Assessment of Parameters of the Generalized Extreme Value Distribution in Rainfall of the Peruvian North
##plugins.themes.bootstrap3.article.main##
Guillermo Arriola
Luis Villegas
Joseph Fernandez
Jheny Vallejos
Cesar Idrogo
Abstract
The maximum rainfall in the Peruvian north behaves seasonally, concentrating between the first months of the year, however, few studies have analyzed its distribution over time through an analysis of extremes. The objective of the research was to evaluate the parameters of location, scale and shape of the generalized extreme value distribution in maximum rainfall in the Peruvian north corresponding to the Pacific 5 and Pacific 6 hydrological regions. The maximum daily rainfall data available was collected in the climatic stations of both regions, considering a minimum number of 15 years of records per station and a filter based on statistical and visual analysis, for which 138 stations were established. Subsequently, the adjustments were applied to ordinary moments and to linear moments of the generalized extreme value distribution and two types of hypothesis tests were used for each region that helped to validate the similarities of each parameter in both regions. The results show significant differences only in the location parameter, while, when contrasting the altitude, average rainfall and maximum rainfall of each hydrological region it was determined that there are high correlations with the location and scale parameters. Finally, it is concluded that both hydrological regions, the scale and shape parameters show a good performance for both adjustments based on the applied hypotheses and the location parameter showed that the Pacific 6 hydrological region is rainier than the Pacific 5 hydrological region.
##plugins.themes.revistapolitecnica.stadistisDownloadTitle##
Downloads
Article Details
References
Abreu, M., de Souza, A., Lyra, G., de Oliveira-Júnior, J., Pobocikova, I., de Almeida, L., de Souza, F., Aristone, F., & Cecílio, R. (2023). Assessment and characterization of the monthly probabilities of rainfall in Midwest Brazil using different goodness-of-fit tests as probability density functions selection criteria. Theoretical and Applied Climatology, 151(1-2), 491-513. https://doi.org/10.1007/s00704-022-04286-z
Adeola, O., Masinde, M., Botai, J., Adeola, A., & Botai, C. (2021). An analysis of precipitation extreme events based on the SPI and EDI values in the Free State province, South Africa. Water (Switzerland), 13(21). https://doi.org/10.3390/w13213058
Alahmadi, F., & Rahman, N. (2020). Climate change impacts on extreme rainfall frequency prediction. Journal of Water and Climate Change, 11(4), 935-943. https://doi.org/10.2166/wcc.2019.138
Back, Á., & Bonfante, F. (2021). Evaluation of generalized extreme value and Gumbel distributions for estimating maximum daily rainfall. Brazilian Journal of Environmental Sciences, 56(4), 654-664. https://doi.org/10.5327/Z217694781015
Alfaro, E., Chourio, X., Muñoz, Á., & Mason,S. (2018). Improved seasonal prediction skill of rainfall for the primera season in Central America. International Journal of Climatology, 38, e255-e268. http://doi.org/10.1002/joc.5366
Arriola, G. (2021). Uso del software libre como aporte al sílabo hidrología de la Universidad Señor de Sipán en tiempos de Covid-19. Revista Hacedor, 5(2), 10-18. https://doi.org/10.26495/rch.v5i2.1923
Arriola, G., Villegas, L., Marín, N., Idrogo, C., Piedra, J., & Arbulú, J. (2022). Assessment of climatic aggressiveness and precipitation concentration in the Chancay-Lambayeque basin, Peru. Revista Politecnica, 50(2), 15–22. https://doi.org/10.33333/rp.vol50n2.02
Bowman, K., & Shenton, L. (2014). Estimation: Method of moments. Wiley StatsRef: Statistics Reference Online. https://doi.org/10.1002/9781118445112.stat01679
Campos-Aranda, D. (2018). Fitting with mobile L moments of the GEV distribution with variable location and scale parameters. Agrociencia, 52(7), 933-950. https://agrociencia-colpos.mx/index.php/agrociencia/article/view/1714
Campos-Aranda, D. (2019). Fitting with L-moments of the non-stationary distributions GVE1 and GVE2 to PMD series. Tecnologia y Ciencias del Agua, 10(5), 75-103. https://doi.org/10.24850/j-tyca-2019-05-03
Campos-Aranda, D. (2021). Flood frequency analysis with the GEV distribution for r-annual events. Tecnologia y Ciencias del Agua, 12(4), 163-218. https://doi.org/10.24850/J-TYCA-2021-04-04
Diriba, T., & Debusho, L. (2021). Statistical modeling of spatial extremes through max-stable process models: Application to extreme rainfall events in South Africa. Journal of Hydrologic Engineering, 26(10). https://doi.org/10.1061/(ASCE)HE.1943-5584.0002123
