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Estimating Thermal Di#usivity of Soil Packed in a Cylinder Using
an Analytical Solution
Kosuke NOBORIO*, Ieyasu TOKUMOTO** and Yoshiaki MUKAIDA****, *** Faculty of Agriculture, Iwate University, Morioka *,*ῌ2//*, Japan** United Graduate School, Iwate University, Morioka *,*ῌ2//*, Japan* Present address : School of Agriculture, Meiji University, Kawasaki ,+.ῌ2/1+, Japan
Abstract
Soil thermal properties are critical to many processes.

For example, germination, crop growth,and nitriﬁcation depend on soil temperature, which is determined by thermal properties.

Ther-

mal properties are usually measured in situ using specially designed probes that enclose a heatsource.

Here we propose and validate an alternative method for estimating soil thermal

di#usivity, based on changes in temperature at the center of a soil core subjected to changing
thermal boundary conditions. This method formerly required numerical analysis because no
analytical solution was known ; here we present an analytical solution. Estimates of thermal
di#usivity of an Andisol at various moisture levels, obtained using the new method, comparedfavorably to results derived with the conventional probe method, showing that the new method
constitutes a viable alternative.
Key words : Andisol, thermal properties, cylinder method, probe method, analytical solution^+    _Bristow et al., +33.` f*<fp*# qr s _,**-` ,[\]^ (TWX

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the soil temperature ({), To the temperatureof a water bath ({), and a the radius of acylinder (m).

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H\ tῌa, ]'_`y de* 'ghij'k62 k !"#yFig. ,

Relationship between kt/a, values (Table +) corresponding to relative soil
temperature and t/a, values measured in a cylinder. The slope of a regression line with a zero intercept value is k, thermal di#usivity.

23 » +*+ ¼ ;,**/<

8

#$%&'῎,  2 

yz{|}~r701 452  !"῎/ k0 tuvw!ef!g 01( +* !"%)*+,-.

! h\1 q

B*.*- m-ῌm- "1ijm/ 01 !"2 31 452
670189: 
=>?@A

;

῎-<  !"%&> TrB+.* 1C

%&DE1F/

TrI+.* J*?KLM0

1 -.1N

!"2GH01O F&PQR)S!"2GH!"2 1 +, TU 2  !"+,V1b .6#S *1 A q*.+, m-ῌm- ef!g$tuvw!1ij& )
R)S1Z[]tuvw! 452)1c3
1 C  Ren et al. ;+333< & 7016 
c3

0 WX !"21YPQR)S1Z[\O;ab Trῌ*.1,<  !"\1c3

1def!g1h ;qB*.*- m-ῌm-< 70
1ij῎. k0 6l ῌ 1 m
PI*.**+< l ῌ 

;rB*.3332

\1 45201(A Shiozawa and Campbell)

-T* \1
1

ῒ

?q

r +*s \& tuvw!1qr
\!T'' *tuvw!
  Uno T-TiB*

1 ln ;t< l ῍ p ln ;t*< ῎/ k 16\11.ῌ ῍ ῐ ῏ ῎῎- ]1^&J* +_,῍ WXPQ k 61  1 W`

῎/ k 1ijA" 01 %&x 1%ῑ¡) +%¢£¤¥¦;B< ;,< +/-2*+0*< A



, ;§-

¡¨©

¡!"#;+33*<  ef!gqrI,s \1$ª«.¬ ­®RR¯/ ¡¦°±C

C*x*1

² +³´µ J¶­®R/)/0·¸¦¦ΐῌ-

tuvw! 
2  !"

!"2N¹6701PQº 1῎+ k
452N¹6N º

Fig. -

Errors, from a pseudo-true value, associated with the number of data used for
calculating thermal di#usivity. The pseudo-true value was assumed to be thethermal conductivity calculated with an eight data set as shown in Table +.

rs : klmn8!tu&%vwefghiTxy!z?(^{:

ῐῌ.

6789:!;<=>?@A%6789BCDEBCFGHI.JK LMN>?OP ῌ QR=NST4& T-TiU* VLMWXY ln Zt*[ ZP ῍[ \]@A^K

Fig. .

Temporal changes in probe temperature measured. A line indicates the regression
line of measured data to Eq. -, and ln(t*) indicates a value in Eq. ..

ῐῌ/Fig. /

9_`abc q !d(^efghi k >?OK jNklmn8:!;opN6789:!;oqS%OT4(K

Thermal di#usivity, k, measured against volumetric water content, q. Symbols ῌ and῍ indicate measured data using a cylinder method and a probe method, respectively.

       !"#$%&'()'% *+,-./01234!5#$%&'()῎ ῒ ῑ ῏Bristow, K.L., White, R.D. and Kluitenberg, G. J. (+33.) :Comparison of single and dual probes for meas- ¦ +*+ § ,**/

10uring soil thermal properties with transient

/01234 567 12-ῌVII--. :heating. Aust. J. Soil Res., -, : ..1ῌ.0.

--ῌ-2.

Carslaw, H.S. and Jaeger, J.C. (+3/3) : Conduction ofNoborio, K. and McInnes, K. J. (+33-) : Thermal con-heat in solids. ,nd ed. Oxford University Press,

ductivity of salt-a#ected soils. Soil Sci. Soc. Am.

New York.

J., /1 : -,3ῌ--..

Fontana, A. J., Wacker, B., Campbell, C.S. and Camp-

Ren, T., Noborio, K. and Horton, R. (+333) : Measuringbell, G.S. (,**+) : Simultaneous thermal conduc-soil water content, electrical conductivity andtivity, thermal resistivity, and thermal di#usi-

thermal properties with a thermo-time domainvity measurement of selected foods and soils.

reﬂectometry probe. Soil Sci. Soc. Am. J., 0- : ./*ῌASAE meeting Paper No. *+ῌ0+*+. St. Joseph, MI.

./1.

Kasubuchi, T. (+311) : Twin transient-state cylindrical-

Riha, S. J., McInnes, K. J., Childs, S.W. and Campbell,probe method for the determination of the ther-

G.S. (+32*) : A ﬁnite element calculation for de-mal conductivity of soil. Soil Sci., +,. : ,//ῌ,/2

termining thermal conductivity. Soil Sci. Soc.

ῌ

ῌ,**- : 

  3- : .1ῌ/*.

Am. J., .. : +-,-ῌ+-,/.
Shiozawa, S. and Campbell, G.S. (+33*) : Soil thermal !" ,**/ : #$% TDR &'$()*+,-.

῍

conductivity. Remote Sens. Rev., / : -*+ῌ-+*.

ῌ

829:+;<=>?@AB)CDEFGHI+J KLM NOABH=PQRSTUVWI+D=XYUZ= 82[\9]^+_4)`ab+J cd 82=efI+D=gQh&'$(Hb+ifj8HI+i kl@&'$(imGHI+J fn
op/qr_4sY9b+;<Ht829ub+vwx$y9z{H|+J }~} ;nH=;HiG EDvJ ;HH= opH7}v_4sYx$y9~v)E=w+;<)*E9ub+n9z}vJ 9>?@A)}E}v= cd&'$(9vn~v<f}vJ cE ;;Hz}v=cd <@+<¡¢+J]£¤¥ : ,**/ ¤ -  ,, ¥]¤¥ : ,**/ ¤ 0  ,, ¥J. Jpn. Soc. Soil Phys.
"1
No. +*+, p. ++ +0 ,**/

 TDR 

*ῌ**ῌ***

Solute Transport Properties of Soil Measured with a Vertically-Installed Time
Domain Reﬂectometry Probe
Kosuke NOBORIO*, Ieyasu TOKUMOTO** and Yoshiaki MUKAIDA****, *** Faculty of Agriculture, Iwate University, Morioka *,*ῌ2//*, Japan** United Graduate School, Iwate University, Morioka *,*ῌ2//*, Japan* Present address : School of Agriculture, Meiji University, Kawasaki ,+.ῌ2/1+, Japan
Abstract
It is crucial to know transport properties of solute in soil when contaminants are spilled into
soil. In +33*’s a procedure using a vertically-installed time domain reﬂectometry (TDR) probe
was developed to estimate solute transport properties for the input of the Dirac delta function.
We proposed a procedure for a step function input, equivalent to a contaminant breakthrough incase of a broken barrier at a ﬁnal deposal site.

With soil column experiments with sand, relative

concentrations measured with TDR and e%uent were analyzed to estimate the retardation factor,
R, and the di#usion coe$cient, D.

For the step function input, R and D values estimated with

TDR agreed well with those from e%uent.
with TDR agreed with that from e%uent.

For the Dirac-delta function, the R value estimated

The proposed procedure using a vertical TDR probe tomeasure solute properties of soil was validated under the step function input.
Key words : break through curve (BTC), electrical conductivity, di#usion coe$cient, retardation
factor, time domain reﬂectometry (TDR)<n|}-* kPa ~23% . M+    !"

#$%&'()*+%,-.

JK

XFE% ;<3% Rhoades and Oster, +320=Kachanoski et al. +33, -.

M_Z"ocd]i^A<pqi TDR time domain reﬂec-

#$%"/&0123%45678967(:

tometry V(WXF. Ru(^A+%bV%;<3%= >?"67"@A-. BCD#E(= ?-. k

F-GHI JKL?
V(WXFIMMNOPQRSTU

e?Gb

TDR S(WXF. AMRu2

M"YZ([\]^A+%>^A(`X= 2-. ?"^AV-. o_2`a%= I J%bV-cd]2efghiAM Ru2"Ru^A4

(+%"2. gj"kl#$%^A-mP

FE% Noborio et al., ,**/= >?"^A2

23%= nb. NOPQRSTUV2-. ocd]i[-. -Ru"{ ¡7_Fk \^A<pq23%<.

%_¢AFE%= G TDR S"rstRuvwxyz{*, *** £¤h¥¦¥§ ¨*,*ῌ2//* ©ª« -ῌ+2ῌ2** £¤h¥h¥¬ ­¦¥®¯° ¨*,*ῌ2//* ©ª« -ῌ+2ῌ2* ±²³ : ´h¥¦¥§ ¨,+.ῌ2/1+ µ¶«g ·¸¹ +ῌ+ῌ+ : cº»¼ BTC. Z. 4567. 8967. TDR V$ 5f » +*+ ¼ 1,**/212
 L
!"













# L

 TDR


$%&'

+04< 6 < 5 567 
89ῌ 1+33,2):; 1,**-2 56

 + ()*+, -./0,#
34 56

Elrick et al. 1+33,2,07# 8!"  >6< )=5!"  $#%8L9) TDR ":;>!k Cr 1t2 pq.#5 1Kachanoski etal., +33,26
Cr1t2r

EFG:H#IJ)KL MNO# $PQ)DR 6 S 0 DR TU]F^&_ `a. $%&'bcde 89) TDR ":;!"  


f

$ 

j $ ¢_+04 1mSῌm2 so O§<ª+$%&'

gh i jO h jO 00. D ,ῑ 1Rxsvt2 ΐῒ. DRt ῔tuv

ῌ1cm,ῌmin2 R wxv

 t nyoz 1min2 v z{F| 1cmῌmin2 .
Jwῌq .#56 Jw F^&_

1cmῌmin2 .}῏+῍vL῏erfc῍ΐexp
῎ D ῐ ῎  ῐ῔,.)+./Z56 h'

Ms1t2r῍  ῏῎  ῐ῍$!k Ms 1t2  q

+  ῑ+῍  ῏erfc
῎  ῐ
L ῒ,+
῍vx῏erfc῍  ῏ΐdxexp
῎ D ῐ ῎  ῐ῔, no!k Cr_s 1t2 

erfc



῍  *  TDR  L .0,."q+῍  ῏ + exp῍vx῏erfc
῎  ῐ ,
῎Dῐ
,

jO

56

!"   x 1cm2 lm j

Cr_s1t2r

q῎

Cr 1t2 ,q ῏

Md 1t2 /q ῐ$F`a

j2®=O)-./,¯+33,26 °:(#> +* ?±

1molῌkg2 ,O+04 s 1mSῌm2

TDR . 

< 

)

*5+,#-5":;,5!

 .e<  ./ 01oz

23+& +, R@²

1³ *.**/῕C῕*.+ molῌkg2 ./5 O C

v#/ 1Akµ¶ +31/26 )# 

Ms 1t2.¬ 1Kachanoski et al.,( ./6
 TDR 

ῐ

 h

,#5 1Skaggs and Leij, ,**,26 00. erfc (,,῏!"   TDR  L$P$ MF& 1cm-ῌcm-2 ./6h'[

00  L  TDR ":;  1cm26

F$ Q 1cm-2  $%&'~% A 1cm,2 ,nyoz
t 1min2$!k Md 1t2  Elrick et al.

῏
ῑ+ erfc῍ῒ,῎  ῐand Leij, ,**,26
exp s



$

Md1t2r+s

no!k Cr_d 1t2  pq.#5 1Skaggs

¢_+04\ pq 3­>TUT.#5  g x 1cm2 5lm. O $

1+33,2 , van Genuchten and Wierenga 1+3202]F^&_ `a j  )

Cr_d1t2r«),¬   TDR  L 

O !k< 0, 3"56j TDR ":;.<) $ ¢_+04 1mSῌm2 si £¤¥¦

P

,+ 

῎

1mSῌm2 ./6,    S

s1t2ssi
sossi

00. s 1t2 nyoz t¨©

TU)6$ 9) TDR 

¡ $O 3¢_+04 no ?@ABCD

V)W0,X./,YZ56 [\.

)6  c>< v

D ,wxvz ´uR  q ῎ .#5< :q ῏ q ῐ BR0,.· ¸C./6  q ῌ 3¹q ῍º F +04< 0, 3DE · ¸C./6 : TQ.UV TDR "MNOmn+!C º»¼ 1 p;677H}NZ.L ῌ 1- 

L ῍ K R  D ! KS-0-  

  ,.0/ Mgῌm-   -./cm +-.3 cm !"#$%&'()*+,#-.

/013+*.2 cm 1234,#-56n K.bI
Mathcad ver. +,Mathsoft, ,**. .  

789: RO ;<=>?

