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MAPPING OF RIVER SURFACE CURRENTSWITH GNSS

Jared Bancroft, Sidney Kwakkel, Brady Troyer and Gérard LachapellePLAN Research Group, University of Calgary, Calgary, Alberta

Information about open channels, such as rivers and other waterways, is becoming an increasinglyinteresting area with the adoption of technologies that give more reliable, precise and comprehensive data,while increasing the safety conditions in which river data is collected. Global Navigation Satellite Systemscan offer centimetre accuracy and be used in a variety of open-channel scenarios. Two rivers in southernAlberta were surveyed using double-differenced, carrier-phase measurements to determine surface currents,as well as trajectory and flow dynamics. Waveforms were measured to the sub-cm level, while velocitieswere measured to an accuracy of a few cm/s. The data is processed with non-technical, end-user interpre-tation in mind to maximize the usefulness of the data and provide a template from which river managementofficials can work.

Introduction

Information about currents in open channels isan oft-studied discipline, since its affects can havea tremendous impact on society. In cities and townsthat are centred on open channels, safety and man-agement of the water is commonly a high priorityand they often have formal strategies in place tohandle local governance and usage of theseresources. In Calgary, for instance, the Bow Riveris monitored and patrolled around the clock withhighly technical equipment and trained safety per-sonnel. Despite the safeguards that are in place,these open channels remain dangerous, and stillclaim lives and involve serious injuries every year.

Much of the information collected about openchannels involves flow rates—as measured byupstream dams and stream-flow stations—andwater levels that are usually monitored at variousintervals along the path of the channel [Hirsch etal. 20041]. These records are kept on a regularschedule and compared in order to ascertain, in ageneral sense, the characteristics of the water flowand movement. Unfortunately, these data sets give

very little indication as to the localized aberrationsand anomalies that are inherent to these ever-changing bodies of water, such as dangerously fastcurrents, water surface topography or even watertrajectory. These types of information would notonly add an abundance of knowledge, and thussafety of the channel, but also possibly improvemanagement and sustainability of these resources.

Up-to-date information of river currentdynamics is also a valuable tool to search-and-res-cue personnel. Surface river trends can provide moreaccurate locations of victims, as well as commoneddies where victims and water vehicles may stop. Ifrescuers are given locations of water accidents andprecise estimates from current analysis, response andrescue times can decrease dramatically.

In the past decade, global navigation satellitesystems (GNSS), such as the Global PositioningSystem (GPS), have become household terms andtheir use has become widespread with an increasingnumber of applications. With the increased popu-

GEOMATICA Vol. 62, No. 3, 2008, pp. 267 to 276

L’information sur les canaux à surface libre, comme les rivières et les autres voies navigables, devientde plus en plus intéressante avec l’adoption de technologies qui donnent des données plus fiables, préciseset complètes, tout en augmentant les conditions de sécurité dans lesquelles les données sur les rivières sontrecueillies. Les systèmes mondiaux de navigation par satellite peuvent offrir une exactitude de l'ordre ducentimètre et peuvent être utilisés dans une variété de scénarios pour canaux ouverts. Deux rivières du sudde l’Alberta ont fait l'objet de levés à l’aide de mesures des doubles différénces de phase de la porteuse pourdéterminer les courants de surface ainsi que les dynamiques de la trajectoire et du débit. Les formes desvagues ont été mesurées à mieux qu'un centimètre près et les vélocités ont été mesurées avec une précision dequelques centimètres par seconde. Les données sont traitées en préfision d'une interprétation d’utilisateurnon technique afin d’optimiser l’utilité des données et de fournir un modèle avec lequel les gestionnairesdes rivières peuvent travailler.

Jared Bancroft

Sidney Kwakkel

Gérard Lachapelle

Brady Troyer

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larity of satellite-based navigation, technology isbecoming lower cost with many more features, andmost importantly is becoming more accessible to awider audience. For instance, a 1994 feasibilitystudy successfully investigated the use of precisekinematic Differential GPS for water-borne levellingon the Fraser River of British Columbia [Lachapelleet al. 1994].

