The history of the
temperature series at Casablanca (Cuba).
The Casablanca
station is located on the north coast of the province of Havana City, Cuba.
Its current position is at 23.15 N and 82.35 W, 50 meters above the sea level.
Measurements started
on April 1908 with bihourly observations of the main meteorological variables
until June 1963, when observations started been made hourly.
The data books of
Casablanca station have no written records indicating changes of place or
instruments, so the information gathered on these issues comes rather from
testimonies of observators or studies of the observation series than from
official documents. These changes can be numbered as follows:
1. On 1926
double shield cottages were put in use and on July 19 1925 an official
change of time was issued for the entire Republic. (National Observatory,
1965).
2. On 1945,
after the strong hurricane of 1944 (category IV), the station was rebuilt
some 50 meters apart from the previous location with some instrumental
changes (Rego, J. S. Chief of the Climatology Dept. from 1970 to 1980,
personal communication) .
3. There is a
remark on the Observer’s book stating that on February 5th 1971
at 1:00 AM the official cottage at 2 meters of height was replaced by the
current one at 1.5 m.
4. Following
a study of temperature observations for the calculation of yearly modes
(Alvarez 1999) at least 2 changes of instruments are suggested with
different scale layouts, in the years 1941 and 1968 approximately. Though
there is no official evidence of them, only the testimony of personnel
working at the station between 1964 and 1972.
The series of yearly
mean temperatures used in this study was calculated from the widest amount of
observations available, once they were validated, for the calculus of the
monthly means and from them the yearly means. The books corresponding to the
years 1916, 1917 and 1918 are currently under reconstruction due to the bad
state of conservation, so monthly mean data were taken from climatic bulletins
issued on those years and kept at the Scientific and Technical Information
Centre of the Institute of Meteorology of Cuba.
This series has been
confronted with series obtained by other researchers for different works
showing similar values.
Testing randomness of
the complete rank series
Difficulties
resulting from the existence of ties, an investigation has first been made on
the number of decimal digits needed for eliminating such perturbation. It was
found here that when rounding up to the first, second and third decimal digit,
the number of untied elements of the series reached respectively 3, 47 and 82.
Ties being absent with 4 decimal digits, the substitution by their
corresponding rank has been made for elements computed with this last decimal
accuracy.
Testing distribution
stability and independence for the complete series gives the test statistic
values of table 1. It appears that, for
this series, the trend u(t) and the serial correlation u(rs)
statistics are highly significant with levels respectively equal to 8.E-5 and
2.E-6, while intermediate statistic values of the sequential onward and
backward trend analysis for the series and for its dispersion appear to be
also highly significant. Both trend and persistence are thus alternatives to
randomness to be considered.
Change-point
determination
Following the method
described above, in a first investigation, 18 possible change-points: 1910,
1912, 1915, 1919, 1923, 1927, 1941, 1945, 1949, 1952, 1956, 1964, 1971, 1975,
1979, 1988, 1991, 1993 have been detected. Among them: 1910,
1912, 1915, 1919, 1941, 1945, 1949, 1952, 1971, 1975, 1979, 1988, 1991, 1993
have been accepted as separating groups of high or low ranks, while the others
have been determined with a sequential trend analysis.
Applying the trend
analysis on the re-arranged partial series with increasing rank means, gives
the first group of sequences with homogeneous rank means (Table
2). Applied on the two-sided probabilities pi derived from the standardized
trend and serial correlation statistics u(t), ud(t)
and u(rs) and from the one-sided probabilities P(N) of the test for
normality, the Fisher test statistic (Sneyers, 1975)
XP
= S i ln pi
(14)
leads to the joint
significance levels a of Table 2.
These results making
acceptable the assumptions of randomness and of normality, further statistical
investigations may thus be performed using parametric tests.
The likelihood-ratio
test of homogeneity of variances has first been applied on the standard
deviations si, by means of the test statistic
Xv
= [S (ni - 1)ln s0 - S
(ni - 1) ln si]/cv
(15)
where s02
= S (ni - 1) s12/S (ni - 1),
cv
= 1 + {S (ni - 1)-1 - [S (n1 - 1)]-1}/[3(k
- 1)], and where k is the number of standard deviations si. Having
a G -distribution with shape parameter (k - 1) = 3.5 and scale parameter 1, Xv
leads to the probability 0.98
Rejected in this
way, complete variance homogeneity is however accepted separately for high and low standard deviations
wih respective values .2296 and .1228..
On the other hand,
applying the Student test on the successive means of Table
2, the grouping of homogeneous ones leads to the five final groups of
sequences with different means. Reducing the probabilities p1
derived with the Student test from the final means of Table 3. with the relation
p0
= (pi)n/ni,
(16)
where n is the size
of the complete series and ni the one of the joined contiguous
homogeneous groups, this relation leads to the high significance levels a
(d
m) of Table 2.
Accounting for these
results show that among all the change-points derived by the preceding
analysis, the single one separating contiguous sequences with equal means is
1952, which reduces the number of partial series from 19 to 18. Table
3 gives the final statistical characterization of the temperature
instability, while Table 4 shows a
chronological temperature evolution which divides the complete period 1908 -
1995 into five sub-periods, the first 1908-1927 one, involving large
differences and the other ones showing a double alternance from 1924 to 1987
and an end in 1995 with the alternance of the highest values of temperature
sequences. In the four last sub-periods, the oscillation amplitude of the
temperature averages remains close to 0.3E.
