def METHOD_NAME(ax: Axes, x: np.ndarray, y: np.ndarray,
                              z: np.ndarray, **kw: Any) -> Union[AxesImage, None]:
    r"""Plot a pcolormesh with some reasonable defaults.
    Input are the corresponding arrays from a 2D ``MeshgridDataDict``.
    Will attempt to fix missing points in the coordinates.
    :param ax: subPlots to plot the colormesh into.
    :param x: x component of the meshgrid coordinates
    :param y: y component of the meshgrid coordinates
    :param z: data values
    :returns: the image returned by `pcolormesh`.
    Keywords are passed on to `pcolormesh`.
    """
    # the meshgrid we have describes coordinates, but for plotting
    # with pcolormesh we need vertices.
    try:
        x = centers2edges_2d(x)
        y = centers2edges_2d(y)
    except:
        return None
    im = ax.pcolormesh(x, y, z, **kw)
    ax.set_xlim(x.min(), x.max())
    ax.set_ylim(y.min(), y.max())
    return im