Convective Lognormal Transfer Function Model Research Articles

Indirect estimation of the Convective Lognormal Transfer function model parameters for describing solute transport in unsaturated and undisturbed soil

Solute transport in partially saturated soils is largely affected by fluid velocity distribution and pore size distribution within the solute transport domain. Hence, it is possible to describe the solute transport process in terms of the pore size distribution of the soil, and indirectly in terms of the soil hydraulic properties. In this paper, we present a conceptual approach that allows predicting the parameters of the Convective Lognormal Transfer model from knowledge of soil moisture and the Soil Moisture Characteristic (SMC), parameterized by means of the closed-form model of Kosugi (1996). It is assumed that in partially saturated conditions, the air filled pore volume act as an inert solid phase, allowing the use of the Arya et al. (1999) pragmatic approach to estimate solute travel time statistics from the saturation degree and SMC parameters. The approach is evaluated using a set of partially saturated transport experiments as presented by Mohammadi and Vanclooster (2011). Experimental results showed that the mean solute travel time, μt, increases proportionally with the depth (travel distance) and decreases with flow rate. The variance of solute travel time σ2t first decreases with flow rate up to 0.4–0.6Ks and subsequently increases. For all tested BTCs predicted solute transport with μt estimated from the conceptual model performed much better as compared to predictions with μt and σ2t estimated from calibration of solute transport at shallow soil depths. The use of μt estimated from the conceptual model therefore increases the robustness of the CLT model in predicting solute transport in heterogeneous soils at larger depths. In view of the fact that reasonable indirect estimates of the SMC can be made from basic soil properties using pedotransfer functions, the presented approach may be useful for predicting solute transport at field or watershed scales.

Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column

This study compared five different models for evaluating solute transport in a 1250-cm long, saturated and highly heterogeneous soil column. The five models were: the convection-dispersion equation (CDE), the mobile-immobile model (MIM), the convective lognormal transfer function model (CLT), the spatial fractional advection-dispersion equation (FADE) and the continuous time random walk model (CTRW). Each of these models was used to fit the breakthrough curve (BTC) at each distance individually and was also used to fit the BTCs at different distances simultaneously. Dependence of estimated parameters on distance was investigated. The estimated parameters at 200 cm were used to make predictions at subsequent distances. Highly anomalous transport behavior was observed in the column as the BTCs demonstrated significantly irregular shape and long tailing. This study indicated that CDE, CLT and FADE were unable to describe the anomalous BTCs adequately and their parameters changed with transport distance significantly. Compared to CDE, CLT and FADE, MIM better captured the evolution of anomalous BTCs. However, MIM did not explain the distinct BTC tailing satisfactorily. In contrast to MIM, CTRW better simulated the long tails of BTCs. The spreading parameter (beta) of CTRW was close to one and remained approximately constant at different travel distances. To make the comparison of these five models more general beyond the specific transport condition in the soil column, a generic evaluation of the advantages and disadvantages of these five models was presented in terms of their theory framework and a priori knowledge of the model behaviors. (C) 2009 Elsevier B.V. All rights reserved.

Transect Scale Solute Transport Measured by Time Domain Reflectometry

Two quasi steady-state solute transport experiments were carried out in a loamy sand under field conditions. The flux was 40 mm/d in experiment 1 and 18.7 mm/d in experiment 2. Both water content (θ) and resident concentration (Cr) measurements were taken using 64 time domain reflectometry probes at depths ranging from 0.05 to 0.90 m. The Cr measurement was calibrated in situ for each probe location in the field. The convective dispersive equation (CDE) and convective lognormal transfer function (CLT) models were fitted to the breakthrough curves (BTCs). The results indicated fingered flow, which has been shown to exist in previous studies of this soil. The finger width was larger in experiment 1 leading to smaller horizontal heterogeneity and a relatively smaller solute transport velocity. The location of the fingers was consistent between the two experiments resulting in a high correlation between the velocity and mass balance fields. Mass balance calculations showed that the solute mass integrated over depth one day after the solute application was larger than the mass balance for the entire experiment (integrated over time). The probable reason being that solutes were transported out of the measurement volume by horizontal flow across the Ap/E horizon boundary. The investigation of the transport parameters revealed that both the CDE and CLT models could be successfully used to predict most individual BTCs. Horizontally averaged global CDE and CLT models were also fitted to the data. Global solute transport was better modeled with the CDE model in experiment 1, while in experiment 2, the CLT model was better. This study clearly shows the applicability of using TDR with the in situ calibration technique in field experiments with varying water content.

