Comparative Analysis of Five Standard Dry Tropospheric Delay Models for Estimation of Dry Tropospheric Delay in Gnss Positioning

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1 American Journal of Geographic Information Sytem 2013, 2(4): DOI: /j.ajgi Comparative Analyi of Five Stanar Dry Tropopheric Delay Moel for Etimation of Dry Tropopheric Delay in Gn Poitioning Opaluwa Y. D, Aejare Q. A *, Suleyman Z. A. T, Abazu I. C, Aewale T. O, Oeanmi A. O, Okorocha V. C Department of Surveying & Geoinformatic, Feeral Univerity of Technology, Minna, Niger State, Nigeria Abtract The atmophere cauing the elay in GPS ignal conit of two main layer, ionophere an tropophere. The ionopheric bia can be mitigate uing ual frequency receiver. Unlike the ionopheric bia, the tropopheric bia cannot be remove uing the ame proceure. Compenation for the tropopheric bia i often carrie out uing a tanar tropopheric moel. In orer to invetigate the impact of ifferent ry tropopheric moel on GPS accuracy, imultaneou hourly obervation wa carrie out at ome electe tation in Minna. The tropopheric error obtaine uing five tanar tropopheric moel namely, the Saatamoinen moel (which wa aopte a the tanar moel), Hopfiel moel, Davi et al. moel, Saatamoinen moel (Uing Groun Meteorological Data) an Althuler an Kalaghan moel were compare. It wa euce from the reult that at all the tation, the Saatamoinen Moel (Uing Groun Meteorological Data), ha 100% correlation with the aopte tanar Dry Tropopheric Moel (Saatamoinen moel). While a tanar error of 0.285mm, 1.446mm an 2.899mm were repectively obtaine for Davi et al. Moel, Hopefiel moel an Althuler an Kalaghan (A&K) Moel. However, the tatitical tet performe on the overall reult inicate that there i no ignificant ifference in the performance of the five tropopheric moel at 0.05 ignificance level. It wa therefore, conclue that either of the five moel evaluate in thi tuy can perform well in the tuy area, neverthele, the choice of Saatamoinen Moel, Saatamoinen Moel (Groun Meteorological Data) an Davi et al. Moel will be more preferable. Keywor Ionopheric Bia, Tropoheric Bia, GPS Signal, Tropopheric Moel 1. Introuction 1.1. Backgroun to Stuy The propagation elay inuce by the electrically neutral atmophere, commonly known a the tropopheric elay, i one of the mot ifficult-to-moel error affecting pace geoetic technique. An unmoelle tropopheric elay affect mainly the height component of poition an therefore contitute a matter of concern in pace-geoey application, uch a ea-level monitoring, pot-glacial reboun meaurement, earthquake-hazar mitigation, an tectonic-plate-margin eformation tuie, where the highet poible poition accuracy i ought, hence the improvement in tropopheric elay moelling i therefore eential[19]. When travelling through the electrically-neutral atmophere, raio ignal ue by raiometric technique are affecte by the variability of the refractive inex, cauing an exce path elay * Correponing author: quariaejare@yahoo.com (Aejare Q. A) Publihe online at Copyright 2013 Scientific & Acaemic Publihing. All Right Reerve. an ray bening. The effect i commonly known a tropopheric propagation elay (or imply tropopheric elay), even though thi eignation i mileaing, a the tratophere ha a ignificant contribution to the total elay[8]. The tropophere i an effectively non-iperive region up to frequencie of approximately 15GHz for microwave ignal. In other wor the propagation through the tropophere i not frequency epenent. The elay caue by the tropophere can be eparate into two main component: the hyrotatic elay an the wet elay [13]. The zenith hyrotatic elay (ry component) contribute