In the past few decades, GPS has been used inmany oceanographic applications concerning cur-rent analysis. The World Ocean CirculationExperiment (WOCE) employed many floatingobservation stations that measured a wide range ofquantities, from water temperature to swell magni-tudes [National Oceanographic Data Center2007]. Each station, and thus the measurements itreported, was geo-referenced with coordinatesderived from GPS. Still, many of the studies con-ducted in this area use GPS as coarse positionaldata, often only employing single point measure-ments that give only metre-level accuracy. Theintention of this study is to give finer positionalaccuracy and define a channel’s shape and speedfor river applications, where constricted waterwaysand rapids present different challenges. For thisapplication, a more precise methodology is needed.

Precise kinematic Differential GPS (DGPS)uses precise timing and carrier-phase measurementsto derive both position and velocity [Leick 2003].The technique has been in existence for nearly 20years and has been successfully used for a variety ofapplications. Given that much information is avail-able in textbooks and in the open literature, its con-cepts will not be repeated here. DGPS is particularly

attractive for the purpose of open-channel manage-ment, since it is available in most arenas where openchannels exist. Indeed, the combination of preciseposition, as well as velocity, is a very suitable solu-tion for trajectory determination and semanticvelocity profiles in these open channels. It is there-fore the goal of paper to discuss the use of DGPStechnology to measure river-current dynamics.

The purpose of this paper is to:1. Develop a procedure for floating GPS

receivers in white water (transferable toslow-moving waters);

2. Ascertain the level of accuracy of positionand velocity using this procedure; and

3, Estimate and visualize the estimated cur-rent velocities and elevation profile.

Rivers Selected for StudyTwo rivers were selected to study based on their

dynamics, accessibility and safety. The first area wasthe Widowmaker portion of the Kananaskis River inAlberta (Figure 1). This section is approximately75 km west of Calgary and is accessible throughHighway 40. It is positioned directly below BarrierLake Dam, which is maintained and monitored byTransAlta, a local power-generation company.

Barrier Lake Dam is used to control the flow ofwater along the Kananaskis River. During stop-flowtimes, the riverbed is largely dry and accessible onfoot. This makes a traditional Real-time Kinematic(RTK) GPS / total station survey of the riverbedpossible. The prescribed flow rates through the dam

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Figure 1: Widowmaker portion of the Kananaskis River. Areas of class 1 and class 3 rapids are visible, as well asthe surrounding trees and mountains, which degrade GNSS signals and observations.

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are publicly available at the Kananaskis InformationCentre and on the TransAlta Web site. The high-flowrate is controlled to be precisely 30.8 cubic metresper second on a daily basis in late summer and earlyfall. The published flow rate for this portion of theriver allows day-to-day repeatable measurements tobe logged and correlated.

The second river selected was a portion of theBow River located in northwest Calgary. Thiseight-km section extends from the northern part ofBowness Park to the pedestrian bridge in EdworthyPark. This section of river was chosen to show theability of the proposed method to collect largemeasurement volumes. The width of this portion ofthe Bow River ranges between 40 to 120 metresand, during the test, had an approximate flow rateof 82 cubic metres per second.

This particular section of the Bow River isused often by recreational enthusiasts and ispatrolled regularly by the Calgary Fire Department.As a result of the frequent recreational use, the riveris subject to many rescue-and-retrieval operationsby the fire department, thus emphasizing the needfor information-rich data, such as trajectory andvelocity information.

Procedure and MethodsIn this research, a Pelican® 1500 case was

used to store a NovAtel OEM4 dual frequencyreceiver, NovAtel 702 antenna and battery pack(Figure 2a). This case provided repeated accessibil-ity to the receiver, robustness during white-watertumbling, protection from collisions with rocks andprolonged longevity of the enclosure containing theGPS components. The attenuation effects of thecase on the GPS signal were determined to be neg-ligible and the C/No measurements unaffected(C/No are shown in Figure 6 and Figure 11).

