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Lance M. Leslie
and
R. James Purser

Abstract

Through the use of the dimensional splitting “cascade” method of grid-to-grid interpolation, it is shown that consistently high-order-accurate semi-Lagrangian integration of a three-dimensional hydrostatic primitive equations model can be carried out using forward (downstream) trajectories instead of the backward (upstream) trajectory computations that are more commonly employed in semi-Lagrangian models. Apart from the efficiency resulting directly from the adoption of the cascade method, improved computational performance is achieved partly by the selective implicit treatment of only the deepest vertical gravity modes and partly by obviating the need to iterate the estimation of each trajectory's location. Perhaps the main distinction of our present semi-Lagrangian method is its inherent exact conservation of mass and passive tracers. This is achieved by adopting a simple variant of the cascade interpolation that incorporates mass (and tracer) conservation directly and at only a very modest additional cost. The conserving cascade, which is described in detail, is a generic algorithm that can be applied at arbitrary order of accuracy.

Tests of the new mass-conserving scheme in a regional forecast model show small but consistent improvements in accuracy at 48 h. It is suggested that the benefits to extended global forecasting and simulation should be much greater.

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Lance M. Leslie
and
Greg J. Holland

Abstract

The potential for predicting the skill of 36-h forecasts from the Australian region limited area model is investigated using three predictors of model forecast error (MFE) for mean sea level pressure. Two of the predictors utilize single forecasts: one is based on statistical regression of the MFE against the initial analysis and the forecast; and the other uses a measure of the degree of persistence in the forecast. The third predictor utilizes the divergence, or spread, of an ensemble of forecasts from other NWP centers.

Based on a 5-month period of daily 36-h forecasts, correlations were found between the above predictors and the MFE of 0.58, 0.18, and 0.40, respectively. Combining the three predictors in an optimal linear manner increased the correlation to 0.71. Further testing of the combined predictors on a 2-month independent dataset produced a correlation of 0.67. Thus, application of the technique to both dependent and independent datasets explained approximately 50% of the variance in the MFE. This demonstrates that the technique has operational utility for differentiating overall poor and good model forecasts. Using case studies concentrating on southeastern Australia, it is further demonstrated that the predictors can provide excellent differentiation of forecast skill across the forecast domain.

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LANCE M. LESLIE
and
BRYANT J. McAVANEY

Abstract

The Helmholtz-type equation arises in many areas of fluid dynamics, and, in recent years, there has been a rapid increase in the numerical procedures available for solving the equation. In this note, the various methods currently available are discussed, and representatives from the main categories are compared.

We suggest that for certain problems, the most important of which is Poisson's equation on a rectangle, direct methods are now available that are far superior to widely used iterative methods. For problems involving irregular domains, mixed boundary conditions, and variable Helmholtz coefficients, however, existing direct methods often cannot be used with the same flexibility as iterative methods; there is a continuing need to extend direct methods to these more general cases.

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Bradford S. Barrett
and
Lance M. Leslie

Abstract

The leading intraseasonal mode of atmospheric and oceanic variability, the Madden–Julian oscillation (MJO), influences tropical and extratropical sea level pressure, temperature, divergent and rotational wind components, moisture, and deep convection. As a 40- to 50-day oscillation, the MJO is also known to influence tropical phenomena, including tropical cyclone (TC) activity in various TC basins. The links between the MJO and multiple measures of TC activity, including genesis, landfall, and an integrative accumulated cyclone energy (ACE) index, were quantified for multiple TC-formation basins across the Western Hemisphere, including the North Atlantic and northeast Pacific Ocean and subbasins, for the period 1978–2006. Using this relatively long (29 yr) TC dataset and employing an upper-tropospheric MJO diagnostic that is physically meaningful over the entire Western Hemisphere, this study extends existing research on the relationships between the MJO and TCs. The NOAA Climate Prediction Center’s operational MJO index, derived from 200-hPa velocity potential data, was divided into three phases. Relative frequencies of the MJO phases were compared with observed levels of TC activity using a binomial distribution hypothesis test. The MJO was found to statistically significantly modulate the frequency of TC genesis, intensification, and landfall in the nine TC basins studied. For example, when an MJO index was large and positive at 120°W, hurricanes and intense hurricanes were 4 times as likely to make landfall in the North Atlantic. This modulation of TC activity, including landfall patterns in the North Atlantic, was physically linked to the upper-atmospheric response to the eastward-propagating MJO and is evident as a dipole of TC activity between Pacific and Atlantic subbasins.

