Review of Dispersivity Lengths for Transport Modeling in Soils

Transcription

1 Review of Dispersivity Lengths for Transport Modeling in Soils Jan Vanderborght and Harry Vereecken Agrosphere ICG-IV Forschungszentrum Jülich GmbH D- Jülich j.vanderborght@fz-juelich.de tel: +9

2 Abstract The one-dimensional convection-dispersion equation is often used to estimate the risk of nonpoint source groundwater contamination and dispersivity is known to be a sensitive parameter for predicting the mass that leaches from through the soil towards the groundwater. We present a database of dispersivities that were derived from leaching studies in soils. Besides dispersivities, the database contains information about experimental parameters: transport distance, scale of the experiment, flow rate, boundary conditions, soil texture, pore water velocity, transport velocity, and measurement method. Dispersivities increase with increasing transport distance and scale of the experiment. Considerably larger dispersivities were observed for saturated than for unsaturated flow conditions. No significant effect of soil texture on dispersivity was observed but interactive effects of soil texture, lateral scale of the experiment, and flow rate on dispersivity were significant. In coarse textured soils, lateral water redistribution may take place over larger distances, which explains the larger dependency of dispersivity on lateral scale of the experiment in coarse than in finer textured soils. The activation of large interaggregate pores may explain the increase in dispersivity with increasing flow rate in finer textured soils, which was not observed in soils with a coarser texture. The distribution of dispersivities is positively skewed and better described by a lognormal than a normal distribution. Different experimental factors explained % of the total variability of log e transformed dispersivities. The unexplained variance of the dispersivity is large and its coefficient of variation amounts 00%.

3 Introduction Models that calculated chemical transport in soils are more and more being used in practice. Risk assessment on the basis of model calculations of leaching of surface applied chemicals (fertilizers, pesticides) or of contaminants from contaminated sites towards the groundwater becomes more and more legally prescribed. Examples are the FOCUS groundwater scenarios (FOCUS, 000) which must be used in the European pesticide registration procedure to estimate the risk of groundwater contamination by surface applied pesticides. The reliability of these model calculations depends on the accuracy with which relevant processes for contaminant transport are implemented in transport models. An important process is the transport in that occurs in the water phase. Reviews of different model approaches to describe transport of dissolved substances are given by Feyen et al. (99); Jury and Flühler (99); Nielsen et al. (9), Vanclooster et al. (00). Besides an appropriate model choice, also the parameterization of the model plays an important role. To parameterize the water flow model, databases of soil hydraulic parameters, e.g., HYPRES database (Wösten et al., 999), the UNSODA database (Nemes et al., 00) and pedotransfer functions relating soil hydraulic with spatialized information about other soil properties have been derived (Schaap et al., 99; Vereecken et al., 990; Vereecken et al., 99). Using pedotransfer functions in combination with soil databases, hydraulic properties and model predictions can be spatialized as well as soil management, and soil and groundwater protection policies. An example of combining modeling of pesticide leaching with spatialized information about soil properties and land use to derive spatial distributions of pesticide groundwater concentrations is given by Tiktak et al. (00). In their study, hydraulic properties and soil properties that are related to pesticide sorption and decay (organic carbon content and soil ph) were spatialized whereas transport parameters were chosen to be constant. Boesten (00) showed that the dispersivity, which is a transport parameter describing spreading or dispersion of a surface applied solute pulse that leaches through the soil, has an important impact on predicted yearly

4 averaged pesticide concentration, especially for substances with a low leaching potential. However, datasets of transport parameters such as those existing for hydraulic parameters are missing. Gelhar et al. (99) reviewed dispersivities derived from groundwater tracer studies and found a scale dependency of the dispersivity, which increases with increasing transport distance. Since the transport distance in groundwater tracer studies is much larger than the typical transport distance in soils, it is questionable whether parameters derived from groundwater tracer studies can be applied to soils. Furthermore, the structural properties of soils and aquifers are substantially different. In soils, flow and transport are perpendicular to the layering whereas in aquifers, they are mostly aligned with stratification. The origin of stratification in soils and aquifers is also substantially different. In aquifers, stratification is mostly the result of a sedimentation process whereas in soils it results from leaching and precipitation processes. Finally, flow and transport processes in aquifers occur under saturated and more or less steady flow conditions. In soils, flow and transport are highly dynamic processes that change in magnitude and direction due to the continuously changing boundary conditions. Also the water content and the pore volume in which transport takes places change continuously. Therefore it is highly questionable whether transport properties obtained from groundwater tracer studies can be translated to soils. The objective of this study is to give an overview of transport properties, more specifically the dispersivity, that were derived from tracer studies in soils. We focus on the dispersivity since the convection dispersion model is the most widely used model to predict transport in soils and to interpret tracer experiments, especially those tracer experiments that were carried out under natural boundary conditions at the field plot scale and in undisturbed soil (which are most relevant for practical applications). Beven et al. (99) made a review of tracer experiments and dispersivities in soils. However, the number of studies, especially the number of field scale studies that could be reviewed at that time was relatively small. Overviews of parameters of other transport models, such as mobile-immobile model

