High-order, direct sensitivity analysis of multidimensional air quality models

Area of Science:

• Atmospheric Chemistry
• Computational Science
• Environmental Modeling

Background:

• Traditional first-order sensitivity analysis in air quality models has limitations in capturing complex nonlinear atmospheric processes.
• Accurate prediction of air pollution, particularly ozone episodes, requires methods that can account for non-linear chemical reactions and emissions.

Purpose of the Study:

• To extend direct sensitivity analysis for calculating higher-order sensitivity coefficients in 3D air quality models.
• To evaluate the efficiency and accuracy of higher-order sensitivity analysis compared to first-order methods.
• To better understand nonlinear responses in ozone formation, especially in nitrogen oxide-rich environments.

Main Methods:

• Direct sensitivity analysis technique adapted for higher-order coefficient calculation.
• Simultaneous time evolution tracking of sensitivity coefficients and pollutant concentrations.
• Application to a simulated ozone episode in central California using a 3D air quality model.

Main Results:

• First-, second-, and third-order sensitivity coefficients were calculated and analyzed.
• Second-order coefficients showed good agreement with brute-force results and reduced noise.
• Inclusion of second-order terms in Taylor series projections significantly improved accuracy.

Conclusions:

• Higher-order sensitivity analysis provides a noticeable accuracy improvement over conventional first-order methods.
• Second-order sensitivity analysis effectively captures nonlinear atmospheric responses, particularly around peak ozone in NO(x)-rich plumes.
• The extended technique is efficient with minimal computational overhead, making it practical for complex air quality modeling.