Producing time series of river water height by means of satellite radar altimetry—a comparative study

104 Hydrological Sciences Journal – Journal des Sciences Hydrologiques, 55(1) 2010

ISSN 0262-6667 print/ISSN 2150-3435 online© 2010 IAHS Pressdoi:10.1080/02626660903529023http://www.informaworld.com

THSJ

Producing time series of river water height by means of satellite radar altimetry—a comparative study

Producing time series of river water height by means of satellite radar altimetry—a comparative studyEmmanuel Roux1, Joecila Santos da Silva3,4, Augusto Cesar Vieira Getirana2,3, Marie-Paule Bonnet2, Stéphane Calmant4, Jean-Michel Martinez2 & Frédérique Seyler1

1IRD, US140 ESPACE, Centre IRD de Guyane, BP165, Route de Montabo, 97323 Cayenne Cedex, French [email protected], IRD-CNRS-Université de Toulouse III, Toulouse, France3Programa de Engenharia Civil, COPPE/Universidade Federal do Rio de Janeiro, PO Box 68506, CEP 21945-910, Rio de Janeiro, Brazil4LEGOS, IRD-CNRS-CNES-Université de Toulouse III, Toulouse, France

Received 12 February 2008; accepted 5 August 2009; open for discussion until 1 August 2010

Citation Roux, E., Santos da Silva, J., Vieira Getirana, A. C., Bonnet, M.-P., Calmant, S., Martinez, J.-M. & Seyler, F. (2010)Producing time series of river water height by means of satellite radar altimetry—comparative study. Hydrol. Sci. J. 55(1), 104–120.

Abstract Satellite radar altimetry is complementary to in situ limnimetric surveys as a means of estimating thewater height of large rivers, lakes and flood plains. Production of water height time series by satellite radaraltimetry technology requires first the selection of radar ground target locations corresponding to water bodysurfaces under study, i.e. the definition of “virtual limnimetric stations”. We propose to investigate qualitativeand quantitative differences between three representative virtual station creation methodologies: (a) a fullymanual method, (b) a semi-automatic method based on a land cover characterization that allows the water bodysurface under study to be located; and (c) an original fully automatic procedure that exploits a digital elevationmodel and an estimation of the river width. The results yielded by these three methods are comparable: maximumabsolute magnitudes of water height differences being 0.46, 0.26 and 0.15 m for, respectively, 95, 90 and 80% ofthe water height values obtained. Moreover, more than 67% and 92% of time series jointly produced by themethods present root mean square differences lower than 20 and 50 cm, respectively. The results show that thefully automatic method developed herein provides as reliable results as the fully manual one. This opens the wayto use of satellite radar altimetry for the generation of water height time series on a large scale, and considerablyextends the applicability of satellite radar altimetry in hydrology.Key words satellite radar altimetry; Amazon basin; water height time series; image classification; digital elevation model

Produire des séries temporelles de hauteur d’eau des cours d’eau grâce à l’altimétrie radar satellitaire—une étude comparativeRésumé L’altimétrie radar satellitaire est complémentaire des relevés limnimétriques in situ pour l’estimation dela hauteur d’eau des grands fleuves, lacs et plaines d’inondation. L’obtention de séries temporelles de hauteurd’eau par altimétrie radar satellitaire requiert la sélection de cibles radar au sol correspondant aux surfaces en eaud’intérêt, i.e. la définition de “stations limnimétriques virtuelles”. Nous proposons de comparer qualitativementet quantitativement trois méthodes de création de stations virtuelles: (a) une méthode entièrement manuelle; (b)une méthode semi-automatique basée sur une caractérisation de l’occupation du sol qui permet de localiser lescours d’eau; et (c) une procédure originale entièrement automatique qui exploite un modèle numérique de terrainet une estimation de la largeur de la rivière. Les résultats fournis par ces trois méthodes sont comparables: ladifférence absolue maximale de hauteur d’eau est de 0.46, 0.26 et 0.15 m pour, respectivement, 95, 90 et 80% desvaleurs de hauteur obtenues. De plus, plus de 67% et de 92% des séries temporelles produites conjointement parles méthodes présentent des erreurs quadratiques moyennes inférieures à 20 et à 50 cm, respectivement. Cesrésultats montrent que la méthode entièrement automatique proposée ici fournit des résultats aussi fiables qu’uneméthode entièrement manuelle. Il est par conséquent envisageable d’exploiter l’altimétrie radar satellitaire afinde générer des séries temporelles de hauteur d’eau à grande échelle, ce qui étend considérablement l’applicabilitéde l’altimétrie radar satellitaire en hydrologie.

Mots clefs altimétrie radar satellitaire; basin Amazonien; séries temporelles de hauteur d’eau; classification d’images; modèlenumérique de terrain

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Producing time series of river water height by means of satellite radar altimetry—a comparative study 105

INTRODUCTION

Water resources management in the great tropicalbasins of the world is a complex issue. For example,in the Amazon basin, the largest river basin of theworld, the hydrological regimes of the main tributar-ies, their typology and water availability, are affectedby human economic activities, such as deforestation,mining, and cereal monoculture. Water use must beregulated between agriculture and rural development,energy and transport, water supply and sanitation,environment and tourism. Many tropical basins aretrans-boundary and conflicting situations arise thatmay increase in time. In the humid tropics, theypresent a dense river network, very variable in shape,length, width and volume. The water rise duringflooding varies spatially from 2 to 20 m, but is regu-lar and persistent in the downstream part of the maintributaries. The water height has well-marked annualvariations which tend to increase in amplitude withclimate change. The Amazon basin includes 50 000 kmof waterway, and, despite a low population density,water quality degradation occurs in several parts ofthe basin. In such a context, as stated by van Griens-ven et al. (2006): “Two instruments play an import-ant role in integrated impact assessment: monitoringand modelling”. The Amazon basin covers about 6000 000 km2. Sixty-three percent of this area is situ-ated in Brazil and is monitored by 435 limnimetricstations (ANA, 2008). Installing and maintaining theoperational networks of hydrological in situ stationsin remote basins is complicated and very costly.Human-based measurements are subjective, and thecompleteness of data records and their qualitydepend on operator availability and assiduity.

