Dynamic Climatology

Dynamic climatology, now frequently termed “climate dynamics”, is an attempt to study and explain atmospheric circulation over a large part of the Earth in terms of the available sources and transformations of energy (Court, 1957). Hare (1957) notes that dynamic climatology is the prime approach for explanation of world climates as integrations of atmospheric circulation and disturbances. It also attempts to derive circulation types at the regional scale.

Agreement on the scope of dynamic climatology is not universal, and differences among dynamic, complex, and synoptic climatology are not always well defined. For example, Bergeron (1930) and others considered what is now synoptic climatology to be dynamic climatology. Interest in weather patterns among synoptic climatologists has also obscured contrasts with complex climatology. A history of the origin and content of dynamic climatology has been given by Rayner et al. (1991) while a modern survey of the field is available in a text by Barry and Carlton (2001).

Principles

The dynamic climatological approach is based on motion characteristics and the thermodynamic processes that produce them. Dynamic meteorologists have as their principal interest the development and interpretation of relationships that describe these latter items; their usage separates the climatologist from the meteorologist, although the boundary between the disciplines is a tenuous one. An excellent introduction to dynamics and thermodynamics as they apply to the atmosphere is contained in Hess (1959) and Atkinson (1981).

Moving air is the result of forces brought about by thermodynamic processes that originate primarily at the Earth-air interface. The driving force for all processes is the radiant energy supplied to the Earth-atmosphere system by the sun.

A small fraction of available solar energy is absorbed directly by atmospheric constituents. About three times as much energy reaches the surface of the Earth and is absorbed in differing amounts, depending on the geometry and physical properties of the surface. Various unevenly distributed energy sources and sinks are thus created. Energy is defined as the capacity to do work, to move an object (mass) through a distance by application of a force. Disposition of thermal energy in this case alters temperature, density, and pressure values, thereby yielding unbalanced vertical and horizontal forces that cause air to move. Heat, moisture, and momentum transfers result from such motions at various scales. Ultimately, the Earth-atmosphere system returns thermal energy to space through radiation in an amount equivalent to the solar energy originally received, thus balancing long-term gains and maintaining the atmospheric heat engine in a steady state.

The fundamental equations (often called the Primitive Equations) that describe processes and motion in the atmosphere are the Ideal Gas Law, the First Law of Thermodynamics, the Equation of Motion, the Equation of Moisture Conservation, and the Equation of Continuity (Table D4). They are used to describe the interactions and characteristics of the basic building blocks comprising the Earth-atmosphere system. Manipulations of the basic equations allow us to decipher relationships among thickness between layers in the atmosphere, temperature, the wind field, and to develop stability-change equations, pressure-tendency equations, and the vorticity equation, among others. Some concepts that follow from these relationships include geopotential and geopotential height, isobaric and constant level representations, streamlines and trajectories, circulation, and divergence.

Imperfect characterization

If the entire atmosphere could be confined to a laboratory setting, application of the equations in Table D4 would be a straightforward problem. Application to the real, unconfined atmosphere presents several difficulties. For example, data on the state of the atmosphere are not available at every point at all possible moments. This means that climatologists must work with average, or smoothed, data among sampled points. Unfortunately, such smoothing often eliminates small-scale density or temperature patterns that may have a significant but unknown effect at some location and time. Ramage (1978) points out that it is small-scale factors embedded within the atmosphere that prevent numerical weather forecasting efforts from being more accurate.

Lack of continuous, pervasive sampling also requires that boundaries be fixed on the edges of an area of interest; the west coast of the United States serves as one such large boundary because data on conditions over the Pacific Ocean are not widely available. Changes at the boundary become difficult to determine and ultimately filter through all equations used to characterize the atmosphere.

Turbulent eddies (small-scale air currents produced by frictional interaction by juxtaposed, unlike airmasses) also contribute substantially to the status of the atmosphere at any time. Again, unfortunately, the ability to describe energy transfers by

Table D4 Fundamental variables and equations

eddy conduction, diffusion and friction within the friction layer (the lowest 1500 m of the atmosphere) is limited; such transfers are neglected.

Finally, the basic equations used to describe the workings of the atmosphere are nonlinear. This means that, even at large scales, irregular fluctuations above and below mean values of variables do not cancel. Equations can be made to perform as though they were linear by using an artifice that considers all turbulent contributions as perturbations on the mean pattern. Given the contribution of turbulence to the mean state of the atmosphere, this introduces errors, is unsatisfactory, but is all that can be done at present without the use of numerical methods.

Description of motion

Although forces producing motion are interwoven in the atmospheric fabric, some equation terms and variables can be excluded at certain scales, because their contribution to an event or process is minimal (Figure D15). For example, at the level of the global circulation, vertical motion can be neglected, but not heat transfer, because at the global scale motion is overwhelmingly horizontal. On the other hand, certain microscale processes allow neglect of all thermodynamic equations and the variables temperature, moisture, and density if the atmosphere is considered incompressible. Thus, complexity is decreased without decreasing understanding of important processes and the results.

Figure D15

Time and space scales of atmospheric motion (after Anthes et al., 1981).

