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Journal of South American Earth Sciences 44 (2013) 94e103

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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

aUniversidad Nacional Agraria La Molina, Av. La Universidad s/n, La Molina, Apartado 12-056, Lima 12, PerubCNRS, Université Rennes 1, Géosciences Rennes, Campus de Beaulieu, 35042 Rennes cédex, Francec IRD, CP 7091 Lago Sul, 71619-970 Brasilia DF, BrazildCESTU, Universidade do Estado do Amazonas, UEA. Av. Manaus, Amazonas, CEP 69058807, Brazil

a r t i c l e i n f o

Article history:Received 15 December 2011Accepted 24 October 2012

Keywords:Hydrodynamic modellingAmazon RiverRadar altimetryModel sensitivity

* Corresponding author.E-mail addresses: echavarri@lamolina.edu.p

(E. Chávarri), alain.crave@univ-rennes1.fr (A. Crave(M.-P. Bonnet), jsdsilva@uea.edu.br (J. Santos Da S(J.L. Guyot).

0895-9811/$ e see front matter � 2012 Elsevier Ltd.http://dx.doi.org/10.1016/j.jsames.2012.10.010

a b s t r a c t

Hydrodynamic modelling of Amazonian rivers is still a difficult task. Access difficulties reduce thepossibilities to acquire sufficient good data for the model calibration and validation. Current satelliteradar technology allows measuring the altitude of water levels throughout the Amazon basin. In thisstudy, we explore the potential usefulness of these data for hydrodynamic modelling of the Amazon andNapo Rivers in Peru. Simulations with a 1-D hydrodynamic model show that radar altimetry canconstrain properly the calibration and the validation of the model if the river width is larger than2500 m. However, sensitivity test of the model show that information about geometry of the riverchannel and about the water velocity are more relevant for hydrodynamic modelling. These two types ofdata that are still not easily available in the Amazon context.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The Amazon River is the largest in the world with a basin area of7.0 � 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 themain channel of communication from the Andes to the Atlantic.Therefore, understanding and modelling the hydrodynamic of thespecific Amazon context is of great interest for environment,economic and social processes. Since the end of the 1980s, extremehydrological events have been increasing in the River Amazon(Espinoza et al., 2009, 2011). These extreme events caused inun-dations, as in 1999, 2006 and 2009, or very low water stages, as in1998, 2005 and 2010, which are harmful to people living nearby thewatercourse 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 theincreased frequency of extreme hydrological events in the Amazonput at risk their vast amount of natural resources and a populationof more than 38 million people. Predicting the impact of climate on

e, echavarriv@gmail.com), marie-paule.bonnet@ird.frilva), jean-loup.guyot@ird.fr

All rights reserved.

water level and discharge variability on Amazonian main rivers is,therefore, a crucial task.

Several hydraulic models are focused on water level andstreamflow prediction on Amazonian context. Here we present themost recent works with their most important results. A distributedLarge Basin Simulation Model, called MGB-IPH (an acronym fromthe Portuguese for Large Basins Model and Institute of HydraulicResearch), was developed by Collischonn (2001). The MGB-IPH wasapplied 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 ofthe simulation (Getirana et al., 2010), where satellite derived rainfallinformation is being used to run the model. But divergencesbetween hydrographs were noted at refined time scale. Also themethodology requires depth and flow relations at virtual stations,which can limit its application. Paiva et al., 2011, present a large-scale hydrologic model with a full one-dimensional hydrodynamicmodule to calculate streamflow propagation on a complex rivernetwork, using limited data for river geometry and floodplaincharacterization. Trigg et al., 2009, proposed that to conducthydraulic modelling of the main channel of the Amazon River, thediffusive terms is sufficient in thehydrodynamic equations. Beighleyet al., 2009, presents the hydrological and hydraulic simulationof the Amazon Basin using a runoff model to surface and subsurfacerunoff, based on the application of kinematic and diffusivemethods. Coe et al., 2007, proposes improvements to the model

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e103 95

THMB (Terrestrial Hydrology model with Biogeochemistry) inrelation to the velocity equation to include the sinuosity of the riverin the calculation of the forces of resistance and incorporatesa roughness empirical equation of data from 30,000 measurementsof the river morphology to determine the flood volume in manyplaces in the basin and ultimately represents themorphology of thefloodplain with a resolution of 1 km from SRTM (Shuttle RadarTopography Mission).

