Modeling macropore flow effects on pesticide leaching: inverse parameter estimation using microlysimeters

Macropore flow is a key factor determining pesticide fate, but models accounting for this process need parameters that cannot be easily measured. This study was conducted to investigate the use of inverse techniques to estimate parameters controlling macropore flow and pesticide fate in the dual-permeability model MACRO. Undisturbed columns were sampled at three landscape positions (hilltop, slope, hollow) with contrasting texture and organic carbon content. Transient leaching experiments were performed for an anionic tracer and the herbicide MCPA (4-chloro-2methylphenoxy acetic acid) during a 4-mo period, first under natural rainfall, and then under controlled irrigation in the laboratory. The tracer breakthrough for the liner-textured soil from the hilltop showed strong evidence of macropore flow, resulting in a rapid leaching of MCPA, while leaching was minimal from the organic-rich hollow soil, since macropore flow was weaker and adsorption stronger. The MACRO model was linked to the inverse modeling program SUFI (Sequential Uncertainty Fitting) to enable calibration of nine key model parameters. Based on calculated model efficiencies, MACRO-SUFI gave generally good predictions of water movement and tracer and pesticide transport, although some errors were attributed to difficulties in simulating the effects of soil moisture on degradation and the timing of water outflows. Even after calibration, significant uncertainties remained for some key parameters controlling macropore flow. Nevertheless, the parameter estimates were significantly different between landscape positions and could also be related to basic soil properties. The posterior uncertainty ranges could probably be reduced with a more exhaustive sampling of the parameter space and improved experimental designs.     

Sensitivity and first-step uncertainty analyses for the preferential flow model MACRO

Sensitivity analyses for the preferential flow model MACRO were carried out using one-at-a-time and Monte Carlo sampling approaches. Four different scenarios were generated by simulating leaching to depth of two hypothetical pesticides in a sandy loam and a more structured clay loam soil. Sensitivity of the model was assessed using the predictions for accumulated water percolated at a 1-m depth and accumulated pesticide losses in percolation. Results for simulated percolation were similar for the two soils. Predictions of water volumes percolated were found to be only marginally affected by changes in input parameters and the most influential parameter was the water content defining the boundary between micropores and macropores in this dual-porosity model. In contrast, predictions of pesticide losses were found to be dependent on the scenarios considered and to be significantly affected by variations in input parameters. In most scenarios, predictions for pesticide losses by MACRO were most influenced by parameters related to sorption and degradation. Under specific circumstances, pesticide losses can be largely affected by changes in hydrological properties of the soil. Since parameters were varied within ranges that approximated their uncertainty, a first-step assessment of uncertainty for the predictions of pesticide losses was possible. Large uncertainties in the predictions were reported, although these are likely to have been overestimated by considering a large number of input parameters in the exercise. It appears desirable that a probabilistic framework accounting for uncertainty is integrated into the estimation of pesticide exposure for regulatory purposes.     

Assessing Parameter Uncertainty of a Semi‐Distributed Hydrology Model for a Shallow Aquifer Dominated Environmental System

This paper examines the performance of a semi‐distributed hydrology model (i.e., Soil and Water Assessment Tool [SWAT]) using Sequential Uncertainty FItting (SUFI‐2), generalized likelihood uncertainty estimation (GLUE), parameter solution (ParaSol), and particle swarm optimization (PSO). We applied SWAT to the Waccamaw watershed, a shallow aquifer dominated Coastal Plain watershed in the Southeastern United States (U.S.). The model was calibrated (2003‐2005) and validated (2006‐2007) at two U.S. Geological Survey gaging stations, using significant parameters related to surface hydrology, hydrogeology, hydraulics, and physical properties. SWAT performed best during intervals with wet and normal antecedent conditions with varying sensitivity to effluent channel shape and characteristics. In addition, the calibration of all algorithms depended mostly on Manning's n‐value for the tributary channels as the surface friction resistance factor to generate runoff. SUFI‐2 and PSO simulated the same relative probability distribution tails to those observed at an upstream outlet, while all methods (except ParaSol) exhibited longer tails at a downstream outlet. The ParaSol model exhibited large skewness suggesting a global search algorithm was less capable of characterizing parameter uncertainty. Our findings provide insights regarding parameter sensitivity and uncertainty as well as modeling diagnostic analysis that can improve hydrologic theory and prediction in complex watersheds. Editor's note : This paper is part of the featured series on SWAT Applications for Emerging Hydrologic and Water Quality Challenges. See the February 2017 issue for the introduction and background to the series.     