Data collected on the river was processed withGrafNav and FLYKIN+™, both of which are dif-ferential GPS carrier-phase solution software pack-ages that solve for kinematic positions and veloci-ties. Both software packages have the ability todetermine and fix Double Differenced (DD) carrier-phase ambiguities of L1 and L2. GrafNav softwarehas the capability to process in forward and reversemode, which allows for a weighted solution of thereceiver position and velocity. This is an importantmethod to use as, after a waterfall or major wave,lock can be lost (creating a cycle slip), and the pro-cessing software may take a while to re-fix the inte-ger ambiguities. In using a forward and reversesolution, this time of un-fixed ambiguities isreduced. With optimum observations (i.e. fixed

integer ambiguities), both packages yield centimetreand centimetre-per-second accuracy in position andvelocity, respectively, which meet the error target forthis project.

FLYKIN+™ outputs the residuals from theestimation process, which is important in analyzingthe solution’s precision. It is noteworthy that thevelocity solution is determined from the Dopplerobservation, a time derivative of the phase observa-tion, and therefore is inherently noisier than theposition solution. Because position and velocityerrors are dependant on satellite geometry, multi-path, noise, data outages and correct ambiguitydetermination, results fluctuated during the test.Because the results contained different precisions,only results less than 10 cm (3D) and 50 cm/s (3D)of the estimated position and velocity standarddeviations, respectively, were used.

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Figure 2a: Receiver and antenna housed in the water-proof enclosure.

Figure 2b: Placement of the sensor in the water directly into the Widowmakerrapids of the Kananaskis River.

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The results from GrafNav were used to formthe general flow diagrams of the river sections.Four segments were then selected from the generalGrafNav solution and processed in FLYKIN+™,which were used to analyze on a closer level, incor-porating the residuals (although only one is pre-sented in this paper).

As mentioned previously, the management ofthe Kananaskis River allowed for the riverbed to beaccessed with traditional survey equipment. As aresult of this topographical survey, a 3D model ofthe river valley, including the river boundaries andsurrounding features, could be formulated usingArcGIS® software. This software was chosen forthe production of the visualizations because of itsinherently extensible Microsoft.NET® integrateddevelopment environment, as well as its vastassortment of built-in tools for spatial analysis.

The riverbed and boundary survey had twopurposes: first, to define the edges of the river; andsecond, to correlate surface currents and elevationswith underlying topography and aspects. From thesedata, traditional metrics have been estimated with ahigh degree of accuracy. For instance, Rantz [1982]showed that surface velocity and depth informationcould be combined to give stream-flow rates.

In the case of the Kananaskis River, topograph-ical points were measured to generate the elevationmodel. Kriging was used to form the elevationmodel and is a preferred method for interpolatingnetworks of irregular observations. For a discussionof Kriging and its implementation, see referenceStein [1999].

For the purposes of interpolation and the pro-duction of a 3D graphical model of the riverbed andsurrounding area, ArcGIS® is a software suitespecifically designed for such operations. This soft-ware also provides utilities for visualization toolsthat will be used to provide the final graphical end-products. In addition to the ready-built tools,ArcGIS also has an integrated development envi-ronment based on the Visual Basic language thatallowed for the development of new visualizationsthat were specific to river-current-velocity analysis.Matlab was also used to display the results obtainedfrom this research.

Kananaskis River DataCollection

For the purposes of this white-water study,safety of the equipment and researchers was a para-mount consideration. The Widowmaker and thesection of river directly downstream had multipleexit points and areas of low-speed current to allowfor the successful retrieval of equipment and safeextrication of individuals from the river. Diligentplanning and constant vigilance was a criticalaspect of this experimental design, as the river hasclaimed numerous lives. Similarly, the Bow Riversurvey was conducted with consideration for exitpoints, and all water-safety precautions should bethe primary concern of any further investigations.

GPS data was collected on the KananaskisRiver on October 16 and December 12, 2006.Ground-control surveys and the topographic surveywere conducted earlier, on October 7, 2006. AnAlberta Survey Control Monument (ASCM) pro-vided the reference location for the ground control,which enabled two reference stations to be sur-veyed (via DGPS) in, with close proximity to theWidowmaker to provide control stations on thetopographic survey and GPS base stations.

