Ralf Wolke

Implicit–explicit Runge–Kutta methods applied to atmospheric chemistry-transport modelling

Abstract Chemistry-transport calculations are highly stiff in terms of time-stepping. Because explicit ODE solvers require numerous short time steps in order to maintain stability, it seems that especially sparse implicit–explicit solvers are suited to improve the numerical efficiency for atmospheric chemistry applications. In the new version of our mesoscale chemistry-transport model MUSCAT [Knoth, O., Wolke, R., 1998a. An explicit–implicit numerical approach for atmospheric chemistry–transport modelling. Atmospheric Environment 32, 1785–1797.], implicit–explicit (IMEX) time integration schemes are implemented. Explicit second order Runge–Kutta methods for the integration of the horizontal advection are used. The stiff chemistry and all vertical transport processes (turbulent diffusion, advection, deposition) are integrated in an implicit and coupled manner utilizing the second order BDF method. The horizontal fluxes are treated as ‘artificial’ sources within the implicit integration. A change of the solution values as in conventional operator splitting is thus avoided. The aim of this paper is to investigate the interaction between the explicit Runge–Kutta scheme and the implicit integrator. The numerical behavior is discussed for a 1D test problem and 3D chemistry-transport simulations. The efficiency and accuracy of the algorithm are compared to results obtained using the Strang splitting approach. The numerical experiments indicate that our second order implicit–explicit Runge–Kutta methods are a valuable alternative to the conventional operator splitting approach for integrating atmospheric chemistry-transport-models. In mesoscale applications and in cases with stronger accuracy requirements the ‘source splitting’ approach shows a better performance than Strang splitting.

Implicit-explicit Runge-Kutta methods for computing atmospheric reactive flows

Air quality modeling is numerically extremely expensive and, therefore, it requires fast algorithms and sophisticated numerical software. This is due to the fact that reacting flow calculations are highly stiff for time-stepping. In this paper implicit-explicit time integration schemes are derived which use explicit higher order Runge-Kutta schemes for the integration of the horizontal advection. The stiff chemistry and all vertical transport processes (turbulent diffusion, advection, deposition) are integrated in an implicit and coupled manner by a higher order BDF method. High order accuracy and stability conditions are investigated for this class of implicit-explicit schemes. The numerical behavior of the new integration schemes is discussed for a 1D and a simple 3D chemistry-transport problem.

The parallel model system LM-MUSCAT for chemistry-transport simulations: Coupling scheme, parallelization and applications

Publisher Summary This chapter discusses the parallel model system LM-MultiScale chemistry aerosol transport (MUSCAT) for chemistry-transport simulations: coupling scheme, parallelization, and applications. The physical and chemical processes in the atmosphere are very complex. They occur simultaneously, coupled and in a wide range of scales. These facts have to be taken into account in the numerical methods for the solution of the model equations. The numerical techniques allow the use of different resolutions in space and also in time. Air quality models base on mass balances described by systems of time-dependent, three-dimensional advection-diffusion reaction equations. A parallel version of the multiscale chemistry-transport code MUSCAT is presented, which is based on multiblock grid techniques and implicit-explicit (IMEX) time integration schemes. The meteorological fields are generated simultaneously by the non-hydrostatic meteorological model LM. Both codes run in parallel mode on a predefined number of processors and exchange information by an implemented coupler interface. The ability and performance of the model system are discussed for a “Berlioz” ozone episode.