A Comparison of Bayesian Methods for Uncertainty Analysis in Hydraulic and Hydrodynamic Modeling

We evaluate and compare the performance of Bayesian Monte Carlo (BMC), Markov chain Monte Carlo (MCMC), and the Generalized Likelihood Uncertainty Estimation (GLUE) for uncertainty analysis in hydraulic and hydrodynamic modeling (HHM) studies. The methods are evaluated in a synthetic 1D wave routing exercise based on the diffusion wave model, and in a multidimensional hydrodynamic study based on the Environmental Fluid Dynamics Code to simulate estuarine circulation processes in Weeks Bay, Alabama. Results show that BMC and MCMC provide similar estimates of uncertainty. The posterior parameter densities computed by both methods are highly consistent, as well as the calibrated parameter estimates and uncertainty bounds. Although some studies suggest that MCMC is more efficient than BMC, our results did not show a clear difference between the performance of the two methods. This seems to be due to the low number of model parameters typically involved in HHM studies, and the use of the same likelihood function. In fact, for these studies, the implementation of BMC results simpler and provides similar results to MCMC. The results of GLUE are, on the other hand, less consistent to the results of BMC and MCMC in both applications. The posterior probability densities tend to be flat and similar to the uniform priors, which can result in calibrated parameter estimates centered in the parametric space.     

Parameter Uncertainty Reduction for SWAT Using Grace,Streamflow, and Groundwater Table Data for Lower Missouri River Basin1

Abstract: This study incorporates the newly available Gravity Recovery and Climate Experiment (GRACE) water storage data and water table data from well logs to reduce parameter uncertainty in Soil and Water Assessment Tool (SWAT) calibration using a SUFI2 (sequential uncertainty fitting) framework for the Lower Missouri River Basin. Model evaluations are performed in multiple stages using a multiobjective function consisting of multisite streamflow and GRACE water storage data as well as a groundwater component. Results show that (1) a model calibrated with both streamflow and GRACE data simultaneously can maintain the water balance for the whole basin, but may improperly partition surface flow and base flow. Additional inclusion of the groundwater constraint can significantly improve the model performance in groundwater hydrological processes. In our case, the estimation of specific yield of shallow aquifers has been increased to 10^?2 from previous much underestimated level (<10^?3). (2) The daily streamflow data are needed to confine the parameters related to water flow in channels such as the Manning’s coefficient, which are less sensitive to the monthly simulations. (3) Parameters are nonuniformly sensitive for different goal variables, and thus, proper specification of a prior distribution of parameters may be the key factor for global optimization algorithms to obtain stable and realistic model performance.     

PARAMETER ESTIMATES FOR A GROUND WATER MODEL1

ABSTRACT: This paper presents a parameter sensitivity study of a two-dimensional flow and transport model of a contaminated site. Hydrogeological and site data from previous investigations were used for calibration. The USGS contaminant transport model (MOC) was used. After flow calibration to establish a reference model, parameters were varied to examine the effect each had on predictions of a contaminant plume. Hydrogeological parameters and a step size parameter were incrementally varied individually. Each result was compared to the reference model output to evaluate changes in concentration values and contaminant plume configuration. The study indicated that a generally predictable trend can be established for some parameters not affected by pumping or similar high stresses. Ranges were identified to relate concentration error or plume change to the amount of parameter error. Some parameter perturbations produced distorted model responses at high stress locations. Porosity and anisotropy were found to be the most influential of the model parameters studied on the plume predictions. (KEY TERMS: ground water hydrology; hydrogeology; pollution modeling; water quality; model calibration.)     

Applications of Explicitly Incorporated/Post‐Processing Measurement Uncertainty in Watershed Modeling

In the field of watershed modeling, the impact of measurement uncertainty (MU) on calibration results indicates the potential issue of inaccurate model predictions. It is important to note that MU refers to the uncertainty in measured data such as flow and nutrient values that are used to evaluate model outputs. The calculation of error statistics assuming measured data are deterministic may not be appropriate as has been frequently stated in literature. Although MU can affect model calibration results, it is rarely incorporated in modeling practice. MU can be incorporated in two schemes: explicitly incorporated (MU‐EI) during model calibration and post‐processed (MU‐PP) after calibration is completed. In this study, both schemes are implemented in a case study of the Arroyo Colorado Watershed, Texas. Unexpectedly, no substantial differences were observed between each scheme for flow predictions. Although MU did not cause dramatic differences in most sediment and NH₄‐N predictions, error statistics were affected in cases with MU greater than 50%, especially for sediment and NH₄‐N. Therefore, it is concluded that MU may not exert a significant impact on model predictions until certain threshold is reached. This study demonstrates that high levels of uncertainty in measured calibration/validation data significantly affect parameter estimation, especially in the auto‐calibration process.     

