῍῎  //  (,*+*)
 +  .+ῌ/+ ῐ ῏
 \\NOPQ,FRSTFUVWXFYZ [,**3 H 2 I -+ JKL ,*+* H + I +/ JKMAtmospheric Correction in EDM by Using the JMA Numerical Weather Model :Application to Measurement at Asamayama Volcano
ῌῌAkimichi TAKAGIῌ,ῌῌ, Keiichi FUKUIῌ, Toshiki SHIMBORIῌ and Sei IIJIMAῌ
Electro-optical distance measurement (EDM) and Global positioning System (GPS) observation are applied
to monitor precise time variation of the ground deformation at active volcanoes. But observations using
electromagnetic waves such as these are accompanied by errors associated with inhomogeneity of refractive index
along the propagation path in atmosphere. In particular, the inhomogeneity in troposphere degrades theaccuracy of positioning. An improved atmospheric correction method in EDM was developed, based on theJapan Meteorological Agency (JMA) operational mesoscale analysis (MANAL) for numerical weather prediction. In this method, the precise velocity and ray path of propagated lights are estimated from the adequate
vertical proﬁle of refractive index by MANAL. Consequently distance along the bowing ray path measured by
EDM is corrected to be precise slope distance. Applying this procedure to EDM data at Asamayama volcano, theseasonal ﬂuctuation caused by inhomogeneity of refractive index in atmosphere was removed entirely.
At Asamayama volcano, very small eruptions occurred in August ,**2 since the latest ,**. eruption, andthen a small eruption occurred in February ,**3. Based on the EDM observation by Meteorological ResearchInstitute and Karuizawa Weather Station, we detected that the slope distance had been shortened since August,**2. Slope distances from the observation site to reﬂectors were corrected by using MANAL in this correction
method. Though slope distances have increased in length at a rate of +ῌ1 mm per year since the ,**. eruptions,
ground deformation turned over to inﬂation in August ,**2 and slope distances shortened to /ῌ,2 mm per ﬁvemonths by January ,**3.
In order to account for those observation data, we assumed a pressure source beneath the summit crater,
whose depth and volume increase were estimated to be at a height of ,-2* m above sea level (,** m under thesummit) and +/,-** m-, respectively.
By developing this atmospheric correction method in EDM with the use of the JMA’s numerical weathermodel, it became possible to precisely detect ground displacements and thus to reliably estimate their sources.
Therefore, this method is very e#ective to monitor activity of volcanoes.
Key words : Atmospheric Correction, EDM, JMA numerical weather model, Asamayama volcano, MANAL -*/ῌ**/,  +ῌ+!"#$%&'("#)
Seismology and Volcanology Research Department,
Meteorological Research Institute, +ῌ+ Nagamine,
Tsukuba, Ibaraki, -*/ῌ**/, Japan.
 3$4 : +**ῌ23/3 56789:;<=> -ῌ,ῌ,?)@AB"#CDE%&F-."#G
Present address : Earthquake and Disaster-Reduction
Research Division, Research and Development Bureau,
Ministry of Education, Culture, Sports, Science andTechnology - Japan.
 -23ῌ*+++  +1*0ῌ2!*+,('(-./012$
Asamayama Resident O$ce for Volcanic Disaster Mitigation, JMA, +1*0ῌ2, Kitakura, Nagakura, Karuizawa,
Nagano, -23ῌ*+++, Japan.
Corresponding author : Akimichi Takagi
e-mail : atakagi@mext.go.jp

!

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Table +.

History of two ANALs’ horizontal resolution used to this atmospheric correction.

JKLMNOP)QRSTOU #V WXY#43

Fig. +. Distribution of horizontal grid points of every
ANALs around Asamayama volcano. Squares,
circles and diamonds denote ,* km-RANAL, +*km-MANAL and / km-MANAL, respectively.

Fig. ,. Distribution of reﬂector sites (M+-M/) andobservation site (a), and topographical proﬁle (b).

'()* +,-./01 (2 !3$ZC

 +* km -, / km .$[\]^_` =ab)cd  efg.3%

[-, ^ [.d"  h&h$ijkl ! MN mn"o,**3% pcn)C kqrst3$ u)$ vwxy3% vwxyz{TOJKLTOU)|"ABCDN

45 63789:);<"=.8>.,.!%$ ,* km EF ANAL ,* km-ANAL }?  / kmpTO45 $ ~)"EFG
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n% ?3% @$ ABCDV W)83ZEFGANAL$ EFGHI

GPV = GPV

Table + )?% "$  ANAL
Fig. + )?%U)!" GPV CD $ ,**0  - }?%u$ C

g.3MN)*?3/ km-ANAL  ** UTC  

ANAL )c3 GPV

JKLTOU)Y$ 

$  / km-ANAL  ,* km-ANAL  ** UTCU?3% Y?3KLHI ,**-  / -, ,**3  1 3$ pw)MNOP¡m¢ $  ANAL  GPV C = d !3% T6.¦

0

 GPV

-



3% "$ TOU ANAL
$ KL

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km EF

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¯W®­ - °b (M+, M,, M-) ) - ±F#²G

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· ,* km .$  RANAL _¸Z

M-  ) M .