In this context, radar altimetry is a promisingcomplementary tool for water-level monitoring inlarge river basins, such as the Amazon basin. Basi-cally, radar altimetry measures the two-way traveltime of a radar pulse between the satellite antennaand the Earth surface at the nadir of the altimeter.This measurement is performed through recordingthe energy bounced back by the reflecting facetswithin the altimeter footprint (typically a few km2).Note that the radar wavelength used, namely K-band,was selected because it does not penetrate water,making energy reflected by water surfaces predomi-nate in the total energy received onboard the satellite.This energy is processed through a ∼0.1-μs receptionwindow. An important consideration is the algorithmused to derive the two-way travel time from the radar

echo, the so called tracker (onboard) or retracker(ground reprocessing) algorithm. Indeed, contrary tothe oceanic domain that the system was tuned for, theshape of the energy distribution in the reception win-dow is highly variable over continental waters. Frap-part et al. (2006) have shown that, among the fourretrackers used for the ground processing of theENVISAT data, ICE-1 (Wingham et al., 1986) wasthe one performing best over rivers. We thereforeused the ICE-1 solution for this work. Travel timepicked up by the retracking algorithm is then con-verted into satellite–ground distance by taking intoaccount corrections associated with electromagneticpulse propagation through the atmosphere and iono-sphere, and solid Earth tides. Orbitography providesthe satellite height relative to a reference ellipsoid.The difference between this height and the distancederived from the radar measurement, including theaforementioned corrections, gives the height of thewater surface with respect to the reference ellipsoid.Altimetry satellites are kept on a fixed ground trackin order to overfly the same locations at regular timeintervals, called repeat cycles. The repeat cycledepends on the orbit parameters selected for the mis-sion. For radar altimetry missions, this typicallyranges from 10 to 35 days. The ability of radar altim-eters to monitor stage elevation of continental watersurfaces has been demonstrated (Birkett, 1998; DeOliveira et al., 2001; Calmant & Seyler, 2006;Frappart et al., 2006). In the Amazon basin, satellitedata very significantly increase the number of waterstage measurement points. The intersections betweenthe river system and the satellite tracks are about tentimes denser than the actual in situ gauging network.Moreover, if radar altimetry sampling periods, whichcorrespond to satellite cycle durations, range from 10(TOPEX/POSEIDON) to 35 days (ENVISAT), it hasbeen shown that daily water stage estimation can beprovided by adequate interpolation techniques asso-ciated with in situ data (Roux et al., 2008). Addition-ally, satellite altimetry already allows river dischargeto be estimated by establishing rating curves usingaltimetric heights and either remotely measured dis-charge (Coe & Birkett, 2004; Kouraev et al., 2004),or local model-based discharge estimates (Leonet al., 2006). Also, lake heights can be predicted(Coe & Birkett, 2004) and flood-plain water storageestimated (Frappart et al., 2005).

The exploitation of satellite altimeter data is per-formed by defining “virtual limnimetric stations”.Basically, a “virtual station” can be defined as any


106 E. Roux et al.

intersection between a water body surface and a sat-ellite ground track (Fig. 1). Ground track locationsshow significant variations that can reach 1 km eitherside of theoretical ground tracks. Thus, in the follow-ing, a “track” includes all satellite radar ground tar-gets and has approximately 2 km width. Severaltechniques have been considered in the literature todefine these virtual stations (see the section below onliterature review of “virtual station” definition).However, these procedures are not extensively dis-cussed and, to our knowledge, have not been quanti-tatively compared in terms of water height timeseries produced. In this context, it is difficult to com-pare and/or jointly analyse water height time seriesprovided by different selection methods. This paperfirst reviews altimetric data selection proceduresfound in the literature. Then, three procedures arechosen for investigation and the methodology forcomparison is detailed. The first method is the fullymanual three-dimensional (3-D) selection methodused in Santos da Silva et al. (2007a,b). The secondis a semi-automatic and precise geographical

selection method based on a land-cover characteriza-tion obtained with the JERS-1 SAR image classifica-tion methodology proposed by Martinez & Le Toan(2007). The third method is original and fully auto-matic. It only exploits a digital elevation model(DEM) of the studied area and basic knowledge onthe river width along the drainage network. Theresults of the investigations are then presented anddiscussed. Finally a conclusion is drawn.

LITERATURE REVIEW OF “VIRTUAL STATION” DEFINITION

Birkett (1998), using AVISO Topex/Poseidon GDRdata, proposed a multi-criteria selection methodol-ogy. The author: (a) supposes that river surfaces areassociated with a radar backscatter coefficient greaterthan 20 dB; (b) uses 1:1 000 000 Operational Navi-gation Charts (ONC) which roughly indicate thebank-to-bank geographical crossing points betweensatellite tracks and rivers; (c) identifies the water sur-face by considering the uniformity of the elevation

Fig. 1 Three-dimensional manual selection: (a) JERS-1 background image, one satellite ground track and the rough geo-graphical selection of the intersection; (b) data selection into the plane perpendicular to the river direction; (c) locations ofselected data; (d) water height time series corresponding to the selected data. The lines link the medians of overpass values.



measurements, i.e. the along-track standard deviationof water height variations; (d) identifies the water sur-face by utilizing an elevation filter (manual selectionbased on ONC map heights and observation of thealtimetric elevations along-track); and (e) separatesriver channel from nearby flood plain by examiningthe seasonal variation of radar backscatter and eleva-tion (river channels showing higher-amplitude eleva-tion variations and lower-amplitude backscattervariations, and flood plains having the opposite trend).

