Journal of South American Earth Sciences xxx (2012) 1e10
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Journal of South American Earth Sciences
journal homepage: www.elsevier.com/locate/jsames
Hydrodynamic modelling of the Amazon River: Factors of uncertainty
Eduardo Chávarri a, *, Alain Crave b, Marie-Paule Bonnet c, Abel Mejía a, Joecila Santos Da Silva d,
Jean Loup Guyot c
a
Universidad Nacional Agraria La Molina, Av. La Universidad s/n, La Molina, Apartado 12-056, Lima 12, Peru
CNRS, Université Rennes 1, Géosciences Rennes, Campus de Beaulieu, 35042 Rennes cédex, France
c
IRD, CP 7091 Lago Sul, 71619-970 Brasilia DF, Brazil
d
CESTU, Universidade do Estado do Amazonas, UEA. Av. Manaus, Amazonas, CEP 69058807, Brazil
b
a r t i c l e i n f o
a b s t r a c t
Article history:
Received 15 December 2011
Accepted 24 October 2012
Hydrodynamic modelling of Amazonian rivers is still a difficult task. Access difficulties reduce the
possibilities to acquire sufficient good data for the model calibration and validation. Current satellite
radar technology allows measuring the altitude of water levels throughout the Amazon basin. In this
study, we explore the potential usefulness of these data for hydrodynamic modelling of the Amazon and
Napo Rivers in Peru. Simulations with a 1-D hydrodynamic model show that radar altimetry can
constrain properly the calibration and the validation of the model if the river width is larger than
2500 m. However, sensitivity test of the model show that information about geometry of the river
channel and about the water velocity are more relevant for hydrodynamic modelling. These two types of
data that are still not easily available in the Amazon context.
Ó 2012 Elsevier Ltd. All rights reserved.
Keywords:
Hydrodynamic modelling
Amazon River
Radar altimetry
Model sensitivity
1. Introduction
The Amazon River is the largest in the world with a basin area of
7.0 106 km2 and an average flow at its mouth to 206,000 m3/s
(Callède et al., 2010). Crossing eight countries, this huge river is the
main channel of communication from the Andes to the Atlantic.
Therefore, understanding and modelling the hydrodynamic of the
specific Amazon context is of great interest for environment,
economic and social processes. Since the end of the 1980s, extreme
hydrological events have been increasing in the River Amazon
(Espinoza et al., 2009, 2011). These extreme events caused inundations, as in 1999, 2006 and 2009, or very low water stages, as in
1998, 2005 and 2010, which are harmful to people living nearby the
watercourse and damaging for agriculture and ecosystems (e.g.
Saleska et al., 2007; Phillips et al., 2009; Asner and Alencar, 2010;
Lewis et al., 2011; Xu et al., 2011).The impacts that may cause the
increased frequency of extreme hydrological events in the Amazon
put at risk their vast amount of natural resources and a population
of more than 38 million people. Predicting the impact of climate on
* Corresponding author.
E-mail
addresses:
[email protected],
[email protected]
(E. Chávarri), [email protected] (A. Crave), [email protected]
(M.-P. Bonnet), [email protected] (J. Santos Da Silva), [email protected]
(J.L. Guyot).
water level and discharge variability on Amazonian main rivers is,
therefore, a crucial task.
Several hydraulic models are focused on water level and
streamflow prediction on Amazonian context. Here we present the
most recent works with their most important results. A distributed
Large Basin Simulation Model, called MGB-IPH (an acronym from
the Portuguese for Large Basins Model and Institute of Hydraulic
Research), was developed by Collischonn (2001). The MGB-IPH was
applied for some Amazonian rivers, the Madeira (Ribeiro et al.,
2005), the Tapajos, and the Negro river (Collischonn et al., 2008).
Spatial altimetry data is being used to complement the validation of
the simulation (Getirana et al., 2010), where satellite derived rainfall
information is being used to run the model. But divergences
between hydrographs were noted at refined time scale. Also the
methodology requires depth and flow relations at virtual stations,
which can limit its application. Paiva et al., 2011, present a largescale hydrologic model with a full one-dimensional hydrodynamic
module to calculate streamflow propagation on a complex river
network, using limited data for river geometry and floodplain
characterization. Trigg et al., 2009, proposed that to conduct
hydraulic modelling of the main channel of the Amazon River, the
diffusive terms is sufficient in the hydrodynamic equations. Beighley
et al., 2009, presents the hydrological and hydraulic simulation
of the Amazon Basin using a runoff model to surface and subsurface
runoff, based on the application of kinematic and diffusive
methods. Coe et al., 2007, proposes improvements to the model
0895-9811/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.jsames.2012.10.010
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
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E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
THMB (Terrestrial Hydrology model with Biogeochemistry) in
relation to the velocity equation to include the sinuosity of the river
in the calculation of the forces of resistance and incorporates
a roughness empirical equation of data from 30,000 measurements
of the river morphology to determine the flood volume in many
places in the basin and ultimately represents the morphology of the
floodplain with a resolution of 1 km from SRTM (Shuttle Radar
Topography Mission).
