Journal of Hydrology 387 (2010) 244–255

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Journal of Hydrology

journal homepage: www.elsevier .com/locate / jhydrol

Integrating spatial altimetry data into the automatic calibrationof hydrological models

Augusto C.V. Getirana *

Programa de Engenharia Civil – COPPE, Universidade Federal do Rio de Janeiro – UFRJ, Rio de Janeiro, BrazilUniversité de Toulouse, UPS (OMP), IRD, LMTG, Toulouse, France

a r t i c l e i n f o

Article history:Received 11 September 2009Received in revised form 15 February 2010Accepted 9 April 2010

This manuscript was handled byK. Georgakakos, Editor-in-Chief

Keywords:Hydrological modelingAutomatic calibrationMOCOM-UAENVISATSpatial altimetryMGB-IPH

0022-1694/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.jhydrol.2010.04.013

* Address: Programa de Engenharia Civil – COPPE, UJaneiro – UFRJ, Rio de Janeiro, Brazil.

E-mail address: augusto@coc.ufrj.br

s u m m a r y

The automatic calibration of hydrological models has traditionally been performed using gauged data.However, inaccessibility to remote areas and lack of financial support cause data to be lacking in large trop-ical basins, such as the Amazon basin. Advances in the acquisition, processing and availability of spatiallydistributed remotely sensed data move the evaluation of computational models easier and more practical.This paper presents the pioneering integration of spatial altimetry data into the automatic calibration of ahydrological model. The study area is the Branco River basin, located in the Northern Amazon basin. Anempirical stage � discharge relation is obtained for the Negro River and transposed to the Branco River,which enables the correlation of spatial altimetry data with water discharge derived from the MGB-IPHhydrological model. Six scenarios are created combining two sets of objective functions with three differ-ent datasets. Two of them are composed of ENVISAT altimetric data, and the third one is derived from dailygauged discharges. The MOCOM-UA multi-criteria global optimization algorithm is used to optimize themodel parameters. The calibration process is validated with gauged discharge at three gauge stationslocated along the Branco River and two tributaries. Results demonstrate that the combination of virtualstations along the river can provide reasonable parameters. Further, the considerably reduced numberof observations provided by the satellite is not a restriction to the automatic calibration, derivingperformance coefficients similar to those obtained with the process using daily gauged data.

� 2010 Elsevier B.V. All rights reserved.

1. Introduction

Hydrological models have been developed over the last fortyyears in order to provide streamflow forecasts and to improvethe prediction of spatially distributed water cycle components.Flood forecasting and water resources management are other fieldswhere hydrological models have been widely used. However, reli-able estimates of model parameters have been a great challengefaced by hydrologists worldwide. There are numerous optimiza-tion approaches which seek more efficient parameter estimatesthrough a computational cost efficacy while maintaining a consis-tent representation of physical processes. Objective functions (OFs)are used to refine parameter estimates using both observed andmodeled time series for a given study site.

Single-criterion optimization approaches, characterized by theuse of only one OF in the optimization process, search for the setof feasible parameters that optimizes the mathematical criteria se-lected to assess model outputs against observed data. Althoughseveral studies reveal the robustness and efficiency of such meth-

ll rights reserved.

niversidade Federal do Rio de

ods (Rotunno Filho, 1989; Duan et al., 1992; Sorooshian et al.,1993; Kuczera, 1997; Thyer et al., 1999), single-criterion methodscan convert the optimization process to a single curve tuningresulting in optimal OFs without physical meaning (Peck, 1976;Boyle et al., 2000). In order to improve the optimization processtaking into account two or more OFs at once, multi-criteria ap-proaches have been developed (Yapo et al., 1998; Gupta et al.,1998). Most of these approaches make use of Pareto optimal solu-tions (Pareto, 1971), which suggests that a user-defined number ofparameter sets will be provided at the end of the optimization pro-cess. These optimal solutions represent the distribution of sets ofunlike parameters that result in a range of modeled minimal errors,according to the OFs considered in the optimization process (Boyleet al., 2000). In the last decade, several global optimization multi-criteria algorithms have been developed for general purposes orspecific hydrological applications. Some of them are the MO-COM-UA (Yapo et al., 1998), the MOSCEM-UA (Vrugt et al.,2003a) and the AMALGAM algorithms (Vrugt and Robinson,2007). These methods are improvements over traditional single-criterion algorithms used for automatic calibrations such as theshuffled complex evolution (SCE-UA) (Duan et al., 1992, 1993)and the shuffled complex metropolis evolution (Vrugt et al.,2003b) (SCEM-UA) global optimization algorithms.

A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255 245

Water discharge time series have been traditionally used inmodel parameter calibration processes as the ‘‘truth”. This crite-rion assures, in most cases, accurate representations of the surfacehydrology and discharge forecasts. On the other hand, remote re-gions of the Amazon basin do not have sufficient available ob-served data to subsidize detailed spatiotemporal water balancestudies. The use of secondary sources of information for continen-tal water monitoring becomes necessary, disclosing the potentialof using remotely sensed data in unequipped areas.

Recent advances in radar altimetry technology have improvedprecision in the monitoring of water height variability of riversand lakes located in ungauged or poorly gauged regions (Koblinskyet al., 1993; Birkett, 2000; Fu and Cazenave, 2001; among others).Taking advantage of water height data which are available at inter-sections between satellite tracks and opened waters (called virtualstation hereafter, or simply VS) and of more dense monitoring net-works in most large basins in the world, efforts have been focusedon the development of techniques in order to improve the compu-tation of water transport and storage with such data (Kouraevet al., 2004; Zakharova et al., 2006; Frappart et al., 2005, 2008).Other spatial altimetry data applications for continental watersconsist in the monitoring of poorly gauged basins based on ratingcurve fitting and river bed slope estimates (León et al., 2006; Get-irana et al., 2009b), and the evaluation of hydrodynamic (Wilsonet al., 2007) and hydrological (Coe et al., 2002, 2008) models. Allthese studies have demonstrated the usefulness of such data forimproving the understanding of regional hydrological processes.

The high accuracy of altimetric data provided by the latest spa-tial missions and the convincing results obtained in previousapplications suggest that these data can also be employed in theautomatic calibration of hydrological models. In order to verifythe practicality of such an application, this paper presents forthe first time the automatic calibration of a hydrological modeluniquely constrained by spatial altimetry data. In this sense, themain objective of this study is to check the feasibility of integrat-ing altimetric data provided by the satellite ENVISAT into thehydrological modeling system and to evaluate its effects on waterdischarge prediction.

