K. Roth

Steady State Flow in an Unsaturated, Two‐Dimensional, Macroscopically Homogeneous, Miller‐Similar Medium

The influence of microscopic heterogeneity on flow through a macroscopically homogeneous, variably saturated medium is studied by numerical simulations in a two-dimensional, Miller-similar medium. As a consequence of the local heterogeneity there appears a complex network of flow channels with interspersed islands of low-flux domains. This hydraulic structure of the medium is characterized by two states which are separated by a critical point at which the hydraulic structure practically disappears. Transitions between the states are governed by the degree of saturation. The flow channels of the two states are complementary in that high-flux regions of one state become low-flux regions of the other one, and vice versa. This variable hydraulic structure clearly has far-reaching practical and theoretical consequences for the transport of dissolved chemicals. The simulations further indicate that the autocovariance model of the microscopic heterogeneity is of minor importance for the global structure of the flow field.

Transport of conservative chemical through an unsaturated two‐dimensional Miller‐similar medium with steady state flow

Numerical simulation of water flow in a two-dimensional, macroscopically homogeneous, Miller-similar medium showed the existence of a network of flow channels with two complementary states separated by a critical point [Roth, 1995]. The consequences of this for solute transport are explored by numerical simulations using particle tracking. It is found that many experimentally observed features of transport through soil are reproduced qualitatively by these simulations. Analyzing the results reveals that in the corresponding effective medium the travel distance for the transition to convection-dispersion and the effective dispersivity depend on the water flux. In particular, the effective longitudinal dispersivity, which is often assumed to be a material constant of the porous structure, is found to vary by more than an order of magnitude with a minimum near the critical point. The simulations further demonstrate that the local structure of the velocity field and the subscale hydrodynamic dispersion are of minor importance for the field-averaged transport process.

Thermal and hydrologic dynamics of the active layer at a continuous permafrost site (Taymyr Peninsula, Siberia)

The ground thermal and hydrologic regimes of a site located in the continuous permafrost landscape of Taymyr Peninsula, northern Siberia, were studied in 1994 and 1995. The aim was to quantify the seasonal fluxes of water and heat in the active layer from spring thaw to fall freeze-back. Liquid water content was measured in frozen and unfrozen soils using time domain reflectometry. Liquid water was present in frozen soil at temperatures down to −12°C, and its volumetric fraction increased with temperature before melting occurred. The ground thermal regime during spring thaw and fall freeze-back was dominated by latent heat fluxes that stabilized soil temperatures at 0°C for extended periods. The transfer of large amounts of latent heat released by freeze-back in the fall suggested convective heat transfer mechanisms. Seasonal fluxes of heat and water were well described using a simple zero-dimensional model of water and energy balance. The dominant heat sinks during the spring and summer were sensible and latent heat fluxes into the atmosphere. During fall freeze-back the dominant heat source was phase change. The soil heterogeneity strongly impacted hydrologic and thermal processes in the active layer. Two direct consequences were the development of preferential flowpaths and the preferential freezing of the profile during freeze-back.

Approximation of asymptotic dispersivity of conservative solute in unsaturated heterogeneous media with steady state flow

The relation between the heterogeneity of hydraulic properties and effective asymptotic transport is studied for microscopically heterogeneous but macroscopically homogeneous unsaturated media with steady flow. Heterogeneity is described by the scaling of the hydraulic functions θ(Ψm) and K(θ). The study is based on an analytical approximation of asymptotic dispersivity under the assumption that matric potential is spatially constant. For the special case of a water-saturated medium the result of the stochastic continuum theory is recovered. When applied to several published numerical simulations, the approximated asymptotic dispersivities are found to agree well with the numerical values. By exploring the heterogeneous media for various hydraulic states, the approximation resolves some apparent inconsistencies found in the simulations. The cases considered span the entire range from perfect to zero correlation between scaling factors of matric potential and hydraulic conductivity. It is demonstrated that this correlation is crucial for the behavior of asymptotic dispersivity with changing flow rate. Since weak to moderate correlations are often found in soils, this result has significant implications for solute transport through heterogeneous soils.

Time domain reflectometry as a field method for measuring water content and soil water electrical conductivity at a continuous permafrost site

Time domain reflectometry (TDR) is evaluated as a field technique for measuring volumetric water content θ and bulk electrical conductivity σb in Arctic soils. Calibration measurements of θ and σb were carried out on three different slopes at a field site in Siberia (74°32′N; 98°35′E). Comparison of θ calculated from TDR using two different approaches and gravimetrically determined water contents shows a close correlation. TDR determined σb, applying theoretical relationships and a simple regression model, are compared with the electrical conductivity σw of soil solutions obtained with suction cups. Best results for σw are obtained using the regression model, with highest precision when probe specific calibration is carried out. In this permafrost setting, TDR can be applied to obtain quantitative estimates of θ and σw in the active layer. The application of the regression model in different permafrost soils to infer σw requires additional calibration.