distribution parameters of annual maximum streamflows in Johor, Malaysia using TL-moments approach. Theoretical and Applied Climatology. 1, 2015.
  • 38. AHMAD I., FAWAD M., MAHMOOD I. At-Site Flood Frequency Analysis of Annual Maximum Stream Flows in Pakistan Using Robust Estimation Methods. Polish Journal of Environmental Studies, 24, 2345, 2015.
  • 39. VOGEL R.M., FENNESSEY N.M. L moment diagrams should replace product moment diagrams. Water Resources Research, 29, 1745, 1993.
  • 40. CUNNANE C. Statistical distributions for flood frequency analysis, Operational hydrological Report No. 5/33, World Meteorological Organization (WMO), Geneva, Switzerland. 1989.
  • 41. CALENDA G., MANCINI C. P., VOLPI E. Selection of the probabilistic model of extreme floods: The case of the River Tiber in Rome. Journal of Hydrology. 371, 1, 2009.
  • 42. HADDAD K., RAHMAN A. Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia. Stoch. Env. Res. Risk Assess, 25, 415, 2011.
  • 43. LAIO F., DI BALDASSARRE G., MONTANARI A. Model selection techniques for the frequency analysis of hydrological extremes. Water Resources Research, 45, 2009.
  • 44. BESKOW S., CALDEIRA T.L., DE MELLO C.R., FARIA L.C., GUEDES H.A.S. Multiparameter probability distributions for heavy rainfall modelling in extreme southern Brazil. Journal of Hydrology: Regional Studies. 4, 123, 2015.
  • 45. SHARMA M.A., SINGH J.B. Use of probability distribution in rainfall analysis. New York Science Journal, 3, 40, 2010.
  • 46. AHMAD I., SHAH S.F., MAHMOOD I., AHMAD Z. Modeling of monsoon rainfall in Pakistan based on Kappa distribution. Sci. Int. (Lahore), 25, 333, 2013.
  • 47. SALARPOUR M., YUSOP Z., YUSOF F. Comparison of Distribution Models for Peak flow, Flood Volume and Flood Duration. Research Journal of Applied Sciences, Engineering and Technology, 6, 733, 2013
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.