Ambiguities inherent in sums-of-squares-based error statistics

Commonly used sums-of-squares-based error or deviation statistics—like the standard deviation, the standard error, the coefficient of variation, and the root-mean-square error—often are misleading indicators of average error or variability. Sums-of-squares-based statistics are functions of at least two dissimilar patterns that occur within data. Both the mean of a set of error or deviation magnitudes (the average of their absolute values) and their variability influence the value of a sum-of-squares-based error measure, which confounds clear assessment of its meaning. Interpretation problems arise, according to Paul Mielke, because sums-of-squares-based statistics do not satisfy the triangle inequality. We illustrate the difficulties in interpreting and comparing these statistics using hypothetical data, and recommend the use of alternate statistics that are based on sums of error or deviation magnitudes.     

Use of principal components analysis (PCA) on estuarine sediment datasets: The effect of data pre-treatment

Principal components analysis (PCA) is a multivariate statistical technique capable of discerning patterns in large environmental datasets. Although widely used, there is disparity in the literature with respect to data pre-treatment prior to PCA. This research examines the influence of commonly reported data pre-treatment methods on PCA outputs, and hence data interpretation, using a typical environmental dataset comprising sediment geochemical data from an estuary in SE England. This study demonstrated that applying the routinely used log (x + 1) transformation skewed the data and masked important trends. Removing outlying samples and correcting for the influence of grain size had the most significant effect on PCA outputs and data interpretation. Reducing the influence of grain size using granulometric normalisation meant that other factors affecting metal variability, including mineralogy, anthropogenic sources and distance along the salinity transect could be identified and interpreted more clearly.     

Enantiomeric ratios as an indicator of exposure processes for persistent pollutants in human placentas

The enantiomeric ratios (ER) of alpha-HCH and o,p'-DDT ((+)-isomer concentration/(-)-isomer concentration) and o,p'-DDD (first eluting enantiomer/second enantiomer) were investigated in 112 human placentas from Finnish boys collected 1997-2001. Both o,p'-DDD and alpha-HCH showed changes in their ER depending on the total concentration of the compound in the sample. Their ERs are approaching a value close to racemic mixture (ER=1) at high concentrations. At low concentrations they often differ from 1. The relationship between concentration and ER is clearly identified and it has been shown that it is not affected by analytical uncertainty. This relationship appears to be important for assessing tissue- and species-specific exposure and risk and it may indicate whether net uptake or metabolic activity is dominant in exposure for the resulting exposure of the enantiomers.     

Congener-specific concentrations and carbon stable isotope ratios (delta13C) of two technical toxaphene products (Toxaphene and Melipax)

In this study we compared the contribution of individual congeners and the ratios of stable carbon isotopes of two technical toxaphene products. The former US-American product Toxaphene was from 1978 and the East-German product Melipax from 1979. Both technical products showed the known complexity in GC/ECD measurements. Contributions of 24 peaks to each of the technical products were determined by gas chromatography in combination high resolution electron capture negative ion mass spectrometry (GC/ECNI-HRMS). The percentages of the compounds studied in the technical mixtures ranged from approximately 0.05% to approximately 2.5% but showed some individual differences. 2,2,5,5,8,9,9,10,10-nonachlorobornane (B9-1025 or P-62) was identified as a major congener in both mixtures. 2-Endo,3-exo,5-endo,6-exo,8,8,10,10-octachlorobornane (B8-1413 or P26) and 2-endo,3-exo,5-endo,6-exo,8,8,9,10,10-nonachlorobornane (B9-1679 or P-50) were found at similar concentration in both technical products. Identical amounts of Melipax or Toxaphene were combusted to CO2 in an element analyzer and their delta13C values were determined relative to the international standard Vienna PeeDee belemnite (VPDB). The mean delta13C values of both products varied by 2.8% (determined at two different locations) which is roughly one order of magnitude more than the precision obtained in repetitive analyses of the individual products. Thus, both investigated products could be unequivocally distinguished by stable isotope ratio mass spectrometry (IRMS). IRMS analyses may thus be a suitable tool for tracing back toxaphene residues in environmental and food samples to the one or both of the products.     