about 90% of the total elay to the tropopheric elay[16]. The ry component i etermine with high accuracy by many tropopheric elay moel erive from urface meaurement. Since the ry part of the tropophere i in hyrotatic equilibrium, the ieal ga law can eaily be applie to it. The wet component, however, i ifficult to preict becaue of the irregular itribution of liqui water an water vapour both horizontally an vertically in the tropophere. Although the wet component of the elay contitute le than 10% of the total effect[9], it till caue the limiting uncertainty in etermining a very accurate remey for the total elay. The tropopheric elay i ifficult to fully correct an contitute one of the major

2 122 Opaluwa Y. D et al.: Comparative Analyi of Five Stanar Dry Tropopheric Delay Moel for Etimation of Dry Tropopheric Delay in Gn Poitioning reiual error ource in moern pace geoetic technique uch a DORIS (Doppler Orbitography an Raio-poitioning Integrate by Satellite), GPS (Global Poitioning Sytem) an VLBI (Very Long Baeline Interferometry) affecting mainly the etimate of the height component of poition[16] Statement of Problem Tropopheric elay i one of the major error in Global Navigation Satellite Sytem (GNSS) Poitioning. Several moel exit for etimating the magnitue of thi error in the etermine poition, but the level of refinement attainable with each of the moel iffer. Furthermore, the effect of tropopheric elay ha been accounte for in ual frequency GPS receiver, but the impact i till ignificant in ingle frequency receiver. Since mot GNSS uer in the tuy area cannot eaily affor ual frequency receiver, there i the nee to ae the performance of ome tanar tropopheric moel in the area. Therefore, thi reearch eek to compare ome ry tropopheric elay moel in Minna uing ata oberve with ingle frequency Differential GPS (DGPS) Aim an Objective The aim of thi reearch i to ientify the optimum ry tropopheric moel uing ingle frequency GPS receiver. Therefore, the objective that will ait in achieving the above aim inclue the following: - To carry out DGPS obervation at three (3) epoch of the ay (i.e. morning, afternoon an evening), a well a atmopheric parameter uch a temperature, relative humiity, preure, etc at ome electe tation in Minna. - To etimate the amount of ry tropopheric elay with each moel at variou epoch of obervation uing a program written in Java programming language. - To examine the ifference in the etimate elay uing the electe moel an perform tatitical tet on the reult. Figure 1(a). Aminitrative Map of Niger State howing Minna. (Source: Niger State Minitry of Lan)

3 American Journal of Geographic Information Sytem 2013, 2(4): SVG/GPS01 Figure 1(b). Oberve tation for the tuy 1.4. Location an Scope of Stuy Location of Project CSN168 (Bae) The project ite wa locate in Minna, the capital of Niger tate. The city i with an etimate population of over 347,788 an lan area of about quare kilometre. Minna lie between latitue an North of the Equator an longitue an Eat of the Meriian, on a geological bae of copper, iron, lea, ilica, clay, an, etc (Niger State Diary, 2010). The tation were carefully electe to cover the major axe of Minna, a they are locate at Houe of Aembly Quarter (09/FUT/055), Tuun Fulani (CSN168), Gian-Kwano campu of Feeral Univerity of Technology Minna (SVG/GPS/01/2008), an at Minna- atum. Figure 1 how the map of the tuy area, with the tation in re Scope of Project The cope of thi project cover ata collection uing DGPS (Differential GPS) technique an the etimation of ry tropopheric elay in the ata uing appropriate moel compute with a Java Program. Thi project oe not cater for the wet tropopheric component an other error ource in GPS obervation. 