The piecewise potential vorticity (PV) inversion method developed by Davis and Emanuel (1991) is used to diagnose the development processes of a polar low over the Sea of Japan in December 2003. The synoptic scale-balanced flows associated with the polar low are successfully captured using the inversion method. It is shown that, antecedent to the development of the polar low, a positive lower-tropospheric temperature anomaly was induced by the approach of a positive tropopause-level PV anomaly over the northern Sea of Japan. The analysis suggests that the polar low was initiated as a result of the combined effect of the positive PV anomaly near the tropopause and the near-surface positive temperature anomaly. The rapid height falls in the lower troposphere were primarily contributed by the upper tropospheric PV anomaly. Further intensification of the polar low was afforded by latent heat release associated with cloud and precipitation processes. After the polar low moved over northern Honshu, quick dissipation was primarily rendered by the thinning and elongating of the upper level PV anomaly that led to a rapid reduction of the lower troposphere height perturbations associated with it.