Gregory J. McRae

An efficient method for parametric uncertainty analysis of numerical geophysical models

A new method for parametric uncertainty analysis of numerical geophysical models is presented. It approximates model response surfaces, which are functions of model input parameters, using orthogonal polynomials, whose weighting functions are the probabilistic density functions (PDFs) of the input uncertain parameters. This approach has been applied to the uncertainty analysis of an analytical model of the direct radiative forcing by anthropogenic sulfate aerosols which has nine uncertain parameters. This method is shown to generate PDFs of the radiative forcing which are very similar to the exact analytical PDF. Compared with the Monte Carlo method for this problem, the new method is a factor of 25 to 60 times faster, depending on the error tolerance, and exhibits an exponential decrease of error with increasing order of the approximation.

A Comparison of Interpolation Methods for Sparse Data : Application to Wind and Concentration Fields

In order to produce gridded fields of pollutant concentration data and surface wind data for use in an air quality model, a number of techniques for interpolating sparse data values are compared. The techniques are compared using three data sets. One is an idealized concentration distribution to which the exact solution is known, the second is a potential flow field, while the third consists of surface ozone concentrations measured in the Los Angeles Basin on a particular day. The results of the study indicate that fitting a second-degree polynomial to each subregion (triangle) in the plane with each data point weighted according to its distance from the subregion provides a good compromise between accuracy and computational cost.

Incorporation of parametric uncertainty into complex kinetic mechanisms: Application to hydrogen oxidation in supercritical water

Abstract In this study, uncertainty analysis is applied to a supercritical water hydrogen oxidation mechanism to determine the effect of uncertainties in reaction rate constants and species thermochemistry on predicted species concentrations. Forward rate constants and species thermochemistry are assumed to be the sole contributors to uncertainty in the reaction model with all other model parameters and inputs treated as deterministic quantities. The analysis is conducted by treating the model parameters as random variables, assigning each a suitable probability density function, and propagating the parametric uncertainties through to the predicted species concentrations. Uncertainty propagation is performed using traditional Monte Carlo (MC) simulation and a new, more computationally efficient, probabilistic collocation method called the Deterministic Equivalent Modeling Method (DEMM). Both methods predict virtually identical probability distributions for the resulting species concentrations as a function of time, with DEMM requiring approximately two orders of magnitude less computation time than the corresponding MC simulation. The results of both analyses show that there is considerable uncertainty in all predicted species concentrations. The predicted H 2 and O 2 concentrations vary ± 70% from their median values. Similarly, the HO 2 concentration ranges of +90 to −70% of its median, while the H 2 O 2 concentration varies by + 180 to − 80%. In addition, the DEMM methodology identified two key model parameters, the standard-state heat of formation of HO 2 radical and the forward rate constant for H 2 O 2 dissociation, as the largest contributors to the uncertainty in the predicted hydrogen and oxygen species concentrations. The analyses further show that the change in model predictions due to the inclusion of real-gas effects, which are potentially important for SCWO process modeling, is small relative to the uncertainty introduced by the model parameters themselves.

Source-receptor reconciliation of routine air monitoring data for trace metals: an emission inventory assisted approach

Inventory procedures for fine-particle trace-metals emissions are developed that assist aerosol source apportionment by receptor modeling techniques. It is shown how sparse routine air monitoring data sets on a very few trace elements can be used in chemical element balance calculations once emission inventory data have shown that a very few source signatures do complete a mass balance on those chemical elements that were measured. Methods developed are tested in the South Coast Air Basin of California for the year 1976, where it is shown that over 80% of the fine lead emissions comes from highway traffic, 81% of the nickel arises from fuel oil fly ash, and more than 90% of the iron and manganese comes from soil-like materials. With use of readily available trace element data from local and Federal monitoring networks, it is found that most monitoring sites are exposed to aerosol containing about 20% highway vehicle exhaust, 1-2% fuel oil fly ash, 20-50% soil dust or road dust, with sulfates and nitrates each present at about 15% of total mass.

An Objective Analysis Technique for Constructing Three-Dimensional Urban-Scale Wind Fields

An objective analysis procedure for generating mass-consistent, urban-scale three-dimensional wind fields is presented together with a comparison against existing techniques. The algorithm employs terrain following coordinates and variable vertical grid spacing. Initial estimates of the velocity field are developed by interpolating surface and upper level wind measurements. A local terrain adjustment technique, involving solution of the Poisson equation, is used to establish the horizontal components of the surface field. Vertical velocities are developed from successive solutions of the continuity equation followed by an iterative procedure which reduces anomalous divergence in the complete field. Major advantages of the procedure are that it is computationally efficient and allows boundary values to adjust in response to changes in the interior flow. The method has been successfully tested using field measurements and problems with known analytic solutions.

Cross road and mobile tunable infrared laser measurements of nitrous oxide emissions from motor vehicles

Abstract Context Abstract: Nitrous oxide (NO2) is a potent greenhouse gas whose atmospheric budget is poorly constrained. One known atmospheric source is the formation of N2O on three-way motor vehicle catalytic converters followed by emission with the exhaust. Previous estimates of the magnitude of this N2O source have varied widely. Two methods employing tunable infrared lasers to measure N2O/CO2 ratios from a large number of on-road motor vehicles have been developed. Both methods add support to lower estimates of N2O emissions from the US motor vehicle fleet, although significant uncertainty remains. Main Abstract: Two tunable infrared laser differential absorption spectroscopy (TILDAS) techniques have been used to measure the N2O emission levels of on-road motor vehicle exhausts. Cross road, open path laser measurements were used to assess N2O emissions from 1361 California catalyst equipped vehicles in November, 1996 yielding an emission ratio of (8.8±2.8)×10−5 N2O/CO2. A van mounted TILDAS sampling system making on-road N2O measurements in mixed traffic in June, 1998 in Manchester, New Hampshire yielded a mean N2O/CO2 ratio of (12.8±0.3)×10−5, based on correlated N2O and CO2 concentration peaks attributed to motor vehicle exhaust plumes. The correlation of N2O emissions with vehicle type, model year and NO emissions are presented for the California data set. It is found that the N2O emission distribution is highly skewed, with more than 50% of the emissions being contributed by 10% of the vehicles. Comparison of our results with those from four European tunnel studies reveals a wide range of derived N2O emission indices, with the most recent studies (including this study) finding lower values.