5 7 9 0 parameters (van Genuchten and Wierenga, 97), were restricted to experiments that were carried out in relatively small soil columns, which were often filled with disturbed soil or artificial media such as glass beads, and which were carried out under high flow rates (Goncalves et al., 00; Griffioen et al., 99; Haggerty et al., 00). In this review, we first define the dispersivity and how it is derived from leaching experiments. Then we present a database of dispersivities derived from leaching experiments in soils. Specific objectives of this paper are to provide, on the basis of available data in literature, answers to the following questions: What is the range of dispersivities observed in leaching experiments and how are they distributed? How does dispersivity depend on experimental factors such as scale of the experiment, leaching rate, and transport distance? Is there a relation between soil texture and dispersivity? This information is needed for a realistic parameterisation of dispersivity and its uncertainty in modelling studies Definition of Dispersivity Flow in the vadose zone is generally in the vertical direction. A common simplification is that of one-dimensional (-D) transport, i.e., solute fluxes and concentration gradients in the horizontal direction are neglected. This assumption follows from the generally widespread application of chemicals or pollutants at the soil surface, i.e., diffuse, or non-point source, pollution. For several practical applications (prediction of transport of agrochemicals and salts) the convection dispersion equation is used:

6 C S C C θ + ρb = θv + θd F( C, S) [] t t z z z where θ is the volumetric water content, C (M L - ) the concentration in the soil water, ρ b (M L - ) the soil bulk density, S (M M - ) the concentration of the sorbed phase, v (L T - ) the pore water velocity, D (L² T - ) the hydrodynamic dispersion coefficient, F(C,S) a function describing reactions of the substance in the solid and liquid phases (e.g. decay, kinetic sorption/desportion, precipitation/dissolution), and z the vertical coordinate. The hydrodynamic dispersion accounts for a solute flux due to a concentration gradient that leads to a decrease of peak solute concentrations with time and a smoothing of concentration gradients. Two mechanisms are responsible for the dispersive solute flux: molecular diffusion and hydromechanical dispersion. The former represents the effect of thermal agitation and molecular collision, the latter represents the effect of variations of the advection velocity that exist at a smaller scale than the scale of the averaging volume. The hydrodynamic dispersion is related to the molecular diffusion constant of the substance in bulk water, D 0, and the pore water velocity, v, as: 7 ( θ ) D0 D = λ v +τ [] 9 0 where λ (L) is the dispersivity, τ a tortuosity coefficient, and D 0 (L² T - ) the molecular diffusion coefficient. Leaching experiment data do not contain information allowing a discrimination between molecular diffusion and mechanical dispersion. However, the effective molecular diffusion coefficient (τ(θ) D 0 ) is in the order of 0. cm² d - and its the contribution to the hydrodynamic dispersion D observed in the leaching experiments was on average %. Therefore, the dispersivity, λ, was simply derived from the ratio D/v assuming that molecular diffusion can be neglected.

7 Derivation of Dispersivity Dispersivities are typically derived either from observed depth profiles of inert tracer concentrations or from breakthrough curves (BTC) of tracer concentrations that are measured in the effluent of columns or that are measured in a soil profile using solution samplers or other devices suchs as time domain reflectometry (TDR) probes that monitor solute concentrations. In general, the hydrodynamic dispersion coefficient, D, and the pore water velocity v are derived from these profiles assuming that v and D are constant in the soil profile and do not change with depth and time, i.e. a hydrodynamically homogeneous soil profile and steady state flow conditions. For such situations, analytical solutions of the transport equation can be derived and fitted to the observed depth profiles or BTCs. An overview of analytical solutions of the -D CDE is given in Toride et al. (999). Alternatively, time moments of BTCs or depth moments of concentration depth profiles may be calculated and used to derive the dispersion coefficient and pore water velocity (Jacques et al., 99; Jury and Sposito, 9; Jury and Roth, 990; Russo, 00). The calculation of time or depth moments does not require the specification of a process model. Time moments can also be related to parameters of other models which were fitted to breakthrough curves, e.g. the mobile-immobile model (Valocchi, 9), the convective lognormal transfer function model (Jury and Sposito, 9) or a stream tube model which accounts for dispersion within stream tubes (Toride and Leij, 99). From time moments that are calculated from parameters of other models an apparent dispersivity can be derived using the relation between the time moments of a BTC and dispersivity. In some field-scale transport experiments, a salt tracer was applied on a large surface and for a given depth in the soil profile, breakthrough curves were measured locally at several locations (Biggar and Nielsen, 97; Bowman and Rice, 9; Vandepol et al., 977). The solution of a -D CDE was fitted to the locally measured BTCs and distributions of 7

