Dynamical cores used to study the circulation of the atmosphere employ various numerical methods ranging from finite-volume, spectral element, global spectral, and hybrid methods. In this work, we explore the use of Flux-Differencing Discontinuous Galerkin (FDDG) methods to simulate a fully compressible dry atmosphere at various resolutions. We show that the method offers a judicious compromise between high-order accuracy and stability for large-eddy simulations and simulations of the atmospheric general circulation. In particular, filters, divergence damping, diffusion, hyperdiffusion, or sponge-layers are not required to ensure stability; only the numerical dissipation naturally afforded by FDDG is necessary. We apply the method to the simulation of dry convection in an atmospheric boundary layer and in a global atmospheric dynamical core in the standard benchmark of Held and Suarez (1994, https://doi. org/10.1175/1520-0477(1994)075<1825:apftio>2.0.co;2).Plain Language Summary Numerical models cannot explicitly represent all degrees of freedom that characterize atmospheric flows due to limitations in computing power. One must allocate the available computational degrees of freedom to reduce the degradation of the solution. In this work, we explore the use of the discontinuous Galerkin numerical method, a hybrid approach that combines the accuracy of spectral methods with the flexibility of finite volume methods. We apply it to idealized dry atmospheric simulations and show that the method is robust and incorporates physical principles to best account for unresolved processes.

Large eddy simulations (LESs) are performed for the area of the Caribbean island Barbados to investigate island effects on boundary layer modification, cloud generation and vertical mixing of aerosols. Due to the presence of a topographically structured island surface in the domain center, the model setup has to be designed with open lateral boundaries. In order to generate inflow turbulence consistent with the upstream marine boundary layer forcing, we use the cell perturbation method based on finite amplitude potential temperature perturbations. In this work, this method is for the first time tested and validated for moist boundary layer simulations with open lateral boundary conditions. Observational data obtained from the SALTRACE field campaign is used for both model initialization and a comparison with Doppler wind and Raman lidar data. Several numerical sensitivity tests are carried out to demonstrate the problems related to “gray zone modeling” when using coarser spatial grid spacings beyond the inertial subrange of three-dimensional turbulence or when the turbulent marine boundary layer flow is replaced by laminar winds. Especially cloud properties in the downwind area west of Barbados are markedly affected in these kinds of simulations. Results of an additional simulation with a strong trade-wind inversion reveal its effect on cloud layer depth and location. Saharan dust layers that reach Barbados via long-range transport over the North Atlantic are included as passive tracers in the model. Effects of layer thinning, subsidence and turbulent downward transport near the layer bottom at z ≈ 1800 m become apparent. The exact position of these layers and strength of downward mixing is found to be mainly controlled atmospheric stability (especially inversion strength) and wind shear. Comparisons of LES model output with wind lidar data show similarities in the downwind vertical wind structure. Additionally, the model results accurately reproduce the development of the daytime convective boundary layer measured by the Raman lidar.

In this work, the fully compressible, three-dimensional, nonhydrostatic atmospheric model called All Scale Atmospheric Model (ASAM) is presented. A cut cell approach is used to include obstacles and orography into the Cartesian grid. Discretization is realized by a mixture of finite differences and finite volumes and a state limiting is applied. Necessary shifting and interpolation techniques are outlined. The method can be generalized to any other orthogonal grids, e.g., a lat–long grid. A linear implicit Rosenbrock time integration scheme ensures numerical stability in the presence of fast sound waves and around small cells. Analyses of five two-dimensional benchmark test cases from the literature are carried out to show that the described method produces meaningful results with respect to conservation properties and model accuracy. The test cases are partly modified in a way that the flow field or scalars interact with cut cells. To make the model applicable for atmospheric problems, physical parameterizations like a Smagorinsky subgrid-scale model, a two-moment bulk microphysics scheme, and precipitation and surface fluxes using a sophisticated multi-layer soil model are implemented and described. Results of an idealized three-dimensional simulation are shown, where the flow field around an idealized mountain with subsequent gravity wave generation, latent heat release, orographic clouds and precipitation are modeled.

