Theoretical and Applied Climatology

, Volume 129, Issue 3–4, pp 1295–1307 | Cite as

Regional maximum rainfall analysis using L-moments at the Titicaca Lake drainage, Peru

  • Carlos Antonio Fernández-PalominoEmail author
  • Waldo Sven Lavado-Casimiro
Original Paper


The present study investigates the application of the index flood L-moments-based regional frequency analysis procedure (RFA-LM) to the annual maximum 24-h rainfall (AM) of 33 rainfall gauge stations (RGs) to estimate rainfall quantiles at the Titicaca Lake drainage (TL). The study region was chosen because it is characterised by common floods that affect agricultural production and infrastructure. First, detailed quality analyses and verification of the RFA-LM assumptions were conducted. For this purpose, different tests for outlier verification, homogeneity, stationarity, and serial independence were employed. Then, the application of RFA-LM procedure allowed us to consider the TL as a single, hydrologically homogeneous region, in terms of its maximum rainfall frequency. That is, this region can be modelled by a generalised normal (GNO) distribution, chosen according to the Z test for goodness-of-fit, L-moments (LM) ratio diagram, and an additional evaluation of the precision of the regional growth curve. Due to the low density of RG in the TL, it was important to produce maps of the AM design quantiles estimated using RFA-LM. Therefore, the ordinary Kriging interpolation (OK) technique was used. These maps will be a useful tool for determining the different AM quantiles at any point of interest for hydrologists in the region.


Return Period Annual Maximum Ordinary Kriging Generalise Extreme Value Generalise Extreme Value Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This study was possible because of the availability (to the scientific community) of various free software packages of statistical software R, particularly, the lmomRFA package for RFA-LM and the gstat package for spatial geo-statistical modelling. Moreover, we thanks the SNF project DECADE by supporting this publication.


