The Evaluation of Sea Surface Topography Models based on the Combination of the Satellite altimetry and the Global Geoid Models in the Persian Gulf

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1 Int. J. Envron. Res., 6(3): , Summer 2012 ISSN: The Evaluaton of Sea Surface Topography Models based on the Combnaton of the Satellte altmetry and the Global Geod Models n the Persan Gulf Sadatpour, S. M.T. 1*, Kamehr, R. 2, Abrehdary, M. 3 and Sharf, A.R. 1 1 Islamc Azad Unversty, North Tehran Branch, Department of Hydrography, Tehran, Iran 2 Unversty of Zanjan,Dvson of Cartography, Zanjan, Iran 3 Royal Insttute of Technology, Dvson of Geodesy and Geomatcs, Stockholm, Sweden Receved 11 Nov. 2011; Revsed 2 Aprl 2012; Accepted 4 May 2012 ABSTRACT: One of the dffcultes n usng absolute alttudes s the separaton between the mean open sea level and geod. Theoretcally, geod s the base level n absolute alttudes, but practcally, the mean open sea level s used as a base level for absolute alttudes. The dfference between these two levels s called as the sea surface topography. In ths research, t s dealt the mean sea level modelng by usng the observatons of three altmeter satelltes (.e. Topex/Posedon, Jason-1 and GFO) n Persan Gulf and then t s dealt wth the evaluaton of exstng models of the sea surface topography based on the altmeter satelltes data and the global geopotental geod models (.e. European Improved Gravty model of the Earth by New technques, Gravty feld and steady-state Ocean Crculaton Explorer, Earth Gravtatonal Model The results of ths research ndcate that the sea surface topographcal model resultng from the EIGEN06C geod s the most precse model wth changes range between m and m and mean m. Key words: Satellte, Sea surface, Persan Gulf, Gravty model INTRODUCTION One of the common parameters n geodetc scences and oceanography s the study of the sea level. The relaton between these two scences s revealed n ths fact that geodeses requre oceanographcal observatons to determne a precse marne geod model and oceanographsts also need marne geod to determne the absolute quanttes of the sea streams velocty n varous depths (Ross, 1995). The opposte pont between these two scences s the separaton of geod and the mean sea level (MSL) whch s called as dynamc sea surface topography or pseudo-statc sea surface topography (Knudsen, 1992b). For all determned geod, t s normally assumed that geod s equpotental surface the same as gravty centre of the earth whch s best concded wth the MSL. Wth a lttle attenton. t s clear that the separaton of the geod from the MSL for a precse geod specally n open oceans s between -2.2 m and 70 cm wth standard devaton ± 62 n global scale (Engels, 1985; Engels, 1987); ths bg separaton s normally due to the oceanc streams resultng from some factors such as wnd, salnty changes, temperature and pressure whch are drectly related to the earth. Gven the geod and the MSL, there are some problems n determnng the alttude reference of the countres; so t s better to determne the sea surface topography (SST) values n tdal reference statons and to use t for the zero heght level n that regon (Ardalan and Mosaebzade 2003). Now, fndng the SST requres calculatng the geod whch s the desred base level. In ths artcle, the global models EGM2008, GOCE and EIGEN06C are used to calculate ths level. In addton, we also examne how to determne the MSL and how to calculate ths level. In ths regard, Fourer analyss and the least squares methods are used to elmnate the perodc dsturbances and anomales. MATERIAL & METHODS The mean sea level (MSL) s one of the mportant and fundamental elements n geodesy and hydrography. MSL s a level on whch the open seas level wll be concded f no turbulences and *Correspondng author E-mal: sadatpour1960@yhoo.com 645

