Hydrodynamic Modelling of the Amazon River Factors of Uncertainty

7232019 Hydrodynamic Modelling of the Amazon River Factors of Uncertainty

httpslidepdfcomreaderfullhydrodynamic-modelling-of-the-amazon-river-factors-of-uncertainty 110

Hydrodynamic modelling of the Amazon River Factors of uncertainty

Eduardo Chaacutevarri a Alain Crave b Marie-Paule Bonnet c Abel Mejiacutea a Joecila Santos Da Silva d Jean Loup Guyot c

a Universidad Nacional Agraria La Molina Av La Universidad sn La Molina Apartado 12-056 Lima 12 Perub CNRS Universiteacute Rennes 1 Geacuteosciences Rennes Campus de Beaulieu 35042 Rennes ceacutedex Francec IRD CP 7091 Lago Sul 71619-970 Brasilia DF Brazild CESTU 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 River

Radar altimetry

Model sensitivity

a b s t r a c t

Hydrodynamic modelling of Amazonian rivers is still a dif 1047297cult task Access dif 1047297culties reduce the

possibilities to acquire suf 1047297cient good data for the model calibration and validation Current satelliteradar 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 andNapo 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 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 of

data 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 theworld with a basin area of

70 106 km2 and an average 1047298ow at its mouth to 206000 m3s(Callegravede et al 2010) Crossing eight countries this huge river is themain channel of communication from the Andes to the AtlanticTherefore understanding and modelling the hydrodynamic of thespeci1047297c 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 in

1998 2005 and 2010 which are harmful to people living nearby thewatercourse and damaging for agriculture and ecosystems (eg

Saleska et al 2007 Phillips et al 2009 Asner and Alencar 2010Lewis et al 2011 Xu et al 2011)The impacts that may cause theincreased frequency of extreme hydrological events in the Amazon

put at risk their vast amount of natural resources and a populationof more than 38 million people Predicting the impact of climate on

water level and discharge variability on Amazonian main rivers istherefore a crucial task

Several hydraulic models are focused on water level andstream1047298ow prediction on Amazonian context Here we present the

most 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 was

applied for some Amazonian rivers the Madeira (Ribeiro et al2005) the Tapajos and the Negro river (Collischonn et al 2008)Spatial altimetrydata is being used to complement the validation of thesimulation(Getirana et al2010) wheresatellite derived rainfallinformation is being used to run the model But divergences

between hydrographs were noted at re1047297ned time scale Also the

methodology requires depth and 1047298ow relations at virtual stationswhich can limit its application Paiva et al 2011 present a large-scale hydrologic model with a full one-dimensional hydrodynamic

module to calculate stream1047298ow propagation on a complex rivernetwork using limited data for river geometry and 1047298oodplaincharacterization Trigg et al 2009 proposed that to conducthydraulic modelling of the main channel of the Amazon River the

diffusivetermsis suf 1047297cientin the hydrodynamic equationsBeighleyet al 2009 presents the hydrological and hydraulic simulationof the Amazon Basinusing a runoff model to surface and subsurfacerunoff based on the application of kinematic and diffusive

methods Coe et al 2007 proposes improvements to the model

Corresponding author

E-mail addresses echavarrilamolinaedupe echavarrivgmailcom

(E Chaacutevarri) alaincraveuniv-rennes1fr (A Crave) marie-paulebonnetirdfr

(M-P Bonnet) jsdsilvaueaedubr (J Santos Da Silva) jean-loupguyotirdfr

(JL Guyot)

Contents lists available at SciVerse ScienceDirect

Journal of South American Earth Sciences

j o u r n a l h o m e p a g e w w w e l s e v i e r c om l o c a t e j s a m e s

0895-9811$ e see front matter 2012 Elsevier Ltd All rights reserved

httpdxdoiorg101016jjsames201210010

Journal of South American Earth Sciences xxx (2012) 1e10

Please cite this article in press as Chaacutevarri E et al Hydrodynamic modelling of the Amazon River Factors of uncertainty Journal of SouthAmerican Earth Sciences (2012) httpdxdoiorg101016jjsames201210010



THMB (Terrestrial Hydrology model with Biogeochemistry) inrelation to the velocity equation to include the sinuosity of the river

in the calculation of the forces of resistance and incorporatesa roughness empirical equation of data from 30000 measurementsof the river morphology to determine the 1047298ood volume in manyplaces in the basin and ultimately represents the morphology of the

