Journal cover Journal topic
Geoscientific Model Development An interactive open-access journal of the European Geosciences Union
Geosci. Model Dev., 10, 4419-4441, 2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
Development and technical paper
05 Dec 2017
The ABC model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations
Ruth Elizabeth Petrie1,a, Ross Noel Bannister1, and Michael John Priestley Cullen2 1Dept. of Meteorology, Univ. of Reading, Earley Gate, Reading, RG6 6BB, UK
2Met Office, FitzRoy Road, Exeter, EX1 3PB, UK
anow at: The Centre for Environmental Data Analysis, RAL Space, STFC Rutherford Appleton Laboratory, Harwell, Oxford, Didcot, OX11 0QX, UK
Abstract. 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 timescales 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 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 timescales 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).

Citation: Petrie, R. E., Bannister, R. N., and Cullen, M. J. P.: The ABC model: a non-hydrostatic toy model for use in convective-scale data assimilation investigations, Geosci. Model Dev., 10, 4419-4441,, 2017.
Publications Copernicus
Short summary
The model and experiments in this paper are to study atmospheric flows on small (kilometre) scales. Compared to larger-scale flows, kilometre-scale motion is more difficult to predict, and geophysical balances are less valid. For these reasons, data assimilation (or DA, the task of using observations to initialise models) is more difficult, as the character of forecast errors (which have to be corrected by DA) is more difficult to represent. This model will be used to study small-scale DA.
The model and experiments in this paper are to study atmospheric flows on small (kilometre)...