All these previous works point out the need of valid high spatialresolution data on channel geometry to improve the prediction ofthe water level of the river or the flood extension. In terms of theriver streamflow, the propagation modelling are related to theinput data uncertainty, e.g. DEM precision, vegetation and crosssection geometry provided by geomorphologic relations (Paivaet al., 2011). Nonetheless, in general, there is limited informationon Amazonian river geometry, streamflow and water depths whichcreate uncertainty in the modelling of the flow profile. Often times,attaining the necessary information for complex models involveslarge amounts of monetary expenses and human effort whichmakes it impractical for the wide and inaccessible Amazon basin.

On the other hand, radar altimetry is a good alternative to getdata on Amazonian channel geometry and water level. However,we must take into account some considerations as explained bySantos da Silva et al. (2010), the water levels measured by radaraltimetry and in situ gauges are fundamentally different. Radaraltimetry measures a weighted mean of all reflecting bodies overa surface several square kilometres in size while gauges pick upriver stages at specific points. Comparison at crossovers and withinsitu gauges show that the quality of the time series can be highlyvariable, from 12 cm in the best cases and 40 cm in most cases toseveral metres in the worse cases in Amazon basin.

Negrel et al. (2011), suggest the possibility of calculating thestreamflow based exclusively on river surface variables accessiblethrough earth observation techniques, namely river width, level,surface slope and surface velocity. The main hypothesis presentedin the former study considered steady flow and rectangular shapedcross-sections.

In the present study, we examine more specifically the uncer-tainty of streamflow modelling induced by the lack of informationon channel cross section geometry and the accuracy of radaraltimetry. The main objective is to fix which radar altimetry accu-racy and channel geometry data are required to improve stream-flow modelling of Amazonian rivers of different sizes. To test ifcurrent radar altimetric data are relevant in Amazonian context,simulation of water level on Amazon and Napo Rivers are comparedwith in-situ measurement of discharge and water level.

2. Methodology

This study is divided in two steps. First, we use 1-D hydrody-namic model to quantified the sensitivity of the variables: waterdepth (y), longitudinal streamflow (Q), bankfull width (w) andvelocity (v) according to the variability of input parameters: thecross section geometry, Manning roughness coefficient (n) andlongitudinal slope of the river (s). This shows how the hydrody-namic model response is related to the level of uncertainty of inputparameters and how they rank in terms of model sensitivity. Inother words, we evaluate theoretical impacts of uncertainties onnatural data on simulation of y, v and Q. Second, we compareuncertainties of y simulation to radar altimetry accuracy applyingthe same 1-D hydrodynamicmodel to the Amazon and Napo Rivers.

The streamflowmodel is an original 1-D hydrodynamicmodel tosimulate unsteady streamflow in anabranching river form such asthe Amazon River and Napo River. In the following text, we presentthemain equations and hypothesis relative to this numericalmodel.

2.1. Hydrodynamic model description

Model inputs are water depth fluctuation at the upstreamboundary, longitudinal slope, Manning coefficient, riverbedgeometry of several cross sections of the river and the sequence ofislands. The minimum number of cross sections is defined by thelongitudinal sequence of diffluent and convergent channels form-ing one or several islands on the stream path. One island is definedfor cross section: one before the upstream divergent flow, two foreach branch of the river on each side of the island and one after thedownstream convergence. Channel reaches without islands aredefined with one cross section in the middle of the reach. Note thatAmazonian rivers are often anabranching meandering channels(Latrubesse, 2008), with a dense longitudinal sequence of islands.Therefore, following the former rule for channel descriptionimplies a relatively complete database on river bathymetry. Usually,such database is not available for Amazonian rivers. To overpass thelack of information on river bathymetry, we characterize thegeometry of each cross section with a surrogate parameter a tosimulate the relation channel width versus water depth (see x 2.2).

Note that this model does not simulate flood. All simulatedwater level stay below the upper limit of bankfull level. Manningroughness coefficient and longitudinal slope are supposed to beconstant over time. Due to the high water turbidity value, aquaticvegetation cannot grow on the riverbed and the roughness of theriverbed does not change. We suppose that erosion and sedimen-tation processes on the riverbed do not change significantly thelongitudinal slope for the time scale of several years.

