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L. M. Leslie

Abstract

One of the most striking synoptic features of the Australian tropics is the well-developed heat low which persists throughout the summer months. In spite of its significance, the heat low has not, up to the present, been well simulated by numerical forecast models.

In this article, a simple surface heat balance scheme has been incorporated in a large-scale numerical forecast model in order to improve the modeling of the heat low.

The scheme was tested on more than a month of consecutive days that were typical heat low situations. In almost all cases there was a significant improvement in the representation of the heat low.

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J. L. McGregor
and
L. M. Leslie

Abstract

It is shown that semi-implicit time differencing on a nonstaggered grid using centered time and space derivatives leads to a decoupling into four separate solutions on different subgrids. This deficiency may be successfully overcome by combining weighted averages of Laplacian operators on the subgrids. However, a far more satisfactory approach is shown to be the use of a staggered grid which appears to be a natural choice for the semi-implicit scheme.

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L. M. Leslie
and
M. S. Speer

Abstract

No abstract available.

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R. J. Purser
and
L. M. Leslie

Abstract

Having recently demonstrated that significant enhancement of forecast accuracy in a semi-Lagrangian model results from the application of high-order time integration methods to the second-derivative form of the equations governing the trajectories, the authors here extend the range of available methods by introducing a class of what they call “generalized Lorenz” (GL) schemes. These explicit GL schemes, like Lorenz’s “N-cycle” methods, which inspired them, achieve a high formal accuracy in time for linear systems at an economy of storage that is the theoretical optimum. They are shown to possess robustly stable and consistent semi-implicit modifications that allow the deepest (fastest) gravity waves to be treated implicitly, so that integrations can proceed efficiently with time steps considerably longer than would be possible in an Eulerian framework.

Tests of the GL methods are conducted using an ensemble of 360 forecast cases over the Australian region at high spatial resolution, verifying at 48 h against a control forecast employing time steps sufficiently short to render time truncation errors negligible. Compared with the performance of the best alternative semi-Lagrangian treatment of equivalent storage economy (a quasi-second-order generalized Adams–Bashforth method), our new GL methods produce significant improvements both in formal accuracy and in actual forecast skill.

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R. J. Purser
and
L. M. Leslie

Abstract

A new method of implementing the semi-Lagrangian technique is presented in the context of a limited-area, barotropic primitive equation model. The most notable feature of the new method is the way in which the semi-Lagrangian advection is treated. Instead of the commonly used backward-trajectory approach, forward trajectories are computed to the next time level using a method formally equivalent to the application of the third-order in time Adams-Bashforth method and incorporating a robust semi-implicit treatment of fast gravity modes.

Extensive comparisons between the new third-order in time forward-trajectory model, a second order forward-trajectory model, and two backward-trajectory schemes are made using the Australian Bureau of Meteorology Research Centre's regional barotropic model. A total of 100 cases is used to compare the methods, and they confirm in practice the theoretical superiority of the third-order method.

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K. Fraedrich
and
L. M. Leslie

Abstract

The results of a major real-time trial of techniques for the short-term (12 h ahead) prediction of precipitation for the Australian tropical city of Darwin are described. The trial compared current operational manual forecasting procedures with a range of alternative techniques including statistical methods, numerical weather prediction (NWP), and model output statistics (MOS) which were developed specifically for the trial.

The only technique of those tested which exhibited skill, i.e., consistent superiority over climatology and/or persistence, was a Markov chain model used either individually or in linear combination with other methods. Of particular significance was the relatively poor showing in the tropics of the numerical weather prediction model products, which were worse than both persistence and climatology. The results of this real-time trial should be treated with care because of the small sample size involved.

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K. Fraedrich
and
L. M. Leslie

Abstract

A “minimal” model is proposed here for the short-term prediction (up to 12 h ahead) of precipitation occurrence in the tropics. The model is purely statistical, consisting of an optimally weighted linear combination of a Markov chain and persistence. It is minimal in the sense that only surface data are needed, and the computing requirements are almost nil.

In this study the skill of the minimal model, i.e., accuracy relative to climatology and/or persistence, is demonstrated in theory and practice. The model was tested in real time during the 1986/87 Australian monsoon season at the tropical city of Darwin.

Results of the real-time experiment reveal that the minimal model was the only model of those available to the Australian Bureau of Meteorology (including manual forecasts, a regional NWP model, and a model output statistics (MOS) scheme) that exhibited forecast accuracy greater than that of both climatology and persistence.

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C. B. Fandry
and
L. M. Leslie

Abstract

A dominant feature of the low-level easterly wind flow in the Australian subtropics during summer is the trough development that occurs on both the western and eastern sides of the continent. This phenomenon is investigated analytically with a two-level model. A generalized solution is derived from the steady-state quasi-geostrophic equations governing uniform flow over arbitrarily shaped orography. The model solutions indicate that orography acting alone is of only marginal importance in producing the western trough. However, the high east coast orography is of significance in the formation of the eastern trough.

Land-sea temperature contrast is parameterized in terms of equivalent orography with localized surface heating being mathematically equivalent to an orographic depression. The solutions including orography and surface heating acting together simulate well the lower layer flow over the Australian subtropics.

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L. M. Leslie
and
R. K. Smith

Abstract

A recent numerical study of vortex growth in a flow configuration which models the principal characteristics of a tornado cyclone (Smith and Leslie, 1978) is extended to take account of vertical stability. It is shown that for a given strength of convection and rotation (in the model, the driving effect of a ‘supercell’ updraft is simulated by an imposed body force), the intensity of the mature vortex which forms in the presence of a typical vertical gradient of potential temperature is significantly lower than that which forms in an adiabatic atmosphere. We conclude that the effects of vertical stratification on tornadogenesis may often be important and may prevent some vortices, which might otherwise do so, from establishing ground contact.

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R. J. Purser
and
L. M. Leslie

Abstract

It is shown both in theory and in practice that the accuracy of time-split finite-difference methods may be increased by the very simple device of incrementally adding a portion of the advection term in the adjustment step of the method.

In the first part of this study, the theory of the approach is described, and large gains in accuracy are demonstrated by comparison with an exact solution to a forced oscillatory system.

The technique is then applied to a considerable number (100) of 48-h forecasts with a barotropic numerical weather prediction (NWP) model using 500-hPa data on the Australian region NWP domain. It is found that the incrementally split scheme is more accurate than the conventional split scheme, which generates more noise and has unrealistically larger values of the root-mean-square ageostrophic wind. A further advantage of the new scheme is that it has superior initialization properties.

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