  In this paper, we consider the modified quasi-geostrophic equation
\begin{gather*} \del_t \theta + (u \cdot \grad) \theta + \kappa \Lambda^\alpha
\theta = 0 u = \Lambda^{\alpha - 1} R^{\perp}\theta. \end{gather*} with $\kappa
> 0$, $\alpha \in (0,1]$ and $\theta_0 \in \lp{2}(\R^2)$. We remark that the
extra $\Lambda^{\alpha - 1}$ is introduced in order to make the scaling
invariance of this system similar to the scaling invariance of the critical
quasi-geostrophic equations. In this paper, we use Besov space techniques to
prove global existence and regularity of strong solutions to this system.
