International Journal of Geosciences, 2011, 2, 248-258
doi:10.4236/ijg.2011.23027 Published Online August 2011 (http://www.SciRP.org/journal/ijg)
The Exchange Processes in the Patos Lagoon Estuarine
Channel, Brazil
Wilian Correa Marques1*, Igor Oliveira Monteiro2, Osmar Olinto Möller2
1Instituto de Matemática, Estatística e Física, Universidade Federal do Rio Grande, Rio Grande do Sul, Brasil
2Instituto de Oceanografia, Universidade Federal do Rio Grande, Rio Grande do Sul, Brasil
Received June 1, 2011; revised July 12, 2011; accepted August 4, 2011
Abstract
Investigation of process controlling the estuarine-shelf interaction in the Patos Lagoon estuarine channel is
accessed using a two-dimensional numerical model. Results obtained suggest this approximation provides
good precision level to investigate the advective transport of oceanic waters near the estuarine mouth. The
introduction of coastal waters in synoptic time scales is dominated by advection in sub-superficial layers.
This process results from the competition between flood currents driven by remote wind effects and gravita-
tional circulation controlled by the intensity of the freshwater discharge. The short term exchange processes
follow one most energetic cycle of 8 days and intense flood events occur during periods of low continental
discharge and higher intensity winds. Very stratified salinity profiles are found during periods of moderated
freshwater discharge. The salt transport is inversely related to the freshwater discharge intensity. It presents a
mean rate of the 105 kg·day–1 transported landward during flood events.
Keywords: Freshwater Discharge, Stratificatio n, Advection, Barotropic Oscillations
1. Introduction
During the last centuries the population has distributed
along the coastal regions using the environment to live,
work and to recreational activities. The population growth
along these regions normally cause modifications in the
river discharge and circulation patterns influencing the
spill of toxic substances, nutrients and suspended sedi-
ments. Among the important coastal sites there are the
costal lagoons occupying more than 13% of the coastal
regions of the world [1]. One important hydrologic re-
source of the South America, the Patos Lagoon, is a
coastal lagoon situated in the southern part of Brazil.
Several studies have investigated the contributions of the
wind effects and the freshwater discharge in synoptic
time scales [2-8, among others]. These studies highlighted
the physical mechanism controlling the hydrodynamic
process and salinity pattern along the estuarine region.
The exportation of continental waters via Patos Lagoon
channel contributes to high primary and secondary pro-
duction along the adjacent continental shelf [9]. This
contribution influence directly the biologic dynamics of
this region considered one the most important fishing
zones of the Brazilian coast [10]. According to Ciotti
et al. [11], the freshwater discharge pattern enhances the
phytoplankton biomass in this region, where annual mean
rates of primary produ ction of around 160 g Cm-2year-1
was observed by Odebrecht and Garcia [12]. The know-
ledge of the process controlling the estuarine-shelf inte-
raction is fundamental to manage correctly this coastal
environment and their adjacencies. In this way, the ob-
jective of this paper is develop a numerical model to
estimate the salinity concentratio n near the Patos Lagoon
mouth, based in current velocity measurements, giving
an insight to the investigation of the exchange processes
and salt mass transportation.
1.1. Description of the Study Area
The Patos Lagoon is a choked coastal lagoon located in
the southern part of Brazil, between 30˚ - 32˚S latitude
and 50˚ - 52˚W longitude (Figure 1). The estuarine region
covers 10% of their total area [13]. The principal rivers
contributing in the north of the lagoon present a dis-
charge pattern of temperate regions influenced in inter-
annual and inter-decadal timescales for processes of cli-
matic order [14]. The wind action is the most effective
forcing of the Patos Lagoon circulation in synoptic Time -