Stochastic modeling of diffuse pesticide losses from a small agricultural catchment

The objective of this study was to identify the main sources of variation in pesticide losses at field and catchment scales using the dual permeability model MACRO. Stochastic simulations of the leaching of the herbicide MCPA (4-chloro-2-methylphenoxyacetic acid) were compared with seven years of measured concentrations in a stream draining a small agricultural catchment and one year of measured concentrations at the outlet of a field located within the catchment. MACRO was parameterized from measured probability distributions accounting for spatial variability of soil properties and local pedotransfer functions derived from information gathered in field- and catchment-scale soil surveys. At the field scale, a single deterministic simulation using the means of the input distributions was also performed. The deterministic run failed to reproduce the summer outflows when most leaching occurred, and greatly underestimated pesticide leaching. In contrast, the stochastic simulations successfully predicted the hydrologic response of the field and catchment and there was a good resemblance between the simulations and measured MCPA concentrations at the field outlet. At the catchment scale, the stochastic approach underestimated the concentrations of MCPA in the stream, probably mostly due to point sources, but perhaps also because the distributions used for the input variables did not accurately reflect conditions in the catchment. Sensitivity analyses showed that the most important factors affecting MACRO modeled diffuse MCPA losses from this catchment were soil properties controlling macropore flow, precipitation following application, and organic carbon content.     

Developing risk models of Cryptosporidium transport in soils from vegetated, tilted soilbox experiments

Transport of Cryptosporidium parvum through macroporous soils is poorly understood yet critical for assessing the risk of groundwater contamination. We developed a conceptual model of the physics of flow and transport in packed, tilted, and vegetated soilboxes during and immediately after a simulated rainfall event and applied it to 54 experiments implemented with different soils, slopes, and rainfall rates. Using a parsimonious inverse modeling procedure, we show that a significant amount of subsurface outflow from the soilboxes is due to macropore flow. The effective hydraulic properties of the macropore space were obtained by calibration of a simple two-domain flow and transport model that accounts for coupled flow in the matrix and in the macropores of the soils. Using linear mixed-effects analysis, macropore hydraulic properties and oocyst attenuation were shown to be associated with soil bulk density and rainfall rate. Macropore flow was shown to be responsible for bromide and C. parvum transport through the soil into the underlying pore space observed during the 4-h experiments. We confirmed this finding by conducting a pair of saturated soil column studies under homogeneously repacked conditions with no macropores in which no C. parvum transport was observed in the effluent. The linear mixed-effects and logistic regression models developed from the soilbox experiments provide a basis for estimating macropore hydraulic properties and the risk of C. parvum transport through shallow soils from bulk density, precipitation, and total shallow subsurface flow rate. The risk assessment is consistent with the reported occurrence of oocysts in springs or groundwater from fractured or karstic rocks protected only by shallow overlying soils.     

Simulating sulfadimidine transport in surface runoff and soil at the microplot and field scale

To prevent residues of veterinary medicinal products (VMPs) from contaminating surface waters and ground water, an environmental impact assessment is required before a new product is allowed on the market. Physically based simulation models are advocated for the calculation of predicted environmental concentrations at higher tiers of the assessment process. However, the validation status of potentially useful models is poor for VMP transport. The objective of this study was to evaluate the dual-permeability model MACRO for simulation of transport of sulfonamide antibiotics in surface runoff and soil. Special focus was on effects of solute application in liquid manure, which may alter the hydraulic properties at the soil surface. To this end we used data from a microplot runoff experiment and a field experiment, both conducted on the same clay loam soil prone to preferential flow. Results showed that the model could accurately simulate concentrations of sulfadimidine and the nonreactive tracer bromide in runoff and in soil from the microplot experiments. The use of posterior parameter distributions from calibrations using the microplot data resulted in poor simulations for the field data of total sulfadimidine losses. The poor results may be due to surface runoff being instantly transferred off the field in the model, whereas in reality re-infiltration may occur. The effects of the manure application were reflected in smaller total and micropore hydraulic conductivities compared with the application in aqueous solution. These effects could easily be accounted for in regulatory modeling.     

