climatic and hydrological variations during the last 117 ... · correlogram allows us to quantify...

Climatic and hydrological variations during the last 117–166 years

in the south of the Iberian Peninsula, from spectral and correlation

analyses and continuous wavelet analyses

B. Andreo a,*, P. Jimenez a, J.J. Duran b, F. Carrasco a, I. Vadillo a, A. Mangin c

a Departamento de Geologıa, Facultad de Ciencias, Universidad de Malaga, E-29071 Malaga, Spainb Direccion de Hidrogeologıa, Instituto Geologico y Minero de Espana, E-28003 Madrid, Spain

c Laboratoire Souterrain de Moulis, 09200 Saint-Girons (Moulis), France

Received 21 April 2004; revised 5 September 2005; accepted 22 September 2005

Abstract

The most complete historical series of instrumental data available, spanning more than a century, on rainfall, temperature and

outflow of a karst spring obtained from gauging stations in the south of the Iberian peninsula were analysed by means of spectral

and correlation analyses and continuous wavelet analyses. Annual periodicity of the rainfall and temperature distributions was

constant over more than 100 years, although weaker (6-month) periodicities have also been observed, as well as rainfall and

temperature periodicities of 5 and 2.5 years, which have also been recorded in other areas of Europe. These multiannual scale

components can be explained by climatic variations or effects described in the literature in connection with the North Atlantic

Oscillation (NAO) and are likely to be the same as the climate variability at decadal to annual scale detected in several proxy

data from geological records. No long-term trends in the distribution of precipitation and temperature were detected.

q 2005 Elsevier B.V. All rights reserved.

Keywords: Climatic change; Correlation and spectral analyses; NAO; Precipitation; South Iberia; Temperature; Continuous wavelet analyses

1. Introduction

Climatic change has been much debated in the

scientific world in recent decades. Many investi-

gations on the climatic and hydrological variations

have been done using carbonate deposits, particularly

speleothems because they are less affected by

postdepositional processes than superficial sediments.

0022-1694/$ - see front matter q 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2005.09.010

* Corresponding author. Tel.: C34 95 2132004; fax: C34 95

2132000.

E-mail address: [email protected] (B. Andreo).

Speleothems can be dated precisely by means of the

U/Th decay series and consequently, they can

contribute to our knowledge of the paleoclimatic

and paleohydrologic events in continental areas

(Schwarcz, 1986). Geochemical studies can be

performed with a very high time resolution from

stable isotopes such d18O and d13C, which, respect-

ively, may reflect paleotemperature and vegetation

(Gascoyne, 1992), and trace elements (Mg, Sr) that

are indicators of paleohydrology (Fairchild et al.,

2001). The geochemical and hydrological results have

been tested with the actual deposits of speleothems in

Journal of Hydrology 324 (2006) 24–39

www.elsevier.com/locate/jhydrol

http://www.elsevier.com/locate/jhydrol

B. Andreo et al. / Journal of Hydrology 324 (2006) 24–39 25

caves (Baker and Smart, 1995; Genty and Deflandre,

1998; Andreo et al., 2002; Tooth and Fairchild, 2003).

Another possibility to study climatic and hydro-

logical changes, without taking into account geological

records, is to examine the period of recorded history (the

instrumental period), but it is necessary to possess both

time series of adequate length and the mathematical

tools that enable us to optimise the results. Thus, the

long-term time series are important because they permit

to study climatic changes using the real data or to

reconstruct longer series using different mathematical

tools. The expected modification in rainfall following

climate change in the South Iberian Peninsula is a

decrease in precipitation in the coming decades or even

the whole twenty-first century (Sumner et al., 2003).

In this work, we have analysed the most complete

historical series available of real data, spanning more

Fig. 1. Location of the meteorologi

than a hundred years, obtained from gauging stations

in the southern Iberian peninsula (Fig. 1): precipi-

tation data obtained at the stations of San Fernando in

the province of Cadiz (127 years) and Gibraltar (166

years), temperature data recorded at San Fernando

(117 years) and the outflow of El Tempul spring (133

years). The exceptional length of these time series in

the study area, and its geographical location, being

influenced both by the Atlantic ocean and the

Mediterranean sea, are two key features of our

study. Two mathematical tools have been applied:

spectral and correlation analyses, and continuous

wavelet analyses.

Correlation and spectral analyses were first

applied, in surface hydrological systems orientated

mainly towards forecasting, completion of data and

estimation of parameters for stochastic models (e.g.

cal and hydrological stations.

B. Andreo et al. / Journal of Hydrology 324 (2006) 24–3926

Delleur, 1971; Spolia et al., 1980). Mangin (1981a,b,

1984) adapted this methodology to study the

discharge from karstic aquifers. Examples of carbon-

ate aquifers studied by this methodology are abundant

in the literature, some of them recently published (e.g.

Padilla and Pulido-Bosch,1995; Larocque et al., 1998;

Jimenez et al., 2002). These studies demonstrate the

application of correlation and spectral analysis to

series of both flow data and precipitation in order to

determine the flow and characterise aquifer beha-

viour. However, correlation and spectral analyses

have not often been applied to very long-time series of

climatic and hydrological data (Kuhnel et al., 1990) in

spite of their advantages in identifying the structures

and periodic components (normally average period-

icities) in these series.

Wavelet transform techniques have been applied in

the fields of hydrology and meteorology to identify

coherent convective storm structures and characterise

temporal variabilities (Kumar and Foufoula-Geor-

giou, 1993; Kumar, 1996; Smith et al., 1998; Szilagyi

et al., 1999), to explain the variability of ocean

temperatures (Meyers and O’Brien, 1994), and the

variations in global mean sea level (Breaker et al.,

2001; Chambers et al., 2002). They have also been

used in oceanography (Meyers et al., 1993), and in

comparing watersheds of the same region (Gaucherel,

2002). Labat et al. (1999a,b; 2000, 2001) also applied

these techniques in the field of karstic hydrogeology

in order to study rainfall rates and outflows of karstic

springs located in the Pyrenees and in the Larzac

plateau (France). By comparison with correlation and

spectral analyses, wavelet tools detect not the average

periodicities in time series, but the distribution of the

periodic variabilities during the time.

