Development of a Local GPS-Leveling Geoid Model for

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1 Development of a Local GPS-Levelng Geod Model for the Gaza Strp Area Maher A. El-Hallaq Assstant Professor, Cvl Engneerng Department, Islamc Unversty of Gaza, Palestne mhallaq@ugaza.edu.ps Abstract Geod model determnaton has an ncreased mportance n most of the practcal applcatons of geodesy n Palestne such as large-scale map producton, GIS applcatons, and engneerng surveyng applcatons. A jont effort between the Brtsh Consulate n Jerusalem and a combned Palestne Fnland project was agreed n order to re-establsh and mprove the geodetc network n Palestne. A msson of a GPS survey team from Ordnance Survey Internatonal was funded by the Brtsh Consulate and conducted n the sprng of Although vertcal control s hghly lkely to be requred to support engneerng projects throughout Palestne, the new geodetc network that was establshed by the Palestne -Fnland project does not meet ths requrement. The statons that comprse the new geodetc network are three dmensonal control ponts of known local horzontal coordnates but known ellpsodal heght rather than orthometrc heght. However, n order to obtan the necessary orthometrc heght for the ponts, a hgh qualty geod model s requred. Ths research ams to develop a GPS- Levelng geod model that provdes a vertcal control of the Gaza Strp area that s compatble wth the use of GPS and to buld up software to convert the GPS ellpsodal heghts to orthometrc heghts. Keywords Geod Model, Heghts transformaton, GPS, Levelng, Gaza Strp. I. INTRODUCTION The geod s an equpotental surface whch would concde exactly wth the mean sea surface of the Earth, f t was to be extended through the contnents. Accordng to C.F. Gauss, who frst descrbed t, "t s the mathematcal fgure of the Earth," a smooth but rregular surface that corresponds not to the actual surface of the Earth's crust, but to a surface whch can only be known through extensve gravtatonal measurements and calculatons [1]. Despte beng an mportant concept for almost two hundred years n the hstory of geodesy and geophyscs, P. Vanek and others have defned t to hgh precson n recent decades. It s often descrbed as the true physcal fgure of the Earth, n contrast to the dealzed geometrcal fgure of a reference ellpsod [2]. Beng an equpotental surface, the geod s a surface to whch the force of gravty s everywhere perpendcular. Ths means that when travelng by shp, one does not notce the undulatons of the geod; the local vertcal s always perpendcular to the geod and the local horzon tangental component to t. Lkewse, sprt levels wll always be parallel to the geod. A GPS recever on a shp may, durng the course of a long voyage, ndcate heght varatons, even though the shp wll always be at sea level. Ths s because GPS satelltes, orbtng about the center of gravty of the Earth, can only measure heghts relatve to a geocentrc reference ellpsod. To obtan one's geodal heght, a raw GPS readng must be corrected. Conversely, heght determned by sprt levelng from a tdal measurement staton, as n tradtonal land surveyng, wll always be geodal heght [1]. The accuracy of GPS heght measurements depends on several factors but the most crucal one s the "mperfecton" of the earth's shape. Heght can be measured n two ways. The GPS uses heght (h) above the reference ellpsod that approxmates the earth's surface. The tradtonal, orthometrc heght (H) s the heght above an magnary surface called the geod, whch s determned by the earth's gravty and approxmated by MSL. The sgned dfference between the two heghts the dfference between the ellpsod and geod s the geod heght (N). FIGURE 1 shows the relatonshp between the dfferent models and explans the reasons why the two hardly ever match spatally [3]. Gaza Strp les along Egypt south and Medterranean Sea west. It s about 45 km long and 6.5 to 12 km wde and covers an area of 365 km2. Its topography s flat and rsng to a maxmum heght of 95 m above the mean sea level. 268

FIGURE 1: THE RELATIONSHIP BETWEEN THE DIFFERENT MODELS OF THE EARTH SURFACE A jont effort between the Brtsh Consulate n Jerusalem and a combned Palestne Fnland project was agreed n order to