8 local CDE parameters, pore water velocities and local dispersivities, λ (local) were derived. Using time moment analysis, the apparent dispersivity of the field scale averaged breakthrough curve, λ (field) can be derived from the distribution of the local CDE parameters (Toride and Leij, 99): ( field ) ( local) ) z λ exp( σ ) + [ exp( σ ) ] λ = ln v ln v [] 7 9 where <λ (local) > is the arithmetic average of the local dispersivities and σ the log e transformed local velocities. ln v is the variance of 0 The analytical solutions of the convection dispersion equation apply for constant flow rates. When the flow rate is not constant, the time coordinate is often transformed to a cumulative infiltration or drainage coordinate I(t): I t = () t Jw( z t' ) 0, dt' [] where Jw(z,t) is the water flux at depth z and time t. This transformation leads to a similarly smooth course of concentrations as under steady state flow conditions and the analytical solution of the steady-state CDE, in which the time coordinate is replaced by I(t), is fitted against the measured concentrations. The transformation in Eq. [] involves a transformation of the dimensions of the fitted parameters, v (I) and D (I). The fitted velocity, v (I) has dimension L L - and represents the distance over which the substance is leached per unit of leached water depth so that ( I v ) = θ. The dispersivity λ (I) has the same dimension as the dispersivity obtained under steady state flow conditions. λ (I) is in general larger than λ (Beese and

9 7 Wierenga, 90; Vanderborght et al., 000b; Wierenga, 977) depending on the temporal fluctuations of the water content during the leaching experiment. Beese and Wierenga (90) report that λ (I) may be a factor larger than λ in the top soil where the dynamics of the water flux and water content are large. The difference between λ (I) and λ decreases with increasing depth and for smaller fluctuations of the water content (Vanderborght et al., 000b). For soil profiles with variable water content with depth, the following depth transform has been proposed (Ellsworth and Jury, 99): 9 z ( z) = ( z' ) z * θ dz' [] 0 0 When depth is transformed by Eq. [], the pore water velocity v (z*) corresponds with the water flux Jw and the dispersivity λ (z*) is expressed in terms of transformed length units. Although a theoretical basis for the use of the depth transform in Eq. [] is basically missing, breakthrough curves in soil profiles with vertically varying soil water contents were often fitted by a solution of the CDE in a homogeneous soil profile after replacing the real depth coordinate by z*. The dispersivity λ (z*) that is derived from a breakthrough curve at 7 transformed depth z* can be expressed in real depth coordinates as: 9 ( z ) z λ = λ ( z* ) [] z * 0 where λ (z) is an apparent dispersivity length in real depth coordinates that predicts the breakthrough at depth z assuming a soil profile with a vertically constant water content θ. The direct effect of vertical variability of θ on the apparent dispersivity length λ (z) can be assessed using the following formula (Vanderborght et al., 000a): 9

10 λ ( ) + ( z ) = λ CV ( θ ) [7] where CV(θ) is the coefficient of variation of the water content and λ is the dispersivity. According to Eq. [7], a vertical variability of water contents leads to larger apparent dispersivities. Since CV(θ) is generally smaller than one, the direct effect of vertical variability of the water content on λ (z) is not so large. However, λ in Eq. [7] is assumed to be a material constant that does not depend on θ neither varies with depth so that the apparent dispersivity λ (z) also changes with depth when λ changes with θ or depth (indirect effect of θ on λ (z) ). Database of Dispersivity Lengths Contents of the database The data base contains entries derived from 7 publications in scientific journals. Since soil structure has an important impact on solute transport, only experiments in undisturbed soils were considered excluding experiments in repacked or refilled soil cores or columns. Besides dispersivities, also experimental factors were included in the data base so that relations between experimental factors and dispersivities can be inferred. The following factors were included: dispersivity λ (cm), Experimental scale 0

11 transport distance z (cm), i.e., the vertical distance that the applied tracer travelled. The transport distance corresponds with the length of the soil column, the depth where a breakthrough curve was measured, or the center of mass of a concentration depth profile. scale of the leaching experiments. Three classes were considered: core-scale (soil cores with a length < 0 cm), column scale (undisturbed soil monoliths with a length > 0 cm), and field scale, Boundary and flow conditions during the leaching experiment transport velocity v (cm d - ) derived from the tracer breakthrough or concentration depth profiles, pore water velocity v p (cm d - ) derived from the flow rate divided by the volumetric water content, ratio of v/v p which is a measure for preferential solute transport (v/v p > ) or solute retardation (v/v p < ), average flow rate J w (cm d - ) which is the net infiltrated water depth during the leaching experiment divided by the duration of the experiment, effective flow rate J weff (cm d - ) which is a measure for the flow rate intensity in the soil during the experiment (for a definition see Vanderborght et al., 000b), flow boundary condition type: steady (steady unsaturated flow obtained from a steady irrigation), ponding or flooding (steady flow under saturated flow conditions), intermittent (periodic flow under unsaturated conditions by intermittent irrigation), interpond (periodic ponding or flooding of the soil surface), climatic (natural rainfall and soil evaporation), interclim (natural rainfall and soil evaporation with intermittent additional irrigation), Soil properties