The aims of this paper are to determine whether

there are periodicities associated with climatic cycles

or oscillations and whether there is any long-term

trend that might be related to the climatic changes. In

order to validate the results obtained using these series

of climatic data (especially rainfall), both method-

ologies have also been applied to a time series of the

outflow recorded over more than a century at El

Tempul spring, which constitutes the main discharge

point of the Sierra de las Cabras carbonate aquifer

(Fig. 1). Thus, it is possible to identify the

correspondence between rainfall and hydrological

variations.

In a previous paper, the evolution of the annual

precipitation recorded at the Gibraltar station from

1791 to 1983 was studied using annual data and it was

concluded that a slight decreasing trend exists in the

rainfall time series, but without statistical significance

(Moreno and Martın, 1986). Similar results were

obtained in other areas of southern Iberia, such as

Granada, eastward of the study area, using monthly

data for the period 1902–1983 (Benavente et al.,

1986) and Huelva, westward of the study area, using

daily data for the same period (Romero and Sainz,

1984). These papers used statistical techniques on

rainfall data in S Iberia in a preliminary manner,

leaving much remaining to be done in terms of

detecting climatic changes.

Other previous papers (Rodrigo et al., 2000; Pozo-

Vazquez et al., 2000) show the results of the

application of different statistical tools to detect

changes in meteorological records in S Iberia. These

works demonstrate the existence of dry and wet

periods into the record, at different timescales, and the

contribution of the North Atlantic Oscillation (NAO)

to rainfall variability in this region.

2. Materials and methods

The time series data used as the material for this

study was the following:

(a) Precipitation and temperature data recorded at

the meteorological station of Real Observatorio

de San Fernando (Cadiz). The precipitation data

correspond to monthly total values for the period

January 1870— December 1997, and the tem-

perature data are mean monthly values for the

period January 1870— December 1987. The

rainfall data available from 1791 to 1870 in

Gibraltar station are annual values and they have

been not used in the present work.

(b) Series of daily rainfall data from October 1834 to

November 2000, obtained at the Gibraltar

weather station.

(c) Series of monthly flow rate from El Tempul

spring, the main discharge point of Sierra de las

Cabras, an aquifer where no pumping exists.

Sierra de las Cabras is a diffuse flow carbonate

aquifer with a surface of 42 km2 and average


resources of 8 – 9 hm3/year which are used for

water supplying to the city of Jerez de la Frontera

(Jimenez et al., 2001). The data series of spring

flow were calculated using the height of the

water surface in the gauging station. Readings

were taken on the 20th day of each month and

then converted to outflow values by the

application of a stage-discharge rating curve.

This series is exceptionally long, extending from

June 1862 to December 1995.

Therefore, three types of climatic and hydrological

data have been used in this work (rainfall, temperature

and springflow rate). The location of the stations is in

Fig. 1 and the statistical parameters of the time series

are in Table 1.

The first method applied was correlation and

spectral analysis, which deals with the whole time

series and can be applied in two domains (Mangin,

1984): time (correlation analysis) and frequency

(spectral analysis). Normally, the data series are first

studied separately by means of a simple analysis to

identify the structure and components, and then by

cross analysis, considering two series (i.e. precipi-

tation and outflow) in order to determine the

relationships between the two. Therefore, correlation

and spectral analysis can be simple or cross-correlated

and, in both cases, in the time (correlation) or

frequency (spectral) domains.

The simple correlation analysis (simple correlo-

gram or auto-correlogram) of a data series is the auto-

correlation function, which shows the linear depen-

dency of successive data for increasingly large time

Table 1

Statistical parameters of the time series of data used in this work

Monthly precipitation Monthly flow

rate

Gibraltar

station (mm)

San Fernando

station (mm)

El Tempul

Spring (L/s)

N 1596 1509 1596

Max 528 471 1951

Min 0 0 20

Average 68 49 286

Standard

deviation

82 57 280

Variation

coefficient

121 117 98

Variance 6788 3288 78334

intervals. Thus, the slope of the auto-correlogram

flattens quickly to values close to zero if the data have

a short-term influence on the time series and,

consequently, are of a random nature. Conversely

the slope of the correlogram flattens more slowly if

the data have a long-term influence on the time series.

The simple correlogram, rk, was calculated using the

formula proposed by Jenkins and Watts (1968):

rk ZCk

C0

with Ck Z nK1XnKk

1

ðxiK �xÞðx1CkK �xÞ

where rk is the value of the correlogram, k is the time

lag varying from 0 to n (cutting point), and xi are

values which have an average of �x. The auto-

correlogram allows us to quantify the ‘memory

effect’, the time in which the correlogram decreases

to values of 0.1–0.2.

The simple spectral analysis (spectral density

function) is the Fourier transformation of the auto-

correlogram, which corresponds to a change from a

time mode (time-series space) to a frequency mode.

The spectral density function, S(f), is calculated by the

formula proposed by Jenkins and Watts (1968):

Sðf ÞZ 2 1C2Xm

1

Dkrk cos 2pFk

" #

where k is the step and FZj/2m with j varying from 1

to m. Dk is a window that is necessary to ensure that

the S(f) estimated values are not biased. The best

windows are those of the Tukey filter (Mangin, 1984).

Dk Z1Ccos pk

m

� �2

The spectral density function normally shows

peaks, which represent periodic phenomena in the

time series. When high-density values are found near

zero frequencies, this indicates the existence of a

long-term trend or a phenomenon in which the

periodicity is longer than the time series studied.

The auto-correlogram and the spectral density

function have been obtained at two levels: a ‘short-

term’ analysis (window 125 months and lag of 1

month) and a ‘long-term’ analysis (window 500 and

475 months and lag of 10 months). Moreover, the

long-term analysis has been carried out with different

lags in order to verify the results and avoid artificial


periodicities inherent to the treatment of the data.