2 Sadatpour, S. M.T.et al. dsturbances exst. Ths level alttude s normally calculated from the nstantaneous mean of the water. The MSL s normally calculated from the observatons of the ponts n an arranged (regular) network. These pont observatons are obtaned from the tdal statons (tde gage) throughout the world or they are obtaned by usng satellte altmetry method. The MSL s tradtonally consdered as zero heght pont and balance sea level n the coast; n order to obtan the, level we should omt the tdal frequences n lmted tme openngs and consder the remanng level as the MSL after omttng the perodc changes. By connectng ths level to the coastal benchmarks, the zero heght wll move to the land. Determnng ths level s very mportant n topography. Determnaton of geod s one of the most mportant uses of the MSL. In order to obtan the geod, we should use an equpotental surface whch ts dfference from the MSL s mnmum. Usng ths level as the base level n navgaton purposes s the other uses of ths level. In ths research, t s dealt wth the MSL modelng by usng the altmeter observatons of the satelltes Topex/Posedon, Jason-1 and GFO n a pont form. To acheve ths goal, data from the altmeter satelltes Topex/Posedon, Jason -1 and GFO contanng the collected nformaton durng years 1992 to 2008 were frstly used whch tme seres were made from the sea level changes n satellte passes n Persan Gulf. Then tdal consttuents could be obtaned n observaton ponts by performng the Fourer spectral analyss and the least squares method on these tme seres. Fg.1. shows the passes of the satelltes Topex/Posedon, Jason-1 and GFO. Accordngly, we can see n ths map that these satelltes have provded a relatvely good coverage. It s necessary to note that the passages of the satelltes Topex/Posedon and Jason-1 are exactly placed on each other whch are shown n blue and the passages of the satellte GFO are llustrated n red (Beckley et al., 2007). In order to determne the sea surface heght (SSH) n observaton pont as compared wth reference ellpsod, we should frstly correct the systematc errors relatng to satellte dstance from the sea level whch s measured by altmeter. All of these correctons are avalable n nformaton fles known as MGDR-B fles. These correctons are provded for each pont separately. After correctng the dstance between the satellte and nstantaneous sea surface (corrected Range), SSH could be obtaned on the same pont n regard to reference ellpsod by havng determned satellte alttude (H sat ) from the ellpsod. One pont should be consdered here s that, as our goal s to make tme seres from the nstantaneous SSH and to analyze these Fg. 1. the passes of the Topex/Posedon, Jason-1 and GFO satelltes over the Persan Gulf seres to fnd the MSL; then the correctons resultng from the tde should not be used for observatons (Marsh, J. G., et al., 1990). (, ϕ, t) = H ( λ, ϕ, t ) Corrected Range SSH λ sat (1) As our goal s to fnd the MSL Heght n satellte passes n whch tme seres are made, so we frst determne MSL and ts tme changes and then we estmate the perodc consttuents. Therefore, assume that the tme seres h{ ( t )} 1,2, K, n = are the observatons relatng to the nstantaneous SSH of the sea surface n a known pont, so the approprate model for tdal modelng s shown below (Yu Wang, 2004): h( ϕ, λ, t) = a ( ϕ, + b ( ϕ, λ ) t (2) n = n [ a ( ϕ, Cos(2π f t) + b ( ϕ, λ ) Sn(2πf t)] In the above-mentoned formula, a0 denotes the MSL and should be determned as Fourer coeffcents; b0 denotes permanent ncrease n the seas water level whch s consdered constant n all of the sea levels due to the pole ces meltng and f denotes the used frequences. Determnaton of the Fourer coeffcents a, b denotes the tdal waves ampltude whch 646

3 Int. J. Envron. Res., 6(3): , Summer 2012 n the above-mentoned extenson, n fact, led to the determnaton of a model for a phenomenon behavor. These coeffcents are determned by usng a sample and provdng a parametrc equatons system. The least squares method s used to solve ths parametrc equaton system. Choosng the number of consttuent depends on dfferent factors such as observatons duraton. After solvng the least squares n equaton2, the ampltude and the tdal.th phase are calculated as follows (P.Vancek, E.Krakwsk 1986): 2 2 A = a + b (3) Ψ 1 a = 2tg ( ) (4) b + A Table 1. Name, frequency, perod and ampltude of the four used tdal ConsttuentsUnt: meter Consttuent Name Mean value Mnmum Table 1 shows four tdal Consttuents parameters. Nowadays t s possble to determne the MSL and geod n seas wth hgh precson by usng satellte altmetry method. It s a common method for usng global geopotental models. The long gravty feld wavelength