W. C. MARQUES ET AL.249
(a)
(b)
Figure 1. Patos Lagoon, their principal rivers and the mea-
surement stations.
scales [5]. The combination of the local and remote wind
action is the principal mechanism to introduce salt into
the estuarine region [2,3,5]. The tides are mixed, with
diurnal dominance, and their effects are restricted to the
coastal zone and the estuarine region of the Patos Lagoon
[5].
2. Methodology
The study is based in development of a numerical model
and signal analysis. In this study were used hourly data
sets of current velocity and salinity obtained near the
Patos Lagoon entrance (Figure 1) during different periods.
The salinity and velocity data sets used in the model
calibration were obtained with thermo-salinometers and
current sensors, respectively. These data were collected
near the Praticagem pilot station of Rio Grande at 1 m
and 10 m depth, from August 2th to August 9th 1999.
The salinity data sets used to validate the model were
obtained with thermo-salinometers near the Rio Grande
Naval station at 1 m and 10 m depth, from April 29th to
May 31st 2004. The current velocity data used to force
the model in the validation experiment were obtained
near the Praticagem pilot station of Rio Grande with a
vertical profiler ADCP (Acoustic Doppler Current
Profiler) between April 29th and May 31th 2004. This
sensor collected current velocity considering 15 vertical
levels through the 15 m depth water column. The case
study was performed using current velocity obtained
with the same profiler ADCP near the Praticagem station,
from August 17th 2005 to Jan uary 31 st 2007, to fo rce the
model and calculate the salinity time series in different
points of the wat e r col umn.
Time series of wind and freshwater discharge were
used to aid in result analyzes. According to Marques [15],
the Taquari and Jacuí rivers (tributaries of the Guaíba
river) and the Camaquã river (Figure 1(a)) are the prin-
cipal tributaries of the Patos Lagoon. Th e river discharge
data are provided by the Brazilian National Water Agency
(www.ana.gov.br, ANA) and the time series ranges
between August 17th 2005 and December 31st 2006.
Time series of winds from August 17th 2005 to January
31st 2007 was obtained from reanalysis project (National
Oceanic & Atmospheric Administration–NOAA, www.
cdc. noaa.gov/cdc/reanalysis) near the Praticagem pilot
station. Table 1 presents the data sets used in this study.
The results obtained with the numerical model were
used to access the spatial and temporal variability of the
power in salinity and velocity near the Patos Lagoon
mouth using wavelet analyses. The spectral content of
the velocity and salinity time series were analyzed using
an adaptation of the Morlet wavelet method described by
Torrence and Compo [16]. The spatial and temporal vari-
ability of the velocity and salinity data series were
accessed by scale-averaging the wavelet power spectra at
multiple locations [16]. The cross-wavelet spectrum was
performed according to Torrence and Compo [16], in
order to verify the covariance between the most energetic
events observed in the salinity and velocity wavelet
power spectrum.

W. C. MARQUES ET AL. 250
Table 1. Data sets and periods us ed in the study.
Experiments Data Period
Calibration Salinity and
velocity August 2th to August 9th 1999
Validation Salinity and
velocity April 29th and May 31st 2004
Case study Velocity August 17th 2005 to January
31st 2007
Case study River Discharge August 17th 2005 to December
31st 2006
Case study Winds August 17th 2005 to January
31st 2007
In order to obtain an esti matio n of th e salt flux thro ugh
the Patos Lagoon estuarine channel was used the appro-
ximation describ ed by Smith [17] to calculate the in stan-
taneous advective salt transport with one-dimensional
flow as:
d
aA
TvsA
(1)
where: Ta is the transport integrated over the cross
section, v is the longitudinal component of velocity, s is
the salinity concentration, and A the cross section area. In
the calculations were used the 15 vertical levels of velo-
city, calculated salinity and the cross section area esti-
mated using topographical charts.
2.1. The Numerical Model
To accomplish the objectives of this study was deve-
loped a two-dimensional numerical model based in the
transport equation o f dissol ve d matter in the sea water as:
 
