The TSCF accounts for the reduction in concentration in the pore water as it crosses the root membrane and moves through the xylem to the stem. Thus, the TSCF represents the ratio of contaminant concentration in the xylem stream of the stem, mg/L, to contaminant concentration in soil solution, mg/L. Hsu et al. and Burken and Schnoor have proposed alternate constants for the Briggs et al. TSCF model using alternate experimental data sets. Briggs et al. also made measurements of chemical uptake in macerated stems from solutions for 8 O– methylcarbamoyloximes and substituted phenylureas in barley shoots to develop a model of the stem to soil-solution concentration ratio . Trapp and Matthies developed a one-compartment differential mass balance model for air-to-plant and soil-to-plant uptake. Included in this model are uptake from soil through the transpiration stream, gaseous deposition, volatilization from leaves, chemical transformation, and growth dilution. Their model provides a method for assessing a transient and long-term BCR from soil solution to leaves. Hung and Mackay followed a similar approach to mass balance as Trapp and Matthies, but used three compartments—roots, stem, and leaves— instead of one compartment. The Hung and Mackay model provides a similar opportunity for constructing a transient and plant-specific method for calculating BCFs, but requires many more plant- and chemical-specific parameters. Dowdy and McKone used the MCI as a quantitative structure-activity relationship for predicting plant-soil bio-concentration. They report that the normal path first-order MCI could reliably predict plant bio-transfer for non-polar compounds without any need for correction factors. But they found that extension of this predictive model to estimate bio-transfer for polar compounds requires an adjustment of the index with correction factors to account for polar group effects. Chiou et al. revisited the data of Briggs et al., Trapp et al. and earlier data for pesticides to propose a novel modeling approach based on the following assumptions: overall transport from soil is driven by soil-water concentration; each volume element within the plant attains equilibrium with the sap in that component; and the contaminant concentration in each volume element can be scaled to the soil-water solution.

In addition to the published experimental data that have been used to develop current bio-concentration models,barley fodder system there have been a number of recent experimental assessments that provide additional opportunities to evaluate the performance of plant-to-soil bio-concentration models. For example, Sicbaldi et al. have compiled new data on root uptake of pesticides.Kipopoulou et al. have measured the plant-to-air and/or plant-to-soil bio-concentration of polycyclic aromatic hydrocarbons in vegetables grown in an industrial area. The US EPA have compiled data on soil and plant concentration data that provides a potential opportunity to assess plant-to-soil partition factors for a number of dioxin congeners. We focus on the collection of BCR data for a single chemical in order to evaluate how experimental variability impacts BCR estimates,. In the next section where overall BCR reliability and uncertainty are considered, we compare this experimental variability to both to conceptual model uncertainty and to model formulation uncertainty. As the single chemical of interest, we select hexahydro-1,3,5-trinitro-1,3,5-triazine , a compound that has been studied extensively. We assembled a number of reports and journal papers describing experiments in which plants were grown in soil or water containing a measured concentration of RDX and in which the plant tissues were sampled for RDX. Through this process we obtained 81 different experimental observations of plant-to-soil BCRs for RDX from experiments with different plant species, plant tissues, experimental conditions, and methods for reporting concentrations in the soil and plant tissues. These measurements are summarized in Table 2. The cited studies include experimental data on ten different plant types–alfalfa, beans, corn, lettuce, tomato, carrot, cucumber, nutsedge, radish, and spinach; seven different plant tissues–roots, stem, leaves, pods, fruits, tassels, and seeds; both dry- and fresh-mass based measures of plant concentrations; measurements of chemical concentration and of radio-labeled tracers; and both dry- and solution-based measures of soil concentrations. The results in Table 2 include observations from six different reports that provide results from multiple experiments, and different experimental protocols. Cataldo et al. used radiolabeled RDX to measure uptake from contaminated soil into the roots, stems, leaves, pods, and seeds of bean plants. They also used beans grown in hydroponic solutions with radio-labeled RDX to compare with their field results.

Cataldo et al. report all plant concentrations on a fresh-mass basis. But they report their soil concentrations on a dry mass basis and also report soil organic carbon. Checkai and Simini used hydroponic studies to measure concentrations of RDX on a fresh-mass and dry-mass basis in tissues of plants grown in a growth solution with a specified RDX concentration. They carried out these experiments for bush bean fruit, corn stover, lettuce leaves, alfalfa shoot, radish roots, and tomato fruit. Price et al. reported the dry mass plant tissue concentration relative to soil fresh-mass concentration for experiments that exposed corn kernel, corn stover, lettuce leaves, nutsedge, and tomato fruit, to RDX in soil and soil solution. Harvey et al.used radio-labeled RDX in 1- and 7-day hydroponic studies to measure uptake in bean roots, bean stems, and bean leaves. Fellows et al.reported the dry mass plant tissue concentration relative to soil dry-mass concentration for corn ear, corn stem, corn leaves, corn tassel, alfalfa roots, alfalfa shoot, alfalfa seeds, carrot shoot, spinach root, spinach shoot, and spinach seeds. Larson et al. measure the uptake on a dry mass basis in the leaves and tassels of corn grown in RDX contaminated solution. The compilation of BCR values in Table 2 shows large variations in the experimental conditions and interpretations of measurements. In order to harmonize these data we converted all the results to an equivalent BCR with units of concentration in plant fresh mass divided by soil solution concentration, that is µg/kg per µg/L. In order to evaluate the reliability of the models and experimental data currently available to assess plant-soil BCR, we consider three issues. First we consider uncertainties that arise from conceptual model formulation. These results are primarily qualitative and subjective, but set the stage for the more quantitative reliability questions. Next, we consider the likely variation in results from mathematical models used to characterize plant uptake from soil. Our focus here is on the residual error associated with the use of models to estimate the BCF for an unspecified soil/plant/plant tissue system. Finally, we consider the estimation error associated with using our collection of experimental observations for RDX to make an estimate for the BCF for RDX in an unspecified soil/plant/plant tissue system and compare this to the uncertainty associated with making BCR estimates from models. Based on our review of available plant bio-transfer models, we find that the range of conceptual model formulation options introduces significant, but difficult to quantify, uncertainty to the process of modeling BCRs. A key source of uncertainty and potential error is in the definition of bio-concentration and selection of the appropriate soil concentration metric and the representative plant concentration metric, plant species, and plant tissue. But even when the concept and metric of BCR is clear, there are additional key uncertainties introduced by the options and limitations for measurements that support the conceptual model.

