Dynamic meteorology

(meteorology) The study of atmospheric motions as solutions of the fundamental equations of hydrodynamics or other systems of equations appropriate to special situations, as in the statistical theory of turbulence.

The study of those motions of the atmosphere that are associated with weather and climate. Atmospheric motions span an enormous range of spatial and temporal scales; dynamic meteorology concentrates mainly on large-scale and mesoscale motions. Large-scale motions are those with horizontal scales in excess of a few hundred kilometers and time scales longer than a day. Such motions are strongly influenced by the rotation of the Earth and by the vertical thermal stratification of the atmosphere. Mesoscale motions have horizontal scales in the range of a few kilometers to a few hundred kilometers; they are often associated with convective clouds and precipitation.

The mechanics and thermodynamics of the unsaturated atmosphere are governed by three fundamental conservation laws: (1) conservation of mass, expressed by the mass continuity equation; (2) conservation of momentum, expressed by Newton's second law of motion; and (3) conservation of thermodynamic energy, expressed by the first law of thermodynamics. For saturated conditions, conservation of water substance must also be considered. See also Conservation of mass; Conservation of momentum; Coriolis acceleration; Newton's laws of motion.

Statics

The vertical structure of the atmosphere is determined by the equation of state for an ideal gas and by the hydrostatic relationship. The former expresses the relationship among pressure, density, and temperature at any point; the latter expresses the balance between the upward-directed component of the pressure-gradient force (associated with the approximate exponential decrease of pressure with height) and the downward-directed gravity force. The equation of state and hydrostatic equation may be combined to form the hypsometric equation (1), which relates the geopotential height differences
1.
(Z₂ − Z₁) between two pressure surfaces p₂ and p₁ to the mean temperature T in the layer between the two surfaces; and where R (the gas constant for dry air) = 287 J · kg⁻¹ · K⁻¹ and g (the acceleration of gravity) = 9.81 m · s⁻². Thus, pressure decreases more rapidly with height in cold air than in warm air. See also Gas; Hydrostatics.

Except in regions of active precipitation, where the heating rate due to latent heat of condensation is large, temperature changes following the motion of individual parcels of air are controlled primarily by adiabatic expansion and compression as the air parcels move to lower or higher pressure. The thermodynamic state of such parcels can be characterized by the potential temperature θ, as in Eq. (2), where p₀ [= 10⁵ pascals (1000 millibars)]
2.
is a reference pressure and cp (= 1004 J · kg⁻¹ · K⁻¹) is the specific heat at constant pressure. The potential temperature is the temperature that a parcel of air at pressure p and temperature T would acquire if it were moved adiabatically to pressure p₀. When all diabatic heat sources can be neglected, θ remains constant in time for each air parcel. Normally, θ increases with altitude in the atmosphere, so that an air parcel displaced upward (downward) has a value of θ less (greater) than that of its environment, and hence experiences a net buoyancy force that tends to return it to its equilibrium level. The atmosphere is then said to be statically stable. When θ is constant with height, a condition that occurs when the temperature decreases with height at a rate 10°C · km⁻¹ (30°F · mi⁻¹), the atmosphere is said to be neutrally stable; if θ decreases with height, the atmosphere is absolutely unstable and convective motion develops spontaneously. If an air parcel is saturated, upward displacement causes water vapor to condense and release its latent heat of condensation; the potential temperature is then no longer conserved.

The hydrostatic relationship implies that pressure decreases monotonically with altitude. Pressure may thus be substituted for height as the independent vertical coordinate. If the atmosphere is everywhere statically stable so that θ increases monotonically with height, potential temperature can also be used as a vertical coordinate. Potential temperature coordinates are useful, for analysis of adiabatic motions, since in that reference frame prediction of adiabatic flow is reduced to a two-dimensional problem of following the motion on θ surfaces. Isobaric coordinates, in which pressure is the vertical coordinate, have the advantage of eliminating any explicit reference to the density field. These are the most commonly used vertical coordinates in dynamic meteorology. See also Convective instability; Dynamic instability; Hydrostatics; Isobar (meteorology).

Baroclinic instability

Baroclinic energy conversion processes are responsible for the growth and maintenance of most large-scale weather disturbances.

In midlatitudes in the troposphere, potential temperature normally decreases from Equator to pole on isobaric surfaces. This decrease does not occur uniformly, but tends to be concentrated in the jet stream, a narrow band of strong westerly winds in the upper troposphere that encircles the globe in midlatitudes. See also Jet stream.

When the shear of the zonal wind is sufficiently strong so that the meridional gradient of potential vorticity on a constant potential temperature surface is locally reversed, or when there is a nonvanishing gradient of potential temperature at the surface of the Earth, the linearized equations have solutions in the form of exponentially growing disturbances. These baroclinically unstable modes have growth rates, structures, and scales similar to those observed in developing extratropical cyclones. Baroclinic instability provides a mode whereby infinitesimal disturbances may amplify into large-amplitude storms. However, in many cases it appears that storms in the atmosphere grow through nonlinear interactions involving preexisting disturbances. Such processes must generally be studied by numerical simulations on high-speed computers.

Mesoscale convective systems

For horizontal scales less than several hundred kilometers, the major energy source is not baroclinic instability; it is latent heat release by cumulonimbus clouds. The convective storms associated with such clouds can occur only when the atmosphere is conditionally unstable [see Eq. (2)], sufficient moisture is present, and there is an initial disturbance strong enough to lift air parcels high enough to release the conditional instability. Mesoscale convective systems take a variety of forms. Among these are hurricanes, squall lines, and mesoscale convective complexes. See also Hurricane; Mesometeorology; Squall line.

Numerical weather prediction

In current global weather prediction models, a mixture of techniques is often employed. Nearly all models use finite difference representations for the vertical coordinate and time; the horizontal variation is generally represented either by a network of grid points at uniform intervals of latitude and longitude or by a finite set of spherical harmonics. See also Spherical harmonics.

To predict the weather dynamically, it is necessary to solve the dynamics equations by integrating in time, starting from an initial state of the atmospheric variables determined from observations. In practice, observational errors and poor data coverage, particularly over the oceans, make it impossible to exactly determine the initial state of the atmosphere. Moreover, the state determined from observations generally does not properly represent the true dynamical balance among the pressure and wind fields. This imbalance introduces noise that is interpreted as high-frequency inertia-gravity waves. If a prediction is attempted from such an initial state, the noise rapidly dominates the true, slowly evolving weather disturbances. In order to prevent the growth of such spurious noise, the analysis must be initialized by processing it in a manner that assures a dynamical balance between the pressure and wind fields while preserving the actual observations as closely as possible. However, even if the initial state were known perfectly, there still would be a limit beyond which errors would dominate the forecast. See also Weather forecasting and prediction.

Global climate modeling

In addition to their role in weather prediction, dynamical models can also be used to simulate global climate. Climate is the study of the average state of the atmosphere and its seasonal and interannual variability. Climate is determined by the joint influence of energy sources and sinks at the Earth's surface, and the transformation and transport of energy in the atmosphere and the oceans. Models that simulate these processes are usually referred to as general circulation models. Such models must contain accurate representations of all the important physical processes that influence the circulation. See also Atmosphere; Climate modeling; Meteorology; Wind.

The study of atmospheric motions as expressed by the fundamental hydrodynamic equations, and other systems of equations specific to special situations, such as turbulence.