Comparison of GPS slant wet delays acquired by different techniques

Ac a Geodyn. Geoma e ., Vol. 9, No. 4 (168), 427–433, 2012 COMPARISON OF GPS SLANT WET DELAYS ACQUIRED BY DIFFERENT TECHNIQUES Michal KAČMAŘÍK 1) *, Jan DOUŠA 2) and Jan ZAPLETAL 3) 1) Ins i u e o Geoin o ma ics, Facul y o Mining and Geology, VŠB–Technical Uni e si y o Os a a, 17. lis opadu 15, 708 00 Os a a Po uba, Czech Republic 2) Resea ch Ins i u e o Geodesy, Topog aphy and Ca og aphy, Geode ic Obse a o y Pecný, 251 65 Ondřejo 244, Czech Republic 3) Depa men o Applied Ma hema ics, Facul y o Elec ical Enginee ing and Compu e Science, VŠB–Technical Uni e si y o Os a a, 17. lis opadu 15, 708 00 Os a a Po uba, Czech Republic *Co esponding au ho ‘s e-mail: [email p o ec ed] (Recei ed Ma ch 2012, accep ed May 2012) ABSTRACT This pape discusses he quali y o slan we delays (SWD) compu ed om GPS measu emen s. The SWDs a e gene ally use d as inpu da a o GPS omog aphy, which allows he h ee-dimensional econs uc ion o wa e apou dis ibu ion in he a mosphe e. The esea ch p esen ed is based on a compa ison o slan we delays acqui ed by di e en s a egies based o n double-di e enced Global Posi ioning Sys em (GPS) da a. The GPS-de i ed SWDs we e compa ed wi h hose di ec ly measu ed by a wa e apou adiome e (WVR). The bes esul s om he applied GPS s a egies we e achie ed by a simple mapping o GPS-de i ed zeni h o al delays in o SWD wi hou adding ho izon al g adien s o pos - i esiduals. KEYWORDS: GPS omog aphy, slan we delay, wa e apou adiome e , pos - i esidual, mul ipa h adiome e (WVR) measu emen s o e alua e he eal impac o ho izon al g adien s and pos - i esiduals wi h o wi hou mul ipa h co ec ions. While Bende e al. (2008) p esen ed a compa ison o SWD om GPS and adiome e da a based on P ecise Poin Posi ioning (Zumbe ge e al., 1997) p ocessing, ou s udy is based on he double-di e encing echnique and econs uc ed ze o-di e ence pos - i esiduals (Albe e al., 2000). The i s sec ion p o ides de ails abou he GPS p ocessing, he second sec ion p esen s he calcula ion o SWDs, he hi d sec ion compa es SWDs achie ed b y a ious GPS s a egies wi h WVR, and he inal sec ion gi es he conclusion. GPS DATA PROCESSING In his s udy, he Be nese GPS So wa e 5.0 (Dach e al., 2007) was used o he ZTD compu a ion. The basic cha ac e is ics o GPS p ocessing a e summa ized in Table 1. A ne wo k o 28 GPS e e ence s a ions was used wi h nine s a ions si ua ed in he Czech Republic and all o he s o e a la ge Eu opean e i o y. The s a ion wi h he lowes ele a ion is si ua ed 45 m abo e sea le el, and he s a ion wi h he highes ele a ion is 951 m abo e sea le el. In gene al, o GPS omog aphy wa e apou econs uc ion, i is help ul o p o ide SWDs de i ed om obse a ions o all a ailable Global N a iga ion Sa elli e Sys ems (GNSS), i.e., in addi ion o GPS NAVSTAR, almos he en i e GLONASS cons ella ion and he i s Galileo sa elli es in he nea INTRODUCTION I has been shown many imes ha he GPS sys em is use ul o he es ima ion o oposphe e pa ame e s - he app oach called GPS me eo ology (Be is e al., 1992; Duan e al., 1996). In a classic GPS me eo ology scena io, we calcula e he zeni h o al delay (ZTD) and po en ially con e i in o