ARTICLES
Dynamics of water flow and sediments in the upper Paraná River between Porto Primavera and Itaipu Dams, Brazil
Débora Pinto Martins 1, Jean-Paul Bravard 2 and José Cândido Stevaux 3
1 Université Lumière Lyon 2, France and Universidade Estadual de Maringá/GEMA, Brazil. E-mail: deby_martins@yahoo.com.br
2 Université Lumière Lyon 2, France. E-mail: jean-paul.bravard@orange.fr
3 Universidade Estadual de Maringá/GEMA and UNESP, Rio Claro, SP, Brazil. E-mail: jcstevaux@uem.br
Received: April 25, 2009 - Accepted: January 28, 2010.
Abstract: The following paper aims to quantify the bedload transport in the Paraná river in the Porto São José cross section (22°45'52"S; 53°10'34"W), between Porto Primavera and Itaipu dams, Brazil. In the used method, the bedload transport is estimated from the height and the displacement of the dunes along a longitudinal profile. The results were compared with those obtained from classical bedload transport equations. In the Porto São José cross section, the estimated average bedload transport applying the Dune Displacement Method (DDM) was 3,157 t d-1, which corresponds to an average annual bedload transport of 1,152,325 t yr-1. Applying the Van Rijn equation the average bedload transport was calculated in 2,830 t d-1 (1,032,950 t yr-1), while using the Engelund-Fredsøe equation the average bedload transport found was 3,135 t d-1 (1,144,378 t yr-1). The obtained values using different methods presented some coherence each other, which means that these results can be used as a starting point to establish bedload transport estimations in the Upper Paraná river.
Keywords: Bedload transport; Dunes; Paraná River; Large rivers.
Resumo: O presente trabalho tem por objetivo quantificar o transporte sólido de fundo do rio Paraná, na seção de Porto São José (22°45'52"S; 53°10'34"W), entre as barragens de Porto Primavera e Itaipu, Brasil. No método utilizado o transporte de fundo é estimado a partir da altura e do deslocamento das formas de leito ao longo de um perfil longitudinal. Os resultados obtidos foram comparados com os resultados obtidos à partir de algumas equações clássicas de calculo de transporte de fundo. Na seção de Porto São José, através do método das dunas, o transporte médio de fundo foi estimado em 3.157 t d-1, o que corresponde a uma carga solida anual de aproximadamente 1.152.325 t/ano-1. Quanto aos valores obtidos através da aplicação das formulas pré-selecionadas, à partir do método de Van Rijn chegou-se um transporte médio de 2.830 t d-1 (1.032.950 t ano-1) e com o método de Engelund-Fredsøe obteve-se um transporte médio de 3.135 t d-1 (1.144.378 t ano-1). Os valores obtidos a partir das diferentes metodologias apresentaram uma coerência entre si, o que pode ser o ponto de partida para estabelecer uma metodologia adequada às condições naturais de fluxo de grandes rios, como é o caso do Paraná.
Palavras chave: Transporte de fundo; Dunas; Rio Paraná; Grandes rios.
INTRODUCTION
The fluvial transport is one of the driving factors
of the fluvial systems and it reflects the erosive
characteristics of the basin through the input of
sediments and the hydrodynamics processes of
erosion/deposition in the channel. The erosion
and sediment transport also are responsible for
the reworking of the channel itself and of its
morphology.
The amount of variables involved in the solid
transport mechanics, as well the complexity of the
interactions among the physical processes, makes
it difficult to establish a fully satisfactory criteria to
determine the solid transport, thus there is not an
acclaimed universal method. Throughout the years,
many researchers were trying to establish some
relations to allow determining the solid transport
with precision (Duboys,1879; Straub, 1935; Einstein,
1942, 1950; Kalinsk, 1947; Schoklitsch, 1962;
Shields, 1936; Meyer-Peter and Müller, 1948; Levi,
1948; Sato et al., 1958; Yalin, 1972; Pernecker and
Vollmer, 1965; Helley and Smith, 1971; Klingeman
and Milhous, 1971; Gregory and Walling, 1985,
Gomez, 1991; Ryan and Troendle, 1997; Ryan and
Porth, 1999). From the methods available in the
literature, there are some purely empirical and others
theoretic complex models.
Most of the methods in the literature were
elaborated from data of flume experiments, where the
researcher has the control of almost all the variables
involved in the transport of the solid material. In the
case of natural channels this condition is impossible.
Besides, the scarcity of data (historical series) and
the relatively short period for field observation
are limiting factors for equation calibrations and
establishment of a universal model.