Fig. 1. Geographical location of the study area and the spatial distribution of virtual andvalidating the MGB-IPH model.

This paper is organized into four sections. Section 2 gives a briefoverview of the study area. Section 3 presents the materials andmethods, including a description of the ENVISAT altimetric data,the description of the MGB-IPH hydrological model (Collischonnet al., 2007), the MOCOM-UA global optimization algorithm andthe stage � discharge relation used to integrate altimetric data intothe automatic calibration of the model parameters. Section 4, re-sults of six scenarios considering different objective functionsand data sources (altimetric data and water discharge) are pre-sented, compared and discussed. Finally, Section 5 details the con-clusions derived from the results.

2. Study area

The Branco River, located in the northern Amazon basin, is themain tributary of the Negro River and covers about 190,000 km2

(Fig. 1). This catchment has been chosen to develop and test theproposed methodology given that previous satellite and numericalmodeling applications have been performed in this region(Frappart et al., 2005, 2008; León et al., 2006; Getirana et al.,2009b). Also, this domain covers part of the Amazon basin, whichhas been the subject of several hydrological studies using satellitedata (e.g. Alsdorf et al., 2000; Coe et al., 2009). The Branco River ba-sin is located within one of the driest regions of the Amazon forest,with mean precipitation and runoff rates of 5.6 mm/day and2.4 mm/day, respectively. Its hydrological cycle is composed ofwell defined wet and dry seasons, with floods between May andAugust, reaching peaks in June and July. Its main tributaries arethe Uraricoera and Mucajaí Rivers.

3. Data sets and methods

3.1. Input dataset for the hydrological modeling

In this study, most of the calibrated parameters and the othercoefficients are are defined as functions of land cover and soil type.Vegetation-related coefficients such as albedo and leaf area index

gauge stations considered for constructing the Q � h relation, and calibrating and

ig. 2. Altimetric time series at four VS’s considered in the optimization process.irtual station vs1 is used in the scenario 1VS.

Table 1Virtual stations considered for the automatic parameterization.

Virtualstation

Drainage area(km2)

Number ofcycles

Distance from Caracaraístationa (km)

vs1 176,664 34 �198.03vs2 154,285 38 �136.11vs3 132,849 37 �48.57vs4 97,437 37 118.05

a Distances increase upward the river.

246 A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255

values are considered as monthly averages, as suggested in the lit-erature (Xue et al., 1991), and soil-related parameters are thoseprovided by the model calibration (Getirana et al., 2010).

Topography data is also required by the hydrological model toprovide estimates of drainage areas, river lengths, slopes, etc. Theland cover map is derived from a classification of multitemporalJERS-1 images, as described by Martinez and Le Toan (2007). Theclassification resulted in eight land cover classes for the Amazonbasin: (1) permanent water, (2) occasionally flooded forest, (3)never flooded forest, (4) never flooded savannah, (5) occasionallyflooded non-vegetated/herbaceous areas, (6) permanently floodedforest, (7) occasionally flooded savannah, and (8) submerged vege-tation. The soil map was acquired from the FAO (1995) database.Four soil types are predominant within the basin: (1) latosol, (2)gleysol, (3) acrisol, and (4) lithosol. The topography was derivedfrom the Shuttle Radar Topography Mission (SRTM) digital eleva-tion model (DEM) (http://srtm.csi.cgiar.org/) and processed byusing the floodplain burning (FB) approach, as suggested in Getir-ana et al. (2009a,c). The FB approach makes use of river and flood-plain maps to gradually change DEM pixel elevations in flat andflooded areas, resulting in more consistent river flow and basindelineation maps.

The Branco River basin is equipped with 41 rain gauge stationsoperated by the Brazilian Water Agency (ANA, 2009). Stations lo-cated within the Negro and Orinoco River basins are also consid-ered for creating the precipitation forcing for the study area.

Climatological data (temperature, solar radiation, humidity,pressure and wind speed) used as forcings to calculate evapo-transpiration rates are derived from the NCEP/DOE AMIP-II reanal-ysis provided by Earth System Research Laboratory (Roads et al.,2002).

Discharge data from three gauge stations are considered in thisstudy (Fig. 1b). They are: the Caracaraí station which is located400 km upstream the confluence of the Branco and Negro Rivers,covering 126,000 km2, the Mucajaí station in the Mucajaí River,draining, approximately, 20,140 km2 and the Fazenda Passarão sta-tion in the Uraricoera River, with a drainage area of about49,700 km2.

3.2. Altimetric data

The main goal of satellite altimetry is to determine the height,H, which represents the instantaneous measurement of the Earth’ssurface height corresponding to a specified reference ellipsoid. Inthis sense, H corresponds to the height of the reflecting surface thatreceives and reflects the satellite radar echoes. Water heights H (m)at VS’s can be related to the river water depth h (m) as follows:

h ¼ H � z ð1Þ

where z (m) stands for the mean height of the river bed related tothe same reference ellipsoid.

The ENVISAT satellite radar altimetry mission data are used inthis study. This satellite orbits on a 35-day repeat cycle, providingobservations of continental water and ocean surfaces from latitude81.5�N to 81.5�S, with an equatorial ground-track spacing of about80 km and an along-track resolution of the range measurements of350 m. Data used in this study ranges from October 1st, 2002 toNovember 12th, 2006, corresponding to cycles 10–52, with a fewmissing cycles, depending upon the track. The parameters requiredfor the computation of water heights in the continental domainhave been extracted from the multi-mission Geophysical Data Re-cords (GDRs) database maintained by the Centre de Topographiedes Océans et de l’Hydrosphère (CTOH). The parameters includegeophysical corrections, and it takes into account troposphericand ionospheric propagation delays of the radar pulse and depar-ture of ground altitude from mean position coming from the Earth

FV

tides. The ranges used in this study are those issued by the ICE-1algorithm. Errors in altimetric time series along rivers within theAmazon basin are from 0.07 m to 0.40 m, with an average of0.22 m (Frappart et al., 2006). The automated method, based onland cover distribution proposed by Roux et al. (2010), has beenused to extract altimetric data. Altimetric data at four VS’s (vs1,vs2, vs3 and vs4) along the Branco River are considered in thisstudy (Fig. 1), providing time series with 34–38 cycles availablefor the optimization process (Fig. 2 and Table 1). A comprehensivedescription of ENVISAT data processing and acquisition over theNegro River basin (including the Branco River basin) can be foundin Roux et al. (2010) and Getirana et al. (2009b, 2010).

