HYDROLOGICAL PROCESSES
Hydrol. Process. (2007)
Published online in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/hyp.6850
Simulating the surface waters of the Amazon River basin:
impacts of new river geomorphic and flow parameterizations
Michael T. Coe,1 * Marcos H. Costa2 and Erica A. Howard3
1
3
The Woods Hole Research Center, 149 Woods Hole Rd, Falmouth, MA 02540, USA
2 The Federal University of Viçosa, Viçosa, MG, Brazil
The Center for Sustainability and the Global Environment, Gaylord Nelson Institute for Environmental Studies, University of Wisconsin-Madison,
Madison, WI 53726, USA
Abstract:
This paper describes the impacts of new river geomorphic and flow parameterizations on the simulated surface waters dynamics
of the Amazon River basin. Three major improvements to a hydrologic model are presented: (1) the river flow velocity
equation is expanded to be dependent on river sinuosity and friction in addition to gradient forces; (2) equations defining
the morphological characteristics of the river, such as river height, width and bankfull volume, are derived from 31 622
measurements of river morphology and applied within the model; (3) 1 km resolution topographic data from the Shuttle
Radar Topography Mission (SRTM) are used to provide physically based fractional flooding of grid cells from a statistical
representation of sub-grid-scale floodplain morphology. The discharge and floodplain inundation of the Amazon River is
simulated for the period 1968–1998, validated against observations, and compared with results from a previous version of
the model. These modifications result in considerable improvement in the simulations of the hydrological features of the
Amazon River system. The major impact is that the average wet-season flooded area on the Amazon mainstem for the period
1983–1988 is now within 5% of satellite-derived estimates of flooded area, whereas the previous model overestimates the
flooded area by about 80%. The improvements are a consequence of the new empirical river geomorphologic functions and
the SRTM topography. The new formulation of the flow velocity equation results in increased river velocity on the mainstem
and major tributaries and a better correlation between the mean monthly simulated and observed discharge. Copyright  2007
John Wiley & Sons, Ltd.
KEY WORDS
Amazon; surface waters; modelling; floodplain morphology
Received 24 January 2007; Accepted 12 June 2007
INTRODUCTION
At 6Ð7 ð 106 km2 , with about 20% of global river runoff
and a massive floodplain system, the Amazon River basin
is an impressive hydrological system by any measure. In
addition to representing a large portion of the tropical
energy and water balance, its floodplain may be a
significant source of carbon to the atmosphere (Richey
et al., 2003). In this context, understanding floodplain
dynamics is fundamental, given its role in the flood wave
timing and in determining the CO2 outgassing area.
In the last few years, numerical models have begun to
integrate the functioning of the Amazon River system,
including its climatic, hydrologic, and biogeochemical
components (Coe et al., 2002; Foley et al., 2002; Richey
et al., 2003; Melack et al., 2004). These tools and the
knowledge derived are an important step towards a better
understanding of how this river system has responded
to natural climate variability and historical land-cover
changes and how it may respond to future land-cover
changes.
* Correspondence to: Michael T. Coe, The Woods Hole Research Center, 149 Woods Hole Rd, Falmouth, MA 02540, USA. E-mail:
[email protected]
Copyright  2007 John Wiley & Sons, Ltd.
A previous study (Coe et al., 2002) described a numerical model system for simulation of the Amazon landsurface hydrology, including river discharge, water level
and flood extent. The validation of the model results
against field measurements and remote-sensing products
indicated that, although basic hydrological characteristics
like discharge and water level are well simulated, the
flooding extension algorithm still needed improvements.
The authors identified three major sources of error in
their simulation of flooding in the Amazon: the simulated river discharge amount, the digital elevation model
(DEM) accuracy, and the floodplain initiation parameter.
Addressing these sources of error required modifications
of the model equations and development of new geophysical datasets.
In this paper we describe improvements to the basic
equations of the Terrestrial Hydrology Model with Biogeochemistry (THMB), describe a new river geomorphology dataset for the Amazon basin, and analyse the
impacts of these changes on the simulations of the surface water dynamics of the Amazon River basin. The
results are validated against observations of river discharge, floodplain inundation, and water height, and compared with the results obtained by Coe et al. (2002).
M. T. COE, M. H. COSTA AND E. A. HOWARD
MODEL DESCRIPTION
The THMB (which was formerly called HYDRA) is
forced by climate data and surface runoff and subsurface
drainage obtained by a land-surface hydrology model to
simulate the water balance of the Amazon River system. In this case, we use the same surface and subsurface runoff used by Coe et al. (2002), with corrections
(described below) to quantify the impact of the changes
made to THMB. Coe et al. (2002) model (hereinafter
termed THMBv1) and the runoff data are described in
Coe et al. (2002). Therefore, only a brief overview of
the structure of THMB will be provided, followed by a
thorough description of the improvements to the model
(THMBv2) and input data.
THMB is a distributed grid model at 50 horizontal resolution that has been developed, calibrated, and validated
specifically for the Amazon and Tocantins River basins,
as part of the NASA LBA-ECO project. The model
uses prescribed river paths and floodplain morphology,
derived from topographic data, linked to a set of linear reservoir equations describing the change with time
of the river and floodplain reservoirs. Mass in the river
and floodplain reservoirs is explicitly conserved. Variation of the total water within the stream at any point in
THMB is the sum of the land-surface runoff, subsurface
drainage, precipitation and evaporation over the surface
waters, and the flux of water from the upstream grid cells
and to the downstream cell. The flux to downstream cells
(discharge) is based on the volume of water in the river
reservoir and river geomorphic characteristics, like slope
and hydraulic radius. The inundation of the river floodplain is a function of the flux of water from the stream
channel to the floodplain, the vertical water balance, and
the geomorphic characteristics of the river and floodplain. The equations are solved with a 1 h time step. The
results of THMB are spatially explicit representations of
the (in-channel) river volume, stage and discharge, and
the (out-of-channel) floodplain volume, stage, and inundated area at the temporal resolution of the input data
(1 h to 1 month).