All these previous works point out the need of valid high spatial
resolution data on channel geometry to improve the prediction of
the water level of the river or the flood extension. In terms of the
river streamflow, the propagation modelling are related to the
input data uncertainty, e.g. DEM precision, vegetation and cross
section geometry provided by geomorphologic relations (Paiva
et al., 2011). Nonetheless, in general, there is limited information
on Amazonian river geometry, streamflow and water depths which
create uncertainty in the modelling of the flow profile. Often times,
attaining the necessary information for complex models involves
large amounts of monetary expenses and human effort which
makes it impractical for the wide and inaccessible Amazon basin.
On the other hand, radar altimetry is a good alternative to get
data on Amazonian channel geometry and water level. However,
we must take into account some considerations as explained by
Santos da Silva et al. (2010), the water levels measured by radar
altimetry and in situ gauges are fundamentally different. Radar
altimetry measures a weighted mean of all reflecting bodies over
a surface several square kilometres in size while gauges pick up
river stages at specific points. Comparison at crossovers and within
situ gauges show that the quality of the time series can be highly
variable, from 12 cm in the best cases and 40 cm in most cases to
several metres in the worse cases in Amazon basin.
Negrel et al. (2011), suggest the possibility of calculating the
streamflow based exclusively on river surface variables accessible
through earth observation techniques, namely river width, level,
surface slope and surface velocity. The main hypothesis presented
in the former study considered steady flow and rectangular shaped
cross-sections.
In the present study, we examine more specifically the uncertainty of streamflow modelling induced by the lack of information
on channel cross section geometry and the accuracy of radar
altimetry. The main objective is to fix which radar altimetry accuracy and channel geometry data are required to improve streamflow modelling of Amazonian rivers of different sizes. To test if
current radar altimetric data are relevant in Amazonian context,
simulation of water level on Amazon and Napo Rivers are compared
with in-situ measurement of discharge and water level.
2.1. Hydrodynamic model description
Model inputs are water depth fluctuation at the upstream
boundary, longitudinal slope, Manning coefficient, riverbed
geometry of several cross sections of the river and the sequence of
islands. The minimum number of cross sections is defined by the
longitudinal sequence of diffluent and convergent channels forming one or several islands on the stream path. One island is defined
for cross section: one before the upstream divergent flow, two for
each branch of the river on each side of the island and one after the
downstream convergence. Channel reaches without islands are
defined with one cross section in the middle of the reach. Note that
Amazonian rivers are often anabranching meandering channels
(Latrubesse, 2008), with a dense longitudinal sequence of islands.
Therefore, following the former rule for channel description
implies a relatively complete database on river bathymetry. Usually,
such database is not available for Amazonian rivers. To overpass the
lack of information on river bathymetry, we characterize the
geometry of each cross section with a surrogate parameter a to
simulate the relation channel width versus water depth (see x 2.2).
Note that this model does not simulate flood. All simulated
water level stay below the upper limit of bankfull level. Manning
roughness coefficient and longitudinal slope are supposed to be
constant over time. Due to the high water turbidity value, aquatic
vegetation cannot grow on the riverbed and the roughness of the
riverbed does not change. We suppose that erosion and sedimentation processes on the riverbed do not change significantly the
longitudinal slope for the time scale of several years.
The output variables of the model are hydrographs of y, Q, w and
v in any section defined at each cross section.
Simulations are done with a classical 1-D-hydrodynamic model.
