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 ana lysis (Dunker, 1984, Journal of Chemical Physics 81; 2385-2393; Gao, 1995, Ph.D. Thesis, University of Connecticut; McCroskey and McRae, 1987 Document ation for the direct decoupled sensitivity analysis method-DDM, Pittsburgh, PA) has been its restriction to the calculation of sensitivity coefficient s for constant rate parameters. Realistic atmospheric simulations require t hat 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 frame work has been devised where time-dependent rate parameters are expressed as products of time-varying profiles and time-independent multipliers. For co mputational convenience the nominal values of the time-independent multipli ers are chosen to be unity. According to the new procedure the decoupled di rect method is used to calculate the derivatives of the concentrations with respect to each time-independent multiplier. These derivatives represent t he sensitivity of the concentrations to the time-varying profiles of the ti me-dependent rate parameters. Local sensitivity coefficients for O-3 and PA N were calculated for a moderately polluted scenario that was free of cloud s and at a constant temperature using the Regional Atmospheric Chemistry Me chanism (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 sho w that sensitivity coefficients calculated using constant, average, rate pa rameter values may be significantly different from sensitivity coefficients calculated using time-varying rate parameters and therefore the relative i mportance of the mechanism's reactions may be different for the two calcula tions. The greatest differences in sensitivity coefficients were found for reactions with rates that have strong diurnal variations, such as photolysi s, HO and NO3 reactions. It was further found that diurnally varying reacti ons have cumulative effects on sensitivity coefficients during the simulati on of an episode that are not present when constant rate parameters are use d. These results have implications, not only for sensitivity analysis and m odelling, but also for the use of measurements to validate chemical models. (C) 1999 Elsevier Science Ltd. All rights reserved.