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Which quantity gives the Rossby depth scale?

  • A.The scale height of the atmosphere multiplied by the ratio of the buoyancy frequency to the Coriolis parameter
  • B.The wind speed divided by beta
  • C.The square root of the ratio of the static stability to the vertical shear of the wind at that level
  • D.The horizontal scale times f divided by N

Answer: D

Multiplying the horizontal scale by \( f/N \), about one in a hundred in the troposphere, gives the depth over which a disturbance of that width influences the flow. A synoptic scale disturbance a thousand kilometres wide therefore reaches through about ten kilometres, which is the whole troposphere. This is the vertical counterpart of the deformation radius and explains the observed aspect ratio of weather systems.

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