A Copulas Approach for Forecasting the Rainfall
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.
KeywordsRainfall forecasting Southern Oscillation Index (SOI) Copulas theory Quantile regression
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