Discussion
In a Barotrophic atmosphere :
Answer: C
In a barotropic atmosphere the geostrophic wind does not change with height.
In a barotropic atmosphere density depends only on pressure, so surfaces of constant pressure and constant temperature coincide and there are no horizontal temperature gradients on pressure surfaces. By the thermal wind relation, the vertical change (shear) of the geostrophic wind is proportional to the horizontal temperature gradient, so with no gradient the geostrophic wind is the same at all heights.
Geostrophic winds that increase or decrease with height require a baroclinic atmosphere. 'Pressure a function of temperature only' reverses the definition: it is density that depends on pressure alone.
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