12 USDA soil texture class: c:clay, sic: silty clay, sc: sandy clay, cl: clay loam, sicl: silty clay loam, scl: sandy clay loam, sil: silt loam, silg: silt loam gravel, l: loam, sl: sandy loam, ls: loamy sand, s: sand, sg: sandy gravel, soil depth. Depth from which soil cores were taken: A (top soil: 0-0 cm), B horizon (0-0 cm), C (subsoil: deeper than 0 cm) Concentration measurements type of concentration that was measured: volume averaged or resident versus flux averaged concentrations, measurement type: direct (in the effluent from soil columns or cores), coring (analysis of soil samples), samplers (extraction of soil solution in the soil profile using suction samplers or suction plates), TDR (concentrations derived from bulk soil electrical conductivity measured with TDR), tile drains, dye tracers (image analysis of photographic recordings of dye stained patterns on excavated soil surfaces), calculated (average concentrations calculated from the average of local concentration measurements), Miscellaneous experiment number. The experiment number groups all dispersivity values that were obtained for the same field plot under the same leaching conditions. name of the field site where experiments were carried out or from where soil samples were taken, author and year of publication. A complete list is given in the Appendix.

13 Effects of experimental conditions: flow rate, scale of the experiment, and transport distance on dispersivity Scale of the study, flow boundary condition type, and soil texture are considered to be important experimental factors influencing the solute dispersion. In Figure, Figure, and Figure, the number of data entries in different factor classes are shown together with the mean dispersivity, mean flow rate, and mean transport distance in the factor classes. With increasing scale of the leaching experiment, the average transport distance increases whereas the flow rate decreases (Figure ). The effect of the experimental scale on the dispersivity length can therefore not be derived without considering the effects of flow rate and transport distance on the dispersivity length. About two thirds of all dispersivities were derived from leaching experiments carried out under steady-state flow conditions (Figure ). Although the mean flow rate in experiments carried out under continuous and intermittent flooding boundary conditions is quite different, the mean dispersivities in these classes are similar and much larger than in the other boundary condition classes. The mean dispersivity was the smallest in experiments that were carried out under steady-state unsaturated flow conditions whereas the mean flow rate was the second largest in these experiments. The degree of saturation of the soil surface, i.e. continuously or periodically saturated (ponded) versus unsaturated, seems to have a larger impact on the dispersivity than the mean flow rate during the experiment. The larger dispersivities observed in leaching experiments with saturated soil surface conditions clearly reflect the effect of flow and transport through larger pores, i.e. macropores, which are activated under saturated conditions. Looking at the combination between soil texture and flow boundary condition class (Figure ), it is remarkable that in clayey soils (c, sic, sc, cl, sicl, and scl) most experiments were carried out under saturated flow conditions. Experiments under climatic boundary conditions were

14 7 9 0 mainly carried out in coarser textured soils. This correlation between boundary condition and soil texture needs to be considered when effects of soil texture and boundary condition on the dispersivity are investigated. For further analysis, all experiments carried out under flooding and intermittent flooding boundary conditions were grouped in a separate class. For the other group of experiments, the soil texture classes were grouped into two texture classes: a coarse texture class that lumps the sand, loamy sand and sandy loam classes and a fine texture class lumping the other texture classes. Experiments that were carried out soils with a large stone content (texture classes sg and silg) were excluded because they were not considered to be relevant for agricultural use Although flow rate, J w, and transport distance are continuous variables, their effect on the dispersivity length was investigated through flow rate and transport distance classes. If available, the effective flow rate, J weff, rather than the time averaged flow rate was considered. For transient flow conditions, the flow rate intensity in the soil column, which is quantified by J weff, was shown to be better correlated to the dispersivity than the time averaged flow rate (Vanderborght et al., 000a). Four flow rate classes were defined: flow rates smaller than cm d -, between cm d - and 0 cm d -, and larger than 0 cm d -, and experiments carried out under flooding and intermittent flooding boundary conditions. Most of the experiments that were carried out under climatic conditions or climatic conditions with intermittent irrigation fell into the flow class with flow rates smaller than cm/d. Exceptions were studies in which a large amount of water was infiltrated during a short time (rainfall events of more than 0 cm d - ). These studies fell into the class with flow rates larger than 0 cm d -. For the transport distances, three classes were defined: studies with a transport distance smaller than or equal to 0 cm, between cm and 0 cm and between and 00 cm. The first class contains all soil core scale experiments and is relevant for the transport through the

