Table 2 Results of regression analyses of annual rainfall for the band of timescales smaller than and greater than 10
years AR: Annual rainfall. AAvAR: Areal Average of Annual Rainfall. Null hypothesis: Slope is zero. Alternative
hypothesis: slope is not zero.
Variable Period
Timescale Slope
p-level AR in Cordoba Observatory
1873–1934 10 years
0.42 0.18
´
AAvAR 1935–1983
10 years 4.72
- 0.0001 AR in Cordoba Observatory
1873–1934 -10 years
0.08 0.93
´
AAvAR 1935–1983
-10 years 0.32
0.79
Time–timescale analysis using the Morlet wavelet indicates that the fluctuation Ž
excited in 1935 does not have precedent in the previous 60 years, since 1873 figure not .
shown .
4. Seasonal variability
In this section, the seasonal variability of the pattern of non-periodic fluctuations is Ž .
analyzed. The following questions are answered: 1 In what seasons the amplifying Ž .
fluctuation excited in the mid-1930s occur? 2 What was the influence of fluctuations at decadal and interdecadal timescales on the trend of seasonal rainfall depending on the
season? To study seasonal variability in non-periodic fluctuations, the year was subdi- Ž .
Ž vided into four 3-month periods. These periods are
1 August to October
late . Ž .
Ž . Ž .
winter–early spring , 2 November to January late spring–early summer , 3 February Ž
. Ž .
Ž .
to April late summer–early autumn , and 4 May to July late autumn–early winter . We reference to these periods as ‘‘seasons’’ or ‘‘3-month period’’ or ‘‘quarterly of
year’’. Morlet wavelet decomposition of seasonal rainfall shows that the amplifying fluctua-
tion is observed only in 3-month periods November to January and February to April. Besides, statistically significant trend occurred in the period 1935–1983 only in same
Ž .
3-month periods see Table 3 . Thus, amplifying fluctuation detection and the trend of seasonal rainfall are restricted to the period of the year from late spring to early autumn
after 1935; subsequent analyses are restricted to this period. Contribution from bands with timescale - 10 years and 10 years during the
seasons November to January, and February to April is given in Table 4. The length of time series has to encompass at least two cycles of dominant timescales to carry out
meaningful analyses of partial contribution from bands of wavelet timescales. To satisfy this requirement, use is made of the time series of areal average of 3-month rainfall for
the period 1935–1983; and the same type of time series from Cordoba Observatory for
´
the period 1873–1934. From Table 4, the conclusion is reached that in these two periods of year, the
contribution from band of timescale smaller than 10 years is negligible, and without
Table 3 Regression analysis of areal average of 3-month rainfall on year for indicated period of the year
p-level of test statistics corresponds to the null hypothesis: Slope is zero, and alternative hypothesis: slope is not zero.
Quarterly Period
Slope p-level
Amplifying fluctuation Ž
. mmryear
is observed? August to October
1905–1934 1.24
0.17 1935–1983
y0.31 0.62
No November to January
1905–1934 1.82
0.30 1935–1983
3.10 0.00039
Yes February to April
1905–1934 1.35
0.30 1935–1983
2.57 0.00079
Yes May to July
1905–1934 0.073
0.94 1935–1983
y0.27 0.40
No
statistical significance. That is, fluctuations with a timescale of less than 10 years do not contribute to trend of seasonal rainfall in the indicated 3-month rainfall. Contributions in
the band of fluctuation with timescale greater than 10 years are the only ones building the trend in annual rainfall as from 1935. In months November to January, during the
period 1873–1934, there was a small trend of y0.9 mmryear. Although statistically significant, this trend is very small compared with trend produced by contribution after
1935. Fig. 10 shows the contribution to 3-month rainfall perturbation from band of fluctuations with timescale greater than 10 years, for indicated period of the year.
Descriptions of contribution to rainfall perturbation in the each quarterly from wavelet periods as function of year are shown in Figs. 11 and 12. These figures depict clearly the
same amplifying fluctuations seen in Fig. 5 for the variable AAvAR. In the period
Ž .
November to January Fig. 11 , the fluctuation that started in the mid-1930s has a structure composed of fluctuations in bands centered in 13.5 years and 22 years
Table 4 Ž
. Regression analysis of rainfall perturbation contribution from indicated timescale band on year for indicated
quarterly of year. Variable of regression on year as indicated Ž
. SR: seasonal rainfall 3-month rainfall . AAvSR: areal average of seasonal rainfall.
Ž .
Variable Season
Period Slope mmryear
p-level NoÕember to January
SR Cordoba Observatory Timescale -10 years
1873–1934 0.02
0.97
´
SR Cordoba Observatory Timescale 10 years
1873–1934 y0.91
- 0.001
´
AAvSR Timescale -10 years
1935–1983 0.14
0.84 AAvSR
Timescale 10 years 1935–1983
2.96 - 0.0001
February to April SR Cordoba Observatory
Timescale -10 years 1873–1934
0.013 0.98
´
SR Cordoba Observatory Timescale 10 years
1873–1934 0.28
0.05
´
AAvSR Timescale -10 years
1935–1983 0.13
0.84 AAvSR
Timescale 10 years 1935–1983
2.44 - 0.0001
O.A. Lucero,
N.C. Rodrıquez
r Atmospheric
Research 52
1999 177
– 193
´
190
Fig. 10. Contribution to perturbation of AAvAR from the band of fluctuations with timescale greater than 10 years for indicated 3-month periods.
Fig. 11. Contribution to reconstruction of perturbation of 3-month rainfall during November to January from Ž
. indicated wavelet timescales. Contour lines in mm are: 0, 2, 4, 6, 8, 10, 12, and their negative counterpart.
Ž .
Ž .
Negative positive contributions to perturbation of annual rainfall are enclosed by dashed full contours. Line starting at 1935 and connecting several negative and positive centers is the same as in the analysis for AAvAR.
Ž .
timescale; whereas in February to April Fig. 12 , it is seen as a chirp-like fluctuation. We are not implying the existence of a chirp-type generating process as signals looking
as chirp-like could be produced also by other mechanisms.
Fig. 12. It has the same meaning as in Fig. 11, but for February to April.
5. Conclusions
