SW—Soil and Water

J. agric. Engng Res., (2001) 78 (1), 109}116 doi:10.1006/jaer.2000.0617, available online at http://www.idealibrary.com on SW*Soil and Water

Two-component Analysis of Flow through Macroporous Soil J. Y. Diiwu; R. P. Rudra; W. T. Dickinson; G. J. Wall School of Engineering, University of Guelph, Guelph, ON, Canada N1G 2W1; e-mail of corresponding author: [email protected] Land 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 1 m by 1 m plots, were separated into macropore 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 at an upper depth in the A horizon of the soil pro"le. The results show that the macropores contributed from 6 to 54% 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 presence of fractures, "ssures, channels, root and worm holes, peds and aggregates would result in multi-modal distribution of pore-size (Uttermann et al., 1990; Durner, 1994). Since pore size directly a!ects soil hydraulic conductivity, a multi-modal pore-size distribution would result in a multi-modal distribution of subsurface #ow and solute transport (White, 1985; Jarvis et al., 1991). When two pore-size classes are considered in the analysis we have a bimodal pore-size distribution, and the corresponding subsurface #ow distribution is bimodal. Apart from having a bimodal pore-size distribution, the occurrence of a bimodal subsurface #ow distribution also depends on such conditions as antecedent soil water content and rainfall intensity (Jarvis et al., 1991). Various categorizations have been used in the literature for de"ning macropores. For instance, macropores have been de"ned as those pores having diameters from 30 to 300 lm. They have also been de"ned based on the matric potential at which they drain such as !6 cm of water; by volume fraction such as 0)001}0)05; or by in"ltration rate such as 1}10 mm h\; or as those pores which empty in 24 h (Beven & Germann, 1982; White, 1985; Chen & Wagenet, 1992). In this paper, macropores are de"ned as those pores which empty at matric potentials greater than !5 cm of water. This corresponds to 0021-8634/01/010109#08 $35.00/0

a diameter of 600 lm for water at surface tension of 0)07 N m\ with a contact angle of 03. The matric potential of !5 cm was selected as one which is greater than the maximum matric potential of !10 cm which was applied in laboratory experiments for determination of soil water characteristics of the study "eld (Diiwu, 1997; Diiwu et al., 1998a). One approach to modelling #ow in macroporous media considers the structural units (peds, aggregates, clods) as sources or sinks for the more mobile water in the macropores. Another approach considers the bimodal medium as two superimposed media, each with its own hydraulic properties. There is the macropore domain in which subsurface #ow and solute transmission is very fast compared to slow subsurface #ow and solute transmission in the micropore domain (Beven & Germann, 1981; Jarvis et al., 1991; Chen & Wagenet, 1992). Exchange of mass between the macropore and micropore domains depends on the degree of saturation of the soil (Jarvis et al., 1991). The two-domain concept has been presented in various forms such as the mobile}immobile form by Beven and Germann (1981), as well as the dual-porosity model by Gerke and van Genuchten (1993) and Durner (1994). The di$culty with these models is the problem of accounting for the exchange of mass between the two domains. Besides, for soils with unstable aggregates it would be extremely di$cult to accurately determine the hydraulic properties

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of the two domains separately due to variability of soil properties in the "eld. In modelling subsurface #ow and contaminant transport through macroporous soil, the uncertainties in the two-domain approach may be quanti"ed by means of probability measures of the hydraulic variables of the two domains. Combining this with dual porosity, the hydraulic processes in each of the macropore and micropore domains may be characterized by a distinct probability distribution (Diiwu, 1997). Derivation of the distinct probability distributions for the macropore and micropore domains requires that #ows and solute concentrations be separated into macropore and micropore components if such components were not separately measured during data collection. Also, for decisionmaking on water management it may be useful to be able to assess the separate contributions of the macropore and micropore domains to subsurface #ows and solute masses transported through the soil system. This may be necessary since macropores tend to transmit water and contaminants rapidly beyond the root zone and into streams and the groundwater system. This paper therefore discusses the application of the dual-porosity concept to separate subsurface hydrographs and breakthrough curves into macropore and micropore components. The analysis of spatial variability of the physical and hydraulic properties of soil in the study "eld had pointed to the possibility of the occurrence of macropore #ow in the "eld (Diiwu, 1997; Diiwu et al., 1998a, 1998b). Hence, the need for subsurface #ow separation in the study. Some existing soil water characteristic models have been found to perform poorly when applied on soil with macropores (Diiwu et al., 1998c). Separation of subsurface #ow would enable such models to be successfully applied to the micropore domain, along with an alternative model for the macropore domain.