This model finds simultaneous solutions of the continuity and
momentum equations (Equations (1) and (2)) proposed by Barre de
Saint-Venant (1871) and in the work of Massau, who in 1889 published some early attempts to solve those equations. The primary
hypothesis of this theory is to consider constant density, hydrostatic
pressures, mild slopes and a sediment velocity that is equal to the
flow mean velocity.
vy 1 vQ
q
þ
¼
vt w vx
wvx
(1)
where q is lateral streamflow [L3T1], x is the length between two
cross sections [L], and t is the time [T].
f
vQ
v
Q2
vy
b
þf
þ gA þ gASf ¼ bqvL
vt
vx
vx
A
(2)
2. Methodology
This study is divided in two steps. First, we use 1-D hydrodynamic model to quantified the sensitivity of the variables: water
depth (y), longitudinal streamflow (Q), bankfull width (w) and
velocity (v) according to the variability of input parameters: the
cross section geometry, Manning roughness coefficient (n) and
longitudinal slope of the river (s). This shows how the hydrodynamic model response is related to the level of uncertainty of input
parameters and how they rank in terms of model sensitivity. In
other words, we evaluate theoretical impacts of uncertainties on
natural data on simulation of y, v and Q. Second, we compare
uncertainties of y simulation to radar altimetry accuracy applying
the same 1-D hydrodynamic model to the Amazon and Napo Rivers.
The streamflow model is an original 1-D hydrodynamic model to
simulate unsteady streamflow in anabranching river form such as
the Amazon River and Napo River. In the following text, we present
the main equations and hypothesis relative to this numerical model.
where Sf is the energy line slope (friction slope), g is the acceleration due to gravity [LT2], A is cross-sectional area of the streamflow [L2], vL is the velocity of the lateral streamflow, that is, in the
same direction as the principal streamflow of the river, f is the
Local partial inertial factor (Fread et al., 1986), b is the Boussinesq
coefficient.
Equations (1) and (2) are solved under the Preissmann numerical scheme. It offers the advantage that a variable spatial grid may
be used; steep wave fronts may be properly simulated by varying
the weighting coefficient of the time interval q and weighting
coefficient of the space interval f, and the scheme yields an exact
solution of the linearized form of the governing equation for
a particular value of Dx and Dt.
The model has the ability to simulate sections with islands,
creating a new hypothesis in the study. To solve this problem, there
exist diverse alternatives such as assuming that the water depths
around the islands are the same. However, in this study we considered
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
the hydrodynamic equations for internal boundary conditions
applied to sections with islands as described in Equation (1) and
energy conservation equations (Equations (3) and (4)) to solve the
convergence and divergence problems.
According to Cunge et al. (1980), for nodes i, i1 and i2, there are:
yi1 þ
1
Q 2
1
Q 2
fi1 i1 ¼ yi þ
fi i
2g
2g
Ai1
Ai
(3)
yi2 þ
1
Q 2
1
Q 2
fi2 i2 ¼ yi þ
fi i
2g
2g
Ai2
Ai
(4)
where: Qi1 and Qi2: streamflows in both side of the island, yi1 and
yi2: water depth in both side of the island, Qi: streamflow in the
confluence. yi: water depth in the confluence.
The spatial and temporal resolution of the model takes into
account the Courant condition. For one-dimensional equations, the
Courant number, or also known as the Courant, Friedrichs and Lewy
(CFL) number, is defined as Abbott (1979).
C ¼
ju cjDt
1
Dx
(5)
where: C: Courant number, u: Medium flow velocity (LT1), c: Flow
celerity (LT1), Dx/Dt: the numeric Celerity (LT1).
According to Lewy and Friedricks, mentioned by Ponce (2002),
the Courant number related the physical celerity and numerical
celerity.
C ¼
c
Dx
Dt
3
(6)
The last equation (Courant number) is very important for
the application of numeric solutions since it allows us to calculate
Dx/Dt and avoid instability in the numerical model.
For the proposed hydrodynamic model it was found that the
Courant number must be equal or greater than 0.23 (C z 0.23) to
assure stability. Consequently, once the spatial resolution (Dx) is
defined according to the stretch singularities and knowing the
celerity, the temporal resolution (Dt) is determined.
According to the mathematical description of the model, in
addition to input parameters n, s and a, there are five more
parameters (C, b, f, q, 4). All the former parameters are calibrated
on a well-documented in-situ streamflow context (see x2.4).
2.2. Riverbed geometry determination
One of the biggest input uncertainties of the model is the lack of
information on bathymetry along the Amazonian rivers. Equations
(1) and (2) are closely related to water depth and the width
riverbed. In order to simulate synthetic cross section geometry, we
suppose that the variability of the depth is linearly related to the
variability of the cross section width following the Equation (7).
a ¼
Dw
Dy
(7)
Fig. 1. (a) Amazon basin, (b) the simulated stretch between Nuevo Rocafuerte station and Tempestad island e Napo river, (c) The simulated stretch between the Tamshiyacu and
Tabatinga stations e Amazonas River. Figures include radar altimetry paths and nodes simulation.