p ecipi able wa e apou , PWV (Be is e al., 1994). The ZTD o PWV is, howe e , no able o p o ide in o ma ion abou he e ical dis ibu ion o wa e apou o i s dense h ee-dimensional ield. This in o ma ion can be ob ained by a GPS omog aphy echnique di iding he space abo e a ne wo k o GPS ecei e s in o a sys em o oxels, econs uc ing wa e apou in each oxel. The p ima y inpu da a o he GPS omog aphy used by mos omog aphy p ojec s a e slan we delays (SWD), which a e ei he ze o- di e enced (Flo es e al., 2001; Noguchi e al., 2001; Champollion e al., 2004; G adina sky and Ja lema k, 2004; Bende e al., 2011) o double-di e enced (T olle e al., 2006). The quali y o GPS-de i ed SWD s ongly in luences he omog aphy esul s and i is he e o e impo an o assess he bes s a egy. Some omog aphy p ojec s use ho izon al g adien s o pos - i esiduals added o aw GPS slan we delays o econs uc he aniso opic pa o he a mosphe e (Flo es e al., 2001; Noguchi e al., 2001; G adina sky and Ja lema k, 2004; Bende e al., 2011), bu o he au ho s (G adina sky and Ja lema k, 2004; Nilsson e al., 2005) a e scep ical o such a p ocess. In his pape , he a ious SWDs we e compa ed wi h wa e apou M. Kačmařík e al. 428 Table 1 Basic cha ac e is ics o ZTD p ocessing in Be nese GPS SW. Epheme ides, Sa elli e clocks IGS Rapid Sampling a e 180 s Ele a ion cu -o angle 3° Mapping unc ion Niell Phase Cen e Co ec ion IGS model applied Ocean Loading Applied Obse ables Double di e ences ZTD, g adien es ima ion in e al 30 min Pole in o ma ion IGS apid Di e en ial Code Bias in o ma ion CODE 30-day solu ion condi ions and using da a om mo e seasons. The PWV alues anged be ween 2 and 28 millime es du ing he selec ed days. We e alua ed he quali y o ou achie ed ZTD solu ions h ough hei compa ison wi h ZTDs o m o he sou ces. Fi s , we compa ed ou solu ions o ZTDs wi h an hou esolu ion om he Geode ic Obse a o y Pecny analysis cen e (GOP) inal daily solu ions con ibu ing o he EUREF Pe manen N e wo k (EPN) based on double-di e ence d obse a ions p ocessed wi h Be nese GPS so wa e. Second, we compa ed hem wi h he inal IGS ZTD solu ions downloaded om CDDIS (C us al Dynamics Da a In o ma ion Sys em) based on he P ecise Poin Posi ioning echnique and p o iding a i e-minu e esolu ion. I should be no ed ha un il GPS week 1631, he IGS inal oposphe ic p oduc was p oduced by JPL using GIPSY/OASIS so wa e (Se e , 2010) and, om 1632 (inclusi e), by USNO using Be nese GPS so wa e (By am, 2011). Because all h ee sou ces use di e en ZTD ime in e als, only hose ZTDs om iden ical epochs we e compa ed. The esul s a e shown in Table 2, and hey gene ally p o e he expec ed quali y o he ag eemen be ween a ious pos - p ocessing ZTD esul s, which can be cha ac e ized wi h a s anda d de ia ion o 2- 3 mm. The la ge biases in June/July and in Oc obe wi h espec o he CDDIS ZTDs could be caused b y he change o he IGS inal ZTD p oduc p o ide (By am, 2011). Highe s anda d de ia ions (SDEVs) du ing he summe and au umn pe iods a e ela ed o he seasonal end o wa e apou de elopmen , wi h much highe alues and a iabili y du ing he wa me pa o yea . SLANT WET DELAY COMPUTATION The zeni h o al delay can be sepa a ed in o a hyd os a ic pa (Zeni h Hyd