Adjoint Sensitivity Analysis of Air Pollution Problems

Exposure to airborne pollutants is associated with adverse health effects. One of the challenges of mitigation efforts is identifying emission sources that contribute the most to air pollution problems. Chemical transport models are used to elucidate relationships between emission sources and the resulting air quality. These models estimate ambient concentrations of airborne pollutants of interest over a user-specified gridded domain, given a description of relevant emissions and meteorological conditions. Sensitivity analysis in chemical transport models aims to quantify changes in air quality resulting from changes in model parameters such as emissions. There can be millions of such parameters, thus calling for the development and use of tools that are effective at calculating a large number of sensitivities. The adjoint sensitivity technique is a receptor-oriented approach that can be used to efficiently calculate sensitivities of selected air quality metrics to large numbers of model parameters.In this work, the adjoint of a chemical transport model is used to identify and map emission sources that influence air pollution at the air-basin scale and in selected urban sub-areas. Air quality metrics of interest are population-weighted concentrations of benzene, diesel black carbon (BC), formaldehyde, and ozone. Benzene and diesel BC are primary pollutants: they are directly emitted into the atmosphere. Ozone is a secondary pollutant, formed in the troposphere from photochemical reactions involving oxides of nitrogen (NOx) and volatile organic compounds (VOC). Formaldehyde is a mixed case: it is both directly emitted and formed photochemically in the atmosphere in significant quantities. Application of the adjoint method is illustrated using the San Francisco Bay area air basin as a case study. Air basin-wide versus local air pollution problems in five urban sub-areas are investigated. Summer- and winter-time conditions are investigated separately. An approach that combines finite difference and adjoint sensitivity techniques is used to calculate second-order sensitivities to emissions. This high-order information is used to investigate the effects of model non-linearities and uncertainties on first-order results.The chemical transport model is evaluated by comparing modeled concentrations to ground-based observations. The agreement is reasonable for daily average concentrations of benzene, BC, and formaldehyde at urban sites. Diurnal ozone concentration profiles are also found to be well represented by the model. The agreement is less satisfactory for other species such as CO, NO, and NO2, especially for winter conditions. These results underline the need to improve model performance for species other than ozone. A comparison of sensitivities calculated with the adjoint method versus finite difference sensitivities shows good agreement between the two methods. The largest discrepancies are generally associated with large sensitivities.The extent of upwind areas influencing primary pollutant concentrations in urban sub-areas is found to depend on location, on the pollutant's atmospheric lifetime, and on the time of year. A measure of the extent of these areas of influence is the relative contribution of local sources (i.e. sources located within the receptor sub-area under consideration) versus upwind sources. Contributions of local sources to benzene pollution range from 38-65% in summer to 56-71% in winter. These contributions are larger for diesel BC pollution due to the shorter atmospheric lifetime of black carbon, and range from 67-74% in summer to 62-85% in winter. Sensitivities to emissions are found to be larger in winter than in summer for both pollutants. This seasonal trend is attributed to less vigorous atmospheric transport and mixing during the winter months. In winter, benzene pollution is dominated by emissions occurring during the 6-9 am and 4-7 pm time periods. The most influential emission time frames are shifted toward midday for diesel BC. The relative importance of late afternoon emissions is reduced in summer for both pollutants.Population-weighted formaldehyde concentrations are found to be generally higher in summer than in winter. The opposite seasonal trend is observed for the sensitivities of these metrics to formaldehyde emissions. In other words, even though formaldehyde air pollution is worse in summer, reducing formaldehyde emissions has a greater impact in winter. In winter, 85-90% of the sensitivity to emissions is attributed to direct formaldehyde emissions. In summer, this contribution is smaller and more variable, ranging from 26 to 72% among the receptor areas investigated here. Higher relative contributions of secondary formation versus direct emissions are associated with receptors located farther away from heavily urbanized and emission-rich areas. In particular, the relative contribution of biogenic VOC emissions (15-41%) is largest for these receptors. Ethene and other alkenes are identified as the most influential anthropogenic precursors to secondary formaldehyde. Isoprene is found to be the most influential biogenic precursor. Sensitivities of formaldehyde air quality to NOx emissions are generally negative, but small in magnitude compared to sensitivities to alkene emissions. The magnitude of anthropogenic emissions of VOC other than formaldehyde is found to be a reasonable predictor of their influence on population-weighted formaldehyde concentrations at the air basin scale, but not on formaldehyde air quality within urban sub-areas. The magnitude of biogenic emissions is not a good predictor of their influence in either case. Formaldehyde emissions that have the greatest influence on formaldehyde air quality metrics occur in the morning around 8 am and in the late afternoon. In contrast, the influence of organic precursors is evenly distributed throughout most of the daytime hours.The spatial extent of areas influencing ozone air quality is larger than for metrics based on concentrations of primary pollutants. The locations of emissions that influence ozone at local receptors is however highly dependent on the receptor of interest. Sensitivity of ozone to NOx emissions is negative and in most cases larger in magnitude than the sensitivity to VOC emissions. No individual species strongly dominates ozone sensitivity to anthropogenic VOC, but sensitivities to emissions of highly reactive aromatic and alkane species are consistently twice as large as the sensitivities to emissions of other organic species. Biogenic emissions account for 22-32% of the overall sensitivity to VOC emissions. The analysis also suggests that Bay area emissions do not contribute much to high-ozone events within the air basin beyond the time frame of the day they are emitted.Second-order sensitivity analysis is conducted for summer-season air basin-wide formaldehyde and ozone air quality metrics. When non-linear effects are significant, their magnitude is large at locations where the magnitude of the underlying first-order sensitivity is also large. Sensitivities of ozone and formaldehyde air quality metrics to NOx emissions are found to be significantly non-linear. The sign of the non-linearities is generally opposite to the sign of the corresponding first-order sensitivities. NOx emissions are found to inhibit the influence on ozone pollution of urban VOC emissions, but to enhance the influence of rural VOC emissions. As a result, a 10% increase in region-wide NOx emissions is estimated to decrease ozone sensitivity to anthropogenic VOC emissions by 4%, but to increase ozone sensitivity to biogenic VOC emissions by 4%. In other words, while an increase in NOx emissions would reduce ozone pollution, it would also decrease the air quality benefits associated with reducing anthropogenic VOC emissions. Additionally, the analysis suggests that reducing anthropogenic VOC emissions tends to mitigate the NOx disbenefit on formaldehyde, and to a lesser extent on ozone. To summarize, the negative sign of the sensitivities to NOx emissions is not a justification to avoid controlling these emissions