Explicit time integration methods are characterised by a small numerical effort per time step. In the application to multiscale problems in atmospheric modelling, this benefit is often more than compensated by stability problems and step size restrictions resulting from stiff chemical reaction terms and from a locally varying Courant-Friedrichs-Lewy (CFL) condition for the advection terms. Splitting methods may be applied to efficiently combine implicit and explicit methods (IMEX splitting). Complementarily multirate time integration schemes allow for a local adaptation of the time step size to the grid size. In combination, these approaches lead to schemes which are efficient in terms of evaluations of the right-hand side. Special challenges arise when these methods are to be implemented. For an efficient implementation, it is crucial to locate and exploit redundancies. Furthermore, the more complex programme flow may lead to computational overhead which, in the worst case, more than compensates the theoretical gain in efficiency. We present a general splitting approach which allows both for IMEX splittings and for local time step adaptation. The main focus is on an efficient implementation of this approach for parallel computation on computer clusters.

Atmospheric particle number size distributions of airborne particles (diameter range 10–500 nm) were collected over ten weeks at three sites in the vicinity of the A100 urban motorway in Berlin, Germany. The A100 carries about 180 000 vehicles on a weekday. The roadside particle distributions showed a number maximum between 20 and 60 nm clearly related to the motorway emissions. The average total number concentration at roadside was 28 000 cm−3 with a total range of 1200–168 000 cm−3. At distances of 80 and 400 m from the motorway the concentrations decreased to mean levels of 11 000 and 9000 cm−3, respectively. An obstacle-resolving dispersion model was applied to simulate the 3-D flow field and traffic tracer transport in the urban environment around the motorway. By inverse modelling, vehicle emission factors were derived that are representative of a fleet with a relative share of 6% lorry-like vehicles, and driving at a speed of 80 km h−1. Three different calculation approaches were compared, which differ in the choice of the experimental winds driving the flow simulation. The average emission factor per vehicle was 2.1 (±0.2) · 1014 km−1 for particle number and 0.077 (±0.01) · 1014 cm3 km−1 for particle volume. Regression analysis suggested that lorry-like vehicles emit 123 (±28) times more particle number than passenger car-like vehicles, and lorry-like vehicles account for about 91% of particulate number emissions on weekdays. Our work highlights the increasing applicability of 3-D flow models in urban microscale environments and their usefulness for determining traffic emission factors.

The novel model system LM-SPECS is presented combining a spectral bin microphysics scheme and the three-dimensional Lokalmodell (LM, today called COSMO) of the German Weather Service (“Deutscher Wetterdienst”). The model is designed to investigate in detail the interaction of atmospheric aerosol particles, clouds and precipitation. The microphysics scheme includes a combined spectrum of wetted aerosols, cloud droplets and rain drops. As a first application of the model, sensitivity studies on an artificial deep convective cloud were done. The results produced by LM-SPECS are satisfying. The studies show, e.g., that a diminished initial particle number leads to larger cloud droplets and thus to a higher efficiency of coalescence. This results in a larger amount of precipitation. Furthermore, studies on mixed phase clouds show the influence of varying ice nuclei, such as bacteria, kaolinite and soot, on cloud properties. Here, a more effective freezing leads to an increased number of ice particles with smaller radii. The results point to the importance of a detailed knowledge of the underlying microphysical processes in order to understand the formation of clouds and precipitation more accurately. Though to date the model was applied to artificial cases only, the use of the mesoscale weather model allows for more complex realistic cases which are subject to further studies.

Quantitative precipitation prediction is one of the most uncertain parts of weather forecast models. The formation of precipitation is strongly connected to the drop number distribution inside a cloud. However, for a given dynamic situation, amount and size of the nucleated droplets depend on the amount, size and chemical composition of the aerosol particles which are available in the atmosphere. Thus, in the numerical prediction of precipitation it is desirable to take into account aerosol particles and the droplet nucleation process as detailed as possible.

An overview of the two FEBUKO aerosol-cloud interaction field experiments in the Thuringer Wald (Germany) in October 2001 and 2002 and the corresponding modelling project MODMEP is given. Experimentally, a variety of measurement methods were deployed to probe the gas phase, particles and cloud droplets at three sites upwind, downwind and within an orographic cloud with special emphasis on the budgets and interconversions of organic gas and particle phase constituents. Out of a total of 14 sampling periods within 30 cloud events three events (El, Ell and EIII) are selected for detailed analysis. At various occasions an impact of the cloud process on particle chemical composition such as on the organic compounds content, sulphate and nitrate and also on particle size distributions and particle mass is observed. Moreover, direct phase transfer of polar organic compound from the gas phase is found to be very important for the understanding of cloudwater composition.For the modelling side, a main result of the MODMEP project is the development of a cloud model, which combines a complex multiphase chemistry with detailed microphysics. Both components are described in a fine-resolved particle/drop spectrum. New numerical methods are developed for an efficient solution of the entire complex model. A further development of the CAPRAM mechanism has lead to a more detailed description of tropospheric aqueous phase organic chemistry. In parallel, effective tools for the reduction of highly complex reaction schemes are provided. Techniques are provided and tested which allow the description of complex multiphase chemistry and of detailed microphysics in multidimensional chemistry-transport models. (c) 2005 Elsevier Ltd. All rights reserved.