1047298oodplain 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 of

the water level of the river or the 1047298ood extension In terms of theriver stream1047298ow the propagation modelling are related to theinput data uncertainty eg DEM precision vegetation and crosssection geometry provided by geomorphologic relations (Paiva

et al 2011) Nonetheless in general there is limited informationon Amazonian river geometry stream1047298ow and water depths whichcreate uncertainty in the modelling of the 1047298ow pro1047297le Often timesattaining the necessary information for complex models involves

large 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 get

data 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 Radar

altimetry measures a weighted mean of all re1047298ecting bodies overa surface several square kilometres in size while gauges pick upriver stages at speci1047297c points Comparison at crossovers and withinsitu 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 toseveral metres in the worse cases in Amazon basin

Negrel et al (2011) suggest the possibility of calculating thestream1047298ow based exclusively on river surface variables accessible

through earth observation techniques namely river width levelsurface slope and surface velocity The main hypothesis presentedin the former study considered steady 1047298ow and rectangular shaped

cross-sectionsIn the present study we examine more speci1047297cally the uncer-

tainty of stream1047298ow modelling induced by the lack of informationon channel cross section geometry and the accuracy of radaraltimetry The main objective is to 1047297x which radar altimetry accu-

racy and channel geometry data are required to improve stream-1047298ow modelling of Amazonian rivers of different sizes To test if current radar altimetric data are relevant in Amazonian contextsimulation of waterlevel on Amazon and Napo Rivers are compared

with 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 quanti1047297ed the sensitivity of the variables waterdepth ( y) longitudinal stream1047298ow (Q ) bankfull width (w) andvelocity (v) according to the variability of input parameters the

cross section geometry Manning roughness coef 1047297cient (n) andlongitudinal slope of the river (s) This shows how the hydrody-namic model response is related to the level of uncertainty of input

parameters 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 applying

the same 1-Dhydrodynamic model to the Amazon and Napo RiversThe stream1047298ow model is an original 1-Dhydrodynamic model to

simulate unsteady stream1047298ow in anabranching river form such asthe Amazon River and Napo River In the following text we present

themain equationsand hypothesis relative to this numerical model

21 Hydrodynamic model description

Model inputs are water depth 1047298uctuation at the upstreamboundary longitudinal slope Manning coef 1047297cient riverbedgeometry of several cross sections of the river and the sequence of islands The minimum number of cross sections is de1047297ned by the

longitudinal sequence of dif 1047298uent and convergent channels form-ing one or several islands on the stream path One island is de1047297nedfor cross section one before the upstream divergent 1047298ow two foreach branch of the river on each side of the island and one after the

downstream convergence Channel reaches without islands arede1047297ned 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 relativelycomplete database on riverbathymetry Usuallysuch database is not available for Amazonian rivers To overpass thelack of information on river bathymetry we characterize the

geometry of each cross section with a surrogate parameter a tosimulate the relation channel width versus water depth (see x 22)

Note that this model does not simulate 1047298ood All simulated

water level stay below the upper limit of bankfull level Manning

roughness coef 1047297cient 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 the

riverbed does not change We suppose that erosion and sedimen-tation processes on the riverbed do not change signi1047297cantly thelongitudinal 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 de1047297ned at each cross sectionSimulations are done with a classical 1-D-hydrodynamic model

This model 1047297nds simultaneous solutions of the continuity andmomentum equations (Equations (1) and (2)) proposed by Barre de

Saint-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 hydrostatic

pressures mild slopes and a sediment velocity that is equal to the1047298ow mean velocity

v y

vt thorn

1

w

vQ

v x frac14

q

wv x (1)

where q is lateral stream1047298ow [L 3T1] x is the length between two

cross sections [L] and t is the time [T]

fvQ

vt thorn f

v

v x

b

Q 2

A

thorn gA

v y

v xthorn gAS f frac14 bqvL (2)

where S f is the energy line slope (friction slope) g is the accelera-

tion due to gravity [LT2] A is cross-sectional area of the stream-

1047298ow [L 2

] vL is the velocity of the lateral stream1047298ow that is in thesame direction as the principal stream1047298ow of the river f is theLocal partial inertial factor (Fread et al 1986) b is the Boussinesq

coef 1047297cientEquations (1) and (2) are solved under the Preissmann numer-

ical scheme It offers the advantage that a variable spatial grid may

be used steep wave fronts may be properly simulated by varyingthe weighting coef 1047297cient of the time interval q and weightingcoef 1047297cient of the space interval f and the scheme yields an exactsolution of the linearized form of the governing equation for

a particular value of D x 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 depths

around theislandsare thesame However in thisstudy weconsidered

E Chaacutevarri et al Journal of South American Earth Sciences xxx (2012) 1 e102




the hydrodynamic equations for internal boundary conditionsapplied to sections with islands as described in Equation (1) and

energy 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 thorn 1

2 g fi1

Q i1

Ai1

2

frac14 yi thorn 1

2 g fi

Q i

Ai

2

(3)

yi2 thorn 1

2 g

fi2

Q i2 Ai2

2

frac14 yi thorn 1

2 g

fi

Q i Ai

2

(4)

where Q i1 and Q i2 stream1047298ows in both side of the island yi1 and

yi2 water depth in both side of the island Q i stream1047298ow in thecon1047298uence yi water depth in the con1047298uence