De Oliveira et al. (2001) and Mercier (2001)tested three criteria in order to automatically selectaltimetric data related to water surfaces: (a) the “lati-tudinal measurement density”, i.e. the percentage ofvalid measurements inside a 1-km-wide window(along the latitudinal dimension) moved along thesatellite ground track (selection threshold is set to50%); (b) the “water level fluctuation”, by statingthat water surfaces have, in the Amazon Basin, anannual amplitude of at least 1 m; (c) the “backscattercoefficient”, s°, with the condition s° > 20 dB. How-ever, Mercier (2001) shows that selection criteria thatonly take into account the intrinsic information ofaltimetric data do not permit: (i) selection of watersurfaces with a geographical resolution lower than1 km, or (ii) permanent water surface to be distin-guished from occasionally flooded areas. As a result,Mercier (2001) performs precise geographical delim-itations of areas within which the satellite’s nadirlocations (satellite ground tracks) and water (lakesand rivers) intersect. For lakes, the author uses thelake contours provided by the CIA World Data BankII, available in the Generic Mapping Tool (GMT)open-source software, and automatically selects thealtimetric measurements. For large rivers such as theAmazon River, Mercier (2001) uses Synthetic Aper-ture Radar (SAR) images provided by the JERS-1satellite, without, however, presenting in detail whathis selection criteria and tools are (form of the selec-tion, selected pixels’ features, etc.).

Berry et al. (2005) also used the CIA WorldData Bank II database to define masks and selectinland altimetric data. These masks are set slightlywider than maximum water extent and a detailedAmazon River mask is also defined. Then retrackingof radar echoes is performed by means of an expertsystem approach (Berry, 2000) and echoes present-ing a “leading edge and a significant power withinthe waveform” are selected (Berry, 2006).

Frappart et al. (2005) used a land-cover charac-terization based on a JERS-SAR image classification

method (Martinez & Le Toan, 2007). Land-covercharacterization involves nine classes: (1) Permanentwater (permanent lakes), (2) Occasionally floodedforest, (3) Never flooded forest, (4) Never floodedsavannah, (5) Occasionally flooded non-vegetated/herbaceous areas, (6) Always flooded forest, (7)Occasionally flooded savannah, (8) Permanent water(main rivers), and (9) Totally submersed vegetation.Intersections between classes of interest and satelliteground tracks are identified, and rectangular selec-tion windows are defined manually.

In Leon (2006), virtual stations are defined bymanually digitizing rectangular windows that sur-round the intersections between the satellite tracks andthe rivers located by means of JERS-1-SAR images.

In Kouraev et al. (2004), the authors performeda more rigorous geographical selection of the alti-metric data by considering 28.5-m resolution Landsatimages and selecting only parts of the satelliteground tracks that cover the main channel of the river(Ob’ River).

Zakharova et al. (2006) used JERS-1-SARimages and defined a virtual station by a rectangularwindow. However, several rectangular windows canbe defined when islands are present.

The previous manual data selection proceduresare two-dimensional. But a simple (even if precise)geographical selection of altimetric measurementsthat “fall” in the water surface, using one image, hastwo main drawbacks: (a) the water surface is onlyknown at the image capture time. So, if the chosenimage corresponds to high water stage, data relatedto non-flooded areas during low water stage areselected and can be unreliable (see Fig. 1(b)). How-ever, if the chosen image corresponds to low waterstage, possibly valid data related to flooded areasduring a high water stage period are ignored; (b) 2-Dgeographical selection does not permit identificationof the off-ranging phenomenon described by Berry(2000). Radar echo retracking is proposed in order toovercome this inland-specific artefact (Berry, 2000;Frappart, 2005). This phenomenon often occurswhen the satellite nadir is not yet (or no more) abovethe river surface and the altimeter is already (or still)locked on the river surface, leading to an underesti-mation of the water height (see Fig. 1(b)). This isreferred to as a “locking” and a “hooking” phenome-non in Santos da Silva et al. (2007a,b) and Frappart(2006), respectively.

In Santos da Silva et al. (2007a,b) the authorsuse a 3-D procedure for the altimetric data selection.


108 E. Roux et al.

First a 2-D geographical selection of the satellitetrack–river intersection is performed by using JERS-SAR images (i.e. a selection in the longitude × lati-tude plane). Altimetric heights associated with theselected radar nadir locations are then projected ontothe plane perpendicular to the main direction of theriver (this direction is characterised manually), i.e.the river section plane. Finally, a second data selec-tion is performed manually in the river section plane.This 3-D procedure has been developed to avoid thetwo previously mentioned drawbacks of the 2-D geo-graphical selection. This is given in more detail in theMethod Section below, as it is one of the three meth-ods extensively studied herein.

All the previously mentioned selection proce-dures are summarized in Table 1. In the following,we present in detail, and compare, three methods foraltimetric data selection.

METHOD

Area of study

The three proposed methodologies have been appliedon the entire Rio Negro basin (Fig. 2). With a meanannual discharge of 29 000 m3 s-1, the Negro River isthe second largest discharge tributary of the Amazonafter the Madeira River. The drainage area of the RioNegro is nearly 700 000 km2 and extends throughparts of Colombia, Venezuela and Brazil. The NegroRiver basin is consequently a typical great andremote trans-boundary tropical basin. Most of thepublished studies related to satellite radar altimetryconsider the Rio Negro basin.

