Summary: We study the fractal and Hausdorff dimensions of the global attractor for the three-dimensional Navier-Stokes-\(\alpha\) model for fast rotating geophysical fluids. The Navier-Stokes-\(\alpha\) model is a nonlinear dispersive regularization of the exact Navier-Stokes equations obtained by Lagrangian averaging and tend to the Navier-Stokes equations as \(\alpha\to 0^+\). We estimate upper bounds for the dimensions of the global attractor and study the dependence of the dimensions on the parameter \(\alpha\). All the estimates are uniform in \(\alpha\), and our estimates of attractor dimensions remain finite when \(\alpha\to 0^+\).