The spatial and temporal resolution of the model takes intoaccount the Courant condition For one-dimensional equations the

Courant number or also known as the Courant Friedrichs and Lewy(CFL) number is de1047297ned as Abbott (1979)

C frac14 ju c jDt

D x

1 (5)

where C Courant number u Medium 1047298ow velocity (LT1) c Flowcelerity (LT1) D xDt the numeric Celerity (LT1)

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

celerity

C frac14 c

D x

Dt

(6)

The last equation (Courant number) is very important forthe application of numeric solutions since it allows us to calculate

D xDt 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 023 (C z

023) toassure stability Consequently once the spatial resolution (D x) isde1047297ned according to the stretch singularities and knowing the

celerity the temporal resolution (Dt ) is determinedAccording to the mathematical description of the model in

addition to input parameters n s and a there are 1047297ve moreparameters (C b f q 4) All the former parameters are calibrated

on a well-documented in-situ stream1047298ow context (see x24)

22 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 wesuppose that the variability of the depth is linearly related to thevariability of the cross section width following the Equation (7)

a frac14 Dw

D y (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

E Chaacutevarri et al Journal of South American Earth Sciences xxx (2012) 1 e10 3






where M Total cases D Total days V output Model variable in thedownstream V reference Model variable forafrac14 106 n frac14 0035 sm1

3 s frac14 007 mkm

24 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 aspectsThe River Napo is mainly located in the foothills of the Amazon

basin and the stretch of the River Amazon of this study is located inthe plain (Fig 1a) both with different 1047298ow regimes and longitu-dinal slope (Table 1)

The simulation of the River Amazon in the Peruvian sector was

conductedfrom thecon1047298uence of the Napo and the River Amazon atthe Francisco de Orellana (FOR)station to the Tabatinga (TAB) stationin Brazil Hydrometric and bathymetry information is only availablesince 2002 for the TAB and Tamshiyacu (TAM) stations due to the

lack of data at FOR However cross sectiongeometry at TAM is a goodproxy of the cross section geometry at FOR and by adding stream-

1047298ows of the Bellavista station (BEL) at the outlet of Napo and TAMThe Napo River hydrodynamic simulation was carried out in the

section 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

upstream of the TEMP where there is an island with radar altimetrydata on both sides of it Stream1047298ow and water level information isavailable since 2002 at ROC At TEMP only radar altimetry infor-

mation is availableFor both rivers a sequence of cross sections (nodes) de1047297ne the

spatial resolution of the river stretch used for the simulations(Fig 1b and c) Note that two parallel nodes de1047297ne an islandrsquos

con1047297guration Tables B1 and C1 of Appendix B and C respectivelysummarize 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 the1047297eld

Longitudinal slopes of Amazon and Napo are supposed to besigni1047297cantly constant and equal to 007 mkm and 017 mkm

respectively Manning coef 1047297cient is supposed to be constant forboth rivers with a value of 0035 sm13 a set values are de1047297ned 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 beconstant whatever the Amazon or Napo con1047297guration 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 thedataset is used for the validation (Fig 3a and b) The goodness of 1047297t

methodologies is evaluated by the Nash and Sutcliffe ef 1047297ciency (E )and Root Mean Squared Error (RMSE) these being indicators of

Table 2

General 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 7486 129 29 sept 2002 to 17 oct 2010 770 58006180 Island

Amazon 164 704 379 06 oct 2002 to 18 sept 2010 3212 58000 Reach

837 716 377 24 sept 2002 to 12 oct 2010 1639 32600 Reach

794 725 352 01 dec 2002 to 10 oct 2010 315 490021100 Island

Fig 4 The sensitivity of model variables according to the Riverbed geometry

sensitivity (a) For a frac14

106

52 and (b) For a frac14

212

52

Fig 5 The sensitivity of model variables according to (a) the Manning roughness

coef 1047297

cient and (b) Longitudinal slope





model error The Nash and Sutcliffe ef 1047297ciency (E ) i s d e1047297nedfollowing Equation (9) (Krause et al 2005)

E frac14 1

PN 1 ethOi P iTHORN

2

PN 1

Oi O

2 (9)

where Oi Observed value P i Predicted value O Mean observedvalue N the numberof observations The range of E lies between 10

