To forecast the weather, we use numerical weather prediction models which are based on mathematical expressions for conservation of energy, mass, and momentum. Climate prediction models are based on the same conservation laws. Conservation simply means that the amount of a quantity such as total energy, mass, or momentum remains constant even though the forms of that quantity may change. Conservation of energy is described by the 1^{st} Law of Thermodynamics, which was discussed in Lesson 2; conservation of mass and conservation of momentum are discussed in this lesson. The total mass of an air parcel is constant, but density and volume may change. The conservation of momentum is based on Newton's 2^{nd} Law and involves forces that can change momentum. This equation is relatively simple when cast in an inertial (non-accelerating) reference frame because there are only three real forces that really matter for atmospheric motion: gravity, the pressure gradient force, and friction. But when cast on a rotating Earth, we need to add apparent forces to this equation in order to compensate for the fact that an air parcel on Earth is always accelerating as the Earth rotates. We end up adding the apparent forces – Coriolis force and centrifugal force – to the real forces to get an equation of motion whose predictions we can readily match with our observations.

Some atmospheric motion occurs with air masses and waves that are thousands of kilometers across, while other motion, such as tornadoes, is at most a few kilometers across. Sometimes air flows in a straight line; sometimes it flows around ridges and troughs. In all of these different cases, the most important forces are different, allowing the momentum conservation equation to be simplified in different ways. We will discuss these different conditions and show how you can determine the wind velocity from knowledge of the balance of the most important forces and thus determine the impact of air motion at upper levels on the air motion near Earth’s surface. Finally, we will describe why midlatitude winds are westerly.

### Learning Objectives

By the end of this lesson, you should be able to:

- explain mass conservation physically, recognize the mass conservation equation, and memorize its form when density is constant
- state the three main conservation laws in atmospheric science: the conservation of mass, the conservation of momentum, the conservation of energy
- name and explain the three fundamental (real) forces in the atmosphere (gravity, pressure gradient, and friction)
- name and explain the two new (apparent) forces that emerge when momentum conservation is written in the rotating reference frame
- draw the balance of forces for geostrophic flow, gradient flow, geostrophic flow with friction, and cyclostrophic flow
- explain why midlatitude winds are westerly

### Lesson Roadmap

Please see Canvas for a list of required assignments, due dates, and submission instructions.

### Questions?

If you have any questions, please post them to the Course Questions discussion forum in Canvas. I will check that discussion forum daily to respond. While you are there, feel free to post your own responses if you, too, are able to help out a classmate.