Generalized Transfer Function Model for Solute Transport in Heterogeneous Soils

The convection‐dispersion (CDE) equation and stochastic–convective models are the most commonly used process representations for predicting solute transport in the field. The convection–dispersion equation assumes that the solute is perfectly mixing in the lateral direction, whereas the stochastic–convective model assumes that the solute moves at different velocities in isolated stream tubes without lateral mixing. However, solute transport in heterogeneous porous media cannot always be conceptualized as being either a convective–dispersive or a stochastic–convective process. In this study, a generalized transfer function model (GTF) was proposed to describe various solute transport processes in heterogenous soils. The model is similar to the convective lognormal transfer function model, but two parameters, λμ and λσ, are introduced to characterize the depth‐dependency of the mean (μ) and standard deviation (σ) of the logarithm of travel time, respectively. The GTF can describe well the two extremes of solute dispersion, the convective–dispersive and stochastic–convective processes, and transport processes between the two extremes. In addition, the GTF can be used to characterize other solute transport processes in heterogeneous soils, such as those in which the mean of travel time increases with depth nonlinearly, and those in which the dispersivity is a scale‐dependent function of the travel distance with any power values.

COMPARISON OF FLUX AND RESIDENT CONCENTRATIONS IN MACROPOROUS FIELD SOILS

In many solute transport studies, either the flux or the resident concentration is used. In some cases, however, the transport parameters obtained from different concentration modes may not be identical, especially for soils having preferential pathways. In this study we investigated differences in the transport parameters between flux and resident concentrations by performing laboratory solute displacement experiments on a number of structured field soils. Breakthrough curves (BTCs) of flux and resident concentrations for a pulse injection of 10 g/L CaCl2 solution were monitored simultaneously at the bottom and middle of soil columns using an EC-meter and time domain reflectometry (TDR) probes, respectively. Transport parameters were then obtained by fitting the convective lognormal transfer function (CLT) model to the observed BTC data and compared for different concentration modes. Flux concentrations predicted from the parameters of resident concentrations based on the CLT model were also compared with the observed BTC data. Comparison of transport parameters between the flux and resident concentrations showed substantial differences caused by preferential movement of solute through soil macropores. The predicted flux concentration BTCs also differed greatly from the observed BTCs in peak and travel time. This suggests that for structured soils having preferential flow, the TDR-measured resident concentrations are not representative of solute transport in the soil macropores but are primarily in the soil matrix region, and use of TDR for monitoring resident concentrations in such soils becomes limited.

Time Domain Reflectometry Measurements of Solute Transport across a Soil Layer Boundary

