
J. Jpn. Soc. Soil Phys.
¼ῌ
No. +*., p. / +, ,**0

TDR 
*ῌῐ*Calibration of Column-attaching TDR Probe Based on Dielectric Mixing Model
Hideki MIYAMOTO* and Jiro CHIKUSHI*
Biotron Institute, Kyushu University, 0῍+*῍+ Hakozaki, Higashi-ku, Fukuoka 2+,῍2/2+, Japan
Abstract
A column-attaching TDR probe (CA probe) was designed to minimize the e#ect of disturbanceon soil matrix during soil-water measurement, and was calibrated using sand for various watercontents (q).

Relative dielectric constant for sand increased with water content, and ﬁnallyreached to +,.1 at saturated condition. Compared with estimate by Topp equation (Topp et al.,+32*), smaller relative dielectric constants were observed at all water contents in case for the CAprobe.

The relative dielectric constants measured by the CA probe should be composite relative

dielectric constant (eT) of , components in sampling volume : medium (em) and acrylic part (eac).
To evaluate the e#ect of acrylic part on eT, contribution of both components was investigatedwith data sets of relative dielectric constant for ethanol having various concentrations, based ondielectric mixing model (eT wema(+w) eaca +/a ; where w and a are parameters).

Combined

Topp equation, substituting em in the equation by the estimate from the mixing model, relatively
agreed with observed eT at various q.

The determination of mixing model parameters (w and a)with ethanol could make it possible to calibrate eT vs. q easier than that with soil.
Key words : Time domain reﬂectometry (TDR), Relative dielectric constant, Volumetric watercontent, Topp equation, Dielectric mixing model+,"- tuk῍_"vwx῍$ {+    

Topp et al. U+32*V |}~(./IO"-῎
 !"#$῎%!"&'()*+,"- %./"0123$456+78

q..-+* 0 em- /./+* . em,,.3,+* , em/.-+* ,ῌ+,"&' 9:;<+=>?@A%(BCTopp ~$ ?[x  !"+,"&'(D9/- &EFGHI JKLMN$/( UMiyamoto et al., ,**+V ?[ /OPQ῏RST^ +.-῍+vwx῍!"&'(+UTime

DomainReﬂectometry,

TDRV W'XYO"%W(Z[\.NO]#^/"-

" UTopp et al., +32*VTDR W$  o1o

TDR W_"%`/^$ Noborio U,**+Vabc/- TDR W$defghi3

 , ~9$ - ~hi3j(?[./IO"- %56$ ./"mno( /¡¢jklmnopq mnors>6HINO

9hi3j(£/¡¢4/- &E TDR W"¤9q |.¥¦§'^ hi3j78

tuk῍ em _ vwx῍ q !"yz* ¨© ª«¬­®¯01°3 ±2+,῍2/2+ ²³´µ¶·¸ 0῍+*῍+ : PQ῏RST UTDRV tuk῍ vwx῍ Topp ~ uk¹º»n7rs t +*. ¼ ,**0

6

 +GHz  / cm  Malicki et al., +33, ,*GHz  ,./ cm  

"!Kelly et al., +33/ # $%&' ()!*+ ,-!./0

1# 2 345 (Nissen etal., +332 ; Selker et al., +33- 6 789/: TDR  ;<#+ # &=<> TDR 789  ? @ AB


!

*C D@ A

 .E( 6 789/:F
GHIJKL!
O

#> IJMN!P 35  &1=1CA ! - EUJUK

Schematic diagram of CA probe and --wireprobe.

2 3QR ,-& #>.4 (&#'1 Topp U(?
ῌ+Fig. +!"#S$%T!)

Selker et al., +33- V#> '*!



1# #

W+DX< ,- YZ[\]^_ *.0 cm /` < /.ab /0QR

1#

C1#1c= 3d2ef'*!

S-!

1 T *.+0 cm, N( +* cm  - 6_\PU1# - EU4wB

23

YZ[\]^_.# VWX

. ?g YZ[\]^_3 Y yZ=1#Xy uv y!A

h44i j5& &V  6kl MNO1#778
9&8m#> no[9pqr%s
:;1# Selker et al. +33- d2-!1[ T&  *.**+. kg- kg¡- \¢] ,.0, Mg m¡- &y!^_&£¤` ¥?1 a¦¥? bfd.§1#!*+ &8cx&8cHe1#¨d CA 

no[<t=789 >0?@:;1#  f] +./ Mg m¡- !

uv CA !A wB1# V1 $%A1#d$%T&# q  * [  *.**, *.*.

