Directory UMM :Data Elmu:jurnal:S:Soil & Tillage Research:Vol54.Issue1-2.Mar2000:

Soil & Tillage Research 54 (2000) 1±9

Scaling the saturated hydraulic conductivity of a vertic
ustorthens soil under conventional and minimum tillage
V. Comegnaa, P. Damiania,*, A. Sommellab,1
a
Dipartimento DITEC dell'UniversitaÁ della Basilicata, Via N. Sauro 85, Potenza, Italy
Istituto di Idraulica Agraria dell'UniversitaÁ di Napoli Federico II, Via UniversitaÁ 100, Portici, Naples, Italy

b

Received 18 January 1999; received in revised form 27 May 1999; accepted 3 November 1999

Abstract
With the aim of setting up a simpli®ed method to measure hydraulic conductivity of structured soils at saturation, a method
reported by Ahuja et al. (Soil Sci. Soc. Amer. J. 48 (1984) 699±702; Soil Sci. 148 (1989) 404±411), which also refers to the
generalised equation of Kozeny±Carman and the scaling theory, is tested in this paper. Data were elaborated from hydraulic
conductivity measurements Ks on undisturbed soil cores taken from three plots of a sloping vertic soil which underwent
various tillage practices for many years. In particular, following the proposed methodology, the spatial distribution effective
soil porosity f was ®rst obtained. Once the distributions of hydraulic conductivity at saturation were obtained, it was possible
to correlate the spatial variability of hydraulic conductivity with the variability of the unique factor a scaled by effective soil

porosity. Statistical elaboration indicated that the log-normal law is the one which best approximates the frequency distribution
of scale factors ak and af. No signi®cant differentiations were noted between the distributions of parameters relative to
different soil tillage systems. # 2000 Elsevier Science B.V. All rights reserved.
Keywords: Hydraulic conductivity; Effective soil porosity; Scale factors; Soil tillage system

1. Introduction
In the last few decades, practices used for the
mechanical manipulation of soil have undergone signi®cant operative and technological changes. Most
recent tillage operations have allowed a substantial
increase in soil productivity and decrease in energy
consumption. Tillage practices generally lead to an
*
Corresponding author. Tel.: ‡39-971-474217; fax: ‡39-97155370.
E-mail address: damiani@unibas.it (P. Damiani).
1
Tel.: ‡39-81-7755341; fax: ‡39-81-7755341.

overall improvement in the hydrological characteristics of soil, thereby helping to create optimal crop
vegetative conditions and markedly reducing soil
erosion problems (Douglas et al., 1981; Hamblin

and Tennant, 1981; Horton et al., 1989; Datiri and
Lowery, 1991; Wu et al., 1992). One major consequence of tillage is that it modi®es some soil physical
and chemical properties, especially at the surface
layer, such as total porosity, continuity and tortuosity
of the pore system, pore-size distribution, surface
roughness, degree of compaction, and hence bulk
density, as well as nutrient distribution. Tillage methods in soils under long-term cultivation generally

0167-1987/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved.
PII: S 0 1 6 7 - 1 9 8 7 ( 9 9 ) 0 0 0 9 8 - 7

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

result in increasing total porosity of the ploughed
layer, reducing consolidation and helping to set up
bigger aggregates (Unger, 1984). However, long-term
tillage operations could exert undesirable effects on
soil properties (Bouma and Hole, 1971) and possible