15 7 9 0 upper soil layer or plough layer. In order to give the same weight to experiments in which dispersivities were determined for several travel distances (e.g in a soil column or a field plot), the data entries in a travel distance class that correspond to the same experiment or experiment number were averaged and further treated as a single entry. In Figure, the distribution of dispersivities in different flow rate and experimental scale classes are shown for the different transport distance classes. Dispersivities derived from experiments that were carried out using a flooding boundary condition were consistently larger than dispersivities that were derived from other experiments. For the 0-0 cm travel distance class, there is a clear increase of dispersivity length with increasing flow rate in the core and column scale experiments. This increase is not or not so clearly seen in field-scale experiments neither in the -0 and -00 cm travel distance classes. Most leaching studies were carried out using artificial leaching rates. In order to reduce the duration of the leaching experiment, the average flow rate in leaching experiments is mostly considerably larger than under natural boundary conditions. For instance, a leaching experiment carried out with a flow rate of 0 cm d - would correspond with a yearly precipitation of 00 mm, which is one to two orders of magnitude larger than the yearly precipitation amount. On the other hand, rainfall and soil water flow are highly dynamic processes with high rainfall or flow intensities occurring during only a short period of time and with long intermittent periods without rainfall or significant downward flow. Therefore, close to the soil surface vertical movement occurs during relatively short pulses with a high flow rate. These high flow rates become sensibly buffered with depth, depending on the hydraulic buffer capacity of the soil. From rainfall intensity records, the amount of rain that falls with intensities smaller or larger than a certain threshold can be derived. As an example, in Jülich (Germany), 0% of the total yearly precipitation occurs with an intensity larger than. cm d - whereas halve of the total yearly precipitation occurs with an intensity larger than. cm d -. In that perspective, leaching experiments in the flow rate class cm d - < J w < 0

16 cm d - may also be considered realistic. Because flow rates larger than 0 cm d - were not considered to be realistic for natural boundary conditions, dispersivities from this flow rate class were excluded from further analyses. However, since the dispersivities in the 0 cm d - < J w class were, except for the core and column scale experiments and travel distances smaller than 0 cm, not very different from dispersivity distributions in other flow rate classes (Figure ), their exclusion does not influence the results of the further analyses considerably. The effect of experimental scale and travel distance on dispersivities derived from experiments with a flow rate smaller than 0 cm d - is shown in Figure. Both the transport distance and the lateral scale of transport experiment have an impact on the dispersivity. Generally, dispersivity increases when the lateral scale of the experiment increases. Therefore, field scale experiments are expected to be more representative for the dispersion process under real conditions than experiments in soil columns or lysimeters that reduce lateral redistribution of water flow, and hence the dispersion process. However, the difference between field and column scale experiments is smaller for larger travel distances where the two distributions tend to converge. Furthermore, solute fluxes can be measured in a column experiment but not in a field experiment. In field experiments, concentrations are measured locally at a number of points and the actually sampled area is only a small fraction of the total cross sectional area of the field plot and may be even smaller than the area of a soil column or lysimeter. Looking at the effect of the transport distance on the dispersivity, the column scale experiments clearly show an increase of dispersivity with transport distance. For the field scale experiments, the dispersivity distribution in the 0-0 cm travel distance class is similar to that in the -0 cm class. The larger dispersivities in the 0-0 cm transport distance class for the field scale experiments may also be the result of transient flow conditions at the soil surface and the transformation of the time coordinate to a cumulative infiltration or drainage coordinate (Eq. []) that is often used to transform BTCs before fitting the solution of the

17 steady-state CDE. The increase of dispersivity with increasing travel distance in soils is in line with a generally observed trend that was reported for dispersivities derived from groundwater tracer studies (Gelhar et al., 99). From those data, a rule of thumb that the dispersivity length is approximately /0 of the travel distance was inferred. Applying this rule of thumb to soil data, the median dispersivity would be overestimated. Considering the large difference between the travel distances of the tracer experiments on the basis of which this rule was derived and the transport distances in soils, this rule of thumb seems to be a quite universal and applicable to obtain a rough estimate of dispersivities in soil. In Figure, median values of dispersivities in the different experimental scale classes are plotted versus the median value of the transport distance in the distance classes together with linear and power law model fits. The plot suggests that the rate of increase of dispersivity with travel distance is larger for smaller than for larger travel distances. The rate of increase of the median dispersivities between the first and second and between the second and third travel distance classes is similar. A constant rate of increase of dispersivity with travel distance can be explained by assuming that velocities of individual solute particles remain perfectly correlated with travel distance. When the spatial scale over which particles travel with a constant velocity is smaller than the transport distance, the rate of increase of the dispersivity decreases with travel distance and the dispersivity reaches an asymptotic value (e.g., Jury and Roth, 990). Figure suggest that, in general, the asymptotic regime is not reached within the first meter of the soil profile. This means that regions with higher or lower water fluxes and particle velocities are vertically continuous over a distance of at least a few decimeter in soils. However, several examples of soil profiles in which the dispersivity reaches an asymptotic value exist so that this statement cannot be applied to each individual soil profile. When the increase of the dispersivity with travel distance is explained by particle velocities that remain constant along their trajectory, it is presumed that the variance of the particle velocities does not change with depth in the soil profile. The increase of λ with travel distance could 7