Interrelationship of macropores and subsurface drainage for conservative tracer and pesticide transport

Macropore flow results in the rapid movement of pesticides to subsurface drains, which may be caused in part by a small portion of macropores directly connected to drains. However, current models fail to account for this direct connection. This research investigated the interrelationship between macropore flow and subsurface drainage on conservative solute and pesticide transport using the Root Zone Water Quality Model (RZWQM). Potassium bromide tracer and isoxaflutole, the active ingredient in BALANCE herbicide [(5-cyclopropyl-4-isoxazolyl) [2(methylsulfonyl)-4-(trifluoromethyl)phenyl] methanone], with average half-life of 1.7 d were applied to a 30.4-ha Indiana corn (Zea mays L.) field. Water flow and chemical concentrations emanating from the drains were measured from two samplers. Model predictions of drain flow after minimal calibration reasonably matched observations (slope = 1.03, intercept = 0.01, and R(2) = 0.75). Without direct hydraulic connection of macropores to drains, RZWQM under predicted bromide and isoxaflutole concentration during the first measured peak after application (e.g., observed isoxaflutole concentration was between 1.2 and 1.4 mug L(-1), RZWQM concentration was 0.1 mug L(-1)). This research modified RZWQM to include an express fraction relating the percentage of macropores in direct hydraulic connection to drains. The modified model captured the first measured peak in bromide and isoxaflutole concentrations using an express fraction of 2% (e.g., simulated isoxaflutole concentration increased to 1.7 mug L(-1)). The RZWQM modified to include a macropore express fraction more accurately simulates chemical movement through macropores to subsurface drains. An express fraction is required to match peak concentrations in subsurface drains shortly after chemical applications.     

Transport of phosphate through artificial macropores during film and pulse flow

Flow through artificial macropores may occur as a water film along the macropore walls (film flow) or as moving water segments separated by air bubbles (pulse flow). To investigate the effect of macropore flow pattern (i.e., film and pulse flow) on the interaction of solutes with macropore walls, we studied orthophosphate (P) transport and sorption in artificial macropores. The experimental setup consisted of a column (height = 20 cm, diameter = 20 cm) homogenously packed with glass beads and fitted at outflow with a vertical artificial macropore placed below the column. The artificial macropore consisted of ceramic tubes (3 or 8 mm i.d.; 31.5 cm long) coated on the inside with iron oxide serving as phosphate sorbents. An orthophosphate solution containing 0.04 mg P L(-1) was applied at a rate of 9 to 12 mm h(-1) to the column, eventually causing macropore flow. In the 8-mm-i.d. tubes only film flow occurred. Pulse flow was dominating in the 3-mm-i.d. tubes. Generally, the flow patterns were reproducible and seldom did pulse flow replaced film flow or vice versa. During film flow, a significantly larger decrease in macropore P concentration per tube was observed relative to that with pulse flow events. However, pulse and film flow lead to almost the same amounts of P sorbed per unit surface area when exposed to the same solute P concentration. Comparison with P sorption capacity experiments indicated that the sorption rate, rather than the sorption capacity, controls the amount of sorbed P during macropore flow in the studied system.     

Impact of Watershed Subdivision and Soil Data Resolution on SWAT Model Calibration and Parameter Uncertainty1

Abstract: Impact of watershed subdivision and soil data resolution on Soil Water Assessment Tool (SWAT) model calibration and parameter uncertainty is investigated by creating 24 different watershed model configurations for two study areas in northern Indiana. SWAT autocalibration tool is used to calibrate 14 parameters for simulating seven years of daily streamflow records. Calibrated parameter sets are found to be different for all 24 watershed configurations, however in terms of calibrated model output, their effect is minimal. In some cases, autocalibration is followed by manual calibration to correct for low flows, which were underestimated during autocalibration. In addition to normal validation using four years of streamflow data for each calibrated parameter set, cross‐validation (using a calibrated parameter set from one model configuration to validate observations using another configuration) is performed to investigate the effect of different model configurations on streamflow prediction. Results show that streamflow output during cross‐validation is not affected, thus highlighting the non‐unique nature of calibrated parameters in hydrologic modeling. Finally, parameter uncertainty is investigated by extracting good parameter sets during the autocalibration process. Parameter uncertainty analysis suggests that significant parameters show very narrow range of uncertainty across different watershed configurations compared with nonsignificant parameters. Results from recalibration of some configurations using only six significant parameters were comparable to that from calibration using 14 parameters, suggesting that including fewer significant parameters could reduce the uncertainty arising from model parameters, and also expedite the calibration process.     