interactions between tillage and space±time variability
in soil properties should also be taken into account
(Cassel and Nelson, 1985; Van Es, 1993).
Given that the soil surface and uppermost horizon
play an important role in determining the amount of
incident water Ð whether rainfall or irrigation water
Ð which becomes runoff, it is apparent that tillage
may considerably affect the hydrology of an agricultural catchment (Freebairn et al., 1989; Mwendera and
Feyen, 1993). An in-depth physical understanding of
this effect can thus be extremely useful for obtaining
reliable results when using comprehensive and dynamõÁcally integrated models developed to predict vegetation growth, in®ltration, overland ¯ow and sediment
yield, and the ways in which such phenomena evolve
in response to variations in climate or land use (Kirkby
et al., 1992).
However, the implementation of such models
requires new technologies and a new class of experiments, preferably to be conducted in the ®eld, in order
to evaluate soil hydraulic properties, the spatial distribution and variation of the porous system.
Many experimental studies have shown that soil
hydraulic properties vary considerably even in the
same mapping area (Nielsen et al., 1973; Comegna

and Vitale, 1993), especially as regards hydraulic
conductivity, which may have coef®cients of variation
in excess of 100%. The study of variability in ®eld of
hydraulic parameters requires a large number of measuring points, thereby making calculations somewhat
time-consuming.
In order to streamline the procedure, it is necessary
to set up simpler Ð though less precise Ð measuring
techniques, preferably evaluating laws h(y) and k(y)
by means of analytical expressions with a small number
of parameters (Mualem, 1976; Van Genuchten, 1980).
Moreover, the description of the spatial variability
of hydraulic parameters may be simpli®ed if we
assume that soil microgeometry in two different sites
may be similar. As shown by Miller and Miller
(1955a,b), values of water potential and hydraulic
conductivity measured in different areas may be
referred to corresponding mean values by means of

spatial distribution of the local similarity ratio a. The
validity of the above assumption was only con®rmed

by laboratory tests on sand ®lters (Klute and Wilkinson, 1958; Elrick et al., 1959) and, although there
has been no actual response in soils, it was used by
various authors (Warrick et al., 1977b; Simmons et al.,
1979; Rao et al., 1983) by referring tensiometric and
conductivity data to degree of saturation, s, rather than
to water content and water content y, and evaluating
the distribution of the similarity ratio not in reference
to the microgeometry of the porous medium, but by
ensuring that the hydraulic conductivity and retention
curve, measured at different points, ®tted in the best
way. Thus we overcome the rigorous concept of
geometric similarity introduced 40 years ago by Miller
and Miller, and the similarity ratio is evaluated using
regression techniques. Such techniques, generally
indicated in the literature as functional normalisation
techniques (Tillotson and Nielsen, 1984), aim to
reduce the dispersion of experimental data, concentrating them on a mean reference curve which
describes the relation to the study.
The a parameters identi®ed using the above procedures often differ in each hydraulic property for which
they were evaluated (Warrick et al., 1977b; Russo and

Bresler, 1980; Ahuja et al., 1984b). Application of the
similarity concept to the water budget of a small basin
or irrigated area has recently produced encouraging
results (Peck et al., 1977; Bresler et al., 1979; Sharma
and Luxmoore, 1979; Warrick and Amoozegar-Fard,
1979). By means of a simulation model, the above
authors examined the effects of spatial variability of
soil hydraulic properties expressed in terms of the
single stochastic variable a, upon water budget components. The various components of the water budget,
simulated by attributing log-normal frequency distributions to a, agree closely with the values measured
experimentally.
Furthermore, the relevant literature shows that
applications of the similarity concept in the ®eld
are still too limited in number and restricted to soils
of reasonable morphological similarity. Recently, the
scaling theory of porous media was combined with
simpli®ed methodologies for hydraulic characterisation in structured soil based on the Kozeny±Carman
equation, which relates hydraulic conductivity at
saturation, Ks, and effective soil porosity f (Ahuja
et al., 1989, 1993; Franzmeier, 1991).

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

The aim of this study is to ascertain the validity of
the above method for a clayey soil within an experimental area which is representative of hilly environments in southern Italy.

