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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, octavian.andrei@fgi.fiChen Ruizhi, professor, Finnish Geodetic Institute, ruizhi.chen@fgi.fi

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