J. Jpn. Soc. Soil Phys.

No. +*2, p. -1./ ,**2ῌ
  °A±²*ῌB³CD*ῌ´ µ¶*Measurement of Water Level, Electrical Conductivity, and Sediment
Surface Level Using Time Domain Reﬂectometry
Hideki MIYAMOTO*, Jiro CHIKUSHI* and Taek-Keun OH** Biotron Institute, Kyushu University, 0ῌ+*ῌ+ Hakozaki, Higashi-ku, Fukuoka 2+,ῌ2/2+, Japan
Abstract
Time domain reﬂectometry (TDR) has been drawing a lot more attention as a way to identify
the interfaces in between di#erent dielectric media. To monitor water level (hw) with electricalconductivity (sw) and sediment surface level (hsed) in river by applying TDR, we developed amathematical model to evaluate these properties and veriﬁed its e#ectiveness by measuring thedielectric constant of conductive ﬂuid media and a soil material (sand) using TDR probes with
di#erent lengths. Although the determination of hw in extremely high-conductive media wastechnically incompleted, we could successfully determine hw, sw, and hsed with a probe in moderateconductive media. Judging from the relatively good agreement between properties evaluatedfrom the model and observed data, we concluded the TDR measurement could be useful toevaluate hw, sw, and hsed with su$cient accuracy for practical use within an appropriate conductive range. In actual application of TDR to a river monitoring, the calibration of the probe usedmust be required to conduct accurate measurement based of the model.
Key words : Time domain reﬂectometry, Microwave, Dielectric constant, Water level, Electricalconductivity, Sediment surface level+()*+', -./0(1234
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 TDR

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Schematic diagram of a TDR waveform
in inserting a probe partly into a dielectric material.

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Lhsed sed  w
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L w

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seff

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£WZ+**

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40

()*+ ,* mm ,-./012
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-- 

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8\! *.*++ S m

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

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



.++ !

TDR "#*..2 m '/012 TDR ; hw*.,/ m 8%@G  ῍- NA !"#$% PCTDR

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H ;!µQcO "´t

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,

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: <= > ?!$(ῌ @ABC#$%DE *..2 m   *.,/ m !
#'( TDR )ῌ/" *..2 m #$% *.31 m

41



&

῍ ῌeff      hw  *  ῍ + ,-./

Fig. - TDR waveforms measured with a *..2-mlong probe in di#erent conductive solutions.

Fig. / Water level (hw) for the square root of
dielectric constant (῍ ῌeff ) measured witha *..2-m long probe and a *.31-m longprobe in di#erent solutions. Brokenlines in the ﬁgure indicate theoreticalvalues estimated from eq. (/).

0 FG t+

H& IJK3L!MN"OPQ

5QR5STU0 VWX0 G t,  YZ-P-H&/(30 [Q\K-]^(
_`UO(1.+,  ῌ.

*..2 m  2  
hw 345(678!#'( TDR )

Fig. . TDR waveforms measured with a *..2-mlong probe in di#erent levels (hw) of
distilled water.

a ῎ / 0 *..2 m #$% *.31 m ) G t, TUH& eeff h w ῍ ῌeffTDRb(1 5#0 G t , -H&^5

Tc *.,** S m+ !#'(῍ ῌeff .PQ5Q1 de!$Of0 +/9   2,.,0 /5ghi3jk!b(lm῍ ῌeff  3.*1 b(1 R ,!#'(< n ,-o/(45(67!#'() pP0 *..2 m 0  ῍ ῌeff  3.*1 $qr"Tc1 2  )-a῎. !./1 5#0

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Q+0 |!#'( ?G-./1 2 ῍ ῌeffhw 3[Q S0

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YZ3£¤"O1Kb(}~i3

 ! _`UO(1hw 3 *.+ m 8 |670  ?!)3!5cR3G t ,!5q0 :&3

 ῍ ῌ eff w^5¡¢-c1 T¥67-¦'f0 ῍ ῌeff {"!/(§@   + b(+0 R @ABC wr!$U¨0 hw

, t *  t + =<=¢- ῌ !¬­P®UO©1 ῍ ῌeff  ¯$`UO0 ¥( L TU0 -%°/(R3^(1 T3!$cP45(R0 ῍ 3$`

0 G t, !±0 !Y/(G t+&²'3r"QR©!ªp«#((³ p´PQ(1 ῍  µmK-]¶/(

+

42

,

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 *..2 m   seff  hw   ῍  !" #$%&'(Fig. 0Electrical conductivity (se#) measured
with a *..2-m long probe for water level(hw) in di#erent ﬂuid media. Fitting
functions of eq. (2) for experimental dataplots are expressed by broken lines.

+*2 - ,**2

ῌ1Fig. 1 sw  b 

A parameter b for electrical conductivity of ﬂuid media (sw).

" #$%&) .ῑ0/ 01 * .ῑ1 )

2 b  sw  34* b )  
56789:;<=* >?@/ ῎ &

 !" #$1A  a BCD b )E/) F/G 

2 eeff &) J K & + LM) ῌ NO῍ ῌeff hw
&VW1A.ῑ/ /01 * ῌ ) 2

H I*.+,, BCD *.3-*

3= *,. , P QR CS/) TU ) /῏ &
&X1 YZ [1A) ῐ  \G /(4] ^1A74

_1 * .ῑ2 ) ^]`NO>NO) abcZ,6&d (4>5 :ῐ /!"1) /(4e hwῌL῏a BCD b &*fg) ehi /(4 sw &[1 .

jk/&l#(4m/) $/(4n

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sw 

) 

/}~&*M CS/) qr  /}~5+,1A

+1<7&*M4 -,534* C=A) ῌ /7A&E) >> | abc 34LMO

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43

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Fig. 2Estimated electrical conductivities of ﬂuid media (sw) for relative water level (hw/L).
lines in the ﬁgure indicate actual electrical conductivity of each ﬂuid medium.

