Use of wavelet transform for temporal characterisation of remote watersheds

Use of wavelet transform for temporal characterisation

of remote watersheds

C. Gaucherel*

IRD, Unite Observatoires Hydrologiques et Ingenierie (OBHI), Antenne de Guyane, Route de Montabo, BP 165, 97323 Cayenne Cedex, France

Received 4 October 2001; revised 10 June 2002; accepted 24 June 2002

Abstract

French Guyana is a remote, wild and little instrumented French department located in South America. Without rainfall

dataset, rivers that can be temporally studied from their outlets offer easy accessible hydrological and climatologic information

on the remote areas that they cover. As part of a large project intended to build a biotic index of water quality, we studied the

hydrological properties of the main French Guyana basins. By computing a set of temporal indicators for flow variability

characterisation, we extracted the most relevant by means of a principal component analysis. A cluster analysis based on the

remaining indicators finally classified the nine watersheds. At this stage, French Guyana hydrology shows a surprising

uniformity. For this reason, standard methods such as the Fourier analysis appear rapidly ineffective to analyse the runoff

variability. Hence, we exploited the potential of continuous wavelet transform on flow curves to detect new periodicities or time

annual features. The wavelet coefficient maps made it possible to detect and explain the so-called ‘Short March Summer’

meteorological phenomenon. The latter, a temporary reduction of rain during the rainy season of the Guyana plateau, has been

explained as the result of the Atlantic Ocean influence on the continent. It permitted to characterise and discriminate more

accurately the studied watersheds.

q 2002 Published by Elsevier Science B.V.

Keywords: Watershed analysis; Guyana plateau; Runoff variability; Continuous wavelet transform

1. Introduction

Watershed characterisation has been an important

topic in hydrology for decades. It has been shown that

characterisation and basin representativeness benefit

from fundamental research, hydrological previsions,

natural change studies and data completion (Toebes

and Ouaryvaev, 1970). A complete description of

watersheds allows a comparison to model their

behaviour and to observe their evolution, whether or

not induced by human activity (e.g. NOAH Project).

These are the reasons behind the large multidisci-

plinary environmental project, ‘Water Quality of

French Guyana Rivers’ (DIREN project) (Carmouze,

1998). This project has grouped biological, chemical

and physical studies prior to the creation of biological

water quality indices for French Guyana. This paper

concentrates on the physical and temporal character-

isation of the watersheds (for a spatial description of

watersheds, in particular the hydrographical study, see

Gaucherel, 2002b).

Hydrobiologists have recently multiplied studies

on the relationship between habitats and animal

populations (Lowe-MacConnell, 1975; Merigoux

0022-1694/02/$ - see front matter q 2002 Published by Elsevier Science B.V.

PII: S0 02 2 -1 69 4 (0 2) 00 2 12 -3

Journal of Hydrology 269 (2002) 101–121

www.elsevier.com/locate/jhydrol

* Address: 300, rue Buffon, 34070 Montpellier, France. Tel.:

þ33-4-67-41-42-81; fax: þ33-3-85-54-56-48.

E-mail address: [email protected] (C. Gaucherel).

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

et al., 1998). It is now commonly accepted that

hydrological properties condition spatial and temporal

distribution of aquatic species. The complex inter-

actions between environmental factors lead to charac-

teristic spatial and temporal variability (Hawkins

et al., 1993). Aquatic fauna such as diatoms, macro-

invertebrates and fish are highly constrained by flow

variability. This parameter effectively controls the

structure and dynamics of a river and consequently

modifies the available habitat (Baudry, 1992; Norris

and Thoms, 1999). Standard statistical descriptions of

river flows, however, provide incomplete information

and only a rough description of runoff variability for

our purpose. It was necessary to quantify precisely

this attribute and we, therefore, developed a new

approach.

Variability (time variations) refers to the time-

scale properties of signals. Many tools have been

developed to describe them. Time–frequency tools

(Cohen and Kovacevic, 1996) and multifractal

analyses in particular have demonstrated their ability

to describe and model complex geophysical processes

that are spread out (scaling over) a range of space and

time scales. Specifically for areas of immediate

interest to the hydrologist, Hubert et al. (1993),

Schertzer and Lovejoy (1987) and Pandey et al.

(1998) used a multifractal approach to study the

scaling behaviour of rainfall, clouds and runoff fields.

The principal limitation of such work is the lack of

time-localisation of specific events, although it can

sometimes be bypassed using the variogram’s fea-

tures. To identify in the signal interannual as well as

intraseasonal events, we naturally thought of using

continuous wavelet analysis.

Grossman and Morlet (1984), working on geophy-

sical seismic signals, introduced for the first time in

earth sciences the continuous wavelet transform. This

technique is nowadays widely used in many different

fields of applied research (Roques and Meyer, 1993;

Meyers and O’Brien, 1994). Applications of wavelet

transforms on runoff curves are still very scarce

(Foufoula-Georgiou and Kummar, 1995). Yet, Smith

et al. (1998) and Labat et al. (2000) have recently used

this technique in the field of hydrology. The latter

authors applied for instance the wavelet method to

rainfall rates and runoffs measured on karstic

watersheds to study the superposition of rapid

response and slower recharge due to the drainage

system. Muzy and Bacry (1991) have also proposed

the Wavelet Modulus Maxima Representation

(WMMR) to classify datasets with the help of wavelet

transforms.