3.3. The approach

Briefly, eight parameters of the MGB-IPH model have beenautomatically calibrated for the period from January 2002 toDecember 2006 with the MOCOM-UA algorithm. Empirical equa-tions have been used to estimate river depths from modeled dis-charges, enabling the integration of spatial altimetry data into theautomatic parameterization process. The calibration procedurehas been performed for six scenarios, differing from each otheraccording to the OFs and the datasets used. The OFs were selected

A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255 247

based on their ability to correlate altimetric data and river waterdepths derived from the empirical relation with modeled dis-charges. Three datasets have been considered: one with altimetricobservations at one VS, another one considering four VS’s at once,and the third one taking into account discharge data at one gaugestation (Caracaraí station). Optimization processes have been per-formed with one and four VS’s in order to study the influence ofthe number of altimetric observations on the results. The param-eterization has been evaluated qualitatively, by means of visualinspection of observed and simulated hydrographs, and quantita-tively, through the analysis of performance coefficients for the cal-ibration (2002–2006) and validation (1997–2001) periods atCaracaraí and other two stations located on tributaries of theBranco River. A detailed description of each step is given in thenext sections.

3.4. The MGB-IPH hydrological model

The MGB-IPH model has been used to simulate the hydrologicalbehavior of the basin. The model is composed of modules enablingthe calculation of the soil water balance, evapotranspiration, flowpropagation within cells, and flow routing through the drainagenetwork. The watershed is divided into elements of area (normallysquare grids or cells) interconnected by channels. Spatially distrib-uted land cover and soil type data are required by the hydrologicalmodel in order to create the grouped response units (GRU) (Kou-wen et al., 1993). These are sub-domains within computationalcells composed of homogeneous vegetation and soil characteris-tics. Runoff generated from the different GRUs in the cell is thensummed and routed through the river network. Flow generatedwithin each cell is routed to the stream network using three linearreservoirs (baseflow, sub-surface flow and surface flow). The Mus-kingum–Cunge method is then used to propagate the water flowthrough the drainage network. Several applications of the modelcan be found in the literature (Tucci et al., 2005; Ribeiro Netoet al., 2005; Paz et al., 2007; Allasia et al., 2006). A full descriptionof the MGB-IPH model is provided in Collischonn (2001) and Collis-chonn et al. (2007).

The Branco River basin was discretized into 447 computationalcells. The precipitation and climatological data were spatially dis-tributed throughout the basin using an inverse distance squaredinterpolation method.

3.4.1. Water depth computationIn order to integrate altimetric data into MGB-IPH, modeled dis-

charges must be converted to river water depths. Simplifying theriver section to a rectangular form, one has:

h ¼ Q=ðw� vÞ ð2Þ

where Q (m3/s), h (m), w (m) and v (m/s) are, respectively, dis-charge, mean river depth and width, and water flow velocity.

MGB-IPH provides Q for each computational cell at a daily timestep. River width w and water flow velocity, v, have been deter-mined by empirical relations derived from statistical regressionsfor the Negro River basin. Data from 36 gauge stations locatedwithin the Negro River basin allowed the determination of the fol-lowing relation for w estimates:

W ¼ 0:2083� A0:7211 R2 ¼ 0:92 ð3Þ

where A (km2) is the drainage area.v can be computed empirically as a function of Q by Eq. (4).

Coefficients a0 and b0 have been estimated for the Negro River basin[Eqs. (5) and (6)] by taking into account the observed data at threegauge stations along the Negro River (Cucuí, Curicuriari and Serrin-ha – Fig. 1), as shown in Fig. 3.

v ¼ a0Q b0 ð4Þa0 ¼ ð0:5957� 103Þ=A ð5Þb0 ¼ �0:44� 10�6 � ðA� 71;132Þ þ 0:5456 ð6Þ

Computed water depths have been compared with observeddata time series at 10 gauge stations located along the Negro Riverand tributaries, including those three used in the parameter esti-mation process, resulting in a mean relative error of 10.9%(Fig. 3). The system of equations gave good results for the BrancoRiver with errors of about 7.9% at the Caracaraí station.

3.5. The MOCOM-UA algorithm

The MOCOM-UA is a global multi-objective optimization algo-rithm. It is based on the SCE-UA single-criterion optimization algo-rithm adapted for multi-objective problems. It provides aneffective and efficient distribution of solutions on the Pareto opti-mum space (Boyle et al., 2000). Its main advantage is the require-ment of only one coefficient to be defined: the population ns ofpoints randomly distributed within the parameter hyper-space de-fined by the n-dimensional feasible parameter space. The popula-tion of ns points is ranked and sorted according to a Pareto-ranking procedure for each iteration, as suggested by Goldberg(1989). A multi-criteria version of the downhill simplex methodis used to evolve each simplex in a multi-objective improvementdirection (Boyle et al., 2000). The optimization process stops whenall ns points are ranked evenly. This means that the entire popula-tion converged toward the Pareto optimum. For further detailsabout the MOCOM-UA algorithm, numerous descriptive paperscan be found in the literature (e.g. Yapo et al., 1997, 1998; Boyleet al., 2000).

The MOCOM-UA algorithm is already included in the currentMGB-IPH version. Although more recent global optimization mul-ti-criteria algorithms exist, the MOCOM-UA has been shown tobe capable of providing a fairly uniform approximation of the Par-eto solution space (Yapo et al., 1997, 1998). Besides, the objectiveof this study is to evaluate the potentials of spatial altimetry datafor the automatic calibration of hydrological models and not theefficiency of the optimization method.

3.6. Parameter selection

According to Collischonn (2001), the MGB-IPH water flow cal-culation presents the highest sensitivity when six parameters vary:Wmi (mm), bi (–), Kinti (mm d�1), Kbasi (mm d�1), CSi (–) and CIi (–).They correspond, respectively, to the water storage in the soil, thevariable infiltration curve parameter, the sub-surface and ground-water flows, and the surface and sub-surface linear reservoirparameters of each GRU i. Details about these parameters can befound in the various MGB-IPH applications (e.g. Collischonnet al., 2007; Getirana et al., 2010). These parameters were consid-ered in the MGB-IPH optimization process, along with parameterWci, which limits the fluxes between the surface and the sub-sur-face layers. Its value is normally defined as a constant function ofWmi (0.10 �Wmi) (Rawls et al., 1993; Collischonn et al., 2007).But for finer spatial scales, it can vary as a function of the soil con-ditions, thereby having a significant import on water storage in thecells.

