LEAD-TO-LEARN

__APPLYING THE QUASI-GEOSTROPHIC OMEGA EQUATION ____TO A DEEPENING SHORTWAVE TROUGH __

**WORK SHEET **

__Introduction __

This module will guide you through a pre-structured IDV bundle focusing on the Quasi-Geostrophic (Q-G) Omega Equation. The model output that is being used will focus on vertical velocities associated with the 500-hPa and 850-hPa levels. The system that will be examined is a deepening trough in the eastern United States between the hours of 00:00:00Z on November 1, 2005 and 00:00:00Z on November 2, 2005. Dynamic equations will be used to analyze the model output; however, these dynamic equations will only supplement the main focus of this module - to visually represent the forcing terms that govern vertical motion.

__Objectives __

In this module, you will observe how the Q-G Omega Equation explains the vertical velocity at the 500-hPa and 850-hPa isobaric surfaces. After completing this module, the user should have an in-depth understanding of the Q-G Omega Equation and how it relates vertical motion to absolute vorticity advection and thermal advection.

__Background __

After eliminating
χ (geopotential height tendency, gpm /s) between the Q-G Thermodynamic and Q-G Relative Vorticity Equations, we are left with a diagnostic equation that simultaneously relates vertical motion (ω) to geopotential height (Z = Ф/g). Through this elimination, the following can be derived:

Term A : three-dimensional Laplacian of omega.

Term B : vertical differential of geostrophic absolute vorticity advection.

Term C : three-dimensional Laplacian of thickness (thermal) advection.

To summarize, the Q-G Omega Equation provides a method to estimate ω that does not depend on observations of the ageostrophic wind (i.e., assume a geostrophic atmosphere). This module will examine each part of the equation in the following sections:

**1) Absolute Vorticity Advection Term (Term B ) **

**2) Thickness Advection Term (Term C ) **

**3) Making A Prediction For the Height Field (Term A)**

__Loading the IDV Bundle __

Click on **QG-OMEGA.jnlp** to load the Q-G Omega bundle. Two main windows should appear; the *Display Window* and the *Data Selector Window*. Once the bundle is loaded, proceed to the next section.