French Guyana is flat (maximum altitude is

,800 m, generally lower than ,200 m) and almost

completely covered with rainforest (94% of the

territory). This uniform landscape associated with

high annual rainfall means that uniform hydrograms

are generated whatever the size of the watersheds.

Standard indicators (or indexes), such as the ones

based on derivatives or Fourier analysis, seem to be

inefficient in discriminating between the French

Guyana watersheds. As a ‘standard statistical anal-

ysis’ failed, we rapidly tried to visualise each time

variation of the streamflows at specific times of the

year by the use of the wavelet transforms.

The paper is organised as follows: in Section 2, the

data used in this study is introduced. A standard

statistical analysis of the French Guyana flow rates is

computed in Section 3. The standard and wavelet

indicators are then merged and classified over the

watersheds set. Sections 4 and 5 present the wavelet

methodology and its results on the French Guyana

runoff measurements. We conclude in Section 7 with

a discussion on the extended possibilities of this new

approach.

2. Data

The data comes from French Guyana, which is a

French department located north of Brazil and covers

about 84,000 km2. Though there was a compilation of

data from UNESCO (1978) on neighbouring water-

sheds and a few other works (Hastenrath, 1990a,b),

hydrology of the Guyana plateau has been studied

little for itself. Most scientific work in this part of

South America has focused on the huge neighbouring

Amazon basin (Marengo, 1995; Jia yu zhou and Lau,

1998; Genta et al., 1998). South America is a wide and

often remote continent with very few data collection

sites and the collection of different measurements at a

unique place (the outlet basin for instance) can be a

convenient and economic way to survey the region.

Considering the streamflows offers the advantage of

integrating spatial variability and climatologic

information within the basin scale. In our case, no

C. Gaucherel / Journal of Hydrology 269 (2002) 101–121102

rainfall rates series was available on the studied period

(because of the remote nature of French Guyana),

except the one registered at the Cayenne airport. The

latter was too far and too isolated from the studied

basins to be relevant for our analysis. Hence, no

rainfall rates study was possible.

For many decades, the ‘Institut de Recherche pour

le Developpement” (IRD, ex. ORSTOM) has

recorded the flow rates of 11 watersheds (Fig. 1).

Karouabo and Camopi hydrological stations, which

are, respectively, short and old time series, are not

included in the studied set and are only shown for

ulterior validation. These basins cover more than 90%

of the territory. The French Guyana flow rates are

‘equatorial of the austral transition type’ and are quite

homogeneous (Hoepffner and Rodier, 1976). The

typical annual hydrogram shows an increasing water

level from December to June, often divided by the so-

called ‘Short March Summer’ (SMS), which corre-

sponds to a deficit of rain (Fig. 2). This well-known

hydro-meteorological event has never been scientifi-

cally described and studied in detail. This deficit is not

so obvious in the annual flow rates averaged over the

11 stations (Fig. 2(a)), but it appears clearly for an

instance at the beginning of the fourth and fifth year of

our studied period (Fig. 2(b)). The dry season occurs

between July and November, with a minimum of

discharge during the last month. The annual French

Guyana rainfall averages 2.5–4 m, with a peak

centred on the southern part of the littoral, the region

of the Kaw Mountains (Groussain, 2000). The specific

flow averages consequently vary from 20 to 60 l/s/

km2, which are typical values in the Amazonian

region.

Our analysis uses the daily average of each rivers

discharge, the accuracy of which is assumed to be

,5%. A very few values have been reconstructed by

correlation of highly correlated neighbouring basins,

except for the Saut Sabbat hydrological station (where

,35% of the values were missing, reconstructed by

correlation with the Langata Biki station). As the

recording duration could greatly affect variability

estimation, we have chosen to study the nine biggest

rivers over a 23-year period (January 1970 to

December 1992). We checked our methodology to

ensure that starting in January would not be

prejudicial to our results.

3. Standard analysis

With the aim of characterising habitats of different

aquatic species, we wanted to describe previously

presented runoff time curves and their variations as

completely as possible. We first used various

statistical indicators based on the flow rate curves.

The three principal moments of the flow distributions

(the arithmetic mean, standard deviation and

Fig. 1. Hydrographical network of French Guyana, digitalised from 1:100,000 maps. Watersheds studied, defined by their outlet hydrological

stations (green crosses) are coloured. Basin limits are drawn in red. As a scale, the Saut Sabbat basin (in yellow) is 300 km long.

C. Gaucherel / Journal of Hydrology 269 (2002) 101–121 103

skewness) and the coefficient of variation were

estimated for the nine basins (kurtosis statistical

moment was also used with the same results). Further,

these moments are computed such that:

flow1 ¼ 1=nX

i

xi;

ðflow2Þ2 ¼

Xi

ðxi 2 flow1Þ2=ðn 2 1Þ;

flow3 ¼ 1=nX

i

ððxi 2 flow1Þ=flow2Þ3;

flowcv ¼ flow2=flow1

Where xi is the flow rate value at the time step i and n

their total number. The discharge averages cover a

wide range, but their coefficient of variation shows a

homogeneous regional variability (,0.76). The flow

distributions are characterised by a positive skewness,

Fig. 2. (a) Annual mean flow curves of French Guyana watersheds (flow in m3/s along the non-normalised y-axis). (b) Averaged standardized

flow rates over the 23 years studied period. As it has been computed on the basis of the nine studied basins over their common period, the curve

shape is characteristic to the French Guyana basins. The tortuous high water season (including the Short March Summer) runs from December to