Parameters values are, a priori, unique for each GRU i. In order tosimplify the number of parameters in the optimization process, asingle value is attributed for the entire catchment. This means thatall GRUs use the same set of parameters. The exception is Wmi: themodeled discharge is highly sensitive to the value of this parame-ter. In this sense, only the latter parameter will be referred to withGRU indexes hereafter.

0

5

10

0 5 10

hobs(m)

hcal

(m) Mocidade

A=43,504km²Erel=±15.5%

0

5

50

hobs(m)

hcal

(m) Uaicas

A=15,520km²Erel=±13.8%

v = 0.0083Q0.5489

R2 = 0.974v = 0.0036Q0.5922

R2 = 0.9782v = 0.0016Q0.6477

R2 = 0.9601

0.0

0.6

1.2

0 10000 20000 30000

Q(m3/s)

v(m

/s)

Cucui Curicuriari Serrinha

v x Q relations

b = 0.0004.(A/1000) + 0.5139R² = 0.984

0.54

0.58

0.62

0.66

0 100 200 300

Draining area (km²/1000)

b

Cucui

Curicuriari

SerrinhaCoefficient "b"

a = 595.7/AR² = 0.981

0

0.003

0.006

0.009

0 0.005 0.01 0.015

1000/Draining area (1000/km²)

a Cucui

CuricuriariSerrinha

Coefficient "a"

5

10

15

5 10 15

hobs(m)

hcal

(m) Curicuriari

A=191,787km²Erel=±10.0%

0

5

10

15

0 5 10 15

hobs(m)

hcal

(m) Cucui

A=71,132km²Erel=±6.0%

2

7

12

2 7 12

hobs(m)

hcal

(m) Taraqua

A=44,255km²Erel=±14.9%

4

9

14

4 9 14

hobs(m)

hcal

(m) São Felipe

A=122,080km²Erel=±6.6%

2

7

12

2 7 12

hobs(m)

hcal

(m) Caracarai

A=126,085km²Erel=±7.9%

5

10

15

5 10 15

hobs(m)

hcal

(m) Serrinha

A=291,150km²Erel=±11.4%

0

5

10

0 5 10

hobs(m)

hcal

(m) Faz. Passarão

A=49,709km²Erel=±9.0%

Fig. 3. Power-law and linear regressions used to adjust Eq. (4): lower left – Power-law relation between v and Q observations at Cucuí, Curicuriari and Serrinha stations;upper left – best fit estimates of a’ [Eq. (5)] and b0 [Eq. (6)] coefficients as functions of the drainage area A; right – scatter plots of calculated (hcal) and observed (hobs) waterdepths.

248 A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255

The ns points randomly distributed within the parameter hy-per-space is an exponential function of the number of parametersto be calibrated. GRUs accounting for small portions of the basinsurface have been merged into those composing more representa-tive areas in order to economize computational time. The processtook into account land cover and soil type similarities in order tomaximize the physical representativeness of parameters. Finally,three GRUs have been considered within the Branco River basin:latosol + forest (GRU1), gleysol + forest (GRU2), and open water(GRU3). It has been assumed that GRU3 (soils covered by riversand lakes) are permanently saturated and, consequently, they areincapable of absorbing more water. This means that Wm3 = 0. Fi-nally, eight parameters were defined for the optimization process(Table 2).

3.7. Hyper-domain, starting point and population

The automatic parameter calibration is commonly performedafter a previous manual adjustment of the values in order to reducethe domain extent where optimal solutions are explored. In thisstudy, relatively large domains have been defined for each param-eter with the purpose of making the automatic calibration animpartial process. The definition of domain extents has taken into

Table 2Model parameters subjected to the automatic calibration.

Parameter First guess Domain Hydrological process

b (–) 1.0 [0.01–2] Variable infiltration curveKint (mm d�1) 25 [0.25–50] Sub-surface flowKbas (mm d�1) 10 [0.1–20] Groundwater flowCS (–) 35 [0.35–70] Surface flowCI (–) 100 [1–200] Sub-surface flowWc (mm) 0.55 �Wm [0.1–

0.825 �Wm]Groundwater vertical flux

Wm1 (mm) 1500 [150–3000] Water storage on the soil(GRU1)

Wm2 (mm) 1500 [150–3000] Water storage on the soil(GRU2)

account previous parameter calibrations in the Amazon basin(Ribeiro Neto, 2006). The first guess (the initial set of parameters)has been defined as the centroid of the parameter domains. Thepopulation ns used to explore optimal solutions for the eightparameters within the hyper-domain has been fixed as 100, in or-der to keep time processing feasible. This value has been chosenbased on a previous sensitivity analysis of MOCOM-UA (Yapoet al., 1998).

3.8. Objective functions

The Nash–Sutcliffe (NS) performance coefficient [Eq. (7)] (Nashand Sutcliffe, 1970) and derivates have been the most commonlyused criteria to quantify the efficiency of hydrological models. Itis defined as:

NS ¼ 1�Pnt

t¼1½XobsðtÞ � XsimðtÞ�2Pntt¼1½XobsðtÞ � Xobs�2

ð7Þ

where t is the time step (one day for this application), nt stands forthe total number of days, Xobs and Xsim are, respectively, the target(observed) and modeled signals at time step t, and Xobs is the meanvalue of the target signal for the entire period.

However, because of the difference z [Eq. (1)], coefficients thatare functions of the difference between the modeled and the ob-served time series do not work when altimetric data are used.Fig. 4a presents examples of observed water height and modeledwater depth time series. If both series were used in their originalforms to calculate traditionally used model performance coeffi-cients such as NS, NS for logarithms or even the relative error(RE) coefficient, results would completely diverge from the realmodel performance. Some ways to resolve this problem are: appro-priated estimates of the z value based on in situ observations, or thecomputation of performance coefficients based on time seriesanomalies. The first solution requires large financial resourcesand manpower for data collection in unequipped areas. Therefore,it is not a convenient solution since in situ data are scarce. The

0

20

40

60

80

10/2002 10/2003 10/2004 10/2005 10/2006

Water depth ENVISAT altimetry

H,h

(m)

H = 1.12h + 60.93R2 = 0.86

67

72

77

5 10 15Water depth (m)

ENVI

SAT

altim

etry

(m)

(a) (b)

Fig. 4. River water depth derived from modeled discharges and ENVISAT altimetric data in the Branco River basin: (a) time series; and (b) scatter plot.