C ).d"% "$ ,**3  .  1 -,$ MANALµ"% # ²Gi

$ ,**/  3 )«¬­®¹) M/´

GPS º % BK  »¼½

./ 0123

44

Table ,.

Table -.

5

Speciﬁcations of electro-optical distance meters.

Location of reﬂector sites and observation site for EDM at Asamayama volcano.

6789: M .  ,**0  / ;<=>? @&GPS HI!JH 

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(KWS)

 

I!wv  xW%& 11./ km .

 

 +./ km  ,**-  /  !"#$  ,**3 u EF& Er&Gyz

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meter 0*** @  %  ,**/  -   ,**1  ,ih

%& , ' ()*+,!- Leica Geo-

ZK gh&AB !D 

systems  TPS+,** (I!

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u £7¤¥¦§ u¨uqD !£7¤ Pn©(!£7¤  K
!-&ª' Table , «K %  Fig. , I!
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 UVW

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 +.* D +*gh . * km h± +/  h²

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

UVW xW&M´TLoGv E

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m,lTT

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

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W5  X Ciddor, +330 ; Hill et al., +32*  Y ; <"E 6 '/5 Barrell

andSears (+3-3) Z[ \] +33.  K,^_`a(n++*0nd ·

pῌp*
eῌp*
 nw ·
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9Q l $OPQR= nd bc nwndng++*0
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nw.1..,.*./+02l,

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

(.)

  







Td ()

 Tetens (+3-*) 

1./Td,-1.-Td(0), 5/de/5

Fig. -. Velocity and ray path e#ect on slope distancecaused by inhomogeneity of refractive index along
the propagation path in atmosphere. Ray path isbended propagating through the inhomogeneous
atmosphere (a). Seasonal changes’ ratios of velocity and path e#ect calculated by actual JMA’s
GPV are +/ ppm and *./ ppm, respectively (b).

6f  ANAL  GPV

8Ug  (0) de(,hij&.

k'$lmn,%&. opAq$BC` rs

5/t0. u$lvw

x8U,j&.( (Fig. -a) y<,z{(FGST, (-)  (/) ,|,}~(2, .(H   9 k3 +./ km G$.ῌ, 

?@A ++ lP Q Fig. -a^$ ; <"#$ 1Q;  N%&'8UST, ,**/  +*  ,*  *0UTC

 KWS

/5 8"|M2uE 6 MANAL  GPV,9.:5"$Q <"#)*.  $ ,*** !$./5

+ >2%&'/5 (Table ,)
6  ANAL  GPV

 (-)(/) , M+ 

j&.(L (:b  9  G,./&9.
/Z[.( <r8U,$c{/:!

5/01.(8UgE ST 29 <:K >t0.( ¡ US¢$c{/"#$%&'()*+, (-)(/) $-./01£¤"¥ ¦E - ppm L{( §.(ST 3, 8"|M2$¨¤(2

©LX ª$«¬"­$c{/  + m "­.

8"629:M t<.(8"|M(9./&Z[$c®32 ,3.45("678"9:#°`$L9,± e(.ῌ- 

.ῌ.  *.**- mm ¯hLM 

ST %²:E &'$c{/; 8U¯gf, 5 6"$³Q8´©STQ(e 8U$³Q6L

698U6µ¡, GPV , 5/t0./

u8U(¶E *+,Z[·$Wl

" )"¸9./)¹.( (Fig. -b)9ª&. "¸(Q8´©"¸»¼  ½$(KWS) ºg ANAL ?@A  > 

46



!"#$%&'()*+,-. /%01 n,2& (-) 3&45'("5 * (+) 345
67 v ,!"*+ 89 :;5<=>,<9?@ A 

BCDEF&/%&= "<BG)*+ H9 
IFJKL+/ ppm M N*<=>&O( PQ 01.R +S)  ! ,2/ ppm .RT8(GN5 U"VW&H) # X$YZIFJ
KL*./ ppm M5 7YZ&4L +ῌ+* [M ;\%]%P&T^'&'()
/    /ῌ+ 

 _( <=`ab&)*B +_(&4Fig. .. Slope distance from KWS to M+ measured with
auto EDM system from March, ,**/ to February,,**1. Distance corrected with MANAL has smaller
seasonal noise than that by the conventional correction. Parenthetic ﬁgures show standard deviation(mm).