July, before to the calm low water season. The deficit of rainfall during the rainy season is not obvious in the first curve, but it appears clearly at

the beginning of the fourth and fifth year (for instance) of the studied period.


indicating less scattered low water days than high

water days. This homogeneity led to the completion of

these calculations by the first and second derivatives

to better quantify the flow variability. The ‘relative’

derivatives, i.e. the first derivative normalised by the

flow at the same day, made it possible to reduce the

unequal high and low water contributions (this

manipulation was not necessary for the second

derivative). New temporal indicators were con-

structed with the three preceding moments and

the coefficient of variation of the three derivative

distributions (further noted: der1, der1rel1 and der2).

Specific periodicities associated with some water-

sheds would also be useful to distinguish them from

others. We therefore applied various mathematical

methods, including auto-correlation and Fourier ana-

lyses, to detect periodical or a-periodical behaviours.

The Fourier spectra and the autocorrelation curves

look very similar between the studied stations and were

ineffective to detect any periodical behaviour (Fig. 3).

Fig. 3. Fourier spectra (a) and autocorrelation curve (b) of the Langata Biki hydrological station. Long (a, left) and short (a, right) trends are

dissociated for a better interpretation. The spectra of the others stations present rigorously the same shape, showing a unique maximum at the

year periodicity. No other maximum (relative to the 95% CL) have been detected.


Neither the complete daily flow curves, nor

the averaged flow curves (annually folded flow curve

for instance) gave relevant information. Except for the

evident annual periodicity, only one other period

appears to be sometimes significant (but still much

lower than the 95% confidence level). It was found to

be ,21–28 days, depending on the watersheds. This

could be attributed to the influence of the moon and

tidal forces. Yet, as seen in the French Guyana

hydrographical map, the hydrological stations were

set up far enough from the coast to avoid tidal

perturbations. No significant link with the atmo-

sphere’s synoptic maximum period (,16 days), the

typical lifetime of planetary-scale atmospheric struc-

tures have been found (Kolesnikova and Monin, 1965).

We rapidly reached the limits of this temporal and

frequency analysis and we had to develop a new

approach to characterise the French Guyana surface

runoff effectively. In particular, we thought that it was

possible to observe distinct responses of the forcing

rainfall, depending on the time of the year and the area

of records. Time-scale properties of each signal could

be simultaneously visualised by the use of a wavelet

analysis.

4. Wavelet analysis

The wavelet transform achieves a time-scale

representation of any temporal phenomenon, in

another way than the Fourier or other time–frequency

decomposition methods. In continuous time, but on a

finite interval, we construct a basis with elementary

wavelets:

cabðxÞ ¼ 1=ffiffia

pcðx 2 b=aÞ; with ða; bÞ [ ðRp

þ £RÞ

This two-parameters basis allows a time-scale dis-

crimination of processes. The definition of the

coefficients of the wavelet transform of a square-

integrable continuous-time signal f(x ) is therefore:

Cf ða; bÞ ¼ðþ1

21f ðxÞcp

abðxÞdx ¼ kf ðxÞ;cabðxÞl

Where p corresponds to the complex conjugate. The

parameter a acts as a dilation factor, while the

parameter b corresponds to a temporal translation of

the function cabðxÞ; which allows the study of the

signal around b. The final wavelet transform of the

signal f(x ) is the whole set of wavelet coefficients.

The main property of wavelet transform is to

provide a time-scale localisation of processes, which

derives from the compact support of its basic function.

This is opposed to the classical (infinite supports)

trigonometric functions of Fourier analysis (for more

details see Labat et al. (2000)). Fig. 4 explains the

principle of the wavelet transform: it searches for

correlations between the signal (here an annual

hydrogram, Fig. 4(c)) and a family of curves with

similar shapes (Fig. 4(a)). The shape is called the

‘mother wavelet’ or ‘wavelet function’. This calcu-

lation is done at different dilation scales a (y-axis) and

locally around the time b (x-axis). The result is a

wavelet coefficient map (Fig. 4(b)) in which the

colour scale indicates the correlation intensity at

different times and dilation scales. It is easy, with a

short experience, to interpret the map features: the red

spots at the bottom come from the very short

fluctuations all around the hydrological year; the

two bigger yellow spots during the first three months

of the year are interpreted as the SMS modulations

(see further); the two intense cyan marks on top of the

map are explained by the smoothed trends of the high

and low water seasons; finally, the white or dashed

lines indicate one of the two season transitions.

Therefore, wavelet transform acts then as a ‘math-

ematical zoom’. Further, it was more convenient to

work with the absolute values of the wavelet

coefficients, as their sign does not carry interesting

additional information for this study (the wavelet

coefficients are positive/negative, for runoff maxi-

mums/minimums). The grey scale, combined with the

absolute values, has been chosen to enhance the

discriminant features of the French Guyana wavelet

maps (i.e. the SMS bumps).

We first wanted the mother wavelet to have the

shape of a unitary hydrogram, which is the response of

the basin (or a part of the basin) to an isolated rainy

event. This was not possible due to some strict

mathematical conditions imposed to the wavelet

functions (Cohen and Kovacevic, 1996). The first

conditions are called ‘admissibility conditions’. They

allow to concentrate the mother wavelet values

around the origin of time and frequency to locally

study the signal:

ðþ1

21cðxÞdx ¼ 0;

ðþ1

21lcðvÞl2=lvl dv ¼ Kc , 1


where ^ is the Fourier transformation of a function.

