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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.

Accurate and temporally consistent measurements of light absorbing aerosol (LAA) heating rate (HR) and of its source apportionment (fossil-fuel, FF; biomass-burning, BB) and speciation (black and brown Carbon; BC, BrC) are needed to evaluate LAA short-term climate forcing. For this purpose, wavelength- and time-dependent accurate LAA absorption coefficients are required. HR was experimentally determined and apportioned (sources/species) in the EMEP/ACTRIS/COLOSSAL-2018 winter campaign in Milan (urban-background site). Two Aethalometers (AE31/AE33) were installed together with a MAAP, CPC, OPC, a low volume sampler (PM2.5) and radiation instruments. AE31/AE33 multiple-scattering correction factors (C) were determined using two reference systems for the absorption coefficient: 1) 5-wavelength PP_UniMI with low time resolution (12 h, applied to PM2.5 samples); 2) timely-resolved MAAP data at a single wavelength. Using wavelength- and time-independent C values for the AE31 and AE33 obtained with the same reference device, the total HR showed a consistency (i.e. reproducibility) with average values comparable at 95% probability. However, if different reference devices/approaches are used, i.e. MAAP is chosen as reference instead of a PP_UniMI, the HR can be overestimated by 23–30% factor (by both AE31/AE33). This became more evident focusing on HR apportionment: AE33 data (corrected by a wavelength- and time-independent C) showed higher HRFF (+24 ± 1%) and higher HRBC (+10 ± 1%) than that of AE31. Conversely, HRBB and HRBrC were −28 ± 1% and −29 ± 1% lower for AE33 compared to AE31. These inconsistencies were overcome by introducing a wavelength-dependent Cλ for both AE31 and AE33, or using multi-wavelength apportionment methods, highlighting the need for further studies on the influence of wavelength corrections for HR determination. Finally, the temporally-resolved determination of C resulted in a diurnal cycle of the HR not statistically different whatever the source- speciation- apportionment used.