῍῎  //  (,*+*)
 +  +ῌ+, ῐ ῏ GPS =>?@ ,


3A B C D 3E F G H

,**3 7 2 8 ,0 9:; ,**3 7 +, 8 +0 9:<

GPS Baseline Solutions with Tropospheric Correction by Using the JMA
Numerical Weather Model for Monitoring Volcanoes
ῌῌAkimichi TAKAGIῌ,ῌῌ, Keiichi FUKUIῌ and Yoshinori SHOJIῌ
Japan Meteorological Agency (JMA) has installed and is operating GPS networks around major active
volcanoes since ,*** in order to monitor volcanic ground deformation. At present, ,, volcanoes are undercontinuous observation using about +** GPS stations. At most observation points single-frequency receivers are
adopted in consideration of power saving and mobility in rugged environments.
GPS baseline solutions include errors due to tropospheric delays which are inhomogeneous in the actual
atmosphere. Generally, computation of baseline solutions is done by using a simple atmospheric model assuming
horizontal homogeneity. But if the adopted model is not consistent with the actual atmosphere, troposphericdelays cannot be accurately estimated, resulting in poor position estimates. Especially with regard to the volcano
observation, the errors in the vertical component of baselines become large according to the large troposphereerrors. In the case of baseline solutions between receivers with large vertical di#erence, the time variation of thevertical length is superposed by seasonal noise caused by spatial and temporal variations of refractive index of theatmosphere. For accurate monitoring of volcanic activities, more precise positioning in the vertical component
is desirable, which should be realized by incorporating more accurate atmospheric model into the analysis
procedure.
For this purpose, an improved analysis process was developed, based on the JMA’s operational meso-scale
numerical weather analysis (MANAL). The MANAL is applied to daily meso-scale numerical weather prediction as initial ﬁeld. Generally in the di#erential analysis process of positioning, zenith tropospheric delay (ZTD)
is estimated by least-squares method together with the positioning. In this case, initial value of ZTD is given froma simple atmosphere model. In our approach, ZTD between both receiver sites is calculated from MANAL, andthen the conventional analysis process is done ﬁxing ZTD between sites. In calculation, analysis software package
Bernese Ver. /.* was used, while a part of the program was personally modiﬁed.
This correction strategy using MANAL was applied to the baseline solutions at Asamayama volcano, where
ground deformation has been observed associated with the eruption activity from ,**2 to ,**3. Consequently we
could approximately eliminate the vertical seasonal noise at a baseline whose vertical di#erence reaches to +./ km.
This approach is quite convenient and e#ective for GPS observation at local and steep areas such as volcanoes.
Key words : GPS baseline solution, tropospheric correction, JMA numerical weather model, Asamayama volcano +ῌ+-*/ῌ**/,

Seismology and Volcanology Research Department,
Meteorological Research Institute, +ῌ+ Nagamine,
Tsukuba, Ibaraki, -*/ῌ**/, Japan.
! : +**ῌ23/3 "#$%&'()*+ -ῌ,ῌ,,-./0123456
Present address : Earthquake and Disaster-Reduction
Research Division, Research and Development Bureau,
Ministry of Education, Culture, Sports, Science andTechnology - Japan.
 +ῌ+-*/ῌ**/,
Forecast Research Department, Meteorological Research Institute, +ῌ+ Nagamine, Tsukuba, Ibaraki,-*/ῌ**/, Japan.
Corresponding author : Akimichi Takagi
e-mail : atakagi@mext.go.jp

&'()*+2+    ,-.$/0/ 123 ,**1 456

645 789/$ :; <=<

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TU  !3VW

/ GPS ;

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, 

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9/$_~;

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o0pq N0[! rs p

qwmGNM-. IQ lVo[

6

GPS AB;C

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}K

MG ,+/-  xk

 ~YGrs pq G ¡ q/;op @ )

IQ

lVo

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++3

 ,**0 ; .  ,0

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z{ ¬ N$/0P.£ I)*+

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0[!j²³#

´|$lVo  ¬ 

B0-Jµ¶ n ©  D!"# "# conventional analysis N·G  ]_[!´|"#N¸0J} >0lVo -.¹
/J­, 0-0/
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"#

I)*+

°0-

¹ %^*+YGJ,- º(HM r - %ZQ"# |]JD!» ¼
$ "N½MB +0[!o  H

Fig. +. Distribution of the GPS receiver sites around
Asamayama volcano. Solid circles and squares
are GPS stations installed by MRI and JMA,
respectively. A temporary station M. near thesummit was newly installed for this study.

