Accuracy of multi-parameter response surfaces generated using sensitivity coefficients
Daniel Cohan and Antara Digar

Accurate representation of pollutant concentrations and their responsiveness to perturbations is critical for air quality management, model evaluation, and other applications. Local first-order sensitivity coefficients, computed by decoupled direct method or other techniques, are known to effectively represent pollutant response to small perturbations in an emission rate or input parameter. Previous studies have shown the extent to which Taylor series expansions incorporating second-order coefficients can predict the impacts of large changes in emissions. However, left unanswered has been how accurately these impacts can be predicted if they are accompanied by simultaneous uncertainties in multiple parameters such as biogenic and anthropogenic emission rates, boundary conditions, and reaction rates. Here, we show how first-order, second-order, and cross-sensitivity coefficients can be used to develop response surfaces representing how pollutant concentrations and their sensitivities to emissions vary with multiple uncertain input parameters. We then quantify the accuracy of these predictions by comparisons with a matrix of brute force runs. We demonstrate that a limited number of sensitivity coefficients, computed only within a base model, can achieve a surprising degree of accuracy in predicting the impacts of control measures under starkly altered circumstances (e.g., 50% changes in biogenic emissions, boundary conditions, and other input parameters). A companion talk by Antara Digar will show how this ensemble of sensitivity coefficients can be used to develop a surrogate analytical model for efficiently creating probability distribution functions of pollutant concentrations and responsiveness to emission controls.