A number of improvements have been made to the
fundamental equations defining the river flow velocity
and floodplain inundation and to the geomorphic data
used as input to the model. The model improvements
and the new geomorphic data are described in detail in
the following sections.
River morphology
We use data collected by the Brazilian Water Agency:
Agência Nacional das Águas (ANA, www.ana.gov.br)
and the Hydrology and Geochemistry of the Amazon basin project HiBAm (www.ana.gov.br/hibam) to
develop general equations defining relationships between
channel width, bankfull volume, and upstream area that
could be applied to the entire Amazon basin. ANA data
are collected as follows: typically, every 3 months, sometimes more often, discharge measurement sites in Amazonia are visited by an engineer who measures the river
Copyright  2007 John Wiley & Sons, Ltd.
cross-section area, width and depth, the river flow velocity, and calculates the river discharge at that point. Raw
data include data collected at more than 300 stations
spread throughout the Amazon and Tocantins basins. Station records shorter than 5 years long or with fewer than
30 measurements are not used in this study. A thorough
analysis eliminated about 10% of the initial data that
are inconsistent (most of them because of typographical errors). The final dataset includes 31 622 observations
of stream morphology from 287 stations corresponding to upstream areas from on the order of 1 ð 102
to 1 ð 106 km2 . We also measured the river width on
920 acoustic Doppler current profiler images obtained
by the HiBam project for the mainstem of the Amazon with upstream areas ranging from 1Ð066 ð 106 to
5Ð751 ð 106 km2 .
A simple statistical relationship is obtained for the
width as a function of the drainage area upstream and
river depth. The equation describing the relationship and
the goodness of fit are
Wi D 0Ð421A0Ð592
r 2 D 0Ð87
!1"
where A !km2 " is the drainage area upstream of that
point and Wi (m) is the river width. Analysis of the data
shows that nearly all cross-sections can be assumed to be
rectangular because, at the large scale, the river width is
much greater than its depth.
Although the river height (stage) Hi at which flooding
begins to occur is usually part of the characterization
of an ANA fluviometric station, this information is not
easily available for the Amazonian stations. Therefore,
to determine Hi for each cross-section, river width is
plotted against the river stage for all available stations.
Hi is determined visually from these plots as the stage
when the width versus river stage curve changes slope
(the width begins to increase rapidly with small changes
in stage as the river leaves its channel). The equation
describing Hi as a function of the drainage area upstream
and the fit are
Hi D 0Ð152A0Ð400
r 2 D 0Ð95
!2"
These relationships are used within THMBv2, as
described in the following sections, to obtain the wetted
cross-sectional area of the stream, flow velocity, and the
river volume of the grid cell when flooding is initiated.
River discharge formulation
The discharge at a given time step and location is
defined as the volume of water in the river divided by
a river water residence time Tr (s). Tr is defined as the
ratio of the distance d (m) between centres of the local
and downstream grid cells and the effective velocity of
the water u (m s#1 ).
Tr D d/u
!3"
In this version of THMB, d is calculated as the
product of the latitude-weighted straight-line distance
Hydrol. Process. (2007)
DOI: 10.1002/hyp
SIMULATING SURFACE WATERS OF THE AMAZON RIVER BASIN
L (m) between the centres of the two communicating
grid cells, and the channel sinuosity cs , which is the
ratio of measured river path length to the latitudeweighted straight-line path length (determined for the
entire Amazon at 50 resolution by Costa et al. (2002)):
d D cs L
!4"
In THMBv1 the effective velocity is proportional to
an approximation of the surface water energy slope S
(unitless):
u D uo1 S0Ð5
!5"
The change with time of Wf (floodplain reservoir, m3 )
is the sum of the fluxes of water to the floodplain from
the
" river Fr and from all upstream floodplain grid cells
Ffi , and from precipitation minus evaporation over the
water surface !Pw # Ew "Af minus that transported to the
downstream floodplain grid cells Wf /Tf (all in m3 s#1 ).
r
if Wr > Wfi Ci
Fr D dW
dt #
$
!10"
r
Fr D min dW
if Wr $ Wfi Ci
dt , 0
!7"
Wr is the volume of water in the river reservoir, Wfi !m3 "
is the volume of the river at flood initiation and Ci is a
dimensionless parameter for tuning the flood initiation
(both are described below). Tf (s) is the flood-flow
residence time. When the river is above flood initiation
(Wr > Wfi Ci ), Fr can be either positive, indicating net
transport to the floodplain from the river, or negative,
indicating net transport to the river from the floodplain.
When the river volume is less than flood initiation !Wr $
Wfi Ci " Fr is constrained to be a maximum of zero;
therefore, flow can only occur from the floodplain to the
river.
Improvements from the original version are described
below and include: (i) calculation of the flood initiation volume from published data; (ii) derivation of
the floodplain flow velocity from a Chezy-like formula; (iii) representation of the sub-grid-scale morphology from high-resolution SRTM data; and (iv) definition
of floodable area from satellite observations.
S is calculated as in Coe02, but using the topographic
gradient from the higher resolution Shuttle Radar Topography Mission (SRTM) data. R is a ratio of the actual
wetted perimeter pc (m), calculated from Equation (1),
the water height in the river, and a reference wettedperimeter po (60 m):
Flood initiation volume. In THMBv1, Wfi is a simple
function of the mean annual river discharge of the cell.