 +2*
0JK+

BrokenE" *.*++ S m+ FGῌHI+ +32+

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UY@Z /[+ \]%9P3456 )2^_
`)2+ 3456 789%)2abRc0
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Dalton and van Genuchten +320 "+ TDR 0

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LMAX:

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῏

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
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
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LMAX:*.**0++   

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applicable to relative water level (hw/L)
measurement.

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34560 a  b '+ ῑ*.*/*+ *.+**+ *.,** S m+ %)2 LMAX  [cN 4%+ #'L 0J2, LMAX "+ V

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44

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Fig. +*

 *..2 m  hsed   
 TDR !

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TDR waveforms measured with a *..2m long probe in di#erent thickness ofsoil sediment.

῏ῌ++

Fig. ++

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Sediment thickness (hsed) for the squareroot of dielectric constant (῍ ῌeff ) measured with a *..2-m long probe and a*.31-m long probe. Solid lines in theﬁgure in the ﬁgure indicate theoreticalvalues estimated from eq. (+.).

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. Y5UZCD '. [)\ ;/ ] ^'. *.32 m  *..2 m  *.31 m   ῍ ῌeff   ῌ () hsed "#$ %&' ῍* +,-$+_ )

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b

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cd

4῍ ῌ eff  h sed "#+P῎++ ),-/ *..2 m  ῍ ῌeff '.

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v<+,_g23'/ῌ ῐ

5 +/0 06' 1,.2
+ . g2]3 TDR )ij6TA)#- eeff  hsed456 78T %uR+\-). 

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Y. << ,?@'06¢  v. £A῎6>3¤%¥)Mo. )%¥%¥CD'A456©ª4@«6)KLM<.

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1

. 23. 

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. ´\.Yµ¶F v

d5/῍ ῒ ῑ ῎Cataldo, A., Tarricone, L., Attivissimo, F. and Trotta,

#$% : &'()*+,-./ῌ012345,6789/:;45

A. (,**0) : Simultaneous measurement of dielec-

Friedman, S.P. (,**-a) : A review of advances intric properties and levels of liquids using a TDR

dielectric and electrical conductivity measure-method. J. Hydrology, in press and available atment in soils using time domain reﬂectometry.

doi : +*.+*+0/j.measurement.,**0.++.**0.

Vadose Zone J., , : ...ῌ.1/.

<=> +330 : TDR +,-?@AB:CD

EF

7GH%$ +2, +0-ῌ+0..

Robinson, D.A., Schaap, M., Jones, S.B., Friedman, S.P.
and Gardner, C.M.K. (,**-b) : Considerations for

Dalton, F.N. and van Genuchten, M.Th. (+320) : The

improving the accuracy of permittivity measure-time-domain reﬂectometry method for measur-

ment using time domain reﬂectometry : Air-water

ing soil water content and salinity. Geoderma, -2 :calibration, e#ects of cable length. Soil Sci. Soc.

,-1ῌ,/*.

Am. J., 01 : 0,ῌ1*.

Heimovaara, T. J., Focke, A.G., Bouten, W. and Verstraten,

IJK> ,**- : L 5,6M:;NOPQ in J.M. (+33.) : Assessing temporal variations in soil
water composition with time domain reﬂectometry.
Soil Sci. Soc. Am. J., /3 : 023ῌ032.

Thomsen, A., Hansen, B. and Schelde, K. (,***) : Ap-

XYZ[ῌ\]^_ +32+ : 01234 .:`a b
- c

h]

,**-  : ++ῌ

+/ RFSTU VW

pp. +00ῌ+03 dGef Wg

plication of TDR to water level measurement. J.
Hydrology, ,-0 (-ῌ.) : ,/,ῌ,/2.

,**- :   !" MS TODAY, +, 2 : ,ῌ-.

Topp, G.C., Davis, J.L. and Annan, A.P. (+32,) : Electromagnetic determination of soil water content

Moret, D., López, M.V. and Arrúe, J.L. (,**.) : TDR

using TDR : I. Application to wetting fronts andapplication for automated water level measure-steep gradients. Soil Sci. Soc. Am. J., .0 : 01,ῌ012.

ment from Mariotte reservoirs in tension discYu, X. and Yu, X. (,**0) : Measurement of simulated

inﬁltrometers. J. Hydrology, ,31 : ,,3ῌ,-/.

scour by time domain reﬂectometry, Proc. TDR

ijkl ,**- : mB TDR n  7op:.`ῌq` :e&;r7o:st 3- : /1ῌ0/.

,**0. available on line at https : //engineering.
purdue.edu/TDR/Papers.

Robinson, D.A., Jones, S.B., Wraith, J.M., Or, D. and῍ῌ&'()* TDR +,-uX:./5,601234789/;: vtwCxy-z{+ 01234N|Q- CaCl,

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y-Nz _r:./N ¡z}~ ./01234:e&;NOP¢- z£ TDR +,-;:4¤;OP( uX.:01234¤¥¦§¨+©ª«¬y-z{ ­®Q¯!°±:C²5,6:³´N¢-µ¶¡z : ,**1  +,  ,  : ,**2  +  ,. 