Concentration statistics for mixing-controlled reactive transport in random heterogeneous media

Uncertainty in the distribution of hydraulic parameters leads to uncertainty in flow and reactive transport. Traditional stochastic analysis of solute transport in heterogeneous media has focused on the ensemble mean of conservative-tracer concentration. Studies in the past years have shown that the mean concentration often is associated with a high variance. Because the range of possible concentration values is bounded, a high variance implies high probability weights on the extreme values. In certain cases of mixing-controlled reactive transport, concentrations of conservative tracers, denoted mixing ratios, can be mapped to those of constituents that react with each other upon mixing. This facilitates mapping entire statistical distributions from mixing ratios to reactive-constituent concentrations. In perturbative approximations, only the mean and variance of the mixing-ratio distribution are used. We demonstrate that the second-order perturbative approximation leads to erroneous or even physically impossible estimates of mean reactive-constituent concentrations when the variance of the mixing ratio is high and the relationship between the mixing ratio and the reactive-constituent concentrations strongly deviates from a quadratic function. The latter might be the case in biokinetic reactions or in equilibrium reactions with small equilibrium constant in comparison to the range of reactive-constituent concentrations. When only the mean and variance of the mixing ratio is known, we recommend assuming a distribution that meets the known bounds of the mixing ratio, such as the beta distribution, and mapping the assumed distribution of the mixing ratio to the distributions of the reactive constituents.     

Stochastic evaluation of mass discharge from pointlike concentration measurements

The contaminant mass discharge crossing a control plane is an important metric in the assessment of natural attenuation at contaminated sites. For risk-assessment purposes, the mass discharge must be estimated together with a level of uncertainty. We present a conditional Monte Carlo approach that allows estimating the statistical distribution of mass discharge. The approach is based on conditioning multiple realizations of the hydraulic conductivity field on all data available. We jointly determine a first-order decay coefficient in each realization, leading to conditional statistical distributions of all estimated parameters and the total mass discharge. The resulting statistical distribution of contaminant mass discharges can be used in the assessment of risks at the contaminated site. The method is applied to data of hypothetical test cases, which gives the opportunity to compare estimation results to the true field. As concentration data, we account for pointlike measurements obtained in multi-level sampling wells. The obtained empirical distribution of mass discharge crossing the multi-level sampling fence could be well fitted by a log-normal distribution.     

The Watershed Deposition Tool: A Tool for Incorporating Atmospheric Deposition in Water‐Quality Analyses1

Abstract: A tool for providing the linkage between air and water‐quality modeling needed for determining the Total Maximum Daily Load (TMDL) and for analyzing related nonpoint‐source impacts on watersheds has been developed. Using gridded output of atmospheric deposition from the Community Multiscale Air Quality (CMAQ) model, the Watershed Deposition Tool (WDT) calculates average per unit area and total deposition to selected watersheds and subwatersheds. CMAQ estimates the wet and dry deposition for all of its gaseous and particulate chemical species, including ozone, sulfur species, nitrogen species, secondary organic aerosols, and hazardous air pollutants at grid scale sizes ranging from 4 to 36 km. An overview of the CMAQ model is provided. The somewhat specialized format of the CMAQ files is not easily imported into standard spatial analysis tools. The WDT provides a graphical user interface that allows users to visualize CMAQ gridded data and perform further analyses on selected watersheds or simply convert CMAQ gridded data to a shapefile for use in other programs. Shapefiles for the 8‐digit (cataloging unit) hydrologic unit code polygons for the United States are provided with the WDT; however, other user‐supplied closed polygons may be used. An example application of the WDT for assessing the contributions of different source categories to deposition estimates, the contributions of wet and dry deposition to total deposition, and the potential reductions in total nitrogen deposition to the Albemarle‐Pamlico basin stemming from future air emissions reductions is used to illustrate the WDT capabilities.     

Using Meteorological Model Output as a Surrogate for On-Site Observations to Predict Deposition Velocity

The National Oceanic and Atmospheric Administration's Multi-Layer Model (NOAA-MLM) is used by several operational dry deposition networks for estimating the deposition velocity of O₃, SO₂, HNO₃, and particles. The NOAA-MLM requires hourly values of meteorological variables. Since collection of on-site meteorology can be expensive, a study was performed to compare NOAA-MLM predicted deposition velocitiesusing modeled meteorological data in lieu of on-site meteorological data. NOAA-MLM was run for three sites in the Clean Air Status and Trends Network using on-site data as well as the output of two mesoscale meteorological models, Eta and MM5. The differences between the deposition velocities predictedusing the mesoscale models and those predicted using the on-sitemeteorological measurements ranged from –0.001 to 0.106 cm s^-1 and were within the model error determined in NOAA-MLM evaluation studies. This research shows that the NOAA-MLM is particularly sensitive to differences in atmospheric turbulence,soil moisture budget, and canopy wetness.(On assignment to the National Exposure Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina.) (author for correspondence, e-mail