Dissolution and transport of TNT, RDX, and composition B in saturated soil columns

Low-order detonations and blow-in-place procedures on military training ranges can result in residual solid explosive formulations to serve as distributed point sources for ground water contamination. This study was conducted to determine if distribution coefficients from batch studies and transport parameters of pure compounds in solution adequately describe explosive transport where compounds are present as solid particles in formulations. Saturated column transport experiments were conducted with 2,4,6-trinitrotoluene (TNT), hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX), and the explosive formulation, Composition B (Comp B) (59.5 +/- 2.0% RDX, 39.5 +/- 2.3% TNT, and 1% wax) in solid and dissolved forms. The two soils used were Plymouth loamy sand (mesic, coated Typic Quartzipsamments) from Camp Edwards, MA and Adler silt loam (coarse-silty, mixed, superactive, thermic Fluvaquentic Eutrudepts) from Vicksburg, MS. Interrupted flow experiments were used to determine if explosives were at equilibrium distribution between soil and solution phases. The HYDRUS-1D code was used to determine fate and transport parameters. Results indicated that sorption of high explosives was rate limited. The behavior of dissolved Comp B was similar to the behavior of pure TNT and RDX. Behavior of solid Comp B was controlled by dissolution that depended on physical properties of the Comp B sample. Adsorption coefficients determined by HYDRUS-1D were different from those determined in batch tests for the same soils. Use of parameters specific to formulations will improve fate and transport predictions.     

Problems in Extinction Model Selection and Parameter Estimation

It is a vexing problem to achieve a consensus about the proper scientific way to assess population viability for habitat conservation plans. Rather than a hypothesis-testing approach, here it is proposed to select population models, estimate extinction parameters, and assess prediction uncertainty using a pragmatic, empirical Bayesian approach. The simplest usable models include the effects of population growth, r; carrying capacity, K; Allee threshold, N(A); and environmental stochasticity, v(r). Analytic predictions of expected extinction times are available for such models. Models that are more complex can be elaborated from this basis. Selection from a hierarchy of nesting population models can often be done through the evaluation of parameters. The estimation of the most important extinction parameters can be undertaken in a variety of ways. Time series can be analyzed to estimate r(d), v(r), rho, and K. Habitat models and individualistic population models may help estimate N(A) and K and demographic stochasticity. Fine-scale biogeography and climatological data may be useful in the estimation of a variety of parameters. Because it takes many years to estimate extinction parameters accurately for a given population of interest, the most efficient estimation procedures are desirable. I propose the use of prior information from an (as yet nonexistent) population biology database. The accumulation of local information through monitoring will improve our estimates allowing adaptive management. Uncertainty in the estimates will always remain, but it may be quantified by the posterior distributions. A crude example is discussed using treefrog population data. Although the motivations, beliefs, and biases of competing stakeholders will differ, a habitat conservation plan could accommodate this variation in the prior distributions. Field experience from monitoring will increasingly clear up any discrepancies between the opposing beliefs and the real ecosystem. As the world is an uncertain place and because there is no universal scientific method, there will always be controversy and surprises. The best we can do is (1) agree about our prior information, (2) agree about the strategy of model selection and parameter estimation, and (3) agree about our strategy for adaptive management. Perhaps the greatest impediment to such prior agreements for HCPs is the likely paranoia inspired by the use of unfamiliar statistical methodology. We need to train students of ecology in a more flexible and deeper understanding of statistics and philosophy of science.     