 EF",c de <=`ab f<) TPS +,** &4V<=`ab

*)

 

g%h ,**/ . - i.R ,**1 . , i;! , .h&

j! +* cm !"k ( 9l), + mh/nopqor<EFM
 *%h xhyz34{.

*h |}1+0t12~56M+

9+  7,&d-G)+9D u=

M+ s0t1+u=^ *Rvw'2M

/ῌ, ANAL& +_(  mh%89), , : P&T * &)M B.B g%=\+.\,z3M5 6<=&B)*B h%8 ANAL  GPV &4 ,**-,**3 .;%5<B<=`ab&G)g ,(G)) =t&>e=EF) ?9 Fig. / & KWS .R M, 5@&>e\% M)JK< B<=`ab&  9 ,* km-ANAL + / km-ANAL)&4.\%,9 *  ,)

&4 EF 89 ? A A +&d-G).e.+BG *%h

B_(M|}1 <g`ab7¡u=m¢CP&T *)*+&9 EF^89

P&T,'()£ g ,)&d¤G)*+ H9

*B

B_(+?j ,* km-ANAL, / km-ANAL &4EF#,.\^\%^'()*+,-.

Fig. . & |}1 KWS .R0t1 M + <=& xhy ,**. . 3 i+, i&: ,M

*)G+_( 7 B

*%h B_(^<¥,  ¦,DE9*u=m¢C 89 ? A A +

+ H9 BG)*+,-., B_(MANAL (/ km-ANAL)B_(M|}1 <g`ab*B,!) A",c§FM B

 EF^89 ¨G©ªH? « _(&.B+

4 G¬­( u=*%hI®&9P&-. ;  ,**2 . 2 iJ: .R¯;_(! , cm ,M&T (mm) M B_(&4 g

;5 ,**3 . , i&':.\,°±BGN5 ~2A 

%h&^u=,M

+K;,M **+B_(,g&L^²M9*+9R6³8M ; 

JK&BG´ BG)*+ 89 #,* km-ANAL



^

*+,
RB


, *

 B.BB_(vw,

+_(&4g.\µAG'() , ",c§FM5 B_(+?jG^P&T 1.. mm \%g&¶·9L£¸¹BG))*+,-. # / km-ANAL

+º¤G4" .\%L * &) ;u=U" +_( &4 GB_(+?

  + cm  
N *%h ,* km-ANAL &?»`¼½

$%& '()* +,-./) 012 3

47

Fig. /. Slope distance corrected with ,* km-ANAL and / km-ANAL from KWS toM, measured with manual EDM from ,**- to ,**3. Triangles and arrows
show the eruptions at Asamayama.

456 ,**1+* 789:+ RANAL  ,* km@4 ,**1ABC(  D++ 7+EL4MNL GANAL OPABC(

^ _L89

4 0* km UV ,* km R;<=>?

45 

E FG+ H IJ K+)* 4'QR+INLD.K $%&"STO+WX YZ9[? ER:\]956 

RANAL +`abc6 E FG+/U 019B%NLde %&"S+f)+D '()* +g4hi ER+F^ +jk4lD mn45  ,**1

opqrs

xyx

 {+|D}~4VL 9: / km-ANAL,* km-ANAL

D4 _L4

:zV

a4/ag+F mnTO+:

? ER:9a x= D.95  / kmANAL   +* km,

ANAL 

)*"S9tGuvRw4F^|}~+9a

ER4cU6 !"#R . "SW# 

0 



,**, +F  r64 ,**3yUV ANAL +F/):uv

/ km. 7y:

!"#RW#+ t        ,**3 ,**3
ANAL +F

"D



&!4cUFG+§¨  01: ,**3

y

/ km-



^

/ 7©89+  ER4VU+ 6 U1¡S¢£¤ K H{+¢¥ S¦9E vD +: GPV 4ª«¬9aQ.­# $ ^"®^ E &! 