(perfect 1047297t) and in1047297nity For the Amazon River simulation therearefewcases with signi1047297cant differences between Q and P for during

1047298oods However E equals 095 and validates the global modelresponse and speci1047297cally the calibration of the internal parameters

The radar altimetry elevation ( yr ) information is collected by theENVISATmissionderived fromexistingrange datapublicly released byESA(EuropeanSpace Agency)Themanual method describedin Santosda Silva et al 2010 and Roux et al (2010) has been used to de1047297ne the

virtual stations wherethe time seriesof thewaterlevelvariationsfromthe radar measurements can be quanti1047297ed We retained the medianand associated mean absolute deviation to construct the time seriesThegeoid undulation is removed to theheight 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





solution (Tapley et al 2004) This study analyses four Envisat satellitetracks that cross theAmazon andNapo Riversand have been providing

data since 2002(Table2)Thesetrackshavebeenchoseninamannertoexplore the in1047298uence of the river width on hr uncertainties and crosstherivers at sections with and without islands Extreme values of riverwidth are 1020 m and 14860 m

3 Results

31 Model sensitivity to input parameters

According to the results of the sensitivity tests w is the mostsensitive output variable to eitherinput upstream1047298oworeithertothe

variability 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 handthere is no sensitivity of w to n and s The of variability comes fromthe distribution of a and do not showanyspeci1047297c trend when n and schange (Fig5a andb) Channelgeometry parameterizationis then the

1047297rst parameter which controls the model response to upstream 1047298ow

32 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 versus

yr shows a signi1047297cant linear trend with linearcorrelation coef 1047297cients

between 064 and 093 (Fig 6eeh) The coef 1047297cient of the lineartrends varies from 06 to 11 Note that a slope coef 1047297cient between yversus yr is smaller than 1 whichmeans that the amplitude of the yr

variationis higherthan the amplitude of the y values and thereforemarks 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 de1047297nitely less rele-

vant than y values because the latterhas been validated with in-situmeasurements 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-situvalidation we cannot reject that y value mayhave a systematic biasHowever 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 wet

cross section area and to a lesser extent the water velocity throughthe section The relationship between the wetted area and the

water depth is then one of the most important input data of our 1-Dhydrodynamic model To simulate this relationship we propose

using the coef 1047297cient 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 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 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 on

the 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 assumptionstheir mathematical formulation or numerical resolution Never-

theless the validationwith physical data is thereforefundamental totest the model Two types of validation data have been used tovalidate the model First we used in-situ measurements of waterlevel and stream1047298ow at the Tabatinga gauging station on the

Amazon River usinga half of the data tocalibrate the model Despitefew non-negligible discrepancies the simulated water level andstream1047298ow variations 1047297t the in-situ measurement variations for a 3

year period This suggests that our model is appropriate to simulate

water level and stream1047298ow simulation Second we compare simu-lated water levels with radar altimetric data at four sections withdifferent widths on the Amazon and Napo Rivers Simulated water

level 1047297t correctlyagain with the radar altimetry measurements 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 thesection width is toosmallthe 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 Manningcoef 1047297cient or channel longitudinal slope the validation procedure

should be focused on the channel width and water velocity varia-tions 1047297tting 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 numerous

section along Amazonian rivers is still a challenge speci1047297cally inareas with sparse population

Acknowledgements

This study was sponsored by the Environmental ResearchObservatory (ORE) HYBAM (Geodynamical hydrological andbiogeochemical control of erosionalteration and material transport

in the Amazon basin) whichhas been operates in Peru since2003 A

scienti1047297c cooperation agreement between the L rsquoInstitut de Recher-

che pour le Deacuteveloppement (IRD-France) and the UniversidadNacional Agraria La Molina (UNALM-Peru) as of 2005 allowing the

participation of master and doctorate programs for students inproject ORE-HYBAM ORE-HYBAM was proposed by team of LMTGscholars (Laboratoire des Meacutecanismes de Transferts en Geacuteologie-

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 de1047297ne a synthetic

shape parameter a in order to quantify the wetted section

Fig 7 Linear coef 1047297cient between the simulated elevation and radar altimetry

elevation versus width river





variability in terms of water depth variability Rivers sectionsgeometries do not correspond to univocal values of a Sections with

different geometries can have the same value of a In this study weassume that each river section can be described by a signi1047297cant

a value To validate this hypothesis we have studied a database of ADCP pro1047297les from the Hybam project acquired during a 1047297eld

campaignon the Napo river from ROC station to BELstation (Fraizy2004) 52 pro1047297les of section bathymetry were measured fromupstream to downstream along 3800 km

