J. agric. Engng Res., (2001) 78 (1), 109}116doi:10.1006/jaer.2000.0617, available online at http://www.idealibrary.com onSW*Soil and Water
Two-component Analysis of Flow through Macroporous Soil
J. Y. Diiwu1; R. P. Rudra1; W. T. Dickinson1; G. J. Wall2
1School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1; e-mail of corresponding author: [email protected] Resource Research Centre, Agriculture and Agri-Food Canada, Guelph, ON, Canada N1H 6N1; e-mail: [email protected]
(Received 28 April 1999; accepted in revised form 22 July 2000; published online 25 October 2000)
Subsurface hydrographs, obtained during rainfall simulation on 1m by 1m plots, were separated intomacropore and micropore components by application of a dual-porosity concept and mass balance analysis.The corresponding solute concentrations in the two domains were also determined by mass balance analysis.Time-domain re#ectometry was then used to estimate similar out#ow hydrographs and breakthrough curves atan upper depth in the A horizon of the soil pro"le. The results show that the macropores contributed from 6 to54% of total subsurface #ow and from 1 to 61% of total solute mass transported through the soil pro"le.
( 2001 Silsoe Research Institute
1. Introduction
In "eld soil heterogeneity caused in part by the pres-ence of fractures, "ssures, channels, root and worm holes,peds and aggregates would result in multi-modal distri-bution of pore-size (Uttermann et al., 1990; Durner,1994). Since pore size directly a!ects soil hydraulic con-ductivity, a multi-modal pore-size distribution wouldresult in a multi-modal distribution of subsurface #owand solute transport (White, 1985; Jarvis et al., 1991).When two pore-size classes are considered in the analysiswe have a bimodal pore-size distribution, and the corre-sponding subsurface #ow distribution is bimodal. Apartfrom having a bimodal pore-size distribution, the occur-rence of a bimodal subsurface #ow distribution alsodepends on such conditions as antecedent soil watercontent and rainfall intensity (Jarvis et al., 1991).
Various categorizations have been used in the litera-ture for de"ning macropores. For instance, macroporeshave been de"ned as those pores having diameters from30 to 300 lm. They have also been de"ned based on thematric potential at which they drain such as !6 cm ofwater; by volume fraction such as 0)001}0)05; or byin"ltration rate such as 1}10 mmh~1; or as those poreswhich empty in 24 h (Beven & Germann, 1982; White,1985; Chen & Wagenet, 1992). In this paper, macroporesare de"ned as those pores which empty at matric poten-tials greater than !5 cm of water. This corresponds to
0021-8634/01/010109#08 $35.00/0 10
a diameter of 600 lm for water at surface tension of0)07 Nm~1 with a contact angle of 03. The matric poten-tial of !5 cm was selected as one which is greater thanthe maximum matric potential of !10 cm which wasapplied in laboratory experiments for determination ofsoil water characteristics of the study "eld (Diiwu, 1997;Diiwu et al., 1998a).
One approach to modelling #ow in macroporousmedia considers the structural units (peds, aggregates,clods) as sources or sinks for the more mobile water inthe macropores. Another approach considers the bi-modal medium as two superimposed media, each with itsown hydraulic properties. There is the macroporedomain in which subsurface #ow and solute transmissionis very fast compared to slow subsurface #ow and solutetransmission in the micropore domain (Beven &Germann, 1981; Jarvis et al., 1991; Chen & Wagenet,1992). Exchange of mass between the macropore andmicropore domains depends on the degree of saturationof the soil (Jarvis et al., 1991). The two-domain concepthas been presented in various forms such as the mo-bile}immobile form by Beven and Germann (1981), aswell as the dual-porosity model by Gerke and vanGenuchten (1993) and Durner (1994). The di$culty withthese models is the problem of accounting for the ex-change of mass between the two domains. Besides, forsoils with unstable aggregates it would be extremelydi$cult to accurately determine the hydraulic properties
9 ( 2001 Silsoe Research Institute
J. Y. DIIWU E¹ A¸ .110
of the two domains separately due to variability of soilproperties in the "eld.
