Multi-domain simulations of the time dependent Navier-Stokes equations: benchmark error analysis of some nesting procedures

A non-hydrostatic mesoscale model formulated by Tapp and White has been extended to include the effects of orography and the variation of the large-scale meteorological situation. Other changes to the model, particularly in the parametrization of boundary layer turbulence, are described and its application as a forecasting tool is illustrated by an extensive study of one situation.

An experimental forecast using a non‐hydrostatic mesoscale model

Publisher Summary This chapter presents a mesoscale numerical modeling for the study of atmosphere. It defines mesoscale as having a temporal and a horizontal spatial scale smaller than the conventional rawinsonde network, but significantly larger than individual cumulus clouds. In more quantitative terms, this implies that the horizontal scale is of the order of a few to 100 km or so, with a time scale of about 1–12 hours. The vertical scale extends from tens of meters or so to the depth of the troposphere. The fundamental conservation relations are introduced, along with appropriate simplifications. The equations are averaged in order to conform to a mesoscale model grid mesh. The types of models are discussed, and their advantages and disadvantages for proper simulation of mesoscale phenomena are outlined. The transformation of the equations to a generalized coordinate representation is presented. The parameterizations in a mesoscale model of the planetary boundary layer, electromagnetic radiation, and moist thermodynamics are also introduced. Methods of solution are illustrated with boundary and initial conditions. The procedure for evaluating models is discussed and examples of mesoscale simulations of particular mesoscale phenomena are illustrated.

Mesoscale Numerical Modeling

In the period June–July 1992, four Doppler sodars were operated simultaneously in Rome and the surrounding area. The data have been used to investigate the contributions from sea breeze events to the local low-level circulation. Three days in which synoptic-scale pressure gradients were weak have been selected. A number of characteristics of the sea breeze are examined including the onset and cessation of the phenomenon, the behavior of the wind speed, and the depth of the density flow. The time propagation of the events and the influence of orography are obtained from a comparison between the data at different sites. The low-level circulation in the early morning is associated with the land breeze and appears to be enhanced by a mountain wind from the surrounding hills. The observed behavior of the vertical velocity field associated with the sea breeze is consistent with model predictions.

Observations of sea breeze events in Rome and the surrounding area by a network of Doppler sodars

The importance of three-dimensional effects in a flow with negative potential vorticity is considered here; this is the three-dimensional counterpart of symmetric instability. the term symmetric instability refers to a two-dimensional flow with negative potential vorticity which develops roll circulations aligned along the thermal wind. the requirement for exact two-dimensionality is here relaxed by using three-dimensional numerical simulations. Two classes of simulation are described; both take a two-dimensional basic flow.



In the first part we explore the response of a flow with uniform negative potential vorticity to localized initial perturbations. It is found that circulations become established which elongate at an angle to the thermal wind. This angle, it is shown, is determined by viscous effects and is in accord with the structure of linear viscous tilted modes for this flow. If, as happens on occasions, such an angle formed by rainbands to the thermal wind is observed in nature, it gives an indication of the importance of viscous effects. In the cases presented here the orientation is such that the rolls tilt towards the warm air as viewed in the direction of the thermal wind; i.e. they are rotated anticyclonically relative to the front. It is shown that these structures, when at finite amplitude, are stable to perturbations imposed along their length.



In the second part localized regions of instability are produced which are confined along the thermal wind direction by prescribing in these zones a reduced static stability for vertical motion. This represents the effects of latent-heat release and it is only in these zones that the effective potential vorticity is negative. It is found that if the length of the zone along the thermal wind direction is smaller than about twice the roll wavelength across that direction then the growth rate is substantially reduced; otherwise it is relatively unaffected by this confinement. It therefore appears that a flow with negative potential vorticity is not only unstable in the pathological two-dimensional case.

G. A. Dalu

Papers

A parameterization of heat convection for a numerical sea breeze model