 GPS   !"
Table +.

'

()*+

#$ % &3

Description of GPS stations around Asamayama volcano.

,-./0

123456

789:;;<=9 !" GPS  +  KWS >?@A B +**0 m #
CD ; BE5 +.,1 m ; 5 1*3, m 
Table + F , #GHI GPS JKL#MN KWS 5 ,   OP
; QR5 +  12S#$: + 12=5 L +  (+/1/.., MHz)  T7 +  12=5 L+ F=#UN
F==N
,ῌ, ῑῒ῏ῐ῎ῌ῍

VWXY

Z[\N !"5 !" $Y ]!#^_9 F$Y #%a=N#`5 "`#$(GSM) = GSM bc#&de=9'#fLghNi
 
FF5

(MSM)

 

j()kl 8mjnopqrst:u#GY



=

vw
#xy$Y5z{|} *+ z{

Fig. ,. Horizontal distribution of MANAL’s grid points
around Asamayama volcano. Open diamonds show+* km-grid MANAL. Solid squares show doublefrequency GPS stations which were used for theionospheric correction. A square box over Mt.
Asamayama indicates the area of GPS observationin Fig. +.

|}5~,!-#-D .$: :0: F,!-# Y^&$ 125 !"

MSM z{#QR= ,!/n#j9# 0$Y 1^_9iQR

 z{|}=:QR#^_N QR

(MANAL) 

5 3". B4 pqs 56

 +* km 72#89$p¡  ¢£¤ !"¥¦:uf 12+1§=9$ 129¨©§t ª«¬­ ,**,

!"®ps1*1¯1¡ " . GPS °' :f : ,**3 ; . ±O'52I¬²< ,**3 # 12#³´z{|}g0no9$>µ¶8·¸S



A9$QR# Y=y(B  129¨0 C !"D +331

 / km =7

12 (GPV)  2I##+1§=9$9¨©§t¹x9 '?@? ,**3 O7 MANAL 
GPV # MANAL =º»NMANAL ¼E4I5µ85:h "Fh½

9:;<=7>?

4

Fig. -. Schematic ﬁgures showing zenith tropospheric delays (ZTD) of two GPS-receiver sites.
(a) In the case of small vertical di#erence between two sites, atmosphere equally inﬂuences
both ZTDs. (b) In the case of large vertical di#erence between two sites, the part ofatmospheric between Receiver+ and Receiver, inﬂuences only ZTD of the lower sites (ZTD+).

@AB@#CDE 0&8 6

Ver/.* (Dach et al., ,**1)

CD!J0&KLM#E

JN0&8OPQR Fortran SN- TUVUGHIOP

 "=CDWXY &CD9# Z#[U\ ]^0&_$ `$ab,=% cd0&

 



  KWS-

M. (9) +./ km  CD++ *m+12 `$& + '\efghijkln$ +,-

8 `$F 0opGqpIr -* .20 

Fig. , 2t_u MANAL v/

z+ 6 345 {

8 ,  '6

F 0 Bernese GHIsr , s

20 w v/x0  y#M 
3'

7#|}8= n  ~w

J Wz+ KWS 9!:3 68 -  t ;Aw<=n

*+ w 9"vw >81_u -,ῌ- 
MANAL

B

2"!"

0l#

C+22W

GPS '()!6_uwDUe

B

0? !@A+6 

40& , m AWA+ GPS MLDL3' 0E$.MLn#Xl#2F+ % 6 M. 