The output variables of the model are hydrographs of y, Q,w andv 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 andmomentum equations (Equations (1) and (2)) proposed by Barre deSaint-Venant (1871) and in the work of Massau, who in 1889 pub-lished some early attempts to solve those equations. The primaryhypothesis of this theory is to consider constant density, hydrostaticpressures, mild slopes and a sediment velocity that is equal to theflow mean velocity.

vyvt

þ 1wvQvx

¼ qwvx

(1)

where q is lateral streamflow [L3T�1], x is the length between twocross sections [L], and t is the time [T].

fvQvt

þ fv

vx

�bQ2

A

�þ gA

vyvx

þ gASf ¼ bqvL (2)

where Sf is the energy line slope (friction slope), g is the accelera-tion due to gravity [LT�2], A is cross-sectional area of the stream-flow [L2], vL is the velocity of the lateral streamflow, that is, in thesame direction as the principal streamflow of the river, f is theLocal partial inertial factor (Fread et al., 1986), b is the Boussinesqcoefficient.

Equations (1) and (2) are solved under the Preissmann numer-ical scheme. It offers the advantage that a variable spatial grid maybe used; steep wave fronts may be properly simulated by varyingthe weighting coefficient of the time interval q and weightingcoefficient of the space interval f, and the scheme yields an exactsolution of the linearized form of the governing equation fora 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, thereexist diverse alternatives such as assuming that the water depthsaround the islandsare thesame.However, in this studyweconsidered

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e10396

the hydrodynamic equations for internal boundary conditionsapplied to sections with islands as described in Equation (1) andenergy conservation equations (Equations (3) and (4)) to solve theconvergence and divergence problems.

According to Cunge et al. (1980), for nodes i, i1 and i2, there are:

yi1 þ12g

�fi1

Qi1Ai1

�2¼ yi þ

12g

�fiQiAi

�2(3)

yi2 þ12g

�fi2

Qi2Ai2

�2

¼ yi þ12g

�fiQiAi

�2

(4)

where: Qi1 and Qi2: streamflows in both side of the island, yi1 andyi2: water depth in both side of the island, Qi: streamflow in theconfluence. yi: water depth in the confluence.

The spatial and temporal resolution of the model takes intoaccount the Courant condition. For one-dimensional equations, theCourant number, or also known as the Courant, Friedrichs and Lewy(CFL) number, is defined as Abbott (1979).

C ¼ ju� cjDtDx

� 1 (5)

where: C: Courant number, u: Medium flow velocity (LT�1), c: Flowcelerity (LT�1), Dx/Dt: the numeric Celerity (LT�1).

According to Lewy and Friedricks, mentioned by Ponce (2002),the Courant number related the physical celerity and numericalcelerity.

Fig. 1. (a) Amazon basin, (b) the simulated stretch between Nuevo Rocafuerte station and TTabatinga stations e Amazonas River. Figures include radar altimetry paths and nodes sim

C ¼ cDx

(6)

Dt

The last equation (Courant number) is very important forthe application of numeric solutions since it allows us to calculateDx/Dt and avoid instability in the numerical model.

For the proposed hydrodynamic model it was found that theCourant number must be equal or greater than 0.23 (C z 0.23) toassure stability. Consequently, once the spatial resolution (Dx) isdefined according to the stretch singularities and knowing thecelerity, the temporal resolution (Dt) is determined.

According to the mathematical description of the model, inaddition to input parameters n, s and a, there are five moreparameters (C, b, f, q, 4). All the former parameters are calibratedon 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 ofinformation on bathymetry along the Amazonian rivers. Equations(1) and (2) are closely related to water depth and the widthriverbed. In order to simulate synthetic cross section geometry, wesuppose that the variability of the depth is linearly related to thevariability of the cross section width following the Equation (7).

a ¼ DwDy

(7)

empestad island e Napo river, (c) The simulated stretch between the Tamshiyacu andulation.

0 200 400 600 800 1000 12001

2

3

4

5

6x 104

Days

Flow

(m3/

s)

0 200 400 600 800 1000 120076

78

80

82

84

86

88

90

Days

Elev

atio

n (a

.m.s

.l)

a

b

Fig. 2. Calibration results: For (a) Streamflow and (b) Water elevation. We presentedthe simulated and recorded hydrographs in Tabatinga station for the first 1100 days (01September 2002 to 04 September 2005).

