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Roger A. Pielke
and
Charles L. Martin

Abstract

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Charles L. Martin
and
Roger A. Pielke

Abstract

Using a linear analytic model and a nonlinear numerical model, the adequacy of the hydrostatic model is investigated for use in the simulation of sea and land breezes over flat terrain. Among the results it is found that for a given horizontal scale of heating, the hydrostatic assumption becomes less valid as the intensity of surface heating increases, and as the synoptic temperature lapse rate becomes less stable. The spatial scale at which the hydrostatic assumption fails is substantially smaller than suggested by Orlanski (1981). For sufficiently stable large-scale thermodynamic stratifications, for instance, aspect ratios of order unity can still produce nearly identical solutions, regardless of whether or not the hydrostatic assumption is used. The difference in the conclusions between our study and that of Orlanski is attributed to Orlanksi's analyses of the characteristic wave equations in the free atmosphere, whereas in a sea-breeze simulation the requirement that vertical velocity at the ground is zero limits the magnitude of the vertical acceleration.

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Roger A. Pielke
and
Charles L. Martin

Abstract

This article uses tensor transformation procedures in order to derive a terrain-following coordinate system that is frequently used in a number of regional and mesoscale hydrostatic models. Tensor transformation procedures are used so as to ensure physical invariance of the primitive equations between the Cartesian and terrain-following systems. Among the major conclusions are as follows:

  1. Applying the chain rule to the hydrostatic equation, before transforming from a Cartesian to a terrain-following coordinate system, yields a different set of equations than if the hydrostatic assumption is applied after the tensor transformation is made. The hydrostatic equations in the two terrain-following representations are the same only when the slope of the terrain in the model is much less than 45°.

  2. Variations of the metric tensor across a grid volume appear in the set of conservation equations as a result of averaging the equations over a grid volume. Such deviations have always been ignored in existing non-hydrostatic and hydrostatic meteorological models.

  3. Care must be taken to assure that parameterizations which are a function of distance above the ground be defined in terms of the original Cartesian system, and not the new generalized vertical coordinate σ. The profile exchange coefficient K(z), for example, cannot be defined simply by replacing z by σ.

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Greg M. McFarquhar
,
Christopher S. Bretherton
,
Roger Marchand
,
Alain Protat
,
Paul J. DeMott
,
Simon P. Alexander
,
Greg C. Roberts
,
Cynthia H. Twohy
,
Darin Toohey
,
Steve Siems
,
Yi Huang
,
Robert Wood
,
Robert M. Rauber
,
Sonia Lasher-Trapp
,
Jorgen Jensen
,
Jeffrey L. Stith
,
Jay Mace
,
Junshik Um
,
Emma Järvinen
,
Martin Schnaiter
,
Andrew Gettelman
,
Kevin J. Sanchez
,
Christina S. McCluskey
,
Lynn M. Russell
,
Isabel L. McCoy
,
Rachel L. Atlas
,
Charles G. Bardeen
,
Kathryn A. Moore
,
Thomas C. J. Hill
,
Ruhi S. Humphries
,
Melita D. Keywood
,
Zoran Ristovski
,
Luke Cravigan
,
Robyn Schofield
,
Chris Fairall
,
Marc D. Mallet
,
Sonia M. Kreidenweis
,
Bryan Rainwater
,
John D’Alessandro
,
Yang Wang
,
Wei Wu
,
Georges Saliba
,
Ezra J. T. Levin
,
Saisai Ding
,
Francisco Lang
,
Son C. H. Truong
,
Cory Wolff
,
Julie Haggerty
,
Mike J. Harvey
,
Andrew R. Klekociuk
, and
Adrian McDonald

Abstract

Weather and climate models are challenged by uncertainties and biases in simulating Southern Ocean (SO) radiative fluxes that trace to a poor understanding of cloud, aerosol, precipitation, and radiative processes, and their interactions. Projects between 2016 and 2018 used in situ probes, radar, lidar, and other instruments to make comprehensive measurements of thermodynamics, surface radiation, cloud, precipitation, aerosol, cloud condensation nuclei (CCN), and ice nucleating particles over the SO cold waters, and in ubiquitous liquid and mixed-phase clouds common to this pristine environment. Data including soundings were collected from the NSF–NCAR G-V aircraft flying north–south gradients south of Tasmania, at Macquarie Island, and on the R/V Investigator and RSV Aurora Australis. Synergistically these data characterize boundary layer and free troposphere environmental properties, and represent the most comprehensive data of this type available south of the oceanic polar front, in the cold sector of SO cyclones, and across seasons. Results show largely pristine environments with numerous small and few large aerosols above cloud, suggesting new particle formation and limited long-range transport from continents, high variability in CCN and cloud droplet concentrations, and ubiquitous supercooled water in thin, multilayered clouds, often with small-scale generating cells near cloud top. These observations demonstrate how cloud properties depend on aerosols while highlighting the importance of dynamics and turbulence that likely drive heterogeneity of cloud phase. Satellite retrievals confirmed low clouds were responsible for radiation biases. The combination of models and observations is examining how aerosols and meteorology couple to control SO water and energy budgets.

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