Fig A1 shows the variability of w versus h for all pro1047297les

between ROC and TEMP stations (34 sections) Linear regressionsquality varies with coef 1047297cients of correlation R2 from 041 to 095The distribution of R2 shows that the linear model of w versus hrelationship has a statistical signi1047297cance (Fig A1 inset) Thereafter

a is calculated regardless R2 value

Fig A2 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 distributionwitha sigma of 52 (Fig A2 inset) a variability

suggests that this shape parameter is a local parameter with anaverage and standard deviation that have to be de1047297ned empiricallyNapo River a values are used as the reference in the 1-D hydro-dynamic model sensitivity analysis A much larger sample of rivers

sections throughout the Amazon basin should be analysed to de1047297neif a follows a continental scale trend

B Amazon River information

Fig A1 Relationship of width versus depth 1047298ow for all pro1047297les between Rocafuerte

Station and Tempestad station and the coef 1047297cients of correlation R2 calculated

Fig A2 Normal variability of a from upstream to downstream (a) Nuevo Rocafuerte

station (b)Tempestad located(c) SantaClotilde station and(d) BellavistaMazaacuten station

Table B1

Amazon River geometry used for the hydrodynamic model

Nodes (52) Downstream

reach length (m)

Width (m) Elevation (m)

Francisco de Orellana Station 130352 3423 88

Island 17 left side 213091 223 876

Island 17 right side 213091 2901 876

PT15 108308 4743 866

Island 16 left side 75771 2248 86Island 16 right side 75771 2038 86

PT14 126649 3669 856



PT13 54115 3982 845Island 14 left side 49215 1222 827


PT12 29529 4384 821


Island 13 right side 89914 2251 798PT11 109257 3205 765



PT10 120867 2467 741



PT9 29134 2929 715




Island 9 right side 39484 1827 71PT7 173091 8076 709Island 8 left side 154478 3266 708


PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644




Island 1 right side 74158 2677 63Tabatinga station 0 4856 625





C Napo River information

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Asner GP Alencar N 2010 Drought impacts on the Amazon forest theremote sensing perspective New Phytologist httpdxdoiorg101111j1469-8137201003310x

Beighley RE et al 2009 Simulating hydrologic and hydraulicprocesses throughout the Amazon River Basin Hydrological Processes 23 (8)1221e1235

Bourrel L et al 2009 Estudio de la relacioacuten entre la pendiente de los riosobtenidas a partir de mediciones DGPS y la distribucioacuten de la granulometriacutea portres tributarios andinos del riacuteo Amazonas el caso de los rios Beni (Bolivia)

Napo (Ecuador-Peruacute) y Marantildeon (Perugrave) Tercera reunioacuten cientiacute1047297

ca del

Observatorio de Investigacioacuten del Medio Ambiente sobre los riacuteos Amazoacutenicos(ORE) HYBAM Tabatinga (Brasil) amp Leticia (Colombia)

Callegravede J et al 2010 Les apports en eau de l rsquoAmazone agrave lrsquoOceacutean Atlantique Revue

des Sciences de lrsquo

Eau Journal of Water Science 23 (3) 247e

273Coe M et al 2007 Simulating the surface waters of the Amazon River basinimpacts of new river geomorphic and 1047298ow parameterizations HydrologicalProcesses httpdxdoiorg101002hyp6850

Collischonn W 2001 Simulaccedilatildeo hidroloacutegica de grandes bacias PhD thesis (inPortuguese) Instituto de Pesquisas Hidraacuteulicas Universidade Federal do RioGrande do Sul Porto Alegre Brazil p 194

Collischonn et al 2008 Daily hydrological modeling in the Amazon basin usingTRMM rainfall estimates Journal of Hydrology 360 (1e4) 207e216

Cunge JA et al 1980 Practical Aspects of Computational River Hydraulics Insti-tute of Hydraulics Research College of Engineering University of Iowa USA

de Saint-Venant Barre 1871 Theorie du Mouvement Non-permanent des Eaux avecApplication aux Crues des Rivieres et l rsquo Introduction des Vareacutees dans leur Lit InCompetes Rendus Hebdomadaires des Seances de lrsquo Academie des ScienceParis France vol 73 148e154

ENVISAT Goid EGM 2008 NOAArsquos National Geodetic Survey USA httpearth-infongamilGandGwgs84gravitymodegm2008

Espinoza JC et al 2009 Contrasting regional discharge evolutions in the Amazonbasin (1974e2004) Journal of Hydrology 375 297e311 httpdxdoio rg

101016jjhydrol200903004Espinoza JC et al 2011 Climate variability and extreme drought in the upper

Solimotildees River (western Amazon Basin) understanding the exceptional 2010drought Geophysical Research Letters vol 38 L13406 httpdxdoiorg1010292011GL047862