These conditions assure a rapid decrease around the

null time and frequency. In case the signal is the mother

wavelet itself, the mother wavelet has to be normalised

(kck ¼ 1; where k·k is the classical L 2-norm).

Though we never tried to reconstruct the signal

from the wavelet coefficient, some additional remarks

on wavelets formulation are appropriate here. In order

to obtain a reconstruction formula for the studied

signal, it is necessary to add ‘regularity conditions’ to

the previous ones:

ðþ1

21xkcðxÞdx ¼ 0 where k ¼ 1;…; n 2 1

Fig. 4. Illustration of the wavelet transform principle with a hydrological signal: it consists of searching for correlation between the signal (c)

and a family of similar curves (a). The chosen mother wavelet (a, left side) used is called ‘Mexican hat’. Resulting wavelet coefficient map (b)

and its colour scale indicates the correlation intensity at different time and dilation scales. The marked red, yellow and cyan spots, respectively,

corresponds to short, SMS and seasonal variations of the flow curves. The vertical white (or superimposed dashed) line indicates one of the two

season transitions. For the corresponding Fourier spectrum, see Fig. 8.


that is to say, the high-order moments of the mother

wavelet are null or nearly so:

f ðtÞ ¼ 1=Kc·ðþ1

0

ðþ1

21Cf ða; bÞ·cabðtÞ·da=a2 db

Several mother wavelets fulfilling, more or less, the

previous conditions are presented in the literature. The

main disadvantage of these non-orthogonal wavelets

is that the continuous wavelet transform of the signal

is characterised by a redundancy of information

among the wavelet coefficients. This redundancy

(intrinsic to this wavelet basis and not to the signal)

can be reduced by the chosen projection basis. It cans

even be avoided with an orthonormal continuous

time-wavelet basis. Hence, the wavelet coefficient

interpretation is strongly dependant on the chosen

projection basis.

The simple and commonly used ‘Mexican hat’

mother wavelet was finally chosen in this study. On

the contrary to other mother wavelets indeed, the

latter allows for a good temporal resolution but a poor

frequency resolution. As we will see, the main feature

of the annual French Guyana hydrograms (the SMS)

has to be precisely localised at the beginning of the

hydrological year.

It should be noted that we only used the continuous

wavelet transform theory. A discrete-time approach

has been imagined to remove the redundancy of

information among the wavelet coefficients and to

help to more properly discriminate the signal

processes (Daubechies, 1992). Nevertheless, it was

not our goal here to study the combination of

processes which leads to the French Guyana flow

rates. We wanted to characterise the different basins

by functional features that could be found in their flow

rates curves. For this purpose, the continuous wavelet

transform, more simple to implement, was suitable

enough. This also explains why we limited the

classification study to a wavelet decomposition and

why we never tried to reconstruct the signal from the

wavelet coefficients.

To control all the computation parameters, a self-

made software was developed with Visual Basic (VB-

pro 6.0) to obtain the results of this practical study.

The results appear like coefficient maps that reflect the

correlation intensity (the correlation coefficient

squared, along the z axis) between the signal at a

precise date (x axis) and a wavelet at a definite scale

(y axis). After an exact polynomial interpolation, it is

possible to use a continuous grey scale. In addition to

the maps, we used the concept of wavelet variance

(Brunet and Collineau, 1995). This concept and its

estimators have been used in various themes such as

fluid dynamics or coastal sea level fluctuations

(Percival, 1995; Poggie and Smits, 1997). The

wavelet spectrum is defined as the average of modulus

of the wavelet coefficients, either in the time or in the

scale dimension. While time average syntheses the

variance signal distribution between the scales, scale

average allows the temporal identification of a

particular component of the signal. The wavelet

spectrum (averaged over time) is qualitatively similar

from Fourier spectrum, but can give new quantitative

information on the studied process.

To detect characteristic interannual variability of

the rivers, we first computed time wavelet spectra on

the daily mean runoff curves. The scale ranges from 1

to 512 days along the 23 years of the nine curves. As

we will see in greater detail later, the high and low

water seasons are dominant, with a 6 month pattern

and impose their rhythm (over the year periodicity).

Each year is marked by two maximums centred on the

5th of June and the 3rd of November (on average and

^1 week). Their relative intensities between the years

reflect the rainfall intensity variability received by the

basins. These spectra were once again very homo-

geneous, showing almost rigorously the same patterns

during the 23 common years. We plotted the average

of the nine wavelet spectra and compared it (after

normalisation) with the averaged flow rates of the

same watersheds (Fig. 5). These curves do not

discriminate between the different basins but offer

interesting information on the annual trend of the

French Guyana hydrology. They have been compared

to El Nino/Southern Oscillation (ENSO) and other

Atlantic indices in another study (Gaucherel, 2002a).

In particular, there is quite a high correlation between

these flow rates and ENSO. Local maximums in the

mean wavelet spectrum are particularly visible for the

years 1971–1972, 1976 and 1989–90. They corre-

spond to flood seasons during La Nina (opposite phase

of El Nino) of the examined period, as the latter

causes an important increase of the French Guyana

rainfall and subsequent runoff.