T&#x*.*3 *.+. *.+2 *.,- *.,1 *.,3 *.-- *.-. *.-1 *.-3

y'* CA z !"#m !!4 {|}C~ !"#

*CA1#*..* *..- m- m¡- &

F*D0"]\]^_*+ +/*,C -| Tektronix © .!" 1# # - EUR¨dA1# CA "ªgf V

4FG !"h«ii3j1# i3¬k­®¯ῌWinTDR!!4 gH= CA 
YZ[\

]^_3RI1#

, 
,+

CA 

Or et al., +332  j1#i3=°=bN La l±1 La !/²N L    

6kl.# , W+ TDR JUKK

mn e³LaῌL, = !"#l±1#
# ^_& DW ´µ {|} ¶·1#{|} ic8# : *., *.. *.0 *.2 kg kg¡+ '1
4 CA z !"#1#CA 

 / cm,  0 cm, .( - cm no[ o¸ #> - EUF

<t=789 (  >0LM N

4F p$ !"#1 a¦ 1( +/ cm, O *., cm, ( *.**2 cm ?@ *.,#ῌ+ zcm  :;1 CA wB1# ,,    _\P1?@Q0!F:

TDR  TD

R1 _\P!F:RM:;

ef ºqp$»MN(

¹3
C

=> :

¹"Nº»?@uAP TDR bDcd¼dgch

7

 Knight et al., +331
 f Poisson (,f)*
e

 r !" #

$%& ' Knight et al., +331reῌ +' x*y ,"-  ./01023 ῌ $ Laplace $"43.

῍5 f 6 5 f῏)*
῎5x, 5y,ῐ
,

,

῍

e

7

89 Richards $3:ῌῌ,

TDR bDcd2efgch+$kFig. ,

Schematic diagram of electric simulation
around TDR probes.

5q)Khῌ(,H5tt ;! K 8<

 van Genuchten +32* 8930῎

T00h =8 H >8+' ??3 80 x*y ,13 8@%0?A ῎ $BCD 83F

qEh)

E

G3.?A H  h "H.IJ K 8LM38<8<Kq)KsqE+ῌ,+*+*qE+ῌ,m,

K 

q E)

῍5 h 6 5 h῏)*
῎5x, 5y,ῐ,ῐa, n, m 89c qE  m Ks H.IJ?%3. #$NO"

43.

++6ahnm

q*qr
qs*qr

m)+*

+
n

ῑ

,

῏

Ks

῏ $ ῍ $!P Laplace 3: qs 8qr 38

3Q LM'" ῐ $"$3QR 80"#S,"-T12U#$

V$"%WX0'?%3. ?Y&'Z- qE+ '0 KqKs & %4/3Q?3 38-Nm~'1]c qs)+ qr)* a)+.* +**+- n)+.***+ 5¡

 =8 8< ($"6 ??3 ,*¢ 8(   2* Nob-

orio, ,**+ 7£¤"~("H.IJ[J?"NR \) 8



,.,¥

ῌ*]9^_"`a HYDRUS-,D-., 3Q (  ¦§ 0J Ks  8

SÀimůnek et al., +330  TDR bDcd¨©ª« 362efgchijkῒ,  - l$bDcd-Nm CA bDcd,"-,.,¥-., !

8" +~"(,.1 "«' *.*-. ¬

0JT2efgch+$k3Q 0- nobDcd"0J­®¯° HYDRUS-,DbDcdpqcdrst ,octluv

30J± ² ¯°A Constant pressure

bDcd+' w +* cm, x +* cm "#Sy!