A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255 249

second solution is only feasible when the NS coefficient is con-cerned, since lnðnÞ ¼ 1;8 n 6 0 and the sum of an anomaly seriesis equal to zero (RE = 0). The NS coefficient for anomalies can be ex-pressed as follows:

NSanom ¼ 1�Pnt

t¼1f½XobsðtÞ � Xobs� � ½XsimðtÞ � Xsim�g2Pntt¼1½XobsðtÞ � Xobs�2

ð8Þ

where Xsim stands for the mean value of the modeled signal for theentire period. The difference between the NS coefficient and NScoefficient for anomalies is that the signals Xobs;simðtÞ found inthe numerator of Eq. (7) are replaced by the annomalies½Xobs;simðtÞ � Xobs;sim� in Eq. (8).

Other two performance coefficients have been proposed: thetangent a derived from a linear regression between observed andmodeled series and the coefficient of determination R2:

a ¼nt �

Pntt¼1½XobsðtÞ � XsimðtÞ� �

Pntt¼1XsimðtÞ �

Pnt

t¼1XobsðtÞ

Pntt¼1Xobs2 ðtÞ �

Pntt¼1XobsðtÞ

� �2 ð9Þ

R2 ¼ a2 � s2obs

s2sim

ð10Þ

where sobs and ssim are, respectively, observed (ENVISAT radaraltimetry) and modeled (modeled river water depth) signal vari-ances. These coefficients are not functions of z, so they can be usedin the study.

Fig. 4b shows the linear regression performed with pairs of alti-metric and river depth data. Ideally, if the altimetric data acquisi-tion/processing and river depth calculation were free from errors,one would achieve the perfect regression. However, the coeffi-cients a and R2 usually differ from the ideal value of 1. The equa-tions considered for the optimization process are:

Minimize NSanom1 ¼ 1� NSanom ð11Þ

Minimize a1 ¼1� a if a � 11� 1

a if a > 1

( )ð12Þ

Minimize R21 ¼ 1� R2 ð13Þ

Six scenarios have been built, and they are distinguished fromeach other by the combinations of OFs and the data used in theoptimization process. Two combinations of OFs have been consid-ered. They are: a1 � R2

1 and NSanom1 � R21, or simply aR2 and NR2.

Two altimetric data sets have been used: data from one VS(vs1); and from four VS’s (vs1, vs2, vs3 and vs4), all of them locatedalong the Branco River. Results from the optimization with dailydischarge data at Caracaraí station have been considered the refer-ence. The three datasets are called, respectively, 1VS, 4VS and OBShereafter.

In order to consider the four VS’s at the same time impartially inthe optimization process, the time series require adaptations. Onecan obtain inconsistent results if a1 is computed taking into ac-count two or more altimetric time series at different VS’s. This oc-curs because VS’s located at different locations and elevations cangenerate shifted scatter plots at asymmetrical scales, as shown inFig. 5a and b. This problem can be resolved by replacing river depthand altimetric time series by their respective anomalies (Fig. 5c).Another important issue concerns the hydrological cycles at differ-ent spatial scales within a catchment. The use of altimetric timeseries from VS’s located in rivers with different regimes (for in-stance, two altimetric time series, one with a high seasonalityand the other with a low seasonality) might reduce, or even pre-vent, the influence of the VS with low seasonality in the optimiza-tion process. The normalization of the time series at each VSseemed to be reasonable to eliminate this problem, as shown inFig. 5d. Then this solution has been applied to scenario 4VS aR2.Once the OFs and the time series have been defined consistently,the optimization process could be performed.

4. Results and discussion

The multi-criteria optimization process of the model parame-ters has resulted in refined simulations for the six scenarios. Allof them have converged to optimal parameter sets. As shown inFig. 6, the use of the MOCOM-UA algorithm has provided convinc-ing representations of the Pareto optimum for both OF combina-tions. Objective functions of the six scenarios have presentedconsiderably improved values compared to those provided by theinitial guess. Coefficients related to the discharge had improve-ments up to 81% (a1 optimized with discharge), whilst those re-lated to stages improved up to 24% (a1 optimized with four VS’s).Parameter sets have varied substantially between the scenarios,which shows the influence of the OF and the quality and quantityof data used as the reference in the automatic parameterization.Correspondingly, this reveals the existence of compensations inrepresenting hydrological processes among model parameters. Itis noteworthy, however, that Wm1 converged to similar values (be-tween 160 and 240 mm) in all scenarios. This reveals a high modelsensitivity to that parameter, which is influenced significantly bythe predominance of GRU1 over the basin, covering about 77% ofthe draining area. Wm2, covering, approximately 20% of the BrancoRiver basin, showed a secondary importance in the groundwaterstorage process, resulting in a high magnitude of values amongscenarios. The resulting parameter sets derived from scenario4VS aR2 have provided solutions within the Pareto space whichwere considerably grouped. This is probably due to the normaliza-tion of altimetric time series to compute a1 only considered in thatscenario.

Normalization

y = 0.971x R² = 0.933

-3

-1

1

3

-3 -1 1 3

Anomalies

y = 1.060x R² = 0.922

-8

-1

6

13

-8 -1 6 13

y = 0.1295x + 2.8942R² = 0.2145

0

15

30

0 20 40 60 8010

30

50

70

9/02 9/03 9/04 9/05 9/06

m39,4s

m72,53x

==

m47,2s

m05,20x

==

(a) (b)

Wat

er d

epth

(m)

Wat

er d

epth

(m)

Spatial altimetry (m)

Spatial altimetry (m)

Wat

er d

epth

(m)

Spatial altimetry (m)

(c) (d)

Fig. 5. Example of altimetric time series at two virtual stations in rivers with unlike hydrological behaviors and at different elevations: (a) time series; (b) scatter plots ofaltimetric data against their respective modeled water depths; (c) anomalies; and (d) normalized data.

-5 0 5 10x 10-4

0.0624

0.0626

0.0628

0.063 0.064 0.065

0.0606

0.0608

0.061

0 1 2x 10-3

0.0545

0.055

0.0555

0.056

0.056 0.058 0.060.0542

0.0544

0.0546

-2 0 20.0639

0.0639

0.0639

0.06 0.08 0.10.06

0.062

0.064

0.066

b Kint Kbas CS CI Wc Wm1Wm20

0.5

1

1.5

2

b Kint Kbas CS CI Wc Wm1 Wm20

0.5

1

1.5

2

b Kint Kbas CS CI Wc Wm1Wm20

0.5

1

1.5

2

b Kint Kbas CS CI Wc Wm1 Wm20

0.5

1

1.5

2

b Kint Kbas CS CI Wc Wm1Wm20

0.5

1

1.5

2

b Kint Kbas CS CI Wc Wm1 Wm20

0.5

1

1.5

2

112 aR × 1anom1

2 NSR ×Pareto solutions Set of parameters

12 aR × 1anom1

2 NSR ×

Parameters Parameters 1a

1a

1a

21R

21R

21R

21R

21R

21R

1anomNS

1anomNS

1anomNS

Pareto solutions Set of parameters

1

Fig. 6. Pareto solutions and parameters resulted from the optimization process. From the top, 1VS, 4 VS and OBS. From the left, scenarios aR2 and NR2.

