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A (2 + 1)-dimensional variable coefficient Korteweg-de Vries (3D VCKdV) equation is first derived in this paper by means of introducing 2-dimensional space and time slow-varying variables and the multiple-level approximation method from the well-known barotropic and quasi-geostrophic potential vorticity equation without dissipation. The exact analytical solution of the 3D VCKdV equation is obtained successfully by making use of CK’s direct method and the standard Zakharov–Kuznetsov equation. By some arbitrary functions and the analytical solution, a dipole blocking evolution process with twelve days’ lifetime is described, and the result illustrates that the central axis of the dipole is no longer perpendicular to the vertical direction but has a certain angle to vertical direction. The comparisons with the previous researches and Urals dipole blocking event demonstrate that 3D VCKdV equation is more suitable for describing the complex atmospheric blocking phenomenon.

3D Variable Coefficient KdV Equation and Atmospheric Dipole Blocking