Figure 3 shows the distribution of points whereraw GPS data was processed within the previouslyspecified precision. Four periods of fixed ambigui-ty solutions have been analyzed (also shown inFigure 3). In the interest of space, segment 4 pro-vides interesting results and similar information tothat of the other three segments. As segment 4 isdownstream of the Widowmaker rapids, this por-tion of the river is also the “favoured” trajectory ofthe sensor, meaning the trajectory taken by the sen-sor as it exited the circulating eddy below theWidowmaker. It provides an area with large stand-ing waves and the largest speeds recorded duringstudies on the Kananaskis River.

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Figure 3: Elevation model as derived from the topographical survey. Pointsindicating processed position and velocities within the specified precision (•).

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From Figure 3, the data coverage is morewidespread in some areas of the river and lesser inothers. More specifically, the northern edge of theriver was covered less because the natural flow ofthe river tended to push the floating sensor towardsthe middle of the river. This was an unexpected out-come, but is a fruitful piece of information as itreveals the natural trajectory of this section of theriver, where there is a flow separation around theisland. This information could be important, forinstance, in rescue-and-retrieval work, where thelocations of floating objects could be better predict-ed using these sorts of models, such as in Figure 4.

Figure 3 also shows the elevation model of theWidowmaker section of Kananaskis section. Detailsof the surrounding topography were surveyed usingRTK (Real Time Kinematic) GPS survey equipment;Trimble 5700 RTK receivers with a Trimble Trimark3 radio. The manufacturer specifications for preci-sion are 10 mm horizontal (RMS) and 20 mm ver-tical (RMS) (over a 200 m baseline). Areas that hadtoo much occlusion from satellites for RTK posi-tioning were surveyed using a reflector-less LeicaTCR803 Power Total Station. The estimated accura-cy of the measurements made in reflector-less modeis approximately 3 cm horizontal and vertical RMS.

Kananaskis River Results Figure 4 shows a vector view of the velocities

measured on the river surface. The size and orienta-tion of the arrows represent the speed and directionof the sensor, respectively. The velocity measure-ment is at a position located at the centre of thearrow. The colour of the arrow represents the threedimensional RMS of the standard deviation of thevelocity measurements. Figure 4 is a visual repre-sentation of the velocity measurements and can beeasily interpreted by safety personnel and water-management officials.

Figure 4 is a good depiction of the quality of themeasurements made on the entire expanse of river.For instance, most of the arrows are green to yellow,indicating that most velocity measurements aremade with a 3D RMS accuracy of 30 cm/s to 40cm/s. Moreover, directly above and belowWidowmaker, the measurements are slightly better.This result is due to better satellite availability. Asthe receiver drifted into the sharp, northward turnabove the Widowmaker, the receiver lost lock onsome satellites, resulting in a weaker satellite geom-etry, thereby causing a degraded estimation of theposition and velocity (and their respective standarddeviations). Figure 1 shows the shaded area abovethe Widowmaker where the receiver had difficultytracking all visible satellites.

While Figure 4 shows a general representationof the speed (and precision) of flow, finer granular-ity may be needed. For this reason, the data can bezoomed in, as in Figure 5. It represents a magnifiedview of the same data centred about theWidowmaker portion of the river. Here, the veloci-ty vector resolution is much better and more dense,and gives a depiction of the relative velocitiesmeasured throughout this smaller subsection of theriver. In this view, the trajectories of the sensor arealso observable. For instance, there is a clearlydefined pool of water directly above theWidowmaker, where floating objects could poten-tially circulate before floating downstream throughthe faster rapids of Widowmaker.

Also observable from Figure 5 is the variabili-ty of the surface velocities throughout the

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Figure 4: Vector field of surface current velocities: size of arrow indicatesmagnitude of velocity; colour of vector indicates the relative standard devia-tion. Also indicated is the river boundary (–).

Figure 5: Vector field of surface current velocities around the Widowmaker:size of arrow indicates magnitude of velocity; colour of vector indicates the rel-ative standard deviation as in Figure 4. Also indicated is the river boundary (–).