2 FIGURE 1: THE RELATIONSHIP BETWEEN THE DIFFERENT MODELS OF THE EARTH SURFACE A jont effort between the Brtsh Consulate n Jerusalem and a combned Palestne Fnland project was agreed n order to re-establsh and mprove the geodetc network n Palestne [4]. A msson of a GPS survey team from Ordnance Survey Internatonal was funded by the Brtsh Consulate and conducted n the sprng of FIGURE 2 shows the Fnland coordnated pont's network n the Gaza Strp. Determnaton of horzontal locatons usng GPS n the Gaza Strp s based on these statons. II. PROBLEM STATEMENT The transformaton between ellpsodal heghts and orthometrc heghts has become more mportant snce the satellte based postonng technques, especally GPS, were beng used n a wde range of geodetc and surveyng applcatons. Geod model determnaton has an ncreased mportance n most of the practcal applcatons of geodesy such as large-scale map producton, GIS applcatons, and engneerng surveyng applcatons especally n Palestne. Although vertcal control s hghly lkely to be requred to support engneerng projects throughout Palestne, the new geodetc network that was establshed n the Palestne - Fnland project does not meet ths requrement. The statons that comprse the new geodetc network are three dmensonal control ponts of known local horzontal coordnates (X,Y) but known ellpsodal heght (Z ellpsod = h) rather than orthometrc heght (Z elevaton = H). A strong need has been arsen to make beneft from the thrd coordnate Z ellpsod that the GPS can calculate. Ths research ams to: III. RESEARCH OBJECTIVES A. Buld a suffcent database to serve the vertcal control n the Gaza Strp. B. Establsh the frst local GPS-Levelng geod model that provdes a vertcal control of the Gaza Strp, whch s compatble wth the use of GPS. C. Develop software to convert the GPS ellpsodal heghts to orthometrc heghts and facltate usng the developed model. IV. METHODOLOGY The methodology steps can be summarzed as follows [5, 6]: A. DATA COLLECTION Gatherng geospatal data, at frst, s very essental. Data about Gaza Strp features ncludng surveyng and geodetc networks s to be collected. Ths requres contactng all the local nsttutons such as surveyng authortes, muncpaltes, organzatons, centers, etc n addton to nternatonal groups as Brtsh consulate, Ordnance Survey n Brtan, Fnland nsttutons, etc. Moreover, performng feld measurements ncludng GPS surveys s very essental. FIGURE 2: THE GEODETIC NETWORK IN THE GAZA STRIP AREA 269

B. VALIDATION PROCEDURE Upon data collecton, a valdaton procedure s to be establshed. Ths step contans dfferent types of checks n order to ensure a hgh precse and more accurate data.

