Abstract. We experimentally quantified the impact of cloud fraction and cloud type on the heating rate (HR) of black and brown carbon (HRBC and
HRBrC). In particular, we examined in more detail the cloud effect on the HR detected in a previous study (Ferrero et al., 2018). High-time-resolution measurements of the aerosol absorption coefficient at multiple wavelengths were coupled with spectral measurements of the direct,
diffuse and surface reflected irradiance and with lidar–ceilometer data during a field campaign in Milan, Po Valley (Italy). The experimental
set-up allowed for a direct determination of the total HR (and its speciation: HRBC and HRBrC) in all-sky conditions (from clear-sky conditions
to cloudy). The highest total HR values were found in the middle of winter (1.43 ± 0.05 K d−1), and the lowest were in spring
(0.54 ± 0.02 K d−1). Overall, the HRBrC accounted for 13.7 ± 0.2 % of the total HR, with the BrC being
characterized by an absorption Ångström exponent (AAE) of 3.49 ± 0.01. To investigate the role of clouds, sky conditions were classified in
terms of cloudiness (fraction of the sky covered by clouds: oktas) and cloud type (stratus, St; cumulus, Cu; stratocumulus, Sc; altostratus, As;
altocumulus, Ac; cirrus, Ci; and cirrocumulus–cirrostratus, Cc–Cs). During the campaign, clear-sky conditions were present 23 % of the time,
with the remaining time (77 %) being characterized by cloudy conditions. The average cloudiness was 3.58 ± 0.04 oktas (highest in February at
4.56 ± 0.07 oktas and lowest in November at 2.91 ± 0.06 oktas). St clouds were mostly responsible for overcast conditions (7–8 oktas,
frequency of 87 % and 96 %); Sc clouds dominated the intermediate cloudiness conditions (5–6 oktas, frequency of 47 % and 66 %); and the
transition from Cc–Cs to Sc determined moderate cloudiness (3–4 oktas); finally, low cloudiness (1–2 oktas) was mostly dominated by
Ci and Cu (frequency of 59 % and 40 %, respectively). HR measurements showed a constant decrease with increasing cloudiness of the atmosphere, enabling us to quantify for the first time the bias
(in %) of the aerosol HR introduced by the simplified assumption of clear-sky conditions in radiative-transfer model calculations. Our results
showed that the HR of light-absorbing aerosol was ∼ 20 %–30 % lower in low cloudiness (1–2 oktas) and up to 80 % lower in
completely overcast conditions (i.e. 7–8 oktas) compared to clear-sky ones. This means that, in the simplified assumption of clear-sky
conditions, the HR of light-absorbing aerosol can be largely overestimated (by 50 % in low cloudiness, 1–2 oktas, and up to 500 % in
completely overcast conditions, 7–8 oktas). The impact of different cloud types on the HR was also investigated. Cirrus clouds were found to have a modest impact, decreasing the HRBC and
HRBrC by −5 % at most. Cumulus clouds decreased the HRBC and HRBrC by −31 ± 12 % and −26 ± 7 %,
respectively; cirrocumulus–cirrostratus clouds decreased the HRBC and HRBrC by −60 ± 8 % and −54 ± 4 %, which
was comparable to the impact of altocumulus (−60 ± 6 % and −46 ± 4 %). A higher impact on the HRBC and HRBrC
suppression was found for stratocumulus (−63 ± 6 % and −58 ± 4 %, respectively) and altostratus (−78 ± 5 % and
−73 ± 4 %, respectively). The highest impact was associated with stratus, suppressing the HRBC and HRBrC by
−85 ± 5 % and −83 ± 3 %, respectively. The presence of clouds caused a decrease of both the HRBC and HRBrC
(normalized to the absorption coefficient of the respective species) of −11.8 ± 1.2 % and −12.6 ± 1.4 % per okta. This study
highlights the need to take into account the role of both cloudiness and different cloud types when estimating the HR caused by both BC and BrC and
in turn decrease the uncertainties associated with the quantification of their impact on the climate.
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