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Widowmaker portion of the river. As the waterapproaches this portion, velocities increase rapidly.In this vane, the trajectories of objects floating inthis portion of the river have two possible out-comes: they are either caught in the fast-movingcurrents and continue downstream, or they float inthe pool directly above the rapids. This is an inter-esting and now clearly observable characteristic ofthe river dynamics.

Another important observation that comes fromFigure 5 is the limitation of the floating sensor.While the surface current velocities are coherentdirectly above the rapids, indicating congruent andmeaningful measurements, the current velocitieswithin the rapids and directly below remain poorlyobserved. From Figures 1 and 2, the white-waterrapids of Widowmaker are clearly visible. In thissection of the river, water moves at such a highvelocity that the turbulence causes undertows,standing white-water rapids and a circulating eddysouth of the white water. As seen in Figure 5, thewhite-water rapids are largely unobserved due to thecase tumbling, but are partially observed by itsmeasurements on the south side in the re-circulatingeddy. In this section, the sensor (typically) exited theWidowmaker and re-circled back into the south sec-tion of the Widowmaker. In fact, the recirculation ofthe water is evident from Figure 5, as water rotatesin a counter-clockwise fashion below the falls.

Figure 6 shows the average GPS signal-carrier-to-noise ratio (C/No) for each of the four segmentsshown in Figure 3. In each case, the C/No is strongand practically the same as under normal line-of-sight conditions, indicating good observability of thesatellite signals. This figure also shows the occur-rence of cycle slips on L1 and L2. This confirmsthat, in the river environment, cycle slips will occurfrequently—however, not so frequently as to affectthe ability of the software to re-fix the ambiguitieswhen processing in forward and reverse.

Segment 4 represents a common stretch of theriver, where water flows in a standing-wave pattern(Figure 7). In this segment, the riverbed descendsand the water flows down a height gradient. Giventhe short distance of this segment, geoidal undula-tion variations will have no affect and the decreasein geodetic height is the equivalent to that in ortho-metric height.

The riverbed descends 25 cm in elevation over35 m of planimetric distance (Figure 7). It is note-worthy that, despite the riverbed’s drop, the surfacecurrents remain constant—indicating that the rivermay be narrowing, thereby compensating for thedeeper channel. In fact, this is observed when ana-lyzing Figure 3, where an island is proximal to theend of segment 4. Interestingly, it is also possible tomeasure the linear slope of each wave, whichranged between 8º and 17º.

Figure 8 shows the horizontal and verticalvelocity components as determined by FLYKIN+™.The periodic motion is apparent in both planes andshows an intriguing result, namely that the hori-zontal speed fluctuates significantly (upwards of0.5 m/s) through waves of only 20 cm in amplitude.

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Figure 6: Signal-to-noise ratio (C/No) of measurements made along segment1 (top), segment 2 , segment 3 and segment 4 (bottom). Also shown are thecycle slips (•) detected during each segment.

Figure 7: Water surface elevation (top) with riverbed elevation (underneath)and L1 RMS (grey) and L2 RMS (black) of the phase residuals for L1 and L2DD position solutions along segment 4.

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As the case floats through the standing waves, thechange in speed is therefore highly correlated withthe slope of the wave.

Figure 9 shows the square magnitude of theFourier transform of the periodic elevation profilefor segment 4. The elevation (shown in Figure 7)was linearly interpolated to form a 1-mm-spaced dis-crete line. The Fourier transform was then estimatedafter removing the mean elevation. It is noted that aslight error is induced from the linear interpolation,which appear as high frequencies. From this figure,the predominant wavelength in section 4 is 2.66 m,with an approximate amplitude of 21 cm. This dis-tance is consistent with casual inspection of theriver, and provides a unique and novel method ofdetermining wavelength and amplitude.