Estimating octanol-air partition coefficients with octanol-water partition coefficients and Henry's law constants

The octanol-air partition coefficient (K(OA)) is useful for predicting the partitioning behavior of organic compounds between air and environmental matrices such as soil, vegetation, and aerosol particles. At present, experimentally determined K(OA) values are available for only several hundred compounds. Therefore, the ability to estimate K(OA) is necessary for screening level evaluation of most chemicals. Although it is possible to estimate K(OA) from the octanol-water partition coefficient (K(OW)) and Henry's law constant (HLC), various concerns have been raised in regard to the usability of this estimation methodology. This work examines the accuracy and usability of K(OW) and HLC in application to a comprehensive database set of K(OA) values for screening level environmental assessment. Results indicate that K(OW) and HLC can be used to accurately predict K(OA) even when estimated K(OW) and HLC values are used. For an experimental dataset of 310log K(OA) values for different compounds, the K(OW)-HLC method was statistically accurate as follows: correlation coefficient (r2): 0.972, standard deviation: 0.526, absolute mean error: 0.358 using predominantly experimental K(OW) and HLC values. When K(OW) and HLC values were estimated (using the KOWWIN and HENRYWIN programs), the statistical accuracy was: correlation coefficient (r2): 0.957, standard deviation: 0.668, absolute mean error: 0.479.     

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.     

A comparison of simulated and observed ozone mixing ratios for the summer of 1998 in Western Europe

This study describes and evaluates the newly developed European scale Eulerian chemistry transport model CHIMERE-continental. The model is designed for seasonal simulations and real time forecasts without the use of super-computers. For the purpose of model evaluation simulated ozone mixing ratios for the period between 1 May 1998 and 30 September 1998 are compared to observational data from 115 European surface sites. In order to facilitate the interpretation of future forecasts a statistic is established to estimate the reliability of a simulated pollution level. Besides this, the comparison is done by means of time series, scatter plots, a spectral analysis and the calculation of RMS-errors and biases of the model results corresponding to each observation site. It turns out that the mean RMS-error of the simulated daily maximum ozone mixing ratio for the sites considered a priori as well suited for a model comparison is about 10 ppb. For the same period but a reduced number of sites observed concentrations of NO₂ and ethene are compared to simulated values. Difficulties encountered with the representativeness of observations when trying to evaluate a mesoscale air pollution model are discussed.     

Study of the enantioselective elimination of four toxaphene congeners in rat after intravenous administration by high resolution gas chromatography negative ion mass spectrometry

This study was performed to investigate the possible enantioselective metabolism of the four chlorinated bornanes: #26, #32, #50 and #62 (according to the Parlar nomenclature) by rats. Rats were exposed to a mixture of these toxaphenes by a single intravenous injection. Enantiomer ratios (ER) as well as the enantiomer fractions (EF) were determined in brain, adipose tissue and liver samples at six time intervals by high resolution gas chromatography (HRGC) coupled to negative ion chemical ionization (NICI) mass spectrometry (MS). Capillaries coated with heptakis-(2,3,6-O-tert-butyldimethylsilyl)-beta-cyclodextrin (TBDMS-CD) or octakis-(2,3,6-tri-O-ethyl)-gamma-cyclodextrin (TEG-CD) were used for the enantioselective separations. Significant time-dependent changes of ER and EF were found in all the three tissues for #26, #50 and #62. Greatest deviations from racemic composition were found in the liver, which is known to be the major metabolizing organ for toxaphenes. #32 was metabolized the fastest, but showed no changes in ER. Brief information is also included about the possible reasons for the different behaviors of the four congeners in the studied tissues.     

The bootstrap and the jackknife in ecotoxicology or nonparametric estimates of standard error

A recently invented statistical method, the bootstrap, is used to verify whether a hypothesis, developed from a limited data set, would be valid if all possible data would have been available, i.e. this statistical method allows generalization to chemicals of the same class not included in the original analysis. The validity of the relation, hypothesized by Neely, between the water solubility of an organic chemical and the ratio of the acute fish LC50 at two different time periods has been tested. The hypothesis has been shown correct by first fitting a linear model with a geometric mean (GM) functional regression, which takes into account errors in both the independent and dependent variables, to compare observed and predicted ratios; the generality of the model has been tested by computing the confidence limits of the correlation coefficient, of the slope and intercept of the GM regression model using the bootstrap. The results show that the correlation between predicted and observed data is statistically significant within one standard deviation, but sometimes it may not be significant at the 95% confidence limit. Neely's model is probably correct but it might have a systematic bias which makes the theoretical ratio somewhat higher than the observed ratio.     

Enantiomer fractions of chiral organochlorine pesticides and polychlorinated biphenyls in standard and certified reference materials

Enantiomeric ratios (ERs) and enantiomeric fractions (EFs) of a number of chiral organochlorine pesticides and PCB atropisomers were measured by chiral gas chromatography/mass spectrometry (GC/MS) in five standard (SRM) and certified (CRM) reference materials: SRM 1588a (organics in cod liver oil), SRM 1945 (organics in whale blubber), Marine Mammal Quality Assurance Exercise Control Material IV (NIST IV, organics in whale blubber), CRM trout, and CRM EC-5 (sediment). Target analytes were cis- and trans-chlordane, heptachlor exo-epoxide, oxychlordane, U82, MC5, MC6, MC7, o,p^′-DDT, and PCB congeners 91, 95, 136, 149, 174, 176, and 183. Measured ERs and EFs are in close agreement with the few literature values reported for some of these analytes in SRMs and CRMs. Chiral PCB ERs and EFs measured by one-dimensional chiral GC/MS were similar to values measured using multidimensional chiral GC/MS. Non-racemic chiral compositions are in agreement with known uptake and biotransformation in the respective environmental matrices. These values should aid in the quality assurance/quality control methodologies for chiral environmental chemistry using standardized reference materials.     

