Precipitation scenarios in the Central-Western Mediterranean basin
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5 Forecast of Rainfall Using Winter's Model
A forecast of precipitation over the Central-Western Mediterranean has been
performed until 2030, by using the Winter's statistical model (Granger and Engle,
1987).
This model has been applied on the series of the pressure field (500 hPa height)
in Algiers, the representative station of the Western part ofthe basin. Then, on the
basis ofthe connection between the Mediterranean Oscillation and the rainfall series
in the Central-Western Mediterranean, also a precipitation prediction has been
performed.
The Winter's multiplicative model, in fact, is useful to make predictions of time
series which present the tendency to a cyclical pattern. This tendency is called
seasonality, while the length of the cycle L is the seasonal period. As found by the
spectral analysis, the Mediterranean Oscillation shows a 22 years periodicity. In this
case L = 22.
Winter's multiplicative model assumes that the given series can be decomposed
into three components, according to the following form:
Y t = ' Fr X S t + e t
(2)
where:
Yt is the observational data at time t,
Tt is the trend component or level of the series, modeled by the linear trend
' Fr = J-lt + fJt ,
St is he seasonal component, modelled by seasonal indicators I i = I i+l.= I i+2L where
L
I Ii = L
i = l.. ..... L,
i=l
e t is a random or error component.
Starting values for T, fl, I, have been selected according to Abraham and
Ledolter (1983).
Winter's model is based on the following equations:
a· Yt
[
]
I; = -1-+ (1- a) Tt-1 + Pt-l
t-L
b·y
It =T+(l-b).I t - L
t
(3)
Pt = c· [Tt - I;-l]+ (1- c)· Pt-l
The prediction at the time tH is given by: