Flow and transport processes in a macroporous subsurface-drained glacial till soil II. Model analysis

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Journal of Hydrology ELSEVIER Journal of Hydrology 207 (1998) 121-135 Flow and transport processes in a macroporous subsurface-drained glacial till soil II. Model analysis K.G. Villholth, K.H. Jensen Department of Hydrodynamics and Water Resources. Technical University of Denmark, 2800 Lwgby. Denmnrk Received 17 March 1997; revised 30 September 1997; accepted 18 February 1998 Abstract The experimental results from a field-scale tracer experiment in a subsurface-drained glacial till soil were analyzed by the application of a single/dual porosity model (MACRO), optionally accounting for concurrent and interacting flow and transport in the bulk soil porosity as well as in the macropores. The mode1 analysis showed that macropore flow is essential in describing the observed transport phenomenon on a short as well as a longer time scale. The diffusive exchange of solute between the matrix and the macropores was very sensitive and critical for the mode1 prediction of the drainage concentration. The exchange was overpredicted and too rapid when the soil aggregate size (distance between macropores) obtained from an image analysis of soil cores was used in the model. On this basis, the mode1 assumption of instant equilibration of the solute across the matrix porosity, disregarding small-scale concentration gradients, is questioned. Decreasing the domain exchange resulted in an improved model correspondence with the drainage chemograph. The drainage flow pattern was altered between drainage seasons owing to the changes in hydraulic efficiency of surface-vented macropores influenced by the physical disturbance and compaction of the soil surface. Hypothetically introducing fully surface-connected macropores into the calibrated model resulted in a 22% increase in the loss of solute to the drain, indicating the significance of the hydraulic conditions at the soil surface and the model specification thereof. 0 1998 Elsevier Science B.V. All rights reserved. Keywords: Structural soils; Macropores; Subsurface-drainage; Conservative tracer: Two-domain model; Mass transfer; Flow and transport processes 1. Introduction Recognition of the prevalence of preferential flow and especially its effects on migration of substances within the terrestrial environment has led to intensi- fied research on quantifying and modeling flow and transport phenomena in natural, structured soils. One of the difficulties involved in formulating a stringent, mathematical formulation of the flow * Corresponding author processes is related to the intricate soil structure superimposed on a texturally heterogeneous soil medium and to the lack of a straightforward relation between easily definable and measurable properties of the soil structure and the actual flow mechanisms. External and initial conditions (Brusseau and Rao, 1990), the physical-chemical properties of the inter- face between the structural pathways and the bulk soil (Gerke and van Genuchten, 1993a; Gerke and van Genuchten, 1993b) as well as the temporal variability of the macropores (Gee et al., 1991; Chen and 0022-1694/98/$19.00 0 1998 Elsevier Science B.V. All rights reserved. /II SOO22-1694(98)00130-9 Wagenet. 1992) infhtence the fluid transport and make a straightforward model description difticult. A range of model approaches to preferential Ilow and transport phenomena has been suggested in the literature during the last couple of decades. Informa- tive reviews are given by Wierenga ( 1987). Addiscott and Wagenet ( 1985), Nielsen et al. ( 1986), van Genuchten and Jury (1987). Germann (1988), Huyakorn (1988), Brusseau and Rao (1990) and Villholth (1994). Modeling of field-scale transport to a subsurface drainage system requires the consideration of the coupled unsaturated-saturated flow system (Vinten et al., 1991). Various approaches to modeling trans- port of non-reactive solutes (van Ommen et al.. 1989a; van Ommen et al., 1989b: Vinten et al., 1991), pesti- cides (van Ommen, 1985a; van Ommen. 1985b; Utermann et al.. 1990), and sediment particles (Bottcher et al.. 1980) in artificially drained soils have been suggested. Common to the work presented is a fragmented technique by which the transport rela- tions are considered separately for the unsaturated and saturated zones. and a coupling is conceptually pro- vided by assuming that output from the former is input to the latter. Simple macroscopic routing or transfer function models are used for the saturated zone, while transport in the unsaturated zone is treated in a more physically based, mechanistic manner allowing for transient flow and preferential flow effects. Usually. no, or very crude, approximations to the evapo- transpiration processes are implemented. These models were apparently developed to ana- lyze single drainage experiments (Bottcher et al., 1980; van Ommen et al., 1989a; van Ommen et al.. 1989b) or to study hypothetical cases (van Ommen, 1985a: van Ommen, 3985b; Utermann et al.. 1990), and only little general applicability can be assessed from their use. Vinten et al. ( 1991), however. applied their mode1 to eight adjacent, equally treated drainage plots and concluded that quite variable mobile water fractions were needed to describe the observed drainage chemographs. Little correspondence with observations was found by van Ommen et al. (1989a); van Ommen et al. (1989b), who attributed this to a lack of considering preferential flow effects in the model. Thooko et al. ( 1994) and Singh et al. ( 1996) combined drainage models and one- dimensional pesticide transport models. No preferential flow was considered. From the reviewed literature. I! appears that a physically based model that simultaneously describes transient flow and transport in the coupled unsaturated-- saturated soil system. including preferential flow.. rvapotranspiration procrsse\, and drainage intei- ception. could considerably, improve the description of field-scale transport in subsurface drained soils. The objectives of the present study were to interpret the experimental held drainage studies presented in Villholth et al. ( 1998) using a model that fultils the requirements stated above. Aside from analyzing the combined flow and transport mechanisms. the aim was to identify and determine the sensitive parameters in the model and to identify model limitations and future research needs. Appropriate question\ arc raised: ( 1 ) is it necessary to include a description of preferential Row to account for the observed pattern of solute dissipation? and (3) can existing models describe/predict how and transport of conservative soluble constituents in highly structured held soils? 2. Materials and methods 2.1. Field-scale truer tests Field-scale tracer tests involving the surface appli- cation of a conservative chloride ion to macroporous. subsurface-drained glacial till soil in Denmark were conducted (Villholth et al., 1998). The three plots (PLOT 1 to PLOT 3) used for individual tracer tests were located on adjacent drain lines (DRAIN I and DRAIN 2) and their hydraulic behavior was assumed to be similar (Villholth et al.. 1998). The tests were performed over a period of three consecutive drainage seasons (SEASON 1. SEASON 2 and SEASON 3 corresponding to the 1989- 1990. 1990- I 99 1 and 1991- 1992 fall-to-spring-periods respectively). For a detailed description of the site layout. the soil char- acteristics, the experimental conditions and the data collection refer to Villholth et al. (1998). 2.2. The MACRO model The numerical mode1 applied in this study is the MACRO model developed by Jarvis ( 1994). MACRO is a deterministic, finite difference model for one- dimensional, non-steady water and solute transport in K.G. Villholth. K.H. Jensen/Journal of Hydrology 207 (1998) 121-135 123 macroporous soil. Classified as a two-domain or double- porosity model, MACRO describes the preferential flow as macropore flow in a separately defined pore domain. No a priori assumptions of the detailed geometry of the macropore network are made. This, in combination with the deterministic and one- dimensional approach, means that the small-scale and the larger-scale variabilities are disregarded, and a necessary lumping of properties is performed in order to equate the scale of the model with the experimental plot scale. Richards equation is assumed applicable for verti- cal water flow in the micropore domain, whereas flow in the macropore domain is assumed laminar and driven by gravity only. The Brooks and Corey (1964) functional relationship describes the retention properties of the matrix. The hydraulic conductivity in the matrix is given by the Mualem (1976) expression, whereas in the macropores a simple power law function is assumed to represent the hydraulic conductivity relation. Drain flow is included as sink terms in the flow description for saturated layers above the drain depth by use of seepage potential theory (Youngs, 1980). Soil evaporation and evapo- transpiration from a defined crop is accounted for. Transport of a conservative solute is described by the convection dispersion equation in both domains. Source/sink terms for the exchange between domains due to water how and solute diffusion are described by linear first-order mass transfer expressions with the first-order rate coefficients being related to the geom- etry and the dimensions of the macropore structure: E,=cr,(eb-~mi) (1) Es=~s(cm,-cmi) (2) where E, (T-l) and E, (M Lm3 T-) are mass transfer of water and diffusive mass transfer of solute from macropores to matrix respectively, orni and eb are the prevailing and saturated volumetric water contents of the matrix, and c,, and c,i are solute concentrations in the macropore and matrix region (M L-). The first-order water and solute mass transfer coefficients (T-l) are given by 12D,-r, %=----$-- (3) 120,8,, 015 = d (4) where D, (L T-) is an effective water diffusivity, D, is an effective diffusion coefficient (M T-l): and yW is a scaling factor, approximately equal to 0.8, introduced to match the approximate and exact solu- tions to the diffusion problem (Jarvis, 1994). An aggregate structure of rectangular-slab geometry is assumed, rendering the effective diffusion path length d (L) equal to the aggregate width. The MACRO model provides an option to run in either one or two domains. In both the one-domain and the two-domain cases the hydraulic properties assumed to characterize the soil as a whole are main- tained, but the preferential movement of solute in a fraction of the pore volume is not possible in the one- domain case. A parallel use of the one and two- domain options thus allows a quantitative assessment of the impact of macropore flow on solute transport in the soil. For a more comprehensive description of the model, including additional features (e.g. pesticide transport and transport in shrinking/swelling soil) refer to Jarvis (1994). The MACRO model has pre- viously been used in the analysis of lysimeter studies involving pesticide applications (Jarvis et al., 1994; Jarvis, 1995) and conservative tracers (Jarvis et al., 1991; Saxena et al., 1994; Saxena and Jarvis, 1995) on undisturbed soils. Application to short-term sub- surface drainage studies has been presented in Andreu et al. (1994). 2.3. Model application 2.3.1. Model set-up and calibration technique Data from PLOT 1 (SEASON 1) and from PLOT 3 (SEASON 3) are used in the model analysis. In addition, the model is used to simulate water flow in PLOT 3 during SEASON 2. Since the most compre- hensive data material was collected on PLOT 3 before and during the tracer test in SEASON 3, the model was calibrated towards this data set and the applica- tion to this scenario is considered the base application. The two-domain version of the MACRO model was used in the calibration. Subsequently, the effect of a one-domain assumption was evaluated. Field-measured data on the physical and hydraulic properties of the soil medium were used as input to the model as far as possible. Calibration targets were the time series data of groundwater level, drainage flow rate, drain water concentration, and the profiles of chloride content sampled at the end of the tracer experiments. The drainage flow rate and the drain water chloride concentration reflected the dynamics of the overall system and hence were used as the primary calibration goal. Some parameters were cali- brated on the basis of a trial-and-error technique and a visual comparison of simulated and observed results, including several iterations between the water flow and the solute transport description. A comprehensive sensitivity analysis was performed in order to identify the most critical parameters for the given situation (Villholth, 1994). In order to convert the one- dimensional drainage flow rate obtained from the MACRO simulations to a volumetric flow rate that could be compared with the observations, a constant catchment area of the drain lines was assumed. Based on the application of a three-dimensional groundwater flow model. this area was estimated to be 430 m for DRAIN 2 on PLOT 3 (Villholth, 1994). A correlation analysis of how in the two drains suggested that the catchment area for DRAIN 1 is 2.49 times larger, giving a catchment area of 1075 m2 for DRAIN 1. The simulated chloride concentration in the drainage water was corrected for the areal fraction of the estimated catch- ment area that received tracer. In this way the simulated drainage outflow is hypothetically diluted by water ori- ginating from contributing areas not receiving the tracer. The soil protile is modeled to a depth of 2 m with the drain at 1.2 m depth and divided into 15 computa- tional increments of increasing thickness with depth (3-52 cm). Bare soil conditions are assumed during SEASON 2 after the previous crop of beets was removed, whereas a vegetation with constant root depth (1 m and 80% of the total root mass in the upper 25 cm) and constant interception capacity (0.1 mm) is used to represent the fallow conditions during SEASON 1 and SEASON 3. On-site measurements of hourly rainfall, together with daily values of potential evapotranspiration obtained from a weather station near the site, are input to the model. The model assumes the traced substance to be applied in dissolved form. Hence, for PLOT 3 the tracer application can be specified according to the actual conditions during the dosage of the CaC12.2H20 solution. For PLOT 1. however, the description of chloride application in solid form is approximated by adding the total chloride input with a relatively small amount of water (1 mm). The lower boundary condition for solution ot the tlow equations is assumed to be a unit hydraulic gra- dient in both flow domains. Advection flux across the lower boundary is assumed. The initial values for soil water content and solute concentration are based on observed groundwater levels and concentration tn extracted soil samples respectively. The spacing between the drain lines, which inllu- ences the lateral flow rate to the drains, was reduced during the calibration (from the actual 20 m to 4 m) in order to account for the apparent anisotropy in the hydraulic conductivity in the shallow groundwatet and because the effective catchment area was smaller than observed (Villholth et al.. 1998). Concerning the overall solute mass balance. it 14 noted that approximately 2-l% of the applied tracer was assumed to be translocated from the tracer area to the non-amended area close to the drain owing to lateral how and transport processes (Villholth et al.. 1998). However. owing to the lack of the lateral dis- cretization in the model it was not possible to account for this loss in a rigorous manner. _.3.2. Parurnrter tlrternlitdotl The parameters characterizing the soil hydraulic and dispersive properties for the base application are listed in Table 1. together with the method used to obtain them. The tortuosity factor tz in the tnicropores is assumed equal to 0.5, which corresponds to the value suggested by Mualem ( 1976) for determining the unsaturated hydraulic conductivity from the Brooks and Corey retention function. The residual water content 0, is assumed to be equal to the water content at permanent wilting, corresponding to an equivalent tension of 160 m (-pF 4.2). The boundary pressure head Gb. corresponding to micropore saturation, is fixed at a value of - 16 cm. This value indicates the delimitation between micro and macro-pores and, according to the capillary equation. pores with an equivalent larger than 0.2 mm will be considered as macropores. A clear-cut threshold value between the micropore and macropore domains may not be physically definable owing to the range of actual pore sizes and their hydraulic properties. However, the tension inliltration experiment involving dye application at 3 cm tension revealed macropore flow (Villholth et al.. 1998). jus- tifying the use of a delimiting value for Gh smaller Table 1 K.G. Villholth, K.H. Jensen/Joumul of Hydrology 207 (1998) 121-135 125 Soil hydraulic and dispersive parameters Parameter Estimation method Parameter value Tortuosity factor in micropores Residual water content in micropores Boundary pressure head Matrix porosity Macroporosity Pore size distribution index. macropores Pore size distribution index. micropores Saturated hydraulic conductivity, micropores Saturated hydraulic conductivity. macropores Diffusion coefficient Impedance factor Dispersivity Effective diffusion pathlength Concentration factor for crop uptake b b b a a b C a.d a.d b b b,d d b 0.5 I2.L 13.6% - 16cm 26.9-35.9% O-2% 3-6 0.08-O. 108 0.015-I mm h- 0.085-23 mm h- 1.9 x lO-ms~ 0.5 3cm 0.06. 