ῐ+ .}#&'!}XZ~CV@   RO ;!ABCD  AEFG 2.,

.7H! Ra TQ.UVmSῌm HI J!4 + TDR "MNO

67 , KL TDR p .b

2.3 cm M&PQ +.0 mm M&}NZb K677 R  D

PRS +./ cm TQ.UV TDR WNOXY$ K¡@ Kachanoski et al.

"MNO M&P

ZN Y'[M\'$]( +/*,C  PC ^_`ab+33, !¢£>cd[efg WinTDR

Or et al., ,**. hi

7Cx¥b TDR mnH!¦.jkD;lX'AEFGmn§x¥1> J¨ .p!Hx©ª -t¤+/ min . TDR M&P 6

1 ,#-5o67!p;d#'qrstu'ZN¥ K.bI Kmn- ¢«7!}NZ.¡=¬­b

.v; v;!CAEFGmn ,#-^67n ws" RO ;

®. $Y&"~V.TQ.UV? +,#-!; d#&'$xnyz{.|

TDR "MNOmnHp!H4 }XZ~V. qs+. *.+ mol ῌ L NaCl  / mL $Y&"~V.

.? 1n ws"! RO;Zs' *.+ molῌL NaCl !Zs'.
TDR mnH}NZ.L ῎ 1L ῏

! Ra ῐ, ¯¯ L ῏  TDR 
mnH}NZ. L ῍ p677
H}NZ.K  R  D  TDR M&P{.~°>±= M&P

L !C z

L .²³abC´

ῌ+TQ.UV TDR "MNOp67}#&'!}XZ~V.abH!µ ¶ ·ab y ¸!¹a¶Fig. +

Temporal changes in relative concentration measured with a vertically-installed
TDR probe and e%uent for a Dirac-delta function input. Arrows indicate thedirection of corresponding y axes.

   +*+  b,**/c

14

῏ῌ,Fig. ,

  TDR -P<=>23EMN$%& y  aGt!CD

Temporal changes in relative concentration measured with a vertically-installed TDR probe
and e%uent for a step function input. Arrows indicate the direction of corresponding y axes.



 

ῐῌ+  t+/ min  !"#$%& '()*+ , 
TDR -./0 L 1234567'()Jjkl JKLMNMN TDR <=>7$%&CD23[rN R pqrN D HI

Table +*+2389:; <=> $%& *+:;?@A῎+ B TDR <=> $%&CD23E3
9 R  D

FGHI

R  D  JKLMNMN7OEJPLQ'(

Retardation factor, R, and di#usivity, D,
for Dirac-delta and step functions input,
estimated using changes in relative concentration measured with TDR and frome%uent.

procedure

input function
Dirac-delta

step

-

q bcm ῌcm c

*4-3

*4-0

v bcmῌminc

*423

*41,

R

+41/

+4.,

D bcm ῌminc

*4*+.

*4+-.

R

+42+

+4.*

*4*0+

*4+*,

RSTUVGWXYZ JKLMNB
TDR <=>7 R[F\9]9 +.1/ +.2+ ^O HI)_`?@ ?a D-[F TDR B *.*+. <=>B *.*0+ bcm,ῌminc
^O TDR 7[F<=>7F d +ῌ.

TDR,^ MN TDR <=>7 R[F \9]9 +..,  +..* e;_`?@ , D

effluent[F# *.+-. D bcm ῌminc,*.+*, bcm,ῌminc  TDR <=>7fg^hi;39^2

/ῌ ῍
Jjkl

TDR Vmn ῍ B +*ῌJKLMN<=>VBmn ῌ o pqrN D
uK

fg`^vPlw0d /ῌ S0`^ ?a

῎

vPlw0

CD s῎+ Bt09

CDA09 D+*ῌDCDx?yRfB# +.1ῌ z&

CD2{9^[B vPl|}

 <=>7 D

B JPLN~>%& & G~ :  : TDR 78X;</ ῑ+  ῌ TDR   ῎  D .

 !"#$%& ῍ "-+*῍  D .  /012 3 +.1῍ -  ῍4 - ῎ "# TDR +56 L

78  ῏ "- +*῍  D .  /0.

12 3 *.,῍   29& D :;

< =


 ῍  ῏> D ? @A{|}TULM5~K NxOPTK 4QTU B , +/-2*+0* 9&TURS > DI
TU  wIxxJxTUVPA N

`a& b> cG

"# TDR  @A
A9 ῑ+ >LA#MN"-+*῍  R 

.  ῌ "-OG$ /0
 ῎ "- CrQ*./ $ /0P ῍ - %&'A P

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A.L. (+33,) : Parameter estimates of ﬁeld solutetransport models based on time domain reﬂectometry measurements. Soil Sci. Soc. Am. J., /0 :+00-ῑ+000j_kῌ ¡lm +33, : TDR>78n^

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ciety of Agronomy and Soil Science Society ofAmerica, Madison, WI, U.S.A.

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Theoretical background. In W.A. Dick and G.C.

lute dispersion coe$cients and retardation fac-

Topp (ed.) Methods of soil analysis. Part .. Phys-

tors. In A. Klute (ed.) Methods of soil analysis.

ical methods. SSSA Book Ser. No. /. pp. +-/-ῌ

Part +. ,nd ed. Agron. Monogr. 3. pp. +*,/ῌ+*/..

+-2*. Soil Science Society of America, Madison,

American Society of Agronomy and Soil Science

WI, U.S.A.

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Pongpattanasiri SUKTHAI*ῌ*ῌ *ῌ**ῌ*Inﬂuence of a Percolation Pattern on the Removal of Soluble Elememts
in Downward Water and Rice Plant with Models of
Cadmium Polluted Paddy Fields
Pongpattanasiri SUKTHAI*, Choichi SASAKI*, Nobuhiko MATUYAMA*,
Kaori NODA** and Akio TONOUTI** Faculty of Agriculture and Life Science, Hirosaki University,- Bunkyo-cho, Hirosaki-shi, Aomori *-0ῌ2/0+, Japan** Faculty of Science and Thechnology, Hirosaki University,- Bunkyo-cho, Hirosaki-shi, Aomori *-0ῌ2/0+, Japan
Abstract
We investigated the inﬂuence of the percolation pattern on the removal of soluble elements and rice
plant under inundation during the cultivation with models of strati-ﬁed layers of cadmium polluted
paddy ﬁelds. At that models, plow layer and plowsole consisted of cadmium polluted soil but gravel
ﬁlled subsoil is not polluted. These models had di#erent percolation pattern in the plowsole andsubsoil. In the closed system model, every layer had water ﬂow in a closed system while the open
system model had water ﬂow in an open system in plosole and subsoil over the groundwater.
The following results were obtained. At low groundwater levels, plow sole and subsoil overthe groundwater had water ﬂow an open system and hence oxidized layers.

On the contrary, athigh groundwater level, every layer had water ﬂow in a closed system and hence reduced layers.
The electrical conductivity values of water ﬂow in a closed system were larger than those inwater ﬂow in an open system.

In the same way, concentrations of iron, calcium and manganese

in water ﬂow in a closed system became larger than those in water ﬂow in an open system.

Plantheight, number of stems and dry matter weight of rice plants under the closed system model arelarger than those of open system model. But no signiﬁcant di#erence is recognizedwhile considering leaf age and heading. The total weight of grains and ﬁlled grain ratio of rice plants underclosed system treatment were better than those in open system.
plants under both the models were about 0* cm.

The root elongation depth ofCadmium concentration in the brown rice ofplants grown under open system models are about ten times higher than that of plants grownunder closed system.
The above results made it clear that under inundation conditions during the cultivation period,
the removal of the soluble elements, concentration of cadmium in brownrice, growth and yield ofrice plant were a#ected by the percolation patterns.
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Key words : Model of polluted paddy ﬁeld with cadmium, Growth and yield of rice plant,
Concentration of cadmium in the brown rice, percolation pattern+ <- j   S ῌ 
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Zhu (,**-) : Interaction of Cd and ﬁve mineral
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gh]"AV Zv ¡¢+ £¤+ ¥@¦+ §¨¦no"©ª«U+ gh][¬'^AV+gh]"" ^"­®¯CZv L"°±²³U 0* cm 9´Zv §¨j"U+ gh][µ' ^"U+ ] gh" ^ " +* ¶(CZv·¸¹ºJ : ,**/ ¹ / º , J·¹ºJ : ,**/ ¹ 0 º ,0 J
J. Jpn. Soc. Soil Phys.
+
No. +*+, p. ,1 -/ ,**/



 *ῌ**ῌ*Development of Automated Suction Controlled Flux Sampler for
Unsaturated Sandy Soil
Naoko HIGASHI*, Yasushi MORI** and Mitsuhiro INOUE** Arid Land Research Center, Tottori University, +-3* Hamasaka, Tottori 02*ῌ***+, Japan** Faculty of Life and Environmental Science, Shimane University,+*0* Nishikawatsu, Matsue 03*ῌ2/*., Japan
Abstract
A sandy ﬁeld has the potential hazard of nitrate contamination because of its low fertilizer
holding capacity. A suction controlled ﬂux sampler (SCFS) consisting of an automated vacuum
system and a sampling ﬁlter device has been developed for accurate measurement of water ﬂux
from the root zone.

Knowing that water content in sandy ﬁeld was highly sensitive to suctionchange, a bu#er container was placed between the pump and a sampling bottle to apply moderate
suction and avoid accidental over-sucking.

A sampling device with a glass ﬁlter was placed in adune sand column and inﬁltration experiments were conducted.

A moderate suction was ac-

hieved and the resulting water-collecting e$ciency was from 3. to +*3῍ under continuous
rainfall. It showed that SCFS collected inﬁltrated water e#ectively without disturbing theinﬁltration streamline.
Key words : dune sand, suction control, unsaturated soil, water-collecting e$ciency.

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rpKTCK( wῌ5wQx=_`a10yGHU¬&­bc.d+f+gh0a_,|c~bMj6Czg{|clm+.na} +*῍+i,0 Suction Controlled Flux Sampler ; ®¯

&7WYbc.d+/e$.~m8

SCFS °V±±ῌ+ ¥ N9 ,*** :TK;;<3<C$WXqK(°Y ;<K( C=tD\N>van Grinsven et al.

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/e$[=

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bc.d+f+gh0a_,|c~b+i,0Fig. +

SCFS °V±

Schematic of the suction controlled ﬂux sampler (SCFS).

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

P1;Q:(<]k¹ºSpeciﬁcation of the glass ﬁlter

Filter No.
Diameter (cm)Thickness (cm)Pore size (mm)Air entry value (cm)Saturated hydraulicconductivity (cm s +)

G.
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Fig. ,

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 E1$\abF+/*%d&eC H
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 -9:.%d 4qs5 f»a-ºFig. -

Schematic of the soil column experimental
set up. Upper part of the column indicatesthe area of the qs for WCE estimation.

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PVC N1 *.2/ mm

 4qi5, @27 +* mm h + F2[\b:®¯ Run-+ 7 qi°, mm h +,- 

m +*/ cm

U.(*I12_­ ` N
Ra9B

 ,* cm

F1G,



ST1±

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AVS h  !"+/*7 +/ cm 1« 

o:p:H? +.// Mg m - F2[\I

 Run-, ³[ Run-- 7 E´E q i °, mm <nA&e=N J 4K +*/ cm5 9B

h + +* mm h +K 1* cm n7L: 1* cm R7L

AVS 1[AGµ¶/· SCFS





!"+/*
3¸¹"

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/* cm



  





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31

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8

 SCFS )7

9 :Water-Collecting Efficiency ; 7;

WCE< )=>?@ # AB C'ῌ

DEF" Run G:+Run  +, HI< JC' Qr :cm-< )K3LMN Run HI&O C'
345 qr :cm hP+<

Q# A SCFS RJ Qe :cm-< ) 

Run HI&hLR Mt ,./ cm &qc L !"#  & ,* mm hP+
i?(Q:;) :hCPhLR<a* cm/>

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?=R+"U#ZR K3L  *[/* cm  :$῎- \%&'%
M](^HI !#Z qs :cm hP+< )<JS # > qs )_) *+ SCFS  WCE ) ῌ `WCE:῍<a+**bqeῌ:qrPqs<(+)

WCE c +**῍ +,H-.c SFD )/]8 0X+cd"!" _eR+ f+**῍ 7\gh SFD 1ijRU)2!

k A _eR+# "M K3L3%RJ4) Qd :cm-<

 ' 5QMN

4lh) K3L 67 !8m)nQ :Change of Water Storage in the column ; 7;
7 ῍ ` ?JS  o_'p

# CWS c +**῍ +,&q+rK3L

67

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d />"#/  cR" A8# >+R> R
hLR )6!

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_ez

-

(,)

-+, '()*+,- .,-/01¢RSc 1** cm (q8"]§¨)©^

gh&(

 -,/** cm- ª4«) +/ _vwQ>&` 2*[-** cm )D¬ >+ )aC Iab )]>c® "# $῎/

? cd"­e<{ ¢ -** cm q

/¢f 2* cm &1¯&1)ncm 

1/B+

aC

#  -**&(°"vwe)n 
cM1!" °"

)g±&1"# /* cm A&ij _e ª4«-+  !

c 2* cm gh&(®" /* cm ck³-++ "#$%&X+

>+A&  vw:;) :hCPhLR<ax*./ cm )l  $῎/ RER"8Q

0-* MN +,/** cm-

hLR c6!

 ! 

M1/cW/>  ¦?

´/ +,/** cm- "8 <{Qy :|= ,***< c>}X+/# /B+gh( :hCPhLR< a* c?~&q>  HYDRUS-,D

ER "#Uh². :$῎,< R ®\ y :Inoue and Dirksen, ,***< z hC

J%c \ ¦?X+ghcq> cc 2* cm HCWS:῍<a+**b:QeuQd<ῌQr

c@A&q#c

Q/c ¤@.A4;[.¥\ HI

?=#CWS<"#S / (RB / A&(TUcS">+RU

VWX+

0&?~

 K3L&; 8"C'& ( vw

O 345 qe :cm hP+< )JSQ# T
!

/8N

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 $῎.῎a 8  BCC'& hC
T;)D?~ "? :hCPhLR<a*

hLR

"R"

µX(_) :Y&1# ¦¢m :Y # A 


c

ª4«

aCHI +* _I&¶&q> )·n #-+- '()*+,-.,-2345
AVS¸n)Xe¹ º ¨»3L$῎yz¶·} ¸ +*+ ¹ !,**/&

32

ῐῌ.

