A Fractal Approach to Model Soil Structure and to Calculate Thermal Conductivity of Soils

Heat transport in soils depends on the spatial arrangement of solids, ice, air and water. In this study, we present a modified fractal approach to model the pore structure of soils and to describe its influence on the thermal conductivity. Three different fractal generators were sequentially applied to characterize a wide range of particle- and pore-size distributions. The given porosity and particle-size distribution of a clay, clay loam, silt loam and loamy sand were successfully modeled. The thermal conductivity of the fractal soil model was calculated using a network of resistors. We applied a renormalization approach to include the effects of smaller scale structures. The predictions were compared with the empirical Johansen' model (Johansen, 1975), that postulates a simple linear relationship between ice content and thermal conductivity. For high ice-saturated conditions, the calculated thermal conductivity agrees well with the empirical model. To describe partial ice saturation, we assumed that some pores were coated by ice films enclosing the air-filled center. In addition, we introduced a reduced heat exchange coefficient of the particles for unsaturated conditions. The ice-saturated and -unsaturated thermal conductivity calculated with this approach was very similar to that estimated by the empirical model. The variation of the thermal conductivities for different spatial arrangements of pores and particles in the prefractals were determined. Extreme values deviate more than 50% from the mean value

Comparative predictions of discharge from an artificial catchment (Chicken Creek) using sparse data

Ten conceptually different models in predicting discharge from the artificial Chicken Creek catchment in North-East Germany were used for this study. Soil texture and topography data were given to the modellers, but discharge data was withheld. We compare the predictions with the measurements from the 6 ha catchment and discuss the conceptualization and parameterization of the models. The predictions vary in a wide range, e.g. with the predicted actual evapotranspiration ranging from 88 to 579 mm/y and the discharge from 19 to 346 mm/y. The predicted components of the hydrological cycle deviated systematically from the observations, which were not known to the modellers. Discharge was mainly predicted as subsurface discharge with little direct runoff. In reality, surface runoff was a major flow component despite the fairly coarse soil texture. The actual evapotranspiration (AET) and the ratio between actual and potential ET was systematically overestimated by nine of the ten models. None of the model simulations came even close to the observed water balance for the entire 3-year study period. The comparison indicates that the personal judgement of the modellers was a major source of the differences between the model results. The most important parameters to be presumed were the soil parameters and the initial soil-water content while plant parameterization had, in this particular case of sparse vegetation, only a minor influence on the results

Water flow between soil aggregates

Aggregated soils are structured systems susceptible to non-uniform flow. The hydraulic properties depend on the aggregate fabric and the way the aggregates are assembled. We examined the hydraulic behavior of an aggregate packing. We focused on conditions when water mostly flows through the aggregates, leaving the inter-aggregate pore space air-filled. The aggregates were packed in 3mm thick slabs forming a quasi two-dimensional bedding. The larger aggregates were wetted with water and embedded in smaller aggregates equilibrated at a lower water content. The water exchange between wet and drier aggregates was monitored by neutron radiography. The three-dimensional arrangement of the aggregates was reconstructed by neutron tomography. The water flow turned out to be controlled by the contacts between aggregates, bottle-necks that slow down the flow. The bottle-neck effect is due to the narrow flow cross section of the contacts. The water exchange was simulated by considering the contact area between aggregates as the key parameter. In order to match the observed water flow, the contact area must be reduced by one to two orders of magnitude relative to that obtained from image analysis. The narrowness of the contacts is due to air-filled voids within the contact

Water flow between soil aggregates

Aggregated soils are structured systems susceptible to non-uniform flow. The hydraulic properties depend on the aggregate fabric and the way the aggregates are assembled. We examined the hydraulic behavior of an aggregate packing. We focused on conditions when water mostly flows through the aggregates, leaving the inter-aggregate pore space air-filled. The aggregates were packed in 3mm thick slabs forming a quasi two-dimensional bedding. The larger aggregates were wetted with water and embedded in smaller aggregates equilibrated at a lower water content. The water exchange between wet and drier aggregates was monitored by neutron radiography. The three-dimensional arrangement of the aggregates was reconstructed by neutron tomography. The water flow turned out to be controlled by the contacts between aggregates, bottle-necks that slow down the flow. The bottle-neck effect is due to the narrow flow cross section of the contacts. The water exchange was simulated by considering the contact area between aggregates as the key parameter. In order to match the observed water flow, the contact area must be reduced by one to two orders of magnitude relative to that obtained from image analysis. The narrowness of the contacts is due to air-filled voids within the contact

Flux and resident injection in gaseous advection experiments

The occurrence of gaseous pollutants in soils has stimulated many experimental activities, including forced ventilation in the field as well as laboratory transport experiments with gases. The dispersion coefficient in advective-dispersive gas phase transport is often dominated by molecular diffusion, which leads to a large overall dispersivity gamma. Under such conditions it is important to distinguish between flux and resident modes of solute injection and detection. The influence of the inlet type oil the macroscopic injection mode was tested in two series of column experiments with gases at different mean flow velocities nu. First we compared infinite resident and flux injections, and second, semi-infinite resident and flux injections. It is shown that the macroscopically apparent injection condition depends on the geometry of the inlet section. A reduction of the cross-sectional area of the inlet relative to that of the column is very effective in excluding the diffusive solute input, thus allowing us to use the solutions for a flux Injection also at rather low mean flow velocities nu. If the whole cross section of a column is exposed to a large reservoir like that of ambient air, a semi-infinite resident injection is established, which can be distinguished from a flux injection even at relatively high velocities nu, depending on the mechanical dispersivity of the porous medium

Modelling the effect of particle size, shape and orientation of light transfer through porous media

In this study, we present a radiative-transfer model to simulate reflectance and transmittance of light by soil slabs. The radiative-transfer model implemented, referred to as the beam-tracing model, uses cross-sectional images of scattering media to describe the geometry of the soil, i.e. soil texture and structure. This model traces the optical path of incident beams through such cross-sectional images. Tracing many light beams simulates the reflected and transmitted light intensities for the media. The accuracy of the beam-tracing model was tested by comparing its predictions with those of analytical solutions and with experimentally measured reflectance and transmittance data of soil samples. We implemented this model to explain the systematic deviation between measured data and those calculated with the four-flux model applied in Banninger (2004). With the beam-tracing model, we show that the small systematic inaccuracies of the four-flux model are caused by the simplified description of the geometry of the scattering medium. The beam-tracing model can be used to describe various optical properties of particulate media. As an application, we calculated the decrease of light intensity with depth