Fraizy P 2004 Reporte de la campantildea EQ 52 (PE 16) Riacuteo Napo e Octubre 2004Environmental Research Observatory (ORE) HYBAM

Fread et al 1986 An LPI numerical implicit solution for unsteady mixed 1047298owsimulation In North American Water and Environmental Congress DestructiveWater ASCE

Getirana et al 2010 Hydrological modelling and water balance of the Negro Riverbasin evaluation based on in situ and spatial altimetry data HydrologicalProcesses httpdxdoiorg101002hyp7747

Krause P et al 2005 Comparison of different ef 1047297ciency criteria for hydrologicalmodel assessment Advances in Geosciences 5 89e97 SRef-ID 1680-7359adgeo2005-5-89

Latrubesse E 2008 Patterns of anabranching channels the ultimate end-memberadjustment of mega rivers Geomorphology 101 (1e2) 130e145 1 October2008 httpdxdoiorg101016jgeomorph200805035

Lewis et al 2011 The 2010 Amazon drought Science 311 554 httpdxdoiorg101126science1200807

Negrel J et al 2011 Estimating river discharge from earth observationmeasurement of river surface hydraulic variables Hydrology and Earth SystemSciences Discussions 7 7839e7861 httpdxdoiorg105194hessd-7-7839-2010 2010 wwwhydrol-earth-syst-sci-discussnet778392010

Paiva R et al 2011 Large scale hydrologic and hydrodynamic modeling usinglimited data and a GIS based approach Journal of Hydrology 406 170e181httpdxdoiorg101016jjhydrol 201106007

Phillips OL et al 2009 Drought sensitivity of the Amazon rainforest Science 3231344e1347

Ponce V 2002 Milestone of Hydrology httpponcetvmilestoneshtmlRibeiro A et al 2005 Hydrological modelling in Amazoniaduse of the MGB-IPH

model and alternative data base In Sivapalan M Wagener T Uhlenbrook SZehe E Lakshmi V Liang Xu Tachikawa Y Kumar P (Eds) Prediction inUngauged Basins Promises and Progress Proc Foz do Iguaccedilu Symp 2006 I AHSPress Wallingford UK pp 246e254 IAHS Publ 303

Roux E et al 2010 Producing time-series of river water height by means of

satellite radar altimetry e

comparison of methods Hydrological Sciences

Table B2

ENVISAT radar altimetry information (geoid EGM2008)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

02 December 2002 8210 11 May 2004 8249 30 January 2006 8203 13 August 2007 7610

06 January 2003 8255 15 June 2004 8233 06 March 2006 8246 17 September 2007 7651

10 February 2003 8162 20 July 2004 8148 10 April 2006 8446 22 October 2007 7606

21 April 2003 8344 24 August 2004 7706 24 July 2006 8200 26 November 2007 8184

26 May 2003 8481 02 November 2004 7983 28 August 2006 7680 31 December 2007 820030 June 2003 8348 07 December 2004 8216 02 October 2006 7595 04 February 2008 8243

04 August 2003 7809 10 January 2005 8144 06 November 2006 7755 11 March 2008 8352

08 September 2003 7732 14 February 2005 8119 11 December 2006 8197 15 April 2008 835913 October 2003 7827 21 March 2005 8243 15 January 2007 8324 20 May 2008 8280

17 November 2003 8024 25 April 2005 8375 19 February 2007 8233 24 June 2008 8106

22 December 2003 8212 30 May 2005 8067 26 March 2007 8280 29 July 2008 7938

26 January 2004 8139 17 October 2005 7552 20 April 2007 8394 02 September 2008 8029

02 March 2004 8021 21 November 2005 7978 04 June 2007 8264 07 October 2008 8007

06 April 2004 8241 26 December 2005 7972 09 July 2007 7992

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

Table C1

Napo River geometry used for the hydrodynamic model


reach length (m)


Cabo Pantoja station 35014 11563 1655



PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158

Island Tempestad left side 35643 3442 157

Island Tempestad right side 35643 4032 157

Tempestad place 35643 1000 1565





Journal Journal des Sciences Hydrologiques 55 (1) 104e120 httpdxdoiorg10108002626660903529023

Saleska SR et al 2007 Amazon forests green-up during 2005 drought Science318 612 httpdxdoiorg101126science1146663

Santos da Silva J et al 2010 Water levels in the Amazon Basin derived from theERS-2-ENVISAT radar altimetry missions Remote Sensing of Environment 114(10) 2160e2181 httpdxdoiorg101016jrse201004020

Tapley B et al 2004 The gravity recovery and climate experiment missionoverview and early results Geophysical Research Letters 31 L09607 httpdxdoiorg1010292004GL019920