18 7 9 alternatively be explained by an increase of the particle velocity variance with depth whereas the particle velocities are correlated only over a microscopic distance. It may be presumed that the top soil is more homogenized due to tillage than the subsoil soil so that the variance of the particle velocities is smaller in the top than in the sub soil. However, there are two arguments against using only this hypothesis to explain the increase of λ with travel distance. An indirect argument is the increase of dispersivity with lateral scale of the experiment. This implies that velocity variations exist on a macroscopic lateral scale and therefore must extend over a macroscopic vertical distance. The second argument is that dispersivities are not larger in soil cores from deeper soil horizons than in cores from the top soil (Figure 7) Effect of soil texture on dispersivity. The effect of the flow rate class on dispersivities in the coarse and fine texture soil classes is shown in Figure. In both soil texture classes, dispersivities are larger for saturated than for unsaturated flow conditions. It should be noted that the opposite was observed in leaching experiments in repacked soil columns (e.g., De Smedt et al., 9; Elrick and French, 9; Maraqa et al., 997). For unsaturated flow experiments, dispersivity distributions do not depend on flow rate class in soils with a coarser texture whereas dispersivities increase with increasing flow rate in soils with a finer texture. In soils with a finer texture, the pores in the soil matrix or the intra-aggregate pores are small so that the soil matrix has a low hydraulic conductivity. When the leaching rate exceeds the conductivity of the intra-aggregate pores, inter-aggregate pores, which are continuous over a much larger distance than the intraaggregate pores, are activated leading to an increase of the dispersivity with increasing flow rate. In soils with a coarser texture, the pore sizes and hydraulic conductivity of the soil matrix are much higher and more soil matrix pores are activated with increasing flow rate so

19 that the water filled pore network gets better connected and the tortuosity of the flow paths decreases. This may even lead to a decrease of the dispersivity with increasing flow rate. In the rest of the analysis, only data from unsaturated leaching experiments with a flow rate smaller than 0 cm d - were considered. Figure 9 displays the effect of the transport distance and texture on the dispersivity and Figure 0 the effect of the scale of the experiment and the texture. In soils with a coarse texture, the dispersivity seems to be smaller than in soils with a finer texture. In both soil classes, the dispersivity increases with travel distance. In finer textured soils, the distributions of disperivities in column and field scale experiments are similar whereas in coarser textured soils, larger dispersivities were observed in field than in column scale experiments. This suggests that the lateral spatial scale of the transport variability is smaller in finer textured soils than in coarser textured soils. In coarser textured soils, lateral redistribution of water and funnelling of water towards preferential flow regions rather takes place in the soil matrix. This lateral redistribution may be strongly reduced by imposing no-flow lateral boundary conditions. Solute spreading and dispersion due to rapid transport in large inter-aggregate pores occurs on a smaller lateral scale which may explain why no increase of dispersivity from the column to the field scale is observed in finer textured soils. 9 0 Variability of dispersivities and analysis of variance The box-plots in Figure, and Figure 7-Figure 0 suggest that the dispersivities are lognormally distributed (the box plots are symmetric around the median when the y-axis of the plots are logarithmically scaled). In Figure, histograms of non- and log e transformed dispersivity distributions in the different travel distance classes are shown. The histograms qualitatively indicate that dispersivity lengths are lognormally distributed. The logarithmic transformation also suggests that the large dispersivity values in the tails of the non- 9

20 transformed distributions should not be considered as outliers, i.e. observations with a probability of exceedance much lower than (#observations) -. An analysis of variance ANOVA was carried out to investigate the significance of the different factor effects and the part of the variance of the log e transformed dispersivity distribution that can be explained by these factors. To reduce the number of factors and have a sufficient number of observations within a factor combination, only the factors transport distance, texture, and experimental scale were investigated. Experiments with a flow rate smaller than 0 cm d - were considered and the effect of flow rate class was not further investigated. Core scale experiments were excluded to avoid factor combinations without data. Since the dataset was not balanced, the data were analyzed within the framework of generalized linear models using the GLM procedure of the SAS software. The outcome of the ANOVA is shown in Table. The total variance of log e transformed dispersivities in the data set, σ loge λ: total = 0.7 and the coefficient of variation of the non transformed dispersivities CV total = 9% ( CV 00 exp( σ ) total = loge λ, total of the total variance and the unexplained variance σ ). The model explained variance is % (R²) log e λ : error = 0.7 and CV error = 0%. The variability of dispersivities within a factor class combination remains therefore relatively large and unexplained. The factor explaining most of the variance is the transport distance. Also the interaction between the scale of the experiment and the texture and the variability explained by the scale of the experiment were significant (at % significance level). The effect of soil texture was not significant. Effect of measurement method The effect of the measurement type is evaluated based on the ratio of the transport velocity that is derived from the tracer movement, v, and the pore water velocity that is predicted from 0