Fig. .

HYDRUS-,D  )*+,-. /* cm j.
a : SFD E$ A-¡¢+q£¤b : ¥¦§ZjyzZ{{¨¤c : ,* mm h+ ©_ª«VyzZ{{¨¤Results of the calculation by HYDRUS-,D with /* cm constant suction at the ﬁlter.
a : Changes of the matric potential inside and outside of the SFD.
b : Soil water content under free drainage.
c : Soil water content under continuous rainfall with ,* mm h-+)*+,-./01

23

V+

Count+

 ++/ 04 +-/   567 +* % 8  9)*+/:;<=23

V,@A)BCDE/F%=#$ !H῏0 (


+* %

0

8> 6?

V- /8G="Count+  ,**I,-* +/ %& (JK

LMN(OP? AVS (QRSTSUPV

WXYZ[R/23  \],-. 2*
I-** cm @A)BCD +,/** cm- [ZCD/
+* %

^_=

'

`abcd[Zef? ῌ @A)BCDghi: K ῍ [ZCD: K^_j  ῎ klmn/F%8>0
ῐῌ/Fig. /¬­,-. 2* cm !®&  -** cm !¯& /°?@A)BCD ± C²[ZCD/ +* % ^_P?³´µ,-.
Maximum suction in di#erent sampling bottles connected with the bu#er container.

"#$o - p/qrKs '7 K6
t6uv/w7x=' (yzZ{|}~ ( i4>`a[Z P
4 STS ]= bc>[Z(?'04 uv/q '(yz
 AVS /Ks '  4

0 

Flag,

ON 



 Count,!+ "#$ *./ %&  


.**

''(

-ῌ,

SCFS ῍῏ῑ῎ῒEyz"fMN SCFS [Z/H῏1 xP? WCE /῏, = Run-+ (qi, mm h+ : NOIJKLMPQ0 c@AV

ῌῌ0Fig. 0

ῌῌ1

AVS 0\]PQ^_`

Time schedule for the suction control by the AVS.

abc SCFS 0@AVdea : fghijkMKlm)(niEopqrJskMKt'uvw
b : Vxyz{Vwc : V|}~r%)|} IJKLMuvw

Fig. 1

33

Inﬁltration water sampling by SCFS under continuous rainfall.
a : Matric potential for suction control.
b : Sampling intensity and cumulative amount of sampled water.
c : Suction in the sampling bottle and the bu#er container.

 */* cm 
- q*.--*.*- m m- CWS !

++.ῌ "#$ %&'()*+,,-."

/0 hC  hLR 1234!56789:;ῌ
1ῌ+ῌa<$ WCE ! /0./ῌ " :=ῌ,<WCE >?

!$ @A%&'()BCD E6FG7
8 /8 AVS BH IJKLMBNOPQE$
RSBT?UVBWXYZ["0Run-, !$ CWS  +++ῌ$ */* cm 

! q*.+3*.*, m- m- #$ WCE ! 3-.0ῌMTbu v +*+ ¼ ,**/

34ΐῌ,Table ,&¹º» SCFS G

j2* ῌ1ῌ+ῌb  * Run-, - 3++

Water-collecting e$ciency under various
rainfall conditions

Runqi (mm hF+)
Qr (cm-)Qd (cm-)Qe (cm-)CWS (ῌ)qs (cm hF+)
qr (cm hF+)
qe (cm hF+)
Standard deviation(mm hF+)*WCE (ῌ)

0 G

-

 4i:5T4.i  ῌ1ῌ,ῌb 1ῌ-ῌb k/Glmi mn6* 7o\]7p2q3r

+

,

-

,
1/-40
10*40
314/
++-43
*4*+1
*4,
*4+*.

,
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+2-41
+++
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+*
-1024*,,-142+*-+4*
2042
F*4**2
+4*
+4*3.

---

*413

,4*1

/04/

3-40

+*24/

Z%./8 sX@A78pt
Run-, <u Run-- 29:

 2qZ%avf/i K; <=* TDR w($#>2?0X@A *H/* cm K
 @A;x/y5* /2qZ%G

BzC:D{* ῌ, Run-, Run-- EGlmi4i /4

|}~1.-4pt  02 . hC  ῌ
1ῌ,ῌa 1ῌ-ῌa* Standard deviation of sampling intensity (mmhF+) under steady state condition.

D2/



 !"#$%&'()

D2/

 Run-, - +F. AVS G-G)D2T+G

 lmi. G ++y64< !"#$%&'()+,y5f./ ῌ, 
Run-+  Run-, i WCE  AVS .ῌ ῍ ῐ ῏ ῎ !"#$%&'()*+,-.
Run-,  WCE  +**ῌ  /0 0

 !"# 1.23
/564. 78

 4 *hC  hL 9 hR  / cm$%&'(01G f./H*\]M< E3

G ++G d(IJ * k, G 02? hCFhLR :2 ;*< ῌ1ῌ,ῌa =2Q0>?@AB<C)D4./E* MN/ O78pt\    , mm hF+

;*  ῌ1ῌ,ῌb G
AVS



 *H. mm hF+

* G

I$%&'()64 J$%&'( -// cm KL M2f./

_#IM1./  !"# 01.$%&'(PQi./ /4,6G

IJ SCFS \]M 3.H+*3ῌ G++./30 SCFS 9w($#

cm  ῌ1ῌ,ῌc
Run--  *H/* cm KLM  qN*.,,
O*.*, m- mF-  AVS R*ST]E3 "(?D!"#$%&'(2TU./,Vi M9W J ,1 cm )* ῌ1ῌ-ῌc WCE  Run-- Xi/fY Z[-\Jfo9 ++-+*2./ῌ P ῌ,  Run--  Run-, ]^_`<uabEV f.o^¡* WCE  +**ῌ - Q0.
"#R03
 +* mm hF+!

 PST/564* G\]7pcU .G 78D 7o

 *H+/ mm hF+ ;* ῌ1ῌ-ῌb < Run-- P 78UVJW X@A!"#$ YZ%
T CWS  +**ῌ.&¢£A.-. ¤W SCFS E3 ]df.ῒῑ[0 ῌ, 

 !"#e2 *f¥4¦g¦"hi§j

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G ++ Run-, - +**ῌ YP7h*.

,-./i.01*
AVS )D0 Run-+<Gm  C. Dirksen n±oa64 ²p* O¬­³¦¬­qr¡´ s¬­
B ; +0-2*+/3 <u ,+ tµ COE =>?@Ar¡~1/,. ¶*·¸f.

q1 : j¦§>d#m#$%( oZM-NPQab S0#XY<=@' ";/ /-0 : ,ῌ3.

ῌ ῐ ῏ ῍ῌῌ

Afῌ

ῌ ,**- : 
!"#$
-

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561 0,ῌ0-.
:!ῌῌBghC ,**- : *ijkl-#m(noM-N PQpD

,**, : p. ,- pp. .,ῌ..  35&' +/ ()/0156*<= --.ῌ--/.
62;oN01

,**+ : qNM-ῌ;oNEF pp.

/*ῌ/1 Grst IuH ,*** : ;oN vwxIb/Jy p. ,/
pp. 00ῌ2, z{71"|1 

ῌ789ῌ:!ῌ ,**. : 

()"#$%;‘imu
S ‡nek, J., Sejna, M. and van Genuchten, M. Th.

(+333) : The HYDRUS-,D software package for &' +0 ()/0156*<= -10ῌ-11.

simulating the two-dimensional movement ofInoue, M. and Dirksen, C. (,***) : An Automaticallywater, heat, and multiple solutes in variably-

operated soil water ﬂux meter of improved de-saturated media. Version ,.*. IGWMC-TPS-/-, In-

sign &' +, ()/0156*<= 0-0ῌ

ternational Ground Water Modeling Center, Colorado School of Mines, Golden, Colorado.

0-2.

0
GH'

=>?1 +332 : +@ABCD

EF

0' pp. 32ῌ33 /01 K}~Lῌ9 ,**. : M-N)@OP;

vwM<=N

j"#XYQR<=

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
IJK, ,*** : #$%

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QVῌW ,**. : Modelling variably.PQR/ S0 N1ῌNTU01V +- 0 :LM-N

saturated ﬂow with HYDRUS-,D Japanesetranslation HYDRUS-,D #m #$%X

.0,ῌ.1+.
Kosugi, K. and Katsuyama, M. (,**.) : Controlledsuction period lysimeter for measuring verticalwater ﬂux and convective chemical ﬂuxes. Soil
Sci. Soc. Am. J.,02 : -1+ῌ-2,.

1 HYDRUS ,
van Grinsven, J. J.M., Booltink, H.W.G., Dirksen, C.,van Breemen, N., Bongers, N. and Waringa, N.

W2 3 +33- : ()#XY4Z5[ \]
62()01V .* , : 11ῌ2*.
7^_ῌ`  pp. +.+ῌ+./- /015G%&(+322) : Automated in situ measurement of unsaturated soil water ﬂux.Soil Sci. Soc. Am. J., /, :8ῌ9:& ,**- : ";#XY+,+/ῌ+,+2.

<= abc >d - '"; M-e?

ῑ῎

ῌ;oN xIe? Y E# @ oZM-N NSXmN #[ \* *+,- ] ^_ b  oZM-NS X` . bAC
PQab  TU c kj¡¢£(#¤¥E *+,-j¦§ >d¦k¨©

ªd« G¬k*+,-#Ej¦§e«­@®i*¯f°@±gh#j¦§ @Yb ²@Aj¦§i"NjSkCi"
(#X£HoZM-N pDd£PN³lbA« ´mµ©!¶nonq· PN
Ml p¸G 3.¹+*3῍¢£PNpDPN³lAab S0 b
º»(¼6 : ,**/ ( , ¼ ,2 6ºG(¼6 : ,**/ ( 1 ¼ +, 6῔
J. Jpn. Soc. Soil Phys.
MN`a"b
No. +*+, p. -1῍/* ῎,**/῏

 *ῌ**ῌPer Moldrup***ῌ  ****ῌ *****

Development and Tests of Predictive Soil-Gas Di#usivity Models
for Japanese Undisturbed Soils
Ken KAWAMOTO*, Toshiko KOMATSU**, Per MOLDRUP***, Seiko YOSHIKAWA****and Tomonori FUJIKAWA****** Faculty of Engineering, Saitama University, ,// Shimo-okubo, Sakura-ku,
Saitama --2ῌ2/1*, Japan** Graduate School of Science and Engineering, Saitama University, ,// Shimo-okubo,
Sakura-ku, Saitama --2ῌ2/1*, Japan*** Department of Life Sciences, Section for Environmental Engineering, Aalborg University,
Sohngaardsholmsvej /1, DK-3*** Aalborg, Denmark**** Department of Hilly Land Agriculture, National Agricultural Research Center
for Western Region, ,/1/ Ikano, Zentsuji, Kagawa 10/ῌ**/***** Department of Regional Resources, National Institute for Rural Engineering,,ῌ+ῌ0 Kannondai, Tsukuba-shi, Ibaraki, -*/ῌ20*3, Japan
Abstract
Accurate description of gas di#usivity in undisturbed soil is required for predicting oxygen
transport in cultivated soil and the fate of greenhouse gases and volatile organic chemicals.
Based on measured data for /+ undisturbed soils, we developed three types of pedotransfer models
for soil-gas di#usivity : (i) a model including the e#ect of pore-size distribution (Campbell typesoil-water characteristic, SWC) ; (ii) a model including the e#ect of pore-size distribution andinactive (isolated) air-ﬁlled pore space ; and (iii) a simple power function model for use in caselimited SWC data are available. The inﬂuence of selecting the reference air-ﬁlled porosity ateither +** and 0- cm of matric potentials (e+** and e0-) on predicting soil-gas di#usivities was
also examined. The new models were compared with recent predictive models such as the Millington-Quirk (MQ) model, the Buckingham-Burdine-Campbell (BBC) model, and Macroporositydependent (MPD) model.
The widely-used MQ model generally underpredicted data. The new models as well as the BBCmodel and MPD model well predicted the measured soil-gas di#usivities, with the BBC model
performing slightly better.

There was no signiﬁcant e#ect of including an inactive pore spaceterm on predicted soil-gas di#usivities. In the new models, there was a tendency that theequations using e+** as a reference point gave a better prediction of soil-gas di#usivities comparedto the equations using e0-.
Key words : soil-gas di#usivity, air-ﬁlled porosity, pore-size distribution, undisturbed soil
*  --2ῌ2/1*  ,//** !"#$% --2ῌ2/1*  ,//*** &'()*+%% &'(), -./)0**** 12345467#$8.9) 54#$8.9) 10/ῌ**/- :;<=*>? ,/1/***** 67#$@ ABCD -*/ῌ20*3 EFGHIJKL ,ῌ+ῌ0ῐῌῒῌῑ : MNOPQRST, UVW, XYZ[\, ]^_MNΐ"/

38(Ev, &*.1*.2 cm- cm- FG) F!G+ῌ ῏ ῍ ῐ ῎



! * NmHIJd6=(1 


o +*+ ¼ &,**/) !"# $%

&' +31, ;  +33. ; ( ,**-)* +( ,Ev,  Y3IijkF+X!
#/m Y3+#-!#./0(12345
6789:

;(< &Osozawa

HIJF=@ @ FJ^$K U^(1*

HIJ@ F|/+  r<HIJ
hT=(1MT &MPD HIJ Dp+**ῌD*and Hasegawa, +33/ ; Hillel, +332 ; Kruse et al., +330)

! e+**) FY3R IZ4F=# GN!

