poster - International Conference of Agricultural Engineering

MULTIVARIATE STATISTICAL OF PRINCIPAL COMPONENTS AND
CLUSTER ANALYSES IN THE STUDY SUPPORT OF
REGIONALIZATION OF FLOW
Abrahão A. A. Elesbon 1 *, Demetrius D. Silva 2 , Gilberto C. Sedyiama 2 , Carlos A. A. S.
Ribeiro 3
1 Federal nstitute of Espírito Santo, Av. Arino Gomes Leal, 1700, Colatina-ES, 29700-558, Brazil.
E-mail: abrahaoelesbon@gmail.com
2 Federal University of Viçosa, DEA. Av. Peter Henry Holfs, s/n, Viçosa-MG, 36570-000, Brazil.
3 Federal University of Viçosa, DEF. Av. Peter Henry Holfs, s/n, Viçosa-MG, 36570-000, Brazil.
Abstract
This study aims to identify: 1) the most representative variables hydrological regionalization
studies, using principal component analysis (PCA) and 2) to optimize the identification of the
hydrologically homogeneous regions in studies of regionalization of water flow using cluster
analysis (CLUSTER) for the rio Doce basin. Fifteen variables were used in the study,
individualized to 61 gauging stations: Q 7, 10 , Q 90 , Q 95 , Q mld , Q max10 , Q max20 , Q max50 , Q max100 , P a ,
P ss , P sc , A d , L p , L t and S L . The results of the principal component analysis pointed out that the
variable SL was the least representative for the study. The first two principal components, Y 1
and Y 2 , were responsible for 77.92% of the total variation of the data. The best divisions of
hydrologically homogeneous regions were obtained using the similarity matrix of
Mahalanobis and the complete linkage clustering method. The Cluster analysis enabled the
identification of four hydrologically homogeneous regions in the watershed of the rio Doce.
Key words: Principal Components, Cluster Analysis e Regionalization of flow.
1. INTRODUCTION
In general, it is understood by hydrological regionalization process the transferring
information from one region of the hydrological behavior known to other sites, often without
observations.
In this context, multivariate statistical analyzes can help significantly in the studies of
hydrological regionalization, reducing processing time from the database and increasing the
reliability of results. At the international level can prove this statement by the development of
numerous studies addressing the hydrological regionalization based on multivariate
statistical analyzes (Assani et al., 2011; Kahya et al., 2007; Mwale et al., 2010, Samuel et al.,
2010; Engeland & Hisdal, 2009; Castiglioni et al., 2009).
The principal component analysis (PCA) aims to examine the correlations between variables,
summarize a large set of variables into a smaller one and the same meaning, evaluate the
importance of each variable and promote the elimination of those that contribute little in
terms variation in the group of individuals evaluated (WILKS, 2006). In recent years, many
applications of this technique have been studied in various fields of knowledge such as:
genetics (Price et al., 2006; Haider et al., 2008), chemistry (Bellomarino et al., 2010),
environment (Reid & Spencer, 2009), among others.
Multivariate statistical analysis of Cluster is a tool of exploratory data with the aim of
classifying homogeneous groups (Wilks, 2006), which has been used in numerous areas of
knowledge, for example, medicine (Mezer et al., 2008 ), geomorphology (Melchiorre et al.,
2008) and environmental engineering (Pires et al., 2007; Hatvani et al., 2011). In hydrology,
the cluster analysis is a technique often used to define classes or for grouping stations into
homogeneous climatic regions.
In view of this, this study aimed to develop a methodology based on multivariate statistical of
principal components and cluster analysis for the identification of variables most
representative studies of hydrological regionalization and optimize the achievement of
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