20 m ta) Directly measured: (b) general knowledge/literature value; (c) derived; (d) calibrated. than -3 cm. The corresponding water content 19b (matrix porosity) is derived from the retention curves. A gradual decrease in et, with depth is assumed in the model by interpolating between the values at 10, 45, and 80 cm depth and extrapolating to a total depth of 2 m. Assuming that the porosity interval between the 0, obtained is attributable to macropores, a macro- porosity ema ranging from 1.4 to 2.9% is obtained for the soil profile down to 80 cm depth. From the image analysis, a total macroporosity of 1.6% was deter- mined as a mean of two soil profiles to a depth of 50 cm. In both cases, no significant and consistent variation of the macroporosity with depth could be identified. Based on these figures a macroporosity of 2% is used as input to the model, decreasing to zero below the drain. The macropores had to end below the drains in order to main- tain the correct water flow to the drain and to limit the loss of solute below the lower boundary. The pore size distribution index n* for the macro- pores may vary in the interval 2.0 to 6.0, according to Jarvis ( 1991). The smaller values represent soils of coarse structure with macropore networks of a narrow pore size distribution and little tortuosity, whereas the higher values apply to soils with a wider macropore size distribution and larger tortuosity. In the model, the top 30 cm, representing the plough layer, is desig- nated by an n* value of 6.0, whereas the lower part of the profile is assigned a value of 3.0, which should characterize a top layer with variably sized and interconnected macropores overlying a soil with more continuous vertical and equal-sized earthworm channels. With 0, I/~, and 19~ thus determined, the remaining parameter for the description of soil water retention X is determined by fitting the Brooks and Corey rela- tionship to the observed water retention data. The shapes of the observed retention curves (averaged at each observation depth) do not lend themselves to accurate fitting of the exponential Brooks and Corey expression over the whole range of water contents. Values for X generating close agreement in the wetter portion of the curves were chosen in order to describe the flow processes in the relatively wet soil during the drainage season. For tensions smaller than 10 rn the retention description is adequately in correspondence with the measurements (Fig. 1). The saturated hydraulic conductivity used in the model is based on the observations obtained from the tension infiltration tests, the tests on the :small soil samples, and slug tests performed in the piezo- meters. The tension infiltration tests yield information on the conductivity close to the soil surface, the :small samples on the conductivity in the upper part of the profile, and the slug tests indicate values for the conductivity at depth in the profile. In addition, cali- bration is used to determine the conductivities. In the model the hydraulic conductivities deeper in the pro- file were decreased compared with the average con- ductivity determined from the slug tests. This was introduced to limit the vertical flux of water and solute 10 cm depth 45 cm depth 1 E+5 1 I!+5 lE+5 I 1 E+4 l&4 1 E+4 I i lE+3 lE+3 lE+3 .g i 8 0 lE+Z lE+Z 1 E+2 3 lE+l lE+l IDI lE+O 1 E+O --t 1 E+O 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 water content, (VOI). % water content. (VOI), % water content, (VOI), % Fig. 1. Observed (0) retention curves. and the curves (0) based on the Brooks and Corey approach. Horizontal error bars Indicate +/ - ooc standard deviation 80 cm depth deeper and out of the profile and reflects the hypoth- esis of anisotropic conditions in the saturated zone because the slug tests primarily yield information on the horizontal hydraulic conductivity. The parameters for the diffusion coefficient Do, the impedance factorp, and the concentration factor for crop uptake are assigned literature values. The dispersivity is calibrated, but with reference to possible values for the given soil medium. Finally, the effective diffusion path length d is determined during the calibration procedure. It should be noted that despite the procurement and use of an appreciable amount of field data for the input parameter set, a cumbersome calibration procedure was needed in order to match simultaneously the dif- ferent observed variables. 3. Results and discussion 3. I. Calibrated model The dynamics of the flow system in PLOT 3 were very well represented by the calibrated model. Though no statistical comparison is presented, this is apparent from the simulated and observed drainage flow rates and hydraulic heads (Fig. 2). A consistent deviation in the hydraulic head is due to the fact that the measurements represent the hydraulic head at depth (2.6 m). whereas the model provides the groundwater table level, and that there is a downward hydraulic gradient at the location. In order to match simulated and observed drainage concentrations, two model adaptations were required. Firstly, the two-domain approach had to be employed. In the one-domain case the hydraulic response was simulated satisfactorily during the tracer experiment, but the solute concentration displayed a much more gradual and delayed breakthrough with a consequent overall underpredicted loss of tracer to the drainage over the first drainage season ( 10% versus the observed 21% of that applied) (Fig. 3(b)). The results of the one-domain solution represent the assumption of the theory of total displacement in the matrix. The comparison between the one-domain and two-domain simulations supports the previous conclusions that solute transport at the particular site is significantly influenced by macropore flow (Villholth et al., 1998). It also demonstrates that the macropore flow mechan- ism is imperative in a model analysis of the short- as well as long-term observations of the flux concentration in the drainage effluent. Finally, it shows that an apparent correspondence between observations and simulations for the water flow is a necessary, but not a sufficient, criterion for success of modeling trans- port processes. The second model adaptation required for obtaining K.G. Villholth, K. H. JenserJJournnl of Hydro1og.y 207 ( 1998) 121~ 135 127 10 , I 8-.------------------------------------------------------------- z - 1 I . ..1 , I1 lid I. .,I. hAllJ_ IlLI L Jan-92 Feb-92 Mar-92 Apr-92 1 44 -J I Ground E 43 r ___ ,.... ._. 5 5 42 8 I 41 Drain -.. I Sep-91 act-91 Now91 Dee-61 Jan-92 Feb-92 Mar-92 Apr-92 1000 3 I I 1 _ 0 c I I sep-9 1 act-9 1 Now91 Dee-91 Jan-92 Feb-92 Mar-92 Apr-92 1 -Observed ~ Simulated A Cladded 1 Fig. 2. Simulated versus observed time series for the calibrated model. PLOT 3, SEASON 3. Inset shows the period immediately following tracer application. an acceptable simulation of solute transport to the drain was a time-variable and event-dependent value for d, the macropore spacing. A small d value was introduced for a relatively short period following the tracer application (d = 60 mm during 6 days, initiated approximately 1 day after tracer input) in order to induce significant convective and diffusive exchange between the two flow domains, according to Eqs. (1) and (2). For the remainder of the simulation period, both in the initial and late stages, d was maintained effectively infinite (d = 20 m), indicating that the exchange processes were negligible. A physical explanation consistent with the required time-variable and event-related d parameter is a dif- fusive solute exchange between pore domains that is influenced by a non-uniform distribution across the micropore domain. This effect is not considered in the first-order mass transfer equation. where lateral concentration gradients within the matrix pore domain are disregarded. In consequence, an accelerated and excessive transfer of solute occurs. Consistent with this, an assumed constant value for ci throughout the simulation resulted in an underprediction of the initial breakthrough. Introducing a constant d value accord- ing to the observed average distance between vertical active macropores (d = 60 mm) entailed a drainage leaching pattern approaching the one-domain case (not shown). Increasing d to reduce the solute exchange (d = I m) improved the modeling results. but with a tendency for an underprediction of the drainage concentration during the first part and for an overprediction during the late part of the season (Fig. 3(c)). In the calibrated model d is initially large in order to limit the diffusion of solute into the matrix, and hence to allow an appreciable amount of solute to reach the drain rapidly via the macropores. The sub- sequent small value for d is applied to allow for dif- fuse solute exchange between the matrix and the macropores. with solute predominantly diffusing from the macropores to the micropores because of the high concentration in the macropore domain. Throughout the remainder of the simulation period a large d ensures a limited back-diffusion of solute from the matrix to the macropores and thereby a less peaky appearance of the drainage concentration. This sup- ports the idea that non-equilibrium solute transfer within the soil profile on a small-scale is dominant, implying that the physical significance of the param- eter d is limited under the given field conditions. It should be noted that the assumption of a correct macropore structure in the description of the mass- exchange is less relevant because the various most likely geometries can be accounted for by including in the denominator of the first-order mass transfer coefficient, 01, (Eq. (4)), a shape factor characteristic for the specific geometry (van Genuchten, 1985). In essence. a change in d may have the same effect. The lack of model tit for any constant d value shows that the discrepancy is not explained by a non-appropriate macropore structure (rectangular-slab aggregates in the model versus vertical cylindrical macropore\ observed). Saxenu et al. ( 1994). in a lysimeter study involving the application of a conservative tracer on undisturbed soil, had similar difficulties in optimizing ~1 and related it to measurements. They suggested ( 1) a dis- crepancy of the first-order treatment of solute exchange. (2) a depth-variable cl. or (3) the two- domain assumption itself to be responsible for lack of model correspondence. Regarding the first expla- nation, Saxena et al. (1994) obtained an improved correlation with their experimental data for the leachate concentration by increasing d by a factor of 3 to 10 compared with the observed value. However. a tendency remained for an underestimation of the initial peak concentration and an overprediction of the late