2. Materials and methods
Ninety tests were carried out on sloping plots
subjected to different tillage systems and located in
the experimental ®eld of Guardia Perticara (Province
of Potenza), whose pedological characteristics and
location have been studied for about 20 years with
regard to surface water erosion.
In the ®eld, 16 rectangular plots (15 m40 m) were
set along the slope lines. The average slope of each
plot along the broader side was 14% while the transverse slope was virtually zero.
The plots underwent three tillage systems: ploughing at 40 cm (PL40); ploughing at 20 cm (PL20); nontillage (NT). For many years the plots were under a
continuos crop rotation of horse bean±wheaten.

The soil examined is pedologically classi®able as
vertic ustorthens, according to the USDA classi®cation. It is therefore a vertic soil characterised by an Ap
horizon which, on average, extends to a depth of
30 cm, followed by a Cca horizon to a depth of about
100 cm.
At the three different depths (zˆ0±15, 20±40, and
40±60 cm) and at 10 sites in the three plots, undisturbed soil samples were collected by driving a steel
cylinder 8 cm in diameter 12 cm high, perpendicularly
into the soil while carefully excavating soil from
around the samples. Then the core was removed.
During sampling care was taken in order to reduce
compaction of the soil and some inevitable disturbance. All cores were plugged at the top and bottom
with rubber band and transported to the laboratory.
There they were stored at 48C constant temperature
before making laboratory measurements.
The measurements carried out in the laboratory on
ninety samples include: texture, bulk density rb and
hydraulic conductivity Ks at saturation, water content
at saturation ys and water content y10 at potential
hˆÿ10 kPa.

The percentages of sand, silt and clay (Table 1),
according to the methods proposed by International
Society of Soil Science (SISS), were calculated with

Table 1
Mean (x), standard deviation (S.D.), coef®cient of variation (CV%)
of some soil physical properties relative to different tillage systems
rb (g/cm3)

Sand (%)

Silt (%)

Clay (%)

NT
x
S.D.
CV%

1.378
0.049
3.6

36.5
2.31
6.3

24.1
1.43
5.9

39.4
1.34
3.4

PL40
x
S.D.
CV%

1.386
0.077
5.6

40.0
3.43
8.5

23.6
2.59
11.0

36.4
2.7
7.5

PL20
x
S.D.
CV%

1.374
0.109
8.0

48.8
2.39
4.9

20.2
1.48
7.3

31.0
2
6.4

the hydrometer method (Gee and Bauder, 1986).
According to the SISS classi®cation, the three soils
have a clayey±sandy texture. Plot PL20 has a slightly
higher sand content than the other two, as well as the
lowest clay content. The bulk density rb was obtained
by oven-drying the soil samples at 1058C. Prior to the
initiation of determining soil hydraulic parameters, the
soil cores were gradually saturated from below, using
de-aerated 0.01 M CaCl2 solution, in the course of
60 h so as to guarantee the complete release of the air,
and then brought to saturation. Saturated hydraulic
conductivity, Ks, was determined using a constanthead permeameter (Klute, 1986).
Only for simpli®ed applications, bearing in mind
that the soil in question behaves like semi-rigid soil
and water stable due to the mineral composition of the
clayey material, in this paper the de®nition of effective
porosity of Brutsaert (1967) and Corey (1977) was
used with ®eld capacity assumed as soil water content
at ÿ10 kPa pressure head, being fully aware that ®eld
capacity is not a precisely de®ned soil parameter.
Water content at saturation ys and subsequently water
content y10 were then measured, by means of kaolinsand box apparatus consisting of two sets of ceramic
tanks each of which could contain up to 12 soil cores.
For the drainage soil cores to measure potential in the
range from 0 to ÿ10 kPa, use whose made of a
reference Mariotte wessel to set values of suction
head. The equilibrium water content corresponding
to the monitored potential was measured gravimetri-