The influence of sampling protocol on nonmethane hydrocarbon mixing ratios

The effect of sampling protocol on ambient air hydrocarbon mixing ratios was examined on eight sampling days in Los Angeles during 2007 and 2008. Four protocols, which were based on previously published multi-city urban hydrocarbon studies in the United States, were compared and differences were quantified. Whole air canister samples were collected and analyzed for nonmethane hydrocarbons (NMHCs). Differing sampling protocols resulted in large differences in mixing ratios, up to an order of magnitude, for certain NMHCs on the same sampling day. However, the magnitude of the variability between NMHC levels obtained by the four protocols was not consistent throughout the eight sampling days. It was found that sampling time, followed by sampling location, had the greatest influence on the magnitude of the mixing ratio. Ratios between hydrocarbons, often used in urban studies to gain information on emission sources, also varied depending on the protocol used. Comparison of absolute NMHC mixing ratios collected in urban environments using differing sampling protocols should be made with care.     

Enantiomer fractions of polychlorinated biphenyls in three selected Standard Reference Materials

The enantiomer composition of six chiral polychlorinated biphenyls (PCBs) were measured in three different certified Standard Reference Materials (SRMs) from the US National Institute of Standards and Technology (NIST): SRM 1946 (Lake Superior fish tissue), SRM 1939a (PCB Congeners in Hudson River Sediment), and SRM 2978 (organic contaminants in mussel tissue--Raritan Bay, New Jersey) to aid in quality assurance/quality control methodologies in the study of chiral pollutants in sediments and biota. Enantiomer fractions (EFs) of PCBs 91, 95, 136, 149, 174, and 183 were measured using a suite of chiral columns by gas chromatography/mass spectrometry. Concentrations of target analytes were in agreement with certified values. Target analyte EFs in reference materials were measured precisely (<2% relative standard deviation), indicating the utility of SRM in quality assurance/control methodologies for analyses of chiral compounds in environmental samples. Measured EFs were also in agreement with previously published analyses of similar samples, indicating that similar enantioselective processes were taking place in these environmental matrices.     

Consistency of ozone and nitrogen oxides standards at tropospherically relevant mixing ratios

The absolute accuracy and long-term precision of atmospheric measurements hinge on the quality of the instrumentation and calibration standards. To assess the consistency of the ozone (O3) and nitrogen oxides (NO(x)) standards maintained at the National Institute of Standards and Technology (NIST), these standards were compared through the gas-phase titration of O3 with nitric oxide (NO). NO and O3 were monitored using chemiluminescence and UV absorption, respectively. Nitrogen dioxide (NO2) was monitored directly by laser-induced fluorescence and indirectly by catalytic conversion to NO, followed by chemiluminescence. The observed equivalent loss of both NO and O3 and the formation of NO2 in these experiments was within 1% on average over the range of 40-200 nmol mol(-1) of NO in excess O3, indicating that these instruments, when calibrated with the NIST O3 and NO standards and the NO2 permeation calibration system, are consistent to within 1% at tropospherically relevant mixing ratios of O3. Experiments conducted at higher initial NO mixing ratios or in excess NO are not in as good agreement. The largest discrepancies are associated with the chemiluminescence measurements. These results indicate the presence of systematic biases under these specific conditions. Prospects for improving these experiments are discussed.     

Linking chemical elements in forest floor humus (Oh-horizon) in the Czech Republic to contamination sources

While terrestrial moss and other plants are frequently used for environmental mapping and monitoring projects, data on the regional geochemistry of humus are scarce. Humus, however, has a much larger life span than any plant material. It can be seen as the “environmental memory” of an area for at least the last 60-100 years. Here concentrations of 39 elements determined by ICP-MS and ICP AES, pH and ash content are presented for 259 samples of forest floor humus collected at an average sample density of 1 site/300 km² in the Czech Republic. The scale of anomalies linked to known contamination sources (e.g., lignite mining and burning, metallurgical industry, coal fired power plants, metal smelters) is documented and discussed versus natural processes influencing humus quality. Most maps indicate a local impact from individual contamination sources: often more detailed sampling than used here would be needed to differentiate between likely sources.     