Altimetric data

In the following, we consider the 18-Hz Ku-rangeENVISAT data contained in the Geophysical DataRecords (GDRs) delivered by the Archiving, Valida-tion and Interpretation of Satellite data in Oceanogra-phy (AVISO) at the Centre National d’EtudesSpatiales (CNES). In particular, the ICE-1 retrackedversion of these data is considered. In fact, among theretrackers Ocean, ICE-1, ICE-2 and Sea Ice, the ICE-1 algorithm (Wingham et al., 1986) gave the mostaccurate results for continental hydrology studies inFrappart et al. (2006). The corrections applied tothese data are on-board instrumental drifts and biases,ionospheric, dry and wet troposphere, solid earth andpoles tide corrections (Chelton et al., 2001).

The data set used in this study ranges from 1October 2002 to 12 November 2006, correspondingto a four-year-long period. The repeat cycle ofENVISAT being of 35 days, data from 35 to 42 satel-lite cycles have been exploited.

Methods for virtual station definition (altimetric data selection)

Three data selection methods have been chosen forinvestigation, according to: (a) their representative-ness of the methodologies already described in theliterature, and (b) their level of automation:

Three-dimensional manual selection (MANU) First a map or an image is selected to identify watersurfaces. Here, the high-water stage mosaic of theAmazon basin provided by the Global Rain ForestMapping (GRFM) Project (Freeman et al., 2002) isused. SAR data characteristics used for this mosaicconstruction can be summarized as follows (Hesset al., 2003): L-band (1275 MHz) frequency and HHpolarization, 34 to 43 degrees for incidence angle,pixel size resampled at 100 m, acquisition periodfrom May to August 1996 for the high-water stagemosaic and from October to November 1995 for thelow-water stage mosaic, –15 to –20 dB for noiseequivalent s°, ±0.2 dB calibration uncertainty.

The MANU selection method consists of a two-step manual procedure:

(1) A geographical delimitation of the intersectionbetween the water surface under study and theground track of the satellite is realized by digi-tizing a shape that can be complex (multiplepolygon, exclusion of non-flooded areas,islands, etc.) (cf. Fig. 1(a)). Then, the user hasto indicate the main flow direction of the riverby pointing two points along the river. Heightsassociated with the radar nadir locations fallingin the previously defined zone are automaticallyprojected onto the plane perpendicular to themain direction of the river, i.e. the river sectionplane. This data representation permits correctvisualization of the altimetric heights associatedwith all satellite passes (cf. Fig. 1(b)).

(2) A second selection is manually performed inthe river section plane (cf. Fig. 1(b)) (the sametool for shape digitizing is used). Data associ-ated with a low intra-pass variability and a highinter-pass variability are selected. These criteria


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110 E. Roux et al.

are also used by Birkett (1998), De Oliveiraet al. (2001) and Mercier (2001) (see Table 1and section on Literature Review).

In this study, 43 virtual stations defined by Santos daSilva et al. (2007a,b) are taken into account. Forcomparison purposes, it would have been “theoreti-cally” possible to manually define a virtual stationfor each selection performed by the two otherapproaches. We used a significant number of previ-ously defined stations (Santos da Silva, 2007a,b) fortwo reasons: (a) the MANU selection technique istime consuming and performing a selection for everyriver–satellite track intersection would have beenparticularly tedious; and (b) virtual stations in Santosda Silva (2007a,b) were created independently of theobjectives pursued in this comparative work andallow the results to be as objective as possible.

Precise geographical selection (AUTO-JERS) This method is semi-automatic and is based on theland-cover characterization derived from a JERS-1SAR image classification (Martinez & Le Toan,2007). Altimetric data that “fall” in pixels labelled“Class 8: Permanent water (main rivers)” areselected (Fig. 3). This method can be compared withthe approach of Mercier (2001) for lakes and more

generally with any methods based only on geograph-ical selection (even if most of the publishedapproaches only require rectangular selections).

In the present study, geographical selections (ormasks) are made one pixel larger than Class 8 areasthat intersect with satellite ground tracks (note that, assatellite ground track location shows significant vari-ations that can extend 1 km either side of the theoreti-cal track, a “track” is approx. 2-km wide in thefollowing, as it includes all the satellite ground targetlocations). Berry et al. (2005) also defined masksslightly wider than maximum water extent. Thisallows virtual stations to be defined for narrow riversand avoids the multiplication of virtual stations forparcelled out satellite track–narrow river intersec-tions. In fact, such rivers can be characterized by dis-continuous areas associated with the Class 8 label(see, for example, Fig. 4). Additionally, intersectionswhose surface is smaller than 150 000 m2 are filtered.

However, despite the one-pixel tolerance and thearea-based filter previously mentioned, a manualpost-processing of the results has to be performed inorder to assemble several virtual stations related tothe same river but separated by islands or river dis-continuities (see Fig. 5(b), (c) and (d) for examples).This post-processing is a time-consuming operationthat has been partially automated by means of a

Fig. 2 Negro River basin delimitation, main tributaries and virtual stations defined by the three selection methods (MANU,AUTO-JERS and AUTO-SRTM). The river network is extracted from the land-cover characterization (Class 8) obtainedfrom JERS mosaics (Martinez & Le Toan, 2007). Grey oblique lines represent ENVISAT satellite ground tracks.



BASH1 script calling GRASS (2006) geographicalinformation system (GIS) functions for drawing,selection and concatenation of the virtual stations(defined by vectorial maps in the GIS).

It is worth noting that the choice of the JERSmosaic for application of the MANU method is con-sistent with the use of the land-cover characterizationexploited by the AUTO-JERS approach and makesthe results of these two methods comparable.

