Essay review
Conceiving processes in atmospheric models—General equations, subscale parameterizations, and ‘superparameterizations’

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Abstract

The scientific understanding of atmospheric processes has been rooted in the mechanical and physical view of nature ever since dynamic meteorology gained ground in the late 19th century. Conceiving the atmosphere as a giant ‘air mass circulation engine’ entails applying hydro- and thermodynamical theory to the subject in order to describe the atmosphere’s behaviour on small scales. But when it comes to forecasting, it turns out that this view is far too complex to be computed. The limitation of analytical methods precludes an exact solution, forcing scientists to make use of numerical simulation. However, simulation introduces two prerequisites to meteorology: First, the partitioning of the theoretical view into two parts—the large-scale behaviour of the atmosphere, and the effects of smaller-scale processes on this large-scale behaviour, so-called parametrizations; and second, the dependency on computational power in order to achieve a higher resolution. The history of today’s atmospheric circulation modelling can be reconstructed as the attempt to improve the handling of these basic constraints. It can be further seen as the old schism between theory and application under new circumstances, which triggers a new discussion about the question of how processes may be conceived in atmospheric modelling.

Introduction

At the end of the 19th century the US–American meteorologist Cleveland Abbe complained that meteorologists were mere statisticians, observers, and empiricists rather than mathematicians and physicists (cf. Nebeker, 1995, p. 28). Abbe and others, e.g. Julius Hann, William N. Shaw, Ludwig Silberstein, Max Margules and Felix Exner, had tried to apply physics to meteorology and used calculations based on hydro- and thermodynamics to achieve results for wind patterns and air pressure changes. But it was the outstanding achievement of Vilhelm Bjerknes that gave the fragmented field of “dynamic meteorology” a sustainable vision. In 1904 Bjerknes published his concept of weather prediction from the ‘viewpoint of mechanics and physics’, laying the foundation of meteorology grounded in the physics of the atmosphere (cf. Bjerknes, 1904). His vision introduced to meteorology the full scope of hydro- and thermodynamics and with it mathematical, and later, numerical models and simulation.

Applying hydro- and thermodynamics to meteorology, as Bjerknes outlined in 1904, introduced the small-scale perspective on the atmosphere’s behaviour. But meteorologists had been applying a view on the atmosphere from the synoptic scale—a horizontal length scale on the order of 1000–2500 km. In fact, there are four main scales in meteorology used to look at typical weather phenomena: the macroscale (global size, e.g. planetary waves), the synoptic scale (from 1000 to 2500 km, e.g. extratropical cyclones), the meso-alpha scale (from 200 to 2000 km, e.g. tropical cyclones), the meso-beta scale (from 20 to 200 km, e.g. mesocyclones), and the microscale (all phenomena smaller than 2 km, e.g. cloud dynamics). Therefore a model of the atmosphere has to combine the small-scale and the large-scale views by deriving equations for a large-scale system that contain terms describing the effects of smaller-scale processes on the large-scale events, so-called parametrizations. However, the use of hydro- and thermodynamics introduced various new conditions into meteorology. On the one hand it led to a ‘peculiar’ situation, as a climate modeller pointed out aptly when he talked about today’s ‘cloud parametrization deadlock’: “Even though the basic physical equations in which we have the most confidence describe small-scale processes, in practice it is the effects of those small-scale processes that are incorporated into our models through the use of uncertain closure assumptions. It is ironic that we cannot represent the effects of the small-scale processes by making direct use of the well-known equations that govern them” (Randall, Khairoutdinov, Arakawa, & Grabowski, 2003, p. 1548). On the other hand, it required an appropriate computational method to make use of mathematical models in order to achieve forecasts. And finally it led to a strong dependency on computational power to perform higher resolutions for ‘better’ numerical solutions. The development of dynamic meteorology from 1904 until today has struggled with these problems. Since conceiving the theoretical foundation of the physics of the atmosphere (cf. Bjerknes, 1904), two approaches of computational methods have been developed for forecasts: a graphical method (cf. Bjerknes & Sandström, 1911) and a numerical one (cf. Richardson, 1922). As the numerical method succeeded, evinced by the successes of Charney, 1950, Charney, 1953 accomplishing the first numerical weather simulation and Phillips (1956) the first climate simulation, computational power has turned out to be a driving force in meteorology.

Against this backdrop the question is posed as to how computational conditions and the scientific understanding of atmospheric processes determine each other. The hypothesis will be discussed that science faces the old schism between theory and application, which it has tried to overcome by introducing numerical simulations (cf. Goldstine & von Neumann, 1946) under new circumstances. Furthermore, considering how modern science has come to be driven by both measurement devices and computational ones, the question will be discussed as to whether current developments in high-performance computing may force a new scientific conception of processes, particularly due to the low performance rates achieved in the computation of subscale parametrizations. Following this aim, Section 2 of this paper will briefly reconstruct the history of dynamic meteorology in an attempt to overcome the purely statistical and empirical view of the atmosphere by introducing hydro- and thermodynamical theory. Then Section 3 will reconstruct efforts to overcome the stagnation of analysis and the schism between theory and application through computation. It continues by analyzing how the effects of small-scale processes on large-scale ones are conceived in Section 4. And it finally discusses in Section 5 the impact of high-performance computing on meteorology. The outlined perspective is gleaned from statements by leading protagonists in the field of dynamic meteorology and their views on the influence of the computer.

Section snippets

The schism between theory and application

In his 1904 paper Vilhelm Bjerknes stated that “as any scientifically thinking man believes, the later state of the atmosphere develops from the former according to physical laws”, and that “the necessary and sufficient conditions for a rational solution of the problem of meteorological prediction are the following: 1. One has to know with sufficient accuracy the state of the atmosphere at a certain time. 2. One has to know with sufficient accuracy the laws according to which a certain state of

Two styles of computing

Regarding this situation, Bjerknes “abandon[ed] any thought of analytical integration methods” (Bjerknes, 2009 [1904], p. 665). Instead, he developed a practical one by introducing a graphical method to compute results from his generalized circulation theorem. In 1900 he had already described a geometrical model of circulation, in which pressure and density intersecting in a three-dimensional surface would form a series of tubes (solenoids). The number of solenoids encompassing the fluid curve

The problem of subscale parametrization

Atmospheric modelling combines two views on the atmosphere: a large-scale view depending on the resolution of the computed model, and a view on subscale processes which have an effect on the large-scale events. When the mathematical model of the atmosphere is translated into a numerical one, the general equations of circulation have to be discretized for a number of grid points, dividing the atmosphere into a number of grid cells and several vertical layers. Each grid point is determined for

Conclusion

It was John von Neumann who pointed out that “it is noteworthy that the physical experimentation which leads to these and similar discoveries [in fluid dynamics] is a quite peculiar form of experimentation [. . .] under conditions where the underlying physical principles are not in doubt, where the quantities to be observed are completely determined by known equations. The purpose of the experiment is not to verify a proposed theory but to replace a computation from an unquestioned theory by

Acknowledgment

The paper is based on a case and laboratory study in climate modelling supported by the Max Planck Institute for Meteorology Hamburg (200–2008) and funded by the German Federal Ministry of Education and Research. I like to thank Johann Feichter from the Max Planck Institute for Meteorology for his comments.

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