In modelling subsurface #ow and contaminant trans-port through macroporous soil, the uncertainties in thetwo-domain approach may be quanti"ed by means ofprobability measures of the hydraulic variables of thetwo domains. Combining this with dual porosity, thehydraulic processes in each of the macropore andmicropore domains may be characterized by a distinctprobability distribution (Diiwu, 1997). Derivation of thedistinct probability distributions for the macropore andmicropore domains requires that #ows and solute con-centrations be separated into macropore and microporecomponents if such components were not separatelymeasured during data collection. Also, for decision-making on water management it may be useful to be ableto assess the separate contributions of the macropore andmicropore domains to subsurface #ows and solute mass-es transported through the soil system. This may benecessary since macropores tend to transmit water andcontaminants rapidly beyond the root zone and intostreams and the groundwater system. This paper there-fore discusses the application of the dual-porosityconcept to separate subsurface hydrographs and break-through curves into macropore and microporecomponents. The analysis of spatial variability of thephysical and hydraulic properties of soil in the study "eldhad pointed to the possibility of the occurrence of macro-pore #ow in the "eld (Diiwu, 1997; Diiwu et al., 1998a,1998b). Hence, the need for subsurface #ow separation inthe study. Some existing soil water characteristic modelshave been found to perform poorly when applied on soilwith macropores (Diiwu et al., 1998c). Separation ofsubsurface #ow would enable such models to be success-fully applied to the micropore domain, along with analternative model for the macropore domain.
2. Materials and methods
2.1. Rainfall simulation experiments
Subsurface hydrographs and breakthrough curveswere measured during rainfall simulation on 1 m by 1 mplots under no-tillage treatment. The plots wereconstructed by installing large steel plates approximatelyof the same dimensions as the plots, at a depth of about55 cm in the soil pro"le to serve as catchment pansto collect subsurface #ow during rainfall event. Thesteel plates were installed by gently driving them hori-zontally into place in the B horizon using hydraulic jacks.The investigation therefore involved the A and B hor-izons of the soil pro"le. The thickness of the A horizonat the site varies between 25 and 30 cm and the portion
of the B horizon above the pans varies between 25 and30 cm.
Plastic bottles were installed in a pit for collecting thesubsurface #ow for subsequent sampling. At the soilsurface, aprons were placed around the plots to directsurface #ow into a V-shaped trough from which sampleswere collected at 1 min intervals to determine volume ofruno! generated and the concentration of tracer presentin the runo!. Pairs of time-domain re#ectometry (TDR)probes, each probe measuring 20 cm in length and 0)2 cmin diameter, were installed horizontally at depths of 2)5,25, and 50 cm in each plot to measure in situ soil watercontent during rainfall simulation. The dielectric con-stant manually measured by TDR (Tectronix instrumentmodel 1502C) was used to infer the water content of thesoil via the emperical relationship by Topp et al. (1980).
Rainfall intensity of 15)6 cmh~1 was simulated byusing the Guelph Rainfall Simulator II with a 12)7 mmfull jet nozzle that was maintained at a height of 1)5 mabove the soil surface and was operated at a pressurebetween 48 and 55 kPa (Tossel et al., 1987). Water forrainfall simulation was supplied by a pump at a rate of2)4 m3h~1. To avoid moving the simulator from one plotto another, three rainfall simulators were used, one oneach of plots 1}3. Characteristics of the three simulatorswere the same, and they were used to produce similarrainfall events. For each experiment bromide tracer solu-tion was applied on the soil surface of each plot usinga hand-held spray. The rainfall simulator was thenturned on and left to run for about 15 min, during whichtime ponding was established and maintained. Over the15 min period the simulator on plot 1 produced a totalvolume of 31 290 cm3 of water, on plot 2 the simulatorproduced 31 800 cm3 of water, and on plot 3 this was32 900 cm3. The slight di!erences in total volume ofwater produced are attributable to unavoidable sourcesof error such as the precise timing of start and end ofsimulation, the variation in nozzle pressure during simu-lation, and the e!ect of wind on the simulated raindrops(Tossel et al., 1987). Surface and subsurface #ows weresampled for volume and bromide concentration at aninterval of 1 min, over a 45 min period from the begin-ning of rainfall simulation.