The Equation of Motion listed in Table D4 describes a vector and thus has three parts, each expressing Newton’s Second Law of Motion (force=mass×acceleration) for three directions in a Cartesian system. Manipulations of this general equation yield the collective forces that must be specifically expressed; namely, gravity, pressure gradient, Coriolis force, and friction. Stated as a vector in words:

Changes in velocity per unit time=Coriolis force+gravitational force−pressure gradient force+effect of friction.

Motion that takes place on a plane (two equations describe motion on a plane) above the friction layer between straight, parallel isobars (i.e. accelerations are not produced by the pressure field), is called the geostrophic wind, and is expressed as a balance between the pressure gradient and Coriolis forces. Consideration of curved isobars and the effect of friction yields other types of flow regimes, such as gradient (observed around low- and high-pressure systems), cyclostrophic (typical of tornadic circulation), and cross-isobaric motion due to the effect of friction on the velocity component of the geostrophic wind. Subtraction of geostrophic winds at two levels yields the thermal wind, which provides ties among thickness between layers, virtual temperature, and warm or cold air advection.

The third equation of motion applies to movement along a vertical axis. The Coriolis and frictional forces are neglected because their vertical components are small. Vertical motion then represents an interplay between an upward-directed pressure gradient force and gravity as a restoring force; this relationship is called the Hydrostatic Equation.

Manipulations of the three motion equations yield other concepts that are used in the dynamic climatological approach. For example, divergence and its opposite convergence occur when flow leads to increasing or decreasing area changes through time, as in Figure D16. Mass is neither created nor destroyed in the Earth-atmosphere system, and this principle (the First Law of Thermodynamics) stated in the form of the Equation of Continuity, ties changes in the horizontal with vertical motion (Figure D17). As the atmosphere contracts horizontally (converges), it expands vertically (stretches), and vice-versa. If we consider the troposphere as the region where these compensating mechanisms operate, then a general pattern like Figure D18 results. These patterns can also be related to vertical motion and typical convergence-divergence patterns in an eastward-moving upper-air wave system (Figure D19).

Figure D16

Horizontal divergence.

Figure D17

Convergence and stretching (upward vertical motion); divergence and shrinking (downward vertical motion).

Figure D18

Convergence, divergence, and vertical motion in a typical atmospheric cross-section in the midlatitudes.

Figure D19

Organized patterns of convergence and divergence in an eastward-moving system in the midlatitudes.

Finally, vorticity (which can be derived from the two horizontal equations of motion) area changes and vertical motion are related through the vorticity equation. Vorticity is defined as circulation (velocity along a closed path times the length of path) per unit area; since circulation for most processes is relatively constant through time, absolute vorticity (composed of relative plus Earth vorticity) times area is a constant. Again, equation of continuity is used to relate area changes to depth changes; i.e. decreases in area are related to convergence, upward motion, and positive vorticity (counterclockwise spin). Positive vorticity is normally associated with weather system development. Negative vorticity (clockwise spin) is associated with divergence, downward vertical motion, and lack of significant system development.

An example of the interplay among area, depth, and vorticity changes is shown on Figure D20. Figure D21 shows these latter items as they change when topographic changes are encountered. Lower-level air moving perpendicular to a topographic barrier is forced to ascend as it approaches. Decreases in absolute vorticity below the value that should exist at the given latitude occur as the cylinder reaches the mountain crest, causing an increase in divergence, subsidence, and ultimately anticyclonic deflection of the air parcel. As the column leaves the crest, the lower levels are free to expand, thereby increasing upward vertical motion and positive spin. The topographically forced condition depicted in the figure often is the situation prevailing to the lee of the Rocky Mountains, and may lead to development of large cyclonic storm systems.

Figure D20

Relationship among vorticity, vertical motion, and area.

Figure D21

Patterns of convergence and divergence in an air current crossing a topographic barrier.

Thermodynamic processes

The use of thermodynamic principles shows how changes in heat content of the atmosphere, which behaves as a fluid under most circumstances, affect its dynamic characteristics. Volume and pressure changes within the atmosphere are produced by heat addition to, or subtraction from, an air parcel or by work done on or by the parcel within its surroundings. Thermodynamic laws describe what occurs among pressure, volume, and heat content as changes take place.

For example, the First Law of Thermodynamics states that heat added to a parcel can be used to increase its internal energy or to do work on its surrounding environment. From the First Law we can derive the adiabatic relationship, which states that all temperature changes within a parcel are due to expansion or compression if no external heat is added or taken away. External heat may come from radiation, eddy heat conduction, evaporation, or condensation. The adiabatic relationship allows stability to be determined and tells us what will happen to parcel air temperatures as parcels move about in the atmosphere.

The state of the atmosphere at any moment can be described by application of the Ideal Gas Law, which relates pressure, density, virtual temperature, and a gas constant for air. The Moisture Equation allows determination of changes in water vapor content of air parcels through time. The equation relates changes in specific humidity (grams of water vapor per unit mass of air including moisture) to occurrence of condensation, evaporation, molecular diffusion and eddy diffusion of vapor between unlike air masses.