On top of the interannual uniformity of French

Guyana runoff, the wavelet maps of such long time


series were not convenient to interpret. Furthermore,

we wanted to examine statistically the short time scale

variations (such as the seasonal ones). This is the

reason why we applied wavelet transform to the daily

means curve averaged over the 23 years (hereafter

compressed curve). The resulting wavelet maps

present scales ranging from 1 to 256 days, as they

are computed on more limited duration (365 days)

than previously. Nevertheless, they effectively appear

to contain the main discriminant information, as we

will see.

5. Indicators merging

To better compare the previously described

compressed curve wavelet maps, it was necessary to

normalise them (by their wavelet coefficient mean)

and use the same grey scale (Fig. 6). For comparison,

the Fig. 7 shows the corresponding annual mean flow

rates. The maps and curves at the right-hand side of

these figures clearly present a higher variability. Yet,

their Fourier spectra and autocorrelation curves do not

exhibit any obvious periodicity, other than the year

periodicity (Fig. 8). It should be explained here why

the standard methods are so ineffective to detect the

SMS presence in the flow curves: this is precisely due

to the localisation of this phenomenon during the year.

As we will demonstrate it, the SMS has a ,2 months

duration but does not reproduce with this periodicity

all around the hydrological year. It disappears during

the 10 next months and so, cannot be detected as a

periodical feature. The time-localisation capacity of

the wavelet transform is the best tool to detect such a

localised process.

To complete the comparison of the French Guyana

watersheds, we first used the global information

contained in the wavelet maps. This suggests

computing statistical variables from the wavelet

coefficient distributions (such as the moments and

coefficient of variation) and does not need 2D

interpolation of the wavelet maps. These variables

will help to quantify the flow trends at different (short)

time scales, that would have been difficult to extract

from the flow derivatives without choosing many

different durations to compute them. We used a few

other variables such as the surface and the volume

(using the Simpson algorithm) of the wavelet mapsFig

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Fig. 6. Wavelet maps of the nine studied French Guyana watersheds and their average (computed on the basis of their compressed daily

mean flow rates averaged over 23 years). The wavelet coefficients are plotted as a function of the time of the year (in days) and as a

dilation factor (up to 256 days durations). For a better comparison, wavelet maps have been normalised (to their wavelet coefficient mean)

and are shown with the same grey scale. The grey scale has been chosen to enhance the medium scale bumps representing the ‘small march

summer’ presence (see text).


Fig. 7. Annual mean flow curves of the nine studied watersheds and their average, computed on the basis of their compressed daily mean flow

rates averaged over 23 years. The flow rates are plotted as a function of the time of the year (in days) and can be directly compared to the maps

of Fig. 6. For a better comparison, flow rates have been standardized (i.e. with a mean equal to 0 and a standard deviation equal to 1).


and their specific values (i.e. normalised by the

wavelet coefficients mean). We tested other types of

variables, which appeared to be redundant.

At this stage, 35 statistical variables characterised

the flow rates and the time variability of the nine

biggest French Guyana watersheds. They have been

standardized (i.e. with a mean equal to 0 and a

standard deviation equal to 1) for a better comparison.

Otherwise, the basins would have been systematically

classified as a function of the basin size, the dominant

Table 1

List of the non-standardized remaining indicators (after selection with Pearson correlation matrices) characterising the nine studied French

Guyana watersheds

Stations Langata Biki Saut Maripa Maripasoula Antecum-Pata Saut Sabbat Pierrette Petit-Saut Degrad-Roche Saut-Bief

flow-1 1712.15 838.41 765.39 355.26 332.42 240.78 251.54 167.78 100.53

flow-3 1.08 1.31 1.28 1.17 1.29 1.34 1.66 1.70 1.46

der1-2 139.02 85.54 60.77 23.40 35.91 24.80 43.64 22.66 19.88

der1-cv 21463.41 24276.90 21599.32 23403.00 1890.11 6200.50 2567.18 1888.17 2568.00

derl-3 1.26 1.22 1.25 1.33 0.67 1.68 0.61 1.30 0.81

der1 rel-1 0.40 0.50 0.42 0.26 0.73 0.65 1.18 0.87 2.58

der2-1 0.45 0.28 0.71 0.33 20.05 20.07 20.15 20.02 0.08

der2-cv 168.49 198.25 44.13 38.17 2434.83 2248.74 2201.95 2692.84 180.83

der2-3 20.38 21.15 20.16 20.35 20.24 20.82 20.97 20.31 20.54

ond-1 2250.72 1084.45 1019.33 407.65 360.94 237.15 247.70 259.17 122.33

ond-cv 1.21 1.21 1.19 1.20 1.21 1.26 1.18 1.18 1.15

ond-3 1.46 1.36 1.43 1.39 1.49 1.46 1.48 1.46 1.45

We used five types of indicators: flow, der1, der1rel, der2 and ond, respectively, for the flow rate, first derivative, relative first derivative,

second derivative and wavelet coefficient distributions. The 2x indicate the statistical moments shown or the coefficient of variation of the

distributions. Der-2 and ond-1 have been given for information and are not used in the cluster analysis.