s shown well because satellte-based observatons wth monotonous coverage and hgh compresson are used n the determnaton of the sphercal harmoncs coeffcents. The global models are used n the determnaton of the satellte orbt, hgh wavelengths of geod, tdal consttuents of the earth, oceanography, oceanc permanent streams and estmatng the earth rotaton parameters and the pole movement parameters.fg. 2. shows local mean sea level model based on the Topex/Posedon, Jason-1 and GFO Data. It s necessary to note that satellte-only observatons are used n calculatng some of these Maxmum frequency (c yc le /day) Perod M.S.L Extreme O K M S Fg. 2. Local mean sea level model on the Topex/Posedon, Jason-1 and GFO Data. Contour lne. Unt: meter 647

4 Sea Surface Topography Models models and n other models combned satellte and ground observatons are used. The former models are known as satellte-only global gepoptental model and the last models are known as combned global geopotental model. By advancng the satellte-based gravtatonal methods and mprovng the compresson and precson of the ground data nowadays, we can see so many geopotental models whch are calculated and presented by dverse research nsttutons and unverstes throughout the world. The compresson, precson and accuracy of the ground data used n combned models n dfferent parts of the world are dfferent, so the precsons of these models dffer from each other and an approprate model should be selected n accordance wth the usage type and geographcal poston. We wll present some new and precse global geod models. The EGM96 model was the last earth geopotental model whch was provded n the mddle1990 by Natonal Geospatal-Intellgence Agency. Ths model has degree and order 360 whch s made for marne regons by usng the gravtatonal data 30 mnute by 30 mnute resoluton, throughout the world, the long wavelength nformaton of about forty satelltes, heght data extracted from twenty nne Sources and the altmeter data of satelltes GEOSAT, ERS-1 and TOPEX. The root mean square (RMS) of model EGM96 s estmated about 0.5 to 1 meters whch s approved by a group of experts n nternatonal assocaton of geodesy (IAG) (Nkolaos et al. 2008). After model EGM96, a global geopotental model known as model EGM2008 was avalable for users n 2008 wth degree and order 2160 (Pavls et al. 2008). Ths model s formed based on usng revsed data of the gravtatonal Informaton throughout the world and the geopotental models are formed based on the GRACE satellte (Gravty Recovery And Clmate Experment) nformaton. The expected accuracy of ths new model EGM2008 was much exaggerated because the gravtatonal dstrbutons 5 x5 mean resoluton, degree and order 2160 and 15 cm for global geod accuracy are consdered. The new model EGM2008 found n Natonal Geospatal-Intellgence Agency (NGA) nsttuton requres gravtatonal data wth global coverage and ntervals 5 x5 mean resoluton. Ths database s formed by usng combned gravtatonal ground (geod), marne and aeral data and gravty anomaly for the most of the oceanc regons usng altmeter satelltes. The long wavelength n EGM2008 s obtaned by usng satellte GRACE data whch s more precse than data contaned n pror EGM models. The most precse and newest model GRACE s used n model EGM2008. Fg. 3 and Table 2 show the geodal heght and ts statstcal values based on the EGM2008 model. Fg. 3. EGM2008 global geod model contour lne. Unt: meter Table 2. the statstcs of the geodal heghts EGM2008" Unt: meter Maxmum Mnmum Mean Standard devaton EIGEN06C model (Förste et al., 2011), s complete to degree and order 1440 and was jontly elaborated by GFZ Potsdam (GeoForschungsZentrum) and CNES/ GRGS Toulouse) Groupe de Recherche de Geodese Spatale(. It s the frst EIGEN model nferred from a combnaton of GRACE and GOCE data, enhanced wth the DTU10 global gravty anomaly grd (Andersen, O. B., P. Knudsen and P. Berry). The combnaton of GRACE and GOCE (The Gravty Feld and Steady-State Ocean Crculaton Explorer) data allows the constructon of an accurate satellte-only model to degree and order 240, the gradometer data of the latter contrbutng only to degrees upwards of 100. Ths s acheved through flterng of the GOCE observaton equatons, whch s necessary because of the degraded