poster - International Conference of Agricultural Engineering

The multiple regression equations were obtained using the application SisCORV 1.0.3
(Sousa et al. 2008) developed by the Research Group on Water Resources - GPRH, linked
to the Department of Agricultural Engineering - DEA, Federal University of Viçosa - UFV.
In the present study were considered 15 variables, eight dependent variables to be
regionalized (minimum flow average of seven consecutive days with a return period of ten
years - Q 7,10 ; minimum flow associated with stays at 90% - Q 90 and 95 % - Q 95 ; long-term
average flow - Q mld ; maximum flow with a return period of 10 years - Q max10 , 20 years - Q max20 ,
50 years - Q max50 and 100 years - Q max100 , in m 3 s -1 ) and seven independent variables (total
annual rainfall - P a , total precipitation in the dry semesters - P ss and rainy - P sc , in mm, area
drainage basin - A d , in km², length of the main river - L p in km, total length of watercourses
basin - L t in km and average Slope basin - S L in%).
3. RESULTS AND DISCUSSION
3.1. PRINCIPAL COMPONENTS ANALYSIS
Based on seven independent variables (Pa, Pss, Psc, Ad, Lp, Lt and S L ) for each of the 61
gauging stations adopted, proceeded to the principal component analysis. The total variance
in the existing set of multivariate data analysis is equal to the number of variables, given that
the data was standardized with an averageand variance equal to 0 and 1, respectively. The
summary of the main components of the variables studied are presented in Table 1.
Table 1 – Principal Components of the study variables
PC's
Variance
Coefficients of standardized variables - eigenvectors
% Var. % acum.
eigenvalue Z 1 (P a ) Z 2 (P ss ) Z 3 (P sc ) Z 4 (A d ) Z 5 (L p ) Z 6 (L t ) Z 7 (S L )
Y 1 2,9628 42,33% 42,33% 0,1216 0,1310 0,1035 -0,5679 -0,5544 -0,5679 0,0700
Y 2 2,4911 35,59% 77,92% 0,6025 0,4858 0,5889 0,1074 0,1207 0,1072 -0,1286
Y 3 0,9950 14,21% 92,13% 0,1430 -0,1534 0,1628 0,0519 0,0427 0,0497 0,9605
Y 4 0,4733 6,76% 98,89% 0,2541 -0,8447 0,4032 -0,0463 -0,0139 -0,0362 -0,2361
Y 5 0,0755 1,08% 99,97% 0,0222 -0,0123 0,0068 0,3960 -0,8220 0,4082 -0,0124
Y 6 0,0020 0,03% 99,996% -0,7317 0,0976 0,6726 0,0369 -0,0144 -0,0330 0,0108
Y 7 0,0003 0,004% 100,000% 0,0379 -0,0108 -0,0307 0,7092 -0,0066 -0,7032 -0,0039
Based on the results presented in Table 1, were considered only the first two components
(Y1 and Y2), by simultaneously meet the two selection criteria (the cumulative variance
explained a value greater than or equal to 75% of the total variation of data and eigenvalues
being greater than or equal to 1). The other components, which together accounted for
22.08% of the total variation, weren’t considered. Table 2 shows the load factors or
correlations among the seven standardized variables and the first two principal components.
Table 2 – Factors loads between the standardized variables (VP's) and the principal
component (PC's), and the variance (λi) of each main component (i = 1, 2)
X
VP’s
Y 1
CP's
Y 2
P a Z 1 0,209226 0,950899
P ss Z 2 0,225520 0,766821
P sc Z 3 0,178086 0,929543
A d Z 4 -0,977547 0,169484
L p Z 5 -0,954338 0,190567
L t Z 6 -0,977535 0,169216
S L Z 7 0,120541 -0,202970
(%) λ i 42,33 35,59
It is noted in Table 2 that the standardized variables Z 4 , Z 5 and Z 6 have higher correlation
with the first principal component (Y 1 ), while the variables Z 1 , Z 2 and Z 3 show higher
correlations with the second principal component (Y 2 ). The variable Z 7 can be discarded from
3