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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def haurwitz(apparent_zenith):
    '''
    Determine clear sky GHI using the Haurwitz model.

    Implements the Haurwitz clear sky model for global horizontal
    irradiance (GHI) as presented in [1, 2]. A report on clear
    sky models found the Haurwitz model to have the best performance
    in terms of average monthly error among models which require only
    zenith angle [3].

    Parameters
    ----------
    apparent_zenith : Series
        The apparent (refraction corrected) sun zenith angle
        in degrees.

    Returns
    -------
    ghi : DataFrame
        The modeled global horizonal irradiance in W/m^2 provided
        by the Haurwitz clear-sky model.

    References
    ----------

    [1] B. Haurwitz, "Insolation in Relation to Cloudiness and Cloud
     Density," Journal of Meteorology, vol. 2, pp. 154-166, 1945.

    [2] B. Haurwitz, "Insolation in Relation to Cloud Type," Journal of
     Meteorology, vol. 3, pp. 123-124, 1946.

    [3] M. Reno, C. Hansen, and J. Stein, "Global Horizontal Irradiance Clear
     Sky Models: Implementation and Analysis", Sandia National
     Laboratories, SAND2012-2389, 2012.
    '''

    cos_zenith = tools.cosd(apparent_zenith.values)
    clearsky_ghi = np.zeros_like(apparent_zenith.values)
    cos_zen_gte_0 = cos_zenith > 0
    clearsky_ghi[cos_zen_gte_0] = (1098.0 * cos_zenith[cos_zen_gte_0] *
                                   np.exp(-0.059/cos_zenith[cos_zen_gte_0]))

    df_out = pd.DataFrame(index=apparent_zenith.index,
                          data=clearsky_ghi,
                          columns=['ghi'])

    return df_out