250 A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255

The evolution of the eight optimized parameters for each sce-nario has been plotted and analyzed. Based on these results, onecan make the following observations:

1. in general, optimization processes considering altimetric datatook a longer time to converge. This can be attributed to twomain causes: first, to the high correlation between OFs, as found

between a1 and R21, making the convergence a longer process;

and second, to the lower availability of observed data consid-ered for the OF computation. A meaningful decrease of compu-tational cost is evident for scenarios aR2 when the 1VS dataset(28,040/141,590 evolutions/generations) is replaced by 4VSand OBS (18,406/78,053 and 3573/18,296 evolutions/genera-tions, respectively), as listed in Table 3;

Table 3Results of the automatic calibration processes.

Scenario Generations Evolutions OF for discharges (�10�2) OF for stages (�10�2)

a1 R21

NS1 a1 R21

NSanom1

First guess – – 44.6 14.6 35.0 16.3 17.2 25.01VS aR2 141,590 28,040 [7.8–6.8] [7.9–7.5] [7.9–7.5] [0.2–0] [5.6–5.5] [9.8–9.7]

NR2 45,856 7517 [7.8–6.8] [8.3–7.3] [8.8–7.4] [1.2–0] [5.5–5.4] [9.8–9.7]

4VS aR2 78,053 18,406 8.2 6.6 6.8 3.2 6.4 8.8NR2 5716 1143 [11.1–0.1] [7.0–6.7] [7.3–6.8] [11.5–0.1] [6.6–6.0] [9.9–6.7]

OBS aR2 18,296 3573 [0.1–0] [6.3–6.2] 6.7 [9.8–9.1] [6.7–6.5] [9.8–9.7]NR2 18,379 2611 [1.9–0.5] 6.1 [6.4–6.3] [8.8–7.0] [7.1–6.9] [9.9–7.0]

0

0.5

1

1.5

2b Kint Kbas CS

0 0.5 1 1.5 2x 104

0

0.5

1

1.5

2CI

0 0.5 1 1.5 2x 104

Wc

0 0.5 1 1.5 2x 104

Wm1

0 0.5 1 1.5 2x 104

Wm2

Fig. 7. Evolution of normalized parameter values of scenario 4VS aR2. The x axis corresponds to the number of evolutions during the optimization processes.

A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255 251

2. although the scenarios considering a1 as an OF had higher com-putational costs, they converged quickly. However, theautomatic calibration continued ad infintum and manual inter-ruptions were necessary as soon as convergence was detected(see Fig. 7 as an example of scenario 4VS aR2).

At the end of each optimization process, the three performancecoefficients [Eqs. (11)–(13)] were computed for both discharge andstage results. Although significant differences are present amongthe optimal parameter sets (as shown in Fig. 6), all of the scenariosprovided excellent performance coefficients. Figs. 8 and 9 illustratesets of hydrographs derived from the six optimization processes.Globally, no significant differences are detected among modeledhydrographs. Remarkable improvements are observed during thewet seasons, compared to the hydrograph provided by the firstguess. Both the first guess and the optimal solutions resulted indischarges close to observations during droughts, indicating thelow sensitivity of the calibrated parameters in representing dryseasons in the Branco River basin. Regardless of the high perfor-mance coefficients and the similarity among modeled hydro-graphs, one can identify small differences among the optimizedresults.

Fig. 10 highlights the year 2005. One can see that a more limitedavailability of altimetric data for the 1VS scenarios resulted inworse discharge simulations during the dry seasons. The increasingof data availability for the optimization process, as provided in thescenarios 4VS and OBS, forced parameters to better represent thedaily altimetric and discharge time series. It is also seen that in-tra-seasonal peaks and droughts are shortened when parametersare optimized taking into account a1. In addition, no significant

interference of errors inherent in both the empirical h � Q relationand the altimetric time series is perceived in the results of theautomatic calibration with spatial altimetry data (1VS and 4VS)when compared to those obtained with discharge (OBS), sincemodeled hydrographs from the six scenarios are very similar andhave similar performance coefficients.

4.1. Validation of the automatic calibration

Optimized parameter sets have also been evaluated at twogauge stations located along the Branco River tributaries (FazendaPassarão station on the Uraricoera River and Mucajaí station on theMucajaí River) during the 1997–2001 and 2002–2006 periods andat the Caracaraí station during the 1997–2001 period. One param-eter set was selected from each of the six Pareto solutions. Resultsfrom the manual calibration with 11 GRUs (Getirana et al., 2010)have also been considered for comparison reasons.

According to Schaefli and Gupta (2007), the NS coefficient rep-resents a form of noise-to-signal ratio, where the average variabil-ity of model residuals is compared to the variability of the targetoutput (TO). It quantifies how a particular model can representTO when compared to a reference signal, which is, in the case ofthe NS coefficient, the mean value of TO. However, depending uponthe case, the mean value of the TO can have a different impact onthe NS computation. For example, a unique mean value of thewhole TO time series can be a poor way for representing high-sea-sonality phenomena. On the other hand, it can be a satisfactoryrepresentation of the TO series if the latter is basically defined assmooth oscillations around a relatively constant value. In thissense, Schaefli and Gupta (SG) suggest the use of a NS-based

0

5000

10000

150001VS aR²

0

5000

10000

150004VS aR²

0 366 731 1097 14620

5000

10000

15000OBS aR²

Obs IGP Otm

Fig. 8. Hydrographs at the Caracaraí station during the calibration period (2002–2006). Observed data (Obs), initial guess parameters (IGP) and optimal solutions provided bythe model for the three scenarios using the combination of objective functions aR2 (Otm).

0

5000

10000

150001VS NR²

0

5000

10000

150004VS NR²

0 366 731 1097 14620

5000

10000

15000OBS NR²

Obs IGP Otm

Fig. 9. Hydrographs at the Caracaraí station during the calibration period (2002–2006). Observed data (Obs), initial guess parameters (IGP) and optimal solutions provided bythe model for the three scenarios using the combination of objective functions NR2 (Otm).