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
The question of cross section geometry definition is reduced to
the definition of the non-dimensional parameter a. Currently, no
study has demonstrated the validity of Equation (7) for any geometry type of natural channel cross section. However, analysing the
database of Hybam project on more than 100 Amazonian river cross
sections shows that Equation (7) is empirical significant (see
Appendix A, Fig. A.1). Because a is a local variable with a wide range
of values, this is one of the main sources of uncertainty in the results.
a
6
4
4
3
2.3. Parameterization and quantification of the sensitivity test of
the hydrodynamic model
2
1
0
b
River Napo
(Bellavista station)
High water period
Low water period
Average streamflow (m3/s)
Average velocity (m/s)
Average width (m)
Longitudinal slope (m/km)
Average water depth (m)
Contribution area (km2)
MarcheMay
AugusteOctober
34,815
1.69
1213
0.08e0.35
23.5
726,403
MayeJuly
JanuaryeFebruary
5838
1.18
1312
0.1e1.8
12.77
100,518
800
1000
1200
800
1000
1200
90
Elevation (a.m.s.l)
86
84
82
80
200
400
600
Days
Fig. 2. Calibration results: For (a) Streamflow and (b) Water elevation. We presented
the simulated and recorded hydrographs in Tabatinga station for the first 1100 days (01
September 2002 to 04 September 2005).
a
6
x 10
4
5
4
3
2
1
1000
1200
1400
1600
1800
2000
2200
Days
90
88
Elevation (a.m.s.l)
River Amazon
(Tamshiyacu station)
600
Days
76
0
(8)
General characteristic
400
78
b
Table 1
General characteristics of Amazon and Napo Rivers in Peru (Hybam project
database).
200
88
Flow (m3/s)
The sensitivity of the model is analysed by looking at the variability of y, Q, w and v at each section of the river, in response to the
variability of a, n and s.
According to the Hybam database, a varies in the range between
20 and 300 following a normal distribution with an average of 106
(Appendix A, Fig A.1). One value of a is defined for each section used
to define the channel geometry for each simulation. Thus, there are
many values of a and sections used to describe the channel. The set
of a is chosen within a normal distribution by random drawing.
Therefore, there are two parameters to define the geometry of the
channel, the average value and the standard deviations s of the
normal distribution of a. The sensitivity of the model to a is estimated doing averages on output variable variability on 10 simulations applying the same normal distribution of a values.
Manning roughness coefficient values are chosen in the range for
natural rivers, meaning between 0.025 s/m1/3 and 0.045 s/m1/3.
Values of longitudinal slope are chosen in the range of slope values
observed for the Amazon and Napo Rivers (Bourrel et al., 2009),
meaning between 0.08 m/km and 0.35 m/km for the Amazon plain
and between 0.1 m/km and 1.8 m/km for the Andeans foothills.
In order to have a baseline of simulation to quantify the sensitivity of the model, a reference theoretical case is chosen which
corresponds to the Napo River dataset information. The geometry of
this theoretical channel is fixed with a a set values by random
drawing within a normal distribution with an average of 106 and a s
of 52. These two values correspond to the analysis performed on the
dataset of the Napo River (Appendix A). Manning coefficient and
longitudinal slope of this theoretical case are fixed to 0.035 s/m1/3
and 0.07 m/km respectively.
To quantify the sensitivity of the 1-D hydrodynamic model to
the input parameters, we calculate differences between the daily
evolutions of each output variables corresponding to a specific
input parameter set of values and the theoretical reference case at
the last downstream station. The criterion of sensitivity is obtained
by percentage of variability using Equation (8).
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
PM PD 1
1 Voutput Vreference
100
%Variability ¼ P P M
D
1
1 Voutput Vreference
x 10
5
Flow (m3/s)
4
86
84
82
80
78
76
1000
1200
1400
1600
1800
2000
2200
Days
Fig. 3. Validation results: For (a) Streamflow and (b) Water elevation. We presented
the simulated and recorded hydrographs in Tabatinga station for the last 1100 days
(05 September 2005 to 28 October 2008).
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
5
Table 2
General characteristics of radar altimetry information.
River
Path (ENVISAT Goid
EGM, 2008)
Latitude
( ) WGS84
Longitude
( ) WGS84
Time period
Distance from upstream
boundary (km)
Width
approx. (m.)
Observation
Napo
Amazon
966
164
837
794
74.86
70.4
71.6
72.5
1.29
3.79
3.77
3.52
29
06
24
01
77.0
321.2
163.9
31.5
580.0/618.0
5800.0
3260.0
490.0/2110.0
Island
Reach
Reach
Island
sept 2002 to 17 oct 2010
oct 2002 to 18 sept 2010
sept 2002 to 12 oct 2010
dec 2002 to 10 oct 2010
The purpose of performing simulations on Amazon and Napo
Rivers is to consider their differences in the hydrodynamic aspects.