The mechanisms governing solute transport through layered soil are not fully understood. Solute transport at, above, and beyond the interface between two soil layers during quasi‐steady‐state soil water movement was investigated using time domain reflectometry (TDR). A 0.26‐m sandy loam layer was packed on top of a 1.35‐m fine sand layer in a soil column (0.15‐m i.d.). Soil water content (θ) and bulk soil electrical conductivity (ECb) were measured by 50 horizontal and 2 vertical TDR probes. A new TDR calibration method that gives a detailed relationship between apparent relative dielectric permittivity (Ka) and θ was applied. Two replicate solute transport experiments were conducted adding a conservative tracer (KCl) to the surface as a short pulse. The convective lognormal transfer function model (CLT) was fitted to the TDR‐measured time integral–normalized resident concentration breakthrough curves (BTCs). The BTCs and the average solute‐transport velocities showed preferential flow occurred across the layer boundary. A nonlinear decrease in TDR‐measured θ in the upper soil toward the soil layer boundary suggests the existence of a 0.10‐m zone where water is confined towards fingered flow, creating lateral variations in the area‐averaged water flux above the layer boundary. A comparison of the time integral–normalized flux concentration measured by vertical and horizontal TDR probes at the layer boundary also indicates a nonuniform solute transport. The solute dispersivity remained constant in the upper soil layer, but increased nonlinearly (and further down, linearly) with depth in the lower layer, implying convective‐dispersive solute transport in the upper soil, a transition zone just below the boundary, and stochastic–convective solute transport in the remaining part of the lower soil.

Modelling of solute transport in a large undisturbed lysimeter, during steady-state water flux

Transport models have often been tested in laboratory studies using soil columns, usually of the order of 1dm3 in size. Even if the columns are undisturbed, their small size does not allow water flow and solute transport to occur as they would in the field. We therefore used a 1.7m3 column and applied steady-state flow rates of the order of 1mmh−1, and then applied pluses of tracers Br−, Cl− and 2H2O, and of atrazine (2-chloro-4-ethylamino-6-isopropylamino-S-triazine) to the surface.Classical models for tracers with these boundary conditions are the Convection–Dispersion model (CD), the two-region (mobile–immobile water) model with first-order exchange of solutes (MIM), and the transfer function models, among which the most widely used is the Convective Lognormal Transfer Function model (CLT). Thanks to simple boundary and initial conditions, analytical solutions are available for all these models.The CD model (1 parameter) was not able to fit the tracer elution curves, but use of the MIM model was satisfactory. The CLT model and the CD model (2 parameters) also gave satisfactory fits. To choose the best model we used the parameters fitted to the elution curves to predict vertical concentration profiles in the lysimeter. These predictions are compared to the profile obtained after thorough sampling of the soil when tracers reached about half way down the lysimeter. The MIM model yielded a better prediction. However, accurate predictions would require taking into account the highly stratified characteristics of this soil.Atrazine simulation was done with the CD-based one-site kinetic sorption and first-order decay equation. Again analytical solutions are provided for our experimental conditions. Values of decay and absorption parameters are in agreement with previous studies.

Determining Convective Lognormal Solute Transport Parameters from Resident Concentration Data

AbstractTime Domain Reflectometry (TDR) has become a popular method to obtain time series of resident concentrations in solute transport studies, so effective interpretation of TDR data is very useful. In this study, we evaluated three procedures to determine the parameters of the convective lognormal transfer function (CLT) model from such time series. In a first approach, the CLT model travel time probability density function (pdf) was related to time series of time‐integral‐normalized flux concentrations, Cf*(z,t). The normalization was based on mass balance calculations performed with time series of resident concentrations measured at several depths. The Cf*(z,t) data thus obtained were very erratic leading to a high parameter uncertainty. In a second approach, the CLT model travel depth pdf was related to time series of depth‐integral‐ or mass‐normalized resident concentrations, Crm*(z,t). This approach suffered from uncertainty regarding calibration coefficients relating TDR measured impedance to resident concentrations and from uncertainty regarding the solute mass crossing the sampling volume of the TDR probe. The third approach used the relation between travel time and travel depth pdf for a stochastic‐convective transport process to formulate a new expression relating time‐integral‐normalized resident concentrations, Crt*(z,t), to the CLT model parameters. No information is needed about calibration coefficients while no a priori assumptions about the solute mass detected by the TDR probe are required. This approach yielded better CLT model fits to observed concentration data, and the variability of parameters fitted at different locations can be related to heterogeneity of solute and water flow after averaging across the TDR measurement window.

