Geostrophic and thermal wind balance: Analysis of observational data
Background
The second half of this course focuses on the dynamics of large-scale flows under the influence of Earth's rotation (Coriolis effect). Analyzing the governing equations of fluid motion in the rotating frame, we find that large-scale flows with Rossby number ~ O(0.1) approximately follow "geostrophic balance" (Eq. 7-3, 7-4, or 7-8 in M&P textbook) that relates horizontal velocity to pressure (or height) gradient. The combination of geostrophic balance and hydrostatic balance leads to "thermal wind balance" (Eq. 7-18 or 7-24), which relates vertical wind shear to horizontal temperature gradient. Through these balance relations, we understand (among other things) why, in the Northern Hemisphere, a low-pressure center is associated with a "cyclonic vortex" with a counterclockwise flow pattern. Given the importance of the balance relations, the purpose of this project is to analyze observational data to determine how accurately these relations hold for the real atmosphere.
In p-coordinate, geostrophic balance can be written as (Eq. 7-7)
V = (1/f)k x gradΦ
where V is the horizontal wind vector on a pressure level, f = 2Ω sin(φ) is the Coriolis parameter, k is the local vertical (upward) unit vector, and Φ = gz is geopotential. For this project, the relation can be recast as
V = (1/f)k x gradΦ + Residual (R1)
In p-coordinate, the thermal wind relation can be expressed as (Eq. 7-24)
(delV)/(del ln(p)) = -(R/f)k x gradT
Or, it can be recast as
(delV)/(del ln(p)) = -(R/f)k x gradT + Residual (R2)
The key task of this project is to quantify the residual (i.e., the deviation from the balance relation) as a function of latitude, height, and other parameters, using an observational data set. Through this exercise, we will also become more familiar with the structures of large-scale wind, temperature, and pressure (or height) fields, and their inter-relations.