The River Napo is mainly located in the foothills of the Amazon
basin and the stretch of the River Amazon of this study is located in
the plain (Fig. 1a), both with different flow regimes and longitudinal slope (Table 1).
The simulation of the River Amazon in the Peruvian sector was
conducted from the confluence of the Napo and the River Amazon at
the Francisco de Orellana (FOR) station to the Tabatinga (TAB) station
in Brazil. Hydrometric and bathymetry information is only available
since 2002 for the TAB and Tamshiyacu (TAM) stations due to the
lack of data at FOR. However, cross section geometry at TAM is a good
proxy of the cross section geometry at FOR and by adding streamflows of the Bellavista station (BEL) at the outlet of Napo and TAM.
The Napo River hydrodynamic simulation was carried out in the
section between the Nuevo Rocafuerte (ROC) station and the
Tempestad (TEMP) location. The ROC is located near the border
between Peru and Ecuador and is located approximately 77 km
upstream of the TEMP where there is an island with radar altimetry
data on both sides of it. Streamflow and water level information is
available since 2002 at ROC. At TEMP only radar altimetry information is available.
For both rivers, a sequence of cross sections (nodes) define the
spatial resolution of the river stretch used for the simulations
(Fig. 1b and c). Note that two parallel nodes define an island’s
configuration. Tables B.1 and C.1 of Appendix B and C respectively,
summarize the characteristics of each node for the Amazon and
Napo Rivers respectively. For both river stretches, the upstream and
downstream limits correspond to altimetry radar tracks on the field.
Longitudinal slopes of Amazon and Napo are supposed to be
significantly constant and equal to 0.07 m/km and 0.17 m/km,
respectively. Manning coefficient is supposed to be constant for
both rivers with a value of 0.035 s/m1/3. a set values are defined by
random drawing within a normal distribution with an average of
106 and a a of 52.
To calibrate the internal parameters which are supposed to be
constant whatever the Amazon or Napo configuration, the model is
applied on the Amazon River between TAM and TAB using half of
the available dataset of Q and y (Fig. 2a and b). The other half of the
dataset is used for the validation (Fig. 3a and b). The goodness of fit
methodologies is evaluated by the Nash and Sutcliffe efficiency (E)
and Root Mean Squared Error (RMSE), these being indicators of
Fig. 4. The sensitivity of model variables according to the Riverbed geometry
sensitivity. (a) For a ¼ 106 52 and (b) For a ¼ 212 52.
Fig. 5. The sensitivity of model variables according to: (a) the Manning roughness
coefficient and (b) Longitudinal slope.
where M: Total cases, D: Total days, Voutput: Model variable in the
downstream, Vreference: Model variable for a ¼ 106, n ¼ 0.035 s/m1/
3
, s ¼ 0.07 m/km.
2.4. Application of the model to Amazon and Napo Rivers
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
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E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
model error. The Nash and Sutcliffe efficiency (E) is defined
following Equation (9) (Krause et al., 2005):
PN
E ¼ 1
Pi Þ2
2
Oi O
1 ðOi
PN 1
(9)
where Oi: Observed value, Pi: Predicted value, O: Mean observed
value, N the number of observations. The range of E lies between 1.0
(perfect fit) and infinity. For the Amazon River simulation, there
are few cases with significant differences between Q and P for during
floods. However, E equals 0.95 and validates the global model
response and specifically the calibration of the internal parameters.
The radar altimetry elevation (yr) information is collected by the
ENVISAT mission derived from existing range data publicly released by
ESA (European Space Agency). The manual method described in Santos
da Silva et al., 2010 and Roux et al. (2010) has been used to define the
virtual stations where the time series of the water level variations from
the radar measurements can be quantified. We retained the median
and associated mean absolute deviation to construct the time series.
The geoid undulation is removed to the height value, referenced to the
ellipsoid WGS84. The geoid used in this study is EGM2008, mean tide
Fig. 6. Radar altimetry values follow the temporal variation of water level simulated. (a) Path 966 e Napo river, (b) Path 794 e Amazon river, (c) Path 164 e Amazon river, (d) Path
837 e Amazon river. Linear correlation between radar altimetry value and water level simulated. (e) Path 966, (f) Path 794, (g) Path 164, (h) Path 837.