These analyses enable us to identify and to describe

the components (trend, periodicity and randomness)

of the time series. Information on the structure of the

time series can only be obtained for window values

that are between double the lag value and one third of

the length of the time series. Thus, the available data

series considered in this work permit us to deduce

components with a periodicity between 2 months and

more than 40 years.

The second method is continuous Morlet wavelet

analysis, which allows the completion of time-scale

representation of localised and transient phenomena

occurring at different time scales. Time-scale dis-

crimination is achieved in a more satisfactory way

than time-frequency decompositions such as the

windowed Fourier method (e.g. Mangin, 1984).

Thus, by comparison with the Fourier and correlation

analyses, wavelet transforms lead to more precise

results especially in the temporal variability of the

processes. The continuous wavelet transform provides

a time-scale discrimination of the signal into sub-

processes. It is defined as the convolution product of a

signal x(t) by functions obtained by dilation (or

contraction) and temporal translation of a function

j(t) called ‘wavelet’, which must satisfy certain

admissibility criteria. The algorithm to compute the

wavelets and plot the results is from Torrence and

Compo (1998). After discriminating the data with the

wavelets, the amplitude of any variable signal within

the data can be determined at various frequencies, as

well as the variation of this amplitude with time. For

the results plotted here, a dark grey shade is assigned

to the lowest value of the wavelet coefficient while a

white shade is assigned to the highest value. Since

wavelet analysis is dealing with finite-length time

series, errors will occur at the beginning and end of

the wavelet power spectrum, while the Fourier

transform assumes the data is cyclic. The errors are

included in the so-called ‘cone of influence’, that is

the region of the wavelet spectrum in which edge

effects become important.

The continuous Morlet wavelet has been applied

because it establishes a clear distinction between

random fluctuations and periodic regions. By analogy

with Fourier analysis, a global wavelet variance

spectrum for continuous wavelet transform can also

be defined, which gives a representation of the

variance distribution across time scales (Liu, 1995).

A mathematical overview of the wavelet transform

(continuous wavelet transform) and its applications to

karstic hydrogeology are given by Labat et al. (1999a,

b, 2000, 2001), emphasising also the statistical

interpretation of the wavelet coefficients and introdu-

cing the concepts of the wavelet spectrum.

3. Correlation and spectral analyses

3.1. Correlation and spectral analysis of the rainfall

time series

We carried out a simple analysis (correlogram and

frequency spectrum) of the time series of monthly

data recorded at meteorological stations of Gibraltar

and San Fernando. The short-term simple correlogram

for rainfall data reveals that both weather stations

(Fig. 2A and C) detected the existence of clearly-

defined annual cycles (kZ12 months). The memory

effect (value of k for rZ0.1–0.2) is several months,

although shorter-term analyses previously done

demonstrated that the distribution of precipitation is

a random phenomenon, with a memory effect of about

2 days (Jimenez et al., 2001). The spectrum of the

variance density for the two time series (Fig. 2B

and D) reveals a very clear peak corresponding to the

annual periodicity of precipitation (frequencyZ0.082), together with a less evident 6-monthly

periodicity (fZ0.165), which is more evident in the

San Fernando data.

Long-term analysis of the time series data from

Gibraltar and San Fernando produced simple correlo-

grams (Fig. 3A and C) showing a periodicity of about

5 years (kZ60 months). This finding was confirmed

by the spectrum of the variance density for the two

time series, which clearly shows the approximately

quinquennial periodicity of rainfall (fZ0.165 in

Fig. 3B and D). In addition, although less evident,

there was a rainfall periodicity of 2.5 years (fZ0.33),

more visible in the San Fernando data. The higher

values of the spectra for 1 and 5 years periodicities in

Figs. 2 and 3 (B and D) provoke that the peaks of 6

month and 2.5 years periodicities are less marked, but

only about 10% of the spectral density variance is

greater than these and, therefore, they can be

considered significant.

-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

110

115

120

125

k (months)

r k

A Gibraltar Stationlag step 1 month

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (f

)

B Gibraltar Stationlag step 1 month

1 year

6 months

-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

110

115

120

125

k (months)

r k

CSan Fernando Stationlag step 1 month

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (f

)D

San Fernando Stationlag step 1 months

1 year

6 months

Fig. 2. Results of short-term correlation analysis (A,C) and spectral analysis (B,D) of monthly precipitation data from the Gibraltar and San

Fernando stations.


The long-term analysis, autocorrelogram and

spectral density, has been also carried out with

different lags (7 and 9 months) and the results are

the same although only the spectral density functions

are represented in Fig. 3E and F to avoid repetition.

We have done the frequency spectrum with different

lags (7 and 9 months) for rainfall data of the San

Fernando station and for the flow data of Tempul

spring and the results (autocorrelogram and spectral

density) are also the same than a lag of 10 months. So,

these periodicities are not derived from the math-

ematical procedure, as sometime occurs (Burroughs,

1992), but are intrinsic periodicities of the time series.

In the long-term frequency spectra obtained as part of

the present study, for the Gibraltar and San Fernando

stations (Fig. 3B and D), no long-term trends were

observed. In order to determine the capacity of

correlation and spectral analysis to establish long-term

trends, we generated several series of rainfall data,

adding to the original series recorded at the Gibraltar

station (the longer series) temporally decreasing

tendencies of different rainfall quantities. The corre-

lation and spectral analysis has been applied to the new

series and we confirm that the correlogram (Fig. 3G) is

quite similar to the above one, but the frequency spectra

(Fig. 3H) permits the clear distinction of the tendency

when a rainfall decreasing trend of 50 mm is added over

the whole period of the record.