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

where Ks may be obtained by the equation
PN p!2
KS;i
iˆ1
S ˆ
K
N

cally. Gravimetric water contents were converted to
volumetric water contents by multiplying with measured oven-dry bulk density values.
Having obtained the values of conductivity and
water contents, we evaluated the possibility of linking
conductivity to effective soil porosity, following the
methodology proposed by Ahuja et al. (1984a). To
estimate the distribution of hydraulic conductivity at
saturation, Ahuja proposes using the spatial distribution of effective soil porosity f (i.e. the difference
between the total porosity P and the water content
y10). He also proposes correlating Ks and f by means
of the law of power proposed by Kozeny±Carman
Ks ˆ Bfn

and ai may be calculated as follows:
p
N KS;i
ai ˆ PN p
KS;i
iˆ1

(4)

once
PN the condition of normalisation has been assumed
iˆ1 ai =N ˆ 1. Finally, combining Eq. (1) with (4),
we obtain
p
N fn
ai ˆ PN pin
(5)
fi
iˆ1

(1)

in which B and n are constants evaluated by simple
linear regression.
Moreover, Eq. (1) may be combined with scaling
theory to deduce the frequency distribution of scale
factors ak starting from the distribution of scale factors
af.
As shown by the above authors, supposing the
surface tension and the coef®cient of kinematic water
viscosity are constant, the following formula holds for
two geometrically similar porous media: Wi ˆ apW;i W
which links a generic hydraulic property Wi measured
at site i, to the value W, at the reference site. The factor
aW,i is the ratio between the lengths characterising the
internal geometry of the medium at site i and that of
the reference medium, while the exponent p assumes a
value of 1 when the hydraulic property considered is
the water potential h, and a value of two when
reference is made to hydraulic conductivity K (Simmons et al., 1979).
In particular, with reference to hydraulic conductivity KS,i we obtain
KS;i ˆ K S a2i

(3)

where fiˆf at site i.
Eq. (5) enables scale factors to be calculated for
each site without knowing the constant B. Thus a few
Ks measurements, preferably taken at the level of
modal soil pro®le, allow us to arrive at an estimate
for average hydraulic conductivity at saturation Ks.

3. Results and discussion
In order to characterise the spatial variability of the
water content, the data were elaborated statistically,
with the frequency distribution being reported in
Table 2, where for each tillage system: mean, standard
deviation and coef®cient of variation of water contents
ys and y10 are presented. The data reported in the table
show low standard deviations and hence low coef®cients of variation, which is highest (10%) in the plot
PL20, while lower values are recorded for the other
plots.
Mean saturated hydraulic conductivity and effective
soil porosity for the three plots are summarised in

(2)

Table 2
Mean (x) (cm3/cm3), standard deviation (S.D.) (cm3/cm3), coef®cient of variation (CV) of water contents ys and y10, relative to different tillage
systems ys and y10 are averaged over the pro®le
NT

x
S.D.
CV%

PL40

PL20

All data

ys

y10

ys

y10

ys

y10

ys

y10

0.430
0.027
6

0.353
0.020
6

0.439
0.035
8

0.344
0.032
9

0.425
0.043
10

0.319
0.025
8

0.431
0.037
8

0.337
0.030
9

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

Table 3
Mean, variance and coef®cient of variation (CV) (for representing log-normally distributed data) of hydraulic conductivity at saturation Ks
(cm/min) and actual porosity f relative to different tillage systems Ks and f are averaged over the pro®le
NT (19 tests)

a

Mean
Varianceb
CV%c

PL40 (28 tests)

PL20 (28 tests)

All data (75 tests)