2. Conceptual Framework FUT09/ Differential Global Poitioning Sytem (DGPS) The DGPS i an enhancement to Global Poitioning Sytem that ue a network of fixe, groun-bae reference tation to broacat the ifference between the poition inicate by the atellite ytem an the known fixe poition. Thee tation broacat the ifference between the meaure atellite peuorange an actual (internally compute) peuorange, an receiver tation may correct their peuorange by the ame amount. The correction ignal i typically broacat over UHF raio moem[11]. DGPS ata collection can be by tatic, top-an-go, an kinematic moe. The three moe run inepenently. In the Static ata collection moe, the GPS receiver ytem imultaneouly collect raw ata from all available atellite while remaining tationary on their repective point. In the Stop-an-Go ata collection moe, the GPS receiver ytem imultaneouly collect raw ata from all available atellite while tationary on their repective point an while moving between point. In the Kinematic ata collection moe, the GPS receiver ytem imultaneouly collect raw ata from all available atellite while a receiver i moving[10] about 100km above it. The lower part of thi hell, ranging from the urface of the Earth to approximately 50km above it, contain about 99.9% of all atmopheric ma. It conit of the tropophere (0-10km), in which temperature ecreae with height, the tropopaue (10km), at which temperature remain contant, an the tratophere (10-50km), in which temperature increae with height. The elay experience by a ignal travelling through the neutral part of atmophere i generally referre to a tropopheric elay, ince the tropophere account for 90% of the total elay. Therefore, when peaking of the tropophere, often the lower 50km of the Earth' atmophere i really referre to[8]. Figure 2. Principle of DGPS Obervation 2.2. Tropophere The neutral (non-ionize) atmophere i an approximately pherical hell extening outwar from the Earth' urface to The tropopheric effect i a further factor elongating the runtime of electromagnetic wave by refraction. The reaon for the refraction are ifferent concentration of water vapour in the tropophere, caue by ifferent weather conition. The error cannot be eliminate by calculation. It can only be approximate by a general calculation moel[16]. The tropopheric elay i eparate into two component: ry an wet. The ry component i etermine with high accuracy by many tropopheric elay moel erive from urface meaurement. The wet component, however, i ifficult to preict becaue water vapour i highly variable in pace an time uch that the wet elay cannot be moelle uing urface meaurement very accurately[1]. The wet component of the elay contitute le than 10% of the total effect; tropopheric effect on GPS ignal i approximately ± 0.5m[8]. Figure 3

4 124 Opaluwa Y. D et al.: Comparative Analyi of Five Stanar Dry Tropopheric Delay Moel for Etimation of Dry Tropopheric Delay in Gn Poitioning how the variou layer of the atmophere an the repone of air temperature to increaing altitue Hyrotatic Moel Early effort to etermine correction for raio propagation elay by the atmophere were prompte by the nee for improvement in atellite tracking from groun tation. Figure 3. The Layer of Earth' Atmophere. Source:[5] [13],[12], an[2] mae ignificant contribution to the tuy of range correction. Saatamoinen Zenith hyrotatic elay an the form of Marini approximation for the mapping function for a horizontally tratifie refractive meium are incorporate in many current moel ue for accurate pace-bae geoetic meaurement. [13] Showe that the