Efron, B. (1979). Bootstrap methods: Another look at the Jackknife. The Annals of Statistics, 7(1), 1-26. https://doi.org/10.1214/aos/1176344552
Fernandez-Palomino, C., Hattermann, F., Krysanova, V., Lobanova, A., Vega-Jácome, F., Lavado, W., Santini, W., Aybar, C., & Bronstert, A. (2022). A Novel high-resolution gridded precipitation dataset for Peruvian and Ecuadorian watersheds: Development and hydrological evaluation. Journal of Hydrometeorology, 23(3), 309-336. https://doi.org/10.1175/JHM-D-20-0285.1
Flores-Rojas, J., Silva, Y., Suárez-Salas, L., Estevan, R., Valdivia-Prado, J., Saavedra, M., Giraldez, L., Piñas-Laura, M., Scipión, D., Milla, M., Kumar, S., & Martinez-Castro, D. (2021). Article analysis of extreme meteorological events in the central andes of Peru using a set of specialized instruments. Atmosphere, 12(3). https://doi.org/10.3390/atmos12030408
Guillén-Oviedo, H., Cid-Serrano, L., & Alfaro-Martínez, E. (2020). Comparison of parameters of the generalized extreme value distribution associated with extreme rainfall events in Central America. Uniciencia, 34(1), 111-128. http://dx.doi.org/10.15359/ru.34-1.7
Halim, S. (2019). Delta change method with cyclic covariate generalized extreme value model for downscaling extreme rainfall. International Journal of Recent Technology and Engineering, 8(2S2), 158-161. https://doi.org/10.35940/ijrte.B1029.0782S219
Herrera, C., Campos, J., & Carrillo, F. (2017). Estimación de datos faltantes de precipitación por el método de regresión lineal: Caso de estudio Cuenca Guadalupe, Baja California, México. Investigación y Ciencia de la Universidad Autónoma de Aguascalientes, 25(71), 34-44. https://doi.org/10.33064/iycuaa201771598
Hosking, J. (1990). L-Moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52(1), 105-124. https://doi.org/10.1111/j.2517-6161.1990.tb01775.x
Hossain, I., Khastagir, A., Aktar, M., Imteaz, M., Huda, D., & Rasel, H. (2021). Comparison of estimation techniques for generalised extreme value (GEV) distribution parameters: a case study with Tasmanian rainfall. International Journal of Environmental Science and Technology. 19(8), 7737-7750 https://doi.org/10.1007/s13762-021-03693-5
Juma, B., Olang, L., Hassan, M., Chasia, S., Bukachi, V., Shiundu, P., & Mulligan, J. (2021). Analysis of rainfall extremes in the Ngong River Basin of Kenya: Towards integrated urban flood risk management. Physics and Chemistry of the Earth, 124. https://doi.org/10.1016/j.pce.2020.102929
Kozanis, S., Christofides, A., Mamassis, N., Efstratiadis, A., & Koutsoyiannis, D. (2010). Hydrognomon - Open source software for the analysis of hydrological data. Conference: European Geosciences Union General Assembly 2010, 12. https://doi.org/10.13140/RG.2.2.21350.83527
Klassou, K., & Komi, K. (2021). Analysis of extreme rainfall in Oti river basin (West Africa). Journal of Water and Climate Change, 12(5), 1997-2009. https://doi.org/10.2166/wcc.2021.154
Lavado, W., Labat, D., & Ronchail, J. (2013). Trends in rainfall and temperature in the Peruvian Amazon–Andes basin over the last 40 years (1965-2007). Hydrological Processes, 27(20), 2944-2957. https://doi.org/10.1002/hyp.9418
Lee, S., & Kim, H. (2023). Two tests using more assumptions but lower power. Communications for Statistical Applications and Methods, 30(1), 109-117. https://doi.org/10.29220/CSAM.2023.30.1.109
Lima, A., Lyra, G., Abreu, M., Oliveira-Júnior, J., Zeri, M., & Cunha-Zeri, G. (2021). Extreme rainfall events over Rio de Janeiro State, Brazil: Characterization using probability distribution functions and clustering analysis. Atmospheric Research, 247. https://doi.org/10.1016/j.atmosres.2020.105221
López, J., Delgado, O., & Campo, M. (2018). Determinación de las curvas IDF en Igueldo-San Sebastián. Comparación de diferentes métodos. Ingeniería del Agua, 22(4), 209-223. https://doi.org/10.4995/Ia.2018.9480
Luna-Romero, A., Ramírez, I., Sánchez, C., Conde, J., Agurto, L., & Villaseñor, D. (2018). Distribución espacio-temporal de la precipitación en la cuenca del río Jubones, Ecuador: 1975-2013. Scientia Agropecuaria, 9(1), 63-70. https://dx.doi.org/10.17268/sci.agropecu.2018.01.07
Mashishi, D., Maposa, D., & Lesaoana, M. (2020). Comparative analysis of the 100-year return level of the average monthly rainfall for South Africa: Parent distribution versus extreme value distributions. Applied Mathematics and Information Sciences, 14(5), 801-807. https://doi.org/10.18576/amis/140507
Min, J., & Halim, S. (2020). Rainfall modelling using generalized extreme value distribution with cyclic covariate. Mathematics and Statistics, 8(6), 762-772. https://doi.org/10.13189/ms.2020.080617