concentration. as also evidenced for a constant increased d in our case. A complicating factor in our model analysis is the effect of lateral flow and transport in the saturated zone. In the model, the diversion of water and solute to the drain from the saturated layers at and above the drain level is assumed to take place instantaneously. In reality. although the application of the tracer occurred very close to the drain (Villholth et al., 1998). a certain residence time in the lateral transport is expected. A finite residence time in the shallow groundwater increases diffusive exchange of solute along the flow paths: however, the significance of this process cannot be assessed based on the present model version. The fact that Saxena et al. ( 1994) had problems in optimizing d in a lysimeter study involv- ing one-dimensional flow suggests, however. that the problem is partly associated with the small-scale dif- fusive processes. To test the second hypothesis of Saxena et al. (1994) in the present study. d was increased with depth, reflecting an observed decrease in macropore intensity with depth (Wildenschild et al.. 1994). The modeling results improved, but the initial breakthrough was not captured and the drainage loss was over- predicted towards the end of the drainage season (Fig. 3(d)). The fundamental concept of a two-domain approxi- mation to the flow regime may also be questioned. The observed initial breakthrough peak occurs during K.G. Villholrh, K. H. Jensen/Journal of Hydrology 207 ( 1998) 12 l-135 129 Z-domain, d time-variable _ . Dee-91 Jan-92 Feb-92 Mar-92 Apr-92 1000 , b Dee-91 Jan-92 Feb.92 Mar-92 Apr-92 1000 t. 2-domain, d constant ~ 800 . . ..___..._...__ _........._.........~.....~... P 2 600 .._ _ _..._..._ _....~...._......~.....-...._...~ 8 400 .._~.__.....~ .._.....~ ~.........~ _... . .._.. 6 Dee-91 Jan-92 Feb-92 MCW92 Apr-92 1000 y 800 F 600 2 8 400 t 200 0 J d. P-domain, d depth-variable Dee-91 Jan-92 Feb-92 Mar-92 Apr-92 Fig. 3. Simulated versus observed drainage concentration in PLOT 3, SEASON 3 for different model scenarios: (a) calibrated model; (b) one- domain case: (c) d = 1 m: (d) d varies with depth Cd = 60 mm-20 m). the 12 h subsequent to the tracer application, whereas the model simulates the breakthrough to arrive more gradually over a 1.5 day period (Fig. 2. inset). This delay in the drain response is simulated in spite of the fact that the model does not account for the routing of the solute through the saturated zone. Additionally, the model predicts no retention of the solute in the gap zone between the drain line and the tracer appli- cation area. The extremely fast breakthrough that is not obtainable with the one-dimensional model thus demonstrates that the preferential pathways can be extraordinarily efficient. Also, it shows that the break- through could be generated by a few, drain-connected macropores, as suggested by Villholth et al. (1998). The model, however, treats the macropores as a second pore domain with average properties and thus cannot describe the effect of the efficient macro- pores, which is mainly observable in the initial break- through where the concentration differences between the pore domains are large. An alternative explanation to the sensitive d param- eter and the need to decrease the associated solute exchange artificially in the modeling is that the hydraulic connection between the two pore domains is restricted. This could occur, as suggested by Gerke and van Genuchten (1993a); Gerke and van Genuchten ( 1993b) in a theoretical two-domain model study. if. for example, a hydrophobic or com- pacted lining along macropore walls develops. This could indirectly be accounted for by increasing d in Eq. (4). In Villholth (1994) this effect was tested using a previous version of MACRO that allowed individual calibration of the convective and the diffusive part of the exchange. Decreasing the convective exchange alone did not have the desired effect, indicating that the problem of excessive exchange is primarily asso- ciated with the simplified diffusive mass transfer. The MACRO model can be regarded as an exten- sion of the popular one-dimensional two-region (mobile-immobile) approach for flow and transport in structured soils (introduced by van Genuchten and Wierenga (1976) and Wierenga ( 1982)). The mass transfer approach to diffusive solute exchange between domains is equivalent in both models, but, in addition, MACRO considers transient unsaturated flow in both domains and it allows for soil layering. Assuming that the lumped approach to solute exchange approximates the physical diffusion process to the same extent in both models. ue can use a \,aild- ity criterion derived for the mobile-immobile model in an evaluation of the MACRO models ability to approximate the diffusion proces\eh in soils of known macropore geometry. Based on a comparative analysis of breakthrough curves, van Genuchten (1985) found that the solution of the mobile- immobile model becomes asymptotically equal to the solution of a physical diffusion model that accounts for small-scale diffusion processe\ in a medium with well-defined macropore or aggregate structure when the dimensionless mass transfer coef- ficient w is large. Given that CYL &,l- 4 where L (L) is the transport distance, -9 (L T - ) is the flow rate and cy (T-l) is a first-order mass transfer coefficient as in Eq. (4). w 2 10 was found to be an adequate criterion in the case of cylindrical macro- pore geometry, a ratio of 5 between the diameter of the macropore and the soil volume surrounding it. a Peclet number of 30, and a mobile pore fraction of 20% of the total porosity. Considering this scenario to be representative of the conditions