  1. Acuña J, Felipe O, Ordoñez J, Arboleda F (2011) Regional analysis of annual rainfall frequency for the determination of drought maps. Rev Peru GEO-ATMOSFÉRICA RPGA 115:104–115Google Scholar
  2. Barnett V, Lewis T (1984) Outliers in statistical dataGoogle Scholar
  3. Bourges J, Cortes J, Salas E (1992) Hydrological potential. In: Dejoux C, Iltis A (eds) Lake Titicaca a synthesis of limnological knowledge. Kluwer, Dordrecht, Boston, London, pp. 523–538CrossRefGoogle Scholar
  4. Cressie N (1985) Fitting variogram models by weighted least squares. J Int Assoc Math Geol 17:563–586. doi: 10.1007/BF01032109 CrossRefGoogle Scholar
  5. Falvey M, Garreaud RD (2005) Moisture variability over the South American Altiplano during the South American Low Level Jet Experiment (SALLJEX) observing season. J Geophys Res 110:D22105. doi: 10.1029/2005JD006152 CrossRefGoogle Scholar
  6. Gálvez JM, Orozco RK, Reyes CR, Douglas MW (2006) Observed diurnal circulations and rainfall over the Altiplano during the SALLJEX, pp 1041–1047Google Scholar
  7. Garreaud R (1999) Multiscale analysis of the summertime precipitation over the central Andes. Mon Weather Rev 127:901–921CrossRefGoogle Scholar
  8. Garreaud R, Aceituno P (2001) Interannual rainfall variability over the South American Altiplano. J Clim 14:2779–2789CrossRefGoogle Scholar
  9. Goovaerts P (1997) Geostatics for natural resources evaluation. Oxford University Press, LondonGoogle Scholar
  10. Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-momentsGoogle Scholar
  11. Johnston K, Ver Hoef JM, Krivoruchko K, Lucas N (2001) Using ArcGIS geostatistical analyst. Esri RedlandsGoogle Scholar
  12. Kendall MG (1975) Rank correlation methodsGoogle Scholar
  13. Kondratieva T, Amarchi H (2015) Regionalization of extreme daily precipitation: case study of the north east region of Algeria. Hydrol Sci J 60:498–507. doi: 10.1080/02626667.2014.988154 CrossRefGoogle Scholar
  14. Koutsoyiannis D, Baloutsos G (2000) Analysis of a long record of annual maximum rainfall in Athens, Greece, and design rainfall inferences. Nat Hazards 22:29–48CrossRefGoogle Scholar
  15. Lavado Casimiro WS, Ronchail J, Labat D, et al. (2012) Basin-scale analysis of rainfall and runoff in Peru (1969–2004): Pacific, Titicaca and Amazonas drainages. Hydrol Sci J 57:625–642. doi: 10.1080/02626667.2012.672985 CrossRefGoogle Scholar
  16. Ljung GM, Box GEP (1978) On a measure of lack of fit in time series models. Biometrika 65:297–303CrossRefGoogle Scholar
  17. Luna Vera JA, Domínguez Mora R (2013) Un método para el análisis de frecuencia regional de lluvias máximas diarias: aplicación en los Andes bolivianos. Ingeniare Rev Chil Ing 21:111–124CrossRefGoogle Scholar
  18. Mann HB (1945) Nonparametric tests against trend. Econ J Econ Soc 13:245–259Google Scholar
  19. McBratney AB, Webster R (1986) Choosing functions for semi-variograms of soil properties and fitting them to sampling estimates. J Soil Sci 37:617–639. doi: 10.1111/j.1365-2389.1986.tb00392.x CrossRefGoogle Scholar
  20. Miller JF, Frederick RH, Tracey RS (1973) NOAA ATLAS 2, Precipitation-frequency atlas of the western United States. U.S. Dept. of Commerce, NOAA, National Weather Service, Washington DC, USAGoogle Scholar
  21. Ngongondo CS, Xu C-Y, Tallaksen LM, et al. (2011) Regional frequency analysis of rainfall extremes in Southern Malawi using the index rainfall and L-moments approaches. Stoch Env Res Risk A 25:939–955CrossRefGoogle Scholar
  22. Noto LV, La Loggia G (2009) Use of L-moments approach for regional flood frequency analysis in Sicily, Italy. Water Resour Manag 23:2207–2229CrossRefGoogle Scholar
  23. Núñez JH, Verbist K, Wallis JR, et al. (2011) Regional frequency analysis for mapping drought events in north-central Chile. J Hydrol 405:352–366CrossRefGoogle Scholar
  24. Pettitt AN (1979) A non-parametric approach to the change-point problem. Appl Stat:126–135Google Scholar
  25. Rahman MM, Sarkar S, Najafi MR, Rai RK (2013) Regional extreme rainfall mapping for Bangladesh using L-moment technique. J Hydrol Eng 18:603–615. doi: 10.1061/(asce)he.1943-5584.0000663 CrossRefGoogle Scholar
  26. Roche MA, Bourges J, Cortes J, Mattos R (1992) Climatología e hidrología de la cuenca del lago Titicaca. In: Dejoux CA (ed) El Lago Titicaca. Síntesis del conocimiento Limnológico actual. Springer Netherlands, Boston, pp. 83–104 (ORSTOM - HISBOL, La Paz, Bolivia)Google Scholar
  27. Salas JD, Obeysekera J (2014) Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events. J Hydrol Eng 19:554–568. doi: 10.1061/(ASCE)HE.1943-5584.0000820 CrossRefGoogle Scholar
  28. Sanabria J, Marengo J, Valverde M (2009) Climate change scenarios using regional models for the Peruvian Altiplano (Departament of Puno). Rev Peru Geo-Atmosférica 1:133–148Google Scholar
  29. Schaefer MG, Barker BL, Taylor GH, Wallis JR (2006) Regional precipitation-frequency analysis and spatial mapping of precipitation for 24-h and 2-h durations in eastern Wahington, Prepared for Washington State Department of Transportation, MGS Engineering Consultants, Olympia, Washington, USAGoogle Scholar
  30. Sylvestre F, Servant-Vildary S, Roux M (2001) Diatom-based ionic concentration and salinity models from the south Bolivian Altiplano (15-23S). J Paleolimnol 25:279–295CrossRefGoogle Scholar
  31. Szolgay J, Parajka J, Kohnová S, Hlavčová K (2009) Comparison of mapping approaches of design annual maximum daily precipitation. Atmos Res 92:289–307CrossRefGoogle Scholar
  32. Tveito O, Wegehenkel M, Van der Wel F, Dobesch H (2008) Use of geographic information systems in climatology and meteorologyGoogle Scholar
  33. Verdon-Kidd DC, Kiem AS (2015) Non–stationarity in annual maxima rainfall across Australia—implications for intensity-frequency-duration (IFD) relationships. Hydrol Earth Syst Sci Discuss 12:3449–3475. doi: 10.5194/hessd-12-3449-2015 CrossRefGoogle Scholar
  34. Viglione A, Laio F, Claps P (2007) A comparison of homogeneity tests for regional frequency analysis. Water Resour Res. doi: 10.1029/2006WR005095 Google Scholar
  35. Vuille M, Ammann C (1997) Regional snowfall patterns in the high, arid Andes. In: Climatic change at high elevation sites. Springer, Berlin Heidelberg New York, pp. 181–191CrossRefGoogle Scholar
  36. Vuille M, Keimig F (2004) Interannual variability of summertime convective cloudiness and precipitation in the central Andes derived from ISCCP-B3 data. J Clim 17:3334–3348CrossRefGoogle Scholar
  37. Wallis JR, Schaefer MG, Barker BL, Taylor GH (2007) Regional precipitation-frequency analysis and spatial mapping for 24-hour and 2-hour durations for Washington state. Hydrol Earth Syst Sci 11:415–442. doi: 10.5194/hess-11-415-2007 CrossRefGoogle Scholar
  38. Weiss LL (1964) Ratio of true to fixed interval maximum rainfall. J Hydraul ASCE 90:77–82Google Scholar
  39. WWAP UN (2003) UN World Water Development Report: Water for People, Water for LifeGoogle Scholar
  40. Yang T, Shao Q, Hao Z-C, et al. (2010) Regional frequency analysis and spatio-temporal pattern characterization of rainfall extremes in the Pearl River Basin, China. J Hydrol 380:386–405. doi: 10.1016/j.jhydrol.2009.11.013 CrossRefGoogle Scholar
  41. Yue S, Pilon P, Phinney B, Cavadias G (2002) The influence of autocorrelation on the ability to detect trend in hydrological series. Hydrol Process 16:1807–1829. doi: 10.1002/hyp.1095 CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2016

Authors and Affiliations

  • Carlos Antonio Fernández-Palomino
    • 1
    Email author
  • Waldo Sven Lavado-Casimiro
    • 1
  1. 1.Servicio Nacional de Meteorología e Hidrología del Perú (SENAMHI)LimaPeru

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