In THMBv2, Wfi is the bankfull volume (determined as
the product of the river length in that grid cell d and the
mean river width Wi and height Hi from the bottom of
the stream channel at bankfull):
R D pc /po
Wfi D Hi Wi d
uo1 is the minimum effective velocity of the river
(0Ð27 m s#1 ). S, as by Miller et al. (1994), is a ratio of
the downstream topographic gradient ic (m m#1 ) and a
reference gradient io D 0Ð5 ð 10#4 m m#1 :
S D ic /io
!6"
This equation, however, causes a decreasing river flow
velocity u as the flow moves downstream, whereas the
reverse is observed. To correct this, in this version of the
model (referred to as THMBv2) the effective velocity
is based on a Chezy-like formula (Dunne and Leopold,
1978), which includes the influence of friction, in addition
to slope, on the velocity. In THMBv2, u is proportional
to the product of an effective energy slope of the water
S and effective hydraulic radius of the river R (unitless):
u D uo1 !RS"0Ð5
!8"
!11"
io , po and uo1 are tuned to match the flow data.
Hi and Wi are derived from Equations (1) and (2).
Floodplain inundation
Flood flow velocity. The flood-flow residence time Tf
is also calculated with Equation (3), but the individual
parameters governing the flow velocity are based on the
physical characteristics of the water on the floodplain.
Whereas S and uo1 are the same as in Equations (4) and
(7), R is approximated by a ratio of the floodplain wetted
perimeter pfc (m, flooded fraction times total cell length
shared with downstream cell) and a reference perimeter
pfo (m, 0Ð1 ð total cell length):
The floodplain volume in THMBv2 is calculated using
the same basic set of equations as those used in THMBv1.
The floodplain and river reservoirs are represented by
parallel sets of equations in which the volume of river
water in excess of river bankfull volume (flood initiation
volume) is added to the floodplain reservoir. Once
on the floodplain, water flows across the land surface
to neighbouring grid cells. Flow direction across the
floodplain is not prescribed, as with the river. Instead, it is
calculated each time step, as the direction corresponding
to the maximum water slope between neighbouring grid
cells.
In THMBv2, the storage and transport of water on
the floodplain is represented by the following differential
equation:
!
dWf
Wf
Ffi C !Pw # Ew "!Af " #
!9"
D Fr C
dt
Tf
Copyright  2007 John Wiley & Sons, Ltd.
R D pfc /pfo
!12"
Grid- and sub-grid-scale morphology. An accurate
simulation of the flooded area depends on an accurate
representation of the surface morphology. THMBv2 uses
the 90 m horizontal resolution SRTM elevation data (Farr
et al., 2007) to represent the surface morphology of the
Amazon rather than the Global DEM5 (GETECH, 1995)
50 resolution digital elevation model used in THMBv1.
Hydrol. Process. (2007)
DOI: 10.1002/hyp
M. T. COE, M. H. COSTA AND E. A. HOWARD
The absolute vertical accuracy of the SRTM data
is estimated to be about š6 m, with relative errors
believed to be less (Smith and Sandwell, 2003). The
height reported in the data is a measure of the centre
of scattering within the vegetation canopy. It is not
a direct measurement of the bald land surface, unless
no vegetation is present. The height reported, therefore,
is a complex function of canopy density and other
land-surface characteristics (Kellndorfer et al., 2004).
Abrupt vegetation discontinuities, such as patchwork
clear-cutting, produce errors that are clearly visible upon
close regional inspection. We attempted to remove the
absolute error introduced by the canopy height in the
following way. The 90 m data are averaged to 1 km
horizontal resolution and a value of 23 m (assumed to be
the mean height of the centre of scattering) is subtracted
from the SRTM 1 km data wherever satellite-derived
data (Hess et al., 2003: for the central Amazon; and
Eva et al., 2002: for the rest of the Amazon basin)
indicate that forest is the predominant vegetation type.
This coarse attempt at forest removal reduces many of the
discontinuities, particularly along the edge of the river in
the central Amazon.
A 50 -resolution topographic dataset is created by averaging the 1 km values and by filling the sinks in ArcInfo
software. This 50 elevation dataset is the mean elevation to which the sub-grid anomalies described below are
applied. It replaces a much less accurate version used in
THMBv1.
The 1 km SRTM data product is used within THMBv2
to calculate the fractional flooding of each individual 50
grid cell. The fraction of the cell flooded at each time step
is approximated using a cumulative distribution function
derived from the 1 km resolution SRTM data and the
volume of water in each 50 grid cell. It is calculated using
the following two-step procedure.
First, the volume of water in the floodplain reservoir
Wf for each grid cell is expressed as the critical value
zx on the probability distribution curve of the 1 km
topography:
%
&
Wf
zx D log
!13"
W50
where W50 !m3 " is the volume corresponding to half
of the potential cell volume. zx is positive when the
floodplain volume is greater than 50% of the potential cell
volume (Wf > W50 ), negative when the volume is less
than 50% of the potential volume (Wf < W50 ), and zero
when equal to 50% of the potential volume Wf D W50 .
Second, the cumulative distribution P!zx " is calculated
by numerically integrating the normal probability density
function p!z" of the sub-grid-scale topography from z D
#4# to zx (it is assumed that P!#4#" D 0). The fractional
area of a grid cell inundated Af by a given water volume
Wf is simply P!zx ". For example, if Wf D W50 , then
zx D 0 and P!zx " D 0Ð5 and, therefore, 50% of the cell
is flooded.
The average depth of the floodwaters Df (m) is the
ratio of the volume of water on the floodplain over the
Copyright  2007 John Wiley & Sons, Ltd.
flooded area of the grid cell:
Df D Wf !Af At "#1
!14"
where At !m2 " is the total cell area. The average height
of the floodwaters Hf (m) is calculated as the sum of Df
and the mean land-surface elevation Z (m a.s.l.) of that
50 cell:
!15"
Hf D D f C Z
The floodplain flow direction is determined each time
step by finding the single neighbouring cell (of eight
possible) for which the difference between local and
neighbouring Hf is greatest.
THMBv1 has no sub-50 topographic data. Fractional
flooded area is derived in THMBv1 as a simple linear
function of water depth. The statistical representation of
the sub-grid-scale topography in THMBv2 adds greater
geophysical reality to the factors controlling the simulated
fractional area, depth, and height of water.
Maximum floodable area. Despite the corrections
made, the composite nature of the SRTM topography may
introduce errors in the determination of the flooded area.