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Lance M. Leslie
and
Gary S. Dietachmayer

Abstract

Over the years there have been a number of studies comparing the relative merits of semi-Lagrangian and Eulerian schemes. These studies, which continue to appear in the literature up to the present, almost invariably conclude that semi-Lagrangian schemes are superior in accuracy, and produce less noise, than Eulerian schemes. It is argued in this note that such conclusions are not justified because they have compared semi-Lagrangian and Eulerian schemes of different orders of accuracy. Typically, the semi-Lagrangian schemes tested have employed cubic spatial interpolation (and therefore are third order) in space, whereas the Eulerian schemes have usually been second order (and sometimes fourth order) in space. It is shown here that when semi-Lagrangian and Eulerian schemes of the same order are applied to the test case, namely, that of “warm bubble” convection, there are almost indiscernible differences between the simulations. The contention presented here, therefore, is that it is the order of the scheme that is of primary importance, not whether it is semi-Lagrangian or Eulerian.

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Lance M. Leslie
and
Milton S. Speer
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Hamish A. Ramsay
and
Lance M. Leslie

Abstract

The interaction between complex terrain and a landfalling tropical cyclone (TC) over northeastern Australia is investigated using the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). Severe TC Larry (in March 2006) made landfall over an area of steep coastal orography and caused extensive damage. The damage pattern suggested that the mountainous terrain had a large influence on the TC wind field, with highly variable damage across relatively small distances. The major aims in this study were to reproduce the observed features of TC Larry, including track, intensity, speed of movement, size, decay rate, and the three-dimensional wind field using realistic high-resolution terrain data and a nested grid with a horizontal spacing of 1 km for the finest domain (referred to as CTRL), and to assess how the above parameters change when the terrain height is set to zero (NOTOPOG). The TC track for CTRL, including the timing and location of landfall, was in close agreement with observation, with the model eye overlapping the location of the observed eye at landfall. Setting the terrain height to zero resulted in a more southerly track and a more intense storm at landfall. The orography in CTRL had a large impact on the TC’s 3D wind field, particularly in the boundary layer where locally very high wind speeds, up to 68 m s−1, coincided with topographic slopes and ridges. The orography also affected precipitation, with localized maxima in elevated regions matching observed rainfall rates. In contrast, the precipitation pattern for the NOTOPOG TC was more symmetric and rainfall totals decreased rapidly with distance from the storm’s center. Parameterized maximum surface wind gusts were located beneath strong boundary layer jets. Finally, small-scale banding features were evident in the surface wind field over land for the NOTOPOG TC, owing to the interaction between the TC boundary layer flow and land surface characteristics.

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Christopher S. Velden
and
Lance M. Leslie

Abstract

A simple barotropic model is employed to investigate relative impacts on tropical cyclone motion forecasts in the Australian region when wind analyses from different tropospheric levels or layers are used as the input to the model. The model is initialized with selected horizontal wind analyses from individual pressure levels, and vertical averages of several pressure levels (layer-means).

The 48-h mean forecast errors (MFE) from this model are analyzed for 300 tropical cyclone cases that cover a wide range of intensities. A significant reduction in the track forecast errors results when the depth of the vertically-averaged initial wind analysis depends upon the initial storm intensity. Mean forecast errors show that the traditionally-utilized 1000-100-hPa deep layer-mean (DLM) analysis is a good approximation of future motion only in cases of very intense tropical cyclones. Shallower, lower-tropospheric layer-means consistently outperform single-level analyses, and are best correlated with future motion in weak and moderate intensity cases.

These results suggest that barotropic track forecasting in the Australian region can be significantly improved if the depth of the vertically-averaged initial wind analysis is based upon the tropical cyclone intensity.

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Lance M. Leslie
and
Klaus Fraedrich

Abstract

It is shown that an optimal linear combination of independent forecasts of tropical cyclone tracks significantly reduces the mean forecast-position errors. In this study the independent forecasts are provided by a statistical scheme (CLIPER) and a numerical weather prediction (NWP) model operating over the Australian tropics.

A comparison is made between the optimal linear combination and four other forecast techniques, over the five Australian tropical cyclone seasons 1984/85–1987/88. The combination method gave a mean position error of 157 km at 24 h using independent “best track” data, an improvement of 15% over the next most accurate method. At 48 h, the mean position error of 312 km was 17% less than the next most accurate scheme.

The combination method was assessed further in a real-time trial on operational data during the 1988/89 Australian tropical cyclone season. The results of this trial confirmed the superiority of the combination technique over the other methods. It will be used operationally in the next Australian tropical cyclone season (1989/90) either in its present form or as part of an integrated “expert” system being developed specifically for tropical cyclone motion prediction.

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