2. Materials and methods 2.1. Rainfall simulation experiments Subsurface hydrographs and breakthrough curves were measured during rainfall simulation on 1 m by 1 m plots under no-tillage treatment. The plots were constructed by installing large steel plates approximately of the same dimensions as the plots, at a depth of about 55 cm in the soil pro"le to serve as catchment pans to collect subsurface #ow during rainfall event. The steel plates were installed by gently driving them horizontally into place in the B horizon using hydraulic jacks. The investigation therefore involved the A and B horizons of the soil pro"le. The thickness of the A horizon at the site varies between 25 and 30 cm and the portion

of the B horizon above the pans varies between 25 and 30 cm. Plastic bottles were installed in a pit for collecting the subsurface #ow for subsequent sampling. At the soil surface, aprons were placed around the plots to direct surface #ow into a V-shaped trough from which samples were collected at 1 min intervals to determine volume of runo! generated and the concentration of tracer present in the runo!. Pairs of time-domain re#ectometry (TDR) probes, each probe measuring 20 cm in length and 0)2 cm in diameter, were installed horizontally at depths of 2)5, 25, and 50 cm in each plot to measure in situ soil water content during rainfall simulation. The dielectric constant manually measured by TDR (Tectronix instrument model 1502C) was used to infer the water content of the soil via the emperical relationship by Topp et al. (1980). Rainfall intensity of 15)6 cm h\ was simulated by using the Guelph Rainfall Simulator II with a 12)7 mm full jet nozzle that was maintained at a height of 1)5 m above the soil surface and was operated at a pressure between 48 and 55 kPa (Tossel et al., 1987). Water for rainfall simulation was supplied by a pump at a rate of 2)4 m h\. To avoid moving the simulator from one plot to another, three rainfall simulators were used, one on each of plots 1}3. Characteristics of the three simulators were the same, and they were used to produce similar rainfall events. For each experiment bromide tracer solution was applied on the soil surface of each plot using a hand-held spray. The rainfall simulator was then turned on and left to run for about 15 min, during which time ponding was established and maintained. Over the 15 min period the simulator on plot 1 produced a total volume of 31 290 cm of water, on plot 2 the simulator produced 31 800 cm of water, and on plot 3 this was 32 900 cm. The slight di!erences in total volume of water produced are attributable to unavoidable sources of error such as the precise timing of start and end of simulation, the variation in nozzle pressure during simulation, and the e!ect of wind on the simulated raindrops (Tossel et al., 1987). Surface and subsurface #ows were sampled for volume and bromide concentration at an interval of 1 min, over a 45 min period from the beginning of rainfall simulation.

2.2. Separation of hydrographs into macropore and micropore components The application of the dual-porosity concept in hydrologic modelling requires that the macropore and micropore #ow components be separated and the corresponding mass of contaminant in each component determined. Everts and Kanwar (1990) represented the transport of solute to subsurface drains by a mass

T W O -C O M PO N E N T AN A LY S IS

balance equation using a hydrograph separation technique proposed by Pinder and Jones (1969). The technique was adapted in this study for separating subsurface #ow into macropore and micropore components. The equations for subsurface #ow and concentration of solute can be written as Q "Q #Q (1) R KG K? Q C #Q C K? K? C " KG KG (2) R Q R where Q denotes the #ow rate measured at the pan in R cm min\, Q denotes the portion of Q associated with KG R the micropore domain in cm min\, Q denotes the K? portion of Q associated with the macropore domain in R cm min\, C denotes the total concentration of solute R measured in Q in lg cm\, C denotes concentration of R KG solute associated with the micropore domain in lg cm\, and C denotes concentration of solute associated with K? the macropore domain in lg cm\. The objective of the separation performed in the study was to obtain values for Q , Q , C and C from the hydrographs and KG K? KG K? breakthrough curves observed at the pan, such that the conditions of mass balance expressed in Eqns (1) and (2) above were satis"ed. For the #ow separation a typical hydrograph obtained from the rainfall simulation experiments and shown in Fig. 1, was partitioned into three stages. The partitioning was based on the assumption that the hydraulic

Fig. 1. Subsurface hydrograph measured at pan on plot 1 for 26 May, 1993 event and corresponding estimated macropore and micropore components: , total yow; , macropore yow; , micropore yow

