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The “ABC model”: a non-hydrostatic toy model for use in convective-scale data assimilation investigations

Petrie, R. E., Bannister, R. N. and Cullen, M. J. P. (2017) The “ABC model”: a non-hydrostatic toy model for use in convective-scale data assimilation investigations. Geoscientific Model Development, 10. pp. 4419-4441. ISSN 1991-959X

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To link to this item DOI: 10.5194/gmd-10-4419-2017


In developing methods for convective-scale data assimilation (DA) it is necessary to consider the full range of motions governed by the compressible Navier-Stokes equations (including non-hydrostatic and ageostrophic flow). These equations describe motion on a wide range of time-scales with non-linear coupling. For the purpose of developing new DA techniques that suit the convective-scale problem it is helpful to use so-called ‘toy models’ that are easy to run, and contain the same types of motion as the full equation set. Such a model needs to permit hydrostatic and geostrophic balance at large-scales, but to allow imbalance at small-scales, and in particular, it needs to exhibit intermittent convection-like behaviour. Existing ‘toy models’ are not always sufficient for investigating these issues. A simplified system of intermediate complexity derived from the Euler equations is presented, which supports dispersive gravity and acoustic modes. In this system the separation of time scales can be greatly reduced by changing the physical parameters. Unlike in existing toy models, this allows the acoustic modes to be treated explicitly, and hence inexpensively. In addition, the non-linear coupling induced by the equation of state is simplified. This means that the gravity and acoustic modes are less coupled than in conventional models. A vertical slice formulation is used which contains only dry dynamics. The model is shown to give physically reasonable results, and convective behaviour is generated by localised compressible effects. This model provides an affordable and flexible framework within which some of the complex issues of convective-scale DA can later be investigated. The model is called the “ABC model” after the three tunable parameters introduced: A (the pure gravity wave frequency), B (the modulation of the divergent term in the continuity equation), and C (defining the compressibility).

Item Type:Article
Divisions:Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO)
Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
ID Code:75739
Publisher:European Geosciences Union


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