=!> !?3@"A# B

U!9!1* +($HIJ &Jury et al., +33* ; Petersen et al., +330 ; El- Y3!W2v"/ &L

Farhan et al., +332 ; Poulsen, et al., +333 ; Gamst et al.,

MNO(v,) 6FP N1(U,**-) C D%&EF:G*

HIJ  K'  Dp F()
 D* L*+ Dp ῌ D* !*, e M!#-+

6mF G;FsQGN! D%!^(1*
N8¡¢  Y3

F

g Y3R IZ4F=#r<

 &Penman, +3.* ; Millington and Quirk, +30+ ;V* # N1(HIJ!r<HIJF=#>!R

Moldrup et al., +333 ; Moldrup et al., ,***)* N1(HIJ(. W2F+X!#1V+1C

HIJF  - 4£¤

1 N1OPQ;RST./0TU1V+1#

>!@

,ῌ ῑ

\    U ] 4   * 5 ^ _ Buckingham-

Burdine-Campbell HIJ &BBC HIJ Moldrup etal., +333)  Macroporosity-dependent HIJ &MPD

HIJ Moldrup et al., ,***)

 `ZabcR

IZ4F[d6+1

HIJ &HIJ

ef gh)*

ῒ   Y3 + R 0 ¦m§. ¨Sl9F= &- +)* l9§.  T F)H U  N VW X+ *῍+*2 cm -Y;(¥"* l9Z/+  ijkU -1 l9

©:U 3 l9 o:; U / l9* l9 [Moldrup et al. &,**-)

mno:;

Fst AzF¥"

* Y3R IZ4F[1V+1HI
J

HIJF1

 78ijk +2 l9 . l9R

IZ4+# BBC H

IJ! MPD HIJFpqr<

HIJF=

ª /.* cm «+ /.+ cm \] +** cm-  5¬ ^­®¯5¤°Z§.*  - + l9R
IZ4± l9 No. 0῍+* -2῍-3 .,_` &+332)

R >!@ Fst* N) BBC HIJl9 No. +0῍+3

MPD HIJ  Penman &+3.*) HIJ Millington²=* O l9 No. +῍/ ++῍+/ -,῍-1 .*῍.+

and Quirk &+30+) HIJ &MQ HIJ) !?u#

..

>!R >vw@@ F!GC N1(HIJ R >FxyAzG{|U

Osozawa and Hasegawa &+33/) ;(Moldrup et al. &,**-) l9 No. ./῍/+rup et al. &,**.) )

Mold-

HIJst=

(1#*

N!F}* B( N~!# MPD HIJ

³l9ab;(cNxFN@d ´eFhT)1# Dp+** ῌ D * ! e+** MTµ²f!¶·fg¸@m  &)h(&e+** :  bk5J y+** cm &pF,.*)+33/)* # N@d ´emv@iF-]G*, Dp+**ῌD* : C pF *+

"/c°Z4 Campbell jN b F¹

) U`ZabcF[1V+1T N1U78 Dp+**ῌD* R IZ4FxyAz
G!D*O BBC HIJ MQ HIJhT)

E

* NN b

Campbell N@d HIJ &Camp-bell, +31.)yῌye&qῌqs)bῌ

v,UpO1* N1(HIJd6ῌst ῌ TklFm=+-} pF &=(1  Ev,*..*.0 cm- cm- FG

log &y)) log q M{!#¹O* ºaZ U)H 78ijkmῌ T y bk5J &cm) ye»n! : " #$% &'()*+ ,ῌῌ+ 
Table +

No.

39  -1  3  /

Soil materials for measuring soil-gas di#usivities (-1 Andosols, 3 Yellow soils, and / Gray
Lowland soils).

Site

Soil*

Layer

Depth

ParticledensityBulk
densityLabeled soil namein the reference

Plowed soil
Plow pan
Subsurface soil
Surface soil
Subsoil
Plowed soil
Plow pan
Subsurface soil
Plowed soil
Plow pan

cm
*ῌ/
,*ῌ,/
..ῌ.3
,/ῌ-*
10ῌ2+
*ῌ,*
,*ῌ.*
.*ῌ0*
*ῌ+0
+0ῌ,+

Mg m,4.1
,4.0
,4.+
,4-3
,42,
,4/1
,4/1
,4//
,4/0
,4/0

Mg m*4/1*41*40+
*4.*
*403
*4/1
*410
*41,
*40*411

Tsumagoi - (Moldrup et al., ,**-)
Tsumagoi + (Moldrup et al., ,**-)
Tsumagoi , (Moldrup et al., ,**-)
Tsumagoi 0 (Moldrup et al., ,**-)
Tsumagoi 1 (Moldrup et al., ,**-) (Osozawa, +332)
 (Osozawa, +332)
 (Osozawa, +332)
 (Osozawa, +332)
 (Osozawa, +332)

Plowed soil
Plowed soil
Subsurface soil
Plowed soil
Plow pan

*ῌ/
-*ῌ-/
/*ῌ//
*ῌ/
-*ῌ-/

,4/+
,4/*
,402
,400
,4/,

*413
*41+
*4.3
*401
*40,

Miura + (Moldrup et al., ,**-)
Miura , (Moldrup et al., ,**-)
Miura - (Moldrup et al., ,**-)
Miura . (Moldrup et al., ,**-)
Miura / (Moldrup et al., ,**-)+ Gunma, (Tsumagoi)
.
/
0
1
2
3
+*

Andosol, H(Cultivated)++ Kanagawa+, (Miura)++.
+/

Andosol, H(Cultivated)+0 Ibaraki+1 (Tsukuba)+2+3

Andosol, H(Cultivated)

Plowed soil
Plow pan
Subsurface soil
Subsurface soil

*ῌ,*
,*ῌ-1
-1ῌ13
13ῌ+*2

,4/1
,4,2
,41/
,41/

*41/
*41+
*4//
*4/1

Ap + (Osozawa & Hasegawa, +33/)
Ap , (Osozawa & Hasegawa, +33/),B+ (Osozawa & Hasegawa, +33/)-B,+ (Osozawa & Hasegawa, +33/),* Tokyo,+ (Nishi,, Tokyo)
,,.
,/
,0
,1
,2
,3
-*
-+

Andosol(Cultivated)

Plowed soil
Plowed soil
Plowed soil
Subsurface soil
Subsurface soil
Subsurface soil
Plowed soil
Plowed soil
Plowed soil
Surface soil
Surface soil
Surface soil

/ῌ+*
/ῌ+*
/ῌ+*
./ῌ/*
./ῌ/*
./ῌ/*
+*ῌ+/
+*ῌ+/
+*ῌ+/
/ῌ+*
/ῌ+*
/ῌ+*

,40+
,40+
,40+
,402
,402
,402
,41,40,400
,40+
,4/0
,40*

*411
*413
*42*
*4/+
*4/,
*40*
*401
*40,
*40,
*42.
*42*
*410














-, Kumamoto
--.
-/
-0
-1
-2
-3
.*
.+
.,
.-

Andosol, H(Cultivated)

Plowed soil
Plowed soil
Plowed soil
Plowed soil
Plowed soil
Plowed soil
Plowed soil
Subsurface soil
Plowed soil
Plow pan
Gley horizon
Buried humic soil

.ῌ3
,/ῌ-*
./ῌ/*
-ῌ2
+1ῌ,,
./ῌ/*
-ῌ2
+/ῌ,*
/ῌ+*
,,ῌ,1
1-ῌ12
12ῌ2-

,4./
,4/3
,40,
,4/,4/2
,4/2
,403
,413
,402
,402
,401
,4.,

*41.
*4/0
*4/,
*40+
*42+
*41/
+4-+4/2
+4*1
+4-1
*43/
*4-,

Kyushu + (Moldrup et al., ,**-)
Kyushu , (Moldrup et al., ,**-)
Kyushu - (Moldrup et al., ,**-)
Kyushu . (Moldrup et al., ,**-)
Kyushu / (Moldrup et al., ,**-)
Kyushu 0 (Moldrup et al., ,**-) (Osozawa, +332)
 (Osozawa, +332)
KyuGL + (Moldrup et al., ,**-)
KyuGL , (Moldrup et al., ,**-) (Osozawa, +332)
KyuGL - (Moldrup et al., ,**-).. Saitama(Kounosu)

Gray Lowland soil
(Paddy ﬁeld)

Plowed soil

*ῌ/

,403

+4*/

KounosuGL (Moldrup et al., ,**-)./ Aichi.0 (Toyohashi)
.1
.2
.3
/*
/+

Yellow soil
(Cultivated)

Plowed soil
Plowed soil
Plowed soil
Plowed soil
Plowed soil
Subsurface soil
Subsurface soil

*ῌ+2
+2ῌ-0
-0ῌ1*
*ῌ++-ῌ,*
,*ῌ,1
,1ῌ0*

,400
,400
,400
,40.
,400
,402
,40+

+4,.
+4/,
+4-1
+4+1
+4./
+4./
+4-2

Yellow + (Moldrup et al., ,**.)
Yellow , (Moldrup et al., ,**.)
Yellow - (Moldrup et al., ,**.)
Yellow . (Moldrup et al., ,**.)
Yellow / (Moldrup et al., ,**.)
Yellow 0 (Moldrup et al., ,**.)
Yellow 1 (Moldrup et al., ,**.)

Andosol, H(Non-cultivated)
Andosol(Cultivated)
Andosol(Cultivated)

Andosol(Cultivated)

Andosol(Cultivated)
Andosol(Pasture)

Andosol, H(Cultivated)
Yellow soil
(Cultivated)
Gray Lowland soil
(Cultivated)

Yellow soil
(Cultivated)* Hhighly humic soil.

6A»«'  +*+ ¼ ,**/40 cm

 m- m-qqs

 m- m- ῏

 +  pF log y
!"#$
2 b

%&'()

log q ῌ *+,- ῌ ./0"13456 ..1῏.*.2 786 1..῏,3.* 98:;6 +-./῏,2< - =>?

@ , - 
6ABCDEF

GHῌIJK +321= Rols-ton and Moldrup ,**, L* MN$OP#$  QRSTUV=῍W DEXYZ[BC\ῌ ]^_`ab=Z[BCcdDEef
 abgh]^_`DEXYijDE`0k
[lmnopqrs t` #$ouvῌw
xyz{|DE}~. Fick  , P k[lmnopq` s=gh 6ABC
DEF Dp cm, s+ $ 

+*

-

y+* -, 0- +** -+0 +.**-.+0+*- +./2+*. cm  2  pF+.*+./ +.2 ,.* ,./ -.* -./ .., %? ]^*` Dp #$?  

Dp abk[

DEF D*  c6ABCDEF DpῌD* rs bc e F=`@ 
 , ]^gh, #Ve-    

Dp ῌ D * = e 

DpῌD*e+.0  DpῌD*

3456#V 786=98:;6¡¢`£*bc¤¥%¦ . 
.+ 



c6ABCDEF DpῌD* §#¨©.

@ªe, Penman ¨ Penman, +3.*

«῎.

@ªe, Millington and Quirk ¨ MQ ¨ Millington and Quirk, +30+

ῌ+

pF log Y= log q ) Campbell +31. %&'()¨gV"1 b ¨F r cF

Fig. +

Relationship between pF (log (Y))and log q.
Solid lines are the Campbell’s soil water
characteristic model (+31.) ﬁtted todata. Values of model parameter Campbell b and correlation coe$cients r foreach soil are given.

¬«῎.@ªe, Buckingham-Burdine-Campbell ¨ BBC ¨ Moldrup et al., +333

Macroporosity-dependent¨ MPD ¨ Moldrup et al., ,*** >­®,¯°e,`*
MQ ¨ ±² F m- m- *`M.@e, :DpῌD*e+*ῌ-ῌF,
BBC ¨

῍

6ABCDEF§#¨ + ³

 Buckingham +3*.

¨ DpῌD*F,=

Burdine +3/- ῏Campbell +31. ´῏µF¨ Moldrup et al., +33, ¶·¸¹f ¨M.@e, :DpῌD*F,eῌF ,º-ῌb῎ :  !"#41

ῌῌ, 
Table ,
No.

Site

Soil physical parameters for soil materials.

Soil*
Andosol, H (Cultivated)

Depth

Total porosity F

e+**

e0-

Campbell b

*ῌ/
,*ῌ,/
..ῌ.3
,/ῌ-*
10ῌ2+
*ῌ,*
,*ῌ.*
.*ῌ0*
*ῌ+0
+0ῌ-/

m- m *411*41+*41/*42*410
*412
*41+
*41,
*41/
*41*

m- m *4-.
*4*2
*4*0
*4,2
*4+1
*4-/
*4+1
*4+*4-0*4+1

m- m *4-,
*4*2
*4*/
*4,0
*4+1
*4-.
*4+/
*4+,
*4-.
*4+.

24/
+24/
+-43
+*42
-.41
34,
+,41
+14141
+04-

*ῌ/
-*ῌ-/
/*ῌ//
*ῌ/
-*ῌ-/

*403
*41,
*42,
*41/
*41/

*4,,
*4,1
*4,*4-,
*4,2

*4+*
*4+2
*4+2
*4,*4,,

34.
141
+/4+
3434-

*ῌ,*
,*ῌ-1
-1ῌ13
13ῌ+*2

*41+
*403
*42*
*413

*4,3
*4,*
*4+0
*4+/

*4,1
*4+0
*4+*4+-

2434*
,-41
+14-

/ῌ+*
/ῌ+*
/ῌ+*
./ῌ/*
./ῌ/*
./ῌ/*
+*ῌ+/
+*ῌ+/
+*ῌ+/
/ῌ+*
/ῌ+*
/ῌ+*

*41+
*41*
*403
*42+
*42+
*412
*41/
*410
*411
*402
*403
*41+

*4++
*4+.
*4+.
*4,*
*4+3
*4,.
*4-+
*4-.
*4-0
*4+,
*4+.
*4+3

NM**
NM**
NM**
NM**
NM**
NM**
*4,3
*4-,
*4-.
*4+*
*4+,
*4+1

+*4+
+-4.
++42
+,4+.4*
+*4+
140
14,
.41
+042
+04,
+,4*

.ῌ3
,/ῌ-*
./ῌ/*
-ῌ2
+1ῌ,,
./ῌ/*
-ῌ2
+/ῌ,*
/ῌ+*
,,ῌ,1
1-ῌ12
12ῌ2-

*41*
*412
*42*
*410
*403
*41+
*4/*
*4.*40*
*4.3
*40.
*421

*4+.
*4*3
*4+*
*4-1
*4,*
*4,*
*4*2
*4*1
*4-*4+*
*4*3
*4*1

NM**
NM**
NM**
NM**
NM**
NM**
NM**
NM**
NM**
NM**
NM**
NM**

+,41
.*42
,24*
+*4+
+.4.
+,4.
,*4*
,34*
+.41
,*4/
,24,14/

+
,
.
/
0
1
2
3
+*

Gunma
(Tsumagoi)

++
+,
++.
+/

Kanagawa(Miura)

+0
+1
+2
+3

Ibaraki(Tsukuba)

,*
,+
,,
,,.
,/
,0
,1
,2
,3
-*
-+

Tokyo
Andosol (Cultivated)(Nishi Tokyo)

-,
--.
-/
-0
-1
-2
-3
.*
.+
.,
.-

Kumamoto..