To avoid runaway flooding in pixels where the vegetation
correction is inaccurate, we constrain flooding to only
those locations where high-resolution satellite imagery
has demonstrated that flooding is appropriate.
An estimate of the maximum floodable area of the
entire Amazon basin, excluding the Tocantins/Araguaia
basins was prepared from synthetic aperture radar
imagery acquired by the Japanese Earth Resources
Satellite-1 (JERS-1; Hess et al., unpublished data). The
1 km resolution floodable area binary mask (0/1) created
by Hess et al. is summed to the 50 resolution of THMB
and this potential floodplain fraction mask is used as input
to THMB. At each time step, water in the floodplain
reservoir is allowed to flow into a neighbouring grid cell
only if that cell has a fractional water area less than the
potential floodplain fraction.
Although this constraint contributes to the overall
better simulation of the flooded area, the maximum
floodable area was determined from imagery acquired in
May–July 1996, during the high-water season, and may
be a limit to the correct simulation of flooding events that
exceed the event of May–July 1996.
Water budget. The basic equations predicting the
volume of water in the river, and thus the floodplain
reservoirs, have been modified to include the influences
of precipitation and evaporation on the flooded areas.
In THMBv1, the change with time of the river reservoir
dWr /dt is calculated as the sum of the surface runoff
SR, the groundwater flow G the influx from upstream
river cells Fri , and the river outflux (discharge) to the
downstream cell Wr /Tr , (all in m3 s#1 ):
!
dWr
Wr
Fri #
D SR C G C
dt
Tr
!16"
Hydrol. Process. (2007)
DOI: 10.1002/hyp
SIMULATING SURFACE WATERS OF THE AMAZON RIVER BASIN
In THMBv2, surface and subsurface runoff is contributed only from the fraction of each grid cell that does
not have standing water (1 # Af ), whereas the fraction
with standing water contributes its vertical water balance
(Pw # Ew ):
dWr
D !SR C G"!1 # Af " C !Pw # Ew "Af
dt
!
Wr
C
Fri #
Tr
!17"
BOUNDARY CONDITIONS AND EXPERIMENTAL
DESIGN
In this study we use a corrected version of surface and
subsurface runoff used by Coe et al. (2002) to force
THMBv2. In Coe et al. (2002), the monthly mean data
of temperature, precipitation, humidity, and cloudiness,
at 0Ð5° ð 0Ð5° latitude/longitude resolution, for the period
1935–1998 from the Climate Research Unit of the University of East Anglia, Norwich (hereinafter referred to
as CRU05; New et al., 2000), are used as climatological
forcing to the IBIS land-surface model. IBIS is run on
a 0Ð5° ð 0Ð5° latitude/longitude grid, extending over the
entire Amazon River basin (21 ° S–6 ° N; 45–80 ° W).
As discussed by Coe et al. (2002) and Foley et al.
(2002), the river discharge simulated by THMBv1 with
the IBIS runoff data is significantly underestimated for
the four major tributaries of the Amazon basin that
drain the Andes. This bias is passed downstream to the
mainstem and results in a 25% underestimation of the
discharge at Óbidos (Figure 1, station #33). The reason
for the systematic bias is most likely linked to the CRU05
gridded precipitation data used as input to IBIS. The
precipitation rates are believed to be extremely high on
the east face of the Andes and contribute about onequarter of the total output of the Amazon River. However,
very little gauge data are available from precisely these
locations. Therefore, the spline interpolation technique
used to create the CRU05 data averages values from
the two nearest sources: the eastern lowlands, which
have lower precipitation rates than the mountains, and
the western Andean Highlands, which are semi-arid. The
result is a systematic underestimation, particularly after
1984, of the precipitation data used as input to our models
and the runoff and discharge simulated by IBIS and
THMBv1. This precipitation bias is consistent with the
bias we find in other precipitation datasets of the Amazon
basin (see discussion in Costa and Foley (1997)).
Because the main goal of this study is to test and
evaluate the simulated time-transient flooded extent in
the Amazon basin, and because the bias in the precipitation data is well understood, we applied a discharge bias
correction to the IBIS simulated surface and subsurface
runoff for the four tributaries affected by the bias and
equal to the amount of discrepancy between simulated
and observed discharge: Japurá #22%, Negro #17%,
Solimões #42%, and Madeira #5% before (and including) December 1984 and Japurá #40%, Negro #34%,
Solimões #56%, and Madeira #37% after December
Figure 1. Location of the 122 gauge stations used for calibration (black dots) and validation (white dots are the 11 sites in Table II, grey dots are all
other validation sites). The coordinates for each station can be found in Coe et al. (2002: table I)
Copyright  2007 John Wiley & Sons, Ltd.
Hydrol. Process. (2007)
DOI: 10.1002/hyp
M. T. COE, M. H. COSTA AND E. A. HOWARD
1984. The large change after 1984 is most likely a result
of a change in the number of precipitation gauge stations reporting data in the 1980s and used in creating
the CRU05 data (New et al., 2000). This correction was
applied evenly to all grid cells upstream of the gauge
station nearest the Brazilian border for all months in the
surface and subsurface runoff files. This corrected runoff
was used as input data to provide the estimates of discharge and flooding presented in this study.
To isolate the influences of the differences between
THMBv1 and THMBv2 on the simulated hydrology of
the Amazon we ran another simulation with THMBv1
used by Coe et al. (2002) but with the corrected surface
and subsurface runoff data, which we refer to as Coe02C. The differences between the simulation in this study
and Coe02-C, therefore, are a result of model changes
only.
MODEL CALIBRATION AND VALIDATION
We calibrated THMBv2 to obtain simultaneously the best
fit (greatest r) of the modelled river discharge and flooded
area against: (1) observed timing and magnitude of mean
monthly river discharge at nine locations (Figure 1, sites
5, 8, 9, 10, 17, 31, 38, 44, and 56) in the Amazon basin
for the periods of observation; (2) flooded area on the
mainstem of the Amazon as estimated by Sippel et al.
