Fundamentals of Atmospheric Science

8.6 What You Experience Depends on Your Point of View: Eulerian vs. Lagrangian


8.6 What You Experience Depends on Your Point of View: Eulerian vs. Lagrangian

car on road with thunderstorm ahead of them
A car travels at the same speed and direction as a thunderstorm
Credit: Nicholas A.Tonelli via flickr

Suppose you were driving underneath an eastward-moving thunderstorm at the same speed and in the same direction as the storm, so that you stayed under it for a few hours. From your point-of-view, it was raining the entire time you were driving. But from the point-of-view of people in the houses you passed, the thunderstorm approached, it rained really hard for twenty minutes, and then stopped raining.

If the people in houses formed a network of observers, and if they talked to each other, they would find that the thunderstorm moved rapidly from west to east in a path that rained on some houses and missed others. This point-of-view is called the Eulerian description because observers are at fixed locations and see the storm only when it is over them. You, on the other hand, followed along with the thunderstorm; any changes you saw were due to changes in the thunderstorm’s intensity only. Your point-of-view was a Lagrangian description because you stayed with the storm.

We can now generalize these ideas to any parcel of air, not just a thunderstorm. An air parcel is a blob of air that hangs more-or-less together as it moves through the atmosphere, meaning that its mass and composition are conserved (i.e., not changing) as it moves. It has a fairly uniform composition, temperature, and pressure, and has a defined velocity. An air parcel needs be large enough so that thermodynamic properties such as temperature, pressure and dewpoint temperature are well defined, but small enough so that it responds quickly to thermodynamic changes induced by air motions.  Air parcel change shape as they move in air and bump into other air parcels. Even though air parcels do not live forever, they are very useful concepts in explaining the differences between the Eulerian and Lagrangian frameworks.

To Summarize

Eulerian Framework:

  • Observes atmospheric properties and their changes at fixed locations
  • Observes different air parcels as they pass by a location
  • Tracks motion only if observers in many locations form a network and communicate their information
  • Is the way most weather observations are taken and the way the most weather prediction models do computations

Lagrangian Framework:

  • Observes atmospheric properties and their changes following a moving air parcel
  • Tracks changes within the air parcel as it moves
  • Being in the same air parcel makes it easier to test and to understand the basic physical principals causing changes in air parcel properties.
  • Is a conceptual or numerical approach and is difficult to realize with observations

Here's an interesting fact. Radiosonde measurements are considered Eulerian for continental or global networks that span thousands of kilometers because they measure properties like temperature and humidity at most a few 10's of kilometers from their launch site. However, radiosonde measurements are actually neither Eulerian nor Lagrangian because a radiosonde moves in air but does not follow the same air parcel. A cup anemometer or sonic anemometer mounted on a stationary tower is an example of a Eulerian method of measuring wind velocity.

Discussion Forum 5: Eulerian and Lagrangian Points-of-View From Your Everyday Life

In the lesson, I presented an example of a driver in a car that happened to be traveling at the same speed as a rainstorm so that to the driver it was raining the entire time, while to the observers in the houses that the driver passed, the rain showers were brief. We could have given a second case in which there was widespread rain so that both the car driver and the house occupants observed constant rainfall for several hours. In the first case, the advection exactly matched the local rainfall change wherever the driver was, so that the driver was in rain constantly, but the house occupants saw rain only for a short while. In the second case, there was no gradient in the rainfall rate, so even if the storm was moving, neither the driver nor the house occupants observed a change in rainfall.

Think of one event or phenomenon from the Eulerian and Lagrangian points-of-view, one in which the event or phenomenon looks very different from the two points-of-view. These events do not have to be weather related. Be creative.

  1. You can access the Eulerian and Lagrangian Points-of-View Discussion Forum in Canvas.
  2. Post a response that answers the question above in a thoughtful manner that draws upon course material and outside sources.
  3. Keep the conversation going! Comment on at least one other person's post. Your comment should include follow-up questions and/or analysis that might offer further evidence or reveal flaws.

This discussion will be worth 3 discussion points. I will use the following rubric to grade your participation:

Discussion Activity Grading Rubric
Evaluation Explanation Available Points
Not Completed Student did not complete the assignment by the due date. 0
Student completed the activity with adequate thoroughness. Student answers the discussion question in a thoughtful manner, including some integration of course material. 1
Student completed the activity with additional attention to defending their position. Student thoroughly answers the discussion question and backs up reasoning with references to course content as well as outside sources. 2
Student completed a well-defended presentation of their position, and provided thoughtful analysis of at least one other student’s post. In addition to a well-crafted and defended post, the student has also engaged in thoughtful analysis/commentary on at least one other student’s post as well. 3