The influence on partial order ranking from input parameter uncertainty. Definition of a robustness parameter

The method of partial order ranking has been used within the environmental area for a variety of purposes as an attractive way of handling complex information. However, the environmental data are often associated with a significant degree of uncertainty. In this investigation the general nature of the influence from data uncertainty on the partial order ranking is analyzed. A Monte Carlo type analysis is performed in which a series of randomly formed data are used to test the influence of data uncertainty. The partial order ranking is interpreted, where the results are transferred to a one-dimensional ranking scale taking into account that not all elements are ranked with the same certainty. A simple general robustness parameter (E) in form of the expected number of comparisons for each ranking element is defined and correlated to the uncertainty analysis results. A simple equation relates E to the number of elements and the number of parameters, respectively. The magnitude of the ranking uncertainty is shown to increase rapidly when the E value decreases below 4-5 comparisons per element. When the E value exceeds 5 the ranking uncertainty becomes nearly constant and independent on the actual E value.     

The dualistic approach of FCA: a further insight into Ontario Lake sediments

The investigation of object-by-attribute matrices is very common in statistics and data analysis with the aim of uncovering every possible relationship among objects and/or attributes. Formal Concept Analysis (FCA) is a method, which stems directly from partial order and lattice theory, which provides an efficient tool to symmetrically uncover linkages among objects and attributes whenever a relation stands among the two sets. It provides efficacious graphical representation and computes association rules between attributes, thus helping in the detection of possible synergism or antagonism of attributes. In this paper, FCA potentialities are discussed and described by means of a case study already investigated by other partial order techniques: the case of Lake Ontario sediment samples. Data derive from a ‘test battery’ for a simultaneous analysis of degradation of Lake Ontario samples, which are basically of two typologies: hygienic and toxicity tests. A multi-valued approach is adopted to cope with the ordinal feature of data. Results highlight interesting interaction among hygienic compounds and a synergism between the two toxicity tests.     

A comparison of numerical solutions of partial differential equations with probabilistic and possibilistic parameters for the quantification of uncertainty in subsurface solute transport

Traditionally, uncertainty in parameters are represented as probabilistic distributions and incorporated into groundwater flow and contaminant transport models. With the advent of newer uncertainty theories, it is now understood that stochastic methods cannot properly represent non random uncertainties. In the groundwater flow and contaminant transport equations, uncertainty in some parameters may be random, whereas those of others may be non random. The objective of this paper is to develop a fuzzy-stochastic partial differential equation (FSPDE) model to simulate conditions where both random and non random uncertainties are involved in groundwater flow and solute transport. Three potential solution techniques namely, (a) transforming a probability distribution to a possibility distribution (Method I) then a FSPDE becomes a fuzzy partial differential equation (FPDE), (b) transforming a possibility distribution to a probability distribution (Method II) and then a FSPDE becomes a stochastic partial differential equation (SPDE), and (c) the combination of Monte Carlo methods and FPDE solution techniques (Method III) are proposed and compared. The effects of these three methods on the predictive results are investigated by using two case studies. The results show that the predictions obtained from Method II is a specific case of that got from Method I. When an exact probabilistic result is needed, Method II is suggested. As the loss or gain of information during a probability–possibility (or vice versa) transformation cannot be quantified, their influences on the predictive results is not known. Thus, Method III should probably be preferred for risk assessments.     

Evaluation of a novel high throughput screening tool for relative emissions of industrial chemicals used in chemical products

Tens of thousands of chemicals are currently marketed worldwide, but only a small number of these compounds has been measured in effluents or the environment to date. The need for screening methodologies to select candidates for environmental monitoring is therefore significant. To meet this need, the Swedish Chemicals Agency developed the Exposure Index (EI), a model for ranking emissions to a number of environmental matrices based on chemical quantity used and use pattern. Here we evaluate the EI. Data on measured concentrations of organic chemicals in sewage treatment plants, one of the recipients considered in the EI model, were compiled from the literature, and the correlation between predicted emission levels and observed concentrations was assessed by linear regression analysis. The adequacy of the parameters employed in the EI was further explored by calibration of the model to measured concentrations. The EI was found to be of limited use for ranking contaminant levels in STPs; the r² values for the regressions between predicted and observed values ranged from 0.02 (p = 0.243) to 0.14 (p = 0.007) depending on the dataset. The calibrated version of the model produced only slightly better predictions although it was fitted to the experimental data. However, the model is a valuable first step in developing a high throughput screening tool for organic contaminants, and there is potential for improving the EI algorithm.     