Uncertainties in Leaching Risk Assessments Due to Field Averaged Transfer Function Parameters

The transfer function model is widely used to estimate solute transport patterns at the field scale. Leaching risk assessments with the transfer function model may be influenced by spatial variability in the net applied water (NAW) distribution, but few researchers have investigated this possibility. The objective of this study was to evaluate the impact of spatial variability in the NAW distribution on leaching risk assessment and identification of leaching risk categories at the field scale. Bromide concentration profiles, irrigation depths, bulk densities, and soil moisture contents were measured in 40 plots across a 57-ha potato (Solanum tuberosum L.) farm, along with field-scale evapotranspiration estimates, to estimate solute transport parameters. Values for field- and plot-scale means and standard deviations for the NAW distribution were estimated using the stochastic convective lognormal transfer function (CLT) model. The probability of NO 3 - leaching below a depth of 2 m was then estimated using field-averaged versus plot-scale estimates for the mean and standard deviation of the NAW distribution. For 30-cm NAW, NO 3 - leaching risks estimated with the CLT model and plot-scale means and standard deviations were very high in 0.4 ha of the field, high in 1.8 ha, moderate in 8.7 ha, low in 23.0 ha, and none in 23.1 ha. In contrast, when field-scale average estimates of NAW were used, there was a low risk of NO 3 - leaching for the entire field. Thus, when estimating leaching risks using the CLT, information about spatial variability of the NAW distribution is important.

Solute Transport in Unsaturated Soil: Experimental Design, Parameter Estimation, and Model Discrimination

The objectives of this study were to: (i) examine the efficacy of two sampling techniques for characterizing solute transport under steady-state water flow, (ii) study the variation in transport model parameters with increasing depth of solute leaching, and (iii) perform model discrimination to examine the transport process operative within a field plot. Bromide, NO?, and Cl- were applied sequentially to a plot instrumented with two sets of 12 solution samplers located at depths of 0.25 and 0.65 m. At the conclusion of the experiment we destructively sampled the entire 2.0 by 2.0 m plot to a depth of 2.0 m. Mass recovery by the solution samplers ranged from 63 to 83% for the three tracers, and recovery by soil excavation ranged from 96 to 105%. The mean solute velocity estimated with the solution sampler data was significantly less than that determined by soil excavation. Mean solute velocity determined from soil excavation implied an effective transport volume equal to 0.828, (where 8, is volumetric water content) for the three tracers. Solution samplers and soil excavation provided similar measures of vertical dispersion. Both sampling methods revealed a scale-dependent dispersion process in which the dispersivity increased linearly with mean residence time. The depth profiles for all three solutes were accurately described with a stochastic convective lognormal transfer function model (CLT) using the applied mass and two constant parameters (estimated from simultaneous fitting to the depth profiles).

Comparison of transfer function and deterministic modeling of area‐averaged solute transport in a heterogeneous field

The predictions of two one‐dimensional solute transport models describing area‐averaged mean field concentrations under steady state water flow conditions were tested through numerical experiments. The two models are based on different solute dispersion process hypotheses, namely, the stochastic‐convective process of the convective lognormal transfer function model and the advective‐dispersive process of the advection‐dispersion equation model. Two hypothetical random fields having different correlation structures for their hydraulic and retention properties were generated through a random scaling factor δ. The numerical experiments were conducted by running solute transport simulations in these hypothetical fields, and the simulation results were used to calibrate the two process models. The simulation results demonstrated that even under steady state, one‐dimensional water flow in the medium having a short correlation length scale, considerable local variations in solute concentration were still present in the simulation results. The observed dispersion in the mean field data was intermediate between the representations in the two extreme process hypotheses of the two models tested, and neither model was accurate over the entire range of testing. Predictions of the asymptotic dispersivity based on the analysis used in saturated flow were not valid under unsaturated conditions. Complete knowledge of the velocity field was required in the latter case to predict the asymptotic dispersivity.