252 A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255

coefficient that takes into account the seasonal variability of thetarget signal. Their objective is to define an equation which is capa-ble of identifying whenever the model has more predictive abilitiesthan those processes already inserted into the seasonality of thereference signal. The SG coefficient is defined as:

SG ¼ 1�Pnt½XobsðtÞ�XsimðtÞ�2

t¼1Pntt¼1½XobsðtÞ � XrefðtÞ�2

ð14Þ

where XrefðtÞ is the reference value at time step t.In this study, besides the traditional NS, three forms of the SG

coefficient are considered, each coefficient differs from the othersas a function of Xref ðtÞ. The first one considers the daily seasonalityof the observed signal (SG.d), having a mean discharge for each ofthe 365 days of the hydrological year. The second one considers

monthly mean discharges (SG.m), from January to December. Thethird variation takes into account the annual mean discharge(SG.y), one for each year of the studied period.

Three other coefficients were considered in order to quantifythe model performance. They are: the tangent a [Eq. (9)], the deter-mination coefficient R2 [Eq. (10)] and the relative error (RE) givenby:

REð%Þ ¼Xnt

t¼1

XsimðtÞ � XobsðtÞXobsðtÞ

� 100 ð15Þ

In a general sense, results were good for the three stations. Theperformance coefficients for the periods 1997–2001 (validation)and 2002–2006 (calibration) are compared in Tables 4 and 5.Differences among scenarios are discussed in the followingparagraphs.

0

5000

10000

150001VS aR²

0

5000

10000

15000

1 3650

5000

10000

15000OBS aR²

1VS NR²

4VS NR²4VS aR²

1 365

OBS NR²

Obs IGP Otm

Fig. 10. Hydrographs at the Caracaraí station during 2005. Observed data (Obs), initial guess parameters (IGP) and the set of optimal solutions provided by the model (Otm)for the six scenarios.

Table 4Performance coefficients for the 1997–2001 period derived from the manualcalibration (Sim) and the other 6 automatic calibration scenarios at Caracaraí,Fazenda Passarão and Mucajaí stations.

Scenario Performance coefficient

SG.d SG.m SG.y NS RE (%) a R2

Faz. PassarãoSim 0.45 0.51 0.73 0.78 12.81 0.93 0.83

1VS aR2 0.47 0.52 0.74 0.78 8.07 0.94 0.82NR2 0.50 0.55 0.76 0.80 6.03 0.94 0.82

4VS aR2 0.56 0.60 0.78 0.82 5.09 0.93 0.84NR2 0.53 0.58 0.77 0.81 7.74 0.93 0.83

OBS aR2 0.43 0.49 0.72 0.77 5.76 1.03 0.83NR2 0.37 0.43 0.69 0.75 7.01 1.02 0.81

MucajaíSim 0.39 0.42 0.66 0.74 22.82 1.01 0.86

1VS aR2 0.27 0.31 0.59 0.68 26.39 1.10 0.87NR2 0.33 0.37 0.62 0.71 24.61 1.10 0.88

4VS aR2 0.35 0.39 0.64 0.72 23.08 1.10 0.88NR2 0.22 0.27 0.56 0.66 25.93 1.11 0.86

OBS aR2 0.15 0.20 0.52 0.63 24.10 1.19 0.86NR2 0.12 0.17 0.51 0.62 25.03 1.16 0.85

CaracaraíSim 0.54 0.58 0.81 0.84 16.64 0.95 0.88

1VS aR2 0.56 0.60 0.82 0.84 10.35 0.92 0.86NR2 0.61 0.64 0.84 0.86 7.04 0.91 0.87

4VS aR2 0.64 0.67 0.85 0.87 5.62 0.91 0.88NR2 0.61 0.64 0.84 0.86 9.37 0.93 0.88

OBS aR2 0.58 0.62 0.83 0.85 7.06 1.00 0.88NR2 0.53 0.57 0.81 0.83 8.17 0.99 0.86

A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255 253

NS and SG coefficients had small variations between scenariosat the Caracaraí station for the 2001–2006 period. The best NSand SG.d coefficients corresponded to scenario OBS NR2

(NS = 0.94 and SG.d = 0.75). The 4VS scenarios had nearly the bestperformances (0.93 and SG.d = 0.73). Similar NS and SG.d coeffi-cients were provided by the manual calibration. The worst results(although still acceptable) at that station for the same period wereprovided by scenario 1VS aR2 (NS = 0.92 and SG.d = 0.69). The besta values were also provided by the OBS scenarios (�1.0). the rela-tive errors improved from the manual (5.8%) to the automatic (bestvalue of 0.3% for 4VS NR2) calibration scenarios.

The predictive ability of the calibrated model at the Caracaraístation was validated with satisfactory NS and SG coefficients com-puted for the 1997–2001 period. Again, automatic calibration (bestvalues for 4VS aR2; NS = 0.87 and SG.d = 0.64) performances sur-passed those provided by the manual calibration. Among auto-matic calibration scenarios, those performed with spatialaltimetry data provided results equal to, or better than, those usingobserved data.

Satisfying results were also found for the Fazenda Passarão sta-tion. As evidenced at the Caracaraí station, automatic calibrationscenarios resulted in better coefficients when compared with themanual approach (NS = 0.78, SG.d = 0.45 and RE = 12.8% for the1997–2001 period) and spatial altimetry-based calibration(NS = 0.82, SG.d = 0.56 and RE = 5.1% provided by scenario 4VSaR2 for the same period) provided a better performance than thedischarge-based calibration (NS = 0.77, SG.d = 0.43 and RE = 5.8%provided by OBS NR2).

In contrast to previous findings, the best performance coeffi-cients were found for the manual calibration for both periods atthe Mucajaí station. For the 1997–2001 period, coefficients at thatstation (NS = 0.74, SG.d = 0.39 and RE = 22.8%) were comparable tothose obtained for the Fazenda Passarão station with the manualcalibration approach. The best performances provided by the

Table 5Performance coefficients for the 2002–2006 period derived from the manualcalibration (Sim) and the other 6 automatic calibration scenarios at Caracaraí,Fazenda Passarão and Mucajaí stations.