2.2. Separation of hydrographs into macroporeand micropore components
The application of the dual-porosity concept inhydrologic modelling requires that the macropore andmicropore #ow components be separated and thecorresponding mass of contaminant in each componentdetermined. Everts and Kanwar (1990) representedthe transport of solute to subsurface drains by a mass
111TWO-COMPONENT ANALYSIS
balance equation using a hydrograph separation tech-nique proposed by Pinder and Jones (1969). The tech-nique was adapted in this study for separating subsurface#ow into macropore and micropore components. Theequations for subsurface #ow and concentration of solutecan be written as
Qt"Q
mi#Q
ma(1)
Ct"
Qmi
Cmi#Q
maC
maQ
t
(2)
where Qtdenotes the #ow rate measured at the pan in
cm3 min~1, Qmi
denotes the portion of Qtassociated with
the micropore domain in cm3 min~1, Qma
denotes theportion of Q
tassociated with the macropore domain in
cm3 min~1, Ctdenotes the total concentration of solute
measured in Qtin lg cm~3, C
midenotes concentration of
solute associated with the micropore domain in lg cm~3,and C
madenotes concentration of solute associated with
the macropore domain in lg cm~3. The objective of theseparation performed in the study was to obtain valuesfor Q
mi, Q
ma, C
miand C
mafrom the hydrographs and
breakthrough curves observed at the pan, such that theconditions of mass balance expressed in Eqns (1) and (2)above were satis"ed.
For the #ow separation a typical hydrograph obtainedfrom the rainfall simulation experiments and shownin Fig. 1, was partitioned into three stages. The partition-ing was based on the assumption that the hydraulic
Fig. 1. Subsurface hydrograph measured at pan on plot 1 for 26May, 1993 event and corresponding estimated macropore andmicropore components: , total yow; , macropore yow;
, micropore yow
conductivity of the macropore domain was several ordersof magnitude greater than the hydraulic conductivity ofthe micropore domain. This condition is re#ected bydouble peaks in the measured hydrograph (Gerke & vanGenuchten, 1993). It was also assumed that there wasnegligible mixing between the two domains, and that themacropores were empty of antecedent soil water prior toeach rainfall simulation event (Everts & Kanwar, 1990).The entire duration of simulation was considered tocomprise three stages. In the "rst stage, the processes ofwater redistribution and drainage were considered to beinitially dominated by macropores. This was followed bya mixed stage when both macropores and microporeswere conducting water, before macropores emptied. Afterthe macropores were empty the micropores were respon-sible for drainage and redistribution of water. The ob-served hydrograph was then partitioned into the threestages as follows.
Stage 1 from the beginning of rainfall simulation up tothe ,rst peak of the hydrograph
In this case, it was assumed that the observed #ow wasonly from the macropore domain. The "rst peak wasattained a few minutes before rainfall simulation ceased.Also it was assumed that micropore #ow was juststarting.
Stage 2 between the two hydrograph peaksIn this case, both macropore and micropore #ows were
likely to be taking place, and hence any observed #owsinclude contributions from the two domains. While thecontribution from the macropores decreased as theyemptied, that from the micropores increased. By the timethe second peak was attained, all macropores have emp-tied, and so the micropore domain would be the only onecontributing to the observed subsurface #ow.
Stage 3 beyond the second peakDuring this stage, all the observed #ow was assumed to
be through the micropore domain and all macroporeshave emptied.
