  We give an alternative proof of the nonuniqueness of weak solutions to the
surface quasigeostrophic equation (SQG) first shown in
[Buckmaster-Shkoller-Vicol, '16]. Our approach proceeds directly at the level
of the scalar field. Furthermore, we prove that every smooth scalar field with
compact support that conserves the integral can be realized as a weak limit of
solutions to SQG.