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conductivity of the macropore domain was several orders of magnitude greater than the hydraulic conductivity of the micropore domain. This condition is re#ected by double peaks in the measured hydrograph (Gerke & van Genuchten, 1993). It was also assumed that there was negligible mixing between the two domains, and that the macropores were empty of antecedent soil water prior to each rainfall simulation event (Everts & Kanwar, 1990). The entire duration of simulation was considered to comprise three stages. In the "rst stage, the processes of water redistribution and drainage were considered to be initially dominated by macropores. This was followed by a mixed stage when both macropores and micropores were conducting water, before macropores emptied. After the macropores were empty the micropores were responsible for drainage and redistribution of water. The observed hydrograph was then partitioned into the three stages as follows. Stage 1 from the beginning of rainfall simulation up to the ,rst peak of the hydrograph In this case, it was assumed that the observed #ow was only from the macropore domain. The "rst peak was attained a few minutes before rainfall simulation ceased. Also it was assumed that micropore #ow was just starting. Stage 2 between the two hydrograph peaks In this case, both macropore and micropore #ows were likely to be taking place, and hence any observed #ows include contributions from the two domains. While the contribution from the macropores decreased as they emptied, that from the micropores increased. By the time the second peak was attained, all macropores have emptied, and so the micropore domain would be the only one contributing to the observed subsurface #ow. Stage 3 beyond the second peak During this stage, all the observed #ow was assumed to be through the micropore domain and all macropores have emptied. With this partitioning of the hydrograph the separation of subsurface #ow was required for stage 2 only. Moreover, there was a point in time during this stage at which the contributions to #ow from the two domains were equal. The #ow separation was thus achieved by constrained spline interpolations through the two peaks and the point of in#exion between them. The receding limb of the macropore component of the hydrograph was spline "tted through three points*the "rst peak at which Q "Q and Q "0, the point on the time axis correK? R KG sponding to the second peak, where Q "0 and K? Q "Q and the third point midway between the two KG R peaks at which Q "Q "0)5 Q . The intermediate K? KG R points of this spline curve were obtained by adjusting the proportions of Q between 1 and 0)5 as well as between K?

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0)5 and 0 such that Eqns (1) and (2) were satis"ed. The lower limb of the micropore component of the hydrograph was spline "tted through three points*the second peak at which Q "Q and Q "0, the point on the KG R K? time axis corresponding to the "rst peak, and the third point midway between the two peaks at which Q "Q "0)5 Q . The intermediate points of this K? KG R spline curve were obtained by adjusting the proportions of Q between 0 and 0)5 as well as between 0)5 and 1 such KG that Eqns (1) and (2) were satis"ed.

2.3. Determination of mass of solute transported through the macropores and micropores The breakthrough curves measured at the pan were used to determine the mass rate of solute transported through the macropores and micropores. A typical breakthrough curve is shown in Fig. 2. The computations were carried out using the following equations subject to the same boundary conditions as in separation of the subsurface hydrographs. In the case of negligible dilution in the micropore domain we have (Diiwu, 1997) M Q K?: K? M Q KG KG This combines with Eqns (1) and (2) to give

Fig. 2. Breakthrough curve measured at pan on plot 1 for 26 May, 1993 event and corresponding estimated macropore and micropore components: , total yow; , macropore yow; , micropore yow

(3a)

M (Q /Q ) M " R K? KG (3b) K? 1#(Q /Q ) K? KG M "M !M (4) KG R K? where M denotes mass #ow rate of solute through the K? macropores in lg min\, M denotes mass #ow rate of KG solute in the micropore component of subsurface #ow in lg min\, and M denotes mass #ow rate of solute in the R total subsurface #ow measured at the pan in lg min\. The portions of the #ow rate in the macropore and micropore domain Q and Q , respectively, are as K? KG de"ned earlier in Eqns (1) and (2). The above Eqn (3a) was checked and found to hold for all the simulation events (Diiwu, 1997).

used for the computations Q *t"< !< #Q *t R R R\ R

(5)

Q *t"< !< #Q *t R R R\ RN?L

(6)

where Q denotes the #ow rate into the A horizon at R time t in cm min\, Q denotes the #ow rate out of the R A horizon and into the B horizon at time t in cm min\, Q denotes the #ow rate to the pan at time t in RN?L cm min\, < denotes storage in the A horizon at time R t in cm, < denotes storage in the A horizon at time R\ t!1 in cm, < denotes storage in the B horizon at time t R in cm, < denotes storage in the B horizon at time R\ t!1 in cm, and *t denotes the time step of the observations, which in this case is 1 min. The macropore and micropore components of breakthrough curves from the A horizon were estimated using the following equations

2.4. Estimation of subsurface -ow and solute transport through the A horizon

M C (A)" K? K? Q (A) K?