With this partitioning of the hydrograph the separ-ation of subsurface #ow was required for stage 2 only.Moreover, there was a point in time during this stage atwhich the contributions to #ow from the two domainswere equal. The #ow separation was thus achieved byconstrained spline interpolations through the two peaksand the point of in#exion between them. The recedinglimb of the macropore component of the hydrograph wasspline "tted through three points*the "rst peak at whichQ
ma"Q
tand Q
mi"0, the point on the time axis corre-
sponding to the second peak, where Qma"0 and
Qmi"Q
tand the third point midway between the two
peaks at which Qma"Q
mi"0)5 Q
t. The intermediate
points of this spline curve were obtained by adjusting theproportions of Q
mabetween 1 and 0)5 as well as between
Fig. 2. Breakthrough curve measured at pan on plot 1 for 26 May,1993 event and corresponding estimated macropore and micro-pore components: , total yow; , macropore yow;
, micropore yow
J. Y. DIIWU E¹ A¸ .112
0)5 and 0 such that Eqns (1) and (2) were satis"ed. Thelower limb of the micropore component of the hydro-graph was spline "tted through three points*the secondpeak at which Q
mi"Q
tand Q
ma"0, the point on the
time axis corresponding to the "rst peak, and the thirdpoint midway between the two peaks at whichQ
ma"Q
mi"0)5 Q
t. The intermediate points of this
spline curve were obtained by adjusting the proportionsof Q
mibetween 0 and 0)5 as well as between 0)5 and 1 such
that Eqns (1) and (2) were satis"ed.
2.3. Determination of mass of solute transported throughthe macropores and micropores
The breakthrough curves measured at the panwere used to determine the mass rate of solute trans-ported through the macropores and micropores. Atypical breakthrough curve is shown in Fig. 2. Thecomputations were carried out using the following equa-tions subject to the same boundary conditions as inseparation of the subsurface hydrographs. In the case ofnegligible dilution in the micropore domain we have(Diiwu, 1997)
Mma
Mmi
:
Qma
Qmi
(3a)
This combines with Eqns (1) and (2) to give
Mma"
Mt(Q
ma/Q
mi)
1#(Qma
/Qmi
)(3b)
Mmi"M
t!M
ma(4)
where Mma
denotes mass #ow rate of solute through themacropores in lg min~1, M
midenotes mass #ow rate of
solute in the micropore component of subsurface #ow inlg min~1, and M
tdenotes mass #ow rate of solute in the
total subsurface #ow measured at the pan in lg min~1.The portions of the #ow rate in the macropore andmicropore domain Q
maand Q
mi, respectively, are as
de"ned earlier in Eqns (1) and (2). The above Eqn (3a)was checked and found to hold for all the simulationevents (Diiwu, 1997).
2.4. Estimation of subsurface -ow and solute transportthrough the A horizon
The subsurface #ow in the macropore and microporedomains of the A horizon in the "eld soil were estimatedby means of mass balance. The storages in the A andB horizons at times t and t!1 were estimated using time-domain re#ectometry readings at the three depths 2)5, 25and 50 cm. The following mass balance equations were
used for the computations
QtA
*t"<tA!<
(t~1)A#Q
tA@B*t (5)
QtA@B
*t"<tB!<
(t~1)B#Q
tpan*t (6)
where QtA
denotes the #ow rate into the A horizon attime t in cm3 min~1, Q
tA@Bdenotes the #ow rate out of the
A horizon and into the B horizon at time t in cm3 min~1,Q
tpandenotes the #ow rate to the pan at time t in
cm3 min~1, <tA
denotes storage in the A horizon at timet in cm3, <
(t~1)Adenotes storage in the A horizon at time
t!1 in cm3,<tB
denotes storage in the B horizon at time tin cm3, <
(t~1)Bdenotes storage in the B horizon at time
t!1 in cm3, and *t denotes the time step of the observa-tions, which in this case is 1 min.
The macropore and micropore components of break-through curves from the A horizon were estimated usingthe following equations
Cma
(A)"M
maQ
ma(A)
(7)
Cmi
(A)"M
miQ
mi(A)
(8)
where Cma
(A) denotes the solute concentration in themacropore domain of the A horizon in lg cm~3, andC
mi(A) denotes the solute concentration in the micropore
113TWO-COMPONENT ANALYSIS
domain of the A horizon in lg cm~3. The variablesM
maand M
miare as de"ned earlier in Eqns (3) and (4).