DEM-based selection (AUTO-SRTM) Hydro-graphical networks can be obtained by means of aDEM. We state that, for the river water height moni-toring, it is possible to define a virtual station at anyintersection between the drainage network extractedfrom a DEM and a satellite ground track. To test thisassumption, we used the Shuttle Radar TopographyMission (SRTM) DEM at 90-m spatial resolution.Flow accumulation for all the Negro River basin wasextracted with the r.terraflow.short function of theGRASS GIS, a flow computation routine for massivegrids (integer version), with the Single Flow Direc-tion (SFD) option. The r.terraflow function wasdesigned and optimized especially for massive datasets, but uses well-known approaches in order tocompute flow direction and accumulation:

(1) r.terraflow first floods the terrain until all thesinks (flat areas that do not spill out, includingone-cell pits) are filled;

(2) flow directions are then computed using eitherthe Multiple Flow Direction model or the SFDmodel. Both methods compute downslope flowdirections by inspecting the 3 × 3 windowaround each cell. The SFD method assigns aunique flow direction towards the steepestdownslope neighbour;

(3) once flow directions are computed for everycell in the terrain, r.terraflow computes flowaccumulation by routing water using the flowdirections and keeping track of how much waterflows through each cell. (For more detail on thealgorithms see Arge et al., 2003.)

1BASH is a free shell-compatible command language interpreter.See http://tiswww.case.edu/php/chet/bash/bashtop.html.

Fig. 3 Two-dimensional precise geographical selection: (a) Eighth class of the JERS-1-based land-cover characterization(permanent water: rivers), one satellite ground track and the geographical selection performed automatically; and (b) waterheight time series corresponding to the selected data.

Fig. 4 An example of a parcelled out intersection betweena satellite track and a narrow river. Performance of geo-graphical selections one pixel larger than the strict inter-section provides a continuous selection area.


http://tiswww.case.edu/php/chet/bash/bashtop.html

112 E. Roux et al.

Once the flow accumulation is computed, thedrainage network can be easily obtained by simplyconsidering the cells in which the flow accumulation isabove a given threshold. The higher this threshold, theless dense the resulting drainage network, ignoringsmall-sized rivers. In this study, the drainage networkhas been extracted by considering an accumulationthreshold equal to one million cells, corresponding to8100 km2 watersheds. This threshold was empiricallydefined in order to make the SRTM-based drainagenetwork and Class 8 of the JERS-based land-covercharacterization visually coincide. At this step of theprocedure, both the rivers extracted from the DEM andthe satellite track–river intersections are one cell wide.Consequently, we propose to define buffers aroundsatellite track–river intersections in order to define thegeographical areas that possibly contain valid

(river-related) altimetric data. For a given satellitetrack–drainage network intersection, we compute thebuffer size as a function of the flow accumulation. Asan intersection is defined by several cells (pixels) withdifferent flow accumulation values, we consider, forthe ith intersection, the average of the flow accumula-tion values: Acc(i). The flow accumulation can be con-sidered as analogous to discharge. In the literature, theriver width W is currently linked to the river dischargeQ by the relationship W = aQb (see, for example, Pis-tocchi & Pennington, 2006, for a recent application ofthis relation and older references). Consequently, forthe ith intersection, the buffer radius r(i) correspondingto the half river width W(i) is defined by:

Fig. 5 Examples of virtual stations for the three altimetric data selection methods.

r i W i i( ) = ( ) = ( ) 5 5 Acc0 0. . α β (1)



where a and b are parameters to be estimated andAcc(i) is the mean accumulation value for the ith sat-ellite track–drainage network intersection. In order toestimate a and b, values for W have been extractedfrom transverse section measurements freely avail-able from the Brazilian Water Agency (AgênciaNacional de Águas, ANA, 2007). Currently, 40 trans-verse sections are available for the entire Negro Riverbasin. Then, to facilitate parameter estimation, weconsidered the following linear form of equation (1):

Finally, log(a) and log(b) (i.e. a and b) were esti-mated with the classical least-squares method in theR (R Development Core Team, 2005) environmentfor statistical computing (R function lsfit). Theresults are shown in Fig. 6. Estimation provided aresidual standard error (RSE) equal to 0.2997 and R2

= 0.9188. We found a = 0.0187 and b = 0.653, andequation (1) can be written as:

Equation (3) enables the river width to be estimatedfor every satellite track–drainage network intersectionand, consequently, one can compute the buffer radius(with equation (1)) that characterizes areas whichpossibly contain valid (river related) altimetric data.Once parameters a and b are obtained, the creation ofvirtual stations for the entire basin is fully automatic.

The three methods described above were imple-mented in BASH language scripts calling GRASSGIS specific functions.

Comparison of methods

The following aspects of the methods areinvestigated:

(1) Number and locations of virtual stations.(2) Station “morphologies”, i.e. shape and com-

plexity of geographical selections as a functionof the method. This point is addressed from aqualitative point of view. [Indeed, even if wefocus on river monitoring, the aim of the paperis not to compare the three methodologies interms of river location identification but interms of water height estimation. It is quite dif-ferent according to altimetric data characteris-tics (footprint size, off-ranging phenomenon,etc.).] Then a quantitative comparison betweenthe three approaches is done in order to charac-terize method differences in terms of waterheight and its variability. Methods are consid-ered pair-wise, by performing paired sampleand one-sided Wilcoxon tests on overpass val-ues. The Wilcoxon test is a non-parametric testto compare two related samples and does notrequire assumptions about the sample distribu-tions. The null hypothesis is that the distributionof the paired sample differences is symmetricabout the median (Hollander & Wolfe, 1973).

log log 2 log log AccW r( ) = ( ) = + ( )( )a b (2)

Fig. 6 (a) Logarithm of the river width as a function of the logarithm of the flow accumulation (points), and the modelestimate (line). R2 = 0.9188 and Residual Standard Error = 0.2997; and (b) river width as a function of the flow accumula-tion (points), and the model estimate (line).