Saitama(Kounosu)

Gray Lowland soil
(Paddy ﬁeld)

*ῌ/

*40+

*4,+

NM**

+.4*

./
.0
.1
.2
.3
/*
/+

Aichi
(Toyohashi)

Yellow soil (Cultivated)

*ῌ+2
+2ῌ-0
-0ῌ1*
*ῌ++-ῌ,*
,*ῌ,1
,1ῌ0*

*4/.
*4.*4.3
*4/0
*4.0
*4.0
*4.1

*4-+
*4+/
*4,*
*4-*
*4+3
*4*1
*4+*

*4,3
*4+.
*4+2
*4,2
*4+1
*4*0
*4*3

24*
+.4+,4314.
++4*,-4+.4-

Andosol, H(Non-cultivated)
Andosol (Cultivated)

Andosol (Cultivated)
Andosol, H (Cultivated)

Andosol (Cultivated)
Andosol, H (Cultivated)

Andosol (Cultivated)

Andosol (Pasture)

Andosol, H (Cultivated)

Andosol, H (Cultivated)

Yellow soil (Cultivated)
Gray Lowland soil
(Cultivated)

Yellow soil (Cultivated)* Hhighly humic soil. ** NMnot measured.



42

ῒῌ,
Fig. ,j ² +*+ ³ ,**/DGHIJK DῌD* $CDE e V23 /+ 5~ -0+ ª«¬ ,/3 ­® 03 ¯®°± --Relative soil-gas di#usivity Dp/D* as a function of air-ﬁlled porosity e.
Data for /+ soils and -0+ measurements (,/3 Andosols, 03 Yellow soils, and -- Gray Lowland
soils).

b    !"#$%&' e*, A, B em - 7n_<' opq  rs 45)"#76tuYZP vwE xy &'z{_N ῍ P  , -ῌb

MPD ()*

Campbell +",- +,0 .

/012345)"#6789:;<()*=> y?@+**cm pF?,.* 7AB&CDE e+** m- m@- $F pF 7

e*, A, B |<7}~&$7S> - # 5()* ()*῏ῐ ῑ _<' :U7 6`CDE e* e+** $ y?@0- cm pF?+.2 7AB&CDE e0- m- m@-,

AB&DGHIJK Dp, +**ῌD* LMNOP

>LM<'  y?@0- cm

:;& :_<pq7AMN]^E~&<
7uLMU;NM&*=>  

DpῌD*? Dp+**ῌD* eῌe+** , -ῌb?Q,.** e+** *.*. e+** R eῌe+** , -ῌb Dp, +**ῌD*?,.** e+** -ῌ*.*. e+**rsG $ 45)"

U +32. ; Hasegawa et al., +33.  y?@+** cm 7A
B& e+** $&<7LM<' e*?e+**e * ?e0-()*7 a,()*7 b &$7S>

#S>TU;< Dp, +**ῌD*@e+** VWXPYZ&_<  - '  , 723  j !"# F

$7S>[\&' MPD ()*  ]^E

e0- e+** AS¡ be+** $_ CDE6`CDE

Moldrup et al.,+330 $_N()*7LMNM&' \< ῌ P

emn_<'()*῏-a AS¡῏-b   MPD ()*$Fa7

BBC (45)"#S>TU;< Dp, +**ῌD*@e+** AS¡ Dp, 0-ῌD*)*$Fa7  , -ῌb 7SbN @e0- VWXPYZ&$7S> A [<' ¢'

- a 7 Dp, +**ῌD*@e+** ¢ - b 7 Dp, 0-ῌD*@e0-

cd()*  ef7O ghPijk& :DpῌD*?A eῌe* B e*Vl B

6`CDE AV

n_<' ¢£ ¤¥¦WXPYZ§¥=> ()*.ῌ, ῔ΐ῏῎ῐ῍ῑ῕

ghP ¨©$%& :῍

e?e* 7AB& DpῌD*!"#$%()*῏-a : DpῌD*?Q+.3, e+** - *.*0 e+** R eῌe+** , -ῌb῎

³´ : 2345µ¶¬­·p

ῌ- ²2345
Table -

43

DpῌD*A eῌe*B  e*, A, B

A list of e*, A, and B of model expressions for relative soil-gas di#usivities Dp/D*A(e/e*)B.
e*

A

B

MQ model*BBC model**MPD model***

F
F
e+**

.ῌ-

F
F,
,4**e+** *4*.0e+**+*ῌ,-ῌb,-ῌbModel I-a
Model I-b

e+**
e0-

+43,e+**-*4*0e+**+40/e0--*4*/e0-

,-ῌb
,-ῌb

Model II-a
Model II-b

e+**
e0-

,4-/ e+**A*4*/- *4+- e+**A*4*/
+432 e0-A*4*/- *4++ e0-A*4*/

,-ῌb
,-ῌb

Model III-a
Model III-b

e+**
e0-

+43,e+**-*4*0e+**+40/e0--*4*/e0-

,4,
,4,

* Millington and Quirk (+30+) ** Buckingham-Burdine-Campbell model (Moldrup et al., +333)*** Macroporosity-dependent model (Moldrup et al., ,***)

STV=& :

-b : DpῌD*+.0/e0--*.*/e0- eῌe0-,-ῌbMPD 

BBC 

 ,-ῌb
-a ()*-bD*

 -a : DpῌD*

+.3,e+**-*.*0e+** eῌe+**,., -b : DpῌD*!"#$%&'

+.0/e0--*.*/e0- eῌe0-,.,+ - a b  Dp, +**ῌDp, 0-ῌD* ,-./ * 0&1 *.*/ 2345

MM

{ | f ,.,

k - q  p % L /+ y z 67#0%1 891 :;$ <=>?

Campbell }~ b {|f +..3 )`#

@91 eA*.*/ BC DE FG +H-

L'  -a ()* -b

I JKL' MM

891 *.*/NOPQRKL' ST+ - a b}~ b f #0%MNO ~v
I,O=$%0%yz#$2345

>U0& :

:h&@9 x&=&'-a : DpῌD*,.-/e+**A*.*/-*.+-e+**A*.*/ eῌe+**,-ῌb-b : DpῌD*+.32e0- A*.*/- *.++e0- A*.*/ e ῌ e0-,-ῌb.- 

B



 {|{ Root Mean
Square Error >U RMSE 3 bias p%

L' RMSEyz Campbell



RMSE

-a ()*-b  ,!V=& :ῌ ῐ ῍
ῑ ῎῏ΐ ῐ ῏ῒῌ

-ῌb )K$!"V=&' M WX#L8MM

di91YZ [\N]^ _V=$(` 

RMSE* %f-f,VabDc.de**.+/ fghM,ijV=$%& Troeh et al., +32,' k]^ :;L89
1 *.*/

lmn. Lai et al., +310

!V=& :
bias

&'


-a ()*-b-a ()* -b 

DE FGvI w x&,   ,-ῌb kyz{|f ,., p%L x` >U

: x&'0` ¡¢,£%M¤¥h&' 3o. Blake and Page, +3.2 p%L-qrstuh

f-f n

3

+ ῐ
ῑ di
n ῏ῒῌ



f,¦§ f,-fl¨# ©ª§ f,-flh&'>« k]^¬­-®¯°± FGfg h +*+ i !,**/"

44

῎ῌ-

Fig. -!a" YKL+** cm &2M?F'NOPQRS Dp, +**ῌD* #EF e+** TRUS /+ !VWX -1 YZ 3 [Z\] /"!b" YKL0- cm &2M?F'NOPQRS Dp, 0-ῌD* #EF e0- TRUS -, !VWX ,/ YZ 1"^_9 ῌ-a 2`aῌ-b (_9 ῍-a 2`a῍-b bc4de_(a) Relative soil-gas di#usivity Dp, +**/D* as a function of air-ﬁlled porosity at Y῍ῌ+** cm e+**, /+measurements (-1 Andosols, 3 Yellow soils, and / Gray Lowland soils), and (b) relative soil-gas
di#usivity Dp, 0-/D* as a function of air-ﬁlled porosity at Y῍ῌ0- cm e0-, -, measurements (,/Andosols and 1 Yellow soils).
Dotted and solid lines are polynomial regression curves for Model I-a, I-b and II-a, II-b,
respectively.

 

 -  ! ῌ ῍ ῎" #789 e+** :;<=>?@ /+ AB()&'.> #CDEF: *+MQ   BBC   MPD  $%

&GH?

&' #()*+,-./AB()&'./00 12 $% #3456 *+

9 e+** # e0- IJ:;<=>? -,z{ : |-}~Z 23 qrCyῌ.

x7 
4a5 MQ  4b5 BBC  4c5 MPD  4d5 ῎-a 4e5 ῏-a 4f5 ῐ-a
YZ -1+ 4 ,/3! 03 "!#$ --5

Fig. .

Scatterplot comparison of predicted and measured soil-gas di#usivities for each model.
(a) MQ model, (b) BBC model, (c) MPD model, (d) Model I-a, (e) Model II-a, (f) Model III-a-1+ measurements (,/3 Andosols, 03 Yellow soils, -- Gray Lowland soils)

HI67  BBC  4 . 4b55 8 *.*+.

/ 
/+

45

JKA

BCDELM FNO &  CD

E8ABP 4RMSEQ*.*+.5 8RS()7 01 
TUVWX YZ -1+ [ F\] 1 ^ .    ! "!#$%&'() RMSE*+,-


MQ ./ 0123  4_7 ,/3 8[<W F` RMSE 8 CDEabK cM7d e>fgh +,0 >?ijkl) MPD  4 . 4c5 ῌ m5

 nopqr /+ >?ijkl)῎-

῎-a ῏-a ῐ-a5 BBC  MPD  

a 4 . 4d5 ῍ m5 

%67 RMSE 8 *.*+. 9( *.*,* :;<=

Dp, +**ῌD* 1um 4v -  A5 tB[vwl) s

67 stB>? @ABCDE8<7F 8G97 RMSE RMSE 

67F

x= jky () » +*+ ¼ :,**/<

46

     !"#$%&BCDE%   :p'( )(*+#,
aῑ- MPD -.//01 RMSE %.

 234567#, ¥G
0

ABCD,EFG

9=> 9H0 I>G%J  !%& JK

L> ῑ-a :@ . :d<< , MPD -.A

No. ++῔+/< , + p

9=>J !a  9

9H

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ABCD,2G§ 9=>  9No. ,*῔-+<9H¨

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 :@ . :c<<9,

01 RMSE   BBC -.¤ΐ-a!#,x%=> :@ / :d<<& ? A

IE%J+*<  :p,§!%&  :p:p

No. +0῔+3<

No. +῔

No. -,῔-1< #ABCD©ª>& J  ef >567#, B3G  

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No. .*῔..< , efgh>ῑ-a ῒ-a ΐ-a 3_T`aK%.

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UV

 MPD 

+,0 p



p

[, /+

FGqJ!aer 

O/> sNῑ-a 

3t% Dp, +**ῌD*

fuvwE%x%:e< :f<< ABCD,@ 0  e+**e0-9=>& ¢

567 '(ῐ v< , k{ E|ΐ-a :῏} :ῌ v>GB< /+ p,., & J ,  p@,2p

L>GaK RMSE

ABCD=>&~9Z[ b aKG% -, pL« efgh> 0    9

yz

K%&

9¨#=>&/- 

ῒ-aῒ-b , Dp, +**ῌD* / Dp, 0-ῌD*  ¬­

%k{$ *.*/ WDXY®>k{$ %* >J !a  aKG¯k{$ >Gv :῍ ῎ v< && %¯k

Dp ῌ D * #x%& ΐ-a :@ .

{$   %, ῒ-a:f<<

RMSE , *.*+0

- ῑ-a :@ . :d<ῒ-b :@ 0 :b< :e<<  %¯k{$°'>G





RMSE;*.*+1< /ῒ-a :@ . :e< RMSE;*.*+0<

 89=>& J J !a  
aKG GWDXYῑ-aῑ-b :@ 0 :a< :d<<

E%J -"#$%&±²³´$ e+**µ ῒ-a2LE

E%, B;,., ΐ#x%% RMSE , *.*+0

"#$%&

01¶·G%& >!> ±²³´$ e0-µ ῒ-b /,   p

: +< G RMSE    I>& @ /  
9  >G 0 p*.*+3 FG¤!

2LE% RMSE , *.*+3*.*+2 FG¤!¨$¶·G%& J

J !a efw> -, p G, %¯k{$:567 . p  '( )(*+ + p < Gῑ-b

 ῑ-aDpῌD*e \Z=>&  ¸E,01.

@,  2L>G. /. BBC   efgh>ῑ-a ῒ-a ΐ-a ±²³´$ e+**

=>&

e0-





 %, ῑ-a :@ 0 :a<<B 567

RMSE E%   :pNo. +῔+*< , BBC  ῒ-a k  ,> :@ / :a<<&  :p
No. +0῔+3<:p

9

8 RMSE =

No. ++῔+/<  :p

No. -,῔-1< , ¡K 

o

%&


ῑ-b :@. :d<< ῒ-a :@ . :b<<ῒ-b :@ . :e<<

34ΐ-a :@ . :c<<ΐ-b :@ . :f<< ab ¹º>E%J -"#$%& 2 
RMSE , e+**





¡K
 e0-

3G.
-. 8 RMSE => :@ / :b< :c<<& ¢ !