0J ³%´i'nopqcdrst

z" - l$-Nm CA bDcd%{|= +

Dcd}"8- l$b

CA bDcd}"8~-%{|'[J ./ f&,o3+ct8 * µ²bDcdª« 3 7¶"0J­®¯°" Knight et al. +331 
9!:" bDcdA¶%·";-R??3 HYDRUS-,D 2efgch¶<i'l %CD '0¶"-T

iO2 ^_30J1]892 #¸#%CD[J ' Noº» K +*. ¼ j,**0k

8flux 



Topp fJ" GHI? TDR #J !" #$Vl(_V`3a6b" cd#(%&'()*[g <(% 2" Selker et al.
j+33-k V- 
-+ - ef>¡J" +,a )V Topp f{|[$b[^?%_V¢a(% cd CA [" Selker etCA +, -. TDR /0123"al. g <(%_23"+ Topp

456$7 q8*.**," *.*3" *.,-" *.--" *..- m- m9- f£aJ" ¤¥?0EF TDR ¦§S.#6:%/0;῍- #<= >?@ABCD¨ 3a%

EFGHI? TDR J" KLMN23K-,OPQRSTUV<=W2:X La J"©῍+ J" - ef6$7 CA {|

CA 



q YZ[#\]^?%_V`3a6b" c45" ª« jCk ¬?%­®¯°" ±²) d - ef[g hi<L%(?(k Lj;J<

" CA [ - efg

CA {|a -³) J" ±²´]" - efµ¶«#" q Vl(.mn L a J\]^?%hiVo3aj;῍-kq Vp^?%" KLMNKOPQRSqPQrstuv wVo3a V" _ wJ"
KOPQRSxyz La {|#J}~?2
;῍. J" - ef CA  TDR /0
23{|

-.)



5

% ?6" ;῍. #J" ῌ f e 
I?% - ef
#" Tq rGH+J ῌ f+#=% Topp f R, J *.322 

#l^" - efJ Topp f# V3aCA #6([" l5

3F]Jo3a%[" q Vl(.mn{|
a%)  V\]^?b" 5 jq8*..-kJ +,.1 #_V" -.V< ) J" - ef+,a $b^" T "

ῌ.

)



5

q r

Fig. .

Volumetric water content q for relative dielectric constant.

ῌ+- ef6$7 CA +, 45jDWk"±²" ª«¬?%­®¯°) q YZ#=%)  YZ[(Table +

Relative dielectric constant of distilled water (DW), air, and ethanol having di#erent
concentration measured by --wire probe
and CA probe.
Relative dielectric constant9+ῌFig. -CA +,
·¸¹ TDR /0

56$75¬?%TDR waveforms for water and sands having various water contents using CA probe.

C (kg kg )--wire probe

CA probe

DW
*4,
*4.
*40
*42
+4*
Air

2+4*
014/04.+40
,340
+34*
+4/

-04.
-*4/
,/42
+340
+.4/
+*4*
-4+

῏² : ³´µN(A- ¡¶D·¸¹ TDR  ºM_ »L¼K

 - 

 2+.* 

9kZ($ OPQ=de fghkZ(@ Noborio, ,**+  !" #$rst*-RS*u3 yOPQ$%&'(ῌ)*+,!"

 D(]^_N`aV-34 #$ yy4#-./01- 23

CA  5 3

6&78

9:;<13=>?1-
HYDRUS-,D;<

+,6&789:;< ῌ+ @ABTopp   Uῌ. ./01-

3 - @AB CA 

n3

CA  |K_K}&~

CD(@E-FGHIJKLMN@ABFGOPQ *.+ cm OPQ$0C

RSTUῌ/ (5V *@ghTijZ[

RSUWX- cm Y\ ]^_N`aV-bcT5V - 



kZ

r de

f

3x *.,*.- cm z{./01-

RT 3T CA  ( FGHIJKLMNde fghT(T+ 334 +,13

ij 3klGmRST5

n3 OPQ o

%&'*R῍T 3./0(de fghpq(@rst*u3 OPQ

1-



s῎v

de

78A¢*£(wQxyz{ -  |K_K}

fghTij

3kl *.0 cm&~./01-
WZ ¡CD(G rW*RRST¤¥T¦§¨©ªs34 CAW*RRST78«¬­ ®¯°n

./01-CA  FGHIJKLMNRS ῌῌ/Fig. /- @AB CA ±X a FGHIJKLMN@AB b FGOPQ(a) Relative electric potential and (b) relative electric ﬁeld intensity around --wireprobe and CA probe.

