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Rainer Bleck

Abstract

Equations are derived in coordinate-invariant vector notation for the time rate of change of shear and curvature vorticity. These equations are a generalization of equations in natural coordinates derived 30 years ago by Hollmann, and serve to elucidate the conversion process between shear and curvature vorticity. The new form of the conversion term will make it easier to diagnose its magnitude by computer-based objective analysis methods.

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Rainer Bleck

Abstract

Using observed data and model simulations, an attempt is made to verify that baroclinic instability can be viewed as an interaction and mutual amplification of a pair of upper- and lower-tropospheric potential vorticity (PV) perturbations. This view has recently been advanced by Hoskins et al. and McIntyre. Two episodes from March and May 1989, encompassing two lee-cyclogenetic events east of the Rocky Mountains and one over the central Gulf states, are selected to demonstrate this concept. In order to depict the low-level PV maximum which forms infinitely thin sheets of infinite PV, the display of PV in cartesian space is replaced by a display of absolute vorticity in isentropic space. Perspective computer drawings of iso-surfaces of absolute vorticity in three-dimensional space are found to be a convenient means of conveying the desired information.

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Rainer Bleck

Abstract

In a few selected cases of explosive cyclogenesis, a “coarse-mesh” nine-level isentropic prediction model conserving potential geostrophic vorticity is shown to yield dependable 36-hr forecasts of developing cyclones. Stagnant cyclones in adjacent areas are handled with the same degree of accuracy, indicating that numerical instability in the model is not a likely cause of the spontaneous cyclonic development. Tentative conclusions are drawn about the advantages of isentropic, as opposed to isobaric, objective analysis.

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Rainer Bleck

Abstract

The problem of transforming fields of atmospheric variables from one vertical coordinate system to another without altering their dynamic balance is discussed. A curve fitting scheme applied to the data points in each grid column is proposed which reduces the onset of barotropic imbalances during the transform process.

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Rainer Bleck

Abstract

A numerical model framed in isentropic coordinates is applied to the problem of predicting lee cyclogenesis south of the Alps. Since “Genoa cyclones” during their initial stage are mesoscale phenomena, while mid-tropospheric flow configurations conducive to Genoa cyclogenesis are not, a grid nesting approach is followed in the model to capture both large-scale and mesoscale aspects of the problem. The two grids differ in mesh aim by a factor of 4 and interact in a two-way mode. The model is dry and uses a highly simplified surface drag formulation.

Twenty-four hour predictions carried out on three occasions of observed cyclogenesis show that the model is capable of simulating cyclonic development approximately in the correct location. However, by slightly underpredicting the development of a high-pressure ridge over the eastern Atlantic the model in two of the three cases fails to build up the lee cyclone to the observed strength.

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Rainer Bleck

Abstract

A comparison is made of several ways to combine isentropic with sigma coordinates in a numerical weather prediction model in order to benefit from the advantage of either coordinate. The resulting hybrid model versions appear to be well-behaved numerically. A noise index introduced to provide a measure of external gravitational imbalances shows that hybrid models are somewhat “quieter” than isentropic coordinate models. Results from a related experiment suggest that this reduction in gravitational noise is not simply due to a fundamental noise difference between isentropic and sigma coordinate models but is likely to be a result of the hybridization.

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Rainer Bleck

Abstract

Two limited-area prediction models in isentropic coordinates, one based on potential vorticity conservation and one using the primitive equations of motion, are tested on 50 synoptic cases chosen from winter and spring of 1972/73. Both models disregard diabatic processes, but incorporate variable terrain height. Numerical instabilities caused by overturning or entwining coordinate surfaces appear to be no problem in this approach, and the gravitational noise generated at the lower boundary in the primitive equation model is shown to remain well within acceptable limits. Skill scores based on displacement errors of surface cyclones and on correlations between predicted and observed sea-level pressure gradients indicate that neither model at this stage can compete with the six-level hemispheric model used by the National Weather Service. Of the two isentropic models, the one using primitive equations shows better skill than the potential vorticity model.

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Rainer Bleck

Abstract

A method for analyzing height fields from simultaneous observations of height and wind is proposed which combines Gandin's optimum interpolation concept with the classical approach of extrapolating height values geostrophically to a grid point from surrounding stations. While recently developed multivariate optimum interpolation techniques using both height and wind data result in a somewhat smaller rms error of the analyzed height field than the present method, they require approximately 33 times as much computer time.

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Shan Sun and Rainer Bleck

Abstract

The thermohaline circulation (THC) in a 1000-yr near-global numerical simulation using the Miami Isopycnic Coordinate Ocean Model is analyzed and compared to observations. The model, driven by observed monthly atmospheric climatology, uses potential density referenced to 2000 m (σ 2) as the vertical coordinate and accounts for compressibility (thermobaricity) effects. Examination of the three-dimensional mass flux field reveals that the model comes fairly close to quantitatively reproducing a number of global and basin-scale circulation features, such as the vertical–meridional overturning rate in the three major basins, the meridional heat flux, and the transport through the major passages. Methods are presented that allow the construction of composite diagrams revealing quantitative regional aspects of the modeled circulation in potential density space. The diagrams reveal many features of the modeled THC that adhere to observations, the most noticeable shortcoming being a weaker-than-observed northward penetration of bottom water into the three major basins caused by insufficient production of Antarctic Bottom Water.

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Helge Drange and Rainer Bleck

Abstract

Multidimensional advection schemes based on the forward-upstream discretization are presented that with only one corrective step produce solutions comparable to the most accurate solutions produced by the multidimensional positive definite advection transport algorithm (MPDATA) family of schemes. The proposed schemes are not positive definite by structure, in contrast to the family of MPDATA schemes. A monotonicity-preserving algorithm is therefore an integral part of the schemes. Based on linear von Neumann analysis and numerical advection experiments in uniform, rotational, and deformational flows, it has been shown that all of the monotone versions of the schemes are stable for ΣMI |α I| ≤ 0.5, where α I and M are the advective Courant number and the dimensionality of the problem, respectively. Five of the proposed schemes have an amplification error close to, or slightly less than, that of the most accurate versions of the MPDATA scheme. The monotone second-order version of the most accurate scheme is 60% more expensive than the basic second-order MPDATA scheme with one antidiffusive correction step, but 70% cheaper than the corresponding monotone version of MPDATA. In addition, the most accurate of the proposed schemes is more cost efficient than any of the MPDATA schemes. All of the second-order versions of the schemes have a phase error similar to the first-order forward-upstream scheme. The phase error can be reduced by compensating for the second-order forward-upstream discretization error term. If the uniform version of the second-order forward-upstream discretization error term is applied to the schemes, the most accurate scheme becomes up to five times as efficient as the most accurate MPDATA scheme.

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