andrei.doc
TRANSCRIPT
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Assessment of tropospheric zenith path delay time series at the Romanian
EUREF permanent GPS stations
Andrei Constantin-Octavian, research scientist, Finnish Geodetic Institute, [email protected] Ruizhi, professor, Finnish Geodetic Institute, [email protected]
This paper investigates the tropospheric zenith path dela !"#$% ti&e series derived fro& the
Glo'al $ata Assi&ilation (ste& !G$A(% nu&erical )eather &odel !*+% for five RF
per&anent G*(( stations operated ' the Ro&anian *ational Agenc for Cadastre and /and
Registration. The G$A( *+ e0tracted &eteorological data )ere used to co&pute the "#$s. The
total "#$ agrees the RF "#$ product )ith R( of 1.2 c& and is su'3ect to so&e &ean 'iases
and discontinuities of up to 4.5 c&. The precision of G$A( *+ "#$ should 'e sufficient for all
G*(( navigation solutions.
Keywords: EUREF • GNSS • GDAS • tropospheric zenith delay • numerical weather model
1. ntrod!ction
The lower part of the atmosphere consists of three main layers: the troposphere from sea le!el to a
hei"ht of a#out $% &m'( the tropopause a thin #oundary layer #etween $% and $) &m' and the
stratosphere from $) to *+ &m', As far as GNSS applications are concerned( the troposphere is a
neutral part of the atmosphere( which causes delay of the transmitted GNSS si"nals tra!ellin"
throu"h it, This effect is normally referred to as the tropospheric delay, -ecause of troposphericdelay the distance determined from the satellite si"nal #etween the user.s recei!er and satellite is
lon"er than the "eometrical distance resulted in case the si"nal would tra!el throu"h !acuum,
/athematically( the tropospheric delay alon" the si"nal path 01D' is determined #y inte"ration of
the refracti!ity alon" the si"nal path
$' ∫ −= *ds "#$ )$+
The refracti!ity can #e determined usin" the followin" e2uation "i!en #y Thayer $345':
%'$
%6%
$
$
−−
++
= )d
d "
T
e6
T
e6 "
T
# 6 *
where 6%$ (( 6 6 6 are the refraction coefficients( d # is the partial pressure of the dry air in h1a
m#ar'( T is the temperature in de"rees of 7el!in( and e is the partial pressure of water !apor in
h1a m#ar', d " and ) " are the compressi#ility factors for dry air and water !apor respecti!ely(
and they account for the de!iation of the "asses from an ideal "as, The first term in the a#o!e
formula is called dry refracti!ity( since it depends only on the dry constituents( while the term in the
last #rac&et is called wet refracti!ity,
Se!eral sets of !alues for the empirical 6 8coefficients ha!e #een determined and there has #een
some dispute o!er which !alues are the #est /endes( $333', -e!is et al, $335' pro!ided a new set
of the 6 8!alues #ased on a re8analysis of older e9perimentally determined coefficients Ta#le $',
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Da!is et al, $3*' introduced another e9pression for the refracti!ity:
6'$
%6%$
−
+′+=
)d "
T
e6
T
e6 R6 * ρ
where the new coefficient is "i!en as d ) , , 6 6 6 $%% −=′ , ) , and d , are the molar mass of water !apor and dry air( respecti!ely, The first term in E2,6'( al#eit it is hdrostatic refractivit(
includes the effect of water !apor !ia the total density ρ , The last term is still #ased on the water
!apor and is thus still called )et refractivit( althou"h the term non8hydrostatic refracti!ity is also
found in the literature,
"a#le 1 Refracti!ity coefficients from -e!is et al, $335'
[ ]h#a 7
6
;
$
[ ]h#a 7
6
;
%
[ ]h#a 7 6
;%6
[ ]h#a 7
6
;
%′
44,)+ ± +,+* 4+,5+ ± %,% 6463++ ± $%+++ %%,$ ± %,%
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)'
c -
' -
a -
c
'
a
- ,
+++
++
+
=
sinsinsin
$$
$
'