1000 1200 1400 1600 1800 2000 22001

2

3

4

5

6x 104

Days

Flow

(m3/

s)

86

88

90

.s.l)

a

b

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e103 97

The question of cross section geometry definition is reduced tothe definition of the non-dimensional parameter a. Currently, nostudy has demonstrated the validity of Equation (7) for any geom-etry type of natural channel cross section. However, analysing thedatabase of Hybamproject onmore than 100 Amazonian river crosssections shows that Equation (7) is empirical significant (seeAppendix A, Fig. A.1). Because a is a local variable with awide rangeof values, this is one of themain sources of uncertainty in the results.

2.3. Parameterization and quantification of the sensitivity test ofthe hydrodynamic model

The sensitivity of the model is analysed by looking at the vari-ability of y, Q,w and v at each section of the river, in response to thevariability of a, n and s.

According to the Hybam database, a varies in the range between20 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 usedto define the channel geometry for each simulation. Thus, there aremany values of a and sections used to describe the channel. The setof a is chosen within a normal distribution by random drawing.Therefore, there are two parameters to define the geometry of thechannel, the average value and the standard deviations s of thenormal distribution of a. The sensitivity of the model to a is esti-mated doing averages on output variable variability on 10 simula-tions applying the same normal distribution of a values.

Manning roughness coefficient values are chosen in the range fornatural rivers, meaning between 0.025 s/m�1/3 and 0.045 s/m�1/3.Values of longitudinal slope are chosen in the range of slope valuesobserved for the Amazon and Napo Rivers (Bourrel et al., 2009),meaning between 0.08 m/km and 0.35 m/km for the Amazon plainand 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 sensi-tivity of the model, a reference theoretical case is chosen whichcorresponds to the Napo River dataset information. The geometry ofthis theoretical channel is fixed with a a set values by randomdrawingwithin a normal distributionwith an average of 106 and a sof 52. These two values correspond to the analysis performed on thedataset of the Napo River (Appendix A). Manning coefficient andlongitudinal slope of this theoretical case are fixed to 0.035 s/m�1/3

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 dailyevolutions of each output variables corresponding to a specificinput parameter set of values and the theoretical reference case atthe last downstream station. The criterion of sensitivity is obtainedby percentage of variability using Equation (8).

%Variability ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPM1

PD1

�Voutput � Vreference

�2r

PM1

PD1

�Voutput � Vreference

� � 100 (8)

1000 1200 1400 1600 1800 2000 220076

78

80

82

84

Days

Elev

atio

n (a

.m

Fig. 3. Validation results: For (a) Streamflow and (b) Water elevation. We presentedthe simulated and recorded hydrographs in Tabatinga station for the last 1100 days(05 September 2005 to 28 October 2008).

Table 1General characteristics of Amazon and Napo Rivers in Peru (Hybam projectdatabase).

General characteristic River Amazon(Tamshiyacu station)

River Napo(Bellavista station)

High water period MarcheMay MayeJulyLow water period AugusteOctober JanuaryeFebruaryAverage streamflow (m3/s) 34,815 5838Average velocity (m/s) 1.69 1.18Average width (m) 1213 1312Longitudinal slope (m/km) 0.08e0.35 0.1e1.8Average water depth (m) 23.5 12.77Contribution area (km2) 726,403 100,518

Table 2General characteristics of radar altimetry information.

River Path (ENVISAT GoidEGM, 2008)

Latitude(�) WGS84

Longitude(�) WGS84

Time period Distance from upstreamboundary (km)

Widthapprox. (m.)

Observation

Napo 966 �74.86 �1.29 29 sept 2002 to 17 oct 2010 77.0 580.0/618.0 IslandAmazon 164 �70.4 �3.79 06 oct 2002 to 18 sept 2010 321.2 5800.0 Reach

837 �71.6 �3.77 24 sept 2002 to 12 oct 2010 163.9 3260.0 Reach794 �72.5 �3.52 01 dec 2002 to 10 oct 2010 31.5 490.0/2110.0 Island

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e10398

where M: Total cases, D: Total days, Voutput: Model variable in thedownstream, Vreference: Model variable for a¼ 106, n¼ 0.035 s/m�1/

3, s ¼ 0.07 m/km.