Mohamed, J., & Adam, M. (2022). Modeling of magnitude and frequency of extreme rainfall in Somalia. Modeling Earth Systems and Environment. 8(3), 4277-4294. https://doi.org/10.1007/s40808-022-01363-0
Nerantzaki, S., & Papalexiou, S. (2022). Assessing extremes in hydroclimatology: A review on probabilistic methods. Journal of Hydrology, 605. https://doi.org/10.1016/j.jhydrol.2021.127302
Oruc, S. (2021). Non-stationary investigation of extreme rainfall. Civil Engineering Journal (Iran), 7(9), 1620-1633. https://doi.org/10.28991/cej-2021-03091748
Padiyedath-Gopalan, S., Kawamura, A., Amaguchi, H., Takasaki, T., & Azhikodan, G. (2019). A bootstrap approach for the parameter uncertainty of an urban-specific rainfall-runoff model. Journal of Hydrology, 579. https://doi.org/10.1016/j.jhydrol.2019.124195
Peleg, N., Marra, F., Fatichi, S., Paschalis, A., Molnar, P., & Burlando, P. (2018). Spatial variability of extreme rainfall at radar subpixel scale. Journal of Hydrology, 556, 922-933. https://doi.org/10.1016/j.jhydrol.2016.05.033
Rollenbeck, R., Orellana-Alvear, J., Bendix, J., Rodriguez, R., Pucha-Cofrep, F., Guallpa, M., Fries, A., & Célleri, R. (2022). The Coastal El Niño event of 2017 in Ecuador and Peru: A weather radar analysis. Remote Sensing, 14(4). https://doi.org/10.3390/rs14040824
Rollenbeck, R., Orellana-Alvear, J., Rodriguez, R., Macalupu, S., & Nolasco, P. (2021). Calibration of X-band radar for extreme events in a spatially complex precipitation region in north peru: Machine learning vs. empirical approach. Atmosphere, 12(12). https://doi.org/10.3390/atmos12121561
Roslan, R., Na, C., & Gabda, D. (2020). Parameter estimations of the generalized extreme value distributions for small sample size. Mathematics and Statistics, 8(2), 47-51. https://doi.org/10.13189/ms.2020.081308
Samantaray, S., & Sahoo, A. (2020). Estimation of flood frequency using statistical method: Mahanadi River basin, India. H2Open Journal, 3(1), 189-207. https://doi.org/10.2166/h2oj.2020.004
Seo, J., Won, J., Choi, J., Lee, J., Jang, S., & Lee, O. (2021). Uncertainty of rate of change in Korean future rainfall extremes using non-stationary GEV model. Atmosphere, 12(2). https://doi.org/10.3390/atmos12020227
SENAMHI. (2017a). Estudio: Regionalización de las precipitaciones máximas del Perú. Lima, Perú: Dirección de Hidrología del Servicio Nacional de Meteorología e Hidrología del Perú. https://repositorio.senamhi.gob.pe/handle/20.500.12542/239
SENAMHI. (2017b). Nota técnica N° 002: Atlas de erosión de suelos por regiones hidrológicas del Perú. Lima, Perú: Dirección de Hidrología del Servicio Nacional de Meteorología e Hidrología del Perú. https://repositorio.senamhi.gob.pe/handle/20.500.12542/261
SENAMHI. (2018). Estudio: Estimación de umbrales de inundación en la Región Hidrográfica del Pacífico. Lima, Perú: Dirección de Hidrología del Servicio Nacional de Meteorología e Hidrología del Perú. https://repositorio.senamhi.gob.pe/handle/20.500.12542/241
Ulrich, J., Fauer, F., & Rust, H. (2021). Modeling seasonal variations of extreme rainfall on different timescales in Germany. Hydrology and Earth System Sciences, 25(12), 6133-6149. https://doi.org/10.5194/hess-25-6133-2021
Vavrus, S., Wang, F., & Block, P. (2022). Rainy season precipitation forecasts in coastal Peru from the North American multi-model ensemble. International Journal of Climatology. 42(12), 6221-6234. https://doi.org/10.1002/joc.7586
Vivekanandan, N. (2018). Comparison of probability distributions in extreme value analysis of rainfall and temperature data. Environmental Earth Sciences, 77(5). https://doi.org/10.1007/s12665-018-7356-z
Vivekanandan, N. (2022). Intercomparison of estimators of extreme value family of distributions for rainfall frequency analysis. Mausam, 73(1), 59-70. https://doi.org/10.54302/MAUSAM.V73I1.5080
Wang, H., & Xuan, Y. (2021). Spatial variation of extreme rainfall observed from two century-long datasets. Geophysical Research Letters, 48(8). https://doi.org/10.1029/2020GL091933
Wang, H., & Xuan, Y. (2022). Spatial variation of catchment-oriented extreme rainfall in England and Wales. Atmospheric Research, 266(2022), 105968. https://doi.org/10.1016/j.atmosres.2021.105968
Yeo, M., Nguyen, V., & Kpodonu, T. (2021). Characterizing extreme rainfalls and constructing confidence intervals for IDF curves using Scaling-GEV distribution model. International Journal of Climatology, 41(1), 456-468. https://doi.org/10.1002/joc.6631
Article Sidebar
Article Sidebar
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.