Scenario Performance coefficient

SG.d SG.m SG.y NS RE (%) a R2

Faz. PassarãoSim 0.49 0.56 0.84 0.85 12.81 0.95 0.89

1VS aR2 0.48 0.55 0.84 0.85 9.39 0.99 0.88NR2 0.51 0.57 0.85 0.86 7.01 1.01 0.88

4VS aR2 0.57 0.63 0.87 0.88 5.35 0.98 0.89NR2 0.53 0.59 0.85 0.87 8.83 0.99 0.89

OBS aR2 0.44 0.51 0.83 0.84 5.88 1.08 0.89NR2 0.45 0.52 0.83 0.84 6.21 1.07 0.89

MucajaíSim �0.66 �0.36 0.62 0.65 �6.00 0.89 0.70

1VS aR2 �0.76 �0.44 0.60 0.63 �1.05 1.01 0.73NR2 �0.97 �0.61 0.55 0.58 �3.77 1.02 0.71

4VS aR2 �0.90 �0.56 0.56 0.60 �5.15 0.98 0.71NR2 �1.01 �0.65 0.54 0.57 �1.96 1.00 0.70

OBS aR2 �1.02 �0.65 0.54 0.57 �4.57 1.08 0.73NR2 �0.82 �0.49 0.58 0.61 �4.78 1.05 0.75

CaracaraíSim 0.74 0.77 0.93 0.93 5.82 0.93 0.94

1VS aR2 0.69 0.73 0.92 0.92 1.30 0.92 0.92NR2 0.70 0.74 0.92 0.93 �1.84 0.93 0.93

4VS aR2 0.73 0.77 0.93 0.93 �3.50 0.92 0.93NR2 0.73 0.76 0.93 0.93 0.29 0.94 0.93

OBS aR2 0.73 0.77 0.93 0.93 �2.27 1.00 0.94NR2 0.75 0.78 0.93 0.94 �1.99 0.99 0.94

254 A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255

automatic calibration approach were those obtained with 4VS aR2

(NS = 0.72, SG.d = 0.35 and RE = 23.1% for the same period). Sce-nario OBS aR2 resulted in lower performance coefficientsNS = 0.63, SG.d = 0.15 and RE = 24.1%.

All the seven scenarios (including the manual calibration) pro-vided negative values for coefficients SG.d and SG.m at the Mucajaístation during the 2002–2006 period. This reveals that model per-formances at that site are worse than those attained if daily ormonthly mean discharges were used to represent hydrographs atthat station. The manual calibration approach provided the best re-sults (NS = 0.64, SG.d = �0.66 and RE = �6.0%) followed by scenario1VS aR2 (NS = 0.63, SG.d = �0.76 and RE = �1.0%). Negative valuesfor SG coefficients can be explained by the following reasons: (i)basin physics are poorly represented; (ii) the parameterizationsare inadequate; and/or (iii) precipitation fields are not consistentwith reality. The first two hypotheses are rejected since good re-sults are attained in the 1997–2001 period, which indicates consis-tency in representing the basin physics. Another reason forrejection is because attempts were performed with several hun-dreds of parameter sets along the optimization processes, whichdemonstrates that the parameterizations are optimal or near-opti-mal. The third hypothesis seems to be a reasonable explanation forthe negative values in the 2002–2006 period.

5. Conclusions

This study presents the pioneering use of spatial altimetry datain the automatic calibration of hydrological models. ENVISAT satel-lite data is used to conduct the search for optimal parameters ofthe MGB-IPH model. Two sets of OFs are minimized with the MO-COM-UA algorithm through the search for Pareto solutions. The

optimization process is carried out for the Branco River basin con-sidering, independently, altimetric data from one VS, four VS’s andone gauge station. Results are analyzed qualitatively through vi-sual inspections of the resultant hydrographs and quantitativelyby means of performance coefficients computed for two periods1997–2001 and 2002–2006, and for three gauge stations locatedin different locations within the Branco River basin.

The first results demonstrated the potential of spatial altimetryfor the automatic calibration of hydrological models in poorlygauged basins. Although divergence between hydrographs werenoted at refined time scales, spatial altimetry-based optimalparameter sets provided performances equivalent to those ob-tained with discharge-based optimization scenarios. In particular,the scenarios considering four VS’s provided competitive results,showing their ability to predict discharge time series in differentperiods and in other locations of the basin. Noise inherent in thealtimetric data acquisition and processing did not seem to be arestriction for obtaining optimal hydrographs. However, these er-rors can influence in the reliability of the optimal parameters.

The proposed methodology requires h � Q relations at virtualstations, which can limit its application. New methodologies mustbe developed using global and generalized h � Q relations and/oroptimization techniques capable of automatically relating the Hand Q. Once these goals are achieved, the methodologies will beable to contribute to applications of future altimetric missions suchas the Surface Water and Ocean Topography (SWOT) mission(Biancamaria et al., 2009), which is planned to be launched withinthe decade.

Another issue raised in this study concerns the choice of thebest OFs for the automatic calibration as a function of the natureof available data. Objective functions must take into account differ-ent aspects of the signal used to calibrate the model. It is importantto use OFs with low correlation (Gupta et al., 1998). For practicalreasons, this study restricted the number of OFs to three.

The validation of a methodology is a long process and requiresassessments of different case studies. The region considered in thisstudy has a well defined seasonality as the main characteristic. Therelatively high value of Rm = 7.7 [the ratio of the maximal (Qmed,-

max) and minimal (Qmed,min) monthly mean discharges] at the Cara-caraí station can be a catalyst for integrating spatial altimetry datainto the automatic calibration of hydrological models. Moreover,the Branco River basin is located in one of the best gauged regionsof the Amazon basin with about 0.28 rain gauge stations per1000 km2. These factors can contribute to obtaining satisfactory re-sults (high performance coefficients) in all of the simulations.Therefore, the application and adjustment of this methodologyare recommended for other locations in the Amazon basin andother tropical basins. By subjecting this method to different hydro-logical conditions and monitoring, the positive and negative as-pects of the introduction of spatial altimetry data into theautomatic calibration of computational models can be studiedand refined.

The generalization of such an approach will be a great advancefor a better understanding of the global water cycle and water re-sources planning and management in poorly gauged and ungaugedbasins. Once data acquisition and processing become efficient pro-cedures, operational hydrological forecasts will be accomplishedbased, not only on gauged data but also on other remote sensingdata, such as spatial altimetry.

Acknowledgements

The author would like to thank CNPq and CAPES/COFECUB (Pro-ject 516/05) financial support. This work benefited from hydrolog-ical data made available by Agência Nacional de Águas (ANA).ENVISAT data are distributed by ESA under the form of Geophysical

A.C.V. Getirana / Journal of Hydrology 387 (2010) 244–255 255

Data Records (GDRs). The multi-mission database of GDRs is main-tained by the Centre de Topographie des Océans et de l’Hydro-sphère (CTOH) at LEGOS. The author also shows gratitude for thecomments provided by A. Boone (CNRM/Météo-France) and twoanonymous reviewers.

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