3. Results and discussion
3.1. Selection of hydrographs and breakthrough curvesfor separation
Most of the subsurface hydrographs measured at thepan exhibited more than one peak, a few did not. Themultiple peaks were considered to be manifestations oftwo-domain #ow, and so such graphs were selected forseparation of #ow and solute concentration into macro-pore and micropore components. It may be noted thatthe lack of multiple peaks does not rule out the possibleoccurrence of two-domain #ow (Gerke & van Genuch-ten, 1993). However, only those hydrographs showingmore than one peak were considered in this work just forease of partitioning the hydrograph for the two-domain#ow separation. If the hydraulic conductivity of the macro-pore domain is not several orders of magnitude greaterthan the hydraulic conductivity of the micropore do-main, the measured hydrograph would be single peaked(Gerke & van Genuchten, 1993). In that case, the hydro-graph partitioning assumptions discussed earlier mayneed to be modi"ed to be applicable for #ow separation.
3.2. Macropore and micropore components of selectedhydrographs and breakthrough curves
The volumes, durations, peak #ows and time to peaksfor the macropore and micropore components of the
TablMacropore (ma) and micropore (mi) co
Date Plot h*a
Volume,cm3
ma mi
26 May 1 0)426 2025 29002 0)361 48 157
1 June 1 0)447 3930 33552 0)415 621 94243 0)418 135 505
8 June 1 0)445 1760 60202 0)416 2885 90553 0)351 1010 1450
7 July 1 0)351 160 6452 0)335 7600 10 710
*Antecedent soil water content.
selected hydrographs are presented in Table 1, along withaverage antecedent soil water content of the plots priorto rainfall simulation. The separation was calculatedusing Eqns (1)}(4). It is clear from these data that for plot1 macropore #ow on June 1 was over 90% greater thanon 26 May, but this was reversed from 8 June to 7 July.For plot 2 macropore #ow increased by a factor of 12from 26 May to 1 June, by a factor of 4 from 1 June to8 June, and by a factor of 2 from 8 June to 7 July. Also forplot 3 the amount of macropore #ow increased from1 June to 8 June. The duration of macropore #ow for plot2 increased from 26 May to 1 June and then decreasedafter that. The duration of macropore #ow for plot 3 didnot change, but this is not clear in the case of plot 1.
For plot 1, the peak due to macropore #ow was greateron 1 June than on 26 May. On 8 June and 7 July the peakwere smaller than on 1 June and occurred earlier than on1 June and 26 May. For plot 2, the peak due to macro-pore #ow not only increased by a factor of 16 but alsooccurred earlier. For plot 3, a much greater and earlierpeak occurred on 8 June than that on 1 June. Thechanges in peak macropore #ow may be attributed tochanges in the number and continuity of macroporesresulting from changes in the degree of saturation of thesoil from May through June to July. Except for the eventof 7 July on plot 2, the changes in macropore #ow fromone simulation event to another closely corresponds withchanges in antecedent soil water content. The exceptionof 7 July event on plot 2 is probably attributable toincreased biological activity in the soil pro"le on thatplot due to decreased degree of saturation, resulting ingreater proportion of continuous macropores.