21 the flow rate and the water content, v p. Deviation of the ratio v/v p from is an indication that the transport process is not well described by a model which presumes that solute transport takes places in the entire water filled pore space or an indication that the observed solute transport is not representative for the overall transport within the soil sample or field site. The v/v p ratios are shown in Figure for different measurement types and transport distance classes and for saturated conditions or high flow rates (J w > 0 cm d - )(Figure a) and unsaturated flow conditions (Figure b). The spreading of the v/v p ratios is the largest for the soil solution samplers whereas direct measurement of the concentration breakthrough in the effluent of a soil core/column leads to smallest variability in v/v p. The TDR technique and soil coring method lead to an intermediate spreading of v/v p. The spreading v/v p can be related to the soil volume that is actually sampled by the method. Soil samplers only sample the soil water locally so that only a small fraction of the cross sectional is sampled, even when a large number of samplers are used. As a consequence, the BTC obtained from averaging the local measurements may deviate considerably from the averaged BTC of local concentrations or solute fluxes at that depth (e.g., Weihermuller et al., 00). Furthermore, suction samplers distort the flow field to a certain extend which also leads to deviations of v estimated from BTCs measured with suction samplers. The cross sectional area sampled by TDR probes and the soil volume sampled by soil coring are larger which explains the smaller variability of v/v p when these methods are used. If the concentration is measured directly in the effluent of a soil core/column, then the entire cross-sectional area is sampled and the BTC is obviously representative. However, also for the direct method, the variability of v/v p may be quite large, e.g for the saturated conditions or high flow rates and small transport distances v/v p was found in several experiments to be considerably larger than. These cases may be attributed to preferential flow and an earlier arrival of the peak concentration than expected based on the flow rate and the volumetric water content. If the total water filled porosity is accessible to the solutes, be it by slow diffusion, a fast breakthrough of the peak concentration is followed by a

22 long tailing of the breakthrough curve due to slow release of solutes from the bypassed pore region. This tailing cannot be described by the CDE so that a CDE fit leads to an overestimation of the average pore water velocity in the total solute accessible pore volume, i.e. inclusive of the pore volume in which water flow is very slow. In the effluent of a soil core/column, flux concentrations or flux weighted averages of local concentrations are measured. By TDR and soil coring methods, volume averaged or resident concentrations are measured. TDR measures time series of resident concentrations whereas concentration depth profiles are derived from soil coring. For small travel distances, v derived from TDR measurements seem to underestimate v p, especially for saturated flow conditions. If preferential flow occurs through a small part of the total pore volume, the early breakthrough in the preferential flow region is hardly seen in volume averaged concentrations measured by TDR. For larger travel distances and transport times, the opportunity for mixing and exchange of solutes between preferential flow paths and bypassed regions increases and the deviation between v and v p decreases. Another explanation for the smaller estimates of v is that solute fluxes and pore water velocities are derived from a BTC of resident concentrations assuming that the transport process can be predicted using a convective dispersion model with a constant dispersivity. When dispersivity scales with travel distance, this approach leads to an underestimation of the pore water velocity (Jacques et al., 99). 9 0 Discussion and Conclusions In agreement with reviews of dispersivities observed in groundwater tracer studies, dispersivity in soils also scales with travel distance. Scaling of dispersivity with transport distance implies that the transport distance in leaching experiments should be similar to the range of transport distances for which predictions of solute concentrations must be made. Scaling of dispersivity with transport distance could not be explained by an increase of the

23 soil heterogeneity in the subsoil, which is not regularly homogenized by soil tillage. This implies that solute particle velocities are correlated over a macroscopic distance or that regions with a higher, respectively lower transport velocity extend over a macroscopic vertical distance. Dispersivities were always derived assuming a vertically homogeneous soil profile with a constant or depth independent dispersivity. Therefore, dispersivities in this review are equivalent parameters that parameterize transport in an equivalent vertically homogeneous soil profile. How to combine this vertically homogeneous equivalent soil profile, in terms of the dispersion parameter, with vertical variations in soil biological and chemical properties requires further investigation. Since no general asymptotic regime was observed within the range of transport distances that is covered by leaching experiments in soils, dispersivities in this review cannot be extrapolated to predict transport over larger distances in deep vadose zones. Information about larger scale transport in the vadose zone is scarce and difficult to obtain because of the long travel times (e.g. Javaux and Vanclooster, 00ab). Dispersivity also scales with lateral scale of the experiment. Considering that solute dispersion is caused by spatial variations in local water velocities, that this spatial variability is predominantly caused by spatial variations in soil water fluxes, which outweigh the effect of soil water content variability, and that the soil water flux at the soil surface is rather homogeneous, the lateral scale of the representative volume is related to the distance over which water can be laterally redistributed within the soil profile. However, this lateral scaling of dispersivity and the scale over which water is laterally redistributed is related to soil texture. In finer textured soils, similar distributions of dispersivities are derived from column and field scale studies indicating that column scale studies may be representative for field scale transport. For coarser textured soils, however, lateral redistribution may take place over a larger distance so that field-scale dispersion is larger than the dispersion observed in column scale studies. Therefore, column scale studies in coarser textured soils, which are for instance

