Investigation of some numerical issues in a chemistry-transport model: Gas-phase simulations

Many numerical strategies have been specifically developed for chemistry-transport models. Since no exact solutions are available for 3-D real problems, there are only few insights to choose between alternative numerical schemes and approximations, or to estimate the performance discrepancy between two approaches. However it is possible to assess the importance of numerical approximations through the comparison of different strategies. We estimated the impact of several numerical schemes for advection, diffusion and stiff chemistry. We also addressed operator splitting with different methods and operator orders. The study is performed with a gas-phase Eulerian model from the modeling platform Polyphemus. It is applied to ozone forecasts mainly over Europe, with focus on a few key species: ozone, nitric oxide, nitrogen dioxide, sulfur dioxide and hydroxy radical. The outcome is a ranking of the most sensitive numerical choices. It stresses the prominent impact of the advection scheme and of the splitting time step.

[1]  Mark Z. Jacobson,et al.  Fundamentals of atmospheric modeling , 1998 .

[2]  P. Frolkovic Flux-based method of characteristics for contaminant transport in flowing groundwater , 2002 .

[3]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[4]  Vivien Mallet,et al.  Development and validation of a fully modular platform for numerical modelling of air pollution: POLAIR , 2004 .

[5]  Adrian Sandu,et al.  Benchmarking Stiff ODE Solvers for Atmospheric Chemistry Problems I: Implicit versus Explicit , 1996 .

[6]  Ralf Wolke,et al.  A Comparison of Fast Chemical Kinetic Solvers in a Simple Vertical Diffusion Model , 1994 .

[7]  J. Seinfeld,et al.  Atmospheric Chemistry and Physics: From Air Pollution to Climate Change , 1997 .

[8]  E. J. Spee,et al.  Numerical methods in global transport-chemistry models , 1998 .

[9]  Riccardo Sacco,et al.  A semi-Lagrangian discontinuous Galerkin method for scalar advection by incompressible flows , 2006, J. Comput. Phys..

[10]  Vivien Mallet,et al.  Inverse modeling of NOx emissions at regional scale over northern France: Preliminary investigation of the second‐order sensitivity , 2005 .

[11]  B. Sportisse An Analysis of Operator Splitting Techniques in the Stiff Case , 2000 .

[12]  Zahari Zlatev,et al.  Computer Treatment of Large Air Pollution Models , 1995 .

[13]  Martin Berzins,et al.  An algorithm for ODEs from atmospheric dispersion problems , 1997 .

[14]  K. P. Brand,et al.  Application of a semi-implicit euler method to mass action kinetics , 1981 .

[15]  B. Sportisse,et al.  Numerical simulation of aqueous-phase atmospheric models: use of a non-autonomous Rosenbrock method , 2002 .

[16]  Adrian Sandu,et al.  Benchmarking stiff ode solvers for atmospheric chemistry problems II: Rosenbrock solvers , 1997 .

[17]  Willem Hundsdorfer,et al.  Stability of implicit-explicit linear multistep methods , 1997 .

[18]  J. B. Perot,et al.  An analysis of the fractional step method , 1993 .

[19]  J. Lamarque,et al.  A global simulation of tropospheric ozone and related tracers: Description and evaluation of MOZART, version 2 , 2001 .

[20]  J. Blom,et al.  An implicit-explicit approach for atmospheric transport-chemistry problems , 1996 .

[21]  R. Wolke,et al.  Strang Splitting Versus Implicit-Explicit Methods in Solving Chemistry Transport Models A contribution to subproject GLOREAM , 1999 .

[22]  Vivien Mallet,et al.  3-D chemistry-transport model Polair: numerical issues, validation and automatic-differentiation strategy , 2004 .

[23]  Bruno Sportisse,et al.  A review of current issues in air pollution modeling and simulation , 2007 .

[24]  Adrian Sandu Positive numerical integration methods for chemical kinetic systems , 2001 .

[25]  Shian‐Jiann Lin,et al.  Multidimensional Flux-Form Semi-Lagrangian Transport Schemes , 1996 .

[26]  Vivien Mallet,et al.  Ensemble‐based air quality forecasts: A multimodel approach applied to ozone , 2006 .

[27]  J. Verwer,et al.  Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling , 1999 .

[28]  J. G. Verwer,et al.  Explicit method for stiff ODEs from atmospheric chemistry , 1995 .

[29]  Robin L. Dennis,et al.  NARSTO critical review of photochemical models and modeling , 2000 .

[30]  V. Mallet,et al.  Uncertainty in a chemistry-transport model due to physical parameterizations and numerical approximations: An ensemble approach applied to ozone modeling , 2006 .

[31]  Willem Hundsdorfer,et al.  A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems , 1999, SIAM J. Sci. Comput..

[32]  Jan G. Verwer,et al.  Gauss-Seidel Iteration for Stiff ODES from Chemical Kinetics , 1994, SIAM J. Sci. Comput..

[33]  Pu Sun A Pseudo-Non-Time-Splitting Method in Air Quality Modeling , 1996 .

[34]  Vivien Mallet,et al.  A comprehensive study of ozone sensitivity with respect to emissions over Europe with a chemistry‐transport model , 2005 .

[35]  Ralf Wolke,et al.  Implicit-explicit Runge-Kutta methods applied to atmospheric chemistry-transport modelling , 2000, Environ. Model. Softw..

[36]  Willem Hundsdorfer,et al.  Numerical time integration for air pollution models , 1998 .

[37]  M. C. Dodge,et al.  A photochemical kinetics mechanism for urban and regional scale computer modeling , 1989 .

[38]  Martin Berzins,et al.  Solving convection and convection-reaction problems using the method of lines , 1996 .

[39]  E. J. Spee,et al.  An efficient horizontal advection scheme for the modeling of global transport of constituents , 1995 .

[40]  Joke Blom,et al.  A comparison of stiff ode solvers for atmospheric chemistry problems , 1995 .

[41]  Ralf Wolke,et al.  An explicit–implicit numerical approach for atmospheric chemistry–transport modeling , 1998 .

[42]  Willem Hundsdorfer,et al.  Numerical time integration for air pollution problems , 2002 .

[43]  Graeme Fairweather,et al.  The current state and future direction of Eulerian models in simulating the tropospheric chemistry and transport of trace species: a review , 1995 .

[44]  William R. Goodin,et al.  Numerical solution of the atmospheric diffusion equation for chemically reacting flows , 1982 .

[45]  Valeriu Damian,et al.  The current state and the future directions in air quality modelling , 1996 .

[46]  Lin Wu,et al.  Technical Note: The air quality modeling system Polyphemus , 2007 .

[47]  Steven J. Ruuth,et al.  Implicit-explicit methods for time-dependent partial differential equations , 1995 .

[48]  F. Kirchner,et al.  A new mechanism for regional atmospheric chemistry modeling , 1997 .