Alan M. Dunker

The decoupled direct method for calculating sensitivity coefficients in chemical kinetics

A version of the direct method for calculating first‐order sensitivity coefficients is extended to nonlinear, time‐dependent models defined by stiff differential equations. In this approach the auxiliary equations for the sensitivity coefficients are solved separately from the model equations. Accuracy and stability are maintained by using exactly the same time steps and numerical approximations in calculating the sensitivities as are used in calculating the model solution. The decoupling procedure also greatly increases the efficiency of the method by taking advantage of the fact that the auxiliary equations for different sensitivity coefficients are quite similar. The decoupled direct method is applied to stiff chemical mechanisms for the oxidation of hydrocarbons in the atmosphere, the pyrolysis of ethane, and the oxidation of formaldehyde in the presence of carbon monoxide. Sensitivity coefficients are also calculated for the three mechanisms by a method employing Green’s function and by actually vary...

Efficient calculation of sensitivity coefficients for complex atmospheric models

Abstract Sensitivity coefficients describe how the solution to a set of equations depends on the parameters in the problem. We discuss here the direct method of calculating these coefficients for atmospheric models based on nonlinear, partial differential equations. A detailed analysis indicates for which models the method will be efficient and shows that calculating several sensitivity coefficients simultaneously improves the efficiency. A technique is given to derive an algorithm for implementing the direct method from the algorithm for solving the governing equations of the model. As a realistic test of the method, we have computed first-order sensitivity coefficients for a photochemical model describing the transport and chemical reactions of pollutants. In this example the direct method has a limiting speed six times faster than the indirect method.

Modeling weekday/weekend ozone differences in the Los Angeles region for 1997

Abstract Numerous studies of ambient ozone (O3) in the Los Angeles (LA) area have found both increases and decreases in elevated O3 levels on weekends, depending on location and year. Since the mid-1990s, average daily maximum O3 levels have been higher on weekends than on week-days throughout most of the area. We used the Comprehensive Air-Quality Model with extensions to investigate causes of weekday/weekend O3 differences in the LA area for August 3–7, 1997, from the Southern California Ozone Study. Weekday/weekend emission changes were estimated, because explicit weekend inventories are not yet available from regulatory agencies. Changes to on-road motor vehicle (MV) emissions were derived from observed weekday/weekend traffic differences. The estimated changes in MV emissions of nitrogen oxides (NOx) were a 5% increase on Friday, a 27% decrease on Saturday, and a 37% decrease on Sunday, relative to Monday–Thursday levels. The corresponding changes in MV volatile organic carbon (VOC) emissions were an 8% increase on Friday, an 8% decrease on Saturday, and a 15% decrease on Sunday. Modeling these MV emissions changes explained the observed weekend O3 effect very well. Furthermore, changes to the mass of MV NOx emissions were the main contributor to O3 differences rather than changes to the timing of MV emissions. Ozone increases on weekends were caused by NOx emission decreases, because O3 formation is strongly VOC-limited throughout most of the LA area.

Ozone Air Quality over North America: Part II—An Analysis of Trend Detection and Attribution Techniques

ABSTRACT Assessment of regulatory programs aimed at improving ambient O3 air quality is of considerable interest to the scientific community and to policymakers. Trend detection, the identification of statistically significant long-term changes, and attribution, linking change to specific clima-tological and anthropogenic forcings, are instrumental to this assessment. Detection and attribution are difficult because changes in pollutant concentrations of interest to policymakers may be much smaller than natural variations due to weather and climate. In addition, there are considerable differences in reported trends seemingly based on similar statistical methods and databases. Differences arise from the variety of techniques used to reduce nontrend variation in time series, including mitigating the effects of meteorology and the variety of metrics used to track changes. In this paper, we review the trend assessment techniques being used in the air pollution field and discuss their strengths and limitations in discerning and attributing changes in O3 to emission control policies.

The reduction and parameterization of chemical mechanisms for inclusion in atmospheric reaction-transport models

Abstract A new approach is described for simplifying and parameterizing a photochemical mechanism so that the effects of nonlinear reactions can be simulated with less computational effort in complex models. The concentrations at the end of a fixed time interval Δt are expanded as functions of the initial concentrations. A number of such expansions are made to cover the concentration ranges of interest. The coefficients in the expansions are calculated by solving the sensitivity equations and then tabulated for later use. Given arbitrary initial concentrations, one extracts the appropriate coefficients from the table and evaluates the expansion to determine the concentrations a time Δt later. The procedure has been applied to a photochemical mechanism for oxidant formation in urban areas. An examination of sensitivity coefficients showed that less than half the number of species in the mechanism need be considered in the parameterization. Results obtained from the parameterization for 15-h simulations of the chemistry alone have been compared to results obtained by solving the rate equations with a standard technique. The concentrations above 1 ppb are generally accurate to 10% and the computational effort is reduced by over two orders of magnitude.

Ozone air quality over North America: part I--a review of reported trends.

ABSTRACT Ozone and precursor trends can be used to measure the effectiveness of regulatory programs that have been implemented. In this paper, we review trends in the concentrations of O3, NOx, and HCs over North America that have been reported in the literature. Although most existing trend studies are confounded by meteorological variability, both the raw data trends and the trends adjusted for meteorology collectively indicate a general decreasing trend in O concentrations in most areas of the United States during 1985-1996. In Canada, mean daily maximum 1-hr O3 concentrations at urban sites show mixed trends with a majority of sites showing an increase from 1980 to 1993. Mean daily maximum 1-hr O3 at most regionally representative Canadian sites appears to decrease from 1985 to 1993 or shows no significant change. There are far fewer data and analyses of NOx and HC trends. Available studies covering various ranges of years indicate decreases in ambient NOx and HC concentrations in Los Angeles, CA, decreases in HC concentrations in northeastern U.S. cities, and decreases in NO concentrations in Canadian cities. Two key needs are long-term HC and NOx measurements, particularly at rural sites, and a systematic comparison of trend detection techniques on a reference data set.

