A Copulas Approach for Forecasting the Rainfall

  • Adelhak ZoglatEmail author
  • Amine Amar
  • Fadoua Badaoui
  • Laila Ait Hassou
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 913)


Rainfall forecasting is a crucial issue in a semi-arid country like Morocco. Information on rainfalls can be used by marketers in the short term, to plan customer allocations and storage requirements. In the middle term, it can provide guidelines for seasonal selection of crops. In the long term, rainfall forecasts are important for hydrologists and water managers to build integrated strategies against potential disasters caused by tremendous floods or severe droughts.

Rainfall forecasting methods are of two kinds. The first one relies on statistical approaches while the second one is based on numerical simulations. Despite their higher cost, numerical simulations are still unable to consistently outperform simple statistical prediction systems. This is essentially related to the uncertainty of the relationship between rainfalls, hydro-climatic variables and climatic variability indices.

This paper aims to present a statistical approach supporting the use of lagged Southern Oscillation Index (SOI) for forecasting seasonal rainfall. We establish a statistical model, based on copulas theory, which takes the SOI and the rainfall relationship into account. Data are obtained from the World Meteorological Organization (WMO), for 6 meteorological stations located in Morocco (Tangier and Casablanca), Spain (La Coruna and Valladolid), and Portugal (Lisboa-Geofísica and Santa Maria). Using the suggested approach, we conduct a deep temporal and regional comparative analysis, which leads to the adjustment of different families of copulas, but with a predominance of Normal and Clayton copulas. For all stations and seasons, final results confirm a delayed effect in the structure between Rainfall and SOI with a strong relationship on the central part, while rainfall extreme events can be related to other atmospheric and climatologic indices.


Rainfall forecasting Southern Oscillation Index (SOI) Copulas theory Quantile regression 