Indicators for persistence and long-range transport potential as derived from multicompartment chemistry-transport modelling

Total environmental and compartmental residence times as a measure for persistence as well as indicators for long-range transport potential (LRTP) have been derived from global geo-referenced modelling and LRTP is characterized in two geographic directions for the first time. A dynamic multicompartment chemistry-transport model (MCTM) was used to study the fate of the insecticides DDT and alpha-hexachlorocyclohexane (alpha-HCH) during the first 2 years upon entry. The indicators for LRTP were defined such as to address the tendencies of substance distributions to migrate ('plume displacement', PD) and to spread into remote areas ('spatial spreading', SS). The indicators deliver values as function of time upon entry. With the aim to address the effect of location of entry on environmental fate, scenarios of emission from the territories of seven countries were studied. It was found that the effect of location of entry on the spatial scale of countries (400-4000 km) is significant for the compartmental distribution and the inter-compartmental mass exchange fluxes (e.g., number of atmospheric cycles, 'hops'). Location of entry introduces uncertainties in the order of a factor of 5 for the total environmental residence time, tau(overall), and a factor of 5-20 for PD and SS. For the 2nd year upon entry into the environment, tau(overall)=317-1527 days are predicted for DDT and 101-463 days for alpha-HCH. The influence of location of entry does affect the substance ranking, i.e. we cannot simply state that DDT is more persistent than alpha-HCH, but for one scenario studied, application in China, the opposite is predicted. Precipitation patterns proved to be significant, besides other climate parameters, for atmospheric residence time. Integration of the location of entry in chemicals risk assessments is therefore recommended. In general, persistence and some indicators for LRTP, pertinent to their definition, refer to the fate of a large fraction, e.g., 63% (=1-1/e) or 90%, but not the total substance burden. The choice of this fraction may have the consequence of a normative step which defines the spatial and temporal extensions of a related chemicals risk assessment and may affect substance ranking.     

Heavy-duty,off-road diesel engine low-load particle number emissions and particle control

Exhaust gas particle and ion size distributions were measured from an off-road diesel engine complying with the European Stage IIIB emission standard. The measurements were performed at idling and low load conditions on an engine dynamometer. Nucleation-mode particles dominated the diesel exhaust particle number emissions at idle load. The nonvolatile nucleation-mode geometric mean diameter was detected at 10 nm or below. The nonvolatile nucleation-mode charge state implied that it has evolved through a highly ionizing environment before emission from the engine. The determined charging probabilities were 10.0 ± 2.2% for negative and 8.0 ± 2.0% for positive polarity particles. The nonvolatile nucleation particle concentration and size was also shown to be dependent on the lubricant oil composition. The particle emissions were efficiently controlled with a partial filter or with partial filter + selective catalytic reduction (SCR) combination. The particle number removal efficiencies of the aftertreatment systems were over 95% for wet total particle number (>3nm) and over 85% for dry particle total number. Nevertheless, the aftertreatment systems’ efficiencies were around 50% for the soot-mode particles. The low-load nonvolatile nucleation particle emissions were also dependent on the engine load, speed, and fuel injection pressure. The low load particle number emissions followed the soot-core trade-off, similar to medium or high operating loads.

Implications:Idling and low-load diesel engine exhaust emissions affect harmfully the ambient air quality. The low-load particle number emissions are here shown to peak in the 10-nm size range for a modern off-road engine. The particles are electrically charged and nonvolatile and they originate from the combustion process. Tailpipe particle control by open channel filter can remove more than 85% of the nonvolatile 10-nm particles and about 50% of the soot-mode particles, while the fuel injection pressure increase can lead to particle number increase. The study provides a new viewpoint for low-load particle emissions and control.     