os a ic Delay, ZHD), ela ed o he a mosphe ic p essu e, and a we pa (Zeni h We Delay, ZWD) which is dependen on he wa e apou in he oposphe e. Using he Saas amoinen model (Saas amoinen, 1973) and alues o a mosphe ic p essu e and empe a u e p ecisely measu ed a GOPE, he ex ac ion o ZWD om ZTD in 30-minu e in e als was pe o med. Slan We Delay can hen be compu ed o each obse a ion be ween a ecei e and a sa elli e using u u e. Howe e , only da a om he GPS NAVSTA R we e used in his s udy because we ocus mainly on a compa ison o a ious SWD s a egies wi h espec o WVR. The WVR was capable o poin ing o GPS sa elli es only, and only some s a ions in he ne wo k obse ed he GLONASS sys em. Finally, adding GLO N ASS obse a ions could add addi ional sys ema ic e o s in o ou solu ions based, o example, om he phase cen e a ia ion model. The e e ence GNSS si e GOPE is he p incipal s a ion o his s udy because i is loca ed only a ew me e s om he Radiome ics TP/WVP- 3000 (No. 3025) wa e apou adiome e on he oo o he main building. This WVR has only GPS N AVSTAR an enna, hus i is no able o ack GLONASS sa elli es. Al hough WVR has also a ull sky scanning mode, a GPS poin ing mode was used in o de o collec as many as di ec obse a ion o GPS sa elli es o compa isons. The TP/WVP-3000 WV R a GOPE si e (ins alled in 2006) has he capabili y o acking 5 K-band (22-30 GHz) and 7 V-band (51- 59 GHz) mic owa e channels. I equi es, howe e , he clea sky wi hou any in e e ence. Since mobile ope a o s’ ansmission owe s using 24 GHz equency o in e - owe communica ions a e loca ed in he eas -wes di ec ion, a speci ic me allic shield was ins alled. Addi ionally, he WVR p o ides a ain de ec ion lag, because such measu emen s a e a ec ed, and da a om hese lagged pe iods we e elimina ed om he compa ison. The WVR beam wid hs ange is 2.5 and 5-6° o V-band and K- b and, espec i ely. An ele a ion angle o WV R measu emen s was selec ed as 10 ° (conside ing an ins alla ion on a oo pa ly a oiding a g ound adia ion) since V- b and is impo an o he es ima ion o humidi y. By analysing he mic owa e spec um emi ed by he a mosphe ic wa e molecules, he WVR p o ides SWDs sui able obse a ions o independen compa isons wi h hose de i ed om he GPS measu emen s. GNSS da a om a o al o 39 days we e p ocessed du ing 2011. These da a we e sepa a ed in o ou 7-11 day pe iods and p ocessed independen ly (Janua y 19 – 27, Feb ua y 17 – 27, June 24 – July 3, Oc obe 17 – 27). These pe iods we e selec ed o e alua e he esul s ga he ed unde di e en wea he COMPARISON OF GPS SLANT WET DELAYS ACQUIRED … 429 Table 2 Compa ison o ZTD om di e en sou ces. P esen ed – GOPE EPN P esen ed – IGS PPP IGS PPP – GOPE EPN Time Pe iod Bias (mm) SDEV (mm) Bias (mm) SDEV (mm) Bias (mm) SDEV (mm) Janua y 1.29 1.49 0.90 1.92 0.36 1.88 Feb ua y 1.11 1.32 0.27 1.73 0.82 1.90 June - July -0.55 2.98 -2.15 3.01 1.56 2.95 Oc obe 0.85 2.42 -1.10 3.22 1.84 2.74 p o ed by Elosegui and Da is (2003), and he e o e does no ep esen an ideal solu ion. The esul ing line-o -sigh (ze o-di e enced) esiduals should mainly con ain he aniso opic pa o he we delay, mul ipa h and unmodeled an enna phase cen e a ia ions. The s acking echnique desc ibed in