῏
J. Jpn. Soc. Soil Phys.
ῐ῎῍ῑῒ῏
No. 3., p. ++ῌ+3 ῍,**-῎Review of Recent Progress in Predicting Gas TransportParameters for Undisturbed Andisols : Campbell b
Dependent Models for Gas Di#usivity
and Air Permeability
Per MOLDRUP*, Seiko YOSHIKAWA (OSOZAWA)**, Toshiko KOMATSU (YAMAGUCHI)***,
Torben OLESEN* and Dennis E. ROLSTON***** Environmental Engineering Section, Dept. of Life Sciences, Aalborg University,
Sohngaardsholmsvej /1, DK-3*** Aalborg, Denmark** Dept. of Hilly Land Agriculture, Natl. Agric. Reseach Center for Western Region,
Ikano ,/1/, Zentsuji, Kagawa 10/ῌ**/-, Japan*** Graduate School of Science and Engineering, Saitama University,,// Shimo-okubo, Saitama --2ῌ2/1*, Japan**** Soils and Biogeochemistry, Dept. of Land, Air, and Water Resources,
University of California, Davis, Ca 3/0+0, USA
Abstract
This paper reviews and connects recent studies on gas transport parameter models for Japanese
volcanic ash soils (Andisols). Soil water retention from ῌ+ kPa to ῌ+./ MPa of matric potential for
di#erently-textured, undisturbed Andisols from three prefectures in Japan was well described by
the simple Campbell (+31.) model. Gas di#usivity in the same matric potential range was well
predicted by two recent soil type (Campbell b) dependent models, while the classical Millington
and Quirk (+30+) model markedly under-predicted gas di#usivity for all Andisols. Air permeability (ka) in wet to medium moist soil (from ῌ+ to ῌ+** kPa of matric potential) was also well
predicted by a Campbell b dependent model, provided that ka at ῌ+* kPa of matric potential wasmeasured and used as a reference point in the model. In conclusion, Campbell-based models
appear highly useful for describing pore characteristics and predicting gaseous phase transportparameters in Andisols.
Key words : gas di#usion, gas transport, Campbell soil water retention model, BBC gas di#usivity
model, soil structure ﬁngerprint+.

Introduction

Predictive models for the key transport parameters in the soil gaseous phase (the soil gas
di#usion coe$cient and the soil air permeability) have until recently only been tested within
limited ranges of soil pore size distribution andsoil total porosity (Moldrup et al., ,**+). Since
volcanic ash soils (Andisols) exhibit soil physical properties that are quite di#erent fromnormal (non-volcanic) mineral soils, including
larger total porosities and higher soil water
retention (broader pore size distributions), data
for Andisols should prove highly valuable intesting the general validity of predictivemodels for the gas di#usion coe$cient (gasdi#usivity) and air permeability, both being
functions of soil air-ﬁlled porosity and soil
type. The distinctive soil physical characteristics of Andisols is typically caused by allo-ῐ12ΐῐ῎῔῕ῑ ῒ 3. ῏ ῌ,**-῍

