Scaling the saturated hydraulic conductivity of a vertic
ustorthens soil under conventional and minimum tillage
V. Comegna
a, P. Damiani
a,*, A. Sommella
b,1aDipartimento DITEC dell'UniversitaÁ della Basilicata, Via N. Sauro 85, Potenza, Italy
bIstituto di Idraulica Agraria dell'UniversitaÁ di Napoli Federico II, Via UniversitaÁ 100, Portici, Naples, Italy
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 measurementsKs 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 porosityfwas ®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 factorascaled by effective soil porosity. Statistical elaboration indicated that the log-normal law is the one which best approximates the frequency distribution of scale factors akand 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 sig-ni®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
overall improvement in the hydrological characteris-tics 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 conse-quence 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 meth-ods in soils under long-term cultivation generally
*Corresponding author. Tel.: 39-971-474217; fax:
39-971-55370.
E-mail address: [email protected] (P. Damiani).
1Tel.:39-81-7755341; fax:39-81-7755341.
0167-1987/00/$ ± see front matter#2000 Elsevier Science B.V. All rights reserved.
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 agricul-tural 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 dyna-mõÁcally integrated models developed to predict vege-tation 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 experi-ments, preferably to be conducted in the ®eld, in order to evaluate soil hydraulic properties, the spatial dis-tribution 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 mea-suring 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) andk(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 ratioa. The validity of the above assumption was only con®rmed by laboratory tests on sand ®lters (Klute and Wilk-inson, 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 contenty, 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, concen-trating them on a mean reference curve which describes the relation to the study.
Theaparameters identi®ed using the above proce-dures 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 variablea, upon water budget com-ponents. The various components of the water budget, simulated by attributing log-normal frequency distri-butions toa, 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 characterisa-tion in structured soil based on the Kozeny±Carman equation, which relates hydraulic conductivity at saturation, Ks, and effective soil porosity f (Ahuja
The aim of this study is to ascertain the validity of the above method for a clayey soil within an experi-mental area which is representative of hilly environ-ments 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 trans-verse slope was virtually zero.
The plots underwent three tillage systems: plough-ing at 40 cm (PL40); ploughing at 20 cm (PL20);
non-tillage (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®ca-tion. It is therefore a vertic soil characterised by anAp
horizon which, on average, extends to a depth of 30 cm, followed by aCcahorizon to a depth of about
100 cm.
At the three different depths (z0±15, 20±40, and 40±60 cm) and at 10 sites in the three plots, undis-turbed 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 distur-bance. 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 rband hydraulic conductivityKsat saturation, water content
at saturation ys and water content y10 at potential hÿ10 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
the hydrometer method (Gee and Bauder, 1986). According to the SISS classi®cation, the three soils have a clayey±sandy texture. Plot PL20has a slightly
higher sand content than the other two, as well as the lowest clay content. The bulk densityrbwas 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
constant-head 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 atÿ10 kPa pressure head, being fully aware that ®eld capacity is not a precisely de®ned soil parameter. Water content at saturationysand subsequently water contenty10were then measured, by means of kaolin-sand 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-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 1.378 36.5 24.1 39.4
S.D. 0.049 2.31 1.43 1.34
cally. Gravimetric water contents were converted to volumetric water contents by multiplying with mea-sured 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 distribu-tion of effective soil porosity f (i.e. the difference between the total porosity P and the water content
y10). He also proposes correlatingKsandfby means
of the law of power proposed by Kozeny±Carman
KsBfn (1)
in whichB andn are constants evaluated by simple linear regression.
Moreover, Eq. (1) may be combined with scaling theory to deduce the frequency distribution of scale factorsakstarting 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:Wia
p W;iW which links a generic hydraulic propertyWimeasured
at sitei, to the valueW, at the reference site. The factor
aW,iis the ratio between the lengths characterising the
internal geometry of the medium at siteiand that of the reference medium, while the exponentpassumes 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 conductivityK (Sim-mons et al., 1979).
In particular, with reference to hydraulic conduc-tivityKS,iwe obtain
KS;iKSa2i (2)
whereKsmay be obtained by the equation
andai may be calculated as follows:
ai
once the condition of normalisation has been assumed PN
Eq. (5) enables scale factors to be calculated for each site without knowing the constantB. 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 saturationKs.