Ks

f

Ks

f

Ks

f

Ks

f

0.361
1.822
374

0.104
0.0024
44

0.269
0.274
194

0.132
0.004
49

0.419
1.569
299

0.148
0.003
40

0.335
0.795
266

0.131
0.004
47

a

exp…m ‡ s2 =2†.
exp…2m ‡ s2 †‰exp…s2 † ÿ 1Š.
p
c
exp…s2 † ÿ 1.
b

Table 3. The data were statistically elaborated taking
account of the fact that parameters Ks and y have a
distribution frequency which is well approximated by
a log-normal law. The table supplies: the mean, variance and coef®cient of variation, with m and s
representing, respectively, the mean and standard
deviation of the natural logarithm of Ks and y. For
the three plots, similar mean parameter values are
recorded, unlike the coef®cients of variation which, as
expected, are rather high, in agreement also with the
literature (Warrick and Nielsen, 1980).
After making the calculations relative to Eq. (1)
Fig. 1 was then obtained in which the hydraulic
conductivity Ks as a function of effective soil porosity
f is reported, for individual plots and for all data.
The dispersion of experimental values around the
regression lines (indicated by letter (a)) con®rms
the existence of a physical link between parameters
Ks and f. Moreover, the slope of the least-squares line
®tted through all the data is 2.573.
According to Ahuja et al. (1989) the value of
exponent n of Eq. (1) could be kept constant for all

the different soils even if the value of the intercept B is
different for each of them.
In our study, Table 1 shows that soil texture does
change signi®cantly in the three tillage systems.
Therefore, holding the value of n as 2.5371 for all
the examined plots new values of B and of the rootmean-squares deviations (RMSE) were calculated.
For the purposes of comparison, the new regression
lines are reported in Fig. 1 with the letter (b). Against
the intercepts of log±log regression are not signi®cantly different from the intercept of any of the
individual soil except for the NT plot data. However,
using estimates nˆ2.5371 provides less accurate estimates (RMSEˆ0.278; 0.203 and 0.327, respectively,
for plot PL40; NT and PL20) than using nˆ2.1265;
3.2361 and 3.1996 (RMSEˆ0.176; 0.153 and 0.301,
respectively).
With further elaborations carried out by means of
Eqs. (2)±(5), we obtained the frequency distributions
of factors ak obtained from Ks and of factors af
obtained from f. Statistical elaboration enabled us
to ascertain that the log-normal law is the one which

Table 4
Mean, variance and coef®cient of variation (CV) (for representing log-normally distributed data) of parameters aK and af relative to different
tillage systems
NT

a

Mean
Varianceb
CV%c
a

PL20

All data

aK

af

aK

af

aK

af

aK

af

1.094
1.158
98

1.035
0.622
76

1.033
0.511
69

1.011
0.283
53

1.093
0.926
88

1.036
0.490
68

1.049
0.754
83

1.017
0.383
61

exp…m ‡ s2 =2†.
exp…2m ‡ s2 †‰exp…s2 † ÿ 1Š.
p
c
exp…s2 † ÿ 1.
b

PL40

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

Fig. 1. Saturated hydraulic conductivity (Ks) as a function of effective porosity (f). See text for description of ®tted lines.

best approximates the frequency distribution both of
ak and af.
Table 4 reports estimates of the mean, variance and
coef®cients of variation of factors a based on the lognormal distribution. Examination of the table shows
that the estimates of parameter means are substantially
similar whether individual plots or all data are considered. Moreover, on elaborating the data of hydraulic
conductivity at saturation the coef®cients of variation
obtained are higher than those from elaborations of
effective soil porosity. Such behaviour is probably due
to both the fact that hydraulic conductivity is much more
sensitive to variations in soil saturation and because the
methods used for measuring conductivity are not yet
very reliable with regard to structured soils.

The ak±af distributions for all the data, reported in
the fractile diagram of Fig. 2, show good agreement
except for the extremes of the distribution where, for
the reasons given above, larger systematic errors are
expected in test observations relative to Ks and f.
Finally, the investigation was extended to a comparison by layer of all the parameters considered. The
data reported in Table 5 show a moderate variabilty in
water contents ys and y10. By contrast, in Table 6
greater spatial variability in the conductivity Ks and
effective porosity f is observed, which may be well
represented by log-normal distributions.
Analysis of Table 7 shows that the estimates of the
main statistical moments of scale factors ak and af are
quite similar. Moreover, Fig. 3 which reports in a log-

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

Fig. 2. Comparison of frequency distributions of aK and af.