phane, a non-crystaline and highly porous mineral. Andisols are found in all parts of Japanand cover more than +0ῌ (more than 0*,***km,) of the total land area of Japan (Adachi,+31+). For more on Andisol and allophane properties and characteristics, we refer to Henmi(+322), Shoji et al. (+33-), Iwata et al. (+33/), andSo (+333).
Gas di#usivity (Dp) controls gas transportand fate in natural soil systems where di#usive
gas transport is typically dominating compared with convective gas transport. Important examples are soil aeration (Buckingham,+3*.) and its e#ects on plant health (Osozawa etal., +33., Hasegawa, +33.), the emission of
fumigants at soil fumigation sites (Brown andRolston, +32*), the di#usion and volatilisationof organic chemicals from polluted soils(Petersen et al., +330), and the di#usion andbiodegradation of greenhouse gases such as
methane and carbon dioxide (Kruse et al., +330,
Yoshikawa and Hasegawa, ,***). One of the“rules of thumb” in soil physics is an almost
universal use of the Millington and Quirk (MQ,
+30+) equation to predict the changes in Dp with
air-ﬁlled porosity (e) in transport and fatemodels for gaseous compounds in soil. Since
the MQ (+30+) equation is (i) originally derived
only for a soil medium with randomly dis
tributed particles of uniform size (most resembling a coarse sandy soil), (ii) derived forthe case of permeability rather than di#usivity, (iii) not taking into account any e#ects
of soil pore size distribution, and (iv) not
validated against undisturbed soil data
representing a broad range of soil texture, thealmost universal use of the MQ (+30+) equation
to predict Dp (e) does not seem warranted.
Air permeability (ka) as a function of air-ﬁlled
porosity (e) governs convective (pressure gradient induced) air and gas transport in soil. The
increased use of soil venting (soil vapor extraction, SVE) systems during vadose zone
remediation at polluted soil sites has created arenewed interest in ka and its dependency onsoil type and e, since ka typically will be thegoverning parameter for SVE system performance and clean-up e$ciency (Poulsen et al.,+332). Also, air permeability is an easily andrapidly measured parameter compared to for
example gas di#usivity (Iversen et al., ,**+),and ka alone or in combination with Dp provides valuable information about soil structure
and pore connectivity (Ball, +32+, Moldrup etal., ,**+, ,**- a). At present, however, no reliable models to predict ka as a function of e inundisturbed soil across soil types are available(Moldrup et al., +332, ,**+, ,**- a).
The objective of this paper is to review, connect, and put into perspective recent tests ofmodels for soil water retention (pore size distribution), gas di#usivity, and air permeability, as
compared with data for undisturbed volcanic
ash soils (Andisols) from three prefectures inJapan. Further details about data and model
tests can be found in Moldrup et al. (,**- a, b).
The use of combined water retention, gas di#usivity, and air permeability data to provide
valuable information about soil aeration, porecharacteristics, and soil structure is brieﬂy discussed.
,.

Materials and Methods,. + Materials
The +2 Andisols considered here represent
di#erent location, soil type, soil depth, and soil
management and cultivation, and can brieﬂy
be described as follows :+) Seven Andisols from Tsumagoi, Gunma
Prefecture, Honshu (labelled Tsumagoi +ῌ1).
The sample area is characterized by humic andﬁne-textured Andisols with typically -*ῌ/*ῌ
clay. The main crop was cabbage (Tsumagoi +ῌ/). Tsumagoi 0ῌ1 were sampled at a noncultivated ﬁeld.
,) Five Andisols from Miura, Kanagawa
Prefecture, Honshu (Miura +ῌ/). The sample
area is characterized by light-clay Andisols.
The main crop was Japanese radish. Miura .ῌ
/ were sampled at a ﬁeld where soil layer exchange treatment had taken place -ῌ. years
previous to sampling.

῔῕ : Review of Recent Progress in Predicting Gas Transport Parameters for Undisturbed Andisols : Campbell b Dependent Models for Gas Di#usivity and Air Permeability 13

Fig. +(a) The Campbell water retention model (Eq. [+]) ﬁtted to measured data for . Andisols. pF
῍Log (ῌycm H, O)῍Log (ῌyPa)ῌ,. (b) Scatterplot comparison of predicted and measured
relative gas di#usivities (Dp/D*) for +2 Andisols (Moldrup et al, ,**- b). Test of theMillington and Quirk (+30+) model (Eq. [,] ; solid circles), and the BBC model (Eq. [-] ; open
triangles). RMSE is root mean square error of prediction.