Shoji e al. (2004) was applied o educe he mul ipa h om he esiduals. S acking maps we e cons uc ed wi h a esolu ion o 1°. Each bin o hose maps ep esen s he mean esidual alues in pa icula azi- mu h/ele a ion di ec ion, compu ed om all a ailable esiduals om a selec ed ime pe iod. The sys ema ic alues in he esiduals a e conside ed o be caused mainly by he mul ipa h e ec , bu po en ially also by he e o s in he phase cen e a ia ion model. The s acking maps we e cons uc ed om 11 days o GPS da a co esponding o he selec ed pe iods. We also ied an op imal in e al o 7 days, as p oposed by Bende e al. (2008), bu i led o wo se esul s in ou case. Figu es 1 and 2 show he mul ipa h maps cons uc ed o he Janua y and June/July pe iods. The ele a ion cu -o angle was se o 5°. I is clea ha he mul ipa h alues du ing he summe pe iod a e mainly a lowe ele a ions highe , mo e so han du ing he win e pe iod. This si ua ion is qui e su p ising, and i may ha e been caused by he inabili y o he used mapping unc ion and he whole oposphe ic modelling o p o ide ine esul s a lowe ele a ion angles when he amoun o wa e apou in he a mosphe e is la ge ; bu his is only an assump ion, and ex ensi e wo k would be necessa y o e i y he si ua ion. COMPARISON OF RESULTS FROM GPS AND RADIOMETER MEASUREMENTS All ypes o compu ed SWDs we e compa ed wi h he WVR measu emen s. S a is ical p ocessing was pe o med using all SWD pai s om he GPS and adiome e , which we e gene a ed om obse a ions a iden ical epochs o a single GPS sa elli e. App oxima ely 1,000 iden ical pai s we e c ea ed o each day. Table 3 shows he esul s o he SWD alues mapped back in o he zeni h di ec ion and hus ep esen ing he ZWDs. Compa ing he biases om he a ious ime pe iods, he e is a signi ican di e ence be ween he i s wo pe iods and he he o mula: SWD(ε,θ) = m(ε)*(ZWD + co g ε(GN*cosθ + +GE*sinθ)) + R, whe e ε, θ is he ele a ion and azimu h angle o a sa- elli e, m(ε) is a mapping unc ion gi ing he ela ion b e ween he zeni h oposphe ic we alue o he we pa h delay in a di ec ion o a pa icula sa elli e, GN and GE a e es ima ed no h and eas ho izon al g adien s, espec i ely, and R ep esen s a pos - i esidual o he ZTD model wi h espec o he obse a ion. The es ima ed pa o he ZTD and ho izon al oposphe ic g adien s a e assumed o be a we pa o he o al oposphe ic delay only. The eason is ha he cu en ly o icial Be nese GPS so wa e ( 5.0) doesn’ suppo he co ec sepa a ion o hyd os a ic and we delays as well as ho izon al oposphe ic g adien s, based e.g. on ex e nal in o ma ion om he Vienna mapping unc ion – VMF1 (Boehm e al., 2006; Boehm and Schuh, 2007) b o h de i ed applying da a om a nume ical wea he p edic ion model. Ho izon al oposphe ic g adien s and line-o - sigh pos - i esiduals could gi e addi ional in o ma ion abou he aniso opic dis ibu ion o wa e apou a ound a s a ion, hus heo e ically p o iding esul s close o he eal s a e o he a mosphe e. In his s udy, ou ypes o SWDs we e e alua ed: 1. SWD1 compu ed only om ZWD, 2. SWD2 compu ed om ZWD and ho izon al g adien s, 3. SWD3 compu ed om ZWD, ho izon al g adien s and pos - i esiduals, 4. SWD4 compu ed om ZWD, ho izon al g adien s and pos - i esiduals a e co ec ion o he mul ipa