# Applications of Vector Operators for Surface Atmospheric/Oceanic Processes

## Summary

Vector operations are crucial for the understanding of many processes affecting surface conditions in the atmosphere and the oceans. Gradients, dot and cross products, and the Laplacian of surface variables (e.g., pressure, temperature, moisture, salinity, wind and ocean currents to name a few) are concepts that create considerable angst for students in meteorology and physical oceanography classes. This lab exercise will provide students with activities utilizing these vector operations within the context of the atmospheric and oceanic environments. It is the intent of this exercise to enhance student's confidence in understanding these operations by utilizing actual datasets relevant to the atmosphere and the ocean. While the activities focus on atmospheric and oceanic surface processes, they could easily be modified for geophysical (or physical) applications.

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## Learning Goals

This activity is designed to introduce (or review) basic vector operations. Vectors are an important concept in meteorology and oceanography because motion (wind and ocean currents) is a fundamental parameter for describing conditions and changes in the atmosphere and the ocean. The purpose is to teach vector concepts within the context of the atmospheric and oceanic environments to enhance the students' understanding of vectors and vector operations through their application to physical processes.

## Context for Use

This activity is part of a course offered to juniors in the Oceanography program at the Naval Academy. The course is called "Quantitative Methods for Meteorology and Oceanography" and is a required course for all Oceanography majors. Many meteorological and oceanographic concepts are expressed as vectors (e.g., wind or ocean currents) which they would have learned in introductory meteorology or oceanography courses. The basic understanding of vectors and vector concepts are learned in Calculus classes. The ideal course setting would be 12-15 students, with no more than 20 students per class. The time needed to complete this exercise is 75-90 minutes.

## Teaching Notes and Tips

Tips:

1) The activity can be easily modified to fit courses in other disciplines by changing the examples or datasets.
2) The instructor should be careful to provide the necessary background to understand the material relevant to the atmospheric and oceanic sciences.
3) Be careful with notation used in this exercise. It is standard notation for meteorology and oceanography, but may not be common knowledge in other disciplines. Most any intermediate level textbook for meteorology and oceanography will assist in understanding the notation.