-) Six Andisols from Kumamoto prefecture
in Kyushu (Kyushu +ῌ0). The sample area
(grasslands) were characterized by humic(Kyushu .ῌ0) and highly humic (Kyushu +ῌ-)Andisols.
,. , Measurements
Soil water retention (pore size distribution),gas di#usivity, and air permeability data were
measured at between 0 and 3 di#erent soil
matric potentials. The measurements weredone on undisturbed +** cm- soil samples in a
broad matric potential interval from ῑ+ kPa(near water saturation) to ῑ+./ MPa (wilting
point). Three closely-sampled soil cores wereused for each soil. Since variability between
samples were low, especially for soil water retention and gas di#usivity, mean values forthree samples were used in the predictivemodel tests. Soil water retention was measured following Klute (+320). Gas di#usivity
was measured as described by Osozawa (+321),
following the principles of Currie (+30*). Air
permeability was measured following the principles of Grover (+3/0).

-.

Modelling Approaches and Results-. + Soil-Water Retention
We applied the Campbell (+31.) soil water
retention (pore size distribution) model,yῌyeῒ῍qῌqs῎ῑbῌ
῏+ῐwhere y is soil matric potential (Pa), ye is soil
matric potential at air entry, q is volumetricsoil water content, qs is volumetric soil watercontent at water saturation, and b (ΐ*) is theCampbell pore size distribution parameter, corresponding to the slope of the soil water retention curve in a Log (q)-Log (ῑy) coordinate
system.
The Campbell model (Eq. [+]) provided anear-perfect ﬁt to the retention data for all +2
Andisols (coe$cient of regression, r,ΐ*.33)
from ῑ+ kPa to ῑ+./ MPa (Moldrup et al., ,**b). Values of Campbell b ranged from 2.(Miura ,) to .*.2 (Kyushu ,). Examples of the ﬁt
by the Campbell (+31.) retention model to measured data are shown in Fig. + a.
Because of the excellent ﬁt by the simple
Campell (+31.) model, more complicated (multiparameter) retention models like the Mualemvan Genuchten (van Genuchten, +32*) model
were not considered and, consequently, predic-

14  3.  ,**-

tive gas di#usivity models linked to theMualem-van Genuchten retention model (e.g. :Freijer, +33.) were also not considered. However, we recognize that bimodal water retention
models based on the Mualem-van Genuchten
or similar unimodal retention models can provide even more accurate ﬁt to soil-water retention data for Andisols, from water saturation to
wilting point (Abenney-Mickson et al., +330).
Bimodal water retention models may therefore
be highly useful to derive further information
on pore size distribution and pore characteristics and to predict unsaturated hydraulic conductivity and water and solute transport inAndisols.
-. , Gas Di#usivity
We tested the Millington and Quirk (+30+)
model,
DpῌD*e-.--ῌ,
,
where Dp is the gas di#usion coe$cient in soil,
D* is the gas di#usion coe$cient in air, e is thesoil air-ﬁlled porosity (volumetric soil air content), and  is the soil total porosity. Furthermore, we tested two recent and soil-type(Campbell b) dependent gas di#usivity models
for undisturbed soil. The ﬁrst is the BBC[Buckingham(+3*.)-Burdine(+3/-)-Campbell(+31.)] model suggested by Moldrup et al.
(+333),
DpῌD*,eῌ,-ῌb
-
and the second is the soil macro-porosity dependent model by Moldrup et al. (,***),
DpῌD*,e +* kPa-*.*.e +* kPaῌeῌe +* kPa,-ῌb
.
where e +* kPa is the soil air-ﬁlled porosity at+* kPa of soil matric potential, corresponding
to the volumetric content of soil pores with anequivalent diameter -* mm, and is labeled thesoil macro-porosity. Moldrup et al. (,***) foundthat the ﬁrst term in Eq. [.] (marked by brackets) well described gas di#usivity at +* kPa
for +.. undisturbed soil from Europe, and thatthe entire equation well predicted Dp as a function of e for further ,+ undisturbed European
soils where complete Dp (e) data sets were available. The BBC model (Eq. [-]) gave equally

