Development of an Approximate Method for Advection of Sensitivity Fields

Abstract

Although advection equation is linear in time and space, positive definite and mass conservative advection schemes in chemical transport models (CTMs) behave nonlinearly mostly due to discontinuous (conditional) operations in discretization. A new approach is developed to indirectly simulate the advection process in CTMs. Instead of integrating the continuity equation directly for various species, advection equations for various pollutants are solved in relations to advected air densities. Our approach relies on the run-time estimation of the Jacobian of the advection operator, and can be based on the native advection algorithm in any CTM. The estimated transport Jacobian for air densities are then applied to other species with corrections that would ensure consistency with the underlying scheme. Since our proposed method is truly linear in species concentration, it is not suspect to complications associated with advecting sensitivities as experienced with nonlinear advection schemes. We implement our advection method in CMAQ 5.0 using its native Piecewise Parabolic Method (PPM) advetion scheme. Our preliminary results show good consistency with the PPM scheme, and potential for truly linear advection of sensitivity fields.

Question and Answer

Questioner: Clemens Mensink

Question: Would it be interesting to simply go to higher order or more accurate schemes?

Answer: More accurate schemes are obviously desirable, but increased accuracy often is accompanied by artificial non-linearity, as well as additional computational cost. We believe that it is physically inconsistent to advect sensitivities of different species (or for that matter their concentrations), differently while they are all advected in the same wind field. This approach aims to address that underlying problem.