h. The Niell mapping unc ion (Niell, 1996) was used in his s udy. The ho izon al g adien s we e es ima ed du ing he GPS da a p ocessing in he same ime in e al as ZTD. Because he double-di e encing was applied o he ZTD es ima ion, he esul ing double-di e enced esiduals had o be ans o med in o ze o-di e enced esiduals, which was sukces- s ully done using he echnique desc ibed by Albe e al. (2000). I is impo an o keep in mind ha his p ocess is buil on speci ic ze o mean assump ions, which can cause signi ican sys ema ic e o s, as M. Kačmařík e al. 430 nega i e impac on he s anda d de ia ion. The able also shows ha including he g adien s in he SWD will no gene ally esul in any ad an age and would possibly make sense only in speci ic a mosphe ic si ua ions wi h an e iden and clea aniso opy in he a mosphe e (e.g., on passage). Adding he pos - i esiduals inc eased he s anda d de ia ion o SWD by app oxima ely 1.1 – 1.7 mm o alues mapped o he zeni h di ec ion. Fo use in GPS omog aphy, he posi i e impac o a sligh ly smalle bias be ween GPS and VWR wi h added esiduals would no compensa e he la ge SDEV, which can esul in signi ican p oblems du ing he omog aphic econs uc ions. The indica ion is ha he pos - i esiduals do no only con ain in o ma ion abou he aniso opic pa o he a mosphe e bu also o he sou ce e o s. The si ua ion imp o es i he mul ipa h s acking maps a e applied, bu he SDEV s ill s ays app oxima ely 0.9 – 1.4 mm la ge han in he aw GPS da a case. These esul s o such a small posi i e impac om applying mul ipa h maps a e e y simila o he esul s by Bende e al. (2008), al hough he PPP echnique was used o he de e mina ion o ZTD o he s. The quali y o he WVR measu emen s du ing 2011 a ied widely, as shown in Figu e 3, which p esen s a compa ison o he ZTD alues om GPS and WVR. A e Janua y and Feb ua y, when he esul s we e in a good ag eemen , he ollowing mon hs show mainly uns able and biased esul s. The si ua ion did no imp o e, e en a e ecalib a ion on May 19 h and Sep embe 13 h. Ne e heless, he main goal o his s udy is o compa e he a ious ypes o SWDs om GPS measu emen s, and hus, he igu e mainly helped us o iden i y he pe iods wi h ei he good o poo quali y WVR measu emen s. The exis ing biases be ween GPS and WVR do no limi ou compa isons (aimed o he s anda d de ia ion); howe e , he uns able WVR quali y, indica ed by he la ge s anda d de ia ions, nega i ely in luences he m (we canno us WVR as we hoped). This si ua ion also shows he a iable s abili y o a long- e m ope a i e un o he WVR a Geode ic Obse a o y Pecny. Acco ding o Table 3, he con ibu ion o ho izon al g adien s o he SWD is e y small unde pa icula a mosphe ic condi ions. The Table shows a p o en ially posi i e in luence on bias, bu also a small Table 3 Compa ison o slan we delays om GPS and WVR mapped o zeni h di ec ion o pa icula ime pe iods. SDEV ep esen s s anda d de ia ion and RMSE oo -mean squa e e o . Pe iod S a is ical pa ame e [mm] ZWD1 - WVR ZWD2 - WVR ZWD3 - WVR ZWD4 - WVR Numbe o pai s Mean ZWD1 alue [mm] Bias -1.18 -1.17 -1.12 -1.14 SDEV 4.43 4.47 5.61 5.31 Janua y RMSE 4.58 4.62 5.72 5.51 6 974 37.50 Bias -2.42 -2.42 -2.45 -2.48 SDEV 4.46 4.49 5.68 5.53 Feb ua y RMSE 5.08 