accurate predictions as Eq. [.], while the MQ(+30+) model (Eq. [,]) gave poor predictions
except for sandy soils.
When tested against the Dp (e) data for the +2
Andisols, the two Campbell b dependent models gave similar and good predictions, while
the MQ (+30+) model markedly under-estimatedthe measured Dp (e) data for all +2 Andisols(Moldrup et al., ,**- b). Figure + b shows acomparison between the performance of the
BBC model, Eq. [-], and the MQ (+30+) model,
Eq. [,], tested against the data for the +2
Andisols. The test results emphasize that thesoil type independent Millington and Quirk(+30+) Dp (e) model cannot provide realistic predictions of gas di#usivity in Andisols. Instead,any of the two soil type dependent (Campbell bdependent) Dp (e) models can be used to obtainrealistic predictions for di#usive gas transport
in undisturbed Andisols.
-. - Air Permeability
We applied a general power function model
for ka (e) with reference point not at air saturation but instead at +* kPa in order to makethe ka (e) model analogous to the above presented gas di#usivity models. Thus,kaka +* kPaeῌe +* kPah/where h is a tortuosity/connectivity parameter. Based on Moldrup et al. (+332, ,**+), we
tested Eq. [/] with (i) h+(b/,*), and (ii) h+(b/.). The original model by Moldrup et al.
(+332) with h+(b/.) did a poor job in predicting ka (e) for the Japanese Andisols, both inmore dry soil (matric potential below +* kPa)
and in more wet soil (matric potential above+* kPa). This is in agreement with the previous
model tests against European soils, where Eq.
[/] with h+(b/.) only could predict ka (e)well for sandy soils with b values below 0(compared to b values always exceeding 2 for
the Japanese Andisols).
The recent model by Moldrup et al. (,**+)
with h+(b/,*) had previously tested wellfor European soils with clay contents between++ and .0῍ and, also, tested well for the Japanese Andisols under wet and medium soil mois-ῑῒ : Review of Recent Progress in Predicting Gas Transport Parameters for Undisturbed Andisols : Campbell b Dependent Models for Gas Di#usivity and Air Permeability 15

Fig. ,.

(a) Scatterplot comparison of predicted (Eq. [/]) and measured air permeabilities for theAndisols (Moldrup et al., ,**- a). (b) Comparison of air permeability (ka) and gas di#usivity(Dp/D*) for Tsumagoi 0. The solid line is the predictive ka (e) model (Eq. [/] with h῍+ῌ(b/,*)).

ture conditions (between ῍+ kPa and ῍+**kPa) (Moldrup et al., ,**-a). However, for thehighly-structured Tsumagoi soils, ka steeply increased with increasing e under dry soil conditions, suggesting the sudden occurrence of ahighly connected air-ﬁlled pore network underdrainage. Because of this, the ka (e) model withh῎+ῌ(b/,*) markedly under-predicted themeasured ka (e) for y῏῍-** kPa (pFῐ-./) forsome soils, see Fig. , a.
The sudden increase in ka at dry conditions isshown for Tsumagoi 0 in Fig. , b. Since thesudden increase in the gas transport parameterand the subsequent under-prediction by asimple power function model is not observed
for gas di#usivity (example given in Fig. , b),
the results clearly imply that ka is markedly
inﬂuenced by soil structure while Dp is muchless a#ected. The solid line in Fig. , b is thepredictive ka (e) model (Eq. [/] with h῎+ῌ(b/,*)). Note that in Moldrup et al. (,**- a), a
di#erent (soil type independent) ka (e) model iscompared with the same data.
To describe ka (e) across the entire matricpotential range, a two- or three-region ka (e)model would be needed to better describe ka inthe dry region (to include soil structure, especially connectivity, e#ects) and in the wet
region (to include e#ects of pore blocking byinterconnected water ﬁlms), cf. Fig. , b. Recently, a two-region probability-law model forka (e) that can accurately describe ka (e) data forwell-structured Andisols (e.g., the Tsumagoi
Andisol shown in Fig. , b) within a broad
matric potential range has been developed(Poulsen et al., ,**-).
At present, measurements of ka at at least
one soil matric potential (suggested to be ῍+*kPa) or preferably more are needed to apply
the predictive model [Eq. [/] with h῎+ῌ(b/,*)]
in the wet to medium soil moisture range.
Without any ka measurements, ka (e) can at present not be realistically predicted in undisturbed soils including Andisols.
-. . Gaseous Phase Fingerprints
The data for the Japanese Andisols, measured by Yoshikawa, are unique because soil
water retention, soil gas di#usivity, and soil air
permeability were measured on the same, undisturbed soil samples at as many as 3 di#erent
soil matric potentials. This enabled us to develop and test new soil indexes based on the gastransport parameters (Dp and ka). In Moldrup etal. (,**- a, b), two such indexes are suggested :+) A soil aeration index based on measurements of Dp and soil water retention on thesame undisturbed soil samples at a minimumof 0ῌ1 di#erent soil matric potentials. This  3.