(1998) for the 48-month period January 1979–December
1982. Calibration consists of tuning (1) uo1 , the minimum effective river velocity to affect the timing of the
river discharge (Equation (3)) and flood wave, and (2) Ci ,
the flood initiation parameter to influence the volume
at which the river may leave its banks and enter the
floodplain reservoir (Equation (8)). The best fit to discharge (r D 0Ð823 and normalized root-mean-square error
(NRMSE) of 31%, Table I) and flooded area (r D 0Ð791)
was achieved with uo1 D 0Ð27 m s#1 and Ci D 1Ð0 for
channels with upstream area <0Ð8 ð 106 km2 or >4Ð4 ð
106 km2 and varying from Ci D 1Ð1 to 1Ð8 for those
channels with upstream area between 4Ð4 ð 106 km2 and
0Ð8 ð 106 km2 .
As in Coe et al. (2002), the simulations are validated against observed river discharge, satellite altimetric
Table I. Comparison of simulated and observed dischargea
Calibration
This study
Coe et al. (2002)
Coe02-C
Pearson
RE (%)
RMSE (%)
0Ð823
0Ð987
0Ð974
0Ð979
0
#1
#7
0
31
30
59
34
a Sample size for the calibration is 2244, representing the mean monthly
discharge for the nine calibration stations. Sample size for the experiments
is 24 993, representing the mean monthly discharge of the 113 stations
not used in the calibration.
observations of water height, and satellite-derived estimates of flooded area.
The simulated river discharge is compared with the
gauge data at 113 locations in the Brazilian portion of
the river basin (122 total stations minus the nine stations
used for calibration; Figure 1). The data were collated
by Costa et al. (2002) from daily river discharge data
provided by ANA. The data series lengths vary by station,
but they average about 18 years each with all data falling
within the period 1968–1998. The accuracy of discharge
measurements is generally believed to be 10–15%.
The inundated area is compared with: (1) estimates
of flooded area derived by Sippel et al. (1998) from
mean monthly passive microwave observations (from
the scanning multichannel microwave radiometer on
Nimbus-7) of surface brightness temperature for the
period 1979–1986 as by Coe et al. (2002); (2) the highwater area derived by Hess et al. (2003) for the central
Amazon basin from synthetic aperture radar imagery
acquired by the JERS-1.
The height of the simulated floodwaters is compared
with mean monthly relative surface water height at nine
locations on the main stem of the Amazon (Figure 2)
for the period 1992–1998 measured by the NASA
radar altimeter aboard the TOPEX/POSEIDON satellite
(Birkett et al., 2002).
RESULTS
Discharge
The simulated discharge compares well with observations for the 24 933 station-months at the 113 gauge
Figure 2. Map of locations of water height and flooded area comparisons. The relative water height locations are labelled a–j; see Table III for the
site coordinates. The reaches where total flooded area comparisons are made are labelled 1–12
Copyright  2007 John Wiley & Sons, Ltd.
Hydrol. Process. (2007)
DOI: 10.1002/hyp
SIMULATING SURFACE WATERS OF THE AMAZON RIVER BASIN
stations not used in the model calibration. The correlation coefficient between the simulated and observed mean
monthly discharge is 0Ð987 (Table I). The average percentage relative error RE is #1%, indicating that the
source of nearly all the error in Coe et al. (2002) was
indeed located outside the Brazilian part of the basin.
The NRMSE is 30% (Table I, Figure 3).
There are important differences between the discharge
simulated by THMBv2 and THMBv1. The correlation
coefficient of the discharge for THMBv2 (0Ð987) is
slightly greater than either of the THMBv1 experiments
(0Ð974 and 0Ð979 for the Coe et al. (2002) and Coe02-C
experiments respectively; Table I, Figure 3), indicating
an improvement of the seasonal discharge timing by
THMBv2. This study has a slight negative bias of the
discharge (RE D #1%), whereas Coe02-C has no bias.
This difference is because THMBv2 includes evaporation
and precipitation of flooded areas in the water balance
calculation of the river, whereas THMBv1 does not. The
net loss of water from the flooded areas is the reason
for the slight underestimation of discharge in THMBv2
compared with Coe02-C.
Eleven major tributary gauge stations were chosen
from the 113 available for a more thorough validation
(Table II, Figure 1). The correlation coefficient of the
discharge is greater than 0Ð8 (Table II) for all of these
stations except for Solimões #3 and Juruá. The NRMSE
and correlation coefficient are improved compared with
Coe02-C for nine of these basins (Table II). The upstream
tributaries of the Purus and Juruá are the exceptions.
On those tributaries there is an apparent shift in the
hydrograph to later in the year compared with THMBv1
(Figure 4c) despite the peak discharge delay (PDD) being
zero (Table II), which indicates a slower river velocity.
The underestimation of the discharge velocity on these
two tributaries is probably related to the fact that these
rivers have the highest sinuosity of any tributaries in the
basin. The sinuosity used here was directly measured by
Costa et al. (2002) for the mainstem of the Purus and
Juruá Rivers. However, extrapolating these values to the
smaller tributaries of these rivers may have produced
errors. RE is closer to zero in this study compared with
Coe02-C for 7 of the 11 stations. The tendency for
reduced RE, and in some cases increased negative RE
(e.g. Óbidos, Solimões, Madeira, Tocantins; Table II),
illustrates the effect of the wetlands evaporation on the
corrected water balance, as discussed previously.
The changes made to the velocity function in this study
had the desired effect of increasing the velocity in the
larger rivers, where the friction between the water and the
channel walls decrease in magnitude. As a result, except
for the Purus and Juruá Rivers (Figure 4), the seasonal
timing of the discharge in the central portions of the basin
is in much better agreement with the observations than
THMBv1. With THMBv2, 7 of the 11 stations have a
0-month PDD, compared with THMBv1 that had only 3
of the 11 stations with a PDD of zero (Table II).