Bow River Data Collectionand Results

Data collected on the Bow River took place onAugust 30, 2007. Three receivers inside Pelican®1500 cases were attached with nylon floating ropesto a six-person commercial raft. The ropes occa-sionally would become taut or caught in a differen-tial current, causing the case to suffer from non-current-generated motion; however, the effect wasminimal. A more robust, but risky, method wouldallow the cases to float free of any hindrance. Threeconsecutive runs down the river were made: thefirst run floating on the right bank, the second onthe left bank and the third in the river centre.Because of the span of the Bow River (often morethan 100 m across), achieving equal coverage withthe three receivers is undoubtedly a limitation(Figure 10). Nine trajectories provided reasonablecoverage of the river, although the number of tra-jectories and coverage that is achieved is dependanton the width of the channel.

Weak satellite signals and blockages wereobserved near bridges and, occasionally, near steepriverbank escarpments (Figure 11), resulting inlower precision measurements (Figure 10).Additionally, the river is contained within a rivervalley, creating a natural elevation cutoff anglewhere satellites were obscured. Occasionally,receivers lost lock on satellites due to obstructionfrom waves, self-induced splashing, pitching androlling, and overhead tree canopy. This providedfewer satellite observations, thereby causing occa-sional discontinuities in the estimated variance ofthe solution (Figure 10c). While the base stationcontinually tracked eight or more satellites, thereceivers in the river tracked an average of 6.6

satellites when a 13º-elevation mask was used. It isnoteworthy that future combinations of GlobalNavigation Satellite Systems, such as GLONASS,Galileo and Compass, will provide ever more satel-lites to observe, and thus satellite availability andgeometry will improve, leading to better positionand velocity estimation.

Because GPS provides precise 3D positionsand velocities, a cross-section of the river is possi-ble, as shown in Figure 10c. The velocities and ele-vations measured along this cross-section areshown in Figure 12. The river at this point is 75 m

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Figure 8: Horizontal (2D) and vertical velocity of the surface currents alongsegment 4.

Figure 9: Fourier analysis of waveforms measured along segment 4.

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wide and the water has some small variations withrespect to the speed (< 0.5 m/s) and elevation (< 3cm). As shown in Figure 12, the north side of theriver does have a faster moving current congruentwith the outside corner of the river. Moreover, allthree receivers during the run provide similarspeeds, again providing confidence in the solution.Additionally, nine independent trajectories meas-ured within 3 cm vertically established excellentresults and point to the high precision and effec-tiveness of the method. In fact, standard deviations

of the elevations ranged from 4.5 cm to 5.7 cm;therefore, 9 independent elevations varying within3 cm show that the estimated standard deviationsare pessimistic.

Figure 13 shows the elevation change over theentire 8.1-km section. The occasional spikes anddiscontinuities that occur are a result of passingunder bridges or high escarpments. Although filter-ing the position standard deviations to less than 10cm (3D), a few outliers can still be seen. The appar-ent linear trend is of particular interest. It shows a

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Figure 10: Stream-flow trajectory measured along the Bow River in Calgary, Alberta, Canada: (a) Entire 8.1 kmpath measured, (b) distribution of measured velocities with magnitudes indicated by the size of arrow and standarddeviations indicated by colour, and (c) the nine trajectories measured, as well as a cross-section shown in Figure 12.

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0.176% river grade, or a 1.76 m drop per km overthe section.

Figure 14 shows a small set of standing wavesthat the case passed through. Remarkably, waves ofonly a few cm are measured distinctly. Comparedwith the waves measured on the Kananaskis River,these waves have linear slopes ranging between 1ºand 6º, with wavelengths of about 1.98 m (Fourieranalysis not shown) and location varying ampli-tudes. A distinct downward trend is also visibleover the last 20 m, as the elevation drops 8 cm. Thisis the result of the case floating around a protrusionin the water, where water accumulated.

One objective of this research was to analyzethe accuracy of using DGPS and to show the relia-bility of GPS receivers on water. Residuals provid-ed by FLYKIN+™ show excellent reliability of theobservations. Figure 15 shows the L1 and L2 phaseand Doppler residuals. Statistically, the L1 RMSaveraged 5.4 mm, L2 RMS averaged 8.6 mm andthe Doppler residual RMS averaged 0.048 m/s.Although the lack of satellites (and therefore satel-lite geometry) used in the computation is marginal,the quality of the observations remains high.