Fig. 8. Averaged flow rates Fourier spectra and autocorrelation curve (a). The flow rates of the nine studied watersheds have been averaged over

the 23-year period. As already mentioned, they are identical to each station curves and they can be directly compared to those of the previous

figures. They do not exhibit any obvious short periodicity that could correspond to the SMS phenomenon. Nevertheless, the arrow shows a non-

significant (relative to the 95% CL) ,55 or 28 day periodicity, that is sometimes observed.


indicator. It was necessary to reduce their number

with examination of the Pearson correlation matrices

of each type of indicators (i.e. flow, der1, der1rel, der2

and ond, for the wavelet coefficients). We system-

atically rejected indicators showing a correlation

higher than 0.8 with another (arbitrary) one and

reduced their number to nine: flow-1 and flow-3, der1-

cv and der1-3, der1rel-1, der2-1 and der2-cv, ond-cv

and ond-3 (Table 1). A Principal Component Analysis

(PCA), which acts as a definite projection of the

indicators scatter-plot to concentrate the information

(i.e. the total variance) on a few components, was then

used to observe the distribution of the information.

PCA have been done in both streamflows series and

wavelet spaces to give the following results. It

confirms that these indicators are quite uniformly

distributed in the first three factors space (,80% of

the variance, Fig. 9) and it explains why we kept all of

them.

Here, we did not want to create an artificial index,

which would have hidden some physical information.

We chose to classify the watersheds on the basis of the

nine remaining indicators. A K-means clustering

analysis helped to gather the dominant hydrological

behaviours (Jambu and Lebeaux, 1979). This method

attempts to minimise the Euclidean distance in the

indicator space between several potential basin groups

(we also used the Pearson and x 2 distances, with

approximately the same results). After forcing the

number of groups to three, the classification appeared

as follows:

G1: [Saut Sabbat, Petit Saut, Degrad Roche and

Saut Bief ] with an inter-distance mean of ,0.65.

Note here that a four group classification rejects

Saut Bief of this first group (this basin is definitely

atypical) and reduces the inter-distance mean to

,0.52;

Fig. 9. Factor loading plot of the last nine variability indicators of French Guyana watersheds. This PCA was initially computed to reduce the

number of indicators, but their distribution in the first three factors space (totalising ,80% of the variance) seems quite isotropic. That is why

we kept all of them.


G2: [Langata Biki, Saut Maripa and Maripasoula ]

with an inter-distance mean of ,0.51;

G3: [Antecum Pata and Pierrette ] with an inter-

distance mean of ,0.67;

The cluster parallel coordinate plots, which show

the distribution of the indicator values in each group,

help to interpret this classification (Fig. 10). The

second group is the most easily interpreted and seems

to define the biggest hydrological stations with their

characteristics: scattered first derivative (i.e. high first

derivative standard deviation, visible in the coefficient

of variation), especially during low water season (i.e.

moderate relative first derivative mean) and high

variability of the flow rate variations (i.e. high second

derivative mean). The first group writes the rivers

with opposite behaviour (and we will see further, with

often a pronounced SMS). These basins generally

have low or moderate flow rates and quite low

derivatives. Yet, the relative first derivative and the

flow distribution’s asymmetry, prove that the high

water season’s variability is more pronounced for

Fig. 10. Cluster parallel coordinate plots of the nine French Guyana watersheds. They show their properties (indicators) distribution and inform

on their main characteristics. The first group (which has to be associated with the fourth atypical one) corresponds to the watersheds with a

pronounced SMS or a behaviour of medium watersheds; the second group concerns the big size basins; and the third one, resting basins.


these basins. It is possible to extract a subgroup from

this one, as Saut Bief has the same but enhanced

behaviour. Its reduced size and above all its higher

rainfall mean (,1 m/year more than the rest of the

territory) seems to accentuate the importance of the

increasing flow rate period, also characterised by a

high variability. The third group consists of the last

basins, with almost no particularity. Nevertheless, the

wavelet transform detects them with either great

asymmetry or great coefficient of variation of the

wavelet coefficients distribution.

Hence, the complete set of temporal indicators and

its associated classification offers a lot of information

on the flow rate variability of the French Guyana

rivers. The attempt to understand how the habitat

could govern the biological traits of a population, by

combining these indicators with biological ones, is

actually in progress. However, this analysis was not

completely satisfying, because it did not strongly

discriminate between the watersheds. It appeared

necessary to compare statistically the short time-

scales of the watersheds.

6. Intra-seasonal interpretation

Wavelet transform has multiple advantages: it can

identify, characterise and quantify each temporal

feature of the flow curves. By reading the wavelet

map vertically, it is possible to dissociate the slow and

rapid responses of the watersheds to the rain and, in

particular for our purpose, to compare the different

river basins. The comparison within French Guyana is

permitted because of the relative homogeneity of the

soil, the vegetation and the topography (Duroin et al.,

1993) and to a certain extent the rainfall (if we except

the Saut Bief station). The frequency information of

the wavelet maps are summarised in the dilation

wavelet spectra, from which the basins average is

presented on Fig. 11. The main periodicity is the ^90

days (i.e. 6 months patterns), found again in the ^280

and ^460 days maximums. It is caused by the dry and

rainy seasons imposing a stronger rhythm than the

annual one (a discreet peak is visible at ^360 days).

Here again the wavelet spectra appear very uniform

over the French Guyana watersheds.

For each station, the low water season presents a

very slow and very smooth annual hydrogram. Hence,

its wavelet response (the white peaks at the top of the

maps, Fig. 6) looks very similar for all of the stations.