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
solution (Tapley et al., 2004). This study analyses four Envisat satellite
tracks that cross the Amazon and Napo Rivers and have been providing
data since 2002 (Table 2). These tracks have been chosen in a manner to
explore the influence of the river width on hr uncertainties and cross
the rivers at sections with and without islands. Extreme values of river
width are 102.0 m and 1486.0 m.
3. Results
3.1. Model sensitivity to input parameters
According to the results of the sensitivity tests, w is the most
sensitive output variable to either input upstream flow or either to the
variability of all input parameters. The y, the Q and the v are almost
constant when input parameters change (Fig. 4a and b). The model
regulates all input variations tuning the value of w at each node. The
sensitivity of w depends linearly to the average and standard deviation of the normal distribution of a values set. On the other hand,
there is no sensitivity of w to n and s. The % of variability comes from
the distribution of a and do not show any specific trend when n and s
change (Fig. 5a and b). Channel geometry parameterization is then the
first parameter which controls the model response to upstream flow.
3.2. Relevance of radar altimetry data
yr values follow the temporal variation of y values (Fig. 6aed) for
whichever site where yr values are available. For these sites y versus
yr shows a significant linear trend with linear correlation coefficients
between 0.64 and 0.93 (Fig. 6eeh). The coefficient of the linear
trends varies from 0.6 to 1.1. Note that a slope coefficient between y
versus yr is smaller than 1 which means that the amplitude of the yr
variation is higher than the amplitude of the y values and, therefore,
marks a greater sensitivity of yr. This sensitivity of yr decreases
linearly when the size of the channel section increases (Fig. 7). For
river sections larger than 2500 m variations of y and yr are similar.
For the Amazon River at TAB, yr values are definitely less relevant than y values because the latter has been validated with in-situ
measurements. Therefore, for this case, yr uncertainty is larger than
y uncertainty without any doubt. For the Napo River case at TEMP,
yr uncertainty looks also larger than y uncertainty. Without in-situ
validation, we cannot reject that y value may have a systematic bias.
However, seven yr values out of eleven are in the range of y
uncertainty and are dispersed throughout the range of y values.
This observation supports that y values are not biased and de facto
that yr uncertainty is larger than y uncertainty for the Napo River.
4. Discussion and conclusion
Our 1-D hydrodynamic model applied to the Amazon basin
adjusts the variation of input parameters changing mainly the wet
cross section area and to a lesser extent the water velocity through
the section. The relationship between the wetted area and the
7
water depth is then one of the most important input data of our 1-D
hydrodynamic model. To simulate this relationship, we propose
using the coefficient a, of the presupposed linear relationship
between the variation rate of the water level and the variation rate
of the cross section width. An analysis of a bathymetric dataset of
52 cross sections of the Napo River supports this assumption. a is
a local parameter and takes a wide range of values. It controls the
level of uncertainties on simulated water velocity and above all
section widths. Our results show a linear relationship between the
level of uncertainty of these two variables and the uncertainty on
the channel geometry. On the other hand, the water depth does not
vary regardless of the range of values for each input parameter.
These results suggest possible errors in the model assumptions,
their mathematical formulation or numerical resolution. Nevertheless, the validation with physical data is therefore fundamental to
test the model. Two types of validation data have been used to
validate the model. First, we used in-situ measurements of water
level and streamflow at the Tabatinga gauging station on the
Amazon River using a half of the data to calibrate the model. Despite
few non-negligible discrepancies, the simulated water level and
streamflow variations fit the in-situ measurement variations for a 3
year period. This suggests that our model is appropriate to simulate
water level and streamflow simulation. Second, we compare simulated water levels with radar altimetric data at four sections with
different widths on the Amazon and Napo Rivers. Simulated water
level fit correctly again with the radar altimetry measurements only
for sections with widths larger than 2500 m. Indeed, satellite radar
altimetry accuracy depends strongly on the size of water surface
spot on which the altitude is calculated (Santos da Silva et al., 2010).
If the section width is too small, the radar spot contains points on the
river banks and vegetation. This work shows that the promising
satellite radar technology has currently limited application for the
calibration and validation of hydrodynamic models.
If we take into account the sensitivity of a standard 1-D
hydrodynamic model to channel geometry description, Manning
coefficient or channel longitudinal slope, the validation procedure
should be focused on the channel width and water velocity variations fitting. Those variables show the greatest sensitivity to input
parameters for Amazonian conditions where topographic roughness is very low. However, reducing uncertainties on a values or
simply acquiring daily in-situ velocity measurements at numerous
section along Amazonian rivers is still a challenge, specifically in
areas with sparse population.
