Atmospheric Vertical Structure and the First Law of Thermodynamics
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This page first made public: Oct 23, 2009
- Introduce the concept of potential temperature used to characterize dry adiabatic processes in meteorology
- Apply elementary calculus skills in interpeting atmospheric vertical structure
- Apply basic graphing skills
Context for Use
Description and Teaching Materials
Homework Assignments (Microsoft Word 66kB Jul17 04)
Homework Solutions (Microsoft Word 186kB Jul16 04)
Instructors Notes (Microsoft Word 26kB Jul16 04)
Teaching Notes and Tips
- Students entering this course typically do not make the connections between the mathematics and physics that they've had and the atmospheric processes they can observe. Making these connections requires a concerted effort at linking the First Law as a statement of energy conservation to its implications for atmospheric structure, stability, and the construction of thermodynamic diagrams. Relating the basic principles to the current weather is an important and useful way to pique the students' interest.
- This activity is designed as a sequence beginning with in-class exercises (In-class Preliminary Activities (Microsoft Word 31kB Jul17 04)) followed by homework exercises (Homework Assignments (Microsoft Word 66kB Jul17 04)).
- The homework assignments are relatively short and should be due the next class period after they are assigned (2 days later typically). I assign questions 1-5 of the first set of problems initially, followed by questions 6-8 which are assigned on the next class day. The second set of questions can be assigned concurrently with questions 6-8, but I make them due a class period later.
- Parts of this exercise can be done in a spreadsheet program, but they can also be done by hand. If a spreadsheet is required of the students, they may need to be given more time to complete the assignment.
- Once the assignment is completed, students can be asked in any subsequent class what they think the vertical profile of Θ is on that day based upon the weather they can observe out the window. For example, for an afternoon class on a day with fair weather cumulus, you'd expect a dry mixed layer with constant potential temperature below the cloud base. After the introduction of the equivalent potential temperature, Θe, later in the course, this oral exercise can be extended to that variable as well.
- In addition, actual soundings taken on a given class day can be investigated for evidence of dry ascent/mixing, moist ascent, subsidence, nocturnal inversions, etc..
- On a subsequent exam, I ask questions like the following using qualitative weather information from a recent event:
- Yesterday in central MN (or wherever), the sky was clear all day with bright sunshine. Based on this information, sketch below what you think the vertical profiles of w (the water vapor mixing ratio), Θ and Θe looked like (below 800 mb) in the Chanhassen sounding from 00Z last night. Be sure to THINK! Briefly explain your reasoning.
- Yesterday in Portland, ME (or wherever), the sky was overcast and light to moderate to heavy rain fell from the afternoon through the evening. Based on this information, sketch below what you think the vertical profiles of w, Θ and Θe looked like in the Portland sounding from 00Z last night from the cloud base upward. Be sure to THINK! Briefly explain your reasoning.