Fig. 3. Comparison by layer of frequency distributions of af.

Table 5
Mean (x) (cm3/cm3), standard deviation (S.D.) (cm3/cm3), coef®cient of variation (CV) of water contents ys and y10, relative to different layers.
ys and y10 are averaged over the pro®le
zˆ0±15 cm

x
S.D.
CV%

zˆ20±40 cm

zˆ40±60 cm

ys

y10

ys

y10

ys

y10

0.443
0.031
7

0.350
0.030
9

0.456
0.019
4

0.321
0.018
6

0.403
0.033
8

0.332
0.031
9

Table 6
Mean, variance and coef®cient of variation (CV) (for representing log-normally distributed data) of hydraulic conductivity at saturation Ks
(cm/min) and actual porosity f relative to the different layers, Ks and f are averaged over the pro®le
zˆ0±15 cm

Meana
Varianceb
CV%c
a

zˆ40±60 cm

Ks

f

Ks

f

Ks

0.368
1.232
301

0.129
0.004
46

0.389
0.286
138

0.179
0.002
24

0.241
0.457
281

exp…m ‡ s2 =2†.
exp…2m ‡ s2 †‰exp…s2 † ÿ 1Š.
p
c
exp…s2 † ÿ 1.
b

zˆ20±40 cm

f
0.103
0.002
41

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V. Comegna et al. / Soil & Tillage Research 54 (2000) 1±9

Table 7
Mean, variance and coef®cient of variation of (for representing log-normally distributed data) parameters aK and af relative to different tillage
systems
zˆ0±15 cm

a

Mean
Varianzab
CV%c

zˆ20±40 cm

zˆ40±60 cm

aK

af

aK

af

aK

af

1.061
0.880
88

1.030
0.507
69

1.013
0.312
55

1.003
0.155
39

1.058
0.814
85

1.012
0.342
58

a

exp…m ‡ s2 =2†.
exp…2m ‡ s2 †‰exp…s2 † ÿ 1Š.
p
c
exp…s2 † ÿ 1.
b

Fig. 4. Correlation between af relative to depth zˆ0±15 cm and af
relative to depth zˆ40±60 cm.

normal probabilistic diagram the factors af relative to
the different layers, shows that the log-normal law best
approximates af distributions.
Finally, Fig. 4 evidences that the theory of similar
media is validated in that the parameters af, relative to
the layers zˆ0±15 and zˆ40±60 cm, are arranged
around a 458 sloping curve and going through the
origin and are well correlated, with a correlation
coef®cient equal to 0.97.

to the relation which links conductivity Ks to effective
soil porosity f, the use of the similar media theory
allows the variability in the hydraulic parameters of
the soil in question to be linked to the variability in
parameter a.
Long-term tillage effects on hydraulic properties of
soil considered here appear to be related more to the
particle-size distribution than to the speci®c treatments. Even though the pore geometry and soil structure at surface undergo important modi®cations due to
the various tillage methods employed, these changes
are nonetheless unstable with time due to alterations
resulting from meteorologic and environmental factors, including wetting and drying cycles in the soil
pro®le. Therefore as a general rule, a progressive
annulment of tillage effects on soil structure and
hydraulic properties can be observed and this behaviour is far more evident in the case of vertisols that
signi®cantly shows a tendency to regenerate their
structure as time elapses.
With a view to supplementing the present research
with ®eld tests, in®ltration tests will be carried out on
the same plots by means of more appropriate equipment, such as tension in®ltrometers which allow better
assessment of the effects of the porous system on soil
hydraulic properties in a ®eld of water content values
close to saturation (Perroux and White, 1988; Shouse
and Mohanty, 1998).
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4. Conclusions
In the light of the above results, we may conclude
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