Modeling of ozone reactions on aircraft-related soot in the upper troposphere and lower stratosphere

Several studies in modeling atmospheric processes have suggested that heterogeneous chemistry on soot emitted from high altitude aircraft could affect stratospheric ozone depletion. However, these modeling studies were limited because they did not adequately consider the decrease in reaction probability with time as the surface of the soot becomes “poisoned” by its interactions with various gases. Here we extend UIUC's two-dimensional chemical-transport model to investigate possible effects of heterogeneous reactions of ozone on aircraft-generated carbon particles, including a treatment of soot poisoning in the model. We generally follow literature recommendations for ozone uptake probabilities and determine the available active sites on soot given partial pressures of the reactants, temperature, and time since soot emission in order to investigate ozone decrease. The regeneration of soot active sites is also taken into account in this study. We find that, even if active sites on soot surfaces are regenerated, upper troposphere and lower stratosphere ozone losses on aircraft emitted soot occurring through heterogeneous reactions are insignificant once poisoning effects are considered.     

Conditions d'acceptation ou de rejet des valeurs obtenues apres denombrement de virus ou bacteries sur milieux de culture solides

Enumeration of viruses or bacteria on solid culture media does not ever give statistically acceptable results. When counting is impossible, we must do it again. For accepting or not the counting, the authors established some probability Tables (95% and 99%) according to microbial densities.     

Backward location and travel time probabilities for a decaying contaminant in an aquifer

Backward location and travel time probabilities can be used to determine the prior position of contamination in an aquifer. These probabilities, which are related to adjoint states of concentration, can be used to improve characterization of known sources of groundwater contamination, to identify previously unknown contamination sources, and to delineate capture zones. The first contribution of this paper is to extend the adjoint model to the case of a decaying solute (first-order decay), and to describe two different interpretations of backward probabilities. The conventional interpretation accounts for the probability that a contaminant particle could decay before reaching the detection location. The other interpretation is conditioned on the fact that the detected contaminant particle actually reached the detection location, despite this possibility of decay. In either case, travel time probabilities are skewed toward earlier travel times, relative to a conservative solute. The second contribution of this paper is to verify the load term for a monitoring well observation. We provide examples using one-dimensional models and hypothetical aquifers. We employ an infinite domain in order to verify the monitoring well load. This new but simple one-dimensional adjoint solution can also be used to verify higher-dimensional numerical models of backward location and travel time probabilities. We employ a semi-infinite domain to illustrate the effect of decay on backward models of pumping well probabilistic capture zones. Decay causes the capture zones to fall closer to the well.     

Detecting Trends Using Spearman's Rank Correlation Coefficient

Spearman's rank correlation coefficient is a useful tool for exploratory data analysis in environmental forensic investigations. In this application it is used to detect monotonic trends in chemical concentration with time or space.     

Detecting Trends Using Spearman's Rank Correlation Coefficient

Spearman's rank correlation coefficient is a useful tool for exploratory data analysis in environmental forensic investigations. In this application it is used to detect monotonic trends in chemical concentration with time or space.     

Ranking tributaries for setting remediation priorities in a TMDL context

The San Joaquin River (SJR) in the Central Valley of California has been designated an impaired waterbody based on its loss of fisheries-related beneficial uses and the river is now subject to regulation under total maximum daily load (TMDL) rules. For impaired waterbodies, numeric standards alone may not be sufficient to establish remediation priorities and priorities must be established by comparing drainages to each other. Data collected as part of regional water quality (WQ) studies in the SJR Valley were not normally distributed, so nonparametric methods based on ranking were used to compare the WQ of individual tributaries and drainages. Normalized rank means (NRMs) were calculated from ranked data and NRMs were mapped to identify priority drainages for WQ improvement activities. NRMs for individual parameters were combined into indexes that are useful for examining the relative importance of different drainages for multiple parameters simultaneously. Indexes were developed for eutrophication and overall WQ. This ranking approach is being proposed as an easily understood, transparent, and scientifically rigorous method to assess the relative WQ impact of individual drainages and set watershed remediation priorities.     

Probability analyses of combining background concentrations with model-predicted concentrations

In order to calculate total concentrations for comparison to ambient air quality standards, monitored background concentrations are often combined with model predicted concentrations. Models have low skill in predicting the locations or time series of observed concentrations. Further, adding fixed points on the probability distributions of monitored and predicted concentrations is very conservative and not mathematically correct. Simply adding the 99th percentile predicted to the 99th percentile background will not yield the 99th percentile of the combined distributions. Instead, an appropriate distribution can be created by calculating all possible pairwise combinations of the 1-hr daily maximum observed background and daily maximum predicted concentration, from which a 99th percentile total value can be obtained. This paper reviews some techniques commonly used for determining background concentrations and combining modeled and background concentrations. The paper proposes an approach to determine the joint probabilities of occurrence of modeled and background concentrations. The pairwise combinations approach yields a more realistic prediction of total concentrations than the U.S. Environmental Protection Agency's (EPA) guidance approach and agrees with the probabilistic form of the National Ambient Air Quality Standards.

