Atmospheric Waves Questions and Answers

Answer: A

The Kelvin wave travels eastward only, the equatorial Rossby wave westward, and the mixed Rossby-gravity wave has westward phase propagation while carrying energy upward. The opposing directions of the first two produce the east-west asymmetry of the Gill response to tropical heating, and the momentum carried by the first and third drives the quasi-biennial oscillation. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

Unresolved gravity waves generated by orography and convection deposit momentum in the stratosphere and mesosphere, and without a parameterisation of that drag models produce a polar vortex far too strong and a mesosphere far from observation. The other processes are important elsewhere in the model but do not control the middle atmosphere circulation in the same way. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: C

The cold pole problem, in which the modelled winter polar vortex is too strong and too cold, was a longstanding defect traced directly to missing wave drag. Adding an orographic gravity wave drag scheme largely resolved it. The other errors listed arise from quite different deficiencies in convection, microphysics and numerical conservation.

Answer: D

The scheme launches a wave momentum flux at the source level and computes where it is deposited, the vertical divergence of that flux being the drag applied to the resolved flow. Saturation criteria determine the deposition level. Counting individual crests is neither possible nor meaningful at model resolution, and the surface amplitude is an input rather than the output of the calculation. Framing the question as which quantity the change acts upon makes the answer follow without calculation.

Answer: A

The wavenumber is defined as two pi divided by the wavelength and gives the number of radians of phase per unit distance. The number of oscillations per second is the frequency, and the distance travelled per oscillation is the wavelength itself. In meteorology a zonal wavenumber is often quoted instead as the number of complete waves around a latitude circle, which is a different convention worth noticing when reading the literature. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: B

Meteorologists count the number of complete waves fitting around the globe, so wavenumber three means three ridges and three troughs at that latitude. At 45 degrees north the corresponding wavelength is about 9400 kilometres. This planetary convention differs from the mathematical wavenumber and both appear in the literature, so checking which is meant is worthwhile. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: C

The stationary pattern forced by the Rockies, the Tibetan Plateau and the land-sea contrasts is dominated by the longest waves, principally wavenumbers one to three. Only these are long enough to satisfy the Charney-Drazin criterion and propagate into the stratosphere. Wavenumbers five to seven describe the travelling synoptic waves, and wavenumber zero is the zonal mean rather than a wave at all. The quantity that varies and the quantity that does not are worth naming before any substitution is attempted.

Answer: D

Substituting a wave solution into the linearised equations yields an algebraic relation between frequency and wavenumber that must hold for the solution to exist. That dispersion relation encodes the whole propagation behaviour of the wave type. Continuity, hydrostatic balance and the thermal wind relation are among the equations from which the dispersion relation is derived rather than substitutes for it. A limit that survives making every external component ideal is an intrinsic one, and worth knowing for that reason.

Answer: A

Small perturbations are superposed on a specified basic state, products of perturbations are discarded, and a solution proportional to a complex exponential is substituted, giving an algebraic condition on frequency and wavenumber. This is the standard method throughout the subject. Numerical integration and observational averaging can confirm the result but do not derive it. A single measurement chosen to respond to the one asymmetry beats several that respond to shared behaviour.

Answer: B

Linearisation requires the perturbation to be small enough that products of perturbation quantities may be neglected, which fails once a wave grows to large amplitude or begins to break. A moving basic state is perfectly acceptable and simply Doppler shifts the frequency. Stationarity and barotropy are special cases rather than requirements of the method.