Numerical Methods in Atmospheric Models

The astonishing development of computer technology since the mid-20th century has been accompanied by a corresponding proliferation in the numerical methods that have been developed to improve the simulation of atmospheric flows. This article reviews some of the numerical developments concern the ongoing improvements of weather forecasting and climate simulation models. Early computers were single-processor machines with severely limited memory capacity and computational speed, requiring simplified representations of the atmospheric equations and low resolution. As the hardware evolved and memory and speed increased, it became feasible to accommodate more complete representations of the dynamic and physical atmospheric processes. These more faithful representations of the so-called primitive equations included dynamic modes that are not necessarily of meteorological significance, which in turn led to additional computational challenges. Understanding which problems required attention and how they should be addressed was not a straightforward and unique process, and it resulted in the variety of approaches that are summarized in this article. At about the turn of the century, the most dramatic developments in hardware were the inauguration of the era of massively parallel computers, together with the vast increase in the amount of rapidly accessible memory that the new architectures provided. These advances and opportunities have demanded a thorough reassessment of the numerical methods that are most successfully adapted to this new computational environment. This article combines a survey of the important historical landmarks together with a somewhat speculative review of methods that, at the time of writing, seem to hold out the promise of further advancing the art and science of atmospheric numerical modeling.

A flexible three-dimensional stratocumulus, cumulus and cirrus cloud generator (3DCLOUD) based on drastically simplified atmospheric equations and the Fourier transform framework

The 3DCLOUD algorithm for generating stochastic three-dimensional (3-D) cloud fields is described in this paper. The generated outputs are 3-D optical depth (τ) for stratocumulus and cumulus fields and 3-D ice water content (IWC) for cirrus clouds. This model is designed to generate cloud fields that share some statistical properties observed in real clouds such as the inhomogeneity parameter ρ (standard deviation normalized by the mean of the studied quantity), the Fourier spectral slope β close to −5/3 between the smallest scale of the simulation to the outer Lout (where the spectrum becomes flat). Firstly, 3DCLOUD assimilates meteorological profiles (humidity, pressure, temperature and wind velocity). The cloud coverage C, defined by the user, can also be assimilated, but only for stratocumulus and cumulus regime. 3DCLOUD solves drastically simplified basic atmospheric equations, in order to simulate 3-D cloud structures of liquid or ice water content. Secondly, the Fourier filtering method is used to constrain the intensity of ρ, β, Lout and the mean of τ or IWC of these 3-D cloud structures. The 3DCLOUD model was developed to run on a personal computer under Matlab environment with the Matlab statistics toolbox. It is used to study 3-D interactions between cloudy atmosphere and radiation.

A flexible three-dimensional stratocumulus, cumulus and cirrus cloud generator (3DCLOUD) based on drastically simplified atmospheric equations and Fourier transform framework

The 3DCLOUD algorithm for generating stochastic three-dimensional (3-D) cloud fields is described in this paper. The generated outputs are 3-D optical depth (τ) for stratocumulus and cumulus fields and 3-D ice water content (IWC) for cirrus clouds. This model is designed to generate cloud fields that share some statistical properties observed in real clouds such as the inhomogeneity parameter ρ (standard deviation normalized by the mean of the studied quantity), the Fourier spectral slope β close to −5/3 between the smallest scale of the simulation to the outer Lout (where the spectrum becomes flat). Firstly, 3DCLOUD assimilates meteorological profiles (humidity, pressure, temperature and wind velocity). The cloud coverage C, defined by the user, can also be assimilated, but only for stratocumulus and cumulus regime. 3DCLOUD solves drastically simplified basic atmospheric equations, in order to simulate 3-D cloud structures of liquid or ice water content. Secondly, Fourier filtering method is used to constrain intensity of ρ, β, Lout and mean of τ or IWC of these 3-D cloud structures. 3DCLOUD model was developed to run on a personnel computer under Matlab environment with the Matlab statistics toolbox. It is used to study 3-D interactions between cloudy atmosphere and radiation.