def _disc_kn(clearness_index, airmass, max_airmass=12):
    """
    Calculate Kn for `disc`

    Parameters
    ----------
    clearness_index : numeric
    airmass : numeric
    max_airmass : float
        airmass > max_airmass is set to max_airmass before being used
        in calculating Kn.

    Returns
    -------
    Kn : numeric
    am : numeric
        airmass used in the calculation of Kn. am <= max_airmass.
    """
    # short names for equations
    kt = clearness_index
    am = airmass

    am = np.minimum(am, max_airmass)  # GH 450

    # powers of kt will be used repeatedly, so compute only once
    kt2 = kt * kt  # about the same as kt ** 2
    kt3 = kt2 * kt  # 5-10x faster than kt ** 3

    bools = (kt <= 0.6)
    a = np.where(bools,
                 0.512 - 1.56*kt + 2.286*kt2 - 2.222*kt3,
                 -5.743 + 21.77*kt - 27.49*kt2 + 11.56*kt3)
    b = np.where(bools,
                 0.37 + 0.962*kt,
                 41.4 - 118.5*kt + 66.05*kt2 + 31.9*kt3)
    c = np.where(bools,
                 -0.28 + 0.932*kt - 2.048*kt2,
                 -47.01 + 184.2*kt - 222.0*kt2 + 73.81*kt3)

    delta_kn = a + b * np.exp(c*am)

    Knc = 0.866 - 0.122*am + 0.0121*am**2 - 0.000653*am**3 + 1.4e-05*am**4
    Kn = Knc - delta_kn
    return Kn, am
Calculate Kn for `disc`

    Parameters
    ----------
    clearness_index : numeric
    airmass : numeric
    max_airmass : float
        airmass > max_airmass is set to max_airmass before being used
        in calculating Kn.

    Returns
    -------
    Kn : numeric
    am : numeric
        airmass used in the calculation of Kn. am <= max_airmass.