A Test Reference Year (TRY) approach to gas dispersion in the atmosphere

For environmental analysis such as the dispersion of pollutants in the atmosphere, it is essential to have meteorological data that are relevant for a long period. In this paper, we explore the possibility of using an environmental Test Reference Year (TRY), i.e., a set of real, contemporaneous and hourly meteorological variables, 'extracted' from a hourly series of at least 10 years, for modelling pollutant dispersion in the atmosphere. The classical approach, based on a statistical data set, implies the loss of important information such as the real correlation between the different meteorological variables, and this implies crude approximation in the simulation results. We compare the simulation results with the long hourly 10 years data set (which can be considered a 'brute force' approach, since it requires a huge amount of data and time processing, but it is here considered the most severe benchmark) and with the statistical data set commonly used. It is shown that the results obtained using the TRY have a good agreement with the ones obtained with the simulation of the 10 years and they are also much better than those obtained using the statistical data set.     

Large variation in lipid content, SigmaPCB and delta13C within individual Atlantic salmon (Salmo salar)

Many studies that investigate pollutant levels, or use stable isotope ratios to define trophic level or animal origin, use different standard ways of sampling (dorsal, whole filet or whole body samples). This study shows that lipid content, SigmaPCB and delta(13)C display large differences within muscle samples taken from a single Atlantic salmon. Lipid- and PCB-content was lowest in tail muscles, intermediate in anterior-dorsal muscles and highest in the stomach (abdominal) muscle area. Stable isotopes of carbon (delta(13)C) showed a lipid accumulation in the stomach muscle area and a depletion in tail muscles. We conclude that it is important to choose an appropriate sample location within an animal based on what processes are to be studied. Care should be taken when attributing persistent pollutant levels or stable isotope data to specific environmental processes before controlling for within-animal variation in these variables.     

Quantification of hourly variability in NO(x) emissions for baseload coal-fired power plants

The objectives of this paper are to (1) quantify variability in hourly utility oxides of nitrogen (NO(x)) emission factors, activity factors, and total emissions; (2) investigate the autocorrelation structure and evaluate cyclic effects at short and long scales of the time series of total hourly emissions; (3) compare emissions for the ozone (O3) season versus the entire year to identify seasonal differences, if any; and (4) evaluate interannual variability. Continuous emissions monitoring data were analyzed for 1995 and 1998 for 32 units from nine baseload power plants in the Charlotte, NC, airshed. Unit emissions have a strong 24-hr cycle attributable primarily to the capacity factor. Typical ranges of the coefficient of variation for emissions at a given hour of the day were from 0.2 to 0.45. Little difference was found when comparing weekend emissions with the entire week or when comparing the O3 season with the entire year. There were substantial differences in the mean and standard deviation of emissions when comparing 1995 and 1998 data, indicative of the effect of retrofits of control technology during the intervening time. The wide range of variability and its autocorrelation should be accounted for when developing probabilistic utility emission inventories for analysis of near-term future episodes.     

Chiral signature of venlafaxine as a marker of biological attenuation processes

The chiral signature of the antidepressant venlafaxine was used in this study to gain insight into biological attenuation processes and to differentiate abiotic and biotic transformation processes in water. Laboratory scale experiments revealed that sorption and phototransformation processes were not enantioselective while venlafaxine was enantioselectively biotransformed into O-desmethylvenlafaxine. The enantiomeric fraction (EF) variations of venlafaxine appeared to be proportional to its microbial fractional conversion. Enantioselective biotransformation of venlafaxine was also investigated in a eutrophic French river. Venlafaxine was found to be racemic at the output of the main wastewater treatment plant discharging into the river, independently of the sampling date during the year. An analysis of EF variations might provide evidence of biodegradation along a 30 km river stretch.     

Risk assessment of heavy metals in soil of Tongnan District (Southwest China): evidence from multiple indices with high-spatial-resolution sampling

Assessment of heavy metal (HM) pollution in soil is critical for human health, ecological remediation, and soil conservation. In this study, statistical analyses and geochemical approaches such as enrichment factor (EF), the index of geoaccumulation (Igeo), and potential ecological risk index (RI) were used for characterization and risk assessment of soil HMs through a high-spatial-resolution 385 samples from Tongnan District, an important agricultural practice area in Chongqing Municipality in Southwest China. Igeo and EF indicated that Hg and Cd could be considered as low and moderate polluted, respectively, and others HMs were not a major concern. Comprehensive ecological risk information further demonstrated that the HMs have caused a moderate risk. Principal component analysis (PCA) extracted two principal components (PCs) with eigenvalue >1 explaining about 66.1% of the total variance in the HM data sets, demonstrating major source of anthropogenic activity, phosphate fertilizers, vehicle, and pesticides. These multi-index methods have the capacity of HM assessment in soil, which are useful for soil conservation and ecological remediation.