An explicit–implicit numerical approach for atmospheric chemistry–transport modeling

Abstract We present the main features of a new atmospheric chemistry–transport code. The employed concepts satisfy essential requirements of third generation atmospheric–transport models. It is shown that our approach can reduce the computational work load of current chemistry transport models by as much as 70–80%. In this paper, we focus on a new temporal integration scheme which is applied to the spatially discretized transport equations. The spatial discretization is performed on a terrain–following grid which allows on-line coupling to existing mesoscale models. Our time integration scheme is of explicit–implicit type. The horizontal advection is integrated explicitly with a large time step and acts as an artificial source in the coupled implicit integration of all vertical transport processes as well as the chemistry. The second-order BDF method is applied for the implicit integration. The linear algebra core in the LSODE code is replaced by a block Gauss–Seidel iteration. This method exploits the sparsity structure of the chemistry–transport problem. We find that two or three iterations suffice, and therefore make the code even faster than the traditional QSSA method. In contrast to the traditional operator splitting, the new approach is free of a transient phase during each implicit integration step. Together with our non–standard starting procedure, large step sizes are maintained throughout integration, with the exception of sunrise and sunset. Large parts of the code are vectorized by loops about the grid cell dimension. Due to memory limitations, a decomposition of the horizontal grid into rectangular subdomains is implemented. The implicit integration is performed with its own time-step selection for each subdomain. The computational efficiency of our approach is investigated with a realistic scenario in Saxony and is compared to the efficiency obtained by an operator splitting approach in combination with a QSSA solver for the chemistry. The sensitivity of our model to three different mechanisms is discussed briefly. Lastly, a technique is introduced with which chemical reaction mechanisms can be easily incorporated into chemistry–transport models.

The Chemistry-Transport Modeling System lm-Muscat : Description and citydelta Applications

Air quality models base on mass balances described by systems of time-dependent, three-dimensional advection-diffusion-reaction equations. The solution of such systems is numerically expensive in terms of computing time. This requires the use of fast parallel computers. Multiblock grid techniques and implicit-explicit (IMEX) time integration schemes are suited to take benefit from the parallel architecture. A parallel version of the multiscale chemistry-transport code MUSCAT (MUiltiScale Chemistry Aerosol Transport) is presented which is based on these techniques (Wolke and Knoth, 2000).

Highly scalable dynamic load balancing in the atmospheric modeling system COSMO-SPECS+FD4

To study the complex interactions between cloud processes and the atmosphere, several atmospheric models have been coupled with detailed spectral cloud microphysics schemes. These schemes are computationally expensive, which limits their practical application. Additionally, our performance analysis of the model system COSMO-SPECS (atmospheric model of the Consortium for Small-scale Modeling coupled with SPECtral bin cloud microphysicS) shows a significant load imbalance due to the cloud model. To overcome this issue and enable dynamic load balancing, we propose the separation of the cloud scheme from the static partitioning of the atmospheric model. Using the framework FD4 (Four-Dimensional Distributed Dynamic Data structures), we show that this approach successfully eliminates the load imbalance and improves the scalability of the model system. We present a scalability analysis of the dynamic load balancing and coupling for two different supercomputers. The observed overhead is 6% on 1600 cores of an SGI Altix 4700 and less than 7% on a BlueGene/P system at 64Ki cores.

An advanced modeling study on the impacts and atmospheric implications of multiphase dimethyl sulfide chemistry

Significance Climate models indicate the importance of dimethyl sulfide (DMS) oxidation in new aerosol particle formation and the activation of cloud condensation nuclei over oceans. These effects contribute to strong natural negative radiative forcing and substantially influence the Earth’s climate. However, the DMS oxidation pathway is not well-represented, because earlier model studies only parameterized gas-phase DMS oxidation and neglected multiphase chemistry. Here, we performed the most comprehensive current mechanistic studies on multiphase DMS oxidation. The studies imply that neglecting multiphase chemistry leads to significant overestimation of SO2 production and subsequent new particle formation. These findings show that an advanced treatment of multiphase DMS chemistry is necessary to improve marine atmospheric chemistry and climate model predictions. Oceans dominate emissions of dimethyl sulfide (DMS), the major natural sulfur source. DMS is important for the formation of non-sea salt sulfate (nss-SO42−) aerosols and secondary particulate matter over oceans and thus, significantly influence global climate. The mechanism of DMS oxidation has accordingly been investigated in several different model studies in the past. However, these studies had restricted oxidation mechanisms that mostly underrepresented important aqueous-phase chemical processes. These neglected but highly effective processes strongly impact direct product yields of DMS oxidation, thereby affecting the climatic influence of aerosols. To address these shortfalls, an extensive multiphase DMS chemistry mechanism, the Chemical Aqueous Phase Radical Mechanism DMS Module 1.0, was developed and used in detailed model investigations of multiphase DMS chemistry in the marine boundary layer. The performed model studies confirmed the importance of aqueous-phase chemistry for the fate of DMS and its oxidation products. Aqueous-phase processes significantly reduce the yield of sulfur dioxide and increase that of methyl sulfonic acid (MSA), which is needed to close the gap between modeled and measured MSA concentrations. Finally, the simulations imply that multiphase DMS oxidation produces equal amounts of MSA and sulfate, a result that has significant implications for nss-SO42− aerosol formation, cloud condensation nuclei concentration, and cloud albedo over oceans. Our findings show the deficiencies of parameterizations currently used in higher-scale models, which only treat gas-phase chemistry. Overall, this study shows that treatment of DMS chemistry in both gas and aqueous phases is essential to improve the accuracy of model predictions.