3 B. VALIDATION PROCEDURE Upon data collecton, a valdaton procedure s to be establshed. Ths step contans dfferent types of checks n order to ensure a hgh precse and more accurate data. For ths purpose, feld surveys are one of these checks. C. CREATION OF AN ARCHIVE The next step s to mantan the collected data through a herarchal database n whch t can be easly retreved, dsplayed, updated etc. The use of GIS as a tool for managng s necessary n spatally analyzng these data. From a data management perspectve, metadata s mportant for mantanng the nvestment n spatal data. A metadata creatng based on a standard can be helpful for the documentaton of geospatal data of the Gaza Strp features. D. GEOID COMPUTATION A precse geod model s an mportant part of the geodetc nfrastructure. To serve the practcal geodetc and surveyng applcatons, determnng the geod model of a lmted area as an analytcal surface usng homogeneously dstrbuted GPS/Levelng reference ponts wth approprate densty consttutes the subject of ths research. From ths vew pont, the followng steps are to be performed: - All benchmark reference ponts n the Gaza Strp are to be well-documented usng ArcGIS software. Ths presents these reference ponts n a geographc format and decdes f densfcaton procedure s requred. - Choosng number of the reference ponts n modelng consderng the topography of the regon and also keepng the homogeneous dstrbuton. - Choosng another number of the reference ponts n testng to ensure the accuracy of the developed geod model. - Examnng the accuracy of both modelng and testng benchmark ponts by conductng feld survey that ncludes levelng traverses. - Performng a hgh accurate GPS survey for all reference ponts usng three GPS base and rover recevers. Two recevers are to be held over two zero- order of the Fnland - Palestne project ponts whle the thrd s over the reference benchmark staton. - Usng nterpolaton and geostatstcal methods to model the geod undulatons n the area based on the 270 modelng reference statons. One of the fttng surface methods whch can be used s the Inverse Dstance Weghng method (IDW). - Testng the developed geod by checkng the undulatons n the testng statons to make sure that the performance of the model s acceptable. - Developng software to assst usng the developed model. E. INTERPRETATION OF THE RESULTS A comprehensve nterpretaton of the results s to be determned wth obtaned conclusons and recommendatons. A. DATA COLLECTION V. GEOID DEVELOPMENT After extensve feld survey ncludng levelng and GPS measurng n addton to data valdaton checks, 403 GPS/Levelng ponts were collected. The number of ponts s adequate to model such small area. 353 ponts were selected as modelng benchmarks and the rest 50 ponts are used to evaluate the performance of the developed model. FIGURE 3 llustrates the dstrbuton of both modelng and testng benchmark ponts n the area. The dstance between any two modelng ponts do not exceed 3 km. All collected data s documented and archved n ArcMap GIS database. Ths can help n the spatally analyzng process of ths data n addton to facltate storng, retrevng, updatng and manpulatng t. FIGURE 3: THE DISTRIBUTION OF MODELING AND TESTING BENCHMARK POINTS IN THE AREA

B. GEOSTATISTICAL INTERPOLATION ALGORTHIMS Interpolaton methods are most common approaches that are used whle modelng the geod heghts (N) n a local area.

4 B. GEOSTATISTICAL INTERPOLATION ALGORTHIMS Interpolaton methods are most common approaches that are used whle modelng the geod heghts (N) n a local area. There are dfferent nterpolaton algorthms and each of them can have dfferent results when nterpretng data. Some of these: - Inverse Dstance Weghtng to a Power - Krgng - Mnmum Curvature - Nearest Neghbor - Polynomal Regresson For the frst stage n ths study, the Inverse Dstance Weghtng to a power (IDW) s chosen to buld up the model. IDW method calculates the undulaton of a consdered pont by nterpolatng the undulaton n the surroundng neghborng ponts that le wthn a userdefned searchng radus. Snce geod undulaton changes for dstances more than 3000 m, modelng ponts are selected so that a dstance between any two ponts should not exceed ths length. Data ponts that le progressvely farther from the consdered pont nfluence the computed value far less than those lyng close to t. Eqs. (1-2) llustrate how to compute the geod undulaton of a pont as related to the surroundng reference ponts. To ensure what searchng radus and power that gve the best accuracy whle usng ths method, dstances at (2000, 2500, 3000) m and powers from 1 to 4 are traled. C. SOFTWARE DEVELOPMENT Software s strongly needed to facltate usng the model n whch GPS ellpsodal heghts can be converted to orthometrc heghts. It s also mportant for analyzng and testng the model. Software s bult usng C sharp programmng language and named as PNGM verson 1. PNGM stands for Palestne Natonal Geod Model. It has the capablty to mport data from GPS recevers and from any other database format lke EXCEL, ACCESS, etc. It s also flexble to select power and searchng radus. In addton, modelng data s not bult n the program and can be mported; therefore, PNGM can be used n other areas. FIGURE 4 shows a screenshot of the graphcal user nterface of PNGM and steps used to test the model by PNGM are llustrated n FIGURE 5. FIGURE 6 shows an example for ellpsodal heghts transformaton of some GPS ponts taken n the Gaza Strp to elevatons and constructng a report for the results. Ths report can then be exported n any format lke EXCEL, SHP, PDF, etc. N n 1 n 1 W N W.. (1) Where, N = geod heght (undulaton) of a consdered pont. N = geod undulaton value of th reference pont. W = weght of th reference pont. W 1 n. (2) D Where, D = dstance between the consdered pont and th reference pont. n = power of the dstance, t can be 1, 2, 3 or FIGURE 4: THE GRAPHICAL USER INTERFACE OF PNGM

