First- and Second-Order Sensitivity Analysis of a Photochemically Reactive System (a Green's Function Approach)

Abstract

Local sensitivity analysis of air quality models permits an estimation of the effects of parameter variations, can help assess uncertainties, and distinguishes important from unimportant model features. While local sensitivity analysis in atmospheric chemistry is usually conducted to the first-order, this work includes second-order sensitivity analysis. A Green's function method is used to compute the sensitivities of a photochemically reactive system. Time-dependent photolytic reaction rate coefficients are speci fied using two-parameter functions of time. The Green's function is used directly to study the temporal dependence of ozone concentrations on the NOx concentrations. ROG-limited (ROG/NOx = 6) and NOx-limited (ROG/NOx = 24) conditions are both evaluated. The importance of NOx, formaldehyde, and aromatic chemistry is emphasized by the high ozone sensitivity to the initial concentrations of these species and to the reaction rate parameters of NO2 photolysis, NO recombination with ozone (NO + O3 → NO2 + O2), formaldehyde photolysis (HCHO + hν → 2HO2 + CO), and NO2 + OH → HNO3. The parameters that ozone concentration is most sensitive to were treated with second-order sensitivity analysis. A comparison of ozone concentration changes predicted by second-order sensitivity analysis with concentration changes computed directly shows that second-order sensitivity predictions are valid for parameter variations as large as ±50% of the parameter's nominal value, whereas first-order predictions are valid for parameter variations of at most ±25%. Even though all of the NOx in these simulations is introduced via initial concentrations, the Green's function reveals that the temporal pattern of NOx emission is likely to influence ozone concentrations.