### Summary

Understanding atmospheric dynamics is built upon three conservation laws: energy (the 1st Law of Thermodynamics), mass, and momentum. When we use conservation of momentum on the rotating Earth, we need to consider not only the real forces of gravity, pressure gradient force, and turbulent drag in the lower troposphere, but also apparent forces—centrifugal and Coriolis. With these terms, we can use conservation of momentum to write down the equations of motion in the Earth's reference frame and then show how they can be transformed into spherical coordinates or even pressure coordinates in the vertical and natural coordinates in the horizontal.

Using natural coordinates simplifies the equation of motion for geostrophic flow (the balance of Coriolis and pressure gradient forces), cyclostrophic flow (the balance of centrifugal and pressure gradient forces), inertial flow (the balance between centrifugal and Coriolis forces), and gradient flow (the balance among the pressure gradient force, Coriolis force, and horizontal centrifugal force). Upper air motion around high and low pressure causes upper-air convergence and divergence, which leads to high and low pressure at the surface.

Finally, the temperature decrease at each pressure level from tropics to the poles leads to a pressure gradient force that drives air toward the poles. The Coriolis force turns the air toward the east, creating westerlies observed in the midlatitudes of both hemispheres. This connection between the latitudinal temperature gradient and wind is expressed in the thermal wind equation. The thermal wind vector, which is the difference between the geostrophic winds at two different pressure levels, is parallel to isotherms, with cold air on the left in the Northern Hemisphere. If the geostrophic wind vector turns counterclockwise with height in the Northern Hemisphere, cold air advection is occurring in that layer of air. This relationship is a handy way to figure out if the advection is cold or warm.

### Reminder - Complete all of the Lesson 10 tasks!

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