3.2. Correlation and spectral analysis of the

temperature time series

In this case, too, we performed a simple analysis

(correlogram and frequency spectrum) of the whole

-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

k (months)

r kAGibraltar Station

lag step 10 months

0.01.02.03.04.05.06.07.08.09.0

10.011.012.013.014.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (

f)

BGibraltar Stationlag step 10 months

5 years

2.5 years

-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

k (months)

r k

CSan Fernando Stationlag step 10 months

0.01.02.03.04.05.06.07.08.09.0

10.011.012.013.014.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (f

)

DSan Fernando Stationlag step 10 months

5 years

2.5 years

0123456789

1011121314

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

frequency

S (f

)

EGibraltar Stationlag step 7 months

5 years

2.5 years

0123456789

1011121314

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

frequency

S (f

)

FGibraltar Stationlag step 9 months

5 years

2.5 years

-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

k (months)

r k

G Gibraltar Stationlag step 10 months.

tendency 50 mm

0.01.02.03.04.05.06.07.08.09.0

10.011.012.013.014.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (f

)

H

Gibraltar Stationlag step 10 months, tendency 50 mm

5 years

2.5 years

Fig. 3. Results of long term correlation analysis (A) and spectral analysis (B) of monthly precipitation data, using a lag of 10 months, from the

Gibraltar station. Results of long-term correlation analysis (C) and spectral analysis (D) of monthly precipitation data, using a lag of 10 months,

from the San Fernando station. Spectral analysis of monthly precipitation data using lag of 7 months (E) and 9 months (F). Correlation (G) and

spectral analysis (H) using a lag of 10 months and a decreasing tendency of 50 mm in the rainfall time series data of Gibraltar. To calculate the

periodicities (in years) from long-term spectra, the lag should be divided by the frequency and, then, the result should be divided by 12.



monthly series of temperature data recorded at the San

Fernando station.

As with the analysis of precipitation data, the short-

term simple correlogram (Fig. 4A) clearly revealed

the existence of annual cycles. The variance density

spectrum (Fig. 4B) indicated a very strong annual

temperature periodicity and a somewhat weaker

6-monthly cycle. The long-term analysis of this series

of monthly temperature data recorded at the San

Fernando station produces a simple correlogram

(Fig. 4C) that shows an average 5-yearly periodicity

of temperature variations. This quinquennial period-

icity is corroborated by the variance density spectrum

(Fig. 4D). We also observed a 2.5 year temperature

periodicity, though this was apparently weaker than

that obtained for rainfall data at the same station.

However is we take into account the different scale for

spectral density in Figs. 3D–B and 4B–D and the

variance of these (only 10% of the variance is higher)

we can deduce that, in both cases, the 6 month and 2.5

years periodicities are significant.

The long-term correlogram of the temperature data

(Fig. 4D) showed no long-term (low frequency) trend

in temperatures, the same as occurs with the analysis

of the precipitation data. In addition, in order to

validate the capacity of correlation and spectral

analysis to establish long-term trends in temperature,

we generated series of data, using those originally

recorded at the San Fernando station and assuming a

tendency to increase between 1 and 3 8C over the

whole period. Correlation and spectral analysis was

then applied to this synthetic data (Fig. 4E and F), and

it was confirmed that the method was indeed capable

of detecting a trend for temperature increases of 1 8C

(Fig. 4F).

3.3. Correlation and spectral analysis of outflow

data series from the El Tempul spring

The short-term correlogram for the series of

monthly outflow values from the El Tempul spring

(Fig. 5A) revealed a strong annual periodicity; the

memory effect estimated in a previous work (Jimenez

et al., 2001) was 95 days, which indicates a high

inertia. In the frequency domain, the spike corre-

sponding to the annual periodicity (Fig. 5B) can be

clearly observed, which is analogous to that detected

for the distribution of precipitation. We also found

weaker periodic components of 4, 2 and 1.4 years, not

observed in the rainfall spectrum (Fig. 2B and D),

which might be related to the strong inertial effect of

the carbonate aquifer of Sierra de las Cabras, that is,

the significant natural attenuation for annual vari-

ations in precipitation. The simple correlogram of

monthly outflow obtained for the long-term analysis

and for the precipitation-series analysis reveals a

fairly well defined five-year cycle (Fig. 5C). The fact

that the quinquennial periodic component for the

outflow series is corroborated in the frequency domain

(Fig. 5D), such as occurs with rainfall and temperature

data series, suggests that the origin of the periodicity

is climatic, as is the case for the annual periodicity

observed in the short-term analysis. Nevertheless, the

spectrum of the outflow data (Fig. 5D) presents a

long-term (low frequency) trend that is not evident in

the spectrum for the precipitation series, despite its

greater duration, and consequently cannot be attrib-

uted to climatic phenomena.

In addition, cross-correlation in frequency domain

has been done with the time series of data from El

Tempul spring and Gibraltar station and only the

annual effect is deduced in the short term analysis

(Fig. 5E) and the quinquennial one in the long term

analysis (Fig. 5F).

4. Continuous-time Morlet wavelet analysis

4.1. Continuous Morlet wavelet analysis of the

rainfall time series

The Morlet wavelet spectrum for rainfall data

obtained by the Gibraltar and San Fernando stations

are calculated and are depicted in Fig. 6A and B. It is a

time-scale plot of the signal where the x-axis

represents position along the signal (time), the

y-axis represents a periodicity scale, and the shade

contour at each x–y point represents the magnitude of

the wavelet coefficient at that point. A dark grey shade

is assigned to the lowest value of the wavelet

coefficient while a white shade is assigned to the

highest value.

Over all the period of the record, light shades can

be seen in both wavelet spectra with a periodicity of 1

year (Fig. 6A and B), so an annual process is visible

but with a higher intensity for the Gibraltar wavelet

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

110

115

120

125

k (months)

r k

ASan Fernando Stationlag step 1 month

0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

90.0

100.0

110.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (f

)

BSan Fernando Stationlag step 1 month

1 year

6 months

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

k (months)

r k

CSan Fernando Stationlag step 10 months

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

frequency

S (f

)DSan Fernando Station

lag step 10 months5 years

2.5 years

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

k (months)

r k

ESan Fernando Station

lag step 10 months, tendency 1ºC

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

frequency

S (f

)

F

San Fernando Stationlag step 10 months, tendency 1ºC

5 years

2.5 years

Fig. 4. Results of short term (A,B) and long-term (C,D) correlation and spectral analysis of monthly temperature data from the San Fernando

station. Correlation (E) and spectral analysis (F) following the addition of a long-term trend of 1 8C in the temperature time series data of San

Fernando.