Due to the inflow and outflow of water and
sediments, in an alluvial channel the sediment
movement changes within time and space, shaping
the channel morphology. In this context, the
understanding of the stream hydro-sedimentological
dynamics demands some knowledge of a wide range
of interactions among water flow, sediment transport
and bed-forms. This paper aims to offer a better
understanding of the bedload dynamics in the upper
Paraná River applying measurements based on dune
displacement (Dune Displacement Method - DDM).
This method determines sediment transport based
on the size of the bed-forms and its velocity of linear displacement along longitudinal profiles (Stuckrath,
1969).
STUDY AREA
The study area is a reach of Upper Paraná River, near the town of Porto São José, between Porto Primavera and Itaipu dams, at the border between the states of Paraná and Mato Grosso do Sul, Brazil (Fig. 1). The reach downstream of the Porto Primavera Dam is defined as anastomosing (Stevaux and Souza, 2004) or anabranching (Latrubesse, 2008) with channels divided by long and stable vegetated islands and mobile sand bars. Structural influence generates nodal sections between multichannel reaches. These sections generally present a single channel with a thalweg asymmetrically shifted to the left bank (Stevaux, 1994; Fortes et al., 2005).
Figure 1. The study area.
At the particular studied section of Porto São José
the Paraná River presents a unique channel (node
point) with a width of 1,260 m and maximum depth
of 10.5 m under normal flow conditions. In this
reach the thalweg is displaced to the left side of the
channels, with islands upstream and downstream of
this node point (Fig. 1). On the left bank of the section
the Porto São José gauging station is located. This
gauge station is operating since 1964 and has been surveyed by the energy company CESP. The mean
annual discharge for the 1964-2006 period is 8,780
m³ s-1 and the extreme records in this section are:
minimum daily discharge of 2,551 m³ s-1, observed
in September 1969, and maximum daily discharge of
34,912 m³ s-1, observed in February 1983.
Even though it is the third largest river in
South America, the studies concerning the
hydrosedimentological dynamics of the Paraná River
are scarce. There are some studies of this nature
in the middle course, in Argentina, mainly in the
reaches close to the cities of Corrientes and Santa Fé.
In the Corrientes reach, Bonetto and Orfeo (1984),
Orfeo (1995) and Orfeo and Patiño (1998) worked
mainly with the suspended load. In the Santa Fé
region, Stuckrath (1969), Lima et al. (1990), Trento
et al. (1990), Amsler and Gaudin (1994), Amsler and
Schreider (1999) worked with the quantification
of the bedload transport. About the Upper Paraná
River in Brazil, during the years of 1986 and 1987,
the Itaipu Binacional Company, responsible for the
Itaipu Dam, developed some studies devoted to
sediment transport in the reach upstream the dam
lake. In these studies was observed that bedload
discharge was inferred indirectly, assuming that it
could represent 20% of the suspended load.
Presently, the hydro-sedimentological dynamics
of the Paraná River is under the control of a series of
dams, which transformed the main channel of the
Paraná River into a sequence of lakes. According to
Itaipu Binacional (1990) the correlations between
the suspended solid concentration and the discharge
in Porto São José section became precarious, because
both the discharge and hydro-transported solids are
very controlled by the upstream dams. In this context,
Martins (2004) and Martins and Stevaux (2005),
based upon the first studies made in the Argentine
reach of the Paraná River (Amsler and Gaudin, 1984;
Amsler and Schreider, 1999; Amsler and Prendes,
2000), determined the bedload transport of the last natural-like reach of the Upper Paraná River in
Brazilian territory. In this paper we present results
on the Paraná River downstream Porto Primavera
Dam, which was constructed from 1989 to 1998
generating one of the largest dam lakes of the world
that spread on 2,250 km2.
METHODOLOGY
The DDM method has been used for estimating the bedload in mobile bed channel, assuming a permanent and "almost" uniform flow in the study reach of an alluvial river (Hubbell, 1964; Simons et al., 1965; Fredsøe, 1981; Engelund and Fredsøe, 1982). In this method, the bedload transport is given by the size of the dunes and by the velocity of displacement of those dunes along a longitudinal profile through the channel (Fig. 2). The quantification of the transported bedload is made using the Stuckrath's equation (1969), as follows:
Cf = (1-p)H k ud (1)
where Cf is the transported bedload; p is the porosity of the sand, H is the mean dunes height, ud is the velocity of displacement of the dunes and k is a coefficient related to the shape of the dunes. The value of porosity depends on the bedload texture, used in the study case (fine to medium sand) the value of 0.6, as it has been suggested by Amsler and Prendes (2000), Stevaux and Takeda (2002), Orfeo and Stevaux (2002). Considering that the longitudinal section of the natural dunes is not a perfect triangle, a coefficient of shape (k) is used in order to minimize the errors issued from this variable. According to Stukrath (1969) and Lima et al. (1990), this coefficient generally varies between 0.50 and 0.66. In this paper we adopted k = 0.67, according to the most recent study carried out by Amsler and Prendes (2000).
