The impact of cloudiness and cloud type on the atmospheric heating rate of black and brown carbon in the Po Valley

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 Kd−1), and the lowest were in spring (0.54± 0.02 Kd−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– Published by Copernicus Publications on behalf of the European Geosciences Union. 4870 L. Ferrero et al.: The impact of cloudiness and cloud type on the atmospheric heating rate 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.

. Comparison between the ADRE values reported in Ferrero et al. (2014) with that recalculated with the present method applied to the same input data present in Ferrero et al. (2014).

Measured and computed C factor
To verify the reliability of the obtained C value, it was also computed following the Collaud Coen et al. (2010) procedure.
They defined the reference value of C (Cref = 2.81±0.11) for the AE31 tape based on data from pristine environments (Jungfraujoch and Hohenpeissenberg sites where aerosol has a single scattering albedo of ~1); at the same time, Collaud Coen et al. (2010) defined C for any kind of aerosol as follows: where α is the parameter for the Arnott (2005) scattering correction (0.0713 at 660 nm) and ω0 the single scattering albedo.
In wintertime in Milan, within the mixing layer, the single scattering albedo was found to be 0.846±0.011 at 675 nm by Ferrero et al. (2014). From eq. 1 it follows that the expected C in Milan is 3.20±0.35; within its range the experimental 3.24±0.03 value lies. With respect to C interpretation, we need to underline first that the nominal AE31 660 nm channel is provided by a Kingbright light-emitting diode (APT 1608SRC PRV 1.6 x 0.8 mm SMD Chip LED Lamp; King bright, 2018) which is characterized by a 20 nm spectral full bandwidth at half maximum under 20mA of supplied current (information from manufacturer). This is in agreement with the absorption photometer intercomparison, reported by Müller et al. (2011), in which the nominal AEs red channel was found to have a 23 nm spectral full bandwidth at half maximum. Thus, for practical purposes, the single scattering albedo (0.846±0.011 at 675 nm) reported in Milan at a wavelength slightly different from the one featured in the AE31 by Ferrero et al. (2014) was applied to eq. S1.

Physical meaning of HR equation (linkage with the actinic flux)
Equation 2 in the main body of the manuscript implies that the calculation of the HR requires the summatory of the total amount of radiative energy interacting with LAA, thus also including the reflected radiance other than the diffuse one and the direct component from the sun. In fact an alternative writing of equations 2 is: where AF(λ) represents the actinic flux, that is the total spectral flux of photons per unit area and wavelength interval available to molecules/aerosol at a particular point in the atmosphere. The radiative flux from all directions onto a volume of air is called the actinic flux (Seinfeld and Pandis, 2006).
The actinic flux consists of three components: direct solar radiation, diffuse radiation originating from scattering in the atmosphere, and diffuse radiation originating from reflection from the Earth's surface.
Thus, for the AF the following sum is valid: The actinic flux at a particular point in the atmosphere is calculated by integrating the spectral radiance over all directions of space. The actinic flux must be distinguished from spectral irradiance, which is the hemispherically integrated radiance weighted by the cosine of the angle of incidence, and represents the photon flux per unit area through a plane surface.
Under the isotropic and Lambertian assumptions, the diffuse and reflected irradiances are related with the corresponding radiances by a factor p; the direct irradiance is related to the radiance as a function of the solar zenith angle (qz).
From a physical point, given a generic monochromatic radiance R(l,q,f) (in function of wavelength, zenith and azimuth), the corresponding AF(l) and irradiance F(l) (Seinfeld and Pandis, 2006;Liou, 2007) are given by: For the direct component, the radiance comes only from the sun direction (the solar zenith angle, qz), it can be assumed to be a collimated beam, essentially parallel, and originates from a very small solid angle and thus: For the diffuse and reflected component (under the isotropic and Lambertian assumptions, respectively) the radiance comes homogeneously from each direction and thus: implying: Now, as in section 2.2 we gave the following definition: we can finally rewrite it (given eq. A7 and A8) as follows: (S11) Figure S3. Milan averaged wintertime lidar range corrected signal during the campaign presented in the manuscript.  Table S1. The empirical coefficients relating the global radiation, at a fixed solar elevation angle (π/2-θ), with the sky conditions (N, in oktas) extracted from the original work of Ehnberg and Bollen (2005).

Wind speed, cloudiness and clouds
The cloudiness is a non-linear function of the cloud type, as cloud type are related to the meteorological patterns: e.g.
highly persistent stratiform clouds generate cloudy weather in conditions with lower wind. A brief explanation could be given considering the wind speed in the 20 minute interval of the Duchon and O'Malley (1999)

method (section 2.3.2).
The SD changes in the global irradiance is due to the wind influence on the cloud dynamic; despite the fact that the wind influence on the aforementioned process is the wind at the clouds altitude, we investigated the ground level wind behavior for the clouds type classified in the present work. Result are reported in Figure S7 (Supplemental material). As expected there is no strong correlation between the two parameters as the wind speed was measured at ground level and reflect the stagnant conditions typical of the Po Valley. The average wind speed during each cloud type and CS condition was below 1 m s -1 . Despite this, it is clearly visible that low-level clouds (e.g. stratus) are present in the lowest wind speed conditions. Particularly, the average ground wind speed in stratus conditions was 0.64±0.02 m s -1 , lower than the 0.92±0.04-1.04±0.03 m s -1 found in cirrus-clear sky conditions.

The role of average photon energy on the HR of BC and BrC
The HRBrC values normalized to the species absorption coefficient in Figure 16 were always greater or equal to the corresponding normalized HRBC for the same cloud type (even though the 95% confidence interval bands overlapped). A possible explanation can be found in the synergic effect of the different spectral absorption of BC and BrC and of the influence of clouds on the energy of the impinging radiation.
The average photon energy (APE) describes the spectral characteristics of direct, diffuse and reflected irradiance modulated by sky conditions with a single parameter. APE quantifies the spectral shape of irradiance and represents the average energy of photons impinging upon a target, in this case the aerosol layer close to the surface. Therefore, a single APE value can identify a unique spectral irradiance distribution which describes the light available for absorption in different spectral regions. APE was determined for each sky condition (and thus cloud type) from the measurements of the multiplexer-radiometer-irradiometer. APE (expressed in eV) was calculated dividing the total energy in a spectrum by the total number of photons it contains (Norton et al., 2015): where q represents the electron charge, Fdir,dif,ref(λ) refers to the spectral direct, diffuse and reflected irradiance at wavelength λ (W m -2 nm -1 ), and Φλ (number of photons m -2 s -1 nm -1 ) is the photon flux density at wavelength λ determined using the Plank-Einstein equation: where h is the Plank constant and c the speed of light.
From eq. S12 it follows that APE is normalized for the total amount of irradiance, and therefore independent from the absolute intensity of light and indicating only the average distribution of light across the spectrum. Particularly, higher APE values describe the shift of a radiation spectrum towards the UV-blue region ( Figure S8).
Characteristic APE values of direct (