-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100

105

110

115

120

125

k (months)

r k

AEl Tempul springlag step 1 month

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

S (

f)

BEl Tempul springlag step 1 month

4years

1 year

2years

1.4years

-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.0

0 20 40 60 80 100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

k (months)

r k

CEl Tempul springlag step 10 months

0.01.02.03.04.05.06.07.08.09.0

10.011.012.013.014.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

frequency

frequencyfrequency

S (f

)DEl Tempul spring

lag step 10 months

5 years

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

S(f

)

EEl Tempul springlag step 1 month

1 year

0.01.02.03.04.05.06.07.08.09.0

10.011.012.013.014.0

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

0.40

0.42

0.44

0.46

0.48

0.50

S(f

)

FEl Tempul springlag step 10 months

5 years

Fig. 5. Results of short term (A,B) and long-term (C,D) correlation and spectral analysis for the monthly outflow series from El Tempul spring.

Cross-spectral analysis of short-term (E) and long-term (F) time series of the outflow at El Tempul spring and rainfall in Gibraltar station.


spectrum (white shade) than for San Fernando (grey

and white shades). At large scales, the Gibraltar

wavelet spectrum reveals two processes that are more

or less localised in time. Areas of white and grey

shades indicate a 2–3 year periodic component during

the whole studied period, less visible in the San

Fernando wavelet spectrum (only grey coulour

appears for this periodicity in Fig. 6B). This first

Fig. 6. Continuous wavelet spectra of monthly precipitation data

from the Gibraltar (A) and San Fernando stations (B) and global

continuous wavelet spectra of monthly precipitation data for both

stations (C). The lighter the grey scales, the higher the value of the


component is a multiannual component and it

becomes a 4–6 year periodicity during the last six

decades: since 1950 appears white shades in Fig. 6A

(Gibraltar) and grey shades in Fig. 6B (San Fernando).

Therefore, as for the annual process, this second

component shows a higher intensity for the Gibraltar

wavelet spectrum. This second component (4–6 years)

does not have the same intensity as the first one but

reflects a periodicity occurrence in the rainfall large

scale distribution.

The Fig. 6A and B also include the cone of

influence which represent the periods with uninter-

pretable results due to edge effects of wavelet

processing, and consequently they should be ignored

in all analysis. These periods are at the beginning and

end of the time-series and for periods greater than

about 8-10 years. So the apparent periodicity of 8–10

years in Fig. 6A and B is not real.

The information provided by the wavelet spectrum

can be time-averaged to obtain a global wavelet

spectrum without temporal variations (Fig. 6C). The

annual process is again marked, whereas the

interannual components 2–3 and 4–6 years appear to

be much attenuated but visible, which corroborates

these periodicities according to the wavelet spectra

and correlation and spectral analysis.

4.2. Continuous Morlet wavelet analysis of

temperature time series

The Morlet wavelet spectrum for temperature data

at San Fernando station is displayed in Fig. 7A.

Regarding small scales (scales of less than 1 year),

high frequency structures (6–9 months) are visible in

several parts of the record. Nevertheless, the annual

component is the one that appears with major intensity

during overall analyzed period (grey and white

shades).

On longer timescales, during the last two decades,

a weak 2–3 year component is visible; moreover, in

the last decade also there is a 4–6 years component

with a similar intensity. Both components had been

already made evident from the correlation and

spectral analysis, as with the rainfall data.

wavelet coefficient. Cross-hatched areas on either end indicate the

‘cone of influence’, where edge effects become important and the

results should be ignored.

3

Fig. 7. Continuous wavelet spectra of monthly temperature data from the San Fernando station (A) and global continuous wavelet spectrum (B).

The lighter the grey scales, the higher the value of the wavelet coefficient. Cross-hatched areas on either end indicate the ‘cone of influence’,

where edge effects become important and the results should be ignored.


Nevertheless this last methodology cannot determine

when within the series exists a certain frequency

component.

The global wavelet spectrum for the whole period

(Fig. 7B) clearly shows the annual component already

mentioned, and this component concentrates practi-

cally all value of the total energy of the signal. Hence

it is not possible to see other component of the signal.

Nevertheless, a detailed analysis of this spectrum

allows us to observe peaks of 2–3 and 4–6 years.

4.3. Continuous Morlet wavelet analysis of the outflow

data from the El Tempul spring and cross-wavelet

analysis of the Gibraltar precipitation—El Tempul

outflow

The Morlet wavelet spectrum of El Tempul

outflow (Fig. 8A) shows that high frequency or short

scale patterns are less visible than in the precipitation

spectra (Gibraltar and San Fernando). At this scale of

analysis (monthly data) it is only possible to

distinguish the classical 1-year process (annual

recharge). Nevertheless, these processes are not

highly variable and are present during the overall

interval of observation as opposed to the precipitation

wavelet spectra (Fig. 6A and B). This indicates the

strong inertia of the aquifer in filtering the rainfall

input signal. The global wavelet spectrum (Fig. 8B)

shows not only the annual component, but this

spectrum makes it possible to see other interannual

components with the following periodicities (in

years): 2–3, 4–6 and 8–10. This last component is

not detected in the correlatory and spectral analysis,

and it is in the cone of influence, which represent the

periods with uninterpretable results.

The precipitation rates and outflow are first studied

separately in order to highlight their time-scale

characteristics via univariate wavelet transform.

Cross-wavelet transforms are then constructed in

order to analyse the variability of the precipitatio-

n/outflow relationship at the monthly sampling rate.