W Q 187 653= 0 0 0. . (3)


114 E. Roux et al.

Characteristic values computed and discussedfor the quantitative investigation are:

(3) Number of selected points per satellite over-pass. Water height derived from very few alti-metric data can be erroneous. The extreme caseis when only one value is selected for a satelliteoverpass. In such a case, the height value can bethe “true” one, but it also can correspond to aninconsistent value due to the off-ranging effect,an altimeter failure, etc.

(4) Water height. For each satellite overpass, whenseveral altimetric measurements have beenselected, the water height is characterized bythe median of the altimetric values, the medianbeing a more robust estimator, less sensitive toextreme values and a fortiori to outliers, thanthe average (see time series in Figs 1 and 3).Methods are compared at two levels:– at the satellite overpass level, by taking into

account: (i) all selected overpasses, and (ii)overpasses for which at least five measure-ments have been selected; and

– at the virtual station level, by computingthe RMS differences between water heighttime series associated with the virtual sta-tions jointly defined by two methods. Nor-malized cumulated histograms of the RMSdifferences are computed. This allowsdeduction of the percentage of virtual sta-tions that can be considered as identicallydefined by two methods, in terms of waterheight and as a function of a RMS differ-ence tolerance.

(5) Water height variability. Overpasses that com-prise at least five selected values are consid-ered. Variability is characterized by the medianabsolute deviation, MAD:

where N is the number of observations, xi is theith observation and xmed is the median of theobservations. The overpass-based and the timeseries-based (or station-based) investigations ofthe methods are performed too. Two stations,S1 and S2, related to the same satellite track–river intersection, provide identically variableresults according to a MAD difference toler-ance, d, if:

MAD(cSji) being the median absolute deviation

of values related to the ith overpass of StationSj.

RESULTS

Number and locations of virtual stations

The 2-D precise geographical selection methodusing the JERS land-cover characterization (AUTO-JERS) initially provided 219 geographical selec-tions. After the post-processing of these 219 areas(see Method Section, paragraph on Precise geo-graphical selection), 128 virtual stations weredefined. The SRTM-based method (AUTO-SRTM)yielded 131 virtual stations. In order to get compara-ble results between methods, seven of these stationswere assembled with the nearest ones only separatedby islands. Consequently, 124 virtual stations werefinally obtained with the SRTM-based method.Eventually, in the following, 43 virtual stationsdefined by Santos da Silva, et al. (2007a,b) with the3-D manual method (MANU) are taken intoaccount.

The AUTO-JERS and AUTO-SRTM methodshave 102 virtual stations in common, i.e. stations cor-responding to the same satellite ground track–riverintersections. The AUTO-JERS and MANU methodshave 40 stations in common, the AUTO-SRTM andMANU procedures 38, and the number of satellitetrack–river intersections jointly considered by thethree methods is 38.

Figure 2 shows the geographical distributionof the stations for each method. In Fig. 2, theNegro River network is extracted from the land-cover characterization (Class 8) obtained fromJERS mosaics (Martinez & Le Toan, 2007).Consequently, all the stations defined by theAUTO-JERS method are represented on the riverin Fig. 2. Stations manually defined (MANUmethod) are not necessarily represented on theriver. Eventually, stations obtained by the AUTO-SRTM methodology can be located on tributariesthat do not appear in Fig. 2, given the fact that, inthis case, the drainage network used for stationdefinition comes from the SRTM data and areindependent from JERS.

MAD( ) medx N x xii

N

= − −=∑1 1

1

/( )

maxi i ic c| |MAD( ) MAD( ) S1 S2− < d



Station “morphologies”

Figure 5 shows different typical virtual station “mor-phologies”, for some stations that significantly differfrom one method to another. For manually definedselections (MANU method), we have represented theselected satellite nadir locations, the geographicalselection alone, performed during the first step of theMANU procedure, not being representative of thefinally selected altimetric data.

Figure 5(b) shows very similar selectionsbetween AUTO-JERS and AUTO-SRTM methods.However, significant differences in data selectioncan be observed between these two methods (Fig.5(c) and (d)). The AUTO-SRTM method selectsareas that (a priori) do not correspond to water,according to JERS-based land-cover characterization(Fig. 5(a) and (c)). In Figs 5(b), and 6(c) and (d), itmay be noticed that the MANU method allows selec-tion of data a long distance away from the river.

Number of selected points per satellite overpass

The AUTO-JERS method allowed 128 virtual sta-tions to be defined, associated with 4399 satelliteoverpasses. In total 124 virtual stations, correspond-ing to 4558 overpasses, were obtained with theAUTO-SRTM method. However, AUTO-JERS andAUTO-SRTM selected at least five height values for,

respectively, only 1318 (30.0%) and 1657 (36.3%)overpasses (see Table 2). Eventually, 1680 over-passes are associated with the 43 stations providedby the MANU approach.

The results concerning the number of selectedmeasurements for satellite overpasses jointly consid-ered by two methods are presented in Table 3. Theyshow that the MANU method allows a significantlygreater number of measurements to be selected thanthe two other methods. The AUTO-JERS approachselects the least number of altimetric measurements.In particular, with such a method, a significantnumber of overpasses (1125, i.e. 25.6%) is character-ized by only one altimetric measurement, makingwater heights unreliable.

Water height

Table 4 shows the results of paired samples and one-sided Wilcoxon tests for water heights (medians) andat the overpass level.