  1. 1.
    American Meteorological Society (AMS), Boston, Massachusetts, United States.
  2. 2.
    Chawla, L., Osuri, K.K., Mujumdar, P.P., Niyogi, D.: Assessment of the Weather Research and Forecasting (WRF) model for simulation of extreme rainfall events in the upper Ganga Basin. Hydrol. Earth Syst. Sci. 22(2), 1095 (2018)CrossRefGoogle Scholar
  3. 3.
    Pham, M.T., Vernieuwe, H., De Baets, B., Verhoest, N.E.: A coupled stochastic rainfall-evapotranspiration model for hydrological impact analysis. Hydrol. Earth Syst. Sci. 22(2), 1263 (2018)CrossRefGoogle Scholar
  4. 4.
    Jha, S.L., Shrestha, D.L., Stadnyk, T.A., Coulibaly, P.: Evaluation of ensemble precipitation forecasts generated through post-processing in a Canadian catchment. Hydrol. Earth Syst. Sci. 22(3), 1957 (2018)CrossRefGoogle Scholar
  5. 5.
    Zhang, S., Zhao, L., Delgado-Tellez, R., Bao, H.: A physics-based probabilistic forecasting model for rainfall-induced shallow landslides at regional scale. Nat. Hazards Earth Syst. Sci. 18(3), 969 (2018)CrossRefGoogle Scholar
  6. 6.
    Kim, K., Lee, S., Jin, Y.: Forecasting quarterly inflow to reservoirs combining a copula-based bayesian network method with drought forecasting. Water 10(2), 233 (2018)CrossRefGoogle Scholar
  7. 7.
    Sene, K., Tych, W., Beven, K.: Exploratory studies into seasonal flow forecasting potential for large lakes. Hydrol. Earth Syst. Sci. 22(1), 127 (2018)CrossRefGoogle Scholar
  8. 8.
    Chiew, F.H., Piechota, T.C., Dracup, J.A., McMahon, T.A.: El Nino/Southern Oscillation and Australian rainfall, stream flow and drought: links and potential for forecasting. J. Hydrol. 204(1–4), 138–149 (1998)CrossRefGoogle Scholar
  9. 9.
    McBride, J.L., Nicholls, N.: Seasonal relationships between Australian rainfall and the Southern Oscillation. Mon. Weather Rev. 111(10), 1998–2004 (1983)CrossRefGoogle Scholar
  10. 10.
    Stone, R., Hammer, G., Nicholls, N.: Frost in northeast Australia: trends and influences of phases of the Southern Oscillation. J. Clim. 9(8), 1896–1909 (1996)CrossRefGoogle Scholar
  11. 11.
    Kirono, D.G., Chiew, F.H., Kent, D.M.: Identification of best predictors for forecasting seasonal rainfall and runoff in Australia. Hydrol. Process. 24(10), 1237–1247 (2010)Google Scholar
  12. 12.
    Hyden, L., Sekoli, T.: Possibilities to forecast early summer rainfall in the Lesotho Lowlands from the El-Nino/Southern Oscillation. WATERSA-PRETORIA 26(1), 83–90 (2000)Google Scholar
  13. 13.
    Hadiani, M., Asl, S.J., Banafsheh, M.R., Dinpajouh, Y., Yasari, E.: Investigation the Southern Oscillation index effect on dry/wet periods in north of Iran. Int. J. Agric. CropSci 4, 1291–1299 (2012)Google Scholar
  14. 14.
    Chifurira, R., Chikobvu, D.: A probit regression model approach for predicting drought probabilities in Zimbabwe using the Southern Oscillation Index. Mediterr. J. Soc. Sci. 5(20), 656 (2014)Google Scholar
  15. 15.
    Rodriguez, D., de Voil, P., Hudson, D., Brown, J.N., Hayman, P., Marrou, H., Meinke, H.: Predicting optimum crop designs using crop models and seasonal climate forecasts. Sci. Rep. 8(1), 2231 (2018)CrossRefGoogle Scholar
  16. 16.
    Zahmatkesh, Z., Goharian, E.: Comparing machine learning and decision making approaches to forecast long lead monthly rainfall: the city of vancouver, Canada. Hydrology 5(1), 10 (2018)CrossRefGoogle Scholar
  17. 17.
    Agilan, V., Umamahesh, N.V.: El Niño Southern Oscillation cycle indicator for modeling extreme rainfall intensity over India. EcologicalIndicators 84, 450–458 (2018)Google Scholar
  18. 18.
    Deheuvels, P.: La fonction de dépendance empirique et ses propriétés. Un test non paramétrique d’indépendence. Acad. Roy. Belg. Bull. Cl. Sci. 65(6), 274–292 (1979). 5e serieMathSciNetzbMATHGoogle Scholar
  19. 19.
    Roncalli, T., Durrleman, A., Nikeghbali, A.: Which copula is the right one. Groupe de Recherche Opérationnelle, Credit Lyonnais, Paris (2000)Google Scholar
  20. 20.
    Embrechts, P., Lindskog, F., McNeil, A.: Modelling dependence with copulas. Rapport technique, Département de mathématiques, Institut Fédéralde Technologie de Zurich, Zurich (2001)Google Scholar
  21. 21.
    Kolev, N., Paiva, D.: Copula-based regression models. Department of Statistics, University of São Paulo (2007)Google Scholar
  22. 22.
    Sklar, A.: Fonctions de répartition à n dimension et leurs marges. Publications de l’Institut Statistique de l’université de Paris 8, 229–231 (1959)zbMATHGoogle Scholar
  23. 23.
    Nelsen, R.B.: An Introduction to Copulas, 2nd edn. Springer, New York (2006)zbMATHGoogle Scholar
  24. 24.
    Joe, H.: Multivariate Models and Dependence Concepts. Monographs on Statistics and Applied Probability, vol. 73. Chapman Hall, London (1997)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Adelhak Zoglat
    • 1
    Email author
  • Amine Amar
    • 2
  • Fadoua Badaoui
    • 3
  • Laila Ait Hassou
    • 1
  1. 1.Laboratory of Mathematics, Statistics and Applications, Faculty of SciencesMohammed V University in RabatRabatMorocco
  2. 2.Moroccan Agency for Sustainable EnergyRabatMorocco
  3. 3.Department of Statistics, Demography and Actuarial SciencesNational Institute of Statistics and Applied Economics RabatRabatMorocco

Personalised recommendations