2
.T
TT
t


u
 T
(2)
Where: T represents an arbitrary concentration of
dissolved tracer (mg·L–1), u is the velocity vector (m·s–1)
and νT the diffusion coefficient (m2·s–1). The equation is
solved using finite difference methods. The TVD scheme
(Total Variance Diminishing) is applied to discretize the
advective part of the equation [18,19]. This method
mounts a first order scheme adding anti-diffusive fluxes
assuring the minimization of the total variance. The base
of this scheme follows the Lax-Wendroff scheme des-
cribed by Kanta and Clayson [20]. The discretization of
the parabolic part of the system represented by the
diffusive term is obtained using the Forward-Time Cen-
tered Space (FTCS) method. This method is an explicit
and first order scheme in time and second order in space
[20].
The model considered is two-dimensional and the do-
main covers the region between the Patos Lagoon mouth
and the Praticagem pilot station (Figure 2(a)). The
numerical domain considered 100 elements with equal
sizes of 200 m. The domain considers a constant water
depth of 16 m, with 15 vertical levels equally spaced at
each 1 m depth. The model ran with 60 s time step and it
was forced only using the longitudinal component of the
current velocity (north-south component) because of the
channel orientation. The diffusion coefficient is con-
sidered constant in time and the boundary condition of
the model considers null salinity in the north boundary
and 34 in the south boundary. The initial condition
considered is a variation curve of the salinity as a func-
tion of the position along the domain (Figure 2(b)).
(a)
(b)
Figure 2. Model domain (a) and initial condition of salinity
as a function of position along the domain (b).

W. C. MARQUES ET AL. 251
2.3. The Model Validation – 2004 Year
2.2. The Model Calibration—1999 Year
The validation test was performed between April 29th
and July 4th 2004 using horizontal diffusion coefficient
of the 100 m2·s–1. The model was used to calculate the
salinity time series at 1 m and 10 m depth near the Prati-
cagem pilot station of Rio Grande using time series of
current velocity.
The calibration test consisted in analyze the influence of
the horizontal diffusion coefficients. The model was
forced with the longitudinal component of the current
velocity measured at 1 m and 10 m depth. The salinity
time series calculated was compared with the measure-
ments between August 2th and August 9th 1999. The results
(Figure 3) indicate that lower diffusion coefficients (1
and 10 m2·s–1) underestimate the mixing process giving
the purely advective character to the salinity time series.
The better results were obtained using a diffusion coeffi-
cient of 100 m2·s–1 (Figure 3(a) and (b)) where the
minimal values of salinity associated to ebb flow periods
(bottom series) are better represented. Fernandes et al. [8]
using the hydrodynamic model TELEMAC3D to study
the Patos Lagoon estuary observed best results of the
model calibration using diffusion coefficients between
10 e 100 m2·s–1.
The results presented (Figure 4) indicate that the sim-
plified model can reproduce satisfactorily the salinity
pattern observed near the entrance of the Patos Lagoon
channel. In order to quantify the reproducibility of the
model, the method proposed by Walstra et al. [21] was
used. This method calculates the Root Mean Square
Absolute Error (RMAE) between measured and cal-
culated time series, and according to Wasltra et al. [21],
values lower than 0.4 indicate good reproduction of the
numerical model. The calculated RMAE during this
period indicate values around 0.33 in the surface and
0.24 near the bottom.
Figure 3. Calculated and observed salinity time series considering horizontal diffusion coefficients of the 100 m2·s–1 to surface
(a) and bottom (b); of the 10 m2·s–1 to surface (c) and bottom (d) and, of the 1 m2·s–1 to surface (e) and bottom (f) between
August 2th and August 9th 1999.