(7)

The subsurface #ow in the macropore and micropore domains of the A horizon in the "eld soil were estimated by means of mass balance. The storages in the A and B horizons at times t and t!1 were estimated using timedomain re#ectometry readings at the three depths 2)5, 25 and 50 cm. The following mass balance equations were

M C (A)" KG KG Q (A) KG

(8)

where C (A) denotes the solute concentration in the K? macropore domain of the A horizon in lg cm\, and C (A) denotes the solute concentration in the micropore KG

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domain of the A horizon in lg cm\. The variables M and M are as de"ned earlier in Eqns (3) and (4). K? KG 3. Results and discussion 3.1. Selection of hydrographs and breakthrough curves for separation Most of the subsurface hydrographs measured at the pan exhibited more than one peak, a few did not. The multiple peaks were considered to be manifestations of two-domain #ow, and so such graphs were selected for separation of #ow and solute concentration into macropore and micropore components. It may be noted that the lack of multiple peaks does not rule out the possible occurrence of two-domain #ow (Gerke & van Genuchten, 1993). However, only those hydrographs showing more than one peak were considered in this work just for ease of partitioning the hydrograph for the two-domain #ow separation. If the hydraulic conductivity of the macropore domain is not several orders of magnitude greater than the hydraulic conductivity of the micropore domain, the measured hydrograph would be single peaked (Gerke & van Genuchten, 1993). In that case, the hydrograph partitioning assumptions discussed earlier may need to be modi"ed to be applicable for #ow separation.

3.2. Macropore and micropore components of selected hydrographs and breakthrough curves The volumes, durations, peak #ows and time to peaks for the macropore and micropore components of the

selected hydrographs are presented in Table 1, along with average antecedent soil water content of the plots prior to rainfall simulation. The separation was calculated using Eqns (1)}(4). It is clear from these data that for plot 1 macropore #ow on June 1 was over 90% greater than on 26 May, but this was reversed from 8 June to 7 July. For plot 2 macropore #ow increased by a factor of 12 from 26 May to 1 June, by a factor of 4 from 1 June to 8 June, and by a factor of 2 from 8 June to 7 July. Also for plot 3 the amount of macropore #ow increased from 1 June to 8 June. The duration of macropore #ow for plot 2 increased from 26 May to 1 June and then decreased after that. The duration of macropore #ow for plot 3 did not change, but this is not clear in the case of plot 1. For plot 1, the peak due to macropore #ow was greater on 1 June than on 26 May. On 8 June and 7 July the peak were smaller than on 1 June and occurred earlier than on 1 June and 26 May. For plot 2, the peak due to macropore #ow not only increased by a factor of 16 but also occurred earlier. For plot 3, a much greater and earlier peak occurred on 8 June than that on 1 June. The changes in peak macropore #ow may be attributed to changes in the number and continuity of macropores resulting from changes in the degree of saturation of the soil from May through June to July. Except for the event of 7 July on plot 2, the changes in macropore #ow from one simulation event to another closely corresponds with changes in antecedent soil water content. The exception of 7 July event on plot 2 is probably attributable to increased biological activity in the soil pro"le on that plot due to decreased degree of saturation, resulting in greater proportion of continuous macropores. Micropore #ow is fairly close to macropore #ow for plot 1 as compared to those for plots 2 and 3. It may also

Table 1 Macropore (ma) and micropore (mi) components of the selected hydrographs Date

Plot

h* ?

Volume, cm3

Duration, min

Peak yow rate, cm3 min\1

Time to peak, min

ma

mi

ma

mi

ma

mi

ma

mi

26 May

1 2

0)426 0)361

2025 48

2900 157

15 20

23 22

390 20

540 30

11 18

15 20

1 June

1 2 3

0)447 0)415 0)418

3930 621 135

3355 9424 505

16 16 17

27 34 22

620 330 50

690 1200 60

13 7 14

16 16 17

8 June

1 2 3

0)445 0)416 0)351

1760 2885 1010

6020 9055 1450

14 15 17

22 33 23

470 630 290

800 1330 320

9 9 12

14 15 17

7 July

1 2

0)351 0)335

160 7600

645 10 710

18 14

24 31

40 1540

80 1460

10 8

18 14

*Antecedent soil water content.