5.10 6.18 6.06 10 593 36.40 Bias -14.59 -14.57 -14.56 -14.59 SDEV 7.66 7.75 9.46 9.09 June - July RMSE 16.48 16.5 17.36 17.19 9 534 103.18 Bias -13.47 -13.47 -13.38 -13.47 SDEV 5.19 5.21 6.63 6.20 Oc obe RMSE 14.44 14.44 14.93 14.83 9 744 69.93 Fig. 3 Compa ison o GPS and WVR ZTD measu emen s o 2011, s a ion GOPE. COMPARISON OF GPS SLANT WET DELAYS ACQUIRED … 431 Table 4 Compa ison o slan we delays om GPS and WVR o he Janua y pe iod, all bias and SDEV alues in [mm]. Ele a ion angle [°] Bias SWD1 - WVR Bias SWD2 - WVR Bias SWD3 - WVR Bias SWD4 - WVR SDEV SWD1 - WVR SDEV SWD2 - WVR SDEV SWD3 - WVR SDEV SWD4 - WVR N umbe o pai s 10 - 20 -7.63 -7.62 -7.38 -7.21 11.27 11.30 13.23 13.09 916 20 - 30 -5.71 -5.71 -5.96 -5.81 7.69 7.72 10.00 9.50 1 329 30 - 40 -1.96 -1.93 -1.64 -1.82 5.47 5.53 7.63 7.26 1 227 40 - 60 -0.70 -0.66 -0.62 -0.75 5.99 6.05 7.95 7.59 1 822 60 - 90 -0.50 -0.50 -0.41 -0.39 6.32 6.38 7.75 7.49 1 680 Table 5 Compa ison o slan we delays om GPS and WVR o he Feb ua y pe iod, all bias and SDEV alues in [mm]. Ele a ion angle [°] Bias SWD1 - WVR Bias SWD2 - WVR Bias SWD3 - WVR Bias SWD4 - WVR SDEV SWD1 - WVR SDEV SWD2 - WVR SDEV SWD3 - WVR SDEV SWD4 - WVR N umbe o pai s 10 - 20 -7.97 -7.97 -7.80 -7.74 9.64 9.64 11.98 11.96 1 643 20 - 30 -6.16 -6.14 -6.49 -6.38 7.61 7.62 9.91 9.54 1 953 30 - 40 -4.10 -4.08 -3.82 -4.26 6.74 6.76 8.76 8.53 1 837 40 - 60 -2.93 -2.92 -3.02 -3.06 6.71 6.75 8.53 8.31 2 643 60 - 90 -2.91 -2.91 -3.02 -2.94 6.15 6.19 7.72 7.54 2 517 Table 6 Compa ison o slan we delays om GPS and WVR o he June-July pe iod, all bias and SDEV alues in [mm]. Ele a ion angle [°] Bias SWD1 - WVR Bias SWD2 - WVR Bias SWD3 - WVR Bias SWD4 - WVR SDEV SWD1 - WVR SDEV SWD2 - WVR SDEV SWD3 - WVR SDEV SWD4 - WVR N umbe o pai s 10 - 20 -49.68 -49.63 -49.19 -49.36 26.89 27.06 32.09 31.13 970 20 - 30 -34.90 -34.91 -34.61 -34.69 17.98 18.09 22.17 21.19 1 912 30 - 40 -24.43 -24.39 -24.24 -24.67 13.89 14.05 17.15 16.55 1 700 40 - 60 -18.47 -18.46 -18.62 -18.43 10.28 10.39 12.59 12.05 2 547 60 - 90 -16.55 -16.61 -16.71 -16.70 8.07 8.20 10.19 9.73 2 405 Table 7 Compa ison o slan we delays om GPS and WVR o he Oc obe pe iod, all bias and SDEV alues in [mm]. Ele a ion angle [°] Bias SWD1 - WVR Bias SWD2 - WVR Bias SWD3 - WVR Bias SWD4 - WVR SDEV SWD1 - WVR SDEV SWD2 - WVR SDEV SWD3 - WVR SDEV SWD4 - WVR N umbe o pai s 10 - 20 -38.99 -39.01 -38.33 -38.70 16.24 16.30 19.21 18.26 934 20 - 30 -28.45 -28.44 -28.27 -28.55 10.56 10.60 13.97 12.59 1 968 30 - 40 -20.99 -21.00 -20.28 -21.10 7.62 7.66 10.33 9.58 1 742 40 - 60 -17.31 -17.31 -17.40 -17.26 5.82 5.85 8.10 7.39 2 653 60 - 90 -17.95 -17.95 -17.97 -17.92 5.89 5.91 7.67 7.29 2 447 s anda d de ia ions a e signi ican ly educed wi h dec easing ele a ion angle, which co esponds o he leng h o he GPS signal p opaga ion h ough he low a mosphe e. Un o una ely, he lowes pa o he a mosphe e is c ucial o he GPS omog aphy econs uc ion because i c osses mo e oxels and con ains mo e in o ma ion abou he wa e apou con en . I can be seen om he ables ha he bias g adually dec eases un il 40° o ele a ion and hen emains highly s able o inc eases sligh ly again. The same si ua ion occu s o he SDEV, bu wi h a change