W. C. MARQUES ET AL. 252
Figure 4. Calculated and observed salinity time series in the surface (a) and bottom (b) between April 29th and July 31st 2004.
3. Results
The numerical model was used to calculate the salinity
near the Patos Lagoon mouth considering the horizontal
diffusion parameter of the 100 m2·s–1. The velocity time
series along the 15 vertical levels are presented as time/
depth profile (Figure 5(a)). The positive values (clearest
values) are associated to flood events alo ng the estuarine
channel while the (grayest values) are associated to ebb
events. The time evolution of the velocity indicates the
intermittent ebb/flood pattern associated to the north/
south quadrant winds influence (Figure 6(a)). The ebbi ng
events are intensified during periods of higher and mode-
rate freshwater discharge conditions (Figure 6(b)) occu-
rring from austral winter to austral spring. The calculated
salinity time/depth profile (Figure 5(b)) indicates the
influence of ebb/flood periods with lowest/highest Sali-
nity values, respectively. During 533 days of simulation,
salinity profiles going from well mixed to very stratified
conditions can be fo und in th is point of the Patos Lagoon
channel. Homogeneous salinity profiles following intense
ebb conditions are observed during the first 100 days
(Figure 5(b)). During this period, the combination of
dominant north quadrant winds and highest freshwater
discharge contributes to the intense ebb flows. Very
stratified periods are observed, from 250 to 450 days,
being performed by south quadrant winds and moderate
freshwater discharge. The weakly stratified periods occur
intermittently from 100 to 250 days during lowest dis-
charge periods. During this period, the influence of the
wind effects is most important controlling the exchange
process (Figures 5(a) and (b)).
The spectral content of the velocity and salinity time
series at 2 and 14 m depth were investigated using wave-
let analysis. This method allowed locating power varia-
tions within a discrete time series in a range of scales
providing the local and the global power spectrum.
Analysis of the local power spectrum (Figures 7(a) and
(b), Figures 8(a) and (b)) indicates that physical process
lower than 16 days are the principal mechanism
controlling the longitudinal component of velocity and
the advection of oceanic water through the estuarine
channel. These processes occur intermittently during the
whole study pe ri od.
Some differences are found in the local power spec-
trum of surface and bottom layers (Figures 7(a) and (b),
Figures 8(a) and (b)) with respect to the energetic levels,
occurrence of events and their influence through the
water column. The global power spectrum of salinity and
velocity (Figures 7(c) and (d), Figures 8(c) and (d))
corroborate this point of view indicating bottom
energetic levels at least 3 times greater than superficial
ones. These results suggest the dominance of remote
wind effects controlling the exchange process.
The scale-averaging wavelet power spectrum at each
position along the water depth was computed using the

W. C. MARQUES ET AL. 253
Figure 5. Time/depth profile of the observed velocity (a) and calculated time/depth profile of salinity (b) from August 17th
2005 to January 31st 2007.
Figure 6. Wind time series (a) and river discharge (b) time series from August 17th 2005 to January 31st 2007.
Figure 7. Wavelet power spectrum of velocity time series at 2 m (a) and 14 m (b) depth. The dashed line indicates the cone of
influence, below which edge effects become important and the solid contour is the 95% confidence level. Global wavelet spec-
trum of the velocity time series at 2 m (c) and 14 m (d) depth. The dashed line indicates the 95% confidence level.