elay in the zenith irection ue to the atmopheric contituent in hyrotatic equilibrium i accurately etermine by meauring the urface preure an making correction for the latitue an height above ea level of the ite from which the obervation wa mae. Hi formula (or lightly more precie form given by[3] provie the zenith hyrotatic path with accuracy better than 1mm uner conition of hyrotatic equilibrium. [15] invetigate the impact of ifferent tanar tropopheric moel (namely, Saatamoinen moel, Hopfiel moel an Simplifie Hopfiel moel) on GPS baeline accuracy, in orer to etermine the bet-fit tanar tropopheric moel in Thailan with the GPS ata collecte in Thailan. The reult inicate that there are no tatitically ignificant ifference in the performance of the three tropopheric moel. However, the ue of the Saatamoinen moel ten to prouce more reliable reult than the ue of the other two moel[15]. (i). Saatamoinen Moel If hyrotatic equilibrium i aume, the hyrotatic elay moel may be expree imply a a function of meaure urface preure.[14] employe thi approach an ue the following repreentation of gravity g m in the zenith hyrotatic moel. g m = 9.784( co 2ϕ H ) (1) Where, ϕ i the latitue of the tation an H i the tation height above ea level, in metre. Saatamoinen ue K 1 refractivity contant given by[3] to etermine the following expreion for the zenith hyrotatic elay: z P h = (2) ( co 2ϕ H ) where, P i the urface preure an K 1 = The mot table tropopheric moel for the equatorial region i the Saatamoinen Moel[15]. Conequently, Saatamoinen Moel ha been aopte a the Stanar ry Tropopheric elay Moel for thi reearch. (ii). Davi et al. Moel The[4] moel lightly iffer from the Saatamoinen moel. Davi el al. ue the K 1 refractivity contant given by[20] an the zenith hyrotatic moel i given by the following expreion: z P h = (3) ( co 2ϕ H ) where, P i the urface preure an K 1 = (iii). Hopfiel Moel [7] aume that the theoretical ry refractivity profile coul be expree uing a quartic moel: e 4 ( H H ) N N e 4 ( H ) = ( T = (4) where, H e ), N i the ry refractivity on the urface obtaine uing the K 2 refractivity 6 P contant etermine by[17] a an H i the T height above ea level, in metre hence, the final expreion for the zenith ry elay can be repreente by the following expreion: z P T e H S T 6 = (4.1) where, P i the urface preure, an i the urface temperature an K 2 i (iv). Althuler an Kalaghan (A&K) Moel Uing the K 2 refractivity contant etermine by[17], the tropopheric elay correction (Δ) in metre i given by[18]: ( E, h, N ) = m( E) H ( h) (5) F( h, N ) metre where, ( ) m ( E) = E E E (5.1) [ ( E 30) ]

5 American Journal of Geographic Information Sytem 2013, 2(4): H ( h) = (5.2) h ( h ) ( h ) ( h ) + FhN (, ) = h N ( ( N 315)) P N = T E = elevation angle in egree h = height above ea level in metre N = global urface refractivity S P = urface preure in milibar T = urface temperature in egree Kelvin (5.3) K 2 = m (v). Saatamoinen Moel (Uing Groun Meteorological Data) Uing the K 1 refractivity contant etermine by[4], the tropopheric elay uing thi moel i given by[18]: where, P = (6) ( co 2ϕ H ) P i the atmopheric preure, ϕ i the latitue of the z h tation an H i the height of the tation above ea level, K1 i in metre. 