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
ysandy10are 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
Table 2
Mean (x) (cm3/cm3), standard deviation (S.D.) (cm3/cm3), coef®cient of variation (CV) of water contentsy
sandy10, relative to different tillage
systemsysandy10are averaged over the pro®le
NT PL40 PL20 All data
ys y10 ys y10 ys y10 ys y10
x 0.430 0.353 0.439 0.344 0.425 0.319 0.431 0.337
S.D. 0.027 0.020 0.035 0.032 0.043 0.025 0.037 0.030
Table 3. The data were statistically elaborated taking account of the fact that parametersKs andy have a
distribution frequency which is well approximated by a log-normal law. The table supplies: the mean,
var-iance and coef®cient of variation, with m and s
representing, respectively, the mean and standard deviation of the natural logarithm of Ks andy. 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 conductivityKsas 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 Ksandf. 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 exponentn of Eq. (1) could be kept constant for all
the different soils even if the value of the interceptBis 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 ofn as 2.5371 for all the examined plots new values of Band of the root-mean-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 estimatesn2.5371 provides less accurate esti-mates (RMSE0.278; 0.203 and 0.327, respectively, for plot PL40; NT and PL20) than using n2.1265;
3.2361 and 3.1996 (RMSE0.176; 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 3
Mean, variance and coef®cient of variation (CV) (for representing log-normally distributed data) of hydraulic conductivity at saturationKs
(cm/min) and actual porosityfrelative to different tillage systemsKsandfare averaged over the pro®le
NT (19 tests) PL40(28 tests) PL20(28 tests) All data (75 tests)
Ks f Ks f Ks f Ks f
Meana 0.361 0.104 0.269 0.132 0.419 0.148 0.335 0.131
Varianceb 1.822 0.0024 0.274 0.004 1.569 0.003 0.795 0.004
CV%c 374 44 194 49 299 40 266 47
aexp ms2=2.
bexp 2 ms2exp ÿs2 1. c
exp ÿs2 1
p
.
Table 4
Mean, variance and coef®cient of variation (CV) (for representing log-normally distributed data) of parametersaKandafrelative to different
tillage systems
NT PL40 PL20 All data
aK af aK af aK af aK af
Meana 1.094 1.035 1.033 1.011 1.093 1.036 1.049 1.017
Varianceb 1.158 0.622 0.511 0.283 0.926 0.490 0.754 0.383
CV%c 98 76 69 53 88 68 83 61
aexp ms2=2.
bexp 2 ms2exp ÿs2 1. c
exp ÿs2 1
p
best approximates the frequency distribution both of
akandaf.
Table 4 reports estimates of the mean, variance and coef®cients of variation of factorsabased on the log-normal distribution. Examination of the table shows that the estimates of parameter means are substantially similar whether individual plots or all data are con-sidered. 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.
Theak±afdistributions 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 toKsandf.
Finally, the investigation was extended to a com-parison 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 fis 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 factorsakandafare
quite similar. Moreover, Fig. 3 which reports in a
Fig. 2. Comparison of frequency distributions ofaKandaf.
Table 5
Mean (x) (cm3/cm3), standard deviation (S.D.) (cm3/cm3), coef®cient of variation (CV) of water contentsy
sandy10, relative to different layers.
ysandy10are averaged over the pro®le
z0±15 cm z20±40 cm z40±60 cm
ys y10 ys y10 ys y10
x 0.443 0.350 0.456 0.321 0.403 0.332
S.D. 0.031 0.030 0.019 0.018 0.033 0.031
CV% 7 9 4 6 8 9
Table 6
Mean, variance and coef®cient of variation (CV) (for representing log-normally distributed data) of hydraulic conductivity at saturationKs
(cm/min) and actual porosityfrelative to the different layers,Ksandfare averaged over the pro®le
z0±15 cm z20±40 cm z40±60 cm
Ks f Ks f Ks f
Meana 0.368 0.129 0.389 0.179 0.241 0.103
Varianceb 1.232 0.004 0.286 0.002 0.457 0.002
CV%c 301 46 138 24 281 41
aexp ms2=2.
bexp 2 ms2exp ÿs2 1. c
exp ÿs2 1
p
.
normal probabilistic diagram the factorsafrelative to
the different layers, shows that the log-normal law best approximatesaf distributions.
Finally, Fig. 4 evidences that the theory of similar media is validated in that the parametersaf, relative to
the layers z0±15 and z40±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.
4. Conclusions
In the light of the above results, we may conclude that, once an analytical expression has been assigned
to the relation which links conductivityKsto 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 treat-ments. Even though the pore geometry and soil struc-ture 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 fac-tors, 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 beha-viour 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 equip-ment, 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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