W. C. MARQUES ET AL. 254
Figure 8. Wavelet power spectrum of the salinity time series at 2 m (a) and 14 m (b) depth. The dashed line indicates the cone
of influence, below which edge effects become important and the solid contour is the 95% confidence level. Global wavelet
spectrum of the salinity time series at 2 m (c) and 14 m (d) depth. The dashed line indicates the 95% confidence level.
Morlet wavelet scale-averaged over the 1 - 20 days band.
The time averaged power spectra of the velocity and
salinity time series as a function of the water depth
(Figures 9(a) and (b)) indicates high energy with 95%
confidence extending along the water depth during some
periods.
The high energy events observed in these wavelet spe-
ctra indicate the introduction of oceanic waters through
the Patos Lagoon estuarine channel via sub-superficial
layers. During some periods, principally from 250 and
500 days, the competition between flood conditions driven
by south quadrant wind effects and ebb flows associated
to the moderate freshwater discharge induces vertical
stratification. However, the most energetic events occur
during periods of most intense south quadrant winds and
low discharge conditions performing well mixed salinity
profiles.
The cross-wavelet spectrum (not shown) indicated large
covariance between the time series at all scales from 1 to
20 days. The depth averaged time series from the cross
spectral analysis (Figure 10(a)) indicates the tendency of
increasing variance to the end of period. The less ener-
getic period is observed during the first 100 days because
the dominance of ebb conditions driven by the most
intense freshwater d ischarge. Between 100 an d 250 days,
the discharge is less intense but there are few events of
south quadrant winds. The variance increases from 250
days to the end of period because of the occurrence of
very stratified and well mixed conditions. The high ener-
getic events observed (Figure 10(a)) occur during periods
of intense salt pumping through the estuarine channel
characterizing vertical well mixed conditions. The time
averaged profile of the cross spectral analysis (Figure
9(b)) suggests that introductio n of oceanic waters occurs
normally below 3 m depth.
The integrated mass transport time series (Figure 11)
suggests a pattern of salt transport through the estuarine
channel inversely related to the freshwater intensity,
corroborating the wavelet analysis. During the first 100
days (austral winter and spring), the high intensity of
freshwater discharge hinders the transport landward and
the ebb events are dominant over the flood ones, there-
fore, periods of null salt transport are observed. From
100 to 300 days (austral summer and fall), the landward
transport is most intensive reaching values of 250 kg·day–1
because of the lower freshwater discharge. The last 200
days present a similar pattern with lower salt transport
during moderate freshwater discharge periods and intense
salt transport when the freshwater discharge decreases.
The high energetic events observed through the
cross-spectrum analysis (Figure 9(a)) are associated to
longer periods of landward salt t ransportation ( Figure 11).
4. Discussion
The investigation of process controlling the estuarine-
shelf interaction is fundamental to develop correct man-
agement strategies of the coastal environment and their

W. C. MARQUES ET AL. 255
Figure 9. The time averaged power spectra of the velocity (a) and salinity (b) time series as a function of the water depth. The
thick white contour is the 95% confidence level.
Figure 10. Time series of scale average variance from cross spectral analysis over all depths (a) and scale average variance
from cross spectral analysis over all times (b). The dashed line indicates the 95% confidence level from the cross spectral
analysis.
Figure 11. Calculated time series of salt transport near the Patos Lagoon estuarine channel.