Figure 2. Typical dune from an alluvial river.
(d: dune displacement after a time interval
(?t); H: dune height; λ: dune wavelength).
Modified from Amsler and Prendes (2000).
The application of this method considers that the bedforms are in equilibrium, which means that the set of dunes must keep its shape while it displaces downstream. This condition, observed by Lima et al. (1990), Stevaux. (1994), Martins (2004), Martins and Stevaux (2005). Cheng and Shen (1975), and Strasser (2008), showed that, even if the shape of an individual dune changes during its displacement, the set of dunes tends to present a morphological constancy. In this study, the morphology of the bed and the morphological constancy of the shapes were determined from bathymetric charts and from threedimensional bathymetric models prepared along this research.
Data acquisition
Dune velocity is obtained through successive bathymetric surveys. As the first step, it is necessary to determine the study period according to the hydrological regime (high and low water level), and to establish the time interval between the two successive bathymetric surveys. This interval depends of the bedform displacement velocity and the potential of dune shape preservation. On this study, field work was performed during 2005, 2006 (medium water level) and 2007 (in flood stage). For each field season two bathymetric surveys were made at an interval of 10 to 15 days as recommended by Stevaux and Takeda (2002), Crispim (2001), Martins (2004) and Martins and Stevaux (2005). A set of 2 km-long longitudinal profiles, 100 m equidistant from each other was obtained (Fig. 3).
Figure 3. Influence width (Lp1 to Lp8) of each longitudinal profile (P1 to P8) in the Paraná River channel cross-section at Porto São Jose.
Bathymetric data was acquired by a Furuno GP-
1650F echo-sounder/GPS system, and recorded in
a portable PC, through software Fugawi3. Data was
exported and treated with MS Excel®, Surfer® 8.0
and AutoCAD® 2000 software.
Bathymetrical data was completed by a zigzag
track over the study reach, in order to produce a
large dataset for 3-D bathymetric models elaboration.
Instantaneous discharge, flow velocity and direction
data were collected by an ADCP - Acoustic Doppler
Current Profiler. Channel bottom sediment was
sampled for textural analyses.
Data Treatment
The estimation of the bedload transport begins with an individual identification of each dune along each longitudinal profile. The dune's height (h) is obtained by the mean height of one specific dune in both measurements (h1 and h2). The displacement (d) is done by the difference of position of the dunes crest in the two successive measurements. Bedload is determined individually for each dune, and then by the mean for the entire profile as the equation:
CfPi= Σ Cfdi/n (2)
where CfPi is the estimated bedload for the entire profile Pi, Cfdi is the bedload estimated for each dune and n is the number of dunes considered in the estimative. The total bedload for the entire section (Cf Total) is obtained by the sum of CfPi for each longitudinal profile multiplied by its width of influence (Lpi) (Fig. 3):
Cf Total = Σ(CfPi * LPi) (3)
RESULTS
Bedload transport
The bathymetric profiles show the dunes as the predominant bedform in the Paraná River channel at Porto São José (Fig. 4). Bedforms are regular in shape and maintain their morphology while moving downstream. At medium discharge stage, dune height varies from some centimetres to 2.5 m (Fig. 4). During the flood season, it is common to find megadunes up to 5 m high with superimposed dunes (Fig. 5).
Figure 4. Longitudinal bathymetric profile of the Paraná River at Porto São José section under medium flow discharge stage.
Figure 5. Longitudinal bathymetric profile of the Paraná River at Porto São José during flood discharge stage.
During the first fieldwork (July 2005), dunes presented an average height of 1.5 m and a linear
displacement velocity of around 1.44 m d-1. On
that occasion, flow velocity varied among 0.22 m
s-1 and 1.18 m s-1 (mean of 0.80 m s-1). The bedload
transport was estimated in 0.96 m3 d-1 m-1 (0.024 kg
s-1 m-1), which represents a total volume of 1,062.52
m3 d-1, or 2,815.67 t d-1. During that period, the
average discharge of the Paraná River at Porto São
José gauging station was 9,769 m3 s-1.