gradometer performance outsde the measurement bandwdth. Analyses of gradometer resduals calculated wth ITG-Grace2010s (Mayer-Gürr et al., 2011), EIGEN-5C and EGM2008 as background models revealed consderable model errors n current combned gravty feld models caused by the ncluson low-qualty and/or low resoluton surface data. Therefore, n EIGEN06C model the combnaton procedure of satellte and surface data was revsted n order to mtgate ths error source. In partcular, the surface data normal equatons are combned wth satellte normal equatons at a hgher degree than presently appled (for nstance at degree 70 n EIGEN-5C). The comparson of test results (orbt computaton, GPS/levelng) of ths latest EIGEN model wth a GOCE-only model, EGM2008 and ITG-Grace2010s demonstrates the gan n accuracy at 648

5 Int. J. Envron. Res., 6(3): , Summer 2012 hgh degrees, whle ts performance remans dentcal compared to a GRACE-only model for the low degrees.fg. 4 and Table 3 show the geodal heght and ts statstcal values based on the EIGEN06C model. The Gravty Feld and Steady-State Ocean Crculaton Explorer (GOCE) s an ESA satellte that was launched on March 17, It s a satellte carryng a hghly senstve gravty gradometer whch detects fne densty dfferences n the crust and oceans of the Earth. trajectory. The craft s prmary nstrument s three pars of hghly senstve accelerometers whch measure gravtatonal gradents along three dfferent axes. In ths artcle, the last accessble model of ths one namely GO_CONS_GCF_2_DIR (Brunsma et al., 2010) was used n 2010 wth degree and order 240 and wthout ground combned data. Fg.5.and Table 4 shows the geod resultng from ths model n regon under study. Fg. 4. EIGEN06C global geod model contour lne. Unt: meter Table 3. the statstcs of the geodal heghts EIGEN06C Unt: meter Maxmum Mnmum Mean Standard devaton Fg. 5. GOCE global geod model contour lne. Unt: meter Table 4. the statstcs of the geodal heghts GOCE Unt: meter Maxmum Mnmum value Mean Standard devaton GOCE data wll have many uses, probng hazardous volcanc regons and brngng new nsght nto ocean behavor. The latter, n partcular, s a major drver for the msson. By combnng the gravty data wth nformaton about sea surface heght gathered by other satellte altmeters, scentsts wll be able to track the drecton and speed of geostrophc ocean currents. The low orbt and hgh accuracy of the system wll greatly mprove the known accuracy and spatal resoluton of the geod (the theoretcal surface of equal gravtatonal potental on the Earth). The satellte s arrow shape and fns help keep the GOCE stable as t fles through the wsps of ar stll present at an alttude of 260 km. In addton, an on propulson system contnuously compensates for the deceleraton of ar-drag wthout the vbraton of a conventonal chemcallypowered rocket engne, thus restorng the path of the craft as closely as possble to a purely nertal RESULTS & DISCUSSION The dstance between the nstantaneous sea surface and the MSL s called as mean sea surface topography whch results from some factors such as sold ground tde, oceanc streams and geology phenomena. The dstance between geod and the MSL s called as sea surface pseudo-statc topography whch results from dverse dynamc phenomena n oceans lke temperature, salnty, unsolvable oxygen quantty n water. It s very mportant to measure the sea level specally the topographcal sea surface because we can obtan the sea dscharge wth the help of measurng the geodesy, geodal heght and hydrology. The SST conssts of two parts: the pseudo-statc part (unchangeable n tme) and the changeable n tme part. The pseudo-statc topography s stable (unchangeable) as the SSH on tme perod and the changeable topography changes wth the slght 649

