R. G. Hills

The Las Cruces Trench Site: Characterization, Experimental Results, and One‐Dimensional Flow Predictions

A comprehensive field trench study was conducted in a semiarid area of southern New Mexico to provide data to test deterministic and stochastic models of vadose zone flow and transport. A 4 m by 9 m area was irrigated with water containing a tracer using a carefully controlled drip irrigation system. The area was heavily instrumented with tensiometers and neutron probe access tubes to monitor water movement and with suction tubes to monitor solute transport. Approximately 600 disturbed and 600 core samples of soil were taken to support deterministic and stochastic characterization of the soil water hydraulic parameters. The core sample-based saturated hydraulic conductivities ranged from 1.4 to 6731 cm/d with a mean of 533 cm/d and a standard deviation of 647 cm/d, indicating significant spatial variability. However, visual observation of the wetting front on the trench wall shows no indication of preferential flow or water flow through visible root channels and cracks. The tensiometer readings and the neutron probe measurements also suggest that the wetting front moves in a fairly homogeneous fashion despite the significant spatial variability of the saturated hydraulic conductivity. In addition to the description of the experiment and the presentation of the experimental results, predictions of simple one-dimensional uniform and layered soil deterministic models for infiltration are presented and compared to field observations. These models are presented here to provide a base case against which more sophisticated deterministic and stochastic models can be compared in the future. The results indicate that the simple models give adequate predictions of the overall movement of the wetting front through the soil during infiltration. However, the models give poor predictions of point values for water content due to the spatial variability of the soil. Comparisons between the one-dimensional infiltration model predictions and field observations show that the use of the layered soil model rather than the uniform soil model does not consistently improve the accuracy of the predictions for this particular field application. This result illustrates that increasing the spatial resolution of the deterministic characterization of the site in the vertical direction does not always improve the model predictions. Uncertainties due to horizontal spatial variability and due to other difficulties associated with experimental characterization appear to be more significant.

Solute transport through large uniform and layered soil columns

Solute transport experiments are often conducted with homogeneous soils, whereas transport in real situations takes place in heterogeneous soils. An experiment was conducted to compare unsaturated solute transport through uniform and layered soils. Pulse inputs of tritiated water, bromide and chloride were applied under steady flow conditions to the tops of two large (0.95 m diameter by 6 m deep) soil columns. One column was uniformly filled with loamy fine sand and the other filled with alternating 20-cm-thick layers of loamy fine sand and silty clay loam. Soil solution samples were collected during the experiment with suction candles installed at various depths in the columns. Solute transport parameters were estimated by fitting the convection-dispersion equation to the observed breakthrough curves for each solute at various depths in each column. The match between the resulting calibrated curves and the experiment was better for the layered soil column than for the uniform soil column. The results displayed no clear relationship between the dispersion coefficients and depth for any of the tracers for either column. However, dispersivities were greater in the uniform column (3.5 cm) than in the layered column (1.2 cm), while retardation factors for bromide and chloride were similar (0.8 and 0.83, respectively, for the uniform and layered columns). A retardation factor less than one is attributed to anion exclusion. There was evidence of preferential flow in the uniform soil column. The peak concentrations at 5 m depth were greater than those observed at 4 m. Such behavior is inconsistent with one-dimensional flow. Similar results were observed in an experiment performed 3.5 years earlier using the same soil column and approximately the same flow rates, but using a different tracer and associated chemical analysis, different soil saturation prior to the execution of the experiment, and different experimental personnel. This supports the thesis that the anomalous behavior is due to some form of preferential flow rather than due to experimental error.

The Second Las Cruces Trench Experiment: Experimental Results and Two-Dimensional Flow Predictions

As part of a comprehensive field study designed to provide data to test stochastic and deterministic models of water flow and contaminant transport in the vadose zone, several trench experiments were performed in the semiarid region of southern New Mexico. The first trench experiment is discussed by Wierenga et al. (this issue). During the second trench experiment, a 1.2 m wide by 12 m long area on the north side of and parallel to a 26.4 m long by 4.8 m wide by 6m deep trench was irrigated with water containing tracers using a carefully controlled drip irrigation system. The irrigated area was heavily instrumented with tensiometers and neutron probe access tubes to monitor water movement, and with suction samplers to monitor solute transport. Water containing tritium and bromide was. applied during the first 11.5 days of the study. Thereafter, water was applied without tracers for an additional 64 days. Both water movement and tracer movement were monitored in the subsoil during infiltration and redistribution. The experimental results indicate that water and bromide moved fairly uniformly during infiltration and the bromide moved ahead of the tritium due to anion exclusion during redistribution. Comparisons between measurements and predictions made with a two-dimensional model show qualitative agreement for two of the three water content measurement planes. Model predictions of tritium and bromide transport were not as satisfactory. Measurements of both tritium and bromide show localized areas of high relative concentrations and a large downward motion of bromide relative to tritium during redistribution. While the simple deterministic model does show larger downward motions for bromide than for tritium during redistribution, it does not predict the high concentrations of solute observed during infiltration, nor can it predict the heterogeneous behavior observed for tritium during infiltration and for bromide during redistribution.