ConclusionsThe management of constricted river channels

is an area of increasing interest, with the availabil-ity of new measurement techniques that provideprecise concentrated positioning information. Thisfeasibility study showed that differential GPS carri-er-phase measurements are sufficiently accurateand available to measure velocities and trajectoriesand to perform wave analysis. It has been shownthat RMS errors are at the cm/s and sub-cm levelsfor velocities and positions, respectively. Thesemeasurements can be obtained with minimal safetyconcerns to field personnel and, as the cost of GPSequipment decreases, they will become moreaffordable to a wide variety of users interested inwater management.

While this paper showed how some of theinformation can be presented to non-technical per-sonnel by means of geospatial information systems,it is by no means an exhaustive treatment of thepossibilities. For instance, time series of the datawould likely allow for predictive modelling of rivercurrents and trajectories. As these technologiesmature, analysis approaches are expected to evolveto provide more specific information to differentuser classes. This is important, given the increas-ingly complex emerging issues related to freshwater availability, use and management.

Acknowledgements

A special thanks to Nexen Inc. of Calgary,Alberta, who supplied the aerial photography of theBow River for this analysis, and to Qais Marji andJalal Al-Azizi, Master’s degree candidates, for theirhelp in collecting the data for this project.

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Figure 11: Average C/No of satellites tracked for one trajectory (above) andthe number of satellites tracked and used in differential solution for one tra-jectory (below).

Figure 12: Cross-section of speed (above) and elevation (below). The southbank represents zero distance.

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ReferencesHirsch, R.M. and J. E. Costa. 2004. U.S. stream flow

measurement and data dissemination improve, EOS,Vol. 85, pp. 197-203.

Lachapelle, G., C. Liu, G. Lu, Q. Weigen and R. Hare.1994. Water-borne leveling with GPS, MarineGeodesy, Vol. 17, pp. 271-278.

World Ocean Circulation Experiment Global DataResource. Col. 2008: National Oceanographic DataCenter, 2007, http://woce.nodc.noaa.gov/wdiu/(Accessed December 2007).

Leick, A. 2003. GPS Satellite Surveying, Third Edition,John Wiley & Sons Inc.

Rantz, S.E. 1982. Measurement and computation ofstreamflow in Measurement of stage and discharge.Vol. 1: U.S. Geol. Surv. Water Supply Pap. 2175.

Stein, M.L. 1999. Interpolation of Spatial Data: SomeTheory for Kriging: Springer.

MS rec'd 08/01/23Revosed MS rec'd 08/05/01

AuthorsJared Bancroft is a Ph.D. candidate in the

department of Geomatics Engineering at theUniversity of Calgary. He received his B.Sc. inGeomatics Engineering in 2007 and has workedwith navigation techniques since 2004. Jared'sresearch interests include pedestrian and vehicularnavigation through data fusion of inertial and satel-lite navigation data.

Sidney Kwakkel is a Master’s graduate studentin the department of Geomatics Engineering at theUniversity of Calgary. He holds a B.Sc. in BiologicalSciences from the University of Calgary. Hisresearch focuses on satellite and inertial navigationand measurement techniques.

Brady Troyer received his B.Sc. in GeomaticsEngineering at the University of Calgary in 2007.He works in the GIS Services department at NexenInc. where he is responsible for geodetic standards,spatial data integrity, LiDAR and GPS spatialmeasurement specifications and geodesy in general.

Dr. Gérard Lachapelle is a Professor ofGeomatics Engineering at the University of Calgary,where he is responsible for teaching and researchrelated to location, positioning and navigation. Hehas been involved with GPS developments andapplications since 1980. He has held a CanadaResearch Chair/iCORE Chair in wireless locationsince 2001 and heads the PLAN Group at theUniversity of Calgary. o

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Figure 14: Bow River wave profile.

Figure 15: RMS of L1 and L2 Doppler of double-differenced residuals.

Figure 13: Bow River elevation profile of a centre trajectory.