῔
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"/

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6789:

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hT=(1MT &MPD HIJ Dp+**ῌD*and Hasegawa, +33/ ; Hillel, +332 ; Kruse et al., +330)

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

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F

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

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

 `ZabcR

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ef gh)*

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mno:;

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J

HIJF1

 78ijk +2 l9 . l9R

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HIJF=

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

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

..

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

Mold-

HIJst=

(1#*

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

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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

IE%¦_`aK%& JKL> !£ :p
ABCD,2G§ 9=>  9No. ,*῔-+<9H¨

RMSE , 89 :RMSE;*.*+1< =>& ? MPD

 :@ . :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  

BCD *.**. MNOP> 9 * QRG%& S¦_/ABCD §T 

'( :p GUVE"b`aK&)(*+ :pNo. -2῔-3 ./῔/+<%J - WDXYZ[  \>G]^

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

4 BBC  .  8 RMSE => :@ /ij bcd#,efgh>

MPD  klmn, o %&efῑ-a

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

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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-

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Millington, R. J. and Quirk, J.P. (+30+) : Permeabilityof porous solids, Trans. Faraday Soc., /1 : +,**ῌ
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Penman, H.L. (+3.*) : Gas and vapor movements insoil : The di#usion of vapors through porous
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D.E. and Yamaguchi, T. (+330) : Transient di#u-

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Analysis Part .-Physical Methods, SSSA Book

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

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