3. Methoology During planning, the tation were carefully electe to cover the major axe of Minna uing the city map of Minna. The tation are 09/FUT/055 at Houe of Aembly Quarter, CSN168S at Tuun Fulani, SVG/GPS/01/2008 at Gian-Kwano campu of Feeral Univerity of Technology Minna, an Nigerian atum (bae tation) ee fig. 1 above. The coorinate of the electe tation were collecte from the Department of Surveying & Geoinformatic, Feeral Univerity of Technology Minna. The etail are a hown in the table below: STATIONS Table 1. Exiting Coorinate of Station Ue NORTHINGS (m) EASTINGS (m) HEIGHT (m) CSN168S FUT 09/ SVG/GPS/ Data Acquiition Proceure Thale ProMark3 Single Frequency DGPS Receiver an the Acceorie were ue. The tatic DGPS proceure wa ue for the fiel operation. The intrument wa et at Minna- atum, which wa aopte a the bae tation. All neceary ajutment were carrie out before the neceary parameter were entere into the receiver to tart obervation. The other three tation were imilarly et up an were imultaneouly log on to capture ata concurrently for an hour, four et of hourly obervation wa mae uring each eion. Thi imultaneou obervation were mae at all tation between 8:30a.m an 12 noon for morning obervation, 2:00p.m an 5:00p.m for afternoon obervation, 6:00p.m an 9:00p.m for evening obervation. Figure 4. Network eign 3.2. Data Proceing Since the ProMark3 Sytem operate in conjunction with GNSS Solution, the acquire fiel ata were procee uing GNSS olution Software. Alo, a Java 1.6.0_15 bae Program wa evelope uing the electe ry tropopheric elay moel. The Java program run with an intalle My SQL Aminitrator (verion 1.1.9) an Net Bean IDE (6.5). The equation efining the moel were coe into the program with SQL for fat, efficient an error-free proceing to obtain the tropopheric elay. 4. Reult an Analyi 4.1. Reult Below are the mean coorinate obtaine from the fiel obervation. Table 2(a). Coorinate of Occupie Station uring Morning Obervation Point ID Eating(m) Northing(m) Height(m) FUTO9/ GPS CSN Table 2(b). Coorinate of Occupie Station uring Afternoon Obervation Point ID Eating(m) Northing(m) Height(m) FUT09/ GPS CSN

6 126 Opaluwa Y. D et al.: Comparative Analyi of Five Stanar Dry Tropopheric Delay Moel for Etimation of Dry Tropopheric Delay in Gn Poitioning Table 2(c). Coorinate of Occupie Station uring Evening Obervation Point ID Eating(m) Northing(m) Height(m) FUT09/ GPSS CSN Table 2(a, b, c) above how the procee three imenional (X, Y, Z) coorinate of the occupie tation uring morning, afternoon an evening obervation uing GNSS Solution. Tropopheric elay affect mainly the height component [19]. Hence, table 3 below how the mean oberve height at the variou occupie tation uring obervation. Table 3. Summary of Oberve Height Statn Epoch L 40 Oberve Height (m) FUT 09/055 SVG/ GPS01 CSN 168S Morning Afternoon Evening Mean of Mean Table 4 (a to E) below how the ry tropopheric error etimate by the ifferent tropopheric moel uring morning, afternoon an evening obervation. Table 5, 6, 7, 8 below how the eviation of the tropopheric elay etimate by the other ry tropopheric moel from the aopte tanar moel (Saatamoinen moel) at each tation. KEY: M 1 : SAASTAMOINEN Moel, M 2 : SAASTAMOINEN Moel (GROUND MET. DATA), M 3 : DAVIS, M 4 : Althuler an Kalaghan (A&K) Moel an M 5 : HOPFIELD Moel NOTE: Stanar Moel aopte i Saatamoinen Dry Tropopheric Moel[15]. Chart 1 below how graphically, the eviation of tropopheric error etimate by other tropopheric elay moel at L 40 atum in the above table. The Chart 2 below how graphically, the eviation of tropopheric error etimate by other tropopheric elay moel at FUT09/055 tation in the above table. The Chart 3 below how graphically, the eviation of tropopheric error etimate by other tropopheric elay moel at SVG/GPS01 tation in the above table. The Chart 4 below how graphically, the eviation of tropopheric error etimate by other tropopheric elay moel at CSN168 tation in the above table. Table 4. Dry Tropopheric Error Etimate by Each Moel per tation A. SAASTAMOINEN MODEL STATION FUT09/ SVG/ CSN EPOCH 055 GPS Morning Afternoon Evening MEAN ESTIMATE B. SAASTAMOINEN (GROUND MET. DATA) MODEL STATION FUT09/ SVG/ CSN EPOCH 055 GPS Morning Afternoon Evening MEAN ESTIMATE C. DAVIS ET. AL MODEL STATION FUT09/ SVG/ CSN EPOCH 055 GPS Morning Afternoon Evening MEAN ESTIMATE D. ALTSHULER AND KALAGHAN (A&K) MODEL STATION FUT09/ SVG/ CSN EPOCH 055 GPS Morning Afternoon Evening MEAN ESTIMATE E. HOPFIELD MODEL STATION FUT09/ SVG/ CSN EPOCH 055 GPS Morning Afternoon Evening MEAN ESTIMATE Table 5. Deviation of Other Moel from the Stanar Dry Tropopheric Moel at L-40 Diff Epoch (M 1 - M 2 ) (M 1 M 3 ) (M 1 M 4 ) (M 1 M 5 ) Dry Tropopheric Error Morning Afternoon Evening Mean

7 American Journal of Geographic Information Sytem 2013, 2(4): Chart 1. Deviation of Other Moel from the Stanar Moel at L-40 Table 6. Deviation of Other Moel from the Stanar Dry Tropoheric Moel at FUT09/055 Diff Epoch (M 1 M 2 ) (M 1 M 3 ) (M 1 M 4 ) (M 1 M 5 ) Dry Tropopheric Error Morning Afternoon Evening Mean Chart 2. Deviation of Other Moel from the Stanar Moel at FUT09/055 Table 7. Deviation of Other Moel from the Stanar Dry Tropoheric Moel at SVG/GPS01 Diff Epoch (M 1 M 2 ) (M 1 M 3 ) (M 1 M 4 ) (M 1 M 5 ) Dry Tropopheric Error Morning Afternoon Evening Mean

8 128 Opaluwa Y. D et al.: Comparative Analyi of Five Stanar Dry Tropopheric Delay Moel for Etimation of Dry Tropopheric Delay in Gn Poitioning Chart 3. Deviation of Other Moel from the Stanar Moel at SVG/GPS01 Chart 4. Deviation of Other Moel from the Stanar Moel at CSN168S Table 8. Deviation of Other Moel from the Stanar Dry Tropoheric Moel at CSN168S Diff Epoch (M 1 M 2 ) (M 1 M 3 ) (M 1 M 4 ) (M 1 M 5 ) Dry Tropopheric Error Morning Afternoon Evening Mean Table 9. Mean Etimate of tropopheric error per tation per moel Statn Saatam. Saa. Grn Met Davi et al. Alth & Kalaghn Hope Fiel FUT09/ SVG/GPS CSN 168S Table 10. Mean eviation per tation per moel Statn Saa. Grn Met Davi et al. Alth & Kalaghn Hope Fiel FUT09/ SVG/GPS CSN168S

9 American Journal of Geographic Information Sytem 2013, 2(4): In a further invetigation, the hypothei tet wa carrie out to fin out if the ifference in the performance of the five (5) tanar tropopheric Moel at each tation are tatitically ignificant at 5% ignificance level uing StatextV1.0 oftware. The hypothei i a follow: H 0 : µ 1 = µ 2 = µ 3 (Null hypothei) H 1 : at leat two are not equal (Alternative hypothei) Reject F, if F 0.95 > F-Table, otherwie accept null hypothei. Chart 5. Mean eviation Table 11. Tet of Significant Difference between Saatamoinen Moel & Davi et al. Moel Statn Epoch Saatamoinen Davi F 0.95 (1,4) Ratio F 0.95 (1,4) Table Rem L 40 FUT09/055 SVG/ GPS01 CSN 168S Morning Afternoon Evening Morning Afternoon Evening Morning Afternoon Evening Morning Afternoon Evening F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept Table 12. Tet of Significant Difference between Saatamoinen Moel & Althuler & Kalaghan (A & K) Moel Statn Epoch Saatamoinen A & K F 0.95 (1,4) Ratio F 0.95 (1,4) Table Rem FUT09/055 SVG/GPS01 CSN 168S Morning Afternoon Evening Morning Afternoon Evening Morning Afternoon Evening Morning Afternoon Evening F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept

10 130 Opaluwa Y. D et al.: Comparative Analyi of Five Stanar Dry Tropopheric Delay Moel for Etimation of Dry Tropopheric Delay in Gn Poitioning Table 13. Tet of Significant Difference between Saatamoinen Moel & Hopfiel Moel Statn Epoch Saatamoinen Hope-fiel FUT 09/055 SVG GPS01 CSN 168S Morning Afternoon Evening Morning Afternoon Evening Morning Afternoon Evening Morning Afternoon Evening F 0.95 (1,4) Ratio F 0.95 (1,4) Table Rem F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept F(1,4) = 7.71 Accept 4.2. Analye of Reult In the following analye, the icrepancie in the ry tropopheric error obtaine by the five tropopheric moel at variou obervation epoch are icue. It can be een from Table 2, 3 an 4 above howe that Hopfiel Moel ha the lowet ry tropopheric elay etimate numerically while the highet ry tropopheric etimate are from Saatamoinen an Saatamoinen (Uing Groun Meteorological Data) Moel. The performance of Saatamoinen, Saatamoinen (Uing Groun Meteorological Data) an Davi et al. tanar tropopheric Moel are very cloe a their ry tropopheric error iffer only by a few centimetre uring morning, afternoon an evening obervation, while Althuler an Kalaghan (A&K) Moel an Hopfiel Moel have centimetre variation among each other but iffer from the other three by about two metre (2m). The reaon for thi i that Saatamoinen, Saatamoinen et al. tanar tropopheric Moel ue the ame empirically etermine refractivity contant (k 1 ), while Althuler an Kalaghan (A&K) Moel an Hopfiel Moel ue the ame empirically etermine refractivity contant (k 2 ). Alo, it can be een that there are no variation in the ry tropopheric error etimate by Saatamoinen Moel an Saatamoinen Moel (Uing Groun Meteorological Data) uring morning, afternoon an evening obervation. Table 5, 6, 7, 8 an Chart 1, 2, 3, 4 epicte the abolute eviation of the ry tropopheric Moel from Saatamoinen Moel which wa aopte a the tanar Moel [15] at each tation. Thi gave the iea of the temporal variability of the etimate tropopheric error by the moel. Since Saatamoinen Moel (Uing Groun Meteorological Data) i highly correlate with the aopte tanar moel becaue of the moel imilarity, the remaining three moel were evaluate. It wa oberve from the table an the chart that Davi et al. Moel gave more conitent reult, followe by Hopefiel moel then Althuler an Kalaghan (A&K) Moel. Furthermore, from the mean etimate in table 9 an the mean eviation in table 10, the tanar error of 0.285mm, 1.446mm an 2.899mm were repectively obtaine for Davi et al. Moel, Hopefiel moel an Althuler an Kalaghan (A&K) Moel. Finally, from table 11, 12, 13, the F-tet howe that the ifference in the performance of the tanar tropopheric Moel at each tation are not tatitically ignificant at 5% ignificance level. 5. Concluion an Recommenation 5.1. Concluion Total zenith elay an graient parameter can be etimate with the preent GPS ata proceing. The zenith hyrotatic elay can be accurately inferre from precie meaurement of atmopheric parameter. The magnitue of the etimate hyrotatic elay at a particular tation epen on the hyrotatic elay moel ue an the time of obervation. Bae on the F-tet performe, all the Moel, i.e. Saatamoinen Moel, Saatamoinen Moel (Groun Meteorological Data), Davi et al. Moel, Althuler an Kalaghan (A&K) Moel an Hopfiel Moel, generally prouce reult that are not tatitically ifferent. But comparatively, the Davi et al. Moel with a tanar error of about 0.3mm gave a better performance cloe to the aopte tanar moel, i.e. Saatamoinen Moel. However, a tanar eviation of about 1.4mm an 2.9mm for Hopefiel an Althuler an Kalaghan (A&K) Moel repectively corroborate with the tatitical tet above. It coul therefore, be conclue that either of the five moel evaluate in thi tuy can perform well in the tuy area, neverthele, the choice of Saatamoinen Moel, Saatamoinen Moel (Groun Meteorological Data) an Davi et al. Moel will be more preferable Recommenation The following recommenation are mae bae on the reearch fining:

11 American Journal of Geographic Information Sytem 2013, 2(4): The bet time for GPS obervation with leat tropopheric effect are between 2p.m an 6p.m. Alo, obervation at evening between 6p.m an 9p.m can be mae a the tropopheric effect i not high uring thoe time. However, obervation at perio when the un i ai to be at it peak (11a.m to 1p.m) houl be avoie. 2. Further reearche like eaonal variation of tropopheric elay, the ue of Continuouly Oberving Reference Station (CORS) to invetigate tropopheric impact, etc, houl be encourage for broaer an better unertaning of tropopheric effect. REFERENCES [1] Bevi, M., S. Buinger, S. Chiwell, T.A. Herring, R.A. Anthe, C. Rocken an R. Ware (1994): GPS Meteorology: Mapping Zenith Wet Delay Onto Precipitable Water, Journal of Applie Meteorology, Vol. 33, pp [2] Chao, C.C. (1972): A Moel for Tropopheric Calibration from Daily Surface an Raioone, Balloon Meaurement, Jet Propulion Laboratory, Paaena, California, Technical Memoranum , pp. 16. [3] Davi, J.L., T.A. Herring, I.I. Shapiro, A.E.E. Roger an G. Elgere (1985): Geoey by Raio Interferometry: Effect of Atmopheric Moelling on Etimate of Baeline Length, Raio Science, Vol., 20, No. 6, pp [4] Een, L. an K.D. Froome (1951): The Refractive Inice an Dielectric Contant of Air an It Principal Contituent at 24, 000 Mc/. Proceeing of the Royal Society B, Vol. 64, pp [5] Encyclopaeia Britannica (2009): Stuent an Home Eition. [6] "Global Poitioning Sytem"(2010). [7] Hopfiel, H.S. (1969): Two Quartic Tropoheric Refractivity Profile for Correcting Satellite Data, Journal of Geophyical Reearch, Vol.74, No. 18, pp [8] Hopfiel, H.S. (1971): Tropopheric Effect on Electromagnetically Meaure Range: Preiction from Surface Weather Data, Raio Science, Vol. 6, No. 3, pp Tracing an Implication for GPS Relative Poitioning, Bulletin Geoeique, Vol. 65, No. 3, pp [10] Kaplan, E. D. an Hegarty, C.J. (2006): Unertaning GPS; Principle an Application, 2 n eition. Artech Houe, Inc. [11] Lachapelle, G. (2001): Avance GPS Theory an Application, ENGO 625 Coure Lecture Note, Univerity of Calgary, Calgary, Canaa. [12] Marini, J.W. (1972): Correction of Satellite Tracking Data for an Arbitrary Tropopheric Profile, Raio Science, Vol. 7, No. 2, pp [13] Saatamoinen, J. (1972): Atmopheric Correction for Tropophere an Stratophere in Raio Ranging Of Satellite, Geophyical Monograph, 15, American Geophyical Union, Wahington, D.C., pp [14] Saatamoinen, J. (1973): Contribution of the Theory of Atmopheric Refraction, Bulletin of Geoeique, No. 105, pp , No. 106, pp , No. 107, pp [15] Satirapo, C., Chalermwattanachai, P. (2004): Impact of Different Tropopheric Moel on GPS Baeline Accuracy: Cae tuy in Thailan. A paper preente at the 2004 International Sympoium on GNSS/GPS. [16] Skone, S., M. El-Gizawy an S. M. Shretha (2001): Limitation In GPS Poitioning Accuracie An Receiver Tracking Performance During Solar Maximum, Proceeing of KIS, Banff, Canaa. [17] Smith, E.K. an S. Weintraub (1953): The Contant in the Equation for Atmopheric Refractive Inex at Raio Frequencie. Proceeing of I.R.E., Vol. 4, pp [18] Spilker, J. J. (1996): Global Poitioning Sytem: Theory an Application; Tropopheric Effect on GPS, Chapter 13, Volume I, The American Intitute of Aeronautic an Atronautic, Inc., Wahington, D.C. [19] Suhir M. S. (2003): Invetigation into the Etimation of Tropopheric Delay an Wet Refractivity Uing GPS Meaurement, Unpublihe Mater Thei, Geomatic Engineering Department, Univerity of Calgary, Alberta, Canaa. [20] Thayer, G.D. (1974): An Improve Equation for the Raio Refractive Inex of Air, Raio Science, Vol. 9, No. 10, pp [9] Jane, H.W., R.B. Langley an S.B. Newby (1991): Analyi of Tropopheric Delay Preiction Moel: Comparion with Ray