Cloud-chemistry models are developed intensively with increasing complexity, leading to new knowledge and offering new possibilities to understand the physico-chemical processes taking place in the atmosphere. Intercomparing such detailed models is the way to test the robustness and reliability of their parameterizations and numerical schemes. The present study involves newly developed parcel models treating microphysics and chemistry with equal rigor. The description of both kinds of processes is given for a size-resolved particle/droplet spectrum. Three different types of models are compared. In the spaccim approach, one- and two-dimensional particle/drop microphysical schemes are used in a time-splitting setup between chemistry and microphysics. The galerkin model employs a one-dimensional scheme in a fully coupled setup. For each of the three types, “fixed bin” and “moving bin” approaches are implemented. A comparison between “fixed” and “moving bin” approaches makes sense only for scenarios without coagulation and breakup. The paper focuses on the effects of different microphysical and numerical approaches on the multiphase chemistry. The resulting changes in the particle/droplet composition feed back on cloud microphysics. Substantiated conclusions can only be derived if these effects are studied for a wide range of cases. Thus, the simulations are performed for three chemical reaction mechanisms of different complexity and four scenarios derived from field measurements. The interaction between numerical schemes, microphysics and multiphase chemistry is discussed. Mostly, the results of the participating models agree in an appreciable way. Observable differences are noticed between the “moving bin” approach and models using fixed grids for the discretization of the particle/droplet spectrum. Furthermore, the initial aerosol composition influences the fate of chemical species as well as the behavior of the numerical solver in a substantial way.

Multiphase processes, such as the uptake of gases by clouds or the production of gas phase halogens from particulate halides are of increasing importance for the understanding of the tropospheric system. Mass transfer and chemical reactions modify the concentrations of stable compounds and oxidants in either phase. The parcel model SPACCIM is presented which combines a complex multiphase chemical model with a detailed microphysical model. For this purpose, a new coupling scheme is implemented. The description of both components is given for a fine-resolved particle/drop spectrum. The SPACCIM approach allows the coupling of multiphase chemical models with microphysical codes of various types. An efficient numerical solution of such systems is only possible utilizing the special structure. An implicit time-integration scheme with an adapted sparse solver for the linear systems is applied. Its numerical efficiency and robustness is analyzed for two scenarios and versions of different complexity of the multiphase chemistry mechanism CAPRAM. The sensitivity of simulation results against variations in the particle/droplet size resolution, the coupling time step and numerical control parameters is discussed. Guidelines for an “optimal” choice of control parameters are derived from this sensitivity study. The coupling scheme operation is always robust and reliable. Model simulations are compared with several measurements from the FEBUKO field campaign. Simulated and measured results show a reasonable agreement.

The formation of clouds is coupled to the vapour saturation condition. Cloud modelling is therefore dramatically disturbed by dilution processes, which are induced by recurrent interpolations on the fixed (Eulerian) grid.The numerical diffusion gives rise to degeneration and premature disappearance of the modelled clouds. The difficulties increase, if sectional mass representation in the drop microphysics and aerosol chemistry is considered. To tackle this problem, stringently defined and tracked phase boundaries are required. The numerical diffusion of clouds can be totally suppressed by the volume-of-fluid (VOF) method, which is applied here in connection with an atmospheric model. The cloud phase is distinguished by prognosing the partial cloud volume in all grid cells near the cloud boundary. Adopting elementary geometrical forms for the intracellular cloud volume and simple diagnostic rules of their alignment, the standard transport fluxes can be used in the new equation. Separate variables for the cloud and environmental phase complete the transport scheme.The VOF method and its realisation are described in detail. Advection, condensation, evaporation, and turbulent diffusion are considered within the VOF framework. The variation of the grid resolution and turbulence conditions for a rising thermal leads to striking arguments in favour of the VOF method, resulting in higher intensity, lifting, and lifetime as well as clear boundaries of the simulated clouds (even for low grid resolution). (c) 2005 Elsevier Ltd. All rights reserved.