Trigg Met al 2009 Amazon1047298ood wave hydraulics Journal of Hydrology 374 92e105Xu et al 2011 Widespread decline in greenness of Amazonian Vegetation due to

the 2010 drought Geophysical Research Letters 38 (L07402) 4 httpdxdoiorg1010292011GL046824


Please cite this article in press as Chaacutevarri E et al Hydrodynamic modelling of the Amazon River Factors of uncertainty Journal of South



THMB (Terrestrial Hydrology model with Biogeochemistry) inrelation to the velocity equation to include the sinuosity of the river

in the calculation of the forces of resistance and incorporatesa roughness empirical equation of data from 30000 measurementsof the river morphology to determine the 1047298ood volume in manyplaces in the basin and ultimately represents the morphology of the

1047298oodplain 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 of

the water level of the river or the 1047298ood extension In terms of theriver stream1047298ow the propagation modelling are related to theinput data uncertainty eg DEM precision vegetation and crosssection geometry provided by geomorphologic relations (Paiva

et al 2011) Nonetheless in general there is limited informationon Amazonian river geometry stream1047298ow and water depths whichcreate uncertainty in the modelling of the 1047298ow pro1047297le Often timesattaining the necessary information for complex models involves

large 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 get

data 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 Radar

altimetry measures a weighted mean of all re1047298ecting bodies overa surface several square kilometres in size while gauges pick upriver stages at speci1047297c points Comparison at crossovers and withinsitu 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 toseveral metres in the worse cases in Amazon basin

Negrel et al (2011) suggest the possibility of calculating thestream1047298ow based exclusively on river surface variables accessible

through earth observation techniques namely river width levelsurface slope and surface velocity The main hypothesis presentedin the former study considered steady 1047298ow and rectangular shaped

cross-sectionsIn the present study we examine more speci1047297cally the uncer-

tainty of stream1047298ow modelling induced by the lack of informationon channel cross section geometry and the accuracy of radaraltimetry The main objective is to 1047297x which radar altimetry accu-

racy and channel geometry data are required to improve stream-1047298ow modelling of Amazonian rivers of different sizes To test if current radar altimetric data are relevant in Amazonian contextsimulation of waterlevel on Amazon and Napo Rivers are compared

with 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 quanti1047297ed the sensitivity of the variables waterdepth ( y) longitudinal stream1047298ow (Q ) bankfull width (w) andvelocity (v) according to the variability of input parameters the

cross section geometry Manning roughness coef 1047297cient (n) andlongitudinal slope of the river (s) This shows how the hydrody-namic model response is related to the level of uncertainty of input

parameters 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 applying

the same 1-Dhydrodynamic model to the Amazon and Napo RiversThe stream1047298ow model is an original 1-Dhydrodynamic model to

simulate unsteady stream1047298ow in anabranching river form such asthe Amazon River and Napo River In the following text we present

themain equationsand hypothesis relative to this numerical model

21 Hydrodynamic model description

Model inputs are water depth 1047298uctuation at the upstreamboundary longitudinal slope Manning coef 1047297cient riverbedgeometry of several cross sections of the river and the sequence of islands The minimum number of cross sections is de1047297ned by the

longitudinal sequence of dif 1047298uent and convergent channels form-ing one or several islands on the stream path One island is de1047297nedfor cross section one before the upstream divergent 1047298ow two foreach branch of the river on each side of the island and one after the

downstream convergence Channel reaches without islands arede1047297ned 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 relativelycomplete database on riverbathymetry Usuallysuch database is not available for Amazonian rivers To overpass thelack of information on river bathymetry we characterize the

geometry of each cross section with a surrogate parameter a tosimulate the relation channel width versus water depth (see x 22)

Note that this model does not simulate 1047298ood All simulated

water level stay below the upper limit of bankfull level Manning

roughness coef 1047297cient 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 the

riverbed does not change We suppose that erosion and sedimen-tation processes on the riverbed do not change signi1047297cantly thelongitudinal 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 de1047297ned at each cross sectionSimulations are done with a classical 1-D-hydrodynamic model

This model 1047297nds simultaneous solutions of the continuity andmomentum equations (Equations (1) and (2)) proposed by Barre de