Implications: EPA's current approaches to determining background concentrations for compliance modeling purposes often lead to “double counting” of background concentrations and actual plume impacts and thus lead to overpredictions of total impacts. Further, the current Tier 1 approach of simply adding the top ends of the background and model predicted concentrations (e.g., adding the 99th percentiles of these distributions together) results in design value concentrations at probabilities in excess of the form of the National Ambient Air Quality Standards.     

On the Evaluation of Predictions from a Gaussian Plume Model

The performance of a CRSTER equivalent Gaussian plume model (CEQM) is examined using data from the EPRI Plume Model Validation study at the Klncaid, Illinois site. Four-way comparisons are made on the ordered statistics or the cumulative frequency distribution (CFD) of maximum hourly observed and predicted concentrations. Using the uniform random distribution and the lognormal random distribution as simple predictive schemes without any physical context, it Is found that the CEQM predicts a concentration CFD which matches the observed CFD significantly closer than the CFD predicted by the uniform random distribution. The two-parameter lognormal random distribution predicts the concentration CFD better than the CEQM over all concentration ranges; however, the CEQM fits the upper range of the concentration distribution better than the lognormal random distribution,, despite the fact that the predictions are generated using dispersion conditions entirely different from those of the observations. The nature of this ergodicity of distribution is probed by exercising CEQM using randomized input based on the observed frequency distributions of the Input parameters instead of feeding the hour-by-hour model input matched by time into CEQM as is customarily done. The exercise of the model by uncoupling the time linkage in model Input has no systematic effect on the predicted cumulative frequency distribution of concentrations. Only at the highest concentration range (99.5% or higher) do the two sets of predictions begin to diverge.     

Design of Adsorption Equipment in Air Pollution Control

The purpose of this paper is to provide a helpful tool for the design of adsorption equipment, recognizing in particular the recent, more stringent regulations on air pollution. This work is based on an earlier paper by Hougen and Marshall,¹ who developed therein an analytical adsorption model. Under certain assumptions, especially that of linear adsorption equilibrium, it is possible to express the results in the form of convenient usable charts. Although more sophisticated models² have recently been developed, the numerical effort involved in solving the associated partial differential equations is such that practical application is often questionable.     

A copula-based chance-constrained waste management planning method: An application to the city of Regina,Saskatchewan, Canada

This study proposes a copula-based chance-constrained waste management planning (CCWMP) method. The method can effectively reflect the interactions between random parameters of the waste management planning systems, and thus can help analyze the influences of their interactions on the entire systems. In particular, a joint distribution function is established using preestimated marginal distributions of random variables and an optimal copula selected from widely used Gaussian, Student’s t, Clayton, Frank, Gumbel, and Ali-Mikhail-Haq copulas. Then a set of joint probabilistic constraints in the chance-constrained programming problems is converted into individual probabilistic constraints using the joint distribution function. Further, this method is applied to residential solid waste management in the city of Regina in Canada for demonstrating its applicability. Nine scenarios based on different joint and marginal probability levels are considered within a multiperiod and multizone context to effectively reflect dynamic, uncertain, and interactive characteristics of the solid waste management systems in the city. The results provide many decision alternatives under these scenarios, including cost-effective and environmentally friendly decision schemes. Moreover, the results indicate that even though the effect of the joint probability levels on the system costs is more significant than that of the marginal probability levels, the effect of marginal probability levels is notable, and there exists a trade-off between the total system cost and the constraint-violation risk. Therefore, the results obtained from the present study would be useful to support the city’s long-term solid waste management planning and formulate local policies and regulation concerning the city’s waste generation and management.Implications: The CCWMP method not only can solve chance-constrained problems with unknown probability distributions of random variables in the right-hand sides of constraints, but also can effectively reflect the interactions between the random parameters and thus help analyze the influences of their interactions on the entire systems. The results obtained through applying this method to the city of Regina in Canada can provide many decision alternatives under different joint probability levels and marginal probability levels, and would be useful to support the city’s long-term solid waste management planning.