16

so-called Gas Di#usion Fingerprint (GDF) plot
provided the ability to clearly distinguish between soils with low and high aeration potential and, thus, to identify soils with a highpossibility of developing plant diseases related
to poor soil aeration.
,) A soil structure index based on measurements of ka, Dp, and soil water retention on thesame undisturbed soil samples at a minimumof 0ῌ1 di#erent soil matric potentials. This incombination with the Millington and Quirk(+30.) convective-di#usive ﬂuid ﬂow model enabled the development of a simple Soil Structure Fingerprint (SSF) plot that clearly showed
the e#ects of soil management and organic
matter content on soil structure.
Such soil gaseous phase ﬁngerprints may bevaluable in evaluating soil management andcultivation e#ects on pore network and soil
and plant health. Also, combined measurements of water retention, gas di#usivity, andair permeability may provide new information
about inactive pore space for gas transport(Schjonning et al., ,**,).
..

Conclusions+) Soil water retention (pore size distribution) from + kPa to +./ MPa of soil matricpotential was well described by the simple
Campbell (+31.) retention model for all +2 undisturbed Andisols. Although the use of multiparameter, bimodal retention models seems
promising for describing pore size distribution
and hydraulic characteristics for Andisols (e.g.
: Abenney-Mickson et al., +330), multi-parameter retention models are likely not necessary in
relation to developing accurate predictivemodels for gas di#usivity.
,) Gas di#usivity in the same matric potential range (+ kPa to +./ MPa) was accurately
predicted by two recent soil type (Campbell b)
dependent models, while the popular Millington and Quirk (+30+) model markedly underpredicted Dp (e) for all +2 Andisols (Moldrup etal., ,**- b). The Millington and Quirk (+30+)
model is not realistic for predicting gas,**-

di#usivity in undisturbed Andisols. Instead,the Campbell b dependent Dp (e) models arerecommended for use in future gas transportand fate models for Andisols.
-) Air permeability in wet to medium moist
soil (+ to +** kPa of matric potential) was
well predicted by a simple Campbell b dependent model, provided that ka at +* kPa ofmatric potential was measured (Moldrup et al.,,**- a). Since + to +** kPa of matric potential is a realistic range for soil venting systems,
the b dependent ka (e) model seems useful insimulating and designing soil venting systems.
Predictions of ka (e) also in more dry Andisol
will require two- or multi-region models for ka(e) together with additional ka measurements.
.) Soil physics has traditionally been dominated by soil water physics. The combined usedof pore size distribution, gas di#usivity, and air
permeability data can give us new information
on soil management and cultivation e#ects on
soil aeration, soil structure and soil pore characteristics and pore networks and can open up
for new and exiting ﬁndings within the area ofsoil air physics.
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18