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Table 2 Proportions of subsurface 6ow and solute transported in the two domains on all plots Horizon

Proportions of total subsurface yow and solute in each domain, %

Pore domain

Flow volume

A

B

Solute mass

Solute concentration

Range

Mean

Range

Mean

Range

Mean

Macro

6}55

31)8

1}62

27)9

10}50

29

Micro

45}94

68)2

38}99

72)1

50}90

71

Macro

6}54

30)1

1}61

35

5}56

22)2

Micro

46}94

71)1

39}99

79

44}95

77)8

be observed that on each day of simulation, antecedent soil water content on plot 1 was higher than those on plots 2 and 3. The relatively high micropore #ow, as compared to macropore #ow on plots 2 and 3, may be attributable to the possibility that many macropores in the A horizon on those plots were not continuous into the B horizon on; #ow through such discontinuous macropores could have ended up as micropore #ow rather than macropore #ow at the observation depth. For plot 2 micropore #ow persisted twice as long as macropore #ow except for the event of 26 May. But for plots 1 and 3 micropore #ow persisted longer than macropore #ow but not twice as long. The peak due to micropore #ow was higher than the peak due to macropore #ow for all simulation events except that of 7 July for plot 2. Also for the simulation events of 1 and 8 June on plot 2 the peak due to micropore #ow was not only over twice as high as the peak due to macropore #ow but the macropore #ow peaks also tended to occur early. For all plots the peak due to micropore #ow tended to occur about 16 min from the start of rainfall simulation, except for the event of 8 June on plot 1 and the event of 7 July on plot 2 for which the peak was delayed by 2 min. Analysis of variance of #ow volumes showed that macropore and micropore #ow varied signi"cantly over the "eld from one rainfall event to another. The change in macropore #ow volume and duration from spring to summer was greater than the change in micropore #ow volume and duration during that period. This is probably because the volume of #ow in the macropore domain is a!ected by the degree of saturation and the spatial distribution of macropores in the soil. It is only the former of these factors which in#uences micropore #ow. Also at high degree of saturation there are likely to be fewer macropores since clay swells more and there is less biological activity. The hydrographs of subsurface #ow from the macropore and micropore domains, for the simulation event of 26 May, obtained by means of the proposed separation technique are shown in Fig. 1 along with the hydrograph

of total subsurface #ow measured at the pan. The corresponding breakthrough curves are then shown in Fig. 2, and a summary of the #ow component proportions are presented in Table 2. Over the "eld, macropore #ow was found to vary from about 6 to over 54% of the total #ow, while the variation in micropore #ow was from 46 to about 94% of total #ow. Average macropore #ow was about 30% of the total #ow in the "eld, while the average proportion of solute mass through the macropore domain was 35%. These proportions show that water reached the pan mostly as micropore #ow, yet the macropore domain contributed a substantial proportion of solute mass measured. The estimated subsurface hydrographs and breakthrough curves for the A horizon are shown in Figs 3 and 4, respectively. The proportions of

Fig. 3. Estimated subsurface hydrographs for macropore and micropore domains in A horizon on plot 1 for 26 May, 1993 event: , macropore yow; , micropore yow

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than expected. Also contaminants can be rapidly transported from the soil surface to surface and subsurface water resources. Consequently, the quantity and quality of surface water and groundwater resources can be greatly a!ected by macropore #ow in "eld soils. It is hoped that the proposed technique, as simple as it is, will prove useful in management decision-making such as those regarding water management, land application of liquid manure and agro-chemicals, and tile drainage of "elds.

Acknowledgements The "nancial support of the Natural Science and Engineering Research Council (NSERC) of Canada to this work is greatly appreciated. Thanks also to Agriculture and Agri-Food Canada for making the necessary facilities available for the "eld experiments. Fig. 4. Estimated breakthrough curves for macropore and micropore domains in A horizon on plot 1 for 26 May, 1993 event: , macropore yow; , micropore yow

the #ows and solute concentrations for A horizon are shown in Table 2, along with those for the B horizon. The results indicate that the macropore domain contribution was higher in the A horizon than in the B horizon. These di!erences probably point to the possibility of discontinuous macropores from A horizon to B horizon. The di!erences were more marked during some simulation events than others, con"rming that the development of macropores depended on antecedent conditions in the soil pro"le and that their occurrence at "eld scale was spatially variable.

4. Conclusions A dual-porosity concept and mass balance analysis have been applied to separate subsurface #ow hydrographs and breakthrough curves into macropore and micropore components. Analysis of the separated subsurface #ows and bromide concentrations shows that the macropore domain is likely to have contributed from 6 to 54% of total subsurface #ow and from 1 to 61% of total solute mass measured at the pan. This emphasizes the fact that the contribution of macropores to subsurface drainage and contaminant transport can be fairly high. One of the consequences of this is that the root zone may not adequately recharge since some of the available water can be rapidly transported into deeper layers of the soil pro"le. Groundwater and streams might recharge sooner

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Uttermann J E; Kladivko J; Jury W A (1990). Evaluation of pesticide migration in tile-drained soils with a transfer function model. Journal of Environmental Quality, 19, 707}714 White R E (1985). The in#uence of macropores on the transport of dissolved and suspended matter through soil. Advances in Soil Science, 3, 95}120