Field Scale Vertical Transport from Horizontally Variable Local Scale Transport Parameters

Abstract

In field soils, transport properties vary vertically and horizontally. With experimental measurements it is distinctly easier to consider the vertical than the horizontal variability. We present a simple approach for considering the horizontal variability of the transport behavior of the soil in a one-dimensional transport model. The model approach assumes independence on dept h of the vertical dispersion coefficient, which is justified by the relatively small effects of the vertical dispersion in comparison to those of the horizontal dispersion only. The approach is based on numerical experiments using different parameter statistics. An analytical expression of the dependence of effective parameters, describing the transport at the field scale, on the statistical lognormal distributions of transport parameters at the local scale is derived heuristically by careful inspection of the numerical experimental results. The model was tested in (1) a reevaluation of a one-dimensional field experiment with chloride tracer in a heavy loam soil of Roth (1989), and (2) a two-dimensional leaching field experiment with the same tracer in a sandy soil plot of 5600 m 2. For both experiments the model using lognormal • local parameter distributions provides a satisfactory representation of field averages of the vertical transport derived from local measurements. IntrOduction In the past few years, some "real" field scale experiments on tracer transport in heterogeneous soils have been done [Butters et al., 1989a, b; Ellsworth et al., 1991; Roth et al., 1991]. Their results call for a concise model description. Deterministic modeling of tracer transport in real Soils necessitates considering the vertical as well as the horizontal variability of transport parameters as well as of upper boundary fluxes. To obtain the transport parameter fields with a field scale three-dimensional approach, we have to solve the inverse problem using threedimensional fields of measured water content and tracer concentrations at different times. Such solutions will be rather difficult or even intractable in the event of limited information about the changing tracer fields. Usually, we are interested in the vertical transport component only. The vertical heterogeneity of transport parameters may be considered by assuming layers Or parameters changing continuously with depth (see, for example, Cvetcovic and Shapiro [1989], Leij et al. [1991], and Destouni [1992]). Depending On the type of soil [Shepard, 1993; Vereecken et al., 1992] or mechanistic model considered, vertical dispersion is neither constant [Tseng and Jury, 1994] nor usually strongly changing with depth for more homogeneous soils. For the case of refilling an emptied soil in fall in temperate climates, we try to neglect the intermediate hysteresis-affected redistributions between different precipitation events and regard, for the sake of

Ion transport through unsaturated soils: field experiments and regional simulations

“…These expressions presume that both parameters are lognormally distributed and uncorrelated. Salzmann (1993) could describe the field‐scale concentration profile well, at least for this experiment and for a field breakthrough curve determined by Roth (1989) using the effective parameter approach (Salzmann & Richter, 1995).…”

“…To describe the one‐dimensional transport of a non‐interacting solute in homogeneous soil, Salzmann & Richter (1995) have used…”

“…The local transport parameters v loc and D loc in were obtained using the common equations with q 0 , θ and λ on the assumption that v loc and D loc are linearly related (e.g. Schulin et al ., 1987; Salzmann & Richter, 1995).…”

“…There are several approaches to describe the transport of non‐sorbing solutes at field scale: the convection–dispersion equation (CDE) with effective transport parameters (e.g. Salzmann & Richter, 1995), stochastic stream‐tube models (e.g. Dagan & Bresler, 1979) or distributed models (Russo, 1984; Beven, 1993).…”

“…(1999) derived effective parameters of the CDE using block means and within‐block variances from kriging. They obtained local transport parameters from results of experiments as described below, calculated and modelled their variograms, estimated them and their variances using block kriging, and derived the effective transport parameters v eff and D eff using the expressions of Salzmann & Richter (1995).…”