% & GPS '()*+  ,- ./w  0 wa Onset Computer Corpo-0 - 1 

ration G HOBO Weather Station UG MR(ZTD) 234 (Fig. -a)jklab 6 Receiver+ (

H20

0***

F 0 + sopGqpIw¡ I¢#

6 Receiver, (22W62 6

0 ,-LwDUeWJ , £ GPS DUe22

1  WKH¤20& ,-L "s +W£¥0 ,**0 J 3 ¦ ,+ L  ^§0 ,**2 J

 Receiver+ 2 Receiver, 4 M"F9 78X

/ ¦ +/ L6 0*, L ,*, L¨L n  # (wGH©ª«NL-w_ + L +, s O&¨ nL ¨L20

CDabPB¬I­-

`$F 0#8,220  -  56-78 (Fig.

QR 6wDUe ®;S¯YTX!
A DUe + sU

F 0 !A DUe¨#8

-a) 0M0 6F9 !8X wCD   !"#$t°±l²VN1 W+ (Fig. -b)=Xjklab ³ 0wCDML-

Y Z'()!6_u1 

ab0&_

GPS `$´pµ`$[©¶·¸¹ Bernese! t- º»U20&¼½Z#  (!"  GPS # $% &'()*+,-.

5   /0&1 &()*+2
 34 Saastamoinen (+31-)

5&+26,  789  -  :  (m) +  3, Bauers̆ı́ma(+32-) ;+<.6
ZTDSAASpTe*.**,,11 ῐ ῌ+,//῎ῒ
*.*/ eBtan,z dRp῏ΐcos z ῑ ῍ T(+)

6,  p, T, e

=>=?@A&B(hPa) &C (K) DEFG&B (hPa) +H6 z +IJK (radian)  B dR

L%M BNO% dRKNO%

M P, p T e?@A0 )QR+S Berg (+3.2) 7TU+

Fig. .. Schematic ﬁgure showing how to estimate ZTD.
ZTD+-, (di#erence between ZTD+i and ZTD, i) is
calculated from MANAL. ZTD and position atreceiver sites are estimated ﬁxing ZTD+-,.

VN6,O%3 
WX

WYZ

[:\=6 W!]+WY^Z [_R`Qab (+) 7 ,cde +fgh=i"j ZTD+i  ZTD,i mnT  ()*.oT=4# #$:pq%rs+3, 7 (/)

  MANAL GPV +tuvwxyz ]{+|z,
Fig. . [}!& Receiver+ ! Receiver, M Receiver, :de

ZTD, +*

MANAL  GPV +~)6,&'* p,, T,, e, +7(+) ./6, +

7 (-) kf\=,lZTD+iZTD,ifixZTD+, i

WYZ

$ i '(_R`Qabi+H
T$ GPS IJ89+, +-$ Vj:+ 686:[  ,ZTD,*ZTDSAASp,T,e,

(,);2 Receiver+ :} Receiver,  ZTD+,   MANAL  GPV+~)6,&'*+Vkf1M l$

(/)

",%0

+# .1
M (Hofmann-Wellenhof et al., ,**.) 686 + ",
 GPS )QR

 +-:. T  ,c + " , # 1 3  4 % , ", GPS #)QR+5 6V. MG,+,* 6

M Hopﬁeld (+303) $[E Essen and Froome (+3/+)+& +5 6, =  "  , ", GPS #89)QR89IJ89+-:+c +-
N+

ῌ
῍

ZTD+,+*0 ῌ hj 11.0.
j+

e+j ῎
-.1+2 · +*T+j,῏/\=  N

MAP _* 7 (*) 7 (l)  (t) p+je+j+,.30T+j
T+j+-:Q* + , 6 =+1h 6 + ", GPS # $IJ8(-)

;8 GPS +5

Receiver+  Receiver, ¨()*:% p+j T+j e+j

Receiver+ ;©j '(()*:$&B &C FG&BM
hj

Receiver+ ;© j-+ '( j '(()*:

º WuW©

9+-:+c .+0jM=>= Receiver + DE Re-+-:O9+%+¡¢  £¤Q¥*T+-¦§ª«Q¤§¬­<®¯iRQ °±= 2. ²³

# ´+hµV6V  
!>+¶·¤Q¸*T?¹ Tv +-¦§ª+jM

ceiver, ()*:º\T
Receiver+ :de
ZTD+*ZTD,*ZTD+,.ῌ ῏ ῒ ῑ ῎

ZTD+* +(.).ῌ+

ZTD ῍ΐῐ

.v +, , »¼]{[ ½)*+,-./01234

6

Fig. /. Temporal changes of ZTD between KWS and M., evaluated by the conventional
analysis (a), by using MANAL (b), by using measured weather data (c), and those refer totemporal change by the conventional analysis.

567"8$ , 9 ZTD  !:; Fig. /$ ,**0  ,**2 B KWS A M . 9 ZTD  + CD
NO7" Fig. /aEF?@PAQR$ST%&'($> ZTD, Fig. /b

MANAL  GPV , 

ZTD Fig. /c

ZTD   !" #$ %&'(

ST

56Au Fig. /d $7

GPV 

ZTD

AVz {
b

ZTD

[V

 MANAL 

wxy$ , cm ijtrhg, 

wxy$ +  . cm 1bhge BZH

csAVz AMANAL  GPV 

P56  %&'(<?@$>56A g5

6VbEFGHI Fig. 0d-e

JKHI7" 0LM

U9VW JKXYBZH[\]^ _$`abcde %&'(BZklVm

fghAW . cm ij(Fig. 0d) V ='($>?@5

6 nopqrcs (Fig. 0e) EFGHI tr
gvs gs (Fig. 0a-b)
.ῌ- 

|$ =}~QR$, 

 , 9  OT  (/)
$

cEF?@

 (-)

(Fig. 0f) ?@MU9VWBZH[V ,**1 BAXY?@56$,- cmklBZ\]^ (Fig. 0d) >ebcsK ='(<sc T ¡R + C ,. R9
?@567" GPS {A#c?@$<V ZTD ST+ CY, R9¤$:mcs (,)  ZTD,  (-)  ZTD+,*

DNO<='($>?@56A !7" Fig. 0a-b

klVAVz %&'($> . cm ij.ῌ, 

<<

 + C

'( (Fig. 0e) $m  {W 

£g



 Saastamoinen (+31-) ¥ῌ$¦§ cP
:;>eW ¨©ygª« ¨©t¥ῌ$¦§ cP

Fig. 0 $ KWS E©A

W MANAL ¢<:;¬V56­®¯V

M. ~%&'(>sAV°±bcs ²³´ ,**, A

$>EF?@56A µO MANAL ¢ OV¶·¸¹º»t$x"¼½¯



GPS

7

Fig. 0. Time series of baseline length (a-c) and height (d-f) of M. refer to KWS. (a) and (d)are calculated with the conventional analysis. (b) and (e) are calculated with this study
method using MANAL. (c) and (f) are calculated using measured weather data. In thecase of using MANAL, vertical seasonal noise could be approximately eliminated (e).

)

*+,-. /0123% , 4567 + 

7 5689:( ;<=$!"#$%&' GPS(

456%>?"@A 7# BC4=DE% FGHIJ K$%LM'".ῌ.

\7 + 4] GPS 56
IJ

N^_`a'"HK$%L' g , 4] GPS 56'"Zn'
wdx

74

OP-QRST=UGKG VW + X 48YZ , X 4['", 

ST=FGbcGde# $

) f

+ 4

56 h ij8k,-. lm7 , 45
6 op%>?"(qe $ rst'"7 / uvc(q GPS rs%'" y





z

(q {| lm7- cm }| lm7, cm

~K , 4]    r

\7 , 456Zn KG k,  r 30*0+.  wd 3/--. /0 HI7 + 456 n@A 7m 

#!

 

 TAN ,

wd ,+3* m %' (Fig. 1c) \[!" 30*0+. 
= TANDE

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8

Fig. 1. Comparison of seasonal noise’s elimination from vertical positioning between doublefrequency analysis (a) and single-frequency analysis (b). (c) Distribution of GPS receivers
around Mt. Ontakesan. Positioning of TAN refer to 30*0+. was calculated.