A NEW LOOK AT FLOOD RISK DETERMINATION1

ABSTRACT: The probability distributions of annual peak flows used in flood risk analysis quantify the risk that a design flood will be exceeded. But the parameters of these distributions are themselves to a degree uncertain and this uncertainty increases the risk that the flood protection provided will in fact prove to be inadequate. The increase in flood risk due to parameter uncertainty is small when a fairly long record of data is available and the annual flood peaks are serially independent, which is the standard assumption in flood frequency analysis. But standard tests for serial independence are insensitive to the type of grouping of high and low values in a time series, which is measured by the Hurst coefficient. This grouping increases the parameter uncertainty considerably. A study of 49 annual peak flow series for Canadian rivers shows that many have a high Hurst coefficient. The corresponding increase in flood risk due to parameter uncertainty is shown to be substantial even for rivers with a long record, and therefore should not be neglected. The paper presents a method of rationally combining parameter uncertainty due to serial correlation, and the stochastic variability of peak flows in a single risk assessment. In addition, a relatively simple time series model that is capable of reproducing the observed serial correlation of flood peaks is presented.     

Uncertainty assessment of the model RICEWQ in northern Italy

Model predictions are often seriously affected by uncertainties arising from many sources. Ignoring the uncertainty associated with model predictions may result in misleading interpretations when the model is used by a decision-maker for risk assessment. In this paper, an analysis of uncertainty was performed to estimate the uncertainty of model predictions and to screen out crucial variables using a Monte Carlo stochastic approach and a number of statistical methods, including ANOVA and stepwise multiple regression. The model studied was RICEWQ (Version 1.6.1), which was used to forecast pesticide fate in paddy fields. The results demonstrated that the paddy runoff concentration predicted by RICEWQ was in agreement with field measurements and the model can be applied to simulate pesticide fate at field scale. Model uncertainty was acceptable, runoff predictions conformed to a log-normal distribution with a short right tail, and predictions were reliable at field scale due to the narrow spread of uncertainty distribution. The main contribution of input variables to model uncertainty resulted from spatial (sediment-water partition coefficient and mixing depth to allow direct partitioning to bed) and management (time and rate of application) parameters, and weather conditions. Therefore, these crucial parameters should be carefully parameterized or precisely determined in each site-specific paddy field before the application of the model, since small errors of these parameters may induce large uncertainty of model outputs.     

Impact of Temporal Resolution of Flow‐Duration Curve on Sediment Load Estimation1

Chen, Li, Rina Schumer, Anna Knust, and William Forsee, 2011. Impact of Temporal Resolution of Flow‐Duration Curve on Sediment Load Estimation. Journal of the American Water Resources Association (JAWRA) 48(1): 145‐155. DOI: 10.1111/j.1752‐1688.2011.00602.x Abstract: Estimates of a channel’s annual sediment transport capacity typically incorporate annualized flow‐duration curves. Average daily flow data, commonly used to develop flow‐duration curves, may not adequately describe sediment‐transporting flows in arid and semiarid ephemeral streams. In this study, we examined impacts of varied temporal resolution flow data on annual sediment load estimation. We derived flow‐duration curves for eight sites in the Southwestern United States based on both 15‐min and daily‐averaged flow data. We then estimated sediment loads for both flow‐duration curves using the Sediment Impact Analysis Method, implemented in HEC‐RAS. When average daily flow is used to generate flow‐duration curves, sediment load estimation is lower by up to an order of magnitude. This trend is generally unaffected by uncertainty associated with sediment particle size or hydraulic roughness. The ratio of sediment loads estimated by 15‐min versus daily‐averaged flow‐duration curves is strongly correlated with channel slope, being greater on steep‐slope channels. Sediment loads estimated by the two types of flow‐duration curves are closely correlated, suggesting possible relationships for improving predictions when high‐temporal resolution data are unavailable. Results also suggest that the largest flow contributes significantly to total sediment load, and thus will greatly impact ephemeral stream geomorphology in arid and semiarid regions.     

ESTIMATING THE PROBABILITY OF EXCEEDING GROUNDWATER QUALITY STANDARDS1

ABSTRACT: A model for estimating the probability of exceeding groundwater quality standards at environmental receptors based on a simple contaminant transport model is described. The model is intended for locations where knowledge about site-specific hydrogeologic conditions is limited. An efficient implementation methodology using numerical Monte Carlo simulation is presented. The uncertainty in the contaminant transport system due to uncertainty in the hydraulic conductivity is directly calculated in the Monte Carlo simulations. Numerous variations of the deterministic parameters of the model provide an indication of the change in exceedance probability with change in parameter value. The results of these variations for a generic example are presented in a concise graphical form which provides insight into the topology of the exceedance probability surface. This surface can be used to assess the impact of the various parameters on exceedance probability.