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
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oguchi, W., Yoshiha a, T., Tsuda, T. and Hi aha a, K.:
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measu emen quali y a e clea ly isible om he
esul s biased up o 49 mm a he lowes ele a ions.
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).
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M. 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.