The QG framework simplifies the equation of motions into a set of **diagnostic equations**

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- QG omega equation
- QG geopotential tendency

geostrophic balance represents the

fundamental balance condition for mid-latitude synoptic-scale flow

The geostrophic wind approximation is only strictly valid in

regions of zero wind acceleration

There are two broad categories of flow in the atmosphere that will violate geostrophic balances

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- Wind speed changes along the flow (i.e. jet streaks, regions of speed convergence/divergence)
- Wind direction changes along the flow (i.e. troughs and ridges, regions of confluence/diffluence)

Define **ageostrophic**** wind**

The degree of departure from geostrophic balance that characterizes synoptic-scale motions can be assessed by considering the difference between the actual wind at a location and the calculate geostrophic wind at the same point.

Ageostrophic wind is defined mathematically as

..........................., this implies that the geostrophic wind is non-divergent.

Because all divergence/convergence necessarily implies an acceleration of the wind field,

ALL........................ in the synoptic-scale..................................... is due to the presence of ageostrophic motion.

divergence , wind field

ALL divergence in the synoptic-scale wind field is due to the

presence of ageostrophic motion.

all vertical motion is due to the presence of

ageostrophic motion.

ageostrophic wind is entirely responsible for

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- the distribution of cyclones,
- anticyclones,
- clouds,
- and precipitation in the atmosphere.

Despite the fact that the mid-latitude atmosphere is predominately in geostrophic balance, all of the important weather with which we are confronted develops as a direct result of the .....................................

often relatively small ageostrophic portion of the wind.

if the geostrophic wind is nondivergent, we have

the equation is for

relationship between ageostrophic wind and vertical motion

the equation means

divergece of ageostrophic wind in upper air causes upward motion

Equation for ageostrophic wind and horizontal acceleration:

Equation for ageostrophic wind and horizontal acceleration

Explain the following equation

V_{ag} = Acceleration term in momentum equation __and__ 1/f

Based on the equation we conclude three properties

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- The ageostrophic wind is a measure of the horizontal acceleration in the atmosphere
- The ageostrophic wind is perpendicular to the horizontal acceleration vector
- The ageostrophic wind is directed to the left of the acceleration vector in the Northern Hemisphere.

To derive the relationship between ageostrophic wind and vertical motion, we first will write the

continuity equation in isobaric coordinates.

Centripital acceleration

ageostrophic wind

The ageostrophic winds converge on ............................of the upper trough (on its ..................side)

the western side, upstream

The ageostrophic winds converge on the western side of the upper trough (on its upstream side), leading to ....................

downward vertical motion.

The ageostrophic winds divergence on the .....................side of the upper trough (on its ..............................side),

eastern , downstream

The ageostrophic winds divergence on the eastern side of the upper trough (on its downstream side), leading to .......................vertical motion.

upward

........................................... explains why there tends to be cloudy/stormy weather downstream of an upper level trough

divergence on the eastern side of the upper trough (on its downstream side), leading to upward vertical motion.

obtain the geostrophic wind equations

based on the properties of the previous mathematical derivation, we see that the ageostrophic wind vector has three properties: