def potential_vorticity_barotropic(heights, u, v, dx, dy, lats, dim_order='yx'):
    r"""Calculate the barotropic (Rossby) potential vorticity.

    .. math:: PV = \frac{f + \zeta}{H}

    This formula is based on equation 7.27 [Hobbs2006]_.

    Parameters
    ----------
    heights : (M, N) ndarray
        atmospheric heights
    u : (M, N) ndarray
        x component of the wind
    v : (M, N) ndarray
        y component of the wind
    dx : float or ndarray
        The grid spacing(s) in the x-direction. If an array, there should be one item less than
        the size of `u` along the applicable axis.
    dy : float or ndarray
        The grid spacing(s) in the y-direction. If an array, there should be one item less than
        the size of `u` along the applicable axis.
    lats : (M, N) ndarray
        latitudes of the wind data in radians or with appropriate unit information attached

    Returns
    -------
    (M, N) ndarray
        barotropic potential vorticity

    Notes
    -----
    If inputs have more than two dimensions, they are assumed to have either leading dimensions
    of (x, y) or trailing dimensions of (y, x), depending on the value of ``dim_order``.

    """
    avor = absolute_vorticity(u, v, dx, dy, lats, dim_order=dim_order)
    return (avor / heights).to('meter**-1 * second**-1')
r"""Calculate the barotropic (Rossby) potential vorticity.

    .. math:: PV = \frac{f + \zeta}{H}

    This formula is based on equation 7.27 [Hobbs2006]_.

    Parameters
    ----------
    heights : (M, N) ndarray
        atmospheric heights
    u : (M, N) ndarray
        x component of the wind
    v : (M, N) ndarray
        y component of the wind
    dx : float or ndarray
        The grid spacing(s) in the x-direction. If an array, there should be one item less than
        the size of `u` along the applicable axis.
    dy : float or ndarray
        The grid spacing(s) in the y-direction. If an array, there should be one item less than
        the size of `u` along the applicable axis.
    lats : (M, N) ndarray
        latitudes of the wind data in radians or with appropriate unit information attached

    Returns
    -------
    (M, N) ndarray
        barotropic potential vorticity

    Notes
    -----
    If inputs have more than two dimensions, they are assumed to have either leading dimensions
    of (x, y) or trailing dimensions of (y, x), depending on the value of ``dim_order``.