Saint-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 hydrostatic

pressures mild slopes and a sediment velocity that is equal to the1047298ow mean velocity

v y

vt thorn

1

w

vQ

v x frac14

q

wv x (1)

where q is lateral stream1047298ow [L 3T1] x is the length between two

cross sections [L] and t is the time [T]

fvQ

vt thorn f

v

v x

b

Q 2

A

thorn gA

v y

v xthorn gAS f frac14 bqvL (2)

where S f is the energy line slope (friction slope) g is the accelera-

tion due to gravity [LT2] A is cross-sectional area of the stream-

1047298ow [L 2

] vL is the velocity of the lateral stream1047298ow that is in thesame direction as the principal stream1047298ow of the river f is theLocal partial inertial factor (Fread et al 1986) b is the Boussinesq

coef 1047297cientEquations (1) and (2) are solved under the Preissmann numer-

ical scheme It offers the advantage that a variable spatial grid may

be used steep wave fronts may be properly simulated by varyingthe weighting coef 1047297cient of the time interval q and weightingcoef 1047297cient of the space interval f and the scheme yields an exactsolution of the linearized form of the governing equation for

a particular value of D x 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 depths

around theislandsare thesame However in thisstudy weconsidered








yi1 thorn 1

2 g fi1

Q i1

Ai1

2

frac14 yi thorn 1

2 g fi

Q i

Ai

2

(3)

yi2 thorn 1

2 g

fi2

Q i2 Ai2

2

frac14 yi thorn 1

2 g

fi

Q i Ai

2

(4)





C frac14 ju c jDt

D x

1 (5)



celerity

C frac14 c

D x

Dt

(6)












a frac14 Dw

D y (7)











3 s frac14 007 mkm



















Table 2



Latitude() WGS84

Longitude() WGS84


Widthapprox (m)

Observation



837 716 377 24 sept 2002 to 12 oct 2010 1639 32600 Reach

794 725 352 01 dec 2002 to 10 oct 2010 315 490021100 Island



106


212

52


coef 1047297







E frac14 1

PN 1 ethOi P iTHORN

2

PN 1

Oi O

2 (9)








837 e








3 Results

































Acknowledgements







Appendices

























Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158





















yi1 thorn 1

2 g fi1

Q i1

Ai1

2

frac14 yi thorn 1

2 g fi

Q i

Ai

2

(3)

yi2 thorn 1

2 g

fi2

Q i2 Ai2

2

frac14 yi thorn 1

2 g

fi

Q i Ai

2

(4)





C frac14 ju c jDt

D x

1 (5)



celerity

C frac14 c

D x

Dt

(6)












a frac14 Dw

D y (7)











3 s frac14 007 mkm



















Table 2



Latitude() WGS84

Longitude() WGS84


Widthapprox (m)

Observation



837 716 377 24 sept 2002 to 12 oct 2010 1639 32600 Reach

794 725 352 01 dec 2002 to 10 oct 2010 315 490021100 Island



106


212

52


coef 1047297







E frac14 1

PN 1 ethOi P iTHORN

2

PN 1

Oi O

2 (9)








837 e








3 Results

































Acknowledgements







Appendices

























Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158





















3 s frac14 007 mkm



















Table 2



Latitude() WGS84

Longitude() WGS84


Widthapprox (m)

Observation



837 716 377 24 sept 2002 to 12 oct 2010 1639 32600 Reach

794 725 352 01 dec 2002 to 10 oct 2010 315 490021100 Island



106


212

52


coef 1047297







E frac14 1

PN 1 ethOi P iTHORN

2

PN 1

Oi O

2 (9)








837 e








3 Results

































Acknowledgements







Appendices

























Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158



















3 s frac14 007 mkm



















Table 2



Latitude() WGS84

Longitude() WGS84


Widthapprox (m)

Observation



837 716 377 24 sept 2002 to 12 oct 2010 1639 32600 Reach

794 725 352 01 dec 2002 to 10 oct 2010 315 490021100 Island



106


212

52


coef 1047297







E frac14 1

PN 1 ethOi P iTHORN

2

PN 1

Oi O

2 (9)








837 e








3 Results

































Acknowledgements







Appendices

























Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158



















E frac14 1

PN 1 ethOi P iTHORN

2

PN 1

Oi O

2 (9)








837 e








3 Results

































Acknowledgements







Appendices

























Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158




















3 Results

































Acknowledgements







Appendices

























Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158

































Table B1



reach length (m)





PT15 108308 4743 866


PT14 126649 3669 856





PT12 29529 4384 821





PT10 120867 2467 741



PT9 29134 2929 715






PT6 205561 2968 699



PT5 75936 2834 69



PT4 117901 3054 675


PT3 10080 4951 661



PT2 99194 2405 65



PT1 11152 2616 644










References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158



















References






ca del




























Table B2


Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)

Day Elevation(amsl)














Table C1



reach length (m)





PT8 52335 1000 1645



PT7 14711 800 1637





PT5 19921 1300 1631


PT4 21728 12207 1625



PT3 21136 980 1615


PT2 32338 730 1605


PT1 19864 500 1595



PT0 35643 750 158


























Documents

Hydrodynamic Modelling of the Amazon River Factors of Uncertainty