During the second fieldwork (May 2006), the
dunes presented an average height of 1.28 m and an
average displacement velocity of 1.72 m d-1 at a flow
velocity varying between 0.5 m s-1 and 1.30 m s-1
(medium flow velocity of 0.80 m s-1). The estimated
bedload for that period was 0.98 m3 d-1 m-1 (0.030
kg s-1 m-1), which correspond to a total volume of
1,219.28 m3 d-1, or 3,258 t d-1. The average discharge
on that period was 7,953 m3 s-1.
During the third fieldwork (January and February
2007), because of the high magnitude of this event
(2.5 times the mean discharge) and the bedform
morphology, the solid transport was estimated
through the velocity of displacement of the megadunes.
They presented an average displacement of
6.30 m d-1, to a flow velocity varying between 0.5
m s-1 to 2.0 m s-1 (medium flow velocity of 1.5 m
s-1). Bedload transport was 3.3 m² m-1 day-1 (0.11 kg
m-1 s-1), which corresponds to 3,757 m3 d-1 or 9,956
t d-1. During that period the Paraná River presented
a discharge of 18,136 m3 s-1, 2.5 times the average
discharge, and the flow velocity two times higher
than that at mean water discharge. Bedload transport was approximately three times the transported
bedload under average flow conditions.
Some control measures were taken in the
section of Porto Camargo, located about 100 km
downstream Porto São José section (Fig. 1). During
the first fieldwork at Porto Camargo (July 2005) the
dunes presented an average height of 1.35 m and a
displacement of 1.65 m d-1, to a flow velocity varying
between 0.31 m s-1 to 1.5 m s-1. The volue of bedload
transported was 647.32 m3 d-1, which represents a
total weight of 1,715.4 t d-1. In the second fieldwork
(May 2006), the dunes presented an average height
of 1.42 m and a displacement velocity close to 1.80
m d-1, under a flow velocity that ranged from 0.5 m
s-1 to 2.0 m s-1. The estimated transport was 712 m3
d-1, which means 1,887.86 ton d-1.
During the third fieldwork (flood season of
January and February 2007), the dunes at Porto
Camargo presented an average height of 1.56 m and
an average velocity of displacement of 3.32 m d-1,
under a flow velocity of 2.0 m s-1. Bedload transport
was 1,925 m3 d-1 or 5,101.36 t d-1.
A comparative analysis of the data obtained in the two sections indicates that the bedload transport
at Porto São José was 1.68 times higher than that at
Porto Camargo. During the flood season the value
at Porto São José was 1.95 higher than at Porto
Camargo.
At Porto São José, three other surveys were
performed by Martins (2004) and Martins and
Stevaux (2005) during 2002 and 2003. In those
surveys, bedload was estimated in 2,940 t d-1
(November/December 2002), 2,710 t d-1 (June/July
2003), and 2,812 t d-1 (November/December 2003).
In all those surveys, field work has been done under
average discharge conditions.
Comparison with bedload transport equations
Values of bedload transport estimated through the dune DDM were compared with those obtained by the application of some classical bedload transport equations chosen from the specific literature. The equations of Engelund-Fredsøe, Van Rijn, and Meyer-Peter & Müller were selected because they have already been used in the middle Paraná, in Argentina (Amsler and Prendes, 2000). The values estimated by the different equations presented some coherence among the values estimated using the DDM (Table 1). This coherence is more expressive with the results estimated using the equations of Engelund-Fredsøe and Van Rijn, while the equation of Meyer-Peter e Müller has resulted in lower values of bedload transport when compared with the results obtained with the method of dunes displacement.
Table 1. Average bedload transport in the Paraná River at Porto São José estimated from different methods.
CONCLUSION
The estimation of bedload transport in the upper
Paraná River has been a need in terms of hydrogeomorphologic,
ecologic and engineering studies.
The effect of dams on solid discharge was rapid an
intensive (Stevaux et al., 2009), but the adjustment of
the alluvial channel in response to these changes are
totally unknown. We provided the first systematic
analysis of bedload transport downstream the huge
Porto Primavera dam. In the Porto São José section,
the average bedload transport was estimated in 3,157
t d-1, which corresponds to 1,152,235 t yr-1. The
bedload transport estimated by using the method
of the displacement of the dunes is coherent with
the results obtained when applying the Engelund-
Fredsøe and Van Rijn equations.
The advantage of using the method of dune
displacement is given by its relative feasibility for
field measurements (through bathymetric surveys)
mainly in large alluvial channels. These are the first
systematic results obtained on bedload transport in
the Paraná River in Brazilian territory. Our results
can be considered a starting point to elaborate a new
method to estimate the bedload transport for the
Paraná River or even to create a rating curve for the
upper course.
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