Upper-Level Troughs and Ridges

• We plot upper-level maps with contours, which are curves that connect places with the same heights (isoheights / isohypse).

• Ridges = areas on upper-level maps with greater heights, representing warmer columns of air.

• Troughs = areas on upper-level maps with lower heights, representing cooler, shorter columns of air.

• Generally, colder, shorter columns are found in the polar regions and the warmer, taller columns are found in the tropical and subtropical regions.

• On upper-level maps, the air is accelerated from the region of greater heights toward the region of lower heights (from high to low pressure).

• Warm air tends to rise ahead of the trough axis, while cold air tends to sink behind the trough axis.

• The rising, warmer air may generate clouds and precipitation ahead of the trough axis, while the sinking, colder air may generate clearing skies behind the trough axis.

• The upper-atmosphere dictates what happens at the surface!

• Wind speed is inversely proportional to the spacing between the height contours (isobars).
• Close height contours = faster wind speeds.
• Far apart height contours = slower wind speeds.

• The upper-level flow is dominated by the location of very large amplitude, synoptic-scale disturbances (troughs and ridges), which generally change in intensity and position from day-to-day.

• Generally, ridges and troughs cancel each other out when averaged for a month, season, or year, providing a more zonal appearance!

http://mp1.met.psu.edu/~fxg1/HEMI500/5dayloop.html

Longwaves

(aka Rossby / Planetary Waves)

• Longwaves have wavelengths of thousands of kilometers and represent the large scale, global flow.

• Generally, move slowly from west to east, but may become stationary or retrogress slowly from east to west.


• In the northern hemisphere, we see 3-7 long waves with wavelengths of 50-120°, with the wave number changing over days or weeks, and through the long waves move the faster short waves.

• Influence the locations of large regions of warm versus cold temperatures, wet versus dry conditions, the position of the jet streams and storm tracks.

• Longwaves are barotropic (in which pressure depends only on density).

Advection

• Advection = horizontal movement of air.

• Warm Advection occurs when the wind blows across the gradient of temperature from higher toward lower temperature / thickness.

• Cold Advection occurs when wind blows across the gradient of temperature from lower to higher temperature / thickness.

Shortwaves

• Shortwaves tend to have wavelengths of less than 3,000 km.

• They move rapidly from west to east, around or through longwaves.

• Represent smaller pools of cold and warm air aloft.
• Shortwaves are baroclinic

• Pools of cold air aloft may lead to instability, outbreaks or rain/snow showers, or thunderstorms (in extreme cases).
• Significant "weather-makers"

• Dry channels ahead, moist channel behind.

Thermal Wind

            Thermal Wind is the vertical shear of the geostrophic wind cause by a horizontal temperature gradient—it “blows” parallel to the thickness contours, leaving low thickness to the left. The Thermal Wind Equation states that the vertically averaged shear of the geostrophic wind (within the layer between any two pressure surfaces) is related to the horizontal gradient of thickness of the layer, in the same manner in which geostrophic wind is related to geopotential height.

Expressed as a linear relationship between vertical wind shear of the geostrophic wind and the horizontal temperature gradient,

            In a barotropic atmosphere—where density is only a function of pressure—the slope of the isobaric surfaces are independent of temperature thus, the geostrophic wind doesn’t increase with height. In other words, there is a complete absence of the horizontal temperature (thickness) gradients such that on constant pressure surfaces. However, the slope of the isobaric surfaces and the speed of the geostrophic wind may vary from level to level due to those thickness variations.

            In an Equivalent Barotropic Atmosphere, isobars and isotherms, on a horizontal surface map, have the same shape.

            In a Baroclinic Atmosphere—where density is a function of both pressure and temperature—the height and thickness contours intersect such that the geostrophic wind exhibits a component normal to the isotherms (or thickness contours). In other words, the horizontal temperature gradients cause the thickness of the layers between isobaric surfaces to increase with higher temperatures. When multiple layers are stacked on each other the geostrophic wind and the slope of the isobaric surfaces increase with height.

Quasi-Geostrophic (Q-G) Omega Equation

            The Quasi-Geostrophic Approximation assumes, among other things, geostrophic and hydrostatic balance. Noting that advection is overshadowed by the geostrophic contribution, only allowing limited departures from the geostrophic balance, is reason it is not simply geostrophic and, instead, quasi-geostrophic. However, the advection of vorticity and thermal gradients usually disturb the geostrophic and hydrostatic balance, which is where the quasi-geostrophic equation could come in handy. To put it briefly, the Q-G equation, on a hypothetical vertical motion field, restores the geostrophic and hydrostatic balance accurately and instantaneously. In other words, the vertical motion could be considered a response to the disrupting factor of geostrophic advection on a system. Although, more importantly, this should be thought of as a hypothetical scenario due to the fact that there is no physical manifestation thus cannot be measured.

The Quasi-Geostrophic Omega Equation represents a method for diagnosing midlatitude, synoptic-scale vertical motions at a specific time. Neglecting diabatic processes, it implies that vertical motion can be calculated from a series of geopotential height analyses at different pressure levels—it is a diagnostic measure of vertical motion based on geopotential height.

For 3-D laplacian of omega, ω (vertical motion) it is important to remember that the sign of the term is proportional to the negative of ω. It is, also, common to assume the dominance of vertical motion is sinusoidal: approximately zero at both the surface and tropopause, and attaining a max/min value in the mid-troposphere hence, qualitatively, like a minus sign.

The vertical differential of geostrophic absolute vorticity advection term is proportional to the rate of increase of geostrophic absolute vorticity advection with increasing height. Overall, vorticity advection increasing with height forces synoptic-scale upward motion. However, vorticity advection at some pressure (mb) alone does not force the vertical motion, it is the change of vorticity advection with height that does.

The 3-D laplacian of thickness (thermal) advection relates to the laplacian of (horizontal) temperature advection to vertical motion, ω—which are greatest when the gradients of temperature advection are large. The dot product, within the brackets, is proportional to the negative of geostrophic advection of thickness.

Nonetheless, warm air advection also plays a role in the Q-G equation because it will increase the thickness of the layer, resulting in higher heights aloft compared to below. Which implies the formulation of anticyclonic vorticity aloft and cyclonic below. In the absence of vorticity advection there is divergence aloft and convergence below. Which, thanks to the vorticity equation, we know that in order to decrease vorticity there has to be negative vorticity advection or divergence.

Forecasting: Short Waves in the Upper Atmosphere and Their Effect on Surface Conditions

Understanding Weather and Climate (7th Edition) (MasteringMeteorology Series) by Edward Aguado, James E. Burt