## Chapter 4

## Q. 4.6

Derive a suitable approximation for the Coriolis parameter for regional scale motions centred on a latitude of θ_{0}.

## Step-by-Step

## Verified Solution

We expand the Coriolis parameter in a Taylor series about the latitude θ_{0} as f = f_{0} + β_{y} + … where β =\left(df/dy\right) _{\theta _{0} } and y = 0 at θ_{0} . Thus, β = 2Ωcos(θ)/s and f_{0}= 2Ωsin(θ_{0}) . If the Taylor series is truncated after the first term, then we have what is termed the ‘f-plane’ approximation which includes for the Coriolis effect but not its variation with latitude. Retaining the first two terms yields the ‘β-plane approximation’, which includes a simplified form of the variation of Coriolis parameter with latitude. Note that in equatorial regions the second term becomes proportionately more important as f_{0} → 0 as θ_{0} → 0.