## Scale analysis and balanced flows

So far we only looked at vertical motions that were governed by gravity and buoyancy. With respect to horizontal motions we only looked at the displacement of air masses in terms of moisture, matter and temperature. In this unit, we will look at the equation of motion in all three dimensions. We will assess the importance of its terms for various kinds of atmospheric spatial and temporal scales to derive simplified descriptions of atmospheric motions. Note that this assessment is needed for the development of atmospheric models.

### Learning goals

After completion of this units the student will be able to

- perform scale analysis of the governing atmospheric equations for various scales
- apply simplified models of the equation of motion to analyze atmospheric processes
- analyze the weather by applying synoptic rules derived from the simplified models
- discuss synoptic systems in terms of their motion

Application of scale analysis to describe atmospheric motion in terms of balanced flows

### Students’ Tasks

- Watch this video

- Read chapter 6.4 to 6.4.5 (included) of
*Lectures in Meteorology*. - Take notes and write down the equations that you identify to be of relevance for the balanced flows.
- Participate in the discussion channel of this unit on the discussion board
- Answer the questionnaire by 2359 AKST on Thursday.
- Solve the problems assigned at your class level in this unit19 work sheet and submit your solutions to cmoelders@alaska.edu by Thursday 2359 AKST

### Supplemental Material (optional)

The movie of the following worked problem shows how to calculate the geostrophic wind.

This worked problem illustrates how to calculate acceleration due to eddy diffusion of momentum.

This worked problem illustrates how to determine the pressure gradient force in horizontal and vertical direction and compares them.

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