Fast Fourier Transform

NARSTO critical review of photochemical models and modeling

Numerical models that combine weather forecasting and atmospheric chemistry are here referred to as chemical weather forecasting models. Eighteen operational chemical weather forecasting models on regional and continental scales in Europe are described and compared in this article. Topics discussed in this article include how weather forecasting and atmospheric chemistry models are integrated into chemical weather forecasting systems, how physical processes are incorporated into the models through parameterization schemes, how the model architecture affects the predicted variables, and how air chemistry and aerosol processes are formulated. In addition, we discuss sensitivity analysis and evaluation of the models, user operational requirements, such as model availability and documentation, and output availability and dissemination. In this manner, this article allows for the evaluation of the relative strengths and weaknesses of the various modelling systems and modelling approaches. Finally, this article highlights the most prominent gaps of knowledge for chemical weather forecasting models and suggests potential priorities for future research directions, for the following selected focus areas: emission inventories, the integration of numerical weather prediction and atmospheric chemical transport models, boundary conditions and nesting of models, data assimilation of the various chemical species, improved understanding and parameterization of physical processes, better evaluation of models against data and the construction of model ensembles. © 2012 Author(s).

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A review of operational, regional-scale, chemical weather forecasting models in Europe

During the last 35 years, well over 100 algorithms for modeling advection processes have been described and tested. This review summarizes the development and improvements that have taken place. The nature of the errors caused by numerical approximation to the advection equation are highlighted. Then the particular devices that have been proposed to remedy these errors are discussed. The extensive literature comparing transport algorithms is reviewed. Although there is no clear cut 'best' algorithm, several conclusions can be made. Spectral and pseudospectral techniques consistently provide the highest degree of accuracy, but expense and difficulties assuring positive mixing ratios are serious drawbacks. Schemes which consider fluid slabs bounded by grid points (volume schemes), rather than the simple specification of constituent values at the grid points, provide accurate positive definite results.

Numerical advection algorithms and their role in atmospheric transport and chemistry models

Test of two numerical schemes for use in atmospheric transport-chemistry models

Comparison of numerical techniques for use in air pollution models with non-linear chemical reactions

Implementation of a variable stepsize variable formula method in the time-integration part of a code for treatment of long-range transport of air pollutants

An Eulerian model, describing the dispersion of pollutants in gases and fluids, is developed. The model is based on numerical integration of the dispersion equation, including the effect of advection, diffusion, sinks and of multiple sources. The pseudospectral method is employed for numerical integration of the dispersion equation. The model is not limited to physical problems with periodic boundary conditions, as imposed by the spectral technique. A filtering procedure prevents instabilities caused by aliasing interactions. The emphasis is placed on numerical tests relevant to air pollution studies. Pseudodiffusion is not present in this model. The error in numerical integration is brought down to a few percent of the concentration level of the pollutant. To our knowledge, the model is the most accurate Eulerian model presently available for dispersion calculations. Applications to air pollution studies are discussed. Accuracy of 19 different numerical methods is compared.

A Pseudospectral Model for Dispersion of Atmospheric Pollutants

The gradient transfer theory for turbulent diffusion is reformulated in order to obtain an improved method for applied dispersion studies. The basic innovation is that diffusivity of single Fourier components of the concentration field is treated separately, i.e., spectral turbulent diffusivity coefficients are introduced. The value of the diffusivity decreases with increasing wave vector k of the concentration spectrum. The rate of growth of an expanding cloud of material thus becomes dependent on the stage of growth. This is in qualitative agreement with the statistical dispersion theory. It is shown that the assumption of k-dependent diffusivity leads to a nonlocal flux-gradient relation. A new function, the turbulent diffusivity transfer function, is introduced. The turbulent diffusive flux depends on concentration gradients at all points in the space. The diffusion equation is written in terms of the turbulent diffusivity transfer function. The width of the turbulent diffusivity transfer fun...

Generalization of K Theory for Turbulent Diffusion. Part I: Spectral Turbulent Diffusivity Concept

The pseudospectral dispersion model (Christensen and Prahm, 1976) is adapted for simulation of the long-range transmission of sulphur pollutants in the European region, covering an area of about 4000 km x 4000 km. Regional ''background'' concentrations of sulphur oxides are found to be highly dependent on distant sources and to correlate poorly with local source strength during the considered three- and four-day episodes. The simulation is based on emission data, given in squares of about 50 km x 50 km and on synoptic wind fields derived from observed wind velocities of the 850 mb level and the surface level. The two-dimensional model includes a constant vertical mixing depth. Appropriate values for the deposition and the transformation rates of SO/sub 2/ and SO/sup /sub 4/ are used. The concentration of pollutants computed from the two-dimensional pseudospectral dispersion model reflects the variable meteorological conditions. Computed concentrations are compared with measurements, giving spatial correlations between 0.4 and 0.8 for more than 400 ground-based 24 h mean values, and a spatial correlation of 0.9 for eight aircraft samples averaged over approx.30 min. A discussion of the influence of different sources of error in the model simulation is given. The high numerical accuracy of themore » pseudospectral model is combined with a modest consumption of CPU computer time. This study is the first application of the pseudospectral dispersion model which compares computed concentrations with measured field data. The model has possible applications as a tool for assessment of the impact of both national and international emission regulation strategies.« less

Lars P. Prahm

Papers

Comparison of numerical techniques for use in air pollution models with non-linear chemical reactions

Implementation of a variable stepsize variable formula method in the time-integration part of a code for treatment of long-range transport of air pollutants

A Pseudospectral Model for Dispersion of Atmospheric Pollutants

Generalization of K Theory for Turbulent Diffusion. Part I: Spectral Turbulent Diffusivity Concept

Long-Range Transmission of Pollutants Simulated by a Two-Dimensional Pseudospectral Dispersion Model.