First-order sensitivity analysis of models with time-dependent parameters: an application to PAN and ozone

A major limitation of the decoupled direct method for local sensitivity analysis (Dunker, 1984, Journal of Chemical Physics 81; 2385–2393; Gao, 1995, Ph.D. Thesis, University of Connecticut; McCroskey and McRae, 1987, Documentation for the direct decoupled sensitivity analysis method-DDM, Pittsburgh, PA) has been its restriction to the calculation of sensitivity coefficients for constant rate parameters. Realistic atmospheric simulations require that the rate parameters in chemical mechanisms, especially photolysis rate parameters and rate parameters strongly affected by temperature variations, vary diurnally during a simulation. For this reason a new conceptual framework has been devised where time-dependent rate parameters are expressed as products of time-varying profiles and time-independent multipliers. For computational convenience the nominal values of the time-independent multipliers are chosen to be unity. According to the new procedure the decoupled direct method is used to calculate the derivatives of the concentrations with respect to each time-independent multiplier. These derivatives represent the sensitivity of the concentrations to the time-varying profiles of the time-dependent rate parameters. Local sensitivity coefficients for O3 and PAN were calculated for a moderately polluted scenario that was free of clouds and at a constant temperature using the Regional Atmospheric Chemistry Mechanism (RACM) (Stockwell et al., 1997, Journal of Geophysical Research 102, 25,847–25,879). Calculations were compared for simulations with constant as well as diurnally changing photolysis rate coefficients. The results show that sensitivity coefficients calculated using constant, average, rate parameter values may be significantly different from sensitivity coefficients calculated using time-varying rate parameters and therefore the relative importance of the mechanismʹs reactions may be different for the two calculations. The greatest differences in sensitivity coefficients were found for reactions with rates that have strong diurnal variations, such as photolysis, HO and NO3 reactions. It was further found that diurnally varying reactions have cumulative effects on sensitivity coefficients during the simulation of an episode that are not present when constant rate parameters are used. These results have implications, not only for sensitivity analysis and modelling, but also for the use of measurements to validate chemical models.