Questions: Absolute and Relative Vorticity

Question 1

An air parcel at 45°N has zero relative vorticity and moves poleward to 60°N. What happens to its relative vorticity, and why?

• A. Relative vorticity increases (becomes more cyclonic) because faster Coriolis deflection at higher latitudes generates additional spin
• B. Relative vorticity remains zero because the parcel started with no spin and nothing has changed the local wind field
• C. Relative vorticity decreases (becomes more anticyclonic) because absolute vorticity is approximately conserved — as planetary vorticity f increases with latitude, relative vorticity ζ must decrease to compensate
• D. Relative vorticity increases because upper-level wind shear intensifies at higher latitudes

Answer: (C)

Absolute vorticity (ζ + f) is approximately conserved following an air parcel. At 45°N, f is some value f₁; at 60°N, f₂ > f₁. To maintain ζ + f = constant, ζ must decrease by the same amount f increased. The parcel that started with zero relative vorticity develops negative (anticyclonic) relative vorticity. This is the fundamental mechanism driving Rossby wave propagation — poleward displacement generates anticyclonic curvature that turns the parcel back equatorward.

Question 2

At the equator, why is planetary vorticity zero even though Earth is continuously rotating?

• A. The Coriolis effect is zero at the equator, which eliminates the contribution of Earth's rotation to vorticity
• B. Equatorial air masses move faster than air at higher latitudes, which cancels Earth's rotational contribution
• C. Planetary vorticity (f = 2Ω sinφ) measures the component of Earth's rotation about a vertical axis; at the equator Earth's rotation axis is horizontal, so there is no vertical-axis spin component to contribute
• D. Equatorial winds are predominantly zonal, so there is no meridional component to generate vertical vorticity

Answer: (C)

Planetary vorticity measures how much of Earth's rotation acts about a local vertical axis. At the poles (φ = 90°), the Earth's rotation axis is vertical, so all of Earth's spin contributes: f = 2Ω. At the equator (φ = 0°), Earth's rotation axis is horizontal — the axis points parallel to the surface, not perpendicular to it — so it contributes zero spin about the local vertical. The sin(φ) factor captures this geometry: it is the projection of Earth's angular velocity vector onto the local vertical.

Question 3

A cyclone in the Northern Hemisphere has positive relative vorticity, and since planetary vorticity at that latitude is also positive, the cyclone's absolute vorticity exceeds its relative vorticity alone.

• T. True
• F. False

Answer: True

Absolute vorticity = ζ (relative) + f (planetary). In the Northern Hemisphere, f = 2Ω sinφ > 0 everywhere. A cyclone has ζ > 0 by definition (counterclockwise rotation). Therefore ζ + f > ζ: absolute vorticity exceeds relative vorticity. This means that even a very weakly rotating cyclone has substantial absolute vorticity because planetary vorticity adds to it. At mid-latitudes, f ≈ 10⁻⁴ s⁻¹, which is comparable to or larger than relative vorticity in many synoptic systems.

Question 4

When an upper-level air parcel moves equatorward, its relative vorticity decreases because it is moving away from the high-latitude source of planetary rotation.

• T. True
• F. False

Answer: False

Equatorward movement decreases planetary vorticity f (since f = 2Ω sinφ decreases toward the equator). To conserve absolute vorticity (ζ + f = constant), relative vorticity ζ must *increase* to compensate. The parcel develops positive (cyclonic) relative vorticity — it begins spinning counterclockwise in the Northern Hemisphere. This cyclonic curvature eventually turns the parcel back poleward, setting up the oscillating Rossby wave pattern. The common error is forgetting the conservation relationship and thinking the parcel simply 'loses' rotation.

Question 5

Explain how conservation of absolute vorticity causes air parcels displaced poleward to develop anticyclonic curvature, and how this produces the wavelike Rossby wave pattern in the mid-latitude upper atmosphere.

Model answer: When a parcel moves poleward, f increases. To conserve ζ + f, relative vorticity ζ decreases — the parcel acquires anticyclonic (clockwise in the NH) curvature. This curves the flow back equatorward. Once moving equatorward, f decreases and ζ must increase — the parcel acquires cyclonic curvature, turning it poleward again. This oscillation between poleward displacement (anticyclonic response, equatorward turning) and equatorward displacement (cyclonic response, poleward turning) produces the large-scale wave pattern. These planetary waves, known as Rossby waves, propagate westward relative to the mean flow and steer surface weather systems.

The key is that absolute vorticity conservation makes the atmosphere behave like a restoring-force system: poleward displacement generates the anticyclonic curvature that returns the parcel equatorward, and equatorward displacement generates the cyclonic curvature that returns it poleward. The result is a standing or slowly propagating wave rather than unlimited straight-line motion. The wavelength and propagation speed of Rossby waves depend on the meridional gradient of f (the β effect), which is why they only form in rotating systems and are absent at the equator.