6 Sadatpour, S. M.T.et al. changes n tme scale and seasonal phenomena. The relaton between geodal heght and the sea surface topography s shown n fg.6. n whch ζ t s the changeable part and ζ c s the pseudo-statc topography part. Fg.6. shows the relaton between the geodal heght, the SST and the nstantaneous SSHs measured by altmeter. SSH = N + SST (5) Equaton5 s a smple equaton whch shows the relaton between Earth s reference ellpsod (h), orthometrc heght (H) and geodal heght (N). h = N + H (6) Fg. 6. The relaton between orthometrc heght, reference ellpsod and geodal heght The SST term n equqton5 shows the contnental orthometrc heght, that s why t s called as the sea surface topography. The SST and the SFT (sea floor topography), of course, have many dstnctons and there s relatvely a relaton between the SST and the SFT; ths shows that these two levels are less n common. In addton to pseudo-statc part whch s stable on tme perod, the SST also has changeable dynamc part whereas the earth topography s always stable. The maxmum and mnmum value for the SST s about 2.2 meters whereas the maxmum earth topography reaches to 8.5 km n Hmalaya. The SST modelng s done by geodetc and oceanc methods. The geodetc methods use the earth 650 gravty centre observatons related to some quanttes such as geodal heght, geod anomaly, gravty anomaly, vertcal deflectons and gravty undulatons. The oceanc methods are based on the observatons of salnty, temperature, pressure and unsolvable oxygen contents n oceans water and they are wrtten based on the complcated dfferental equatons. Generally, more precse modelng s performed by geodetc technques of the SST. In all usages of physcal geodesy whch am to determne the geod, t s assumed that geods don t change n a specfc tme perod. Therefore, only pseudo-statc part of the SST s needed. The tme changeable part of the SST could be calculated by analyzng the satelltes crossover ponts durng the repettve altmeter msson perod and t also could be omtted durng the altmeter data processng and then t could be fltered by the momentary sea observatons as parameters bas and tlt. The geodetc modelng methods for the SST are classfed n three classes. The frst method s based on the sphercal harmoncs extenson whch s offered by (Engels, 1987). In ths method, the satellte altmetry observatons and the geopotental model wth low degrees have been used. The shortcomng of ths method s that the whole sphere functon and the whole earth observatons should be covered n order to extend to a sphercal harmonc seres. Unfortunately, part of the earth s covered by land and so the altmeters can t observe some parts of oceans n hgh lattudes. In the second method, we use orthonormal functons nstead of sphercal harmoncs. In ths sense, hgh lattudes are not consdered. The ntentoned functons are defned n specfc regons n the earth, and they aren t consdered n hgh lattudes regons and marne zones such as Medterranean Sea, Black Sea and so on. Ths method s offered by Rapp. Thrd method, extendng the frequency space, s offered by Anderson n 2000 and t modulates the SST n remote marne zones wth good results. The precse determnaton of the SST depends on the precse determnaton of the MSL and geod. SST = MSL N (7) ( ϕ, ( ϕ, geod ( ϕ, Fg.7. and Table.5. Show the SST map based on the global geod models EGM2008, GOCE and EIGEN06C and comparng the statstcal results of the models. Table 5. comparng the statstcal results of the sea surface topography based on the global geod models EGM2008, GOCE AND EIGEN06C Unt: meter Geod Models Maxmum value Mnmum value Mean value Root Mean Squares EGM GOCE EIGEN06C

7 Int. J. Envron. Res., 6(3): , Summer 2012 EGM2008 GOCE EIGEN06C Fg. 7. The sea surface topography based on the global geod models EGM2008, GOCE AND EIGEN06C Unt: meter CONCLUSION The measurng base of the absolute alttude n every country s resulted from the tde gage nformaton measurements. The exstence of the SST leads to the separaton between the geod and the MSL. The alttudes measurement base dffers n dfferent countres. As a result, the alttudes base dfference should be determned n dfferent countres n order to relate the geodesy researches and mappng projects together n dfferent countres so that they relate to the ponts absolute alttudes. In order to fnd the dfference between the absolute alttudes base levels, only the SST of the countres lattude base ponts should be determned. In order to determne the SST, the geod model whch s the desred base level requres to be calculated. Dfferent global geod models are used to calculate the SST. In addton, n ths artcle the MSL s calculated and t s determned n detal how to determne ths level. For ths purpose, the Fourer analyss method and the least squares