262
M.1. Esteban-Parra, D. Pozo-Vazquez, F.S. Rodrigo, Y. Castro-Dfez
(Empirical Orthogonal Functions)are the eigenvectors with an associated variance
equal to their corresponding eigenvalue.
The rule N (Preisendorfer, 1988) was applied in order to select the number of the
significant EOFs. This is a MonteCarlo procedure to obtain the eigenvalue
distribution of random covariance matrix. An alternative and possibly better
interpretation of the results can be attained by rotating the significant EOFs by the
Varimax procedure (Preisendorfer, 1988).
To detect trends and abrupt changes in the PCs series we used the sequential
Mann-Kendall test. Descriptions of this non-parametric test can be found in Sneyers
(1975), Goossens and Berger (1986) and Esteban-Parra et al. (1995). One problem
in applying this test is the presence of the serial correlation in the data (Kulkarni
and von Storch, 1995), and therefore caution is advisable when applying this test.
The test consists of the graphical representation of two curves, computed in a
similar way. Mathematically, an abrupt change is a particular case of a trend,
characterized by two stable sub-series with different means. We have a significant
trend when the curve CI surpasses the 5% significance level. For an abrupt change,
the curve Cl will not present a trend for the first sub-series (with a particular mean),
and will pass the 5% significance level after the point of change, when the second
sub-series begins. On the other hand, the retrograde curve C2 (which is equivalent
to Cl), will not present a trend for the second of the sub-series, and thus will not
pass the significance level. However, both curves have the same behaviour at the
change point, and therefore the two curves must intersect at this point.
4 Temperature Analysis
4.1 EOF Patterns
Except for winter, which has only one significant EOF, two significant EOFs were
found for the rest of the seasonal and annual series. At this point we should note that
the first unrotated EOF explains most ofthe variance (more than the 50%) with high
correlations for all stations, and the second one less than the 10%, with significant
correlations for stations on the Mediterranean and East Cantabric coasts. When we
rotate these EOFs, the second has the effect of pulling the first, in such a way that
in some cases the rotation divides the first unrotated EOF into two. Both have
significant correlations for almost all the stations, although the first rotated EOF
represents slightly better the western part and the second the eastern part. This is the
case for example of the annual data and, to a lesser extend, for summer data that is,
the regions most influenced by Atlantic weather types, and by the Mediterranean
climate. In any case, the regionalisation drawn by these two rotated EOFs is quite
limited and the first unrotated EOF can be considered representative of the entire
area under study. Fig. 2 shows the loading factors associated with the first unrotated
EOF for the annual and seasonal data.
M.1. Esteban-Parra, D. Pozo-Vazquez, F.S. Rodrigo, Y. Castro-Dfez
(Empirical Orthogonal Functions)are the eigenvectors with an associated variance
equal to their corresponding eigenvalue.
The rule N (Preisendorfer, 1988) was applied in order to select the number of the
significant EOFs. This is a MonteCarlo procedure to obtain the eigenvalue
distribution of random covariance matrix. An alternative and possibly better
interpretation of the results can be attained by rotating the significant EOFs by the
Varimax procedure (Preisendorfer, 1988).
To detect trends and abrupt changes in the PCs series we used the sequential
Mann-Kendall test. Descriptions of this non-parametric test can be found in Sneyers
(1975), Goossens and Berger (1986) and Esteban-Parra et al. (1995). One problem
in applying this test is the presence of the serial correlation in the data (Kulkarni
and von Storch, 1995), and therefore caution is advisable when applying this test.
The test consists of the graphical representation of two curves, computed in a
similar way. Mathematically, an abrupt change is a particular case of a trend,
characterized by two stable sub-series with different means. We have a significant
trend when the curve CI surpasses the 5% significance level. For an abrupt change,
the curve Cl will not present a trend for the first sub-series (with a particular mean),
and will pass the 5% significance level after the point of change, when the second
sub-series begins. On the other hand, the retrograde curve C2 (which is equivalent
to Cl), will not present a trend for the second of the sub-series, and thus will not
pass the significance level. However, both curves have the same behaviour at the
change point, and therefore the two curves must intersect at this point.
4 Temperature Analysis
4.1 EOF Patterns
Except for winter, which has only one significant EOF, two significant EOFs were
found for the rest of the seasonal and annual series. At this point we should note that
the first unrotated EOF explains most ofthe variance (more than the 50%) with high
correlations for all stations, and the second one less than the 10%, with significant
correlations for stations on the Mediterranean and East Cantabric coasts. When we
rotate these EOFs, the second has the effect of pulling the first, in such a way that
in some cases the rotation divides the first unrotated EOF into two. Both have
significant correlations for almost all the stations, although the first rotated EOF
represents slightly better the western part and the second the eastern part. This is the
case for example of the annual data and, to a lesser extend, for summer data that is,
the regions most influenced by Atlantic weather types, and by the Mediterranean
climate. In any case, the regionalisation drawn by these two rotated EOFs is quite
limited and the first unrotated EOF can be considered representative of the entire
area under study. Fig. 2 shows the loading factors associated with the first unrotated
EOF for the annual and seasonal data.