to the one obtained from large all-sky redshift surveys.

A particularly useful method for performing a velocity-velocity comparison is the modal expansion method[@nd]. This method expands the velocity fields by means of smooth functions (Bessel and spherical harmonics) defined in redshift space, thus alleviating the Malmquist biases inherent in real space analysis. Furthermore, the modal expansion smooths the observed and predicted velocities in the same way, so that the smoothed fields can be compared directly. Because the number of modes is substantially smaller than the number of data points, the method also provides the means of estimating $\beta$ from a likelihood analysis carried out on a mode-by-mode basis, instead of galaxy-by-galaxy. The similar smoothing and the mode-by-mode comparison substantially simplify the error analysis. The modal expansion method has been used in comparisons between the 1.2 Jy predicted velocities and observed velocities inferred from TF measurements[@dnw] in the Mark III catalog, yielding $\beta_I\sim$ 0.4. However, examination of the residual field showed a strong dipole signature suggesting a significant mismatch between the Mark III and the fields. The reasons for the mismatch are still not well-understood.

More recently, the same method has been employed in the comparison of the 1.2 Jy and 