/ore recently( some enhanced mappin" functions ha!e #een introduced, /appin" functions li&e the
@so#aric /appin" Function @/F Niell( %+++'( Bienna /appin" Functions B/F$ -oehm( %++5' or
Glo#al /appin" Function G/F -oehm et al,( %++)' are #ased on data from numerical weather
model N>/' such as the EF European /8#ased mappin" functions use output of the EF model( they
differ in the easiness of parameter computation and the amount of data used from N>/,
The main purpose of this study is to compare the zenith path delays deri!ed from numerical weather
model N>/ 01Ds' o#tained at the Romanian EUREF permanent GNSS stations to the EUREF
01D product released with a latency of appro9imately 5 wee&s, The files can #e downloaded from
the EUREF product directory at -7G$ -undesamt fCr 7arto"raphie und Geodsie' since G1S
wee& $$$+ April $*th( %++$', For the comparison a period of two years was used( i,e,( Fe#ruary
%++) Fe#ruary %++,
"a#le $ Appro9imate positions latitude( lon"itude and ellipsoidal hei"ht' of the Romanian EUREF
GNSS stations used for comparisons( durin" Fe#ruary %++) Fe#ruary %++
Station Name φ λ h m'
-A
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-etween %++$8%++6( fi!e new permanent G1S;GNSS stations were installed in municipalities of
Sucea!a(
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Fi'!re $ Data representation in
the Glo#al Data Assimilation
System GDAS' numerical
weather model N>/'
Schueler %++$' analyzed different approaches to e9tract meteorolo"ical data from a N>/, @n
#rief( three main steps for data e9traction mi"ht #e carried out: $' !ertical interpolation that is
performed with respect to the o#ser!in" site hei"ht a#o!e mean sea le!el for all four nearest
nei"h#ourin" horizontal "rid points of a weather field, 1ressure data are interpolated #y an
e9ponential function( while temperature and relati!e humidity are o#tained #y linear interpolationH
%' horizontal interpolation that is performed with all four nei"h#ourin" points usin" normalized
wei"hts defined #y the reciprocal spherical distance #etween the o#ser!in" site and "rid pointH and
6' temporal interpolation or interpolation in the time domain that is performed usin" either linear
functions when the forecast !alues are outputted' or cu#ic splines in case of four epochs per day',
As mentioned earlier( many tropospheric models need meteorolo"ical information at the hei"ht of the o#ser!in" site as input( with pressure #ein" of an essential parameter for determination of
hydrostatic zenith delay as showed in Da!is et al, $3*'
4'h
# "8$
)$+%:,+'%cos++%)),+$++%%44,+ −⋅−⋅−
⋅=ϕ
while temperature and relati!e humidity are usually re2uired in modellin" the wet zenith delay as
"i!en in Saastamoinen $346',
' eT
"+$ ⋅
+⋅= +*,+$%**++%%44,+
where # denotes the total pressure in h1a( T denotes the temperature in °7( e denotes the water
!apor partial pressure in h1a( and '( hϕ representin" the latitude and the hei"ht in meter at the
o#ser!in" site,
-ecause relati!e humidity is temperature dependent and water !apor partial pressure e ' is the
2uantity re2uired in the computation of the wet component of the delay( the followin" e2uation is
used to con!ert relati!e humidity R8 ' to water !apor partial pressure eic&( $33*':
3'
−−⋅⋅⋅=5*,6:
5):5$*,$4e9p
$++$+:,)
T
T R8 e
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*. )ata analysis and disc!ssions
The computation of the tropospheric delay was carried out usin" an application de!eloped on the
#asis of the o#ect8oriented approach in /8deri!ed mappin" function', @n case of zenith tropospheric
delay calculation( the slant an"le e2uals 3+° and all mappin" functions at zenith e2uals to unity,
a. +eteorolo'ical data comparison