Micropore #ow is fairly close to macropore #ow forplot 1 as compared to those for plots 2 and 3. It may also
e 1mponents of the selected hydrographs
Duration,min
Peak yow rate,cm3 min~1
Time topeak, min
ma mi ma mi ma mi
15 23 390 540 11 1520 22 20 30 18 20
16 27 620 690 13 1616 34 330 1200 7 1617 22 50 60 14 17
14 22 470 800 9 1415 33 630 1330 9 1517 23 290 320 12 17
18 24 40 80 10 1814 31 1540 1460 8 14
Table 2Proportions of subsurface 6ow and solute transported in the two domains on all plots
Horizon Pore domain Proportions of total subsurface yow and solute in each domain, %
Flow volume Solute mass Solute concentration
Range Mean Range Mean Range Mean
A Macro 6}55 31)8 1}62 27)9 10}50 29
Micro 45}94 68)2 38}99 72)1 50}90 71
B Macro 6}54 30)1 1}61 35 5}56 22)2
Micro 46}94 71)1 39}99 79 44}95 77)8
Fig. 3. Estimated subsurface hydrographs for macropore andmicropore domains in A horizon on plot 1 for 26 May, 1993 event:
, macropore yow; , micropore yow
J. Y. DIIWU E¹ A¸ .114
be observed that on each day of simulation, antecedentsoil water content on plot 1 was higher than those onplots 2 and 3. The relatively high micropore #ow, ascompared to macropore #ow on plots 2 and 3, may beattributable to the possibility that many macropores inthe A horizon on those plots were not continuous into theB horizon on; #ow through such discontinuous macro-pores could have ended up as micropore #ow rather thanmacropore #ow at the observation depth. For plot2 micropore #ow persisted twice as long as macropore#ow except for the event of 26 May. But for plots 1 and3 micropore #ow persisted longer than macropore #owbut not twice as long. The peak due to micropore #owwas higher than the peak due to macropore #ow for allsimulation events except that of 7 July for plot 2. Also forthe simulation events of 1 and 8 June on plot 2 the peakdue to micropore #ow was not only over twice as high asthe peak due to macropore #ow but the macropore #owpeaks also tended to occur early. For all plots the peakdue to micropore #ow tended to occur about 16 minfrom the start of rainfall simulation, except for the eventof 8 June on plot 1 and the event of 7 July on plot 2 forwhich the peak was delayed by 2 min.
Analysis of variance of #ow volumes showed thatmacropore and micropore #ow varied signi"cantly overthe "eld from one rainfall event to another. The change inmacropore #ow volume and duration from spring tosummer was greater than the change in micropore #owvolume and duration during that period. This is probablybecause the volume of #ow in the macropore domain isa!ected by the degree of saturation and the spatial distri-bution of macropores in the soil. It is only the former ofthese factors which in#uences micropore #ow. Also athigh degree of saturation there are likely to be fewermacropores since clay swells more and there is less biolo-gical activity.
The hydrographs of subsurface #ow from the macro-pore and micropore domains, for the simulation event of26 May, obtained by means of the proposed separationtechnique are shown in Fig. 1 along with the hydrograph
of total subsurface #ow measured at the pan. The corre-sponding breakthrough curves are then shown in Fig. 2,and a summary of the #ow component proportions arepresented in Table 2. Over the "eld, macropore #ow wasfound to vary from about 6 to over 54% of the total #ow,while the variation in micropore #ow was from 46 toabout 94% of total #ow. Average macropore #ow wasabout 30% of the total #ow in the "eld, while the averageproportion of solute mass through the macropore do-main was 35%. These proportions show that waterreached the pan mostly as micropore #ow, yet the macro-pore domain contributed a substantial proportion ofsolute mass measured. The estimated subsurface hydro-graphs and breakthrough curves for the A horizon areshown in Figs 3 and 4, respectively. The proportions of
Fig. 4. Estimated breakthrough curves for macropore and micro-pore domains in A horizon on plot 1 for 26 May, 1993 event:
, macropore yow; , micropore yow
115TWO-COMPONENT ANALYSIS
the #ows and solute concentrations for A horizon areshown in Table 2, along with those for the B horizon. Theresults indicate that the macropore domain contributionwas higher in the A horizon than in the B horizon. Thesedi!erences probably point to the possibility of discon-tinuous macropores from A horizon to B horizon. Thedi!erences were more marked during some simulationevents than others, con"rming that the development ofmacropores depended on antecedent conditions in thesoil pro"le and that their occurrence at "eld scale wasspatially variable.