2.4. Application of the model to Amazon and Napo Rivers

The purpose of performing simulations on Amazon and NapoRivers is to consider their differences in the hydrodynamic aspects.The River Napo is mainly located in the foothills of the Amazonbasin and the stretch of the River Amazon of this study is located inthe plain (Fig. 1a), both with different flow regimes and longitu-dinal slope (Table 1).

The simulation of the River Amazon in the Peruvian sector wasconducted from the confluence of theNapo and the River Amazon atthe FranciscodeOrellana (FOR) station to theTabatinga (TAB) stationin Brazil. Hydrometric and bathymetry information is only availablesince 2002 for the TAB and Tamshiyacu (TAM) stations due to thelack of data at FOR.However, cross section geometryat TAM is a goodproxy of the cross section geometry at FOR and by adding stream-flows of the Bellavista station (BEL) at the outlet of Napo and TAM.

The Napo River hydrodynamic simulation was carried out in thesection between the Nuevo Rocafuerte (ROC) station and theTempestad (TEMP) location. The ROC is located near the borderbetween Peru and Ecuador and is located approximately 77 km

Fig. 4. The sensitivity of model variables according to the Riverbed geometrysensitivity. (a) For a ¼ 106 � 52 and (b) For a ¼ 212 � 52.

upstream of the TEMPwhere there is an island with radar altimetrydata on both sides of it. Streamflow and water level information isavailable since 2002 at ROC. At TEMP only radar altimetry infor-mation is available.

For both rivers, a sequence of cross sections (nodes) define thespatial resolution of the river stretch used for the simulations(Fig. 1b and c). Note that two parallel nodes define an island’sconfiguration. Tables B.1 and C.1 of Appendix B and C respectively,summarize the characteristics of each node for the Amazon andNapo Rivers respectively. For both river stretches, the upstream anddownstream limits correspond to altimetry radar tracks on thefield.

Longitudinal slopes of Amazon and Napo are supposed to besignificantly constant and equal to 0.07 m/km and 0.17 m/km,respectively. Manning coefficient is supposed to be constant forboth rivers with a value of 0.035 s/m�1/3. a set values are defined byrandom drawing within a normal distribution with an average of106 and a a of 52.

To calibrate the internal parameters which are supposed to beconstant whatever the Amazon or Napo configuration, the model isapplied on the Amazon River between TAM and TAB using half ofthe available dataset of Q and y (Fig. 2a and b). The other half of thedataset is used for the validation (Fig. 3a and b). The goodness of fitmethodologies is evaluated by the Nash and Sutcliffe efficiency (E)and Root Mean Squared Error (RMSE), these being indicators of

Fig. 5. The sensitivity of model variables according to: (a) the Manning roughnesscoefficient and (b) Longitudinal slope.

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e103 99

model error. The Nash and Sutcliffe efficiency (E) is definedfollowing Equation (9) (Krause et al., 2005):

E ¼ 1�PN

1 ðOi � PiÞ2PN1

�Oi � O

�2 (9)

where Oi: Observed value, Pi: Predicted value, O: Mean observedvalue, N the number of observations. The range of E lies between 1.0(perfect fit) and �infinity. For the Amazon River simulation, thereare fewcaseswith significant differences betweenQ and P for during

Fig. 6. Radar altimetry values follow the temporal variation of water level simulated. (a) Pat837 e Amazon river. Linear correlation between radar altimetry value and water level simu

floods. However, E equals 0.95 and validates the global modelresponse and specifically the calibration of the internal parameters.

The radar altimetry elevation (yr) information is collected by theENVISATmissionderived fromexisting rangedatapublicly releasedbyESA(EuropeanSpaceAgency). Themanualmethoddescribed inSantosda Silva et al., 2010 and Roux et al. (2010) has been used to define thevirtual stationswhere the time series of thewater level variations fromthe radar measurements can be quantified. We retained the medianand associated mean absolute deviation to construct the time series.The geoid undulation is removed to the height value, referenced to theellipsoidWGS84. The geoid used in this study is EGM2008, mean tide

h 966 e Napo river, (b) Path 794 e Amazon river, (c) Path 164 e Amazon river, (d) Pathlated. (e) Path 966, (f) Path 794, (g) Path 164, (h) Path 837.

