  The response of a semi-infinite ocean to a slowly travelling atmospheric
perturbation crossing the coast provides a simple example of the breakdown of
nearly geostrophic balance induced by a boundary. We examine this response in
the linear shallow-water model at small Rossby number $\varepsilon \ll 1$.
Using matched asymptotics we show that a long Kelvin wave, with
$O(\varepsilon^{-1})$ length scale and $O(\varepsilon)$ amplitude relative to
quasigeostrophic response, is generated as the perturbation crosses the coast.
Accounting for this Kelvin wave restores the conservation of mass which is
violated in the quasigeostrophic approximation.