Application of Similar Media Scaling and Conditional Simulation for Modeling Water Flow and Tritium Transport at the Las Cruces Trench Site

Similar media scaling and geostatistical analyses are used to characterize the spatial variability of soil hydraulic properties at the Las Cruces Trench Site in New Mexico. A simple method is described for conditioning the hydraulic properties used for unsaturated water flow and solute transport modeling, based on the spatial distributions of initial field-measured water contents and a set of scale-mean hydraulic parameters determined from the scaling analysis. This method is used to estimate hydraulic properties for numerical simulations of the latest field-scale flow and transport experiment conducted at the Las Cruces Trench Site. Relatively good matches between the observed and simulated flow and transport behavior are obtained without model calibration. The results of this study suggest that using similar media scaling in conjunction with the described conditioning procedure can significantly reduce the uncertainty in predictions of water flow and solute transport in spatially variable soils.

Statistical Validation of Engineering and Scientific Models: Validation Experiments to Application

Several major issues associated with model validation are addressed here. First, we extend the application-based, model validation metric presented in Hills and Trucano (2001) to the Maximum Likelihood approach introduced in Hills and Trucano (2002). This method allows us to use the target application of the code to weigh the measurements made from a validation experiment so that those measurements that are most important for the application are more heavily weighted. Secondly, we further develop the linkage between suites of validation experiments and the target application so that we can (1) provide some measure of coverage of the target application and, (2) evaluate the effect of uncertainty in the measurements and model parameters on application level validation. We provide several examples of this approach based on steady and transient heat conduction, and shock physics applications.

Statistical Validation of Engineering and Scientific Models: A Maximum Likelihood Based Metric

Two major issues associated with model validation are addressed here. First, we present a maximum likelihood approach to define and evaluate a model validation metric. The advantage of this approach is it is more easily applied to nonlinear problems than the methods presented earlier by Hills and Trucano (1999, 2001); the method is based on optimization for which software packages are readily available; and the method can more easily be extended to handle measurement uncertainty and prediction uncertainty with different probability structures. Several examples are presented utilizing this metric. We show conditions under which this approach reduces to the approach developed previously by Hills and Trucano (2001). Secondly, we expand our earlier discussions (Hills and Trucano, 1999, 2001) on the impact of multivariate correlation and the effect of this on model validation metrics. We show that ignoring correlation in multivariate data can lead to misleading results, such as rejecting a good model when sufficient evidence to do so is not available.

ONE-DIMENSIONAL NONLINEAR INVERSE HEAT CONDUCTION TECHNIQUE

The one-dimensional nonlinear problem of heat conduction is considered. A noniterative space-marching finite-difference algorithm is developed to estimate the surface temperature and heat flux from temperature measurements at subsurface locations. The trade-off between resolution and variance of the estimates of the surface conditions is discussed quantitatively. The inverse algorithm is stabilized through the use of digital filters applied recursively. The effect of the filters on the resolution and variance of the surface estimates is quantified. Results are presented which indicate that the technique is capable of handling noisy measurement data.

STEADY-STATE TWO-DIMENSIONAL INVERSE HEAT CONDUCTION

A method for analysis of multidimensional steady-state inverse heat conduction problems is presented. The method employs an adjoint formulation to approximate a set of sensitivity coefficients that relate temperature and heat flux observations to unknown surface conditions. The resulting nonsquare system of equations is regularized and subsequently solved in a least-squares sense. A technique is presented for evaluating the accuracy of the estimated surface conditions in terms of resolution and variance. The method is applied to example problems in two dimensions for cases in which limited information about the surface condition is available.

Case study for model validation : assessing a model for thermal decomposition of polyurethane foam.

A case study is reported to document the details of a validation process to assess the accuracy of a mathematical model to represent experiments involving thermal decomposition of polyurethane foam. The focus of the report is to work through a validation process. The process addresses the following activities. The intended application of mathematical model is discussed to better understand the pertinent parameter space. The parameter space of the validation experiments is mapped to the application parameter space. The mathematical models, computer code to solve the models and its (code) verification are presented. Experimental data from two activities are used to validate mathematical models. The first experiment assesses the chemistry model alone and the second experiment assesses the model of coupled chemistry, conduction, and enclosure radiation. The model results of both experimental activities are summarized and uncertainty of the model to represent each experimental activity is estimated. The comparison between the experiment data and model results is quantified with various metrics. After addressing these activities, an assessment of the process for the case study is given. Weaknesses in the process are discussed and lessons learned are summarized.

SURFACE VARIANCE ESTIMATES USING AN ADJOINT FORMULATION FOR A ONE-DIMENSIONAL NONLINEAR INVERSE HEAT CONDUCTION TECHNIQUE

The one-dimensional nonlinear inverse heat conduction problem is considered. A new technique for estimating the surface variances of the predicted surface fluxes and temperatures based on an adjoint formulation is presented. The surface variances are related to the measurement variances and to an estimate of the initial condition variances. The only assumption necessary to apply the technique is that of additive measurement errors. Two test cases with three sets of boundary conditions are studied. The surface variance estimates given by the adjoint formulation and direct estimation are shown to be in good agreement.