Median heights obtained with AUTO-SRTMappear to be significantly lower than those resultingfrom the other two methods. The results related tooverpasses that contain at least five selected measure-ments are presented in the second part of Table 4.Water heights obtained with the MANU method aresignificantly higher than those obtained by the twoother methods. Water heights provided by the AUTO-

Table 2 Number of virtual stations and of altimetric values provided by the three selection methods.

MANU AUTO-JERS AUTO-SRTM

Stations 43 128 124Satellite overpasses 1680 4399 4558Overpasses with only one value 5 (0.3%) 1125 (25.6%) 129 (3.0%)Overpasses with at least five values 1263 (75.2%) 1318 (30.0%) 1657 (36.3%)Stations with at least one pass of at

least five values35 (81.4%) 71 (55.5%) 69 (55.6%)

Table 3 Comparison of the three altimetric data selection methods in terms of number of selected measurements percycle (Nb).

Method X vs Method Y

MANU vs AUTO-JERS

MANU vs AUTO-SRTM

AUTO-JERS vs AUTO-SRTM

Number of common satellite overpasses 1501 1451 3681Paired, one-sided Wilcoxon test > > <Nb(X) vs Nb(Y) (p << 0.01) (p << 0.01) (p = 0.0080)

Distribution of Nb(X)–Nb(Y) 95% confidence interval [–19, 51] [–20, 63] [–5, 17][min, max] [–31, 64] [–30, 73] [–21, 54]


116 E. Roux et al.

SRTM method are still the lowest. However, the rela-tive differences are small, the maximum (absolutemagnitude) bound of the 95% confidence intervalbeing 0.46 m (between MANU and AUTO-SRTM).

This maximum bound is 0.26 and 0.15 m for the 90and 80% confidence intervals, respectively.

The normalized cumulated histograms in Fig. 7can be interpreted as the percentage of virtual

Table 4 Comparison of the three altimetric data selection methods in terms of median water height (h).


MANU vs AUTO-JERS

MANU vs AUTO-SRTM

AUTO-JERS vs AUTO-SRTM

All satellite overpasses

Paired, one-sided Wilcoxon testh(X) vs h(Y)

NS >(p << 0.01)

>(p = 0.00040)

Distribution of h(X)–h(Y)

95% confidence interval

[–0.36, 0.46] [–0.62, 0.84]

[min, max] [–3.03, 2.60] [–68.86, 36.13]

At least five selected values per overpass

Paired, one-sided Wilcoxon testh(X) vs h(Y)

>(p = 0.015)

>(p << 0.01)

>(p = 0.0008)

Distribution of h(X)–h(Y)

95% confidence interval

[–0.33, 0.39] [–0.26, 0.42] [–0.28, 0.33]

[min, max] [–0.92, 1.86] [–0.77, 2.60] [–19.65, 1.68]

Fig. 7 RMS differences between water height time series of coinciding stations for each pair of methods.



stations that can be considered as identically definedby two methods as a function of the RMS difference.Of the stations jointly defined by MANU andAUTO-JERS methods, 67.5 and 95% present RMSdifferences of less than 0.2 and 0.5 m, respectively.These proportions are 73.7 and 92.1% for MANUand AUTO-SRTM methods, respectively. In the caseof AUTO-JERS and AUTO-SRTM, these propor-tions are 60.8 and 83.3%. For the latter two methods,stations for which the RMS differences are high arethose that comprise a low number of selected altimet-ric measurements per overpass. In fact, Fig. 7(d)reports the RMS differences between time seriesjointly defined by AUTO-JERS and AUTO-SRTMmethods, as a function of the minimum number ofmeasurements per overpass. It appears that by takinginto account only overpasses characterized by at leastfive measurements, 85.7 and 97.9% of stationsjointly defined by the two methods present RMS dif-ferences equal to 0.2 and 0.5 m, respectively.

Water height variability

Table 5 presents the median, the 80th and the 95thpercentiles of the MAD distribution over all over-passes with at least five measurements and foreach method. The three methods provide very sim-ilar variabilities, with about 0.1, 0.2 and 0.5 m for

the median, the 80th and the 95th percentiles,respectively.

In the following, results are presented as in theprevious paragraph: Table 6 gives the paired samplesand one-sided Wilcoxon test results, the extremesand the 95% confidence interval of differencesbetween selection methods considered pair-wise. Thetest results show significant differences in variabilityin all cases. However, we show that the methodolo-gies slightly differ in terms of absolute magnitudes ofthe differences: the maximum absolute bound of the95% confidence interval, 0.31 m, is obtainedbetween MANU and AUTO-SRTM (this value isonly 0.15 m for the 80% confidence intervals).

Figure 8 presents the cumulative percentage ofstations considered to have identical variability as afunction of a MAD difference value. Of the 102 sta-tions jointly defined by the AUTO-JERS and AUTO-SRTM methods, 53.1 and 79.6% present MAD dif-ferences below 0.20 and 0.50 m, respectively. TheMANU and AUTO-SRTM methods present thegreatest divergence in terms of results variability,with “only” 20.0 and 70.0% of stations “identically”variable to within 0.2 and 0.5 m, respectively. Theseproportions are 34.4 and 81.2% for the MANU andAUTO-JERS methods, respectively.

DISCUSSION

The MANU and AUTO-SRTM methods permit thedefinition of virtual stations at the very upstream partof the hydrological network: for AUTO-SRTM, thiscan be realized by considering a lower accumulationthreshold (1 million cells is used in this study).Another advantage of the MANU method is that, byproposing an altimetric measurement selection in theriver section, it does not take into account only theinformation derived from images or DEM. TheAUTO-JERS and AUTO-SRTM selection proce-dures, in turn, exploit images or DEM established at

Table 5 Intra-pass variability: median, 80th and 95th per-centiles of the median absolute deviation (MAD) valuescomputed for all selected satellite overpasses and as afunction of the altimetric data selection method.

