Page 42 - Contributed Paper Session (CPS) - Volume 5

CPS795 Nestor B.
rainy season and precipitations in the time and space. To Le Barbé and al.[5]
we got a reduction from 15 to 20 per cent of Benin yearly precipitations from
the seventies. Those kind of modifications can be very well analysed with
stochastic method, taking into account random and dynamic aspects of rainy
events occurrence.

2. Main Objectives
The objective of our work is to study a model stochastic able to describe
and analyze the variability of daily rainfall and the climatic impact on the
precipitation at Benin. For that we will break down the study in several stages:
1. Build a stochastic model, we realize the implementation of a Markov
hidden model with a periodicity on the Markov chain (which is non-
homogeneous) and a mixture as a law of emission, the study of the
ergodicity of the Markov chain, and finally the identifiability of the
model.
2. Implementation of an EM algorithm for the adjustment of the data to
model by the maximum likelihood method in using the Baum-Welch
procedure and the Viterbi algorithm.
3. Estimation of a break in the model corresponding to a climatic evolution
by likelihood ratio.
4. Application to the series of daily levels of precipitation in Benin.
Materials and Methods

Station start end days
Cotonou 1952 2007 20440
Bohicon 1940 2007 24820
Save` 1921 2007 31755
Parakou 1921 2007 31755
Kandi 1921 2007 31755
Natitingou 1921 2007 31755
Table 1: Start, end and length of daily precipitation

We assume that the set of the generating mechanisms of the precipitations
is a process hierarchical unobserved. For the analysis of such a system of data,
the hidden Markovs models (HMMs) are more adapted. These models not only
take in account the observed precipitations but also the risk to the level of the
generating processes of its observations.
Model
A hidden Markov model is a discrete-time stochastic process
{( , )} such that (i) { } is a finite-state Markov chain, and (ii) given

{ },{ } is a sequence of conditionally independent random variables

with the conditional distribution of depending on { } only throught

.

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