Numerical methods for the solution of large kinetic systems

Abstract The photochemical reaction mechanisms used in air pollution models usually consider 40 to 100 pollutant species and more than 150 reactions. The equations resulting from these chemical mechanisms are nonlinear, highly coupled and extremely stiff depending on the time of the day. Therefore, the simulation time of the models is determined to a large degree by the computational burden associated with the solution of the chemistry equations. In recent years, the Quasi Steady State Approximation (QSSA) method is favored for solving the chemistry equations. In the QSSA the solution of large linear systems is not necessary. In this paper we investigate a new approach based on the BDF which solves the sparse linear equations during the Newton iteration by linear Gauss-Seidel iterations. The Jacobian is computed explicitly and not by finite differences. The effect of different numbers of Gauss-Seidel sweeps is investigated. In addition, sparsing techniques proposed by Nowak (1992) and Zlatev (1991) are tested with respect to their efficiency in our algorithms. Our method is compared with respect to its accuracy as well as computational speed with a method of Verwer (1993) which is also based on the two-step BDF combined with nonlinear Gauss-Seidel iterations to approximately determine the implicitly defined solution. The results show that our BDF code reaches the nonlinear Gauss-Seidel approach of Verwer (1993) with respect to the computational speed.

A COMPARISON OF FAST CHEMICAL KINETIC SOLVERS IN A SIMPLE VERTICAL DIFFUSION MODEL

The photochemical reaction mechanisms used in regional air quality models usually consider 20 to 100 pollutant species. The equations resulting from these chemical mechanisms are nonlinear, highly coupled and extremely stiff depending on the time of the day. Therefore, the simulation time of the models is determined to a large degree by the computational burden associated with the solution of the chemistry equations.

Time-integration of multiphase chemistry in size-resolved cloud models

The existence of cloud drops leads to a transfer of chemical species between the gas and aqueous phases. Species concentrations in both phases are modified by chemical reactions and by this phase transfer. The model equations resulting from such multiphase chemical systems are nonlinear, highly coupled and extremely stiff. In the paper we investigate several numerical approaches for treating such processes. The droplets are subdivided into several classes. This decomposition of the droplet spectrum into classes is based on their droplet size and the amount of scavenged material inside the drops, respectively. The very fast dissociations in the aqueous phase chemistry are treated as forward and backward reactions. The aqueous phase and gas phase chemistry, the mass transfer between the different droplet classes among themselves and with the gas phase are integrated in an implicit and coupled manner by the second order BDF method. For this part we apply a modification of the code LSODE with special linear system solvers. These direct sparse techniques exploit the special block structure of the corresponding Jacobian. Furthermore we investigate an approximate matrix factorization which is related to operator splitting at the linear algebra level. The sparse Jacobians are generated explicitly and stored in a sparse form. The efficiency and accuracy of our time-integration schemes is discussed for four multiphase chemistry systems of different complexity and for a different number of droplet classes.