.01¶  - %J 

£ :p

!%&

No. ,*῔-+< , efgh>ῑ-a ῒ-a¡ : ijkl&"xij¢ ῐῌ/Fig. /

OP'UV.ijkl&"S

Comparison of four predictive models for soil-gas di#usivities with measured data.

e+** 



47



 Dp ῌ D * Dp, +**ῌD* Dp, 0-ῌD* #$%&

!" e0- _T*`a. DpῌD*  !AB 0e+** b Dp ῌ D * [*.*/* e0- b

 Dp ῌ D * ['*.*-3 c , ]d 0Dp ῌ D * [e+.01 "ed()*"+,-./ e+**  0῎-a

0DpῌD*[e-1 _TYZ1 'C "@f'#$?.@"

῏-a ῐ-a1 " e0-  0῎-b ῏-b ῐ-b1 ./

2-3- 0e+** Dp, +**ῌD*1 " 0e0- Dp, 0-ῌD*1 456

gh' ijklmnijFopq9r

"789:;<=>?.@" @-456

ijsts;u 0vwxyFos1 E'z{|-

Dp ῌ D * ij}~'"* klmn*".

"F'!AB'CDE".*"G-./0Moldrup et al., ,**+1/ _T 7ijFo}~

HIJKL()MN7 -, OP e+** " e0- QR '78 ij'UV.klmnS2-3- *.,, *.+3 "T @-JKL'UV}?5a./. DpῌD*  ῎-a "῎-b  0ῌ W ῍
W1 X'78YZ?." 2-3- *.*-. *.*,, "0ῌ ῎ ῍ ῏./ @-S 0e+** Dp, +**ῌD*1 [ 0*.,, *.*-.1 0e0- xij 8 - 

Dp, 0-ῌD*1 [ 0*.+3 *.*,,1  DpῌD*\e ]^." e+**7/ 278 @-"  +*+  ,**/

48

ῐῌ0

%Ba ῌ-a b ῍-a c ῎-a d ,-/ r +13  /0
Fig. 0

῎-b_MM`aMbcRMdeRfgahWXY GdeKLM ,+ ijkdelmdeno

MQ 
MPD ῍-b fScatterplot comparison of predicted and measured soil-gas di#usivities for each model.
(a) Model I-a, (b) Model II-a, (c) Model III-a, (d) Model I-b, (e) Model II-b, (f) Model III-b,-/ measurements (+13 Andosols, /0 Yellow soils)

#ῌ-b e!" BBC 

$%&'()#*+,-

'%./01 2pqrstuvw xx%yz {|}~
2D

$

ῌ ῒ ῑ ῍%34$56 *.*/ 789:;< =>?@

Blake, G.R. and Page, J.B. (+3.2) : Direct measurement

6 e+** A# e0- BC'of gaseous di#usion in soils, Soil Sci. Soc. Am.

()DEF#9:;

Proc., +- : -1῏.+.

῏

῎G HI%JC KLMNMOPQNMRST UVWXY 2 Z[\]%JC ^Buckingham, E. (+3*.) : Contributions to our knowledge of the aeration of soils, U.S.D.A. Bur. Soil
Bull. : ,/.
Burdine, N.T. (+3/-) : Relative permeability calcula-4 : ,-stuvi y 

49

tions from pore size distribution data, Trans.

soil resistance to plant water uptake, Soil Sci.,

AIME : 1+ῌ11.

+/- : 21ῌ3-.

Campbell, G.S. (+31.) : A simple method for determin-

Moldrup, P., Kruse, C.W., Rolston, D.E. and Yama-

ing unsaturated conductivity from moisture re-guchi, T. (+330) : Modeling di#usion and reaction

tention data, Soil Sci., ++1 : -++ῌ-+..

in soils : III. Predicting gas di#usivity from the

El-Farhan, Y.H., Scow, K.M., de Jonge, L.W., Rolston,
D.E. and Moldrup, P. (+332) : Coupling transportand biodegradation of toluene and trichloroeth-

Campbell soil-water retention model, Soil Sci.,+0+ : -00ῌ-1/.
Moldrup, P., Olsen, T., Yamaguchi, T., Schjonning, P.

ylene in unsaturated soils, Water Resour. Res., -.

and Rolston, D.E. (+333) : Modeling di#usion and: .-1ῌ../.

reaction in soils : IX. The Buckingham-Burdine-

Gamst, J., Moldrup, P., Rolston, D.E., Scow, K.M. andKomatsu, T. (,**-) : Comparison of naphthalene

Campbell equation for gas di#usivity in undisturbed soil, Soil Sci., +0. : /.,ῌ//+.

di#usion and nonequilibrium adsorption-desor-

Moldrup, P., Olsen, T., Schjonning, P., Yamaguchi, T.

ption experiments, Soil Sci. Soc. Am. J., 01 : 10/ῌand Rolston, D.E. (,***) : Predicting the gas di#u-

111.

sion coe$cient in undisturbed soil from soil +33. :  

ῌ

 03 : //ῌ00.

water characteristics, Soil Sci. Soc. Am. J., 0. :3.ῌ+**.

Hasegawa, S., Osozawa, S. and Ueno, H., (+33.) : Meas-

Moldrup, P., Olsen, T., Komatsu, T., Schjonning, P.

urement of soil water ﬂux in Andisols at a depth

and Rolston, D.E. (,**+) : Tortuosity, di#usivity,

below a root zone of about + meter, Soil Sci. Plant

and permeability in the soil liquid and gaseous

Nutr., .* : +-1ῌ+.1.

phases, Soil Sci. Soc. Am. J., 0/ : 0+-ῌ0,-.

Hillel, D. (+332) : Environmental Soil Physics. pp. -*,ῌ-*., Academic Press, San Diego, California.

Moldrup, P., Yoshikawa, S., Olsen, T., Komatsu, K.
and Rolston, D.E. (,**-) : Gas di#usivity in undis-ῌ

!ῌ"#$% ,**- : &'()*

turbed volcanic ash soils : Test of soil-water-+CO, O, ,-./012 34

characteristic-based prediction models, Soil Sci.

5 ,,/ : +++ῌ++2.
Jury, W.A., Russo, D., Streile, G. and El Abd, H (+33*) :Soc. Am. J., 01 : .+ῌ/+.
Moldrup, P., Olsen, T., Yoshikawa, S., Komatsu, K.

Evaluation of volatilization by organic chemi

and Rolston, D.E. (,**.) : Three-porosity modelcals residing below the soil surface, Water Re-

for predicting the gas di#usion coe$cient insour. Res., ,0 : +-ῌ,*.

undisturbed soil, Soil Sci. Soc. Am. J., 02 : 1/*ῌKruse, C.W., Moldrup, P. and Iversen, N., (+330) : Modeling di#usion and reaction in soils : II. Atmos-

1/3.

+^_`ῌ

!ῌabcῌdef +33/ : pheric methane di#usion and consumption in a ghijkW pp. 1.ῌ21 \]MVlmn \forest soil, Soil Sci., +0+ : -//--0/.

]W678ῌ9:;<ῌ=>?@ῌAB CῌDEFGῌ
HIJῌDEKLῌMN OῌPQKRῌS"T< +32. : UVW pp. ++,ῌ++. XYZ[ \]W
Lai, Sung-ho, Tiedje, J.M. and Erickson, A.E. (+310) :In situ measurement of gas di#usion coe$cientin soils, Soil Sci. Soc. Am. Proc., .* : -ῌ0.
Millington, R. J. and Quirk, J.P. (+30+) : Permeabilityof porous solids, Trans. Faraday Soc., /1 : +,**ῌ
+,*1.
Moldrup, P., Rolston, D.E., Hansen, J. AA. and Yamaguchi, T. (+33,) : A simple, mechanistic model for

obp:ῌ6qEr +321 : ,-stuv

ijk wx /2 : /,2ῌ/-/.
obp: +332 : +,-

stijkyz{|},-/~  3gh 12 +/ : -0ῌ.2.
Osozawa, S. and Hasegawa, S. (+33/) : Diel and seasonal changes in carbon dioxide concentrationand ﬂux in an Andisol, Soil Sci., +0* : ++1ῌ+,..
Penman, H.L. (+3.*) : Gas and vapor movements insoil : The di#usion of vapors through porous
solids, J. Agric. Sci., -* : .-1ῌ.0,.
Petersen, L.W., El-Farhan, Y.H., Moldrup, P., Rolston,$O  +*+50

,**/

D.E. and Yamaguchi, T. (+330) : Transient di#u-

Rolston, D.E. and Moldrup, P. (,**,) : Methods of Soilsion, adsorption, and emission of volatile organic

Analysis Part .-Physical Methods, SSSA Book

vapors in soils with ﬂuctuating low water con-Series No. /, Soil Science Society of America :

tents, J. Environ. Qual., ,/ : +*/.ῌ+*0-.

+++-ῌ++-3.

Poulsen T.G., Moldrup, P., Yamaguchi, T., Schjonn-

Troeh, F.R., Jabro, J.D. and Kirkham, D. (+32,) : Gase-

ing, P. and Hansen, J.A. (+333) : Predicting soil-

ous di#usion equations for porous materials,

water and soil-air transport properties and theire#ectsonsoil-vapor

extraction

e$ciency,

Geoderma, ,1 : ,-3ῌ,/-.

  +31, :   -  

GROUND WATER MONITORING & REMEDIA-   ODR  !"TION, +3 : 0+ῌ1*.

#$%&'()* +,* .- : ,,-ῌ,-*.

῍ῌ- ./ 0123456789:*  ;< 67=>?@AB5* C&- DEFGAHI8JK!L MNOPQRS$TUB VW!L X Y85*
Z[\]^_ `ab* cdefgO* hicdj* `k ljmnopqrs* - _tu67=>Bv]woxyr/X "rs* z{|v]w!}~ Millington & Quirk
MQ v]w* Buckingham-Burdine-Campbell BBC v]w* Macroporosity-dependent MPDv]wo)ns* B!\!SOor* Bv]wo /Xxyr/Bv]w!* BBC v]w* MPD v]w5\!c eLSOoPr/X z8 BBC v]wEnSOor/X /* MQ v]w5\obr/X B
v]w!\!SO hicdj5|{* `k lj!rs e+** pF,.*;<

lj o)n/v]wEnSOo |{/X : ,**/  /  3  : ,**/  3  + 
J. Jpn. Soc. Soil Phys.
-"¼
No. +*+, p. /+ /0 ,**/

ῌ


*ῌ῍*ῌ

*Annual Soil Water Flux through Forest Soil Measured
by Porous Plate Tension Lysimeter Method
Tatsuya TSURITA*, Shuichiro YOSHINAGA* and Toshio ABE*
* Forestry and Forest Products Research Institute, Ibaraki -*/ῌ2021, Japan
Abstract
A Porous Plate Tension Lysimeter (PPTL) method was used to measure the vertical water ﬂux
through a forest soil where the use of electric power is restricted.

The PPTL was installed at thedepth of *.3 m in the upper, middle, and lower slopes of Katsura Headwater Catchment, and soil
water ﬂux was measured throughout the year.

The vacuum pressure of PPTL was adjusted

manually once a week to a target value determined by the matric potential of the adjacent naturalsoil proﬁle measured by tensiometer. Annual soil water ﬂux was ,1/, 0*2, and 0*+ mm for theupper, middle, and lower slopes, respectively, showing similar ﬂuxes to annual runo# rate in the
middle and lower slopes.

This result shows that the PPTL method is applicable to measure

annual soil water ﬂux.
Key words : forest soil, soil water ﬂux, porous plate, lysimeter, Katsura Headwater Catchment+    ,*** ; F( ,**- ; Lentz and Kinkaid, ,**-]9 IGF'( VWQXUY;a{T|b}OPQ_ῌῌ

~)( vwxyza{T|b}OPQ_~7

 !"#$%&'( ))*+,-.

>LJKVWQXUYstu!$I)/012!34$56789 :%&(J?( yz/m012$2!

!;<=>?012!@A$BC7DEFG=$BCm89 I/m( qr Z,***] '; ,1?H%9 IJKLBC)>?MN( OPQRPSTU

cm }UVU{;a{T|b}OPVWQXUYC Z[\( +32,]( ^_`VTUVWQXU

Q_~)( vwxyza{T|b}OPQ_YC ZHolder et al., +33+ ; Maeda et al., +333]( aWb~7vLJK( }UVU{stu!

cVWQXUYC ZdF( +33+]( OPQRPVWQmy1$QO!BC!

XUYC ZefF( +33/] Lg7hiFG?H%9 >j%9 Kosugi and Katsuyama Z,**.] '( IBC!

>( IGFBC'( kl῎m01$2!@

Controlled-suction period Lysimeter method ZCSPL>

A$BC)>?'( :GnGop78 Zqr(C] )>( ῌw -* cm  .** 

,***]9012!Fj>%9:Im( VWQXUYstu!vwxyz

IGFBCJ ( MNBCJ *01

a{T|b}OPQ_~i?>?!

2¡¢!Fj$I)7£¤)L%9 >j>(=$BC7 G% ZDuke and Haise, +31- ;¥¦§J ¨©G%ῌi?'( stuyvan Grinsven et al., +322 ; Brye et al., +333 ; qr(

1%&!ª$I)7«¬m89* ῌ­®¯°± ²-*/ῌ2021 ³´µ¶·¸¹ + : ῌ( 012( }UVU{( VWQXUY( ºD»#"KLB M +*+ ¼ 8,**/952   !"#$"%  &' ()* " 
CSPL

+ ,()-"./ 0

ῌ12342 536 7 8PPTL9* 0 PPTL

:;< #"=>) !"#$"% ( "?@"AB'C*, 
,+ 
PPTL

#$"%"  DEFD

EGE"HIJKL) 8M +9* HIJNO"PQ RSK/ TU ,.- ha 
.* VWXUY Z[\]^_Sῌ+* #`ab< .* cXdef"»

Fig. +

Topographic map of study site.

ῌ12342ghijkl"mn o p!O  gefh -3 X qrs .*,,  ,,+PPTL 

HIJ""g"t  ef#"e^$"Luv + %w ( PPTL Q&()
8M +9* xy 8,***9 z '{ ,1 cm " 8soilmoisture |} +3/*B./9 #(" B )*~R 3* cm +Q() 8M ,9* A "]
Rt  SS +, 2 -1 cm ./) - %-d",-~R -* cm -.
( 3* cm ~ /n(Le)* LK - %-pK01_S) $"N
(RS*
,,,
CSPL

ῌ,
Fig. ,



536

7

"JM
Schematic diagram of porous plate tension lysimeter method.