The low variation of the high water season as well

presents a strong response in the wavelet maps. The

very short time scale responses (the small white

structures at the bottom of the maps), though different

between the two seasons, suggest short rainy events

and seems to be still uniform between the basins as

well. These characteristics should differ in another

part of the world, depending on the retention or runoff

capacities of the regional watersheds. Transitions

between the dry and wet seasons are revealed as white

vertical lines in the wavelet maps (Fig. 4). Seasonal

transitions seem to be scale invariant, with no

particularity and show how the basin responds to the

beginning and the end of rainy events at different time

scales. Despite our effort, it has not been possible to

extract relevant information about these properties

from the wavelet maps. Basins of this region have too

homogeneous behaviour for this purpose.

Finally, the main discriminating feature between

watersheds clearly appears at medium time scales

Fig. 11. Dilation wavelet spectra average (over the nine French

Guyana watersheds). This summarises the frequency distribution of

the regional hydrological behaviour. The main maximum (and its

multiples) corresponds to the combined high and low water season

responses of the wavelet maps (180 days structures). While the year

periodicity is visible (though very weak, arrow), the SMS impact in

particular is completely hidden.


Fig. 12. Time wavelet spectra of the nine French Guyana watersheds and the Karouabo (computed over standardized absolute values maps, to be

compared). We successively recognise the SMS bumps (if existing for the corresponding basin), the high water and the low water seasons. The

positions (dates of the year) and the intensities of each bump inform on the importance of the corresponding event. We extracted from these

curves several indicators to characterise the watersheds and their behaviour.


during the rising water (at the ,64 ¼ ^32 days

scale). These are the two distinct peaks which

remained ‘hidden’ in the standard analysis, but

which were enhanced by the grey scale (black on top

of the peaks). The compressed flow curves effectively

show many mixed fluctuations at the beginning of the

rainy season (Fig. 7). While the first peak has to be

attributed to the first (and shorter) part of the rainy

season, the second one (negative in relative values)

corresponds to the decreasing intensity of the rain in

the middle of this season. Hence, the second peak

perfectly characterises the watershed’s SMS, highly

heterogeneous on French Guyana. Four of the nine

studied basins have a pronounced SMS, still visible in

the time wavelet spectra, despite the importance of the

two main season responses (Fig. 12): Petit Saut,

Pierrette, Saut-Bief and Saut-Sabbat. To compare

them, we standardized the spectra and recorded their

most changing properties: the minimum (min1) and

maximum (max1), the intensities at the 20th (d20) and

110th (d110) days of the year, and the date of the low

water maximum (lw) (Table 2).

Nevertheless, the best mean to characterise the

peaks seems to be the 32nd dilation curves, as these

features for the four concerned watersheds have a 2

months duration and have a maximal response in the

wavelet maps at medium time scales. We averaged

these curves for the French Guyana basins with and

without SMS (Fig. 13). The SMS bumps appear

clearly in these curves. We repeat here that this hidden

feature in the classical analyses is due to its precise

and limited localisation during the hydrological year.

On the four curves of basins with SMS, the first part of

the rainy season arrives on the 21st25þ7 of January and

the SMS arrives on the 16th ^ 2 of March. Consider-

ing the transition dates, the SMS has a mean duration

of 56 ^ 2 days, that is to say ,2 months. After

Table 2

List of the non-standardized ‘SMS indicators’ as a new characterisation of the nine studied French Guyana watersheds

Stations surface sms0 Gc min1 max1 lw d110 d20

Langata Biki 60,930 0.5188 3.2 20.98608745 2.73020355 306 20.08802276 20.80676083

Saut Maripa 25,120 20.4854 2.2 21.07729516 2.73781085 313 0.26171049 20.84404175

Maripasoula 28,285 20.19 3.5 21.01556547 2.65116831 311 0.49595317 20.79884835

Antecum Pata 10,300 20.2995 4.1 21.09 2.46 305 0.46035524 20.87377421

Saut Sabbat 10,255 1.1238 1.7 20.92146593 2.64293296 293 20.5305363 20.81699974

Pierrette 6105 0.4236 1.9 20.9361397 2.80962568 302 20.08945721 20.86664529

Petit Saut 5900 1.3382 1.4 20.90273403 2.87837003 285 20.3502173 20.7333368

Degrad Roche 7655 20.2954 3.2 20.96940903 2.82132312 314 0.60713991 20.69900707

Saut Bief 1760 1.3794 1 20.91019107 2.86846149 279 20.38479539 20.68733462

Camopi 5920 21.1731 3 21.30 2.33 327 0.61785308 20.91088222

Karouabo 77 1.6551 0.3 20.92745838 3.00032065 288 20.50789312 20.46675584

We add the surfaces and gravity centre distance to the coast (gc, in 102 km unity) of each basin. See the text for their definition.