A comparison of chemical mechanisms used in atmospheric models

Four chemical mechanisms used in current photochemical models are compared in detail. Isopleths of the maximum hourly average concentrations of O3, NO2 and PAN were constructed for the EPA, FSM, CBII and ELSTAR mechanisms in atmospheric simulations employing the same meteorological conditions and representation of the pollutant mix for all mechanisms. The four mechanisms differ substantially in their predictions of maximum hourly average O3 and PAN concentrations. However, the mechanisms agree well in their NO2, predictions, and all show NOx inhibition of O3 formation. Using the Empirical Kinetic Modeling Approach, the NMOC (nonmethane organic compounds) reductions necessary to meet the O3 standard were determined for various O3, design values and NMOC/NOx ratios. These calculated NMOC reductions are very sensitive to the chemical mechanism employed, the ELSTAR mechanism requiring the largest NMOC reductions and the EPA and FSM mechanisms the smallest. Simulations of two smog chamber experiments used in developing the mechanisms show that some of the differences between the predictions of the mechanisms are due to different assumptions on aldehyde photolysis rates and radical sources in the chambers.

Effect of nitrogen oxides (NOx) emission rates on smog formation in the California South Coast Air Basin.

The effect of changes in NO/sub x/ emissions on downwind regions of the California south coast air basin was investigated with th elstar trajectory model. Smog formation was simulated in air parcels which originated near Los Angeles in the early morning, passes through the San Gabriel Valley, and arrived at or near San Bernardino in the mid to late afternoon on days of moderate to high ozone. With nonvehicular emissions held fixed at the 1973 levels, the planned reduction in motor vehicle emissions is predicted to result in reduced atmospheric concentrations of CO, NO, NO/sub 2/, O/sub 3/, pan, and HNO/sub 3/ along the air parcel trajectories. However, when the hydrocarbon emissions are held fixed at a projected future level, a decrease in NO/sub x/ emissions will result in a decrease in NO/sub 2/ concentrations, but an increase in O/sub 3/ and pan concentrations at all positions along the trajectories.

The response of an atmospheric reaction-transport model to changes in input functions

Abstract We define auxiliary parameters which scale the input functions required by an atmospheric model and expand the output concentration of each species as a Taylor series in these parameters. The response of the model to changes in a scaling parameter is defined to be linear if the quadratic and higher order terms in the Taylor series vanish identically or are small. Using a model with nonlinear chemical reactions simulating Los Angeles, we investigated numerically the magnitude of the constant, linear, and quadratic terms in the Taylor series for scalings of the initial conditions, emission rates, and boundary conditions. The input functions for hydrocarbon, NO, and NO 2 were scaled individually and in pairs. For very large changes in these input functions the model responds nonlinearly. However, the quadratic terms in the Taylor series are negligible and the model responds linearly if these input functions are changed by less than 20–30% of their values in the base case.

Sensitivity of urban airshed model results for test fuels to uncertainties in light-duty vehicle and biogenic emissions and alternative chemical mechanisms—Auto/oil air quality improvement research program

Abstract Three sources of uncertainty in the air quality modeling performed for the Auto/Oil Air Quality Improvement: Research Program, Phase I, were investigated to assess their impact on predicted ozone for test fuels in Los Angeles in year 2010. First, quadrupling the estimated total organic gas (TOG) and tripling the CO emissions from light-duty gasoline vehicles in the air quality model increases the predicted peak ozone, as expected. The percent increase in peak ozone for the test fuels, about 25% of total ozone, is essentially the same as the percent increase in TOG emissions, about 25% of the total emissions from all sources. However, there is no important effect on the ranking of the test fuels from lowest to highest in predicted ozone formation. Second, replacing the original biogenic emission inventory with an alternative inventory having substantially lower biogenic emissions reduces the predicted peak ozone. The percent decrease in peak ozone, about 6% of total ozone, is considerably less than the percent decrease in TOG emissions, about 34% of total emissions. Fuel rankings are unchanged except for a reversal of two test gasolines in the ranking based on peak ozone. However, this reversal is not found in fuel rankings based on other measures of ozone formation. Third, replacing the Carbon Bond Mechanism version IV (CBM-IV) in the air quality model with an alternative representation of atmospheric chemistry, the Statewide Air Pollution Research Center (SAPRC) mechanism, increases the peak ozone by about 9%. There are also important changes in fuel rankings. For one research test gasoline, the contribution of light-duty gasoline vehicles to ozone is similar with both chemical mechanisms, but for another test gasoline that gives the lowest ozone with the CBM-IV, the contribution of light-duty gasoline vehicles to ozone is substantially higher with the SAPRC mechanism. With the CBM-IV mechanism, the most promising of the test gasolines studied has lower predicted ozone than any of the cases representing use of methanol fuels in prototype, flexible/variable fuel vehicles. With the SAPRC mechanism, the most promising test gasoline studied has lower predicted ozone than one methanol case and higher ozone than the other methanol case. These changes in fuel rankings are probably due to known differences in the reactivity of toluene and formaldehyde in the two mechanisms.