24 carried out to evaluate the risk of pesticide leaching, may not be representative for field scale dispersion and, since pesticide leaching is positively correlated with dispersion, underestimate field scale pesticide leaching. Larger scale structures such as compacted areas under wheel tracks alternated with homogenized seed beds (Coquet et al., 00ab), sand lenses (Hammel et al., 999), soil horizons with spatially variable thickness (van Wesenbeeck and Kachanoski, 99), or layers with different texture that extend over large distances (Kung, 990) may also play an important role and redistribute water over larger lateral distances. Lateral redistribution of water at the soil surface and within the soil profile on sloping terrain may lead to lateral variations in vertical infiltration or leaching. Finally, variability in plant water up take on both local and larger scale may lead to an additional variability of vertical water fluxes. Since most leaching experiments were carried out in bare soils, the effect of plants on solute spreading requires further investigation. The fact that dispersion is caused by macroscopic variations of pore water velocities has also important implications for the prediction of non-linear transport processes. Due to these macroscopic variations in pore water velocities, concentrations vary in the horizontal direction. If local processes (e.g. decay, sorption) depend in a non-linear way on the local concentrations, then it is trivial that the lateral average of the local process cannot be described by implementing the averaged concentration in the non-linear process model (e.g., Janssen et al., 00; Vanderborght et al., 00). Dispersivities seem to be larger in finer textured soils but the difference between dispersivities in fine and coarse textured soils was not found to be significant. Besides the interaction between lateral scale of the leaching experiment and soil texture, there is also an interactive effect of soil texture and flow rate on dispersivity. In finer textured soils, dispersivity increases with flow rate also for unsaturated flow conditions. In soils with a coarser texture, dispersivity distributions were not found to be different for different flow rate classes, except for the case that the soil surface was saturated.

25 7 9 0 Dispersivity distributions were better described by a lognormal than a normal distribution. The lognormal shape of the distribution in combination with a relatively large variance implies that large dispersivity values, i.e. much larger than the median value of the distribution, must be expected and considered in sensitivity studies. However, a large part of the variance of the dispersivity distribution could not be explained by the above mentioned parameters or factors. Since solute dispersion is a parameter that quantifies the effect of the water velocity variability on transport, it should be related to soil properties that entail information about this variability. In the field of stochastic continuum modelling of unsaturated flow and transport processes, dispersivity is derived or predicted from the spatial variance and spatial covariance of soil hydraulic parameters (e.g., Rubin, 00). Unfortunately, obtaining information about the spatial variability of soil hydraulic parameters is at least as elaborate as carrying out a leaching experiment. Therefore, relying on indirect information about soil heterogeneity such as soil structure and soil classification seems to be more within reach to improve the prediction of dispersivity and eventually spatialize dispersivity parameters. 7

26 7 Tables Table : Analysis of variance of log e transformed dispersivities measured in column and field scale experiments for fluxes smaller than 0 cm d -. Source DF SS MSS total model 9. error Source DF SS (Type III) Pr > F scale. 0.0 texture transport distance scale*texture scale*transport distance texture*transport distance scale*texture*transport distance DF: degrees of freedom SS: sum of squares MSS: mean sum of squares (SS DF - ). Pr > F: Probability for an F value that is larger than (SS DF - ). Bold values are significant factors at a significance level of %.

27 Figures λ (cm), travel distance (cm), or flow rate (cm d - ) 00 0 dispersivity: λ flow rate travel distance # Observations core column Figure : Number of observations (bars), mean flow rate (blue line), mean transport distance (black line), and mean dispersivity (red line) in the experiment scale classes. field 7

28 λ (cm), travel distance (cm), or flow rate (cm d - ) dispersivity: λ flow rate travel distance # Observations climatic climatic+irrigation intermittent irrigation intermittent flooding flooding steady irrigation Figure : Number of observations (bars), mean flow rate (blue line), and mean dispersivity in the flow boundary condition classes.

29 00 intermittent flooding flooding intermittent irrigation steady irrigation climatic + irrigation climatic c sic sc cl sicl scl sil silg l sl ls s sg Figure : Number of observation in different soil texture classes (c:clay, sic: silty clay, sc: sandy clay, cl: clay loam, sicl: silty clay loam, scl: sandy clay loam, sil: silt loam, silg: silt loam gravel, l: loam, sl: sandy loam, ls: loamy sand, s: sand, sg: sandy gravel) and flow boundary condition classes. 9

30 z = 0 to z = 0 cm core column field z = to z = 0 cm column field z = to z = 00 cm column field λ (cm) λ (cm) 0 7 λ (cm) Jw < cm/d < Jw < 0 cm/d Jw > 0 cm/d ponded Jw < cm/d < Jw < 0 cm/d Jw > 0 cm/d ponded Flow rate class Jw < cm/d < Jw < 0 cm/d Jw > 0 cm/d ponded 0. Jw < cm/d < Jw < 0 cm/d Jw > 0 cm/d ponded Jw < cm/d < Jw < 0 cm/d Flow rate class Jw > 0 cm/d ponded 0. Jw < cm/d < Jw < 0 cm/d Jw > 0 cm/d Jw < cm/d < Jw < 0 cm/d Flow rate class Jw > 0 cm/d ponded Figure : Effect of flow rate class and scale of the experiment on the dispersivity length for the different transport distance classes. The boxes span the % and 7% percentiles, the thick black line is the median, and the 0% and 90% percentiles correspond with the extremities of the vertical bars. The numbers above or below the boxes correspond with the number of observations in the class (Data from the same experiment in a travel distance class were averaged and treated as a single entry). 0