Including the influence of precipitation and evaporation
on the flooded areas in the water balance of the river
is also important. The mean annual discharge error of
the Tapajós River at Barra São Manoel (station #38) is
decreased from 58% in Coe02-C to 24% in this study
(Figure 4b). In watersheds where there is little flooding
simulated (e.g. Tocantins at Descarreto; Figure 4d) there
is little difference in the discharge magnitude between
the two versions of the model.
Flood regime
Figure 3. Scatter diagram of simulated mean monthly river discharge
versus observed for this study (top) and Coe02-C (bottom). The sample
size is 26 573 (113 stations with about 20 years of data for each station)
Copyright  2007 John Wiley & Sons, Ltd.
Coe et al. (2002) identified three major sources of
error in their simulation of flooding in the Amazon: the
Hydrol. Process. (2007)
DOI: 10.1002/hyp
M. T. COE, M. H. COSTA AND E. A. HOWARD
Table II. Comparison of simulated and observed discharge for 11 stations throughout the basina
n
Óbidos #33
Negro #21
Solimões #18
Solimões #3
Juruá #59
Purus #16
Madeira #30
Tapajós #39
Xingu #41
Tocantins #111
Araguaia #81
350
328
186
268
223
372
268
258
244
296
256
RE (%)
r
RMSE (%)
PDD (months)
THMBv2
THMBv1
THMBv2
THMBv1
THMBv2
THMBv1
THMBv2
THMBv1
0Ð920
0Ð845
0Ð902
0Ð608
0Ð675
0Ð833
0Ð853
0Ð935
0Ð918
0Ð885
0Ð891
0Ð786
0Ð841
0Ð817
0Ð466
0Ð785
0Ð889
0Ð838
0Ð928
0Ð908
0Ð870
0Ð817
#4
10
#3
#9
29
18
0
20
45
#11
18
1
14
2
#5
32
21
3
23
48
#9
22
12
44
13
28
62
44
29
39
70
38
29
18
45
16
33
57
40
31
43
75
41
33
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
a Coefficient of correlation r, relative error RE, root mean square of the error RMSE, and peak discharge delay PDD, between simulated and observed
discharge. The number of months n is shown in column 2. Columns labelled THMBv1 have results from the simulation Coe02-C described in the
text. See Figure 2 for station locations.
Figure 4. Mean monthly discharge for the Amazon at (a) Óbidos,
(b) Tapajós station #38, (c) Purus #17 and (d) Tocantins # 111 for the
observations (solid), simulated with THMBv2 (dashed) and THMBv1
(dotted). See Figure 1 for station locations. The monthly means were
created for only those months in which observations existed
Copyright  2007 John Wiley & Sons, Ltd.
simulated river discharge amount, the DEM accuracy,
and the floodplain initiation parameter. All three of these
sources of error have been addressed in THMBv2: the
river discharge matches the observations better, the DEM
is much closer to reality (although not free of error)
and explicitly contains sub-grid cell information, and the
flood initiation parameter is based on local and regional
geomorphologic characteristics.
The sum of the simulated flooded area for the 12
mainstem reaches during the wet season (April–June
or May–July depending on the location) is about
40 250 km2 with THMBv2, which is 5% less than
the Sippel et al. (1998) value of about 42 500 km2
(Table III). Simulated values range from about 40% less
than the Sippel et al. (1998) estimate on reaches 9 and 12
to 60% and 80% greater on reaches 11 and 2 respectively.
The spatial variability of the mainstem flooding matches
the Sippel et al. (1998) values well (Table III) with the
greatest wet-season flooding at reaches 4 (>5100 km2 )
and 6 (¾5300 km2 ) and the least on reaches 1 and 8
(<2000 km2 ). The flooded area with THMBv1 is about
80% greater than Sippel et al. (1998) for the sum of all
reaches and is overestimated on all reaches: from 23%
greater on reach 12 to 210% greater on reach 1. Part
of the improvement in agreement of THMBv2 results
compared with Sippel et al. (1998) is because of the maximum floodable area mask (discussed in the ‘Maximum
floodable area’ section). In a simulation without the mask
(results not shown), THMBv2 underestimated the total
flooded area of the Sippel et al. (1998) region by 16%
(compared with 5% with the mask). The mask forces the
floodwaters to remain on the defined floodplain, within
the Sippel et al. (1998) region, rather than diffuse outward beyond the floodplain boundary.
Although the correlation coefficients between the simulated and observed flooded area (n D 144, 12 months
at 12 sites) for THMBv1 and THMBv2 are comparable (0Ð963 and 0Ð961 respectively; Table III), the details
of the simulated water area in this study compare much
more favourably to the observations (Figures 5 and 6).
Hydrol. Process. (2007)
DOI: 10.1002/hyp
SIMULATING SURFACE WATERS OF THE AMAZON RIVER BASIN
Figure 5. Monthly mean flooded area of reaches 8 (top) and 10 (bottom) from January 1983 to August 1987 (see Figure 2 for location) for the Sippel
et al. (1998) estimates (solid), simulated by THMBv2 (dotted) and THMBv1 (grey)
The 1996 wet-season flooded area derived by Hess
et al. (2003) for the central Amazon basin from synthetic
aperture radar imagery acquired by JERS-1 provides
another assessment of the simulated flooded area. Compared with the Hess et al. estimate, THMBv2 captures the
gross features of the seasonal flood but underestimates
the total area flooded in the central Amazon (Figure 6a
and b). The maximum simulated wet-season flooded area
within the central Amazon is 155 550 km2 , which is about
30% less than the 220 222 km2 estimated by Hess et al.
The underestimation of the total flooded area compared
with the Hess et al. estimate is due to a combination of:
(1) on the mainstem where flooding does occur it tends
to be less than the fraction observed by Hess et al., which
suggests that there is still work to be done representing
the sub-grid-scale topography; and (2) on many of the
smaller tributaries, e.g. between the Madeira and Tapajós
and the Negro and Solimões Rivers, no significant flooding occurs in the model (Figure 6a and b). There are
several possible reasons for underestimation of flooding
Copyright  2007 John Wiley & Sons, Ltd.
on the small streams: (1) the topography at 1 km resolution may not be adequate for resolving the floodplain on
small streams; (2) the flood initiation parameter is derived
from data including relatively small streams (hundreds of
square kilometres) but we do not have the data to tune the
parameter specifically to these small streams; and (3) the
equations of flow used in the model are approximations of
fluid dynamics and do not include all aspects of backwater flooding that may be very important. For example, the
approximation used allows water to flow from the mainstem floodplain into tributaries’ floodplains but it does
not account for the damming of tributaries that occur as
a floodwave passes on a mainstem and, thus, misses the
potential local contribution to the tributary flood.
The difference in total flooded area between THMBv1
and THMBv2 can be attributed in large part to the
difference in the DEM used and to the spatially variable
flood initiation parameter. The DEM provides the pattern
of flooding across the landscape and within a grid cell,
whereas the flood initiation parameter determines when in
Hydrol. Process. (2007)
DOI: 10.1002/hyp
M. T. COE, M. H. COSTA AND E. A. HOWARD
results of THMBv1 are likely to be poor: the correct
amount and timing of water entering the floodplain would
still yield 100% coverage of most nearby cells because
of the DEM. THMBv2, because it incorporates higher
resolution topography, floods each cell more slowly and
rarely 100% of a cell (Figure 6). Therefore, with a more
realistic flood initiation parameter the total flooded area
is more representative of actual flooding.
Water height
Nine locations along the mainstem of the Amazon were
chosen for comparison of simulated monthly mean water
height with the water height observed by the altimeter
aboard the TOPEX/POSEIDON satellite (Birkett et al.,
2002). The nine locations (Figure 3) correspond to nine
of the ten locations used by Coe et al. (2002). Site f in
Coe et al. (2002) is eliminated because it is very close to
site e.
The correlation coefficient r between simulated and
observed water height at the nine locations for the
648 months of observations (January 1993–December
1998) is 0Ð700 for this study, compared with 0Ð749 for
the Coe02-C simulation (Table IV). The best correlation
occurs at the five sites furthest downstream (sites a–e,
r D 0Ð819–0Ð699).
Despite the overall good correlation with Birkett et al.
(2002), the THMBv1 results show much greater variation from the observations than THMBv2 (Table IV,
Figure 7). The standard deviation of the relative water
height simulated with THMBv2 (2Ð8 m) is less than that
of the observations (3Ð1 m), due to low standard deviation at sites c, h, and j (Table IV), whereas the THMBv1
standard deviation of 3Ð2 m is comparable to the observed
deviation (3Ð1 m) for all locations combined. However,
this good agreement is a result of averaging simulated
large overestimations (a, b, g) and strong underestimations (d, h, i, j) (Table IV).
The interannual variability is also improved from
THMBv1, when compared with the observations. The
relatively low-water years (1995 and 1998) and the highwater years (1994, 1997) agree with the observations
(Figure 7), as does the decreasing trend over the 6-year
period. The standard deviation of the simulated annual
Figure 6. The 1996 wet-season (May–July) flooded fraction derived from
synthetic aperture radar imagery (Hess et al., 2003) for the central
Amazon basin (top), simulated by THMBv2 (middle) and THMBv1
Coe02-C experiment (bottom)
the course of the year water may enter the floodplain and,
therefore, the total amount of water available to flood.
The poor agreement of the THMBv1 flood results with
the satellite estimates is due mainly to the coarse DEM
used in that model. Once flooding is initiated in THMBv1
the flooded area rapidly goes from 0% to 100% of a grid
cell and moves to other grid cells because there is only a
simple linear approximation of sub-grid-scale topography
and the overall landscape is very flat. Even with a much
more physically based flood initiation parameter, the
Copyright  2007 John Wiley & Sons, Ltd.
Figure 7. Relative water height at site g (see Figure 2 for site location)
on the Amazon River, for the satellite altimetric observations (solid)
simulated by THMBv2 (dashed) and simulated by THMBv1 (dotted)
Hydrol. Process. (2007)
DOI: 10.1002/hyp
SIMULATING SURFACE WATERS OF THE AMAZON RIVER BASIN
Table III. Average 1983–1988 wet-season flooded area for 12 reaches of the mainstema
Reach
Flooded area
Sippel et al. (km2 )
1
2
3
4
5
6
7
8
9
10
11
12
All
r
THMBv2
1 228
2 746
4 970
6 058
3 030
5 291
2 403
1 940
4 797
3 951
2 200
3 881
42 493
THMBv1
(km2 )
Diff. (%)
(km2 )
Diff. (%)
1 317
4 928
3 528
5 141
3 255
5 290
2 593
1 817
2 771
4 122
3 581
2 238
40 253
7
80
#29
#15
7
0
8
#6
#42
4
63
#42
#5
3 827
6 475
8 072
9 072
5 961
7 907
5 242
4 310
7 781
8 162
6 261
4 789
77 860
212
136
62
50
97
49
118
122
62
107
185
23
83
THMBv2
THMBv1
0Ð790
0Ð622
0Ð780
0Ð739
0Ð937
0Ð949
0Ð936
0Ð947
0Ð831
0Ð940
0Ð926
0Ð922
0Ð961
0Ð690
0Ð482
0Ð816
0Ð861
0Ð939
0Ð959
0Ð948
0Ð833
0Ð862
0Ð930
0Ð863
0Ð867
0Ð963
a Wet
season is defined as April–June. Estimated and simulated areas for this study (THMBv2) and the previous model (THMBv1), percentage
difference from the observations, and the coefficient of correlation between the simulated and observed wet-season area. See Figure 2 for reach
locations.
Table IV. Comparison of simulated and observed relative water height at nine locations on the mainstem
ID
a
b
c
d
e
g
h
i
j
All
Lat.