Parameterization of urban subgrid scale processes in global atmospheric chemistry models

We have derived a parameterization consisting of a set of analytical expressions that approximate the predictions by the California Institute of Technology - Carnegie-Mellon University (CIT) Urban Airshed Model for the net export to the environment (i.e., effective emissions) of several chemical species, as functions of 14 input parameters. For each species, effective emissions are a function of actual urban emissions of this and other species and of other urban domain properties such as meteorology. Effective emissions may be “aged” emissions of primary pollutants or actual production of secondary pollutants. To develop the parameterization we have applied the probabilistic collocation method, which uses the probability density functions of the inputs to generate a set of orthogonal polynomials. These polynomials are then used as the basis for a polynomial chaos expansion that approximates the actual response of the CIT model to its inputs. We assume that seasonal variations can be represented by sinusoidal functions. The parameterization provides a computationally very efficient simulation of the actual model behavior. We have compared the outputs of the parameterization with the outputs of the CIT model, and we conclude that it gives a quite good approximation for effective emissions, at least in the regions of highest probability of the input parameters. This parameterization is applicable to detailed uncertainty and sensitivity analyses and enables computationally efficient inclusion of urban-scale processes as subgrid scale phenomena in global-scale models.

Osmolyte controlled fibrillation kinetics of insulin: New insight into fibrillation using the preferential exclusion principle

Amyloid proteins are converted from their native‐fold to long β‐sheet‐rich fibrils in a typical sigmoidal time‐dependent protein aggregation curve. This reaction process from monomer or dimer to oligomer to nuclei and then to fibrils is the subject of intense study. The main results of this work are based on the use of a well‐studied model amyloid protein, insulin, which has been used in vitro by others. Nine osmolyte molecules, added during the protein aggregation process for the production of amyloid fibrils, slow‐down or speed up the process depending on the molecular structure of each osmolyte. Of these, all stabilizing osmolytes (sugars) slow down the aggregation process in the following order: tri > di > monosaccharides, whereas destabilizing osmolytes (urea, guanidium hydrochloride) speed up the aggregation process in a predictable way that fits the trend of all osmolytes. With respect to kinetics, we illustrate, by adapting our earlier reaction model to the insulin system, that the intermediates (trimers, tetramers, pentamers, etc.) are at very low concentrations and that nucleation is orders of magnitude slower than fibril growth. The results are then collated into a cogent explanation using the preferential exclusion and accumulation of osmolytes away from and at the protein surface during nucleation, respectively. Both the heat of solution and the neutral molecular surface area of the osmolytes correlate linearly with two fitting parameters of the kinetic rate model, that is, the lag time and the nucleation rate prior to fibril formation. These kinetic and thermodynamic results support the preferential exclusion model and the existence of oligomers including nuclei and larger structures that could induce toxicity.

An optimization model for photochemical air pollution control

One difficulty in developing effective ozone control strategies is to incorporate the complex and nonlinear relationship between photochemical pollutants and their precursors into a mathematical programming model. In this paper, we develop a locally linear approximation to the nonlinear relationship between photochemical pollutants and their precursors. We then develop a mathematical programming model for optimal control of photochemical pollutants. The model minimizes the net present value (NPV) of precursor emission control costs from various emission sources which, subject to meeting ambient air quality goals for different pollutants at different geographical locations over the planning time periods. At the end of this paper, we provide a case study examining photochemical smog occurring in Los Angeles. We discuss what data inputs are required for the air quality management model, the kind of outputs can be obtained from this model and policy implications of the model results.

A kinetic model unifying presynaptic short-term facilitation and depression

Short-term facilitation and depression refer to the increase and decrease of synaptic strength under repetitive stimuli within a timescale of milliseconds to seconds. This phenomenon has been attributed to primarily presynaptic mechanisms such as calcium-dependent transmitter release and presynaptic vesicle depletion. Previous modeling studies that aimed to integrate the complex short-term facilitation and short-term depression data derived from varying synapses have relied on computer simulation or abstract mathematical approaches. Here, we propose a unified theory of synaptic short-term plasticity based on realistic yet tractable and testable model descriptions of the underlying intracellular biochemical processes. Analysis of the model equations leads to a closed-form solution of the resonance frequency, a function of several critical biophysical parameters, as the single key indicator of the propensity for synaptic facilitation or depression under repetitive stimuli. This integrative model is supported by a broad range of transient and frequency response experimental data including those from facilitating, depressing or mixed-mode synapses. Specifically, the theory predicts that high calcium initial concentration and large gain of calcium action result in low resonance frequency and hence depressing behavior. In contrast, for synapses that are less sensitive to calcium or have higher recovery rate, resonance frequency becomes higher and thus facilitation prevails. The notion of resonance frequency therefore allows valuable quantitative parametric assessment of the contributions of various presynaptic mechanisms to the directionality of synaptic short-term plasticity. Thus, the model provides the reasons behind the switching behavior between facilitation and depression observed in experiments. New experiments are also suggested to control the short-term synaptic signal processing through adjusting the resonance frequency and bandwidth.