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@ABSjIFkHI; ABl1mnopq r+ kPasr+./ MPa t=uvwfxy:Campbell C+31.E Fz{; z|}~STXb`d l1mnopqtb=:; , G=_HAB+ CCampbell-b E Fz{; z|PQb`d, G=:; ῌ BBC CBuckingham-Burdine-CampbellE X; ῍ lmnpo4 Cr+* kPa FkTJFSTE bcTd ; |IHT Millington and
Quirk C+30+E b:;  : +2 =>?@ABSjIb|`d $A

B Cl1mnopqr+sr+** kPaE =J ka :; Q`l1mnopqr+* kPa b= ka V[HTXFz{;¡h Campbell-b Fz{; z|PQb`d ¢8X_

I; Campbell-b F£¤H`:; >?@AB=¥ῌwf CABuvwfxy; AB¦§¨©E V}~_; JKLMNO+VPQST=Fª«F¬­bcTX®¯Xhi`d234 :  ;LM; Campbell ABuv°±; BBC; AB¦§¨©
²³´µ< : ,**- ´ 0 µ 0 <²/´µ< : ,**- ´ 2 µ 1 <¼e : Review of Recent Progress in Predicting Gas Transport Parameters for Undisturbed Andisols : Campbell b Dependent Models for Gas Di#usivity and Air Permeability 19

Dr. Moldrup  : 

ῌ     !"#$% &'Moldrup :() &*+,- .
 "/ 0ῌ
1 
123 4' ,&, 516
7 867 9:;< bimodal 23=, ῌ
40 &>' : 0$&'
Moldrup :67 ῌ
?@: ,ABCDE(F:G- ( HIAndisol (J/<&>' Andisol 67 K!
L.
& >'   ῌM   ῌNO5
 pF ,.* 51 4F"P0 
 - Q'-( 67 pF,.* 51&R, ("&%#" '  51+67 STUVSF" 1+<W4(+ 1+W W$,#JX!
(Y",Z(.  51+67 [\1]"$# .< *+#$("& %#" ' :U V ^ _ finger print `GDFa  b c finger
print %%/&<dG:e,#J""'
Moldrup :fgh &; ijklmVnopqrEs(P&UV^_ # ' --(P&UV^_ . nopqrE(UV^_Di 5'(^_ D* (t>( `DiῌD*a ( *A+
(u ' v wijklmVnopqrEx+* cm H, O ῌ x-* cm H, O ῍ .
 )nG

opqrE( air ﬁlled pore  e+, e,, P&UV^_ D+, D, G ' ,# ynopqrE(
P&^_z air ﬁlled pore z(t>({`D,xD+aῌ`e,xe+a| }G ' -( ijklm
VnopqrE8G 4 `-67x+* cm H, O
&x-* cm H, O 4a $* UV^_~+, ῌ'O:&=,#" '  " !nopqrE4(, air ﬁlled
pore $* UV^_~+,#" &=,#"' v, ($" Andisol "-&`x+* cm H, Oa &.6$/(0" ' " airF " (.
ﬁlled pore , 1^_
J2(.
"- =G' !< Andisol :&.6$/(0 G"^_3"( " (. 'K% 45(u67 Andisol 8
air ﬁlled pore ,1^_"F]: - :" (.
 ' - :" (9
( - :+ 9;5<,#"="#" ' ->
6"# K?CDE$"#*G (:< UV^_@¡ air ﬁlled pore dG"&$&A, %%BC(.<-¢(£TUV^_ finger print %%(.
' -¤D¥&FE¦8,G§#"¨&JF"' ¥& -ῌbc ,#+30. G Millinton and Quirk =,H©ªCDE
?,#" «§"' ,&, -¬IῌbcF  J + ­®¯pDlmV
fg°K@±#" ' L . H²M³´ "67 -NO,ῌ´<P,' -¬I&BC#" J µQG - (¶¢R:·,3 - µQGT ("]  : J -  ¬ I    # @ ¸ 9  7  - Andisol " F 51=,
'J(. - F - (
`S¹ : º¢ »}a