W. C. MARQUES ET AL. 256
adjacencies. The salt plays an important role in deter-
mining the estuarine characteristics serving as a natural
tracer and supporting different applications. According to
Smith [17], the energetic balance of a coastal lagoon
depends principally of the access channel configuration
controlling the exchange rates of materials, residence
time and water quality. The development of simplified
numerical models to understand the physical process
occurring in these regions is attractive, because of the
low computational cost compared with complex model-
ing systems. The high costs associated to obtaining of
direct measurements are other important difficulty in-
volving the monitoring of the estuarine-shelf process. In
this sense, this paper suggests the use of two-dimensional
numerical model to investigate the salinity behavior, in
time and through the water depth , near the Patos Lagoon
estuarine mouth. The results obtained are satisfactory
according to the calibration and validation experiments,
and considering that their application involved a very
low computational cost. This model is applied to study
salinity patterns, but, this approx imation could be used to
any conservative dissolved substance present in coastal
waters in same way.
The results of the calculated salinity along the water
depth are compatible with the velocity pattern measured
in situ. The salinity variations near the estuarine mouth
ranged from 0 to 34 and the main vertical salinity struc-
tures described by Cameron and Pritchard [22] were ob-
served during the study period. Very stratified conditions
occurred during periods of moderate continental dis-
charge (austral winter and austral spring) taking place
during several days. Hartmann and Schettini [2], and
Möller and Castaing [23] analyzing field data sets ob-
served similar conditions occurring along the whole es-
tuarine region. The introduction of coastal waters through
the estuarine channel is dominated by advection through
the sub-superficial layers. This process results from the
competition between flood currents driven by remote
wind effects and the gravitational circulation modulated
by the intensity of the freshwater discharge. These results
corroborate the prev ious studies done by Möller et al. [5],
Castelão and Möller [24], Fernandes et al. [8]. These
authors have demonstrated the combination of local and
remote wind action controlling the exchange process
between the Patos Lagoon and adjacent coast, during low
river discharge conditions, in synoptic time scales from 3
to 17 days.
The physical mechanisms responsible to maintain the
exchange process in synoptic time scales from 17th Au-
gust 2005 to 31st Januar y 2007 followed cycles from 1 to
10 days. The most energetic cycle (8 days band) indi-
cates the dominant timescale associated to the short term
exchange process coincident to the frontal system pas-
sage over the study region. The frontal systems passage
in this region is associated to the south quadrant winds,
and the resultant Ekman transport along the adjacent
continental shelf induces the propagation of barotropic
oscillations transporting oceanic waters landward. The
wind acts an important forcing mechanism of the estua-
rine circulation [25] and the far field wind plays as im-
portant mechanism controlling the water exchange with
the continental sh elf [26].
The freshwater discharge is important to perform ver-
tical stratification along the Patos Lagoon estuarine re-
gion during periods of moderate intensity, and to prevent
the introduction of coastal waters during high intensity
periods. Marques et al. [27] verified that the intensity of
the river discharge at the northern boundary of the Patos
Lagoon controls the ebb conditio ns (93% of the variance)
in the mouth of the estuary. These authors verified that
longer periods of ebb flow higher than 2000 m3·s-1 can
prevent the wind action hindering the introduction of
marine waters on the south part of the estuarine region.
The most energetic flood events near the estuarine mouth
occur during periods from low to moderate continental
discharge and higher intensity winds. These events are
characterized by longer periods of flood conditions con-
tributing to higher salt input through the estuarine chan-
nel. The salt transport through the estuarine channel oc-
curs in sub-superficial layers (below 3 m depth) being
inversely related to the intensity of the freshwater dis-
charge. In this way, it follows a seasonal pattern and the
integration of the salt transport time series during the
study period suggests a mean rate of the 105 kg·day–1
transported landward through the Patos Lagoon estuarine
channel during flood events.
5. Conclusions
The analysis of the exchange process trough the Patos
Lagoon estuarine channel from 17th August 2005 to 31st
January 2007 considering observed velocity fields and
calculated salinity indicates that:
1) The exchange-process near the estuary mouth can
be investigated using a two-dimensional approximation
with good precision level, but the principal process con-
trolling the introduction of oceanic waters, in synoptic
time scales, is the advection along that channel.
2) The introduction of oceanic waters through the es-
tuarine channel is dominated by advection through the
sub-superficial layers. This process results from the
competition between the flood currents driven by remote
wind effects (barotropic oscillations) and gravitational
circulation controlled by freshwater discharge. The baro-
tropic oscillations forced by the frontal system passage
over the adjacent coastal region follows a dominant time

W. C. MARQUES ET AL.257
scale of 8 days.
3) Freshwater discharge is important to create vertical
stratification during periods of moderate intensity, and to
hinder the introduction of coastal waters during high
intensity periods (normally from austral winter to spring).
The most energetic flood events occur during periods of
low continental d ischarge and higher intens ity winds.
4) The salt transport through the estuarine channel
follows a seasonal pattern modulated by the intensity of
freshwater discharge. The integrated transport indicates a
mean rate of the 105 kg·day–1 advected landward during
flood events.
6. Acknowledgments
The authors are grateful to the Fundação de Amparo à
Pesquisa do Estado do Rio Grande do Sul (FAPERGS)
for sponsoring this research under contract 1018144.
Further acknowledgements go to the Brazilian National
Water Agency (ANA) and the National Oceanic & At-
mospheric Administration (NOAA) for supplying the
fluvial discharge and wind data sets, respectively to ac-
complish this research.
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