def atmospheric_emissivity_inst(vp_i, t_air_k_i):
    """
    Computes the atmospheric emissivity according to Brutsaert [1]_.

    .. math ::
        \\varepsilon_{a}=a\\left(\\frac{e_{a}}{T_{a}}\\right)^{b}

    where the following constants are used

    * :math:`a` = 1.24
    * :math:`b` = 1/7

    Parameters
    ----------
    vp_i : float
        instantaneous vapour pressure
        :math:`e_{a}`
        [mbar]
    t_air_k_i : float
        instantaneous air temperature
        :math:`T_{a}`
        [K]

    Returns
    -------
    emiss_atm_i : float
        instantaneous atmospheric emissivity
        :math:`\\varepsilon_{a}`
        [-]

    References
    ----------
    .. [1] Brutsaert, W., On a derivable formula for long-wave radiation
        from clear skies, Water Resour. Res, 1975, 11, 742-744.
    """
    return 1.24 * (vp_i / t_air_k_i) ** (1.0 / 7.0)