a an ele a ion o 30°. In June-July and Oc obe , he abo e-men ioned p oblems wi h WV R and non-di e enced pos - i esiduals es ima ed di ec ly in hei s udy. The absolu e SDEV alues and biases om he i s wo pe iods a e also compa able wi h he esul s om Bende e al. (2008). This esul deno es a com- pa able quali y o he double-di e ence- b ased p ocessing wi h esiduals con e ed o undi e enced ones using addi ional ze o-mean condi ions wi h he PPP esul s p o iding di ec ly undi e enced esiduals. Tables 4 o 7 show he dependence o he SWD compa isons on he ele a ion. I mus be kep in mind ha hese SWDs a e no mapped back o he zeni h, as in he compa ison in Table 3. Bo h biases and M. Kačmařík e al. 432 By am, S.: 2011, IGS Final T oposphe e p oduc ansi ion o USNO [IGSMAIL-6443]. 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CONCLUSION The esul s p esen ed he e indica e a high co ela ion be ween he slan we delays de i ed o m GPS using double-di e encing and wa e apou adiome e measu emen s. Adding he pos - i esiduals o he GPS SWD had only a e y small p osi i e impac on bias, while i nega i ely in luenced he s anda d de ia ion. The si ua ion sligh ly imp o ed a e using he s acking maps o emo ing he mul ipa h e ec om he esiduals. The esul s show ha he pos - i esiduals, e en a e mul ipa h elimina ion, do no ep esen only he aniso opic pa o he wa e apou dis ibu ion bu ep esen u he insu iciencies in he model. Based on ou esul s, we would he e o e no ecommend adding he pos - i esiduals o SWD, a leas wi h s anda d models cu en ly used in Be nese GPS so wa e. Gene ally, we ob ained he bes ag eemen be ween he GPS SWDs and WVR da a-de i ed SWDs when he o me we e compu ed only om ZWD wi hou any u he in es iga ion o ho izon al g adien s o esiduals. ACKNOWLEDGEMENT This s udy was inanced om he p ojec o he S uden s´ G an Compe i ion n. SP/2011104 a VŠB- Technical Uni e si y o Os a a and pa ly suppo ed b y he Czech Science Founda ion (No. P209/12/2207). Da a acquisi ion o he Wa e Vapou Radiome e and GOPE GNSS s a ion a e suppo ed by he p ojec o la ge esea ch in as uc u e CzechGeo/EPOS (P ojec N o LM2010008) and he Minis y o Educa ion, You h and Spo s (P ojec No LC506). REFERENCES Albe , C., Wa e, R.H., Rocken, C. and B aun, J.J.: 2000, In e ing GPS double di e ences o ob ain single pa h p hase delays. Geophysical Resea ch Le e s, 27, 2661–2664. Bende , M., Dick, G., Ge, M., Deng, Z., Wicke , J., Kahle, H.-G., Raabe, A. and Te zla , G.: 2011, De elopmen o a GNSS wa e apou omog aphy sys em using algeb aic econs uc ion echniques, Ad ances in Space Resea ch, 47, Issue 10, 1704–1720. 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Kačmařík e al.: COMPARISON OF GPS SLANT WET DELAYS ACQUIRED … Fig. 5 Examples o ime se ies o WLBR (ASG-EUPOS s a ion) and o he new KSIA GPS s a ions o m p elimina y PPP daily solu ions. Red e ical lines indica e he momen da e o he e e ence ame changing (IGS05 > IGS08). In hese g aphs jumps ha e been pa ially emo ed o be e de e mine linea ends in each componen . Fig. 1 Mul ipa h s acking map o s a ion GOPE, compu ed om GPS days 18 – 28, yea 2011. Fig. 2 Mul ipa h s acking map o s a ion GOPE, compu ed om GPS days 175 – 184, yea 2011.