The Morlet wavelet cross-spectrum of the monthly

data is displayed in Fig. 8C, which shows again the

event of annual periodicity. Moreover, at large scale

there are two components (2–3 and 4–6 years), the

latter being stronger. This amplification of the signal

at large scales must be related to the importance of the

internal groundwater reserves, which clearly depends

on the long-term behaviour of precipitation rates

(Labat et al., 1999b).

The global Morlet wavelet cross-spectra (Fig. 8D)

again shows the importance of the annual component.

This component practically concentrates all value of

the total energy of the signal; therefore the interannual

components (2–3 and 4–6 years) are scarcely visible

inside the signal.

Fig. 8. Continuous wavelet spectra for the monthly outflow series from the El Tempul spring (A) and global continuous wavelet spectrum (B).

Continuous cross-wavelet spectra of monthly precipitation at Gibraltar station and outflows of El Tempul (C) and global continuous cross-

wavelet spectrum (D). The lighter the grey scales, the higher the value of the wavelet coefficient. Cross-hatched areas on either end indicate the

‘cone of influence’, where edge effects become important and the results should be ignored.


5. Discussion

The results of correlation and spectral analysis and

wavelet continuous analysis applied to long time

series of rainfall data recorded in Gibraltar and San

Fernando stations (South of the Iberian peninsula)

demonstrate that, a short-term, the annual and a lesser

periodicity of 6-month exist. Furthermore, long-term

analysis reveals a rainfall periodicity of 5 (and 2.5)

years. These periodicities have never been detected in

previous work on rainfall data series from the

southern Iberian peninsula (Romero and Sainz,

1984; Moreno and Martın, 1986; Benavente et al.,

1986). However, Rodrigo et al (2000) detected a 2.1-

year periodic component in rainfall data series, which

could be coherent with the 2.3-year dominant

oscillation of the NAO index (Qian et al, 2000).

Analysis of rainfall time series with a recording

period similar to those used in this study, mainly

obtained at stations located in the Midlands of


England and in Wales (Burroughs, 1992), also reveals

a periodicity of 5 years in the distribution of

precipitation. This fact might be due to a climate

presenting more extreme characteristics approxi-

mately every 5 years (Burroughs, 1992), which is

coherent with the alternation of dry and wet periods of

the ‘Joseph effect’ described by Mandelbrot and

Wallis (1968). In addition, Rogers (1984) analysed the

Fourier spectrum of the NAO winter index from 1900

to 1983, using atmospheric pressure data from Iceland

and the Azores islands, and found the peak of 5-year

period. All the aforementioned data probe the

influence of the NAO in the rainfall distribution in

South Iberia.

Moreno and Martın (1986) detected a slight

downward tendency in total annual precipitation

values in the south of the Iberian Peninsula, but also

remarked that these findings were not statistically

significant. Benavente et al. (1986) studied rainfall

records from the city of Granada and they concluded

that the quantity of precipitation is virtually unchan-

ging, although they detect also a general trend towards

more extreme variations of climate. In these last

works the length of time series data are shorter than

the used in the present study. However, taking into

account the data used in the present study and the

methodologies applied, no long term trends in the

precipitation pattern in the south of the Iberian

peninsula were detected. If a trend had existed

involving a rainfall variation, for example R50 mm,

it would have been detected by the correlation and

spectral analysis.

The analysis of the monthly outflow data series

from the El Tempul spring identified two period-

icities, of 1 and 5 years, which seem to be of climatic

origin. On the other hand, the long-term trends

deduced from the outflow data by the present

methodology cannot be attributed to an increase in

the use of the groundwater, because the aquifer was

not exploited by pumping during the study period. In

addition, there is no detection of the type of recharge

(i.e. diminution of stormy recharge periods). There-

fore, the trend detected in the outflow from the El

Tempul spring is not of climatic origin, but it is

related, with a high modulation capacity, to the long-

term distribution of the precipitation.

The continuous wavelet-transform method allowed

us to corroborate the precipitation and outflow annual

components during the whole analyzed period. So, as

well as annual components there are 2–3 and 4–6 year

components, which show a shift from a dominant 2–3

year period in the first part of the record to a 4–6 year

period in the later part of the record. These

components are more visible for Gibraltar rainfall

than for San Fernando, probably because of the

Gibraltar data series is larger and with higher

variability (Table 1). The transition between the

interannual components has already been make

evident by others authors in precipitation records in

Southern France (Labat et al., 2000), and interannual

variations in global mean sea level (Chambers et al.,

2002). The multiannual scale components are linked

to the alternation of dry and wet periods inherent to

the NAO (Rodrigo et al., 2000).

Regarding temperature distribution, the annual

periodicity indicative of temperature differences

between summer and winter periods has also been

constant for over a century. Moreover, we detected a

6-monthly periodicity that is indicative of the similar

values of temperature during spring and autumn times

in the south of the Iberian Peninsula. Long-term

correlation and spectral analysis corroborated the

periodicity of approximately 5 (and 2.5) years found

for the precipitation series. The approximately 5-year

periodicity of temperature distribution has also been

detected in other parts of the world, such as Great

Britain, Canada and the USA (Burroughs, 1992),

where the temperature recording periods used were

very similar to those available for the present study.

The continuous wavelet transform method allows us

to deduce new interannual information, so during the

last two decades of the record periodicities of 2–3 and

4–6 years have also been detected in temperature,

according to the periodicities deduced from corre-

lation and spectral analysis. Nevertheless, no long-

term trends were detected for the temperature data

time series, if a temperature increase of 1 8C or more

had existed, it would have been detected by the

correlation and spectral analysis.

In summary, in spite of the relative brevity of the

time series of rainfall, temperature and outflow data,

all the periodicities detected in this work can be

compared with the climate variability at decadal to

annual scale detected in several proxy data from

geological records (Alverson and Oldfield, 2000;

Cane et al., 2000; Frisia et al., 2003).