#2Ð540
#2Ð540
#3Ð210
#3Ð125
#3Ð875
#3Ð290
#2Ð540
#3Ð040
#4Ð290
Lon.
#56Ð540
#56Ð960
#58Ð875
#59Ð875
#62Ð875
#64Ð625
#65Ð540
#67Ð875
#69Ð710
r
Annual #
#
THMBv2
THMBv1
Obs.
THMBv2
THMBv1
Obs.
THMBv2
THMBv1
0Ð819
0Ð804
0Ð647
0Ð735
0Ð699
0Ð659
0Ð640
0Ð207
0Ð114
0Ð700
0Ð762
0Ð696
0Ð766
0Ð781
0Ð696
0Ð693
0Ð686
0Ð595
0Ð658
0Ð749
1Ð9
2Ð4
3Ð0
3Ð5
2Ð9
3Ð2
2Ð7
1Ð7
3Ð0
3Ð1
2Ð3
2Ð3
1Ð9
3Ð3
2Ð9
3Ð1
0Ð8
2Ð2
0Ð8
2Ð8
3Ð2
3Ð3
2Ð9
2Ð6
3Ð0
4Ð7
0Ð6
0Ð9
1Ð4
3Ð2
0Ð5
0Ð8
0Ð9
1Ð1
1Ð1
1Ð2
1Ð0
0Ð6
1Ð1
0Ð93
0Ð86
1Ð08
0Ð78
1Ð29
1Ð75
1Ð76
0Ð46
1Ð42
0Ð53
1Ð10
1Ð10
1Ð10
0Ð77
0Ð63
0Ð75
1Ð28
0Ð15
0Ð13
0Ð31
0Ð69
a Coefficient of correlation between the 12 mean monthly simulated and observed relative water heights at nine locations on the Amazon mainstem (see
Figure 2 for locations). Monthly and annual standard deviations of the observations and experiments in columns 6–11. Columns labelled THMBv2
have results of the improved model presented in this study; columns labelled THMBv1 have results from the Coe02-C experiment described in the
text.
mean height improved from 0Ð69 m with THMBv1 to
1Ð10 m with THMBv2, compared with 0Ð93 m for the
observations (Table IV).
The improved response of the simulated water height
with THMBv2 compared with THMBv1 is a function of
the flood parameter construction; flooding in THMBv1 is
initiated too early and it quickly covers most or all of the
floodplain, resulting in large, rapid seasonal fluctuations
in height but reduced interannual variations.
SUMMARY AND CONCLUSIONS
Models of Amazon River basin hydrology have been
identified as an important part of improving our
understanding of the spatial and temporal variability
of its hydrology and biogeochemistry and the implications of future land cover and land use changes. In this
Copyright  2007 John Wiley & Sons, Ltd.
paper we describe improvements made to our THMB
and the resulting changes to the simulated river discharge and flooding compared with THMBv1 (Coe et al.,
2002).
Three major improvements were made in THMBv2
that incorporate significantly improved data and process implementation: (1) the river velocity equation was
expanded to include river sinuosity in the calculation of path length and the frictional force to represent the observed increase in river velocity with
increased river volume; (2) an empirical relationship
was derived from >30 000 measurements of river morphology to determine the river flood initiation volume at all locations in the basin (from watersheds
of hundreds to millions of square kilometres); (3) a
statistical representation of sub-grid-scale floodplain morphology was derived from 1 km resolution SRTM
data.
Hydrol. Process. (2007)
DOI: 10.1002/hyp
M. T. COE, M. H. COSTA AND E. A. HOWARD
These changes result in significant improvements in the
simulated discharge, flooded area, and water height. On
almost all tributaries the agreement between simulated
and observed discharge improves with the new version
of the model, except for those streams for which the
observed river sinuosity is very high (Purus and Juruá),
indicating the need for better sinuosity data for the
smaller streams.
The changes in the floodplain morphology and flood
initiation parameter result in significant improvements
to the simulated seasonal and interannual flooding. The
THMBv2 average wet-season flooded area on the Amazon mainstem for the period 1983–1988 is within 5% of
the estimate of Sippel et al. (1998), whereas THMBv1
overestimates the flooded area by about 80%. Additionally, the standard deviation of the annual water height
(1Ð10 m) simulated by THMBv2 at nine locations on the
mainstem compares favourably with the standard deviation of the water height observed from satellite altimetry (0Ð93 m). THMBv1 exhibited much lower interannual variability (standard deviation of the annual mean:
0Ð69 m). Subtle differences in flooded area and water
height between years are simulated by THMBv2 because
of the high-resolution morphology and flood initiation. In
THMBv1, the coarse DEM and linear approximation of
sub-grid-scale morphology result in rapid expansion of
flooding from 0% to 100% of a grid cell once flooding
is initiated; as a result, little difference between years is
simulated.
The simulated flooded area summed for the central
Amazon basin for the wet season of 1996 is underestimated by THMBv2 by about 30% compared with the
1 km resolution JERS-1 observation. This is in large
part due to the failure to capture widespread flooding of
the small tributaries. However, despite the differences in
magnitude, the good agreement of the interannual variability of the simulated flooded area suggests that the
model is appropriate for investigating the response of
the Amazon flood regime to climate variability and land
cover changes. Ongoing research will address the impact
of future potential land cover changes to influence the
flooded area and timing, and the impacts on goods and
services provided by the river.
ACKNOWLEDGEMENTS
We sincerely thank Dr John Melack for providing helpful
discussion and insights and Dr Laura Hess and Dr Melack
for providing unpublished JERS-1 data of flooded area
for the Amazon basin. We also thank Dr Christine Delire,
Copyright  2007 John Wiley & Sons, Ltd.
Daniel Steinberg and two anonymous reviewers for their
constructive comments on the manuscript. Finally, we are
indebted to Paul Lefebvre for his work with many of the
figures. The research was funded by NASA LBA-ECO
grant NCC5-687.
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