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e103100

solution (Tapley et al., 2004). This study analyses four Envisat satellitetracks that cross theAmazonandNapoRivers andhavebeenprovidingdata since2002(Table2). Thesetrackshavebeenchosen inamanner toexplore the influence of the river width on hr uncertainties and crossthe rivers at sectionswith andwithout islands. Extreme values of riverwidth 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 mostsensitive output variable to either input upstreamfloworeither to thevariability of all input parameters. The y, the Q and the v are almostconstant when input parameters change (Fig. 4a and b). The modelregulates all input variations tuning the value of w at each node. Thesensitivity of w depends linearly to the average and standard devia-tion of the normal distribution of a values set. On the other hand,there is no sensitivity ofw to n and s. The % of variability comes fromthe distribution of a and do not show any specific trendwhen n and schange (Fig. 5a andb). Channel geometryparameterization is then thefirst parameter which controls themodel response to upstream flow.

3.2. Relevance of radar altimetry data

yr values follow the temporal variation of y values (Fig. 6aed) forwhichever site where yr values are available. For these sites y versusyr showsa significant linear trendwith linear correlation coefficientsbetween 0.64 and 0.93 (Fig. 6eeh). The coefficient of the lineartrends varies from 0.6 to 1.1. Note that a slope coefficient between yversus yr is smaller than 1 whichmeans that the amplitude of the yrvariation is higher than the amplitude of the y values and, therefore,marks a greater sensitivity of yr. This sensitivity of yr decreaseslinearly when the size of the channel section increases (Fig. 7). Forriver sections larger than 2500 m variations of y and yr are similar.

For the Amazon River at TAB, yr values are definitely less rele-vant than y values because the latter has been validatedwith in-situmeasurements. Therefore, for this case, yr uncertainty is larger thany uncertainty without any doubt. For the Napo River case at TEMP,yr uncertainty looks also larger than y uncertainty. Without in-situvalidation, we cannot reject that y valuemay have a systematic bias.However, seven yr values out of eleven are in the range of yuncertainty and are dispersed throughout the range of y values.This observation supports that y values are not biased and de factothat yr uncertainty is larger than y uncertainty for the Napo River.

4. Discussion and conclusion

Our 1-D hydrodynamic model applied to the Amazon basinadjusts the variation of input parameters changing mainly the wetcross section area and to a lesser extent the water velocity throughthe section. The relationship between the wetted area and the

Fig. 7. Linear coefficient between the simulated elevation and radar altimetryelevation versus width river.

water depth is then one of themost important input data of our 1-Dhydrodynamic model. To simulate this relationship, we proposeusing the coefficient a, of the presupposed linear relationshipbetween the variation rate of the water level and the variation rateof the cross section width. An analysis of a bathymetric dataset of52 cross sections of the Napo River supports this assumption. a isa local parameter and takes a wide range of values. It controls thelevel of uncertainties on simulated water velocity and above allsection widths. Our results show a linear relationship between thelevel of uncertainty of these two variables and the uncertainty onthe channel geometry. On the other hand, the water depth does notvary 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. Never-theless, the validationwithphysical data is therefore fundamental totest the model. Two types of validation data have been used tovalidate the model. First, we used in-situ measurements of waterlevel and streamflow at the Tabatinga gauging station on theAmazon River using a half of the data to calibrate themodel. Despitefew non-negligible discrepancies, the simulated water level andstreamflow variations fit the in-situ measurement variations for a 3year period. This suggests that our model is appropriate to simulatewater level and streamflow simulation. Second, we compare simu-lated water levels with radar altimetric data at four sections withdifferent widths on the Amazon and Napo Rivers. Simulated waterlevel fit correctly againwith the radar altimetrymeasurements onlyfor sections with widths larger than 2500 m. Indeed, satellite radaraltimetry accuracy depends strongly on the size of water surfacespot onwhich the altitude is calculated (Santos da Silva et al., 2010).If the sectionwidth is too small, the radar spot contains points on theriver banks and vegetation. This work shows that the promisingsatellite radar technology has currently limited application for thecalibration and validation of hydrodynamic models.