6. Conclusions

From the results of the correlation and spectral

analysis and wavelet continuous analysis applied to

various long time series of climatic and hydrological

data recorded in the south of the Iberian Peninsula, the

following conclusions are drawn: the annual periodicity

of the distribution of precipitation has been constant

over more than 150 years, although lesser (6-monthly

periods) and weaker periodicities have also been

observed. Furthermore, long-term analysis reveals a

rainfall periodicity of 5 (and 2.5) years, which has also

been recorded in other areas of Europe due to the

influence of the NAO. However, no long term trend in

the rainfall and temperature distributions has been

detected, perhaps because monthly data of rainfall,

temperature and flowrate are not the best variables to

observe climate change or because the climate change

really started a few years ago and the time series do not

yet contain these tendencies or perhaps both.

The two methodologies used in this work, correlation

and spectral analysis (with different lags) and continu-

ous wavelet transform methods, obtain similar results

when they are applied to three type of data (rainfall,

temperature and flow rate). This means that both

methods are useful and complementary to study climatic

changes: the correlation and spectral analysis is a

powerful tool to detect average periodicities in long

term series of climatic and hydrological data, while the

wavelet transforms show the distribution of periodic

variabilities with time. Therefore climatic and hydro-

logical variations deduced are congruent and they can be

compared with the geological record.

Acknowledgements

This study is a contribution to the projects IGCP-

513 of the UNESCO, PB98-1397 and REN 2002-

01797/HID of the DGI and to the Research Group

RNM 308 of the Junta de Andalucıa. We thank the

Real Observatorio de San Fernando (Cadiz) for

providing rainfall and temperature data from the San

Fernando meteorological station, the Confederacion

Hidrografica del Sur de Espana and the Gibraltar

Meteorological Office for rainfall data from the

Gibraltar station and the Aguas de Jerez (AJEMSA)

company for outflow data from the El Tempul spring.

We are very grateful to Prof. Ian Fairchild (University

of Birmingham) for his suggestions and English

corrections on this manuscript, and to the anonymous

referees for their contructive criticisms.

References

Alverson, K., Oldfield, F., 2000. Abrupt climate changes. PAGES-

CLIVAR Exchanges, vol. 5, pp. 7–10.

Andreo, B., Carrasco, F., Linan, C., Vadillo, I., 2002. Epigenic CO2

controlling the drip water chemistry and speleothem growth in a

Mediterranean karst area (Nerja Cave, S Spain). In: Daoxian, Y.,

Cheng, Z. (Eds.), Karst Proceses and the Carbon Cycle, pp. 51–

64.

Baker, A., Smart, P.L., 1995. Recent flowstone growth rates: field

measurements and comparison with the theoretical predictions.

Chemical Geology 122, 121–128.

Benavente, J., Frontana, J., Chica, M., 1986. Estudio del regimen

pluviometrico en la ciudad de Granada durante el periodo 1902–

1983. II Simposio sobre el Agua en Andalucıa 1, 581–588.

Breaker, L.C., Liu, P., Torrence, C., 2001. Intraseasonal oscillations

in sea surface temperature, wind stress, and sea level off the

central California coast. Continental Shelf Research 21, 727–

750.

Burroughs, W.J., 1992. Weather Cycles: Real or Imaginary.

Cambrige University Press, Cambrige, 201 p.

Cane, M.A., Clement A., Gagan, M.K., Aylife, L.K., Tudhope, S.,

2000. ENSO trough the Holocene, depicted in corals and model

simulations, PAGES-CLIVAR Exchanges vol. 5, pp. 3–7.

Chambers, D.P., Mehlha, C.A., Urban, T.J., Nerem, R.S., 2002.

Analysis of interannual and low-frequency variability in global

mean sea level from altimetry and tide gauges. Physics and

Chemistry of the Earth 27, 1407–1411.

Delleur, M., 1971. Developpements recents en matiere d’analyse

des chroniques d’evenements hydrologiques: liaison en chaıne,

analyse spectrale. Houille Blanche 3, 147–157.

Fairchild, I.J., Baker, A., Borsato, A., Frisia, S., Hinton, R.W.,

McDermott, F., Tooth, A.F., 2001. Annual to sub-annual

resolution of multiple trace-element trends in speleothems.

Journal of the Geological Society of London 158, 831–841.

Frisia, S., Borsato, A., Preto, N., McDermott, F., 2003. Late

Holocene annual growth in three Alpine stalagmites records the

influence of solar activity and the North Atlantic Oscillation on

winter climate. Earth and Planetary Science Letters 216, 411–

424.

Gascoyne, M., 1992. Paleoclimate determination from cave

deposits. Quaternary Science Review 11, 609–632.

Gaucherel, C., 2002. Use of wavelet transform for temporal

characterisation of remote watersheds. Journal of Hydrology

269, 101–121.

Genty, D., Deflandre, G., 1998. Drip flow variations under a

stalactite of the Pere Noel cave (Belgium). Evidence of seasonal

variations and air pressure constraints. Journal of Hydrology

211, 208–232.


Jenkins, G.M., Watts, D.G., 1968. Spectral Analysis and its

Applications. Holden Day, San Francisco, 525 p.

Jimenez, P., Andreo, B., Duran, J.J., Carrasco, F., Lopez-Geta, J.A.,

Vadillo, I., Vazquez, M., 2001. Estudio hidrodinamico del

manantial de El Tempul (Sierra de las Cabras, Cadiz, Sur de

Espana). Boletın Geologico y Minero 2, 85–102.

Jimenez, P., Andreo, B., Carrasco, F., Duran, J.J., Lopez-Geta, J.A.,

2002. Caracterizacion de acuıferos carbonaticos del sur de

Espana a partir de su respuesta hidrodinamica. In: Carrasco, F.,

Duran, J.J., Andreo, B. (Eds.), Karst and Environment, pp. 105–

113.

Kuhnel, I., McMahon, T.A., Finlayson, B.L., Haines, A., Whetton,

P.H., Gibson, T.T., 1990. Climatic influences on streamflow

variability: a comparison between southeastern Australia and

southeastern United States of America. Water Resource

Research 26 (10), 2483–2496.

