The physical parameterizations implemented in the reference version of the non-hydrostatic mesoscale model GESIMA (=Geesthacht Simulation Model of the Atmosphere) are presented and discussed, namely the turbulent diffusion, the cloud physics, the radiative transfer, and the lower boundary treatment (energy budget). Three different applications show satisfactory agreement with either measurements or physical reasoning

The comprehensive numerical model MODIS for the simulation of pollutant dispersion from a point source is integrated in the graphical shell of Hydro-Quebec. The shell has been developed by Hydro-Quebec to offer a valuable scheme for various applications of software products, which were originally conceived only for scientific purposes. MODIS, developed by the GKSS Research Centre Geesthacht and the Ontario Ministry of Environment, is a powerful simulation model, which calculates the behaviour of plumes in the lower atmosphere. The model was validated under a bilateral project in the framework of Canadian-German co-operation by using data of the EPRI Plume Model Validation Project. A further application of MODIS has been undertaken to determine the dispersion of gaseous mercury from a previous strong emission source located in the former German Democratic Republic.

Difficulties are investigated which occur when trying to specify a noise-free initial model state as the solution of a variational data assimilation problem. A linear shallow water model is used to investigate the existence and physical basis of the model fit to data. As in this context the shape of the cost function is of crucial importance, the interrelations between the cost function's Hessian and specific model-data configurations are investigated. Special emphasis is put on the influence of the temporal/spatial data distribution and the choice of the scheme used for numerical model integration. It is illustrated how such details may cause intolerable uncertainties for those aspects of the recovered solution that are related to very small eigenvalues of the curvature operator. Due to the shortcomings of descent algorithms, uncontrolled large-amplitude error modes may remain invisible if a limited number of minimization cycles is applied. However, to render the retrieved smooth fields stable with respect to further iterations, prior knowledege has to be taken into account in the cost function definition.

A three-dimensional mesoscale model with parameterized microphysics of clouds and precipitation has been extended to include wet scavenging and deposition of trace metals from the atmosphere. As a sample case the wet removal of atmospheric lead has been chosen. Simulations were carried out in a domain of 200 × 200 km2 in the southeastern part of the North Sea including many clouds in various stages of development. The basic assumption is that the particles acting as host for the lead particles are cloud condensation nuclei (CCN) calculated in the model as part of aerosol particles in the air. The variation of the average concentration of aerosol particles with height as a function of size is based on data given in Pruppacher and Klett (1978, Microphysics of Clouds and Precipitation, Reidel, Dordrecht). Both calculated (long range transport model) and measured atmospheric monthly mean concentration of lead at the German coast of North Sea and Baltic Sea given by Petersen et al. (1989, NATO) and Stöβel (1987, Ext. Rep. GKSS 87/E/34) are used as an input pollution level by calculation of the vertical profile of the initial mean mass lead concentration in the air. The lead is assumed to be distributed uniformly on the aerosol particles, and the vertical profile of the initial mass concentration of lead in the air is assumed to be proportional to the vertical profile of number of aerosol particles as a function of size with height. In other words, in the model we deal with that fraction of lead, which can enter cloud water mainly through nucleation scavenging (in-cloud scavenging, ‘rainout’).

Levkov, L., Jacob, D., Eppel, D. and Grassl, H., 1989. Test of a parametrization scheme for cloud microphysical processes in a 3-D mesoscale model. Atmos. Res., 24: 193-208. A parametrization scheme for the simulation of ice in clouds is incorporated into the hydrostatic version of the FZG (Forschungszentrum Geesthacht) three-dimensional mesoscale model. Numerical simulations of precipitation are performed for observed meteorological conditions over the North Sea. Major features of convective structures have been simulated. Also a scheme for cloud aerosol interaction has been developed, however, it could not be compared to measurements due to the lack of observed aerosol parameters.

A comprehensive numerical model for the simulation of pollutant dispersion from a point source into the mixing layer of the atmosphere over flat terrain is described. A moment reduction technique is used (MODIS = MOment Distribution) to combine the simplicity of the Gaussian plume description with the versatility of Eulerian grid formulations. Turbulent dispersion coefficients are parameterized in terms of mean square wind variances which in turn are obtained by a simplified second order closure model. The data base of the ‘EPRI Plume Model Validation and Development Project’ is used to validate the model for wind velocities above 0.5 m/s and for horizontal scales up to about one hundred kilometers. The model describes the three-dimensional structure of a plume also for stable conditions including a nighttime low level jet. For a convective planetary boundary layer it underestimates maximum ground concentration as do other models. However, it is capable of approaching measured maximum ground concentration under stable conditions.

An operations research method is presented for deriving a conservative, non-negative computational scheme for advective transport. Finite elements in space and time are used to approximate the solution, and the integral of the square of the residual is minimized over the entire spatial domain and over a single temporal element. Negative values are excluded by inequality constraints and conservation is enforced by Lagrange multipliers. The method is then generalized to show how negative values arising in conventional finite-difference methods can be eliminated.

AbstractThis paper gives the results of an application of the SWEs (shallow water equations) to a part of the Hamburg harbour area, which is a complex flow domain, using the BFG approach, outlined in Part I. The results of a grid doubling procedure generating the desired computational grid from a coarse initial mesh are also presented. A second class of problems which is addressed, demands time‐dependent co‐ordinate systems. The problems which are solved are the free surface problem for a moving wave which eventually breaks and for a wave which is reflected by the solid walls of a rectangular basin.

AbstractMany problems of applied oceanography and environmental science demand the solution of the momentum, mass and energy equations on physical domains having curving coastlines. Finite‐difference calculations representing the boundary as a step function may give inaccurate results near the coastline where simulation results are of greatest interest for numerous applications. This suggests the use of methods which are capable of handling the problem of boundary curvature.This paper presents computational results for the shallow water equations on a circular ring of constant depth, employing the concept of boundary fitted grids (BFG) for an accurate representation of the boundary. All calculations are performed on a rectangle in the transformed plane using a mesh with square grid spacing. Comparisons of the simulations of transient normal mode oscillations and analytic solutions are shown, demonstrating that this technique yields accurate results in situations (provided that there is a reasonable choice of grid) involving a curved boundary. The software developed allows application to any two‐dimensional area, regardless of the complexity of the geometry.Simulation runs were made with two co‐ordinate systems. For the first system, the grid point distribution was obtained from polar co‐ordinates. For the second one, grid point positions were calculated numerically, solving Poisson's equation. It was found that small variations in the metric coefficients do not deteriorate the accuracy of the simulation results.Moreover, comparisons of surface elevation and velocity components at grid points near the inner and outer radii obtained from an x−y Cartesian grid model with the BFG simulation were made. The former model produced inacccuracies at grid points near boundaries, and, owing to the large number of mesh points used to yield the necessary fine resolution, the computation time was found to be a factor of three higher.

Two-dimensional numerical simulations of sea breeze development over a large sandbar on the North Sea coast of Germany are reported. The numerical model used in these experiments contains a detailed treatment of soil moisture, which allows evaluation of the effects of differential surface characteristics on the airflow pattern. Results of the simulations indicate that the contrast between the moist sandbar and adjacent dry land, the tidal inundation of the sandbar, and the westward penetration of the Baltic sea breeze play important roles in the development of mesoscale airflow patterns in the sandbar region.

The paper presents a far field mathematical model for numerical simulation of transient one- or two-dimensional thermal distributions in regions with severe reversing flow conditions. The Eulerian formulation employs the integral form of the conservation principles for mass and thermal energy. The two-dimensional (2D) solution area is spanned by discrete elements of variable size and shape. The three-dimensional geometry of the flow region is accounted for by spatially integrating over the enclosure surfaces of the discrete element. The derivation of the two-dimensional depth-averaged temperature equations includes the contributions of the vertical variations of velocity and temperature. Surface heat transfer as well as turbulent effects are taken into account.

Coupled Channels calculations have been performed for the reaction40Ca(6Li,d)44Ti(3−)3.94 assuming coupling of α-transfer with inelastic scattering in both the entrance and the exit channels. The effect of several competing transition routes is discussed. A relative spectroscopic factor (44Ti(3−);40Ca(3−), α) is derived.