Fig. 13. Averaged 32th dilation wavelet curves of the French

Guyana watersheds (including Camopi and Karouabo ). The plain

(resp. dotted) curve shows the mean 32th dilation wavelet curve of

the five (resp. six) watersheds with a pronounced (resp. absent)

SMS. Their behaviour at the beginning of the year is opposite and

permit to construct a reliable indicator: the difference between the

coefficient values at the 25th and 75th day of the year (arrows).


numerous tests, we choose to keep a simple indicator

(sms0) for SMS quantification: the difference of the

two peaks intensities, measured on standardized

curves. These peaks are assumed to be at the

previously mentioned dates of the year, even on

the basin curves without peaks. The latter effectively

show a stronger increase, opposite to the SMS

decreasing impact. A Pearson correlation matrix

shows the maximum correlation of ,0.93 between

sms0 and lw or d110. A cluster analysis on the basis of

the three indicators effectively separates the basins

into two groups: [Langata Biki; Maripasoula; Saut

Maripa; Degrad Roche; Antecum Pata ] and [Saut

Sabbat; Petit Saut; Saut Bief; Pierrette ], while

Langata Biki and Pierrette could be grouped in a

third quite neutral group (Fig. 14). It is effectively

possible to detect a weak increase of the SMS peak in

these latter curves.

Fig. 14. Cluster parallel coordinate plots of the nine French Guyana watersheds, considering the SMS indicators. They show their properties

(indicators) distribution and inform on their main characteristics. The first group corresponds to the watersheds without SMS; the second group

concerns the basins with pronounced SMS; and the third one, the neutral behaviour basins (more similar to the first one).


Fig. 15. (a) As a validation of the hypothesis that the SMS is due to an oceanic influence, here are the wavelet spectra of Camopi and Karouabo

stations. Their gravity centres are, respectively, located at ,300 and 30 km from the coast. (b) Their respective compressed flow curves are

shown for comparison. The Camopi (resp. Karouabo ) flow rates have been recorded over a 23 (resp. 10) year period.


Considering our poor data collection in the interior,

it was not easy to interpret this separation. We noticed

that the four basins showing a SMS are not far from the

coast, as their gravity centre (gc) is perpendicularly

,100–200 km away from the littoral. The shortest

distance between the gravity centre of each basin and

the coast have been visually measured. The cross

correlation coefficient between the estimated distances

and the sms0 indicator for the nine basins is as high as

, 2 0.78, indicating that the SMS perturbation has an

oceanic origin. On the contrary to popular thought, the

SMS is not uniformly distributed in French Guyana

and seems to be a coastal phenomenon. It is the

consequence of the oceanic influence of the winds

during the rainy season. At this date, the Inter-Tropical

Convergence Zone (ITCZ, a ‘meteorological equator’

materialising the trade wind convergence) usually

moves on the equator, beneath French Guyana

(Marengo and Hastenrath, 1993). The latter benefits

then from the North East trade winds, which clear the

sky. Further inland, the atmospheric moisture caused

by evapo-transpiration and other processes still favour

the rain (even with a far ITCZ). During approximately

three months, the ITCZ situated on the Amazon mouth

is too low to influence French Guyana rainfall.

We checked this description by estimating the

Karouabo and Camopi wavelet maps, whose gravity

centres are, respectively, 30 and 300 km away from

the coast and for different periods (Fig. 15). Their

annual mean flow curves are also plotted for

interpretation. Their respectively absent and marked

SMS peaks confirm our assumption. No other

gradients (such as in the eastern direction or with

the basin sizes) have been found. The Kaw mountains

(and a possible Foehn effect) as well, have not been

identify as a major contribution to the SMS presence,

since the Saut Sabbat basin is far away from them but

still presents a marked SMS. The Langata Biki and

Pierrette SMS peaks can now be understood as the

lower part (closest to the coast) of the basin for the first

one, and as the distance to the coast of the compact

second one. As yet, no better cross correlation has

been found with a linear regression using the distance

to the coast and the basin’s surface area. This

important result, proving a strong relation between

the SMS and ITCZ, should be true for the whole

Guyana plateau and has yet to be more precisely

described.

7. Discussion and conclusion

Using nine flow curves, continuously recorded

over a period of 23 years at the major hydrological

stations of French Guyana, we studied by different

means the flow rates and their variations. Initially,

classical tools such as derivatives calculation, Fourier

and autocorrelation analyses were used to search for

discrepancies between the basins. Except for the

annual period, no significant periodicity in the daily

mean curves appears. A cluster analysis helped to

classify the basins, where their sizes remain the main

discriminant criterion.

The continuous wavelet transform method adapted

to the hydrograms allowed us to deduce new

information. Interannual information was first

extracted with the time wavelet spectra such as the

ENSO impacts, but still keeping the homogeneity of

the French Guyana watersheds. Always seeking to

discriminate between the basins, we searched for

statistical features with short time scales (intraseaso-

nal) using compressed (daily means) flow curves and

their associated wavelet maps. While the main

features were the low trends of rainy and dry seasons,

the medium time scales clearly showed the SMS

present in the behaviour of some of the watersheds. It

has been possible to clearly describe this well-known

phenomenon and, in particular, to explain it as an

oceanic influence. Only for coastal watersheds, the

ITCZ moving beneath the French Guyana tends to

reduce the rainfall over a two month period, centred

around mid-March. More continental watersheds are

not affected by this phenomenon.

Here again, hydrograms appear to be a powerful

means of compensating for missing meteorological

data. While wavelet transforms help to describe the

watersheds globally. We highly recommend develop-

ing the wavelet method in hydrology. It was used here

on very similar watersheds of the same region. It

would be interesting to observe the results obtained on

different basins or on a larger spatial scale such as the

Amazonian basin.

Acknowledgments

The authors would like to thank M. Lointier, A.

Occolier and C. Deakin for their valuable help. This


study was conducted with the financial support of the

DIREN of French Guyana.

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