Kumar, P., 1996. Role of coherent structure in the stochastic

dynamic variability of precipitation. Journal of Geophysical

Research 101 (26), 393–404.

Kumar, P., Foufoula-Georgiou, E., 1993. A multicomponent

decomposition of spatial rainfall fields. Segregation of large

and small scale features using wavelet transform. Water

Resource Research 29 (8), 2515–2532.

Labat, D., Ababou, R., Mangin, A., 1999a. Analyse en ondelettes en

hydrologie karstique: 1re partie: analyse univariee de pluies et

debits de sources karstiques. Comptes Rendus Academy

Scientific Paris, Series IIa 329, 873–879.

Labat, D., Ababou, R., Mangin, A., 1999b. Analyse en ondelettes en

hydrologie karstique: 2e partie: analyse croisee pluies-debits.

Comptes Rendus Academy Scientific Paris, Series IIa 329, 881–

887.

Labat, D., Ababou, R., Mangin, A., 2000. Rainfall runoff relations

for karstic springs: continuous wavelet and multiresolution

analyses. Journal of Hydrology 238, 149–178.

Labat, D., Ababou, R., Mangin, A., 2001. Introduction of wavelet

analyses to rainfall-runoffs relationship for karstic basins: the

case of Licq-Atherey karstic system (France). Ground Water 39

(4), 605–615.

Larocque, M., Mangin, A., Razack, M., Banton, O., 1998.

Contribution of correlation and spectral analyses to the regional

study of a large karst aquifer (Charente, France). Journal of

Hydrology 205, 217–231.

Liu, P.C., 1995. Wavelet spectrum analysis and ocean wind

waves. In: Foufoula-Georgiou, E., Kumar, P. (Eds.),

Wavelets in Geophysics. Academic Press, New York,

pp. 151–166.

Mandelbrot, B.B., Wallis, J.R., 1968. Noah, Joseph and operational

hydrology. Water Resource Research 4 (5), 909–918.

Mangin, A., 1981a. Utilisation des analyses correlatoire et spectrale

dans l’approche des systemes hydrologiques. Comptes Rendus

Academy Scientific Paris 293, 401–404.

Mangin, A., 1981b. Apports des analyses correlatoire et spectrale

dans l’approche des systemes hydrologiques. Comptes Rendus

Academy Scientific Paris 293, 1011–1014.

Mangin, A., 1984. Pour une meillure connaissance des systemes

hydrologiques a partir des analyses correlatoire et spectrale.

Journal of Hydrology 67, 25–43.

Meyers, S.D., O’Brien, J.J., 1994. Spatial and temporal 26-day SST

variations in the equatorial Indian Ocean using wavelet analysis.

Geophysics Research Letter 21 (9), 777–780.

Meyers, S.D., Kelly, B.G., O’Brien, J.J., 1993. An introduction to

wavelet analysis in oceanography and meteorology with

application to the dispersion of Yanai waves. Monthly Weather

Review 121 (10), 2858–2866.

Moreno, M.C., Martın, J., 1986. Estudio preliminar sobre las

tendencias de la precipitacion anual en el Sur de la Penınsula

Iberica. El caso de Gibraltar. II Simposio sobre el Agua en

Andalucıa 2, 37–44.

Padilla, A., Pulido-Bosch, A., 1995. Study of hydrographs of karstic

aquifers by means of correlation and cross-spectral analysis.


Pozo-Vazquez, D., Esteban-Parra, M.J., Rodrigo, F.S., Castro Dıez,

Y., 2000. An analysis of the variability of the North Atlantic

Oscillation in the time and the frequency domains. International

Journal of Climatological 20, 1675–1692.

Qian, B., Xu, H., Corte-Real, J., 2000. Spatial-temporal structures of

quasi-periodic oscillation in precipitation over Europe. Inter-

national Journal of Climatological 20, 1583–1598.

Rodrigo, F.S., Esteban-Parra, M.J., Pozo-Vazquez, D., Castro Dıez,

Y., 2000. Rainfall variability in S Spain on decadal to centennial

time scales. International Journal of Climatological 20, 721–732.

Rogers, J.C., 1984. The association between the North Atlantic

Oscillation in the Northern Hemisphere. Monthly Weather

Review 112, 1999–2015.

Romero, S., Sainz, S., 1984. Evolucion pluviometrica en el

observatorio de Huelva: periodo 1903–1982. I Congreso

Espanol de Geologıa 4, 331–344.

Schwarcz, H.P., 1986. Geochronology and isotope geochemistry of

speleothems. In: Fritz, P., Fontes, J.C. (Eds.), Handbook of

Environmental Isotope Geochemistry, vol. 2. The Terrestrial

Environment, pp. 271–303.

Smith, L.C., Turcotte, D.L., Isacks, B.L., 1998. Streamflow

characterization and feature detection using a discrete wavelet

transform. Hydrological Processes 12, 233–249.

Spolia, S.K., Chander, S., O’Connor, K.M., 1980. An autocorrela-

tion approach for parameter estimation of fractional order equal-

root autoregressive models using hyper geometric functions.


Sumner, G.N., Romero, R., Homar, V., Ramis, C., Alonso, S.,

Zorita, E., 2003. An estimate of the effects of climate change on

the rainfall of Mediterranean Spain by the late twenty first

century. Climate Dynamics 20, 789–805.

Szilagyi, J., Parlange, M.B., Katul, G.G., Albertson, J.D., 1999. An

objective method for determining principal time scales of

coherent eddy structures using orthonormal wavelets. Advances

Water Resource 22 (6), 561–566.

Tooth, A., Fairchild, I.J., 2003. Soil and karst aquifer hydrological

controls on the geochemical evolution of speleothem-forming

drip waters, Crag Cave, southwest Ireland. Journal of Hydrology

273, 51–68.

Torrence, C., Compo, G.P., 1998. A practical guide to wavelet

analysis. Bulletin American Meterological Society 79, 61–78.

climatic and hydrological variations during the last 117 ... · correlogram allows us to quantify...

Documents