 JK

LMN# ,. >?9:OPQ6RST'+, >?9:UVKWXYZQ[\&)]^#

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p*6chi * =&'d -* 

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EU MANAL- >?uvw* 4x eX5?

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}TwpZ rs6vw  U-/ 
Fig. 2. Comparison of seasonal noise’s elimination fromvertical positioning between ,.-hours analysis (a)and +,-hours analysis (b) by using MANAL. M.
refer to KWS.

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9:# GPS c.gpqp)9`wp* W??# o ¡\& ,**2 J 2 M.

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9

Fig. 3. Time series of height of all stations refer to KWS around Asamayama volcano from ,**0
to ,**3. (a) Conventional analysis. (b) By the method of this study using MANAL. Thoseof all stations could be approximately eliminated the vertical seasonal noise, especially G and
TAK where are high.

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Fig. +*. Estimation of the inﬂation pressure source of Asamayama volcano by GPS observation from
June, ,**2 to January, ,**3. (a) Result estimated by --D component of displacement with themethod of this study using MANAL. (b) Result estimated by --D displacement with theconventional analysis. (c) Result estimated by only horizontal component of displacement withthe conventional analysis.

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  Fig. 3a  TAK 

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03*0&'(9Y$ ,c *+, ¶)¥;+®1 \]^9R·³¸)  ,  GPS!"#$% +  !"&#$'(F)Y,849:;< ¦b*- !" 4´¹&% MANAL 39>=U0º(9J@6 MANAL bcjE, GPS  bcj U,p`9®¯aD)Y,
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Bauers̆ı́ma, I. (+32-) NAVSTAR/Global Positioning System(GPS), II., Mitteilungen der Satelliten-Beobachtungsstation Zimmerwald. +*, Astronomical Institute, University of Berne.
Berg, H. (+3.2) Allgemeine Meteorologie, Dümmler’s
Verlag, Bonn.
Dach R., U. Hugentobler, P. Fridez and M. Meindl ed.
(,**1) Bernese GPS Software Version /.*. AstronomicalInstitute of University of Berne, 0+,p.
Essen, L. and K.D. Froome (+3/+) The refractive indicesand dielectric constants of air and its principal constituents at ,.*** Mc/s. Proceedings of Physical Society, 0.
(B), 20,ῌ21/.
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῏ !"#$%&'  (,**/) ()*+,-./01234567
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V*//P-*--.
Hobiger, T., Ichikawa, R., Takasu, T., Koyama, Y. andKondo, T. (,**2) Ray-traced troposphere slant delays
for precise point positioning. Earth Planets Space, 0*, e+ῌe..
UVW5XYZ9[!\]^_`abcdefgh  ijklm  ")n;  opq῏ (,**1)
rstuCvwxNyz{|} GEONET ~s/0* +JL OP +*2 P-2.
Hofmann-Wellenhof, B., Lichtenegger, H. and Collins, J.
(,**.) Global Positioning System : theory and practice,/th, rev. ed., Springer Wien New York, 33ῌ+*/.
¢£¤¥ῑ£ ¦ (,**3) §¨ῌJ>3 . ?@ABCª «¬ ,+ ­®¯°Y5  0/ῌ1+.
Hopﬁeld, H.S. (+303) Two-quadratic tropospheric refractivity proﬁle for correcting satellite data. J. Geophys. Res.,1., ..21ῌ..33.

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Q RST .2 -1ῌ/3.
(+331)  
Q RST .- +00pp.
Mogi, K. (+3/2) Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them. Bull. Earthq. Res. Inst., -0, 33ῌ+-..
Saastamoinen. J. (+31-) Contribution to the theory of
atmospheric refraction. Bulletin Géodésique, +*1, +-ῌ-..
"#$%dq\]^_ ;Z9[!N ῒ (,**3) GPS  J : GPS  Y J +JJ
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)± « (,**/) o²()³ ῍´µ¶³·]¸v () /* S1ῌS+2.
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