TABLE I The RMS n (m) of the results at dfferent powers and searchng rad. Power n Searchng Radus (meter) 2000 2500 3000 1 0.0613 0.0569 0.0586 FIGURE 5: PNGM STEPS TO TEST THE MODEL 2 0.0577 0.0552 0.

2. A GPS Levelng geod model was developed to model the Gaza Strp area wth an accuracy ± 4.28 cm RMS at a searchng radus 3000 m and power n = 4.

5 TABLE I The RMS n (m) of the results at dfferent powers and searchng rad. Power n Searchng Radus (meter) FIGURE 5: PNGM STEPS TO TEST THE MODEL VI. CONCLUSION AND FUTURE WORK 1. A suffcent database was performed to archve and analyze all the Benchmark ponts n the Gaza Strp usng GIS technques. 2. A GPS Levelng geod model was developed to model the Gaza Strp area wth an accuracy ± 4.28 cm RMS at a searchng radus 3000 m and power n = 4. FIGURE 6: AN EXAMPLE FOR ELLIPSOIDAL HEIGHTS TRANSFORMATION AND REPORTING D. RESULTS ANALYSIS After developng the software, testng the model becomes easy. Consderng the 50 testng Benchmark ponts, ther elevatons are computed usng PNGM as llustrated n Fgure 5. As mentoned earler, choosng sutable power and searchng radus are necessary to reach the best accuracy. The measured elevaton of each pont of the 50 testng benchmarks s compared wth ts known elevaton. Table 1 shows the RMS of the results at dfferent powers and searchng rad. As a result, t can be seen that the model ftted the data wth ± 4.28 cm root means square error at searchng radus 3000 m and power n = 4. It s an ndcator that the model can be used to compute the elevatons of new ponts wthn ths accuracy range. 3. A graphcal user nterface was ntroduced to facltate usng the developed model. 4. Other data modelng technques such as Krgng can be used and added wthn PNGM. 5. It s recommended to combne the developed model wth another gravmetrc geod model for the area. ACKNOWLEDGEMENTS At frst, all thanks and apprecatons go to Allah for Hs unlmted blessngs and for gvng me the strength to complete ths research. Specal thanks are extended to the Scentfc Research Deanery at the Islamc Unversty of Gaza for ts valuable fnancal support that enabled me to fnsh the practcal ssues. My apprecaton s also extended to the workng team; Al Masr, Yamn Harbd and Saeed Abu Warda for assstng me to perform feld surveys and data collecton. 272

6 References Internatonal Journal of Emergng Technology and Advanced Engneerng [1] Bomford G. (1980), Geodesy, Forth Edton, Clarendon Press, Oxford, England. [2] Vanek P. and Martnec, Z., "Complaton of a precse regonal geod". Manuscrpta Geodaetca 19, 1994: [3] Wtold Fraczek Mean Sea Level, GPS, and the Geod Esr Applcatons Prototype Lab. (URL: [4] Brtsh Consulate-General at Jerusalem, 1999 Geodetc Network for West Bank and Gaza Strp. Addendum to Fnal Report, Occuped Terrtores 129B/98, Palestne. [5] Erol B. and Celk R. N., "Precse local geod determnaton to make GPS technques more effectve n practcal applcatons of geodesy", FIG workng week 2004, Athens, Greece, May [6] Erol B. and Celk R. N., "Modelng local GPS/Levelng geod wth the assessment of nverse dstance weghtng and geostatstcal krgng methods", Athens, Greece,

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