 AC 2P  - 3=(* S4( PPTL"2 ) ῌ56(N"«6 7 8>¬2­ ®¯¥2°|} PS19 

ῌ5()*  t()* LK $?=* ")

.$7)8 0 L "7" "@A±²=K N=³""=6 Pc 8kPa9 ()*(  Pc / - kPa B5,!(Pc+y3*Hῌ)*,,-   

~R 3* cm "k¡¢£12

$ef8 .** m .C´DE3¤¥ 8kPa9 .*  ':"9#k `µ¶ ()* ª$IJF"~R 2* cm  +** cm "k¡¢£123¤¥";

Q&RS)$·K( $~¸()* #$"%-$"U

y3* 9#K¦< y3* () 8M ,9* H 8kPa9 7"="&123¤¥"§)*¹($~¸()* $ $ª #$

./ "¨=§ h 8cm9  *.*32 ©>)*"%"±²= ,**-  . º 2 Gef ,**.  . º

#$"k¡¢£123¤¥2ª>"1230 G"8 + =./ H±²="I

  :

ῌ!"#"#DdῌFig. -_ 

Sd   

53



Weekly precipitation, weekly runo# rate, and weekly soil water ﬂux.

     +  h i Y L  = 8 9 &    

4 5 6 , +.1

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- 
-+ 



-, - WXDSMK PZ[9?@jR

 3* cm







h9 &k -' - (lm 79H +/.0!"#$

mm ,7H n (op3YjRqrh% &y3*' ()* * +*,-.+0.+/.-.0

st>RM 3=3PZ[K( 2./.2/.+.2 .+,.1/.+.0 kPa

01,23 45

6()* * +*,-.1.* .-.. ...+ kPa,789 )*

y3*+:6 &.+0.+ kPa' ( 3 ; / <=> ++ <?@39AB C>9 F G * +*kPa ,7H )*uvw39  2uh9
0 ;=> ++ ;(Bhxe nD(hyzMNOPQ39 {9 ,iy

3 ; +0 <DE

B &|B +0* mm' h789 2 ; 0/+3 < D

y3* (-././ ...+

( )* * +*, +- <,- ,* -/ -0

y3* (* +*DIJKAB

mm

DLMNOPQ39 RS y3* T DUM9 2*

cm  +** cm789 3=3 !"#$% V( - WX

YPZ[K +/, kPa \],789
^_` abc( - WX  456,
Pc dH ..* kPa Le WXf,( )* abc gh9 F (n+ῌ2/+ῌ.   &0- mm'



(}

+ῌ-/-ῌ/ , &|B /mm' Y?@3Kyze )* * +*, 1 <,- / ++ ++ mm ,789 F d~D h9D - D89  ¥ » +*+ ¼ A,**/C54

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Fig. .

ῌ+
[\

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

M

Relationship between weekly soil water ﬂux and weekly runo# rate.

Dm´D5

YZAnnual soil water ﬂux and ratio of annual soil water ﬂux to annual runo#
rate


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AmmC

AaC D5
A0,2 mmC YZ[\

,1/
0*2
0*+

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*431
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.
/
0

656.]^_` ab!c5HIdab!efghW*+ 78R SEX,f<6ij!cm qrkl m<f PPTL Eno,p 3*
0s thZ36! 4puE

vwZR S HIE 5 xZ6eZ36* / 0  D D5
649*+ 3 36 PPTL   ^_`my5 x, Ez*3
6EX,f< V /60   

 +,! -'-+1 & - (, -3'+1 &{cW |5 {cW |678},f<36- AB /C 0~ my0> 
 "#$ %) ",,/ &5 x,f<36EX,f<*+ ,*-  . /kl*(*+ 0* 2 & *12 +.. ..* -.+ mm *+ M*$ 341

5

,./ mm 67849*

 \  +  65- |6,  | ,,  :!;+  <65-<=>?@! AB .C

36- 3 w m<f`6p 3* cm 



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-- 

V - `6- p 2* cm +** cm D. / 0*12 ,1/

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EvGf WEX,fm

0*2 0*+ mm D  +,,/* mm D5 0,2

/ my ,f< ¡mm *+ A +C D !D5EFG

> ¢ EZ£ ,¤¥HI 0,, mm *+ 3JKEL$MNOP¦< PPTL *§. £EzZ36

Q R S

0**'3** mm AT

 +33,C*¤*+ 1 0>¢ ,z*< ,+  DD -U$ V, ¨©ª <£

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WEX,  D D5 YZ[l «¬6±²³ V\ . / 0*12 *... *.31 *.30 *+"m´1µ¶*·µ¸¹6 A¯°! +32/ ; º°ῌ +322C ,fkl ` m<f D  EzZ

]^¹W : ¨W®°~ºWῌ©Uª»U®³ª¼WV7./  Y

ῌ/Fig. /µ/ ¶/7Q./, Dh K%./B7QEFB @ %   
    ! "# $% &'

C.S. (,**.) : Passive pan sampler for vadose zone
leachate collection. Soil Sci. Soc. Am. J., 02 : 1..ῌ:;

Equilibrium tension lysimeter for measuring,1/ 0*2 0*+ </=?+,

'

1.3.
Brye, K.R., Norman, J.M. and Gower, S.T. (+333) : An

PPTL 7   8 3* cm>Barzeger, A.R., Herbert, S. J., Hashemi, A.M. and Hu,(/   

mm + ,]D -+2 : ++ῌ12.

-'./  0123456+9./W·X¸

Cumulative precipitation, runo# rate, and soil water ﬂux.

)*'+ ,55

dranage through soil. Soil Sci. Soc. Am. J., 0- :/-0ῌ/.-.
Duke, H.R. and Haise, H.R. (+31-) : Vacuum extractors

to assess deep percolation losses and chemical

PPTL @AB'C !D 

constituents of soil water. Soil Sci. Soc. Amer.

""E./ F2GH #
I+





Proc., -1 : 30-ῌ30..
Holder, M., Brown, K.W., Thomas, J.C., Zabcik, D. and

J$K%L&MNOK%L&P7QK%RSTU
VWXYZ'F[ K%(\]^_.

Murray, H.E. (+33+) : Capillary-wick unsaturated
zone soil pore water sampler. Soil Sci. Soc. Am. J.,// : ++3/ῌ+,*,.

/GῌHuῌ% e+33/h : AIK%*]^`ab cd efg K%(\]^_$)>

<9.E_h *+i,d j- .d k/0ld mn

@ K% 11 : /+0ῌ0,0.

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1 YZ'[ o23p3pq4p]^rstu5 e,***h : LMN.O./Lstu5dvwYxyF[ ,,zPH /Qῌ/ Ap¡ +- : .0,ῌ{F6|G -]^ K%(\]^_@7}~

.1+.

 ,****- K%ῌ4ῌ/<F8 9m

Kosugi, K. and Katsuyama, M. (,**.) : Controlled-:;<RS 7QK%RSTUVWR

suction period lysimeter for measuring verticalS6 K%<9=>? @ =>water ﬂux and convective chemical ﬂuxes. Soil 7 #uA e+32,h : K%./B @JG]^ eC

Sci. Soc. Am. J., 02 : -1+ῌ-2,.

¢R£,ῌST¤u e+322h : ¥U9 , ¦§./B¨©Uª«¬BV ­®¯°±@ ²³´W +2 : 0,ῌ1-.

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56

Lents, R.D. and Kincaid, D.C. (,**-) : An automated=IHJCKI<ILM% NO'( 1. : 11-῎12*.

vacuum extraction control system for soil water

P"QRῌST,ῌUVW῔ +33+ : XΐY$Z

percolation samplers. Soil Sci. Soc. Am. J., 01 :῍[\]^_ῌῑ`Qab ῌ cde+**῎+*0.

fΐg8Jh>ijk=lmJh>iNn

Maeda, M., Liyanage, B.C. and Ozaki, Y. (+333) : Water
collection e$ciency of wick samplers understeady state ﬂow conditions. Soil Sci. Plant Nutr.,./ : .2/῎.3,.

ῌῐῌ

`Q% &ΐ'( 1- : +-/῎+...
ῐo +33, : Xΐpq% p. 31( prstu( vw%van Grinsven, J. J.M., Booltink, H.W.T., Dirksen, C.,ῒvan Breemen, N., Bongers, N. and Waringa, N.

῍ !"#(+322) : Automated in situ measurement of unsat-+32/ :


῏$% &ΐ'( 01 : -2-῎-3*.

urated soil water ﬂux. Soil Sci. Soc. Am. J., /, :)*+,ῌ-./ῌ0123 ,**- : 4"567+,+/῎+,+2.

8῍9ῑ:;<=>?@AB>CD>EFGH

῍ῌxyz+{|}~Xΐ( #( ( PPTL  @Nnῑ@ PPTL ( Nnk=B>CFIHc
Ik ¡¢( £¤¥¦ Nnῑ( #( §¨©¨( ,1/( 0*2(
0*+ mm ª( «ῑ +,,/* mm¬­®¯( #i῏tῑ 0,/ mm i°±ª²@ PPTL ³´Nnῑµ¶¦£iῌ·ª¸¹º& : ,**/  - º + &¸῎º& : ,**/  1 º 1 &῏ῐῑ῎
J. Jpn. Soc. Soil Phys.

No. +*+, p. /1 ῌ,**/῍       *

  +**

        !" #$% &'()*+, #-./ /0 102345 06. 7 89:;
#< " !"=>" + ?@ TDR #$%A7  B&'#$(  8-)*+,&-.CD;EFG< / + H:IJKLF
MN:;/" 0O1. , PQ - PQR 2)*S34T2UNV:2WF
S\] /^=>" +S06XYZ[5/6 < "
_7

= `8S9) :;)a <=(>(> 7 b

 4T<=db

+ e*>+ )> Df!"  EYFg5h%>*iG/j(*Hk />lI5/m=c234S?T@A B5C"+. (> JK/ ="n(>oLk  pM)*7qrq+ "("st 

Nu. eq"pMvOP=/ EY@( h%>* 7q/&v>)w>*+. QRS*xK2:Ty  z{|F}5 E~:>7
UQRS*'!dVW" e'( VW"
M X. +30* YG-j([2\-k r*+ # 5/(v_Cv_7

+ "("

VWZ*   e. eq" M]^*H

j2\`?_avA/

-./nq(+
/W?  $%b"# #y%  #

(R-k+  R #*(>VW"

2\5/Jqc_ d.  e0)f" g #t( h- *@+1Mi. z{|F}5 E~:>UQRS*'!v_jMi ,Childs & Collis George yk) M Miller & Miller BT Philip & de Vries )l&T'! m M Nielsen & Bigger _j34Tn¡/¢o'" + p + £. 34*¤ M5lIX Taylor Mi 1+ ¥R ' = < -k*@¦qr k.§_7 ¨MI:©sª'  «t" go'-k+ ¬ '+ῌ, "u­®"   k?¯ , Y°u2E:o'" + "(" _±)²Avj?/> wx2E:
y³"q¥´-k+  1Mi ez¦µ ¦Av{|¶·f¸wgR*@¹-k+* º@d »¼}
J. Jpn. Soc. Soil Phys.
FG' hNo. +*+, p. /301 ,**/



G.I. Taylor 
*ῌ**
Reviewing classical studies in soil physics“Dispersion of Soluble Matter in Solvent Flowing Slowly through a Tube.”By G.I. Taylor
Proc. Roy. Soc. Ser. A,+3, No. ++-1, +20ῌ,*- (+3/-)
Munehide ISHIGURO and Nobuo TORIDE+

B :8+:  }=>BA~ }=> (Taylor 

Taylor  ,* 

 :8B$ Q x9 CD  Prandtl    Taylor   + Taylor  , Taylor

 - Proud-

man-Taylor   . Taylor  ! / Taylor "# 0 Taylor $%& 1 Taylor '(5

C @nB6#9oB6#9B G #()6#9 F 
6(98 % E#98QF#)_8AFG8H+: FG jwH0bIJ19 IlA~) 2 Taylor *+,-  ./+ 5_8jxxFG!67_

01 21

K/F G2BC : *ZBP!_3 +33,4  5678 9 :;<

=>

?@



:A

8 F G XL_68MF :1
1  G  56#)C>BC :  Batchelor 3+31/4 

$B'

Taylor 8DEF

"8$H/C*Z+,BLM34JN19 XL_C G:A#: =>  G  I/$34 IlFG `A

JF=>B Taylor K$BLMNO,P8QFRQ OA1 

!1 G%ST  Taylor  &' $(U8VW
8XY )9B *Z+,B[\9]^-.8/C_68+: C`

$ a=]^$ a= 0bBcdefd1  2 g9*
ZB348Rhij>i_68MF,   Taylor Taylor  Fig. + 5^-.8 $H

58ZP1Q 5R: ¡¢¡1ST£8U1 ST£(`658k`l97F m 5n61
l78!8 o ( _ Griffiths 3+3++4G¤18¥ TVW:VX#98YC ST£8Z

Ncf[\R H¦p qUC 56#9 !8r:1

2 F§ ZP ]9^T ¨PN[ C©

$; <=1 * >o1

ª[\R_D1]^8«`C 

A::s< 6

5n7t?8!8 u o ( 1  G

Fig. ,  `¬$6lA~5!VX#9

_vw@+xxyzC G ]Y"­1  ®r x R:5t?1

C Taylor   Ncf[ 68A~ 3I¯1F]^ =` {|j=>* °±;²³ ´a µ1**ῌ2/-* °±¶bc! -ῌ+ῌ+** ·;d'¸¹a µ/+.ῌ2/*1 b¶ºef»f +/11 : #) #() 7 67 7#)3g¼



60

ῌῌ+Fig. ++*+  ,**/

Taylor WX`abcd efWX A Fghi# d jk E lmnF oO
p<q N Frs9OnFWXY 9 o!d $%n& 1 E Fngh ot[Ouv !d Taylor +3/-, Figure ,

Taylor’s experimental setup. Initially pure water is supplied in the tube A. A coloredsolution is poured into the bottle E, and introduced into the tube by adjusting withcock N. In case of rectangular step solute input pure water is introduced into thebottle B after the solute. (Taylor +3/-, Figure ,)ῌῌ,Fig. ,

P8 9#'(w3DEd A, 1:;<=&  A- 1$%&WXz + mm
{| +./ }~d Taylor +3/-, Figure -xydMeasured solute concentration distributions at faster velocity. The result A,
is for a step input and the result A- is for a rectangular step input. The tube
diameter is + mm. +./ sec. after introduction. (Taylor +3/-, Figure -)Fig. 3  A, x* 

>?:&  Fig. . @A B8C4!DEF !" #$%& 

G " 5DE1HIJKDEL44M" # :'( )* Fig. 3  A- 

;<=& NMO

+,-. /0123+4!"+56 78 9#'( :;<=&  Fig. -PQ.R STUV WXYSTP !+Z[#'(UV F\] + +9#^UVDEF_

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ῌῌ.

