The solute concentrations measured in the field experiment of G. L. Butters et al. (this issue) are used to compare two models of vadose zone solute transport: the deterministic one-dimensional convection-dispersion model, which represents solute transport far from the source of solute entry, and the stochastic-convective lognormal transfer function model, which represents solute transport near the source. The stochastic-convective model provided an excellent representation of the spreading of the solute pulse to a depth of 3 m after calibration at 0.3 m. Conversely, the deterministic model dramatically underpredicted solute spreading beyond 0.3 m after calibration. An analysis of the area-averaged solute concentration revealed a nearly linear scale effect in the dispersivity to a depth of at least 14.8 m. A change in the growth pattern of dispersion observed in the breakthrough curve at 4.5 m was attributed to a soil texture change near 3 m, which caused the apparent dispersivity of the pulse to decrease between 3.0 and 4.5 m, after which it increased significantly between 4.5 m and the final profile sampling between 0 and 25 m.

Modeling the field scale movement of chemicals in unsaturated soil is of intense interest to both the public and private sectors and has become an area of active theoretical research in a number of environmentally based disciplines. However, the experimental data needed to validate existing solute transport models and to inspire the development of more refined approaches is very limited. In this research study, the movement of a mobile tracer (Br-) was monitored as it moved through the unsaturated zone beneath the soil surface of a 0.64 ha loamy sand field. Under flux-controlled, steady state water flow achieved by bidally sprinkler irrigation, a narrow pulse of 58.9 mol/m -3 NaBr(aq) was applied uniformly to the field and subsequently leached downward while monitored by vacuum solution samplers replicated 16 times at each of 6 depths between 0.3 and 3.0 m and 6 times at the 4.5 m depth. Six deep soil cores to a maximum of 25 m were taken to characterize the final field average bromide depth profile after the pulse had passed the 4.5-m depth. Although the mass recovery of the area-averaged pulse was near 100% at all depths, the coefficient of variation (CV) of mass recovery between samplers at a given depth was near 50%. Lateral variations in apparent vertical solute velocity or in solute transport volume were considerable, with CVs near 50% in the shallow monitoring depths. However, variations in transport volume with depth at a given site were also large, even though the solution samplers for different depths were displaced laterally by only 0.3-0.6 m at different sites. The mean vertical velocity of the area-averaged solute pulse was significantly less than the ratio of the average net water flux to the average volumetric water content, until approximately 1.8 m. The difference between the two average velocities near the surface was large enough (nearly a factor of 2) to suggest that transient effects from the bidaily irrigations were influencing solute transport. Sci., 27, 460-466, 1976. Yeh, T. C. J., Comment on "Modeling of scale-dependent dispersion in hydrogeologic systems," by J. F. Pickens and G. E. Grisak, Water Resour. Res., 23,522, 1987.

[1] Laboratory assays of methanotroph activity in upland (i.e., well-drained, oxic) ecosystems alter soil physical structure and weaken inference about environmental controls of their natural behavior. To overcome these limitations, we developed a chamber-based approach to quantify methanotroph activity in situ on the basis of measures of soil diffusivity (from additions of an inert tracer gas to the chamber headspace), methane concentration change, and analysis of results with a reaction-diffusion model. The analytic solution to this model predicts that methane consumption rates are equally sensitive to changes in methanotroph activity and diffusivity, but that doubling either of these parameters leads to only a p 2 increase in consumption. With a series of simulations, we generate guidelines for field deployments and show that the approach is robust to plausible departures from assumptions. We applied the approach on a dry grassland in north central Colorado. Our model closely fit measured changes in methane concentrations, indicating that we had accurately characterized the biophysical processes underlying methane uptake. Field patterns showed that, over a 7-week period, soil moisture fell from 38% to 15% water-filled pore spaces, and diffusivity doubled as the larger soil pores drained of water. However, methane uptake rates fell by $40%, following a 90% decrease in methanotroph activity, suggesting that the decline in methanotroph activity resulted from water stress to methanotrophs. We anticipate that future application of this approach over longer timescales and on more diverse field sites has potential to provide important insights into the ecology of methanotrophs in upland soils.

Most of the existing data on vadose zone field scale solute transport have been obtained from experiments conducted under transient, nonmonotonic water flow. However, the majority of the theoretical analyses of these experiments have used models which assume monotonic steady state water flow and uniform water content for the entire profile. In this study, transport of nonreactive solutes under nonmonotonic, transient water flow is analyzed numerically. The effect of hysteresis on solute transport is evaluated by making the soil hydraulic properties hysteretic using the procedure of Kool and Parker (1987). The effect of profile heterogeneity on solute transport is analyzed by assuming that the medium is scale heterogeneous in a vertical direction, with a random scale factor. Results of the simulations show that under transient water flow, analysis of solute transport data with a steady state water flow model may considerably overestimate the effective vertical pore water velocity. Under nonmonotonic water flow, when the hysteretic characteristics of the soil are important, transient flow models which neglect hysteresis can also seriously overestimate the solute velocity. In addition, failure to account for profile heterogeneity will also overestimate the solute velocity, because both hysteresis and profile heterogeneity change the water content profile and concurrently retard solute transport relative to the movement predicted if the soil water system is considered as homogeneous and nonhysteretic. Analyses of the computed breakthrough curves suggest that direct estimates of the amount of water drained below a given depth may improve the goodness of fit of the solution of the convection dispersion equation with constant effective parameters to the breakthrough curves obtained under transient conditions. The fitted parameters, however, are depth dependent and the resulting effective solute velocity is smaller than the steady state pore water velocity. Wierenga, P. J., Solute distribution profiles computed with steadystate and transient water movement models, Soil Sci. Soc. Am. J., 41, 1050-1055, 1977. Wild, A., and I. A. Babiker, The asymmetric leaching pattern of NO 3 and C1 in a loamy sand under field conditions, Soil $ci., 27, 460-466, 1976.

An inverse problem for the identification of an unknown coefficient in a quasilinear parabolic partial differential equation is considered. We present an approach based on utilizing adjoint versions of the direct problem in order to derive equations explicitly relating changes in inputs (coefficients) to changes in outputs (measured data). Using these equations it is possible to show that the coefficient to data mappings are continuous, strictly monotone and injective. The equations are further exploited to construct an approximate solution to the inverse problem and to analyze the error in the approximation. Finally, results of some numerical experiments are displayed.