U ANAL : "S¯°±441+f²? «UU

g+F ´¦µ¶!
+: » .R +U _LR)*
95

U%·?

y de+c6"SRwVU+IJNLv95 ER 

9a

45 
89+'

9 ¢¥ S¦ K+:_Ly³

ANAL ,+¸¹NL  ( yº FCST R &? ¼½  D

2 3 4567488  9: ; <= >? "@A:B<CD: E+ FG HIJKLM(NOP  LM (FCST) QBR+S
T FCST (<,(2 UVHKWXYZ# 4[\ ,**0 ]^ _?< `  FCST
"a+, bc &'<Z"# a(! RANAL <">defN1g.  (FCST) h!+ . ij#$%ekl&mnKop"qrs/%t ANAL
(1aST"&' ST"#$u(s/  ! ** UTC
Fig. 0. Standard deviation of corrected distance.
Open squares show S.D. of distance corrected by
ANAL. Open diamonds and solid diamonds showthat by FCST of **UTC and +,UTC initial time,
respectively.

FCST "#$% +, UTC

FCST "#$% +,,. UTC

abc

&

'< ANAL &)v./w\"#x"  !* FCST yz{| +
+%}0/t( /~$%a+bc &'}:+% +v+FCST ~!+abc(,Y' <." L (ANAL) ~$
T FCST ~$

aS

aST QC$*(}v$ /< GPV%+$%

-UVHK(./|#

 {"<KWS-M+ M /Mcekl" 0,< ,**0 1

ANAL ~!+:}% FCST "3$(a2". ,**0 1 +, "# :N /"&' &#+%

' =ss `a 3s Y

:N ,**3 1 2 {X , $  2 2}:$ /Fig. 0 ( ,* km-ANAL (RANAL) a(1 !4

km-ANAL ()%&' BRY5#bc&'Y  6 7" **UTC "&' / mm +%
 ,**0 1 +, ,** UTC< ,**0 1 . abc

&' / mm "#$Y !Q+% ** UTC (,. UTC) - &'=sDv :N  ,,* km-ANAL < 01 

1ῌ+ 

8

,(

, /Mcekl( / km-ANAL ~!+%
a+F%
,

M

bc

,#m Fig. 1 (Yh/2$-,**2 1 3 v0 =qrs/%N a(< , (9+%~!+: ,**3 1 ,  , ; <Y

%

"

,**3 1 + / v( F% bc<=>(? + )

i( ANAL "<:} FCST ~!+abc

@ABCY¡¢+ . D< 0,2 mm "&'()%* @(£yz} ¤¥(# M/

RANAL 

Y">def(1 FCST < + ; , ¦ ** UTC #mD  ? D<  , bc#mE+, UTC  !+% ,.

,-"

, 

"£§+%¨t#m©v0_?+ ,**3 1 , ! 

GPV "a+bc

wª< M/ "<«g(FG+¡¢* ./&'7(H"+ IH< ** UTCw¬<JK+% :N M- <F­ L®(1



FCST

+

!Y FCST "a_s/bc,**2 1 .  M(-(¯M°±+% ²h/&'+ ³H< +, UTC  !Y, ,**. 1 h/M+%LMs/F­< M"# ./0(1  ! ** UTC"#$% +, UTCFCSTFCST "#$% , (*1  +3

UTC) (<&'(&'}:¡¢"#$¡¢< ANAL ~!+ST"&'"#$

Mcekl Q¸<-"}¹:0: " º»< GPV (#0/ ./<; +  M,´"# , "#mDQY², #mD< ,**. 1h/N$)"#$ ¦ :h/ ,**. 1 3 +,  µO+
E-v0 ¶}=·P::,¯ (<+²¦h/ ,**2 1 2 ,**3 1 /  (R"h/¼½+ . , bc#m* 

 !"#$%&'()*+,-%./ 012345

49

Fig. 1. Temporal change of slope distance corrected with / km-ANAL and distribution ofreﬂectors on and around the summit.

67!8"9:;6< =>? @AB
=;<E  HI2JK=LM

NOPQ

CD ,,** m  E

DFG ,**/ ,**2,**3

RSTS:UV@WXY  Z[\]^2

B_`Ta!T1^bcdefg V 8"hUV@0AiX jkl!m7  ZB 89nopB=qgA ZBr8"9"9stq[\] uF'() (Mogi,+3/2) vw++./

@lw

 xyz[\]{|1.1 mmῌyear  E  I  RST}~2Jxyw  8"9a!$[\]<$A M/ = :-q<E  _`T2JK

= giXh mO +* mLM ^ ./<^q1 h +** m- 1

6 I Fig. 2b [\]

,* km-ANAL ./: M / ^q

4$ 8"9a!$$p 8@Ag<E  BB^ / km-ANAL e./=%"9^ { )¡¢dO£¤&¥¦§¨©

Be

1ῌ, ῑ῎ῐῐῒΐῌ῍῔῏,**.