Fig. .

61

ῌῌ-ghijRST:UVW4XYZ[\JK !
"] ./M *./*. mm WT^_#$ +21 `Rb] Taylor +3/-, Figure .

Fig. -

Measured solute concentration distribution
at slower velocity with a step input. The
tube diameter is *./*. mm. +21 min. after introduction. (Taylor +3/-, Figure .)PQRST:UVW4XYZ[\JK !"] ./M *./*. mm WT^_#$ῌ] ,3 ` ῍] ,3a-0 ` ῎] ,3a-0a/./ `Rb] cB < =d
FYZ῎3e f[ !"] Taylor +3/-, Figure 2

Measured solute concentration distribution at slower velocity with a rectangular step
input. The tube diameter is *./*. mm. ῌ. ,3 min. after introduction, ῍. ,3a-0 min after
introduction, and ῎. ,3a-0a/./ min. after introduction. Broken line shows the predicteddistribution for ῎ when molecular di#usion is neglected. (Taylor +3/-, Figure 2)   Fig. /45678 Fig. 0 9:; r 78 )< =   !"#>?:@ A Taylor BCDE;45F  G$%&'(")*+,- ./0123

H  012IJK<./LM a NOA< ¡ ¢ +*+ £ ,**/62  D

/@[\ PQF >?$DM U= ]^_`abcd`6 P >?

 t+
t+

a,
-.2,D

ῌ

e^fg@hi j) )k.
@lm

 Fig. 1 C( $n! "#$%&o '+pqXJ<r s _t'+pu ' Fig. , ()*+,-./ )

J<6 $ vwxy)z{|



t+ 01  !  Fig. -}~ Pcfgvwxy6 r f

Fig. . ()2345/,)6

gW`<;  J< $n X

7 89:;<=(6 '= >?@'MM`'MF [ n XAB$ Fig. 0 C( $DE x*

'Md`'MF [ Fig.

F

1 6

GHIJ< KLM. NOPQR ST

UV6 WX '+YJ<6 NOZM.

  7 X M.

)M.) lm 

ῑῌ/S xu*tῌ, < [L>?-./ :  ++,,* 1  ,.* 1 +, 1  . 1  +./ 1 NO* *./*. mm
++,* 1=NO* + mm Taylor +3/-, Figure /Fig. /

Measured solute concentration distributions shown by the relative distance which isstandardized by mean ﬂow distance x῍u*t/,. ῎ after ++,,*s, ῏ after ,.*s, ῌafter +,s,῎ after .s, ῐ after +./s. The tube diameter is *./*. mm. For the result at ++,*s thediameter is + mm. (Taylor +3/-, Figure /)ῑῌ0Fig. 0'=>?  PQRp@DM ]^_bcd)Movement of solute molecules (῎) only with convection. That in the center of the tube
ﬂows fastest. The ﬂow becomes slower when it is closer to the tube wall.

¬­ : G.I. Taylor ® ¯"#%¤vE8 ;°$±z;<3n ²

63 

'kl!mn ! o;<$VW8    $VWp;<+XqrFGs

 ! "#$%&'() [\p;<tdeusvwssm*+,- .Fig. /, /0 %12+ *3

 r dex;< t @AyKFG x+45678 9 : ;<

2z{|=+>? @ABC8D ,*+EFGHI .Fig. /, J0

K Taylor LMNOP%QRS῍}v  "#~\%Q8 Fig. 2 fS fyq;<$8A+mnw7- 
-+ 

x`u*t.+ar,ῌa,0;<$,  "#, *C*  ,

 

Z%8  8;mE%

"#$- KTU$VWXYZ u* $VW&m~\, Cm % n[\ * ]^\_%8u`u*.+ar,ῌa,0-,ῌ 

(, C* ;<%w sE t`

RR u $VW ! r FG a "#bc*  *xX , C* ;<+ Fig. 2 $VW !FG r de;< fE

fSm%fS w2 X  nFG

 u g @A t hi *+ j

8 

nA;<$VW ῌ1

¤vE8;+  r W¥¦*3fE ;< .J0 =m'p .J0 §¨©ª«E

Fig. 1

When the ﬂow is slower, solute molecules () change to neighbor streamlines ()of di#erent velocities with molecular di#usion of r direction randomly.

ῌ2f;<*+E
]^_£(8mv *+Fig. 2¡ X ¢;< t @AyfE

Solute spread only with convection. Initial solute mass with width X
spreads and takes parabolic shape after time t.

«¬­®¯  +*+ ° 4,**/564 

r

r

r

dr 



 ,pr C* Xdr  
,prC* Xdr 0 Fick kpqrw#`
C

a,
dx
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dx
,u*t

ῌ( C
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,

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r, ῎ (Ca,῏ (xu* +$% x x x dx  &'() Cm    D !xkp  !p "#*+,- pa dx ./# r qkp # x qkpY

,

C m

C* X
u* t



01 2/# *3x3u*t   Cm  C* Xῌ4u*t5 x3* 0 x6u*t  * 78 4Fig. 3, A+5

9:() C* ;<=>?@ABCDEByz{ + -  "#r qZ[ zrῌa {0  `

1
(,C
(z,

a,u* ῌ
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+$z,
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+ (C

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

FGHI;?DEJK LM 4Fig. 3, A+5 ()!xkp /# r q()!NYr)

!NOPQRESCTUVW"# Fig. 3, A, J

9 1 cd r qi g

KX Y X Z[

S\/#]^?

w#   x q () C ¡Y1

_ADE `abcd;<=>?_A

w0"# 4(Cῌ(x* 0"#5 g¢£ x qyz"

QRESC0ef#  CC* x3X
C*

 g

x6X

C$C* x3*
C*



x6*

2/# Fig. 3, A- !N8
h1i  j@iYkYlDEmn + `oj@!pqrstuv1w

. 
.+ 



!xkpYyz{1wDE j|}~qr

ῌ3

(,C
(z,

a, (C
+ (C

z (z
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01
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w0
+

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CB4a5e$at J*4aa , D

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z5

!xkpY1 j@iYj|DE¨©&'()!Nª 4Taylor +3/-, Figure +5

Fig. 3Distribution of cross sectional mean concentration due to convection in absence of molecular
di#usion. (Taylor +3/-, Figure +)¸ : G.I. Taylor ¹ º03¨B»D5'4\SO]¼

am,  B a>! 

D
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m



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    z+ 
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 ! z "#$% &  '(῍
῎CCx+fA z,) Cx+)

J+aa D+,*  J++  
 !#" *  *+,-./01234
 !
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"Ce)+Ba J*aa , D)+,

z 50

>?@ t+ ! +,e)+Ba J*aa D

+
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+
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z 
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 ! 50 AB t++ῌa 50 ' , C4DEF#  ! GB HIA*?@ t+ AD-J?@KL>'( MNOPQ; R'

pa.u*, (Cx++3,D (x+z* \ C 8 Cx+Cm   Cm

c/d_5;  !   + 
XO!
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k
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+3,D

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' NOW!  S >5YTa>5;
 X x  b!x( "3TOW+ 

STUVW!  ! + X!67"A!50

* YZ u*ῌ, T>[\T]

/^_'(A ]`D x ab  x+ ab
c/d_
x+x)



e*>5 !

9 "#850

 

 #5" $? Taylor %&A*0' MN
+
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e*>5  ! A*0"e./0PQ-_ ST

(,C
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O£¤ ¥'5 + R¡¦>5§D `# - XSTUVW! * GB eT>S  z¨ + XTOW!67/5"#j C ( ]/3kl> MNOAB

q  U,©0^_5"ª/«;'z jmS;NO"#n z jo /_( Sa#man, +3/3 ; Bear, +31, ; Jury and Hor-

0 C ( ]/]p3 ]`D z j

ton, ,**. ; .¬ῌ­® +322 YZo0 C (]/;ST,-MNOA¯°±0O 

sqt5u!"#A*YZ , ²1/>z"

v?@wxy x z"530"  !{@³´ῌ°2*S¯°;±µ¶S·| + 2}~> z+  (Cῌ(z* YZ + ²1/"Sa#man, +3/3 ; Bear, +31, ;PQ> eqr>#& C61!º » +*+ ¼ +,**/

66ῌ +322 ῌ ῏ ῎ ῍   ῎ & !" #$% ῍

 '

Batchelor, G.K. (+31/) : An unﬁnished dialogue with

( , )* +Valocchi, +32/ ; , ,**/

G.I. Taylor, J. Fluid Mechanics, 1* (.) : 0,/῏0-2.

-! Taylor .!/012#3'

Bear, J. (+31,) : Dynamics of ﬂuids in porous media,

456789*:; +Iwata

Dover, New York, /13῏00-.

and Ishiguro, +33* <=>3  ?@/8

9=¢> ++33, : t*u ?£¤@¥

 ,A=>*789 BC

Ishiguro, M. (+33+) : Solute transport through hard

3DE89F= ῌ &38 + GH/

pans of paddy ﬁelds : +. E#ect of vertical tubular

&I JKL9. +Ishiguro, +33+ ;pores made by rice roots on solute transport, Soil

MN +33. O, PQR' /STUV
X

'/789W Taylor 

YZ3.9 [ \!OL

Science, +/, (0) : .-,῏.-3.

MN¦§ ++33. : 6/Sc¨*<=>BC 9A© 0/ +- : -.3῏-/0.

9. +Jury and Horton, ,**. ; ]^ +331 Taylor

Iwata, S. and Ishiguro, M. (+33*) : Characteristics of"#% 6_$`WO: , absolute transport under unsaturated conditions,

8!cd %e /fgῌhifg3&

Transactions, American GeoPhysical Union, 1+,j*k + lmZ3n89oL'
pq,8O rsZcd

(,2).
Jury, W.A. and Horton, R. (,**.) : Soil physics, 0th ed.,() Taylor % t*uvwx9y+z{

pp. ,,/῏,01, Jhon Wiely & Sons, New York.

%|j,KL -}~.t fg3

ª«ῌ¬­ ++322 : ®u1/[9. +Batchelor, +31/ 89 :z{% u/0 . F  1 B© /0 : +++/῏++,+.
Sa#man, P. (+3/3) : A theory of dispersion in a porouscd89Wy+r:328

medium, J. Fluid Mechanics, 0 (-) : -,+῏-.3.

9. -! cI;hifgI¯°ῌ]^±Cῌk²³ +,**/ : 453´

33d tz{4 356O lNµ¶ l.9 ~#ῌ~·¸u¹b9. t*u Taylor© +2 +. : .*+῏.+*.

 7FS.9

628 $*v9z{:;89]^±C ++331 : '~L33d.!:%r Taylor %<rx!   / ~#ῌ~·¸u¹© +* +/ : .2/῏.31.

rL 61!u=_ ¡%cW

Valocchi, A. J. (+32/) : Validity of the local equilibri-

x!jW0L.

um assumption for modeling sorbing solute transport through homogeneous soils. Water Resour.
Res., ,+ : 2*2῏2,*.

 : G.I. Taylor  M=*#:    ῍
"#$%

b !

67

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Taylor  Taylor   !

&'()*+  

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J. Jpn. Soc. Soil Phys.
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No. +*+, p. 03 ῌ,**/῍

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  
 

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LMC" 6 N!>5% (D( OP!

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Journal of the Japanese Societyof
Soil Physics
November ῍ῌῌ῎

No. +*+
Contents

Foreword ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌH. INOUEῌ+

Original Papers
Estimating Thermal Di#usivity of Soil Packed in a Cylinder Using an Analytical
SolutionῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌK. NOBORIO, I. TOKUMOTO and Y. MUKAIDAῌ/Solute Transport Properties of Soil Measured with a Vertically-Installed Time Domain Reﬂectometry Probe ῌῌῌῌῌῌῌK. NOBORIO, I. TOKUMOTO and Y. MUKAIDAῌ ++Inﬂuence of a Percolation Pattern on the Removal of Soluble Elememts in Downward
Water and Rice Plant with Models of Cadmium Polluted Paddy FieldsῌῌῌῌῌS. PONGPATTANASIRI, C. SASAKI, N. MATUYAMA, K. NODA and A. TONOUTIῌ +1
Development of Automated Suction Controlled Flux Sampler for Unsaturated Sandy
SoilῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌN. HIGASHI, Y. MORI and M. INOUEῌ ,1
Development and Tests of Predictive Soil-Gas Di#usivity Models for Japanese Undisturbed Soils
ῌῌῌῌK. KAWAMOTO, T. KOMATSU, P. MOLDRUP, S. YOSHIKAWA and T. FUJIKAWAῌ -1
Notes
Annual Soil Water Flux through Forest Soil Measured by Porous Plate Tension Lysimeter Method ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌT. TSURITA, S. YOSHINAGA and T. ABEῌ /+Lectures
Reviewing classical studies in Soil Physics
Introduction ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌN. TORIDEῌ /1”Dispersion of Soluble Matter in Solvent Flowing Slowly through a Tube.” By G.I.
Taylor ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌM. ISHIGURO and N. TORIDEῌ /3
Readers’ column ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌI. KITAGAWAῌ 03
Book review ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌK. KOGAῌ 1+
Announcements ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌ 1Editor’s Postscript ῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌῌ 12

Japanese Society of Soil Physics
Division of Environmental Resources
Graduate School of Agriculture, Hokkaido University
Sapporo, *0*ῌ2/23 Japan