Acknowledgements
This study was sponsored by the Environmental Research
Observatory (ORE) HYBAM (Geodynamical, hydrological and
biogeochemical control of erosion/alteration and material transport
in the Amazon basin) which has been operates in Peru since 2003. A
scientific cooperation agreement between the L’Institut de Recherche pour le Développement (IRD-France) and the Universidad
Nacional Agraria La Molina (UNALM-Peru) as of 2005, allowing the
participation of master and doctorate programs for students in
project ORE-HYBAM. ORE-HYBAM was proposed by team of LMTG
scholars (Laboratoire des Mécanismes de Transferts en GéologieUMR 5563 CNRS-UPS-IRD) which has been conducting research
projects in hydro geodynamics in the Amazon basin since 1995.
Appendices
A. Methodology for calculating the variability of the a parameter
Fig. 7. Linear coefficient between the simulated elevation and radar altimetry
elevation versus width river.
According to the Equation (7), we propose to define a synthetic
shape parameter, a, in order to quantify the wetted section
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
8
E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
variability in terms of water depth variability. Rivers sections
geometries do not correspond to univocal values of a. Sections with
different geometries can have the same value of a. In this study we
assume that each river section can be described by a significant
a value. To validate this hypothesis, we have studied a database of
ADCP profiles from the Hybam project acquired during a field
campaign on the Napo river, from ROC station to BEL station (Fraizy,
2004). 52 profiles of section bathymetry were measured from
upstream to downstream along 380.0 km.
Fig. A.1 shows the variability of w versus h for all profiles
between ROC and TEMP stations (34 sections). Linear regressions
quality varies with coefficients of correlation R2 from 0.41 to 0.95.
The distribution of R2 shows that the linear model of w versus h
relationship has a statistical significance (Fig. A.1 inset). Thereafter,
a is calculated regardless R2 value.
Fig. A.1. Relationship of width versus depth flow for all profiles between Rocafuerte
Station and Tempestad station and the coefficients of correlation R2 calculated.
Fig. A.2 shows that a variability on the river from upstream to
downstream has no spatial trend across the study area. For the
Napo River, a values vary around a mean value of 106 according to
a normal distribution with a sigma of 52 (Fig. A.2 inset). a variability
suggests that this shape parameter is a local parameter with an
average and standard deviation that have to be defined empirically.
Napo River a values are used as the reference in the 1-D hydrodynamic model sensitivity analysis. A much larger sample of rivers
sections throughout the Amazon basin should be analysed to define
if a follows a continental scale trend.
B. Amazon River information
Table B.1
Amazon River geometry used for the hydrodynamic model.
Nodes (52)
Downstream
reach length (m)
Width (m)
Elevation (m)
Francisco de Orellana Station
Island 17 left side
Island 17 right side
PT15
Island 16 left side
Island 16 right side
PT14
Island 15 left side
Island 15 right side
PT13
Island 14 left side
Island 14 right side
PT12
Island 13 left side
Island 13 right side
PT11
Island 12 left side
Island 12 right side
PT10
Island 11 left side
Island 11 right side
PT9
Island 10 left side
Island 10 right side
PT8
Island 9 left side
Island 9 right side
PT7
Island 8 left side
Island 8 right side
PT6
Island 7 left side
Island 7 right side
PT5
Island 6 left side
Island 6 right side
PT4
Island 5 left side
Island 5 right side
PT3
Island 4 left side
Island 4 right side
PT2
Island 3 left side
Island 3 right side
PT1
Island 2 left side
Island 2 right side
PT0
Island 1 left side
Island 1 right side
Tabatinga station
13,035.2
21,309.1
21,309.1
10,830.8
7577.1
7577.1
12,664.9
30,320.2
30,320.2
5411.5
4921.5
4921.5
29,529
8991.4
8991.4
10,925.7
12,639.7
12,639.7
12,086.7
15,349
15,349
2913.4
4733.5
4733.5
5780.1
3948.4
3948.4
17,309.1
15,447.8
15,447.8
20,556.1
10,764.7
10,764.7
7593.6
7601.1
7601.1
11,790.1
9653.9
9653.9
10,080
10,661.4
9919.4
9919.4
11,024.1
11,024.1
11,152
14,167.9
14,167.9
7415.8
7415.8
7415.8
0
342.3
223
290.1
474.3
224.8
203.8
366.9
491.4
218.2
398.2
122.2
150.8
438.4
139.5
225.1
320.5
206.7
167.7
246.7
231.2
138.5
292.9
158.4
195.7
912.2
543.8
182.7
807.6
326.6
79.3
296.8
243.7
139.1
283.4
538.1
142.8
305.4
123.5
344.9
495.1
285.9
339.6
240.5
136.8
278.5
261.6
360.3
309.5
314
237.6
267.7
485.6
88
87.6
87.6
86.6
86
86
85.6
85.4
85.4
84.5
82.7
82.7
82.1
79.8
79.8
76.5
75.9
75.9
74.1
73.5
73.5
71.5
71.3
71.3
71.2
71
71
70.9
70.8
70.8
69.9
69.7
69.7
69
68.2
68.2
67.5
66.8
66.8
66.1
65.8
65.8
65
64.6
64.6
64.4
64
64
63.4
63
63
62.5
Fig. A.2. Normal variability of a from upstream to downstream. (a) Nuevo Rocafuerte
station, (b) Tempestad located, (c) Santa Clotilde station and (d) Bellavista Mazán station.