°xRST8"9^ ,**2  ,**3ª«  CD ,-2* m 2Jz¬ ,** m [\] +/,-** m- h­®=

7¯a!$

:e,stB=q  Bm^±²xy³}´RSTe:-q<E  BµT^ M+ M, M-  -¶UV@0K  }~_`Tk· / Hbcdbcd¸a!  lw¹:-qAº;d}µa!=m77= !w$ :e,stq[\]^xyz"9><[\]¼V Bj RST¼IE,**/

3 »,**2

. »8

'

50

( )*+,- .

Fig. 2. Distribution of changes of slope distances corrected by / km-ANAL and estimated pressure source
beneath the summit crater. Arrows show changes of slope distance projected toward to KWS. White
arrows show changes measured by EDM and black arrows show changes calculated from the estimatedpressure source. a : Quiet period, Sep., ,**/-Apr., ,**2. b : Active period, Sep., ,**2-Jan., ,**3.
Both pressure sources (open and solid circles) are at same depth right beneath the crater.

/0"12345 ' ,-0* m  +,,/** m- 67

89 (GPV) : ;:<=>?#@ABCD (Fig. 2a) EFGHI:J "K

LMNO6PQRSTU6"6VWXY 63/0(MANAL) : Z6<[\]6

@ ^_#'

<:`a!" bc<# de@&/f g3"!h !AE"stnA

i! jkjlW

# GPS utnAvF w6VW7%{| / km &}6~'U km

5A



 ,**/ # !6/0 #Q5A  !6a   n% 5A

m"6BnD@ ;6#$ocpqr
x12yzD,**- 

 <I:("!h )G:*aaoi!
    !"#$%&60$o 7+! !646VW
6i!" #@ #)G  ῑῐ,:n%  Y  46jkji!" jk
jlW"st KXY 6 7+!:\

6;Q v)0-\G ./0106  e2$o:Lx:RoABono % !63`$A 4  5¡ ¢67:o£/0:VW" 8¤+!Q5A

"F$G i!i ¥$ Q :o 9¦6§¨ :©ª« ¬)­`6
:3 ®¯°;±²³<´µ10[\=>?@¶

2ῌ ῎ ῍ ῏

cp?6Tcp@·=¸A¹  Q§¨ vºBCPQRS (ANAL) 6E

D E»¼½# »¼6, vF'()*+,- ! "#$%&./ 0 1 23 

BCDEF,G,HIJKLM+,-, Z[()\]H 3

cdefg- hhigHj'df%klm*!gfp
ῌ ῏ ῎ ῍Barrell, H. and Sears, J.E. (+3-3) The refraction anddispersion of air for the visible spectrum. Phil. Trans.
Roy. Soc. London, A, ,-2, +ῌ0..
Ciddor, P.E. (+330) Refractive index of air : new equations
for the visible and near infrared. Appl. Opt., -/, +/00ῌ
+/1-.
Fujii, Y. and Miyamoto, H. (+321) A general formula foratmospheric correction in electro-optical distance measurement. J. Geod. Soc. Japan, --, ,*/ῌ,+..
Hill, R. J., Cli#ord, S.F. and Lawrence, R.S. (+32*)
Refractive-index and absorption ﬂuctuations in the infrared caused by temperature, humidity, and pressure
ﬂuctuations. J. Opt. Soc. Am., 1*, ++3,ῌ+,*/.
7¦ §¨5 (,**0) Vr^8©ª« 7
 ,-ῌ¬ +2 *.­®¯°± ²,1.
 9³  :´ (,**3) ;µ<`;< . =>»¼½ 7¬ ,+ *.­®¯°± ²
 0/ῌ1+.

51456789 : (,**,) ;< . => ? @A .2 -1ῌ/3.
NO (+320) EPQRSTUVWXY^_  V`ab -, ,,.ῌ,,/.
NO$no (+32+) 
RST^!V`ab ,1 +1-ῌ+2,.
Mogi, K. (+3/2) Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them. Bull. Earthq. Res. Inst., -0, 33ῌ+-..
qr " (,**/) GPS #st uvwxypT"#z${|{}~ z$ /* -.1ῌ-0+.
%  &'( (,**-)  ) $ $
+33/ *+zQ$ , z$ .2 ,1/ῌ,2,.
 (+31*) \T - RST!pT V`ab +0 +-1ῌ+.1.
 (+33.)     ,., p.
. /
0
 (+31*)  - ! (ῌ)1\TY^t 
V`ab +/ +,+ῌ+,3.
23 r 4. $56  $¡ (,**/) V¢,£¤¥deT ,**. *"#$+zPQ"{|{}~ z$ /* -0-ῌ-1/.
Tetens, O. (+3-*) »Uber einige meterologische begri#e.
Zeitschrift für Geophysik, 0, ,31ῌ-*3.
=¶·> ¸¹!º