If we take into account the sensitivity of a standard 1-Dhydrodynamic model to channel geometry description, Manningcoefficient or channel longitudinal slope, the validation procedureshould be focused on the channel width and water velocity varia-tions fitting. Those variables show the greatest sensitivity to inputparameters for Amazonian conditions where topographic rough-ness is very low. However, reducing uncertainties on a values orsimply acquiring daily in-situ velocity measurements at numeroussection along Amazonian rivers is still a challenge, specifically inareas with sparse population.

Acknowledgements

This study was sponsored by the Environmental ResearchObservatory (ORE) HYBAM (Geodynamical, hydrological andbiogeochemical control of erosion/alteration andmaterial transportin the Amazon basin) which has been operates in Peru since 2003. Ascientific cooperation agreement between the L’Institut de Recher-che pour le Développement (IRD-France) and the UniversidadNacional Agraria La Molina (UNALM-Peru) as of 2005, allowing theparticipation of master and doctorate programs for students inproject ORE-HYBAM. ORE-HYBAM was proposed by team of LMTGscholars (Laboratoire des Mécanismes de Transferts en Géologie-UMR 5563 CNRS-UPS-IRD) which has been conducting researchprojects in hydro geodynamics in the Amazon basin since 1995.

Appendices

A. Methodology for calculating the variability of the a parameter

According to the Equation (7), we propose to define a syntheticshape parameter, a, in order to quantify the wetted section

Table B.1Amazon River geometry used for the hydrodynamic model.

Nodes (52) Downstreamreach length (m)

Width (m) Elevation (m)

Francisco de Orellana Station 13,035.2 342.3 88

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e103 101

variability in terms of water depth variability. Rivers sectionsgeometries do not correspond to univocal values of a. Sections withdifferent geometries can have the same value of a. In this study weassume that each river section can be described by a significanta value. To validate this hypothesis, we have studied a database ofADCP profiles from the Hybam project acquired during a fieldcampaign on the Napo river, from ROC station to BEL station (Fraizy,2004). 52 profiles of section bathymetry were measured fromupstream to downstream along 380.0 km.

Fig. A.1 shows the variability of w versus h for all profilesbetween ROC and TEMP stations (34 sections). Linear regressionsquality varies with coefficients of correlation R2 from 0.41 to 0.95.The distribution of R2 shows that the linear model of w versus hrelationship 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 RocafuerteStation and Tempestad station and the coefficients of correlation R2 calculated.

Island 17 left side 21,309.1 223 87.6Island 17 right side 21,309.1 290.1 87.6PT15 10,830.8 474.3 86.6Island 16 left side 7577.1 224.8 86Island 16 right side 7577.1 203.8 86PT14 12,664.9 366.9 85.6Island 15 left side 30,320.2 491.4 85.4Island 15 right side 30,320.2 218.2 85.4PT13 5411.5 398.2 84.5Island 14 left side 4921.5 122.2 82.7Island 14 right side 4921.5 150.8 82.7PT12 29,529 438.4 82.1Island 13 left side 8991.4 139.5 79.8Island 13 right side 8991.4 225.1 79.8PT11 10,925.7 320.5 76.5Island 12 left side 12,639.7 206.7 75.9Island 12 right side 12,639.7 167.7 75.9PT10 12,086.7 246.7 74.1Island 11 left side 15,349 231.2 73.5Island 11 right side 15,349 138.5 73.5PT9 2913.4 292.9 71.5Island 10 left side 4733.5 158.4 71.3Island 10 right side 4733.5 195.7 71.3PT8 5780.1 912.2 71.2Island 9 left side 3948.4 543.8 71Island 9 right side 3948.4 182.7 71PT7 17,309.1 807.6 70.9Island 8 left side 15,447.8 326.6 70.8Island 8 right side 15,447.8 79.3 70.8PT6 20,556.1 296.8 69.9Island 7 left side 10,764.7 243.7 69.7Island 7 right side 10,764.7 139.1 69.7PT5 7593.6 283.4 69Island 6 left side 7601.1 538.1 68.2Island 6 right side 7601.1 142.8 68.2PT4 11,790.1 305.4 67.5Island 5 left side 9653.9 123.5 66.8Island 5 right side 9653.9 344.9 66.8PT3 10,080 495.1 66.1Island 4 left side 10,661.4 285.9 65.8

Fig. A.2 shows that a variability on the river from upstream todownstream has no spatial trend across the study area. For theNapo River, a values vary around a mean value of 106 according toa normal distributionwith a sigma of 52 (Fig. A.2 inset). a variabilitysuggests that this shape parameter is a local parameter with anaverage and standard deviation that have to be defined empirically.Napo River a values are used as the reference in the 1-D hydro-dynamic model sensitivity analysis. A much larger sample of riverssections throughout the Amazon basin should be analysed to defineif a follows a continental scale trend.