4. Conclusions
A dual-porosity concept and mass balance analysishave been applied to separate subsurface #ow hydro-graphs and breakthrough curves into macropore andmicropore components. Analysis of the separated subsur-face #ows and bromide concentrations shows that themacropore domain is likely to have contributed from 6 to54% of total subsurface #ow and from 1 to 61% of totalsolute mass measured at the pan. This emphasizes thefact that the contribution of macropores to subsurfacedrainage and contaminant transport can be fairly high.One of the consequences of this is that the root zone maynot adequately recharge since some of the available watercan be rapidly transported into deeper layers of the soilpro"le. Groundwater and streams might recharge sooner
than expected. Also contaminants can be rapidlytransported from the soil surface to surface and subsur-face water resources. Consequently, the quantity andquality of surface water and groundwater resources canbe greatly a!ected by macropore #ow in "eld soils. It ishoped that the proposed technique, as simple as it is, willprove useful in management decision-making such asthose regarding water management, land application ofliquid manure and agro-chemicals, and tile drainage of"elds.
Acknowledgements
The "nancial support of the Natural Science andEngineering Research Council (NSERC) of Canada tothis work is greatly appreciated. Thanks also to Agricul-ture and Agri-Food Canada for making the necessaryfacilities available for the "eld experiments.
References
Beven K; Germann P (1981). Water #ow in soil macropores II.A combined #ow model. Journal of Soil Science, 32, 15}30
Beven K; Germann P (1982). Macropores and water #ow in soil.Water Resources Research, 18, 1311}1325
Chen C; Wagenet R J (1992). Simulation of water and chemicalsin macropore soils. Part 1. Representation of the equivalentmacropore in#uence and its e!ect on soil water #ow. Journalof Hydrology, 130, 105}126
Diiwu J Y (1997). Transfer function modelling of drainage andsolute transport through layered macroporous soil. Ph.D.Thesis, School of Engineering, University of Guelph, Guelph,Ontario, Canada
Diiwu J Y; Rudra R P; Dickinson W T; Wall G J (1998a).Dependence of variability of hydraulic properties on physicalproperties of "eld soil. Journal of Environmental Systems,26(2), 171}189
Diiwu J Y; Rudra R P; Dickinson W T; Wall G J (1998b). E!ectof tillage on the spatial variability of soil water properties.Canadian Agricultural Engineering, 40(1), 1}8
Diiwu J Y; Rudra R P; Dickinson W T; Wall G J (1998c).Tillage and heterogeneity e!ects on the performance of soilwater characteristic models. Journal of Agricultural Engin-eering Research, 71(3), 307}313
Durner W (1994). Hydraulic conductivity estimation for soilswith heterogeneous pore structure. Water ResourcesResearch, 30(2), 211}223
Everts C J; Kanwar R S (1990). Estimating preferential #ow toa subsurface drain with tracers. Transactions of AmericanSociety of Agricultural Engineering, 33(2), 451}456
Gerke H H; van Genuchten M T (1993). A dual-porosity modelfor simulating the preferential movement of water and solutesin structured porous media. Water Resources Research, 29,305}319
Jarvis N J; Jansson P -E; Dik P E; Messing I (1991). Modellingwater and solute transport in macroporous soil. I. Modeldescription and sensitivity analysis. Journal of Soil Science,42, 59}70
J. Y. DIIWU E¹ A¸ .116
Pinder G F; Jones J F (1969). Determination of groundwatercomponent of peak discharge from chemistry of total runo!.Water Resources Research, 5, 438}445
Topp G C; Davis J L; Annan A P (1980). Electromagneticdetermination of soil water content: measurement in coaxiallines. Water Resources Research, 16, 574}582
Tossel R W; Dickinson W T; Rudra R P; Wall G J (1987).A portable rainfall simulator. Canadian AgriculturalEngineering, 29, 155}162
Uttermann J E; Kladivko J; Jury W A (1990). Evaluationof pesticide migration in tile-drained soils with a transferfunction model. Journal of Environmental Quality, 19,707}714
White R E (1985). The in#uence of macropores on the transportof dissolved and suspended matter through soil. Advances inSoil Science, 3, 95}120