MANU AUTO-JERS AUTO-SRTM

Median (m) 0.12 0.10 0.1080th percentile (m) 0.24 0.21 0.2295th percentile (m) 0.46 0.52 0.56

Table 6 Comparison of the three altimetric data selection methods in terms of height median absolute deviation (MAD).


MANU vs AUTO-JERS

MANU vs AUTO-SRTM

AUTO-JERS vsAUTO-SRTM

At least five selected values per overpass

Paired, one-sided Wilcoxon test MAD(X) vs MAD(Y)

>(p << 0.01)

>(p << 0.01)

>(p = 0.0018)

Distribution of MAD(X)–MAD(Y)

95% confidence interval [–0.26, 0.23] [–0.31, 0.31] [–0.27, 0.31][min, max] [–2.06, 0.89] [–2.24, 1.26] [–54.60, 22.64]


118 E. Roux et al.

a given time, whereas river width and even riverchannel location change over time.

If flood plains adjoin the river, data related tothese flood plains tend to be selected by the MANUmethod. This explains why some selected altimetricdata are far away from the river channel (see Fig. 5).This shows that, although the 43 virtual stationsdefined with the MANU method were intended forriver monitoring, selection criteria associated withthe second selection step (low intra-pass height vari-ability and high inter-pass height variability) arefavoured and the geographical selection associatedwith the first step of the procedure appears to have anegligible effect on the final selection in this case (ofcourse, this would not have been the case if strictergeographical selections had been done according toJERS data). One of the main drawbacks of the

MANU method is that, being entirely manual, it istime consuming and is likely to provide results thatare poorly repeatable and reproducible.

The drainage network obtained with the SRTMdoes not reproduce the complexity of the river mor-phology, the presence of islands for instance. Thisexplains why selections resulting from AUTO-SRTM can be very different from those provided bythe two other methods (Fig. 5(c) and (d)). Moreover,this drainage network presents some aberrations, e.g.sudden direction changes and rectilinear segmentsthat occur in flat areas (see Fig. 5(a) and (c)). Anadditional limitation of the SRTM-based method isthat the line obtained by means of the flow accumu-lation method does not necessarily coincide with theline at equal distance from each true river bank (seeFig. 5(a)). Eventually, the model (equation (1)) used

Fig. 8 Number of virtual stations that can be considered as identically variable in terms of MAD(cSji), i.e. the median abso-

lute deviation of values related to the ith cycle of station Sj.



by the AUTO-SRTM method only represents anaveraged (or smoothed) river morphology and cannottake into account the river morphology variability(see Fig. 5(a)). From a geographical point of view, allthese drawbacks contribute to questionable riverlocation identifications. Nevertheless, AUTO-SRTMis a fully automatic method that provides comparableresults, in terms of water height time series andresults variability, to manual and consequently moresubjective, less repeatable and reproducible, andtime-consuming methods. Moreover, most of drain-age network inconsistencies can be repaired by pre-viously smoothing the DEM (Grohmann et al.,2007), or by forcing flow directions to knownriver locations as proposed by Hutchinson (1989),Saunders (1999) and Getirana et al. (2007). Theseapproaches would improve the drainage networkreliability and, consequently, the virtual station defi-nition and have to be tested in further works.

The previous remarks have to be moderated bythe quantitative comparison of results. These resultsshow that the RMS differences between the waterheight time series provided by the three methods areof the same order of magnitude compared to the alti-metric height RMS errors mentioned in the literaturefor the ENVISAT-RA2 altimeter and the ICE-1retracker. These RMS errors range between 0.11 and0.53 m, depending on the water surface under study(Frappart et al., 2006).

One may wonder why the water height obtainedwith the MANU method is significantly higher thanthat provided by the two other selection procedures.One explanation is that, being entirely manual, theMANU method avoids the selection of altimetricmeasurements associated with the “hooking” phe-nomenon (see Fig. 1(b)). Hooking leads to underesti-mation of the water height (see Fig. 1(b)).Consequently, the AUTO-SRTM method, whichtends to select altimetric measurements out of watersurfaces (see. Fig. 5(a) and (c)), is more likely toselect radar nadir locations associated with the altim-eter locking phenomenon and consequently to under-estimate the water height.

CONCLUSION

Continental water height time series obtained withsatellite altimetric data result from the definition of“virtual limnimetric stations”, that is the selection ofradar nadir locations possibly related to the water sur-face of interest. In practice, researchers use different

procedures in order to define these virtual stations,making the results described in the literature difficultto compare. The present study compares differentaltimetric data selection procedures: (a) a fully man-ual 3-D selection procedure, (b) a method exploitinga land-cover characterization that permits the loca-tion of water body surfaces (rivers in this study), and(c) a fully automatic and original procedure that usesa DEM and an estimation of the river width. Weshow that the great majority of result differences, interms of water height and results variability, are com-parable with the absolute altimetric data errorsreported in the literature. Consequently, from a glo-bal point of view, we can consider the fully auto-matic method to define all the virtual stations of agiven basin. This opens the way to use of satelliteradar altimetry for water height time series genera-tion on a large scale and, consequently, considerablyextends the applicability of satellite radar altimetry inhydrology.

However, a minority of virtual stations jointlydefined by the three methods are significantly differ-ent. This demonstrates that from the point of view ofa single station level, differences can be significant,and, therefore, the reliability of a virtual station defi-nition method depends on the context. In the future,we should focus on these differences in order to char-acterize them as a function of the context, i.e. theriver morphology, the relief, the tracking algorithm,etc. This would allow one to automatically select thevirtual station definition methodology that is betteradapted to the observed context.

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Producing time series of river water height by means of satellite radar altimetry—a comparative study

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