Fig. A.2. Normal variability of a from upstream to downstream. (a) Nuevo Rocafuertestation, (b) Tempestad located, (c) Santa Clotilde station and (d) BellavistaMazán station.

Island 4 right side 9919.4 339.6 65.8PT2 9919.4 240.5 65Island 3 left side 11,024.1 136.8 64.6Island 3 right side 11,024.1 278.5 64.6PT1 11,152 261.6 64.4Island 2 left side 14,167.9 360.3 64Island 2 right side 14,167.9 309.5 64PT0 7415.8 314 63.4Island 1 left side 7415.8 237.6 63Island 1 right side 7415.8 267.7 63Tabatinga station 0 485.6 62.5

B. Amazon River information

Table B.2ENVISAT 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 December 2002 82.10 11 May 2004 82.49 30 January 2006 82.03 13 August 2007 76.1006 January 2003 82.55 15 June 2004 82.33 06 March 2006 82.46 17 September 2007 76.5110 February 2003 81.62 20 July 2004 81.48 10 April 2006 84.46 22 October 2007 76.0621 April 2003 83.44 24 August 2004 77.06 24 July 2006 82.00 26 November 2007 81.8426 May 2003 84.81 02 November 2004 79.83 28 August 2006 76.80 31 December 2007 82.0030 June 2003 83.48 07 December 2004 82.16 02 October 2006 75.95 04 February 2008 82.4304 August 2003 78.09 10 January 2005 81.44 06 November 2006 77.55 11 March 2008 83.5208 September 2003 77.32 14 February 2005 81.19 11 December 2006 81.97 15 April 2008 83.5913 October 2003 78.27 21 March 2005 82.43 15 January 2007 83.24 20 May 2008 82.8017 November 2003 80.24 25 April 2005 83.75 19 February 2007 82.33 24 June 2008 81.0622 December 2003 82.12 30 May 2005 80.67 26 March 2007 82.80 29 July 2008 79.3826 January 2004 81.39 17 October 2005 75.52 20 April 2007 83.94 02 September 2008 80.2902 March 2004 80.21 21 November 2005 79.78 04 June 2007 82.64 07 October 2008 80.0706 April 2004 82.41 26 December 2005 79.72 09 July 2007 79.92

Source: Joecila Santos da Silva, CESTU, Universidade do Estado do Amazonas, UEA e Brasil.

E. Chávarri et al. / Journal of South American Earth Sciences 44 (2013) 94e103102

C. Napo River information

Table C.1Napo River geometry used for the hydrodynamic model.

Nodes (32) Downstreamreach length (m)

Width (m) Elevation (m)

Cabo Pantoja station 3501.4 1156.3 165.5Island 9 left side 3629 321 165Island 9 right side 3629 562.6 165PT8 5233.5 1000 164.5Island 8 left side 4138.1 590 164Island 8 right side 4138.1 657.7 164PT7 1471.1 800 163.7Island 7 left side 2565.3 506.3 163.5Island 7 right side 2565.3 450 163.5PT6 1884.9 840 163.4Island 6 left side 2432.4 600 163.3Island 6 right side 2432.4 609.3 163.3PT5 1992.1 1300 163.1Island 5 left side 1115.1 626.9 163Island 5 right side 1115.1 300 163PT4 2172.8 1220.7 162.5Island 4 left side 1440.7 496.2 162Island 4 right side 1440.7 324.3 162PT3 2113.6 980 161.5Island 3 left side 4871.4 551.8 161Island 3 right side 4871.4 415.4 161PT2 3233.8 730 160.5Island 2 left side 2727.8 592.9 160Island 2 right side 2727.8 460 160PT1 1986.4 500 159.5Island 1 left side 1055.9 390.7 159Island 1 right side 1055.9 500 159PT0 3564.3 750 158Island Tempestad left side 3564.3 344.2 157Island Tempestad right side 3564.3 403.2 157Tempestad place 3564.3 1000 156.5

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