The mesoscale and local flow conditions during the ground-based cloud passage experiment FEBUKO performed at the Schmücke Mountain (Thüringer Wald) during October 2001 and 2002 are investigated and discussed. Several methods are applied to characterise and classify the cloud episodes in terms of the flow conditions and their consistency to the philosophy of cloud passage experiments. For this the flow over the mountain range and a flow that connects the experimental sites are of crucial importance. The resulting selection of events is based on a synoptical evaluation (Part I of the work) and provides a recommendation of events, which are adequate for subsequent investigations. The mesoscale air flow over the complex terrain is characterised by means of non-dimensional flow parameters like Froude number and the non-hydrostatic meteorological model LM. An analysis of the locally measured natural tracer ozone is intended to assure that measurements were performed in identical air masses at the different locations during the 14 cloud events. It is found that the flow connecting the measurement sites is distinctly associated with the flow over and/or around the Thüringer Wald, which in turn is determined by the synoptical flow and the thermal stratification. Furthermore, applications of tracer techniques using the inert SF6 for studies of transport processes in the experimental site and verification of the location of measurement stations are presented. For the tracer experiments in October 2001 and 2002 an attempt is made to reproduce them with an anelastic non-hydrostatic model in conservation form in order to understand the tracer dispersion.

A new atmospheric micro-scale chemistry, transport and stream model, MITRAS, has been developed within the Tropospheric Research Program (TFS). MITRAS is an obstacle resolving model solving simultaneously the governing equations for chemistry, pollutant transport including soot as well as for the flow and temperature field. The chemical reaction module is based on a simplified RACM mechanism. MITRAS has been tested against quality ensured wind tunnel data. The model results on soot and ozone concentrations as well as on the spatial representativeness of measurement sites underline the necessity for high-resolution flow simulations for case studies on close-to-source chemistry and pollutant transport within the urban canopy layer.

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 should 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 informations by an implemented coupler interface. The ability and performance of the model system are discussed for a "Berlioz" ozone episode.

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.

Summary An updated version of the obstacle resolving microscale model MITRAS has been developed. Several modules of the model (turbulence parameterization, chemistry, soot transport, solvers) have been updated, tested stand-alone and are now tested in the framework of MITRAS. For comparison with model results wind tunnel measurements are available. An evaluation scheme for microscale obstacle resolving models has been finalised. Aim of the research This SATURN contribution aims to develop an obstacle resolving microscale model (MITRAS, Panskus et al.; 1997; Lambrecht et al., 1998) which can be used to simulate atmospheric flow and pollutant transport in an area of several hundreds to some thousands of metres with a horizontal resolution of some metres. MITRAS includes passive tracer transport as well as chemical reactions by directly solving the gas phase chemistry within the micro- scale model. The chemistry module considers all important chemical reactions close to traffic sources. Soot is transported as aerosol with its deposition dependent on size. Soot is treated as a sink for VOC compounds. For a realistic simulation of mixing effects a turbulence parameterization for obstacle resolving models has been developed. To evaluate the model performance an evaluation strategy was introduced which is using wind tunnel data as well as field measurements. MITRAS is prepared to be nested in urban scale models by application of the nudging technique. The MITRAS development is a result of a co-operation of the Alfred Wegener Institute for Polar and Marine Research, Bremerhaven, the Fraunhofer Institute for Atmospheric and Environmental Research, Garmisch-Partenkirchen, the Institute for Tropospheric Research, Leipzig, and the Meteorological Institute, University of Hamburg. Activities during the year The modules of the updated model (turbulence parameterization, chemistry, soot transport, solvers) have been tested separately first. Currently the modules are tested in the framework of the MITRAS model. An evaluation concept for obstacle resolving microscale models has been developed and tested (Panskus, Schlünzen, 2000; Panskus, 2000). The updated version of MITRAS includes an K-ε-turbulence closure scheme (SATURN activity 19), an improved numerical solver (SATURN activity 6) and an on-line calculation of chemistry (SATURN activity 27). In addition, a module for calculation of shading effects by buildings was implemented in MITRAS. The gasphase chemistry was enhanced by heterogeneous reactions (SATURN activity 27). The complete model MITRAS containing all new modules is now tested by using the new evaluation concept which is applicable to urban transport and flow models (SATURN activity 29; Panskus, Schlünzen, 2000). All validation data have been

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. (C) 2000 Elsevier Science Ltd. All rights reserved.