By the end of this chapter, you should be able to:
- calculate partial derivatives
- implement vector notation, the dot product, the cross product, and the del operator
- explain the different coordinate systems and how they are used
- convert between math and meteorological wind directions
- calculate temperature advection at any point on a map of isotherms (lines of constant temperature) and wind vectors
In previous lessons, we were able to explain physical and chemical processes using only algebra and differential and integral calculus. Thermodynamics, moist processes, cloud physics, atmospheric composition, and atmospheric radiation and its applications can all be quantified (at this level of detail) with fairly simple mathematics. However, to understand and quantify the dynamics of the atmosphere requires more math skill.
- 8.3: Describing weather requires coordinate systems.
- In meteorology and other atmospheric sciences, we mostly use the standard x, y, and z coordinate system, called the Cartesian coordinate system, and the spherical coordinate system. Let’s review some of the main points of these two systems.