Please cite this article in press as: Chávarri, E., et al., Hydrodynamic modelling of the Amazon River: Factors of uncertainty, Journal of South
American Earth Sciences (2012), http://dx.doi.org/10.1016/j.jsames.2012.10.010
E. Chávarri et al. / Journal of South American Earth Sciences xxx (2012) 1e10
9
Table B.2
ENVISAT radar altimetry information (geoid EGM2008).
Day
Elevation
(a.m.s.l)
Day
Elevation
(a.m.s.l)
Day
Elevation
(a.m.s.l)
Day
Elevation
(a.m.s.l)
02
06
10
21
26
30
04
08
13
17
22
26
02
06
82.10
82.55
81.62
83.44
84.81
83.48
78.09
77.32
78.27
80.24
82.12
81.39
80.21
82.41
11
15
20
24
02
07
10
14
21
25
30
17
21
26
82.49
82.33
81.48
77.06
79.83
82.16
81.44
81.19
82.43
83.75
80.67
75.52
79.78
79.72
30
06
10
24
28
02
06
11
15
19
26
20
04
09
82.03
82.46
84.46
82.00
76.80
75.95
77.55
81.97
83.24
82.33
82.80
83.94
82.64
79.92
13
17
22
26
31
04
11
15
20
24
29
02
07
76.10
76.51
76.06
81.84
82.00
82.43
83.52
83.59
82.80
81.06
79.38
80.29
80.07
December 2002
January 2003
February 2003
April 2003
May 2003
June 2003
August 2003
September 2003
October 2003
November 2003
December 2003
January 2004
March 2004
April 2004
May 2004
June 2004
July 2004
August 2004
November 2004
December 2004
January 2005
February 2005
March 2005
April 2005
May 2005
October 2005
November 2005
December 2005
January 2006
March 2006
April 2006
July 2006
August 2006
October 2006
November 2006
December 2006
January 2007
February 2007
March 2007
April 2007
June 2007
July 2007
August 2007
September 2007
October 2007
November 2007
December 2007
February 2008
March 2008
April 2008
May 2008
June 2008
July 2008
September 2008
October 2008
Source: Joecila Santos da Silva, CESTU, Universidade do Estado do Amazonas, UEA e Brasil.
C. Napo River information
Table C.1
Napo River geometry used for the hydrodynamic model.
Nodes (32)
Downstream
reach length (m)
Width (m)
Elevation (m)
Cabo Pantoja station
Island 9 left side
Island 9 right side
PT8
Island 8 left side
Island 8 right side
PT7
Island 7 left side
Island 7 right side
PT6
Island 6 left side
Island 6 right side
PT5
Island 5 left side
Island 5 right side
PT4
Island 4 left side
Island 4 right side
PT3
Island 3 left side
Island 3 right side
PT2
Island 2 left side
Island 2 right side
PT1
Island 1 left side
Island 1 right side
PT0
Island Tempestad left side
Island Tempestad right side
Tempestad place
3501.4
3629
3629
5233.5
4138.1
4138.1
1471.1
2565.3
2565.3
1884.9
2432.4
2432.4
1992.1
1115.1
1115.1
2172.8
1440.7
1440.7
2113.6
4871.4
4871.4
3233.8
2727.8
2727.8
1986.4
1055.9
1055.9
3564.3
3564.3
3564.3
3564.3
1156.3
321
562.6
1000
590
657.7
800
506.3
450
840
600
609.3
1300
626.9
300
1220.7
496.2
324.3
980
551.8
415.4
730
592.9
460
500
390.7
500
750
344.2
403.2
1000
165.5
165
165
164.5
164
164
163.7
163.5
163.5
163.4
163.3
163.3
163.1
163
163
162.5
162
162
161.5
161
161
160.5
160
160
159.5
159
159
158
157
157
156.5
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