As observed previously by Paterson et al., three types of factors affect the uptake and distribution of chemical compounds within plants. First and foremost are physicochemical properties of the compound such as water solubility, vapor pressure, molecular weight, and octanol/water partition coefficient. Second are environmental characteristics including temperature of the soil as well as organic and mineral matter content and water content of the soil. Third are plant characteristics such as the type of root system,hydroponic barley fodder system shape and composition of the leaves, and lipid content. These three issues limit the options for reducing uncertainty at the model formulation stage. The reliability of any model based on physicochemical properties is also limited by the accuracy and availability of these properties. Physicochemical properties for many compounds are not accurately known. Soil characteristics are highly variable from one location to another and also vary seasonally at a single location. In addition, plant characteristics also vary significantly from one plant species to another, and seasonally in the same plant. Our confidence about the ability of models to provide estimates of BCRs derives both from the ability of a single model to match its calibration set of chemicals and from the consistency with which different models produce similar BCR values. Our evaluation reveals that the residual errors of the log BCR among different models relative to measured values range between 0.12 to 0.9 log units, which is equivalent to a geometric standard deviation range of 1.3 to 8, corresponding to a coefficient of variation of between 0.27 and 8.6. While this is not a measure of overall model uncertainty, it does measure how well a model fits its own calibration set. The more important issue, however, is the expected reliability of the models for predicting BCR values for chemicals not included in their calibration set. This test has rarely been applied, but we can use the results above to make some general comparisons. In Fig. 2 we provide a plot of the BCR estimates for several models with log Kow as the predictive parameter. We also include in this figure the calibration data for each model to get a sense of how the results converge or diverge among the different models. To construct this figure, we converted all the measured values and the model predictions to equivalent plant-fresh-mass-soil-solution BCR ratios. This figure has a log-log scale and reveals a significant divergence among the models. In Fig. 2 we include two lines that capture the roughly 4 standard deviation interval around both the experimental and model results. These lines indicate that the differences among both the models and the observations used to construct them have an estimated GSD of 10 with a corresponding CV of 14.

These are large uncertainties. But, this ensemble uncertainty is not significantly higher than the residual estimation error of models that are designed to capture variability of BCR across a broad range of chemical properties. For example the residual error of the MCI-based regression model, as reflected in Equation 14 has GSD of 8. The resulting cumulative probability plot for the 81 RDX BCR observations is shown in Fig. 3 as a series of open circles. Also plotted for comparison in Fig. 3 is a cumulative log normal probability distribution with GM 1.1 and GSD 3.5. We see here that the log normal distribution with these moments provides a good fit to the variance in BCR from the set of experimental observations. We focus on the single compound RDX to gain insight on the relative contributions of model uncertainty and experimental variability to our ability to estimate a BCR for a selected organic chemical. Fig. 4 summarizes our comparison presented as two cumulative probability distributions. The two log normal distributions in Fig. 4 show the relative variance attributable to experimental variability and to model uncertainty for estimating the BCR value for a chemical such as RDX that has an expected BCR value of 1.1. The log normal distribution for variance in BCR obtained from 81 experiments is taken from Fig. 3 . We estimate that, in the absence of any chemical and site-specific experimental information, the expected uncertainty of a BCR model for RDX can be represented by a log normal distribution with a GM of 1.1, a GSD of 10, and a CV of 14. This is the second cumulative distribution shown in this figure. Also shown are estimated 95% confidence intervals on the BCR estimate based on model uncertainty and experimental variability. In order to compare the relative contribution of experimental variability and model uncertainty, we used the R2 squared statistic, which is a measure of variance in one set of observations explained by a second set. We computed R2 from the two the sources of variation– the variance of the experimental measures about the mean BCR and the variance attributable to the uncertainty in results from the model-based estimates of the BCR. We did this by using random sampling to obtain 3000 samples from the log normal distribution of model uncertainty and 3000 samples from the log normal distribution for experimental variability. Based on the correlation coefficient R between these two samples, we obtained an R2 equal to 0.57. This indicates that a significant fraction of the overall BCR estimation uncertainty is attributable to experimental variability.