*º"{ » +*. ¼ (,**0)10-- 

+ 

      e+  e, 





 ! "#$  eT %&'(RotheT*+we+a,(+-w)e,a.+ῌa a

῍



4'5  Nissen et al. (+332)/"0123 

 6789:;<=3>'?@
/ CA <=3>_*..+, Xq Fw

NOPrst'RIm  mm  u w
 + dI<=3>vwxyq Topp &zw {Jyq mJK" |4}3~ A/I ῎ &b01234/@"   <=3>Vz{/@

et al., +33*)

w

EF


8

l" F'  '5 EF-.  Topp '  CA <=3> - T&<=3>/8
A?@ 
CA <=3>'?@

 !

" AAB CD EF8

NOP /l" m'R8 Bm' ῎GHIJ CA <=3>K"/ ?

&/ em I" B / ῌ &!" @LM'5

 ANOP 

%&



EF ῍ & e+ /?@ A em, e, /NOP eac QRSF  %&eT*+wema ,(+-w)eaca .+ῌa

ῌ + e a- +-w e a῎-ῌa
ac
῍w T
῏
w

q*..-+*-0῎

ῌ + e a- +-w e a῎,ῌa
ac
῍w T
῏
w

-/./+*-.

B ῑ+ ?@ - T&<=3>K"ῌ + e a- +-w e a῎+ῌa-/.-+*-,
ac
῍w T
῏
w

,,.3,+*-,/ A6U em, NOP
eac / ,.1 EF TVWXY01234 w

 a WZ/[\8 ]ῑ0eT  em `a' ]b ^ A_eT*em cTTV

WXY'8defTJgI 
WZ8 w*..+, aiQῐ &  ῏

eT*em cThNOP

'l8 A&/
]ῑ. #T'g8

AjkXl I m  n8 NOPopI Topp & # m CA <=3>'?@rs/D8 #'5  m

+.*1  defT eT*(*..+, em+.*1,*./22 eac+.*1)+ῌ+.*1

ῐ
῏

 w

CA <=3>/I?8$
Topp &

\8 (]ῑ.) 

8 ?L"

Topp & { %&8 (R,**.3+2) mm  /

!<=3> w  a /@" CA <=3>'

/

m

V/¡ TDR <=3>IJ Topp &¢('5 m/KI 
ῐ & #  Topp &
8£ ῏¤¥/¦_§I'I EF8¨ )*z©

/ªq«*L 'RI¢({yI B8*IJ +¬;<=3>'?
@

8~o& ῎ &/

#

m

ῐ &, ' V<=3> 8&
 ῏
ῌ0

A em L"8  eT

CA <=3>'?@Fig. 0Composite relative dielectric constant eTmeasured by CA probe for relative dielectric constant of media em.

/ m'R EF m8-./E/"  ,­*L?@ 8~o&/®q¯'R ¢({5 °±P>²3³´µ0¶·¸/8¹RIEF#$ : )*+,#- F@AB% MNO TDR /012345



  ῐ ῕ ῔ ῑ ! "#$%&'( )*+,#-%.(/012345

11

Kelly, S.F., Selker, J.S. and Green, J.L. (+33/) : Using

67%8(9:;< =>short soil moisture probe with high-bandwidth.ῌ ῎ ῍ ῏time domain reﬂectometry measurements. Soil
Sci. Soc. Am. J., /3 : 31ῌ+*,.

?@ABCDE!FGH 7IJ%

Knight, J.H., Ferré, P.A., Rudolph, D.L. and Kach-

KL(  @ABMNO TDR % PCA 

anoski, R.G. (+331) : A numerical analysis of theQ %RS( T%UV /012345%WXL

e#ects of coatings and gaps upon relative dielec-L"  Ytric permittivity measurement with time domain

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probes measure water distributions in an andisoln{ Pῌ+Q> L  )under di#erent tillage systems in Japan. Soil &71- Fl 515r')b l L P ῌ/Q>

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tent and electrical conductivity by time domain ~<+ )

reﬂectometry : a review. Computers and elec-U(  1- xgL  { g>1-6%n  ) {tronics in agriculture, -+ : ,+-ῌ,-1.

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Roth, K., Schulin, R., Flühler, H. and Attinger, W.
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M. and van Genuchten, M. Th.
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van Genuchten, M. Th. (+32*) : A closed-form equa-Topp, G.C., Davis, J.L. and Annan, A.P. (+32*) : Elec-tion for predicting the hydraulic conductivity oftromagnetic determination of soil water content :unsaturated soils. Soil Sci. Soc. Am. J., .. : 23,ῌ

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