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SUMMARYLooking forward towards mesh adaptivity for simulating turbulent atmospheric=oceanic ows, we are pursuing advanced algorithms for evaluating vector di erential operators cast in time-dependent curvilinear co-ordinates. In this paper, we review our e ort to date with the development of a deformableco-ordinates multi-scale anelastic model designed from the bottom-up relying on strengths of non-oscillatory transport methods. We have shown in earlier works that e ective multi-scale adaptive numerical models for high-Reynolds-number meteorological ows can be designed that dispense with rigorous evaluation of the more cumbersome of the vector di erential operators, such as the curl or the strain rate. These operators are nonetheless important for budget analyses of the model results, estimating physical uncertainties, driving the mesh adaptivity itself, and extending the model's applicability beyond standard meteorological situations. Here, we discuss selected extensions of the generic explicitly inviscid approach.

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Decreases in shelter temperature during eclipse events were quantified on the basis of observations, numerical model simulations, and complementary conceptual evaluations. Observations for the annular eclipse on 10 May 1994 over the United States are presented, and these provide insights into the temporal and spatial changes in the shelter temperature. The observations indicated near-surface temperature drops of as much as 6°C. Numerical model simulations for this eclipse event, which provide a complementary evaluation of the spatial and temporal patterns of the temperature drops, predict similar decreases. Interrelationships between the temperature drop, degree of solar irradiance reduction, and timing of the peak eclipse are also evaluated for late spring, summer, and winter sun conditions. These simulations suggest that for total eclipses the drops in shelter temperature in midlatitudes can be as high as 7°C for a spring morning eclipse.

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SUMMARYGeophysical ows can profoundly a ect human activities. Often characterized by an astonishing range of signiÿcant scales and a rich assortment of physical processes, the complexity of such ows generally precludes all but numerical simulation for prediction and understanding-yet even state of the art computational models may be severely challenged by problems such as hurricane intensiÿcation. Although a number of signiÿcant issues are involved, a major factor is often grid resolution, for which grid adaptivity (GA) can be useful. Our experience has been that MPDATA is particularly well suited for GA. This paper sketches general details of a model that blends MPDATA with continuous GA; highlights a tensor viewpoint of the geometric conservation law; and presents results for both global and regional atmospheric applications. Together, the examples demonstrate the advantages of using GA with MPDATA to resolve ÿne-scale features-explicit gravity waves generated by ow over orography. Resolution of these waves (or lack thereof) are shown to a ect global climate; furthermore, wave resolution is shown to depend upon the regional atmospheric environment. Finally the regional simulations show a surprising increase in the complexity of the waveÿelds as resolution is increased to the point of resolving nonhydrostatic e ects.