-ecause three stations -A/ and in situ meteorolo"ical
parameters, As one can see( despite the fact that the N>/8e9tracted meteorolo"ical data may ha!e
some offsets with respect to the in situ o#ser!ations( they are relia#le and can #e used to compute
tropospheric delays in a#sence of in situ o#ser!ation,
"a#le ( Statistical results of the assessment of N>/8e9tracted meteorolo"ical parameters
Station
name
/eteo
2uantity
Statistics
/ean /in /a9 Std R/S Samples
-A
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Fi'!re ( =isto"rams of the GDAS N>/8e9tracted and in situ meteorolo"ical parameters
pressure( temperature and relati!e humidity' for three of test stations: -A/ 01Ds,
5 S@NE is the acronym for Software @Ndependent Echan"e* wwwwd denotes the G1S wee& and day of the wee&
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Fi'!re * The GDAS N>/
01D differences with
respect to EUREF 01D
solutions for the Romanian
EUREF GNSS test stations(
only one +8h UT' epoch is
used for each day durin" theinter!al Fe#ruary %++) 8
Fe#ruary %++
Fi"ure 5 shows the differences #etween GDAS N>/ 01D solutions and the EUREF 01Ds for the
two8year considered time inter!al Fe#ruary %++) Fe#ruary %++', Some discontinuities can #e
seen for two stations -U/ tends to underpredict the 01Ds( at least for the case of Romanian territory,
Ta#le 5 left' shows the mean #iases and standard de!iations for the hourly differences of the
GDAS N>/ 01D and EUREF 01D solutions for all * Romanian EUREF stations, The lar"est
standard de!iation of the total 01D differences is o#ser!ed for stations -U
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Fi'!re /onthly mean #iases
and standard de!iations of the
differences GDAS N>/
EUREF' for the * Romanian
EUREF GNSS stations( durin"
Fe#ruary %++) Fe#ruary
%++, =ourly differences wereconsidered in the monthly
statistics,
. /oncl!sions
The GDAS N>/ 01Ds estimated at the Romanian EUREF permanent GNSS stations demonstrate
a "ood a"reement with the EUREF solutions, There were( howe!er( some nota#le e9ceptions of
lar"e differences and discontinuities( up to $+ cm( most of which were attri#uta#le to the N>/
e9tracted meteorolo"ical parameters, >hile the N>/ e9tracted pressure data were well compared
less then +,* h1a in standard de!iation' with the in situ meteorolo"ical measurements( thetemperature and especially relati!e humidity showed a poor a"reement with sensors data, >hile
temperature a"reement was less then 6°< in standard de!iation( the relati!e humidity a"reement
was around $*?, 1oor estimation of the relati!e humidity also means poor estimation of the partial
pressure of water !apor( which com#ined with temperature lead to less accurate estimation of the
wet component of the tropospheric delay,
Since a medium resolution model was used in this in!esti"ation and the co!ered area was limited to
5° × )° de"rees( it is e9pected that a hi"her resolution model will impro!e these results, E!en so( the
fact that the GDAS N>/ tropospheric delays a"ree the EUREF solutions at a le!el of %86 cm for
any location almost in real8time( ma&es them useful not only for static( #ut also for &inematic and
su#8meter positionin",
Ac&nowled'ements: The in situ data and EUREF 01D com#ined solution -ruynin9
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%, -oehm O,( Schuh =,( %++5( :ienna &apping functions in :/;I analses, Geophysical Research
etters 6$:+$)+6, doi:$+,$+%3;%++6G+$35,
6, -oehm O,( >erl -,( and Schuh =,( %++)( Troposphere &apping functions for G#( and ver long
'aseline interfero&etr fro& uropean Centre for ediu&-Range +eather Forecasts
operational analsis data, Oournal of Geophysical Research $$$:-+%5+),
5, -ruynin9