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Which pair of approximations must be applied together for consistency?

  • A.Incompressible and hydrostatic, which together remove both sound waves and vertical accelerations
  • B.Shallow atmosphere and traditional
  • C.Hydrostatic and geostrophic, since neither is valid without the other in large scale atmospheric flow
  • D.Boussinesq and anelastic

Answer: B

Applying the shallow atmosphere approximation without the traditional approximation, or the reverse, destroys the conservation of angular momentum and energy in the resulting system. The two must therefore be adopted or rejected as a pair, a result established by Phillips. Hydrostatic and geostrophic approximations are logically independent, and the other pairs listed are alternatives to one another rather than partners. Reading the definition literally, rather than recalling a formula, is the reliable route through questions of this shape.

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