method are used to remove the perodc anomales. By comparng the pctures n fg.7, we can see an approprate conformty between models EIGEN06C and EGM2008. In comparson wth two other models, the model resultng from GOCE has more detals about the SST. Table.5. also shows that the model EIGEN06C has the Root mean Squares wth about 8cm more than other models. Meanwhle, the models EIGEN06C and EIGEN06C have the least (about 2.82 m) and the most (about 4 m) range for the SST changes respectvely. The exstence of the more detals for the SST of the model GOCE could be very mportant from the vewpont of the oceanography studes specally the marne streams studes. By comparng the squares sum parameter of 651

8 Sea Surface Topography Models the mean sea surface topography n dfferent geopotental models, t s evdent that the geopotental model EIGEN06C whch contans a combnaton of the ground and satellte-based data has the nearest dstance from the MSL among the other models. REFERENCES Andersen, O. B. and Knudsen, P. (2009). DNSC08 mean sea surface and mean dynamc topography models. Geophys. Res., 114, do: /2008jc Ardalan, A. A. and Mosayebzadeh, M. (2004). Sea surface topography n Oman and Persan Gulf based on the combnaton of tde gauge and GPS. J Engneerng Faculty, Tehran Unversty, 37 (2), Andersen, O. B. Knudsen, P. and Berry, P. (2010). The DNSC08GRA global marne gravty feld from double retracked satellte altmetry, Journal of Geodesy, 84 (3), Beckley, B. D., Lemone, F. G., Luthcke, S. B., Ray, R. D. and Zelensky, N. P. (2007). A reassessment of global and regonal mean sea level trends from TOPEX and Jason-1 altmetry based on revsed reference frame and orbts. Geophys. Res. Lett., 34, do /2007GL Brunsma, S. L., Marty, J. C., Balmno, G., Bancale, R., Foerste C., Abrkosov, O. and Neumayer, H. (2010). GOCE Gravty Feld Recovery by Means of the Drect Numercal Method. Presented at the ESA Lvng Planet Symposum, 27th June - 2nd July 2010, Bergen, Norway; See also: earth.esa.nt/goce Engels, T. (1985). Global crculaton from Seasat altmeter data. Marne Geodesy, 9(1), DOI: / Engels, T. (1987). Sphercal harmoncs expanson of the Levtus Sea Surface Topography. Report No. 385, Department of Geodetc Scence and Surveyng, The Oho State Unversty, Columbus, Oho. Förste, C., Brunsma, S., Shako, R., Marty, J. C., Flechtner, F., Abrkosov, O., Dahle, C., Lemone, J. M., Neumayer, K. H., Bancale, R., Barthelmes, F., Köng, R. and Balmno, G. (2011). EIGEN-6 - A new combned global gravty feld model ncludng GOCE data from the collaboraton of GFZ- Potsdam and GRGS-Toulouse; Geophyscal Research Abstracts, Vol. 13, EGU , EGU General Assembly. Kamehr, R., (2007). A new heght datum for Iran based on the combnaton of gravmetrc and geometrc models. Acta Geod. Geoph., Hung, 42 (1), Kamehr, R., (2006). A strategy for determnng the regonal geod n developng countres by combnng lmted ground data wth satellte-based global geopotental and topographcal models. A case study of Iran. Geod, 79 (10-11), Knudsen, P. (1992). Estmaton of sea surface topography n the Norwegan sea usng gravmetry and Geosat altmetry. Bulletn Géodésque, 66, Marsh, J. G., Koblnsky, C. J. Lerch, F., Klosko, S. M., Robbns, J. W., Wllamson, R. G. and Patel, G. B. (1990). Dynamc sea surface topography, gravty, and mproved orbt accuraces from the drect evaluaton of seasat altmeter data. Geophys. Res., 95, Mayer-Gürr, T. Kurtenbach, E. Ecker, A. and Kusche, J. (2011). The ITG-Grace2010 gravty feld model (submtted) In: Geophyscal Research Letters, submtted. Jg. Pavls, N. K., Holmes, S. A., Kenyon, S. C. and Factor, J. K. (2008). An. Earth Gravtatonal Model to Degree 2160: EGM2008, Presented to EGU-2008, Venna, Austra, Aprl, Rapp, R. H., and Smth, D. A. (1994). Prelmnary estmates of Gulf Stream characterstcs from TOPEX data and a precse gravmetrc geod. J. Geophys. Res., 99 (24), Ross, D. A. (1995). Introducton to Oceanography. HarperCollns College Publshers, NewYork. Vancek, P. and Krakwsky, E. (1986). Geodesy the concepts, Chapter 15, Second Edton,unversty of New Brrunswck, Canada. Yu, W. (2004). Ocean Tde Modelng n Southern Ocean, Department of cvl and Envronmental Engneerng and GeodetcScence., Report No.471, The oho state Unversty Columbus. 652