for the MACRO application, we find that the observed w ranges from 0.17 (for flow conditions varying from those during tracer breakthrough. i.e. high flow) to 2.9 (for those just initiating macropore flow). This result shows that the first-order mass transfer description, theoretically, is not a good approximation to the solute transport problem and that the limitation can be related to a combination of a relatively high flow rate in the soil and a large distance between the macropores. The analysis supports the results from the modeling, where the mass transfer artificially had to be decreased in order to match the observations. The variation of soil water concentration with depth in PLOT 3 after the tracer experiment could be simu- lated satisfactorily by the calibrated model. Assuming either one-domain or two-domain with a depth- variable macropore spacing yielded a simulated chloride distribution with a higher total solute mass consistent with the simulated delayed and reduced drainage loss (Fig. 4). Taking into account the spatial variability associated with the chloride content in the soil water the results obtained with the alternative K.G. Villholth, K.H. Jensen/Journal of Hydrology 207 (1998) 121-135 131 Cl-cont., mg/l 0 500 1000 1500 2000 2s.m 3000 o Observed I .i * L -.-.-.-+ -2.domain. d time-vmiabk l-domain 1.8 - Z-domain. d constant TO = - -Z-domain, d depth-varloble Fig. 4. Simulated versus observed chloride concentration distribu- tion with depth in PLOT 3 at the end of SEASON 3 (April 34, 1992) for different model scenarios. Horizontal error bars indicate +/ - one standard deviation. modeling approaches are, however, equally accepta- ble. The same conclusion holds for the simulation of the time series of soil water concentrations at 0.3 and 0.6 m depths based on suction cup sampling (not shown). Realizing that soil water concentrations will be highly variable in space in heterogeneous soils, and that soil water sampling by soil excavation and by vacuum extraction primarily represents solute resid- ing in the micropores and that the contribution from macropores will generally be small (owing to transi- ent flow and little water retention in the macropores), the results indicate that the observed resident concen- trations reveal relatively little information on the dynamic flow and transport processes. In contrast, the field-average flux concentration observed in the drainage discharge proved to be very valuable for the model calibration and for the interpretation of the results. 3.2. Model application to cl different season To test the ability of the model to predict system response, the calibrated model was evaluated using the observed hydraulic data for PLOT 3 during SEASON 2, when no tracer was applied. The simulation results of the drainage flow rate reflect the observa- tions, but with a tendency for the flow peaks to be delayed or to show a more gradual rising limb com- pared with the observations, especially for peaks suc- ceeding a period with little or no flow (Fig. 5(b)). With the domain exchange kept at a minimum Cd = 20 m) throughout the simulation, this discrepancy could be related to an overpredicted infiltrability of the soil matrix in SEASON 2 and, hence, a decreased activa- tion of the macropores. By reducing the saturated hydraulic conductivity of the matrix in the upper two compartments, Kb., and Kb,?, by a factor of 20 and 2 respectively, a larger fraction of the precipita- tion was infiltrated through the macropores and, con- sequently, the responsiveness of the drain was increased. The overall improvement of the simulated drainage response (Fig. 5(c)) indicates that a seasonal change in hydraulic properties in the upper soil 1aLyers may have occurred in PLOT 3 and that this change from SEASON 2 to SEASON 3 could be attributed to decreased effectiveness or surface connectivity of the macropores. This conclusion is consistent with the finding that soil surface compaction had occurred on PLOT 3 between SEASON 2 and SEASON 3 (Villholth et al., 1998). Messing and Jarvis (1993) found in a tension infiltration study that seasonal decreases in the K(I)) function close to water satura- tion at the soil surface could be related to the pro- gressive decrease in contribution from meso- and macro-pores to the infiltration process, presumably due to breakdown of soil structure. The hypothetical effect of increased macropore efficiency on solute transport was evaluated by simulating the tracer experiment in SEASON 3 using the soil hydraulic parameters optimized for SEASON 2. In this scenario, the accumulated drain loss was increased by 22% and the solute reached deeper into the profile, indicating that the surface hydraulic Icon- ditions are very important and need special attention when characterizing a macroporous soil for modeling purposes. Finally, the disagreement between obse:rved and simulated drainage rates in late February, which is not ameliorated by the changed hydraulic properties, is explained by snow accumulation, soil freezing and sub- sequent thawing, for which the model cannot account. 3.3. Model application to a different plot Simulating the tracer experiment in PLOT 1 also 32 0 i Nov-90 Jan-91 Feb-91 Nov-90 Dee-90 Jan-91 Feb-91 Nov-90 Dee-90 Jan-91 Feb-91 44 - : d. Ground E 43 I_-. .._ B - 5 42 - B41r 0 Drain An -- . Nov-90 Dee-90 Jan-91 Feb-91 1 -Observed - Simulated I Fig. 5. Simulated versus observed time series from PLOT 3, SEASON 2: (a) rainfall: (b) simulation accordmg to the calibrated model; (c) simulation according to model with adjusted infiltration characteristics: (d) head elevation. Insets show in detail the drain flow immediately following a dry period. entailed adjustments to the calibrated model in order to match the observations. The main observed differ- ences in this plot were the lack of immediate drainage breakthrough in response to the surface application and a fairly deep penetration of the solute. The adjust- ments included an increase in drain spacing (4 to 10 m) and an increase in the saturated hydraulic con- ductivity of the macropores in the lower part of the K.G. Villholth, K.H. Jensen/Journal of Hydrology 207 (1998) 121-135 133 Cl-cone., mg/l 1000 2000 3000 4000 5000 6000 7000 Fig. 6. Simulated versus observed chloride concentration distribu- tion with depth in PLOT I at the end of SEASON 1 (June 2 1, 1990) according to model with adjusted parameters. Horizontal error bars indicate +/ - one standard deviation. profile (factor 5 100). In this way, solute was trans- ported more vertically and less laterally in accordance with observations. The macropore spacing was assumed to be time-variable in the same way as the simulation of the tracer experiment in PLOT 3, with the temporal change of the d value governed by accu- mulated rainfall amounts after the tracer application. Finally, the solute was applied in the model at the onset of the first rain event after the real application time. This was introduced because the model could not accommodate solid input, and an application in accordance with the actual situation assuming dis- solved substance resulted in excessive solute retention in the upper soil layers. The model attempt was partly successful, with a satisfactory hydraulic response of the drain and a lack of drainage breakthrough (results not shown). However, the model (Fig. 6) did not cap- ture the deep percolation of the solute. This dis- crepancy is mainly explained by the lack of a description for lateral transport below the drain depth. With no sink available for the water and solute at depth in the macropores and with no dispersion in the macropore region, the solute remained at shal- lower depths. The interpretation of the model results of the tracer experiment in PLOT 1 is in accordance with the suggested explanations given earlier (Villholth et al., 1998). Preferential flow is responsible for the rapid and deep distribution of the solute. As speculated, the tracer apparently was not mobilized until rain occurred subsequent to the application of the solid tracer. The required delay in the tracer input to the model shows the great sensitivity to the top boundary condition. It also emphasizes the difficulty of specifying approximate input conditions for a non-dissolved tracer with the present model. The deeper penetration combined with the smaller loss of solute to the drain in PLOT 1 compared with PLOT 3 was explained by a different macropore structure with more vertically connected macropores in PLOT 1. The modeling was consistent with this explana- tion. Furthermore, the results showed that the model was equally efficient in describing the responses in the two plots, despite apparent differences in soil structure, when a consistent variation in d was taken into account. 4. Conclusions The model analysis of the results presented from the controlled tracer experiments by Villholth et al. (1998) supported the conclusions that macropore flow is significant at the site investigated. Agreement with the observed chloride concentrations in the subsurface drain effluent could only be obtained by including the macropore flow domain in the MACRO model that optionally operates in a continuum mode or a bi- continuum mode. A large sensitivity of the upper boundary condition with respect to water and solute entry into the soil was found, indicating that special emphasis is required in the determination of parameters related to infiltration. Tension infiltration tests proved to be a valuable tool for in situ determination of the saturated hydraulic conductivities pertaining to the soil matrix that is required by the MACRO model. The finding that macropore structure is dynamic and spatially variable underlines the importance of relying on current and site-specific measurements of hydraulic conductivity of the matrix and the macropores. Large sensitivity to the macropore spacing in the mass transfer description of water and solute tratrsport between domains was found. There was a lack of model agreement when the observed macropore spacing was used and an improved correspondence when the solute exchange between the domains was artificially delayed and reduced (by assuming time- variable macropore spacing). This was explained by the model approximation of the exchange processes in which a time-independent mass transfer process is assumed, leading to total and instantaneous mixing within the matrix domain. The shortcomings of the first-order mass transfer approach were supported by a theoretical evaluation based on a comparison with a more physically correct diffusion, mobile-immobile model. Although the application of a one-dimensional model to an essentially three-dimensional problem hampered a comprehensive analysis of the experimental data. the results suggest that short- and long-term field transport in structured soils may not easily be described by existing two-domain, mass-transfer-based models. A remedy is to include the small-scale diffusion processes across the micropore space or to include more domains in the model description (Brusseau and Rao. 1990; Saxena et al.. 1994: Gwo et al.. 1996). Both solutions, however, require more elaborate models and/or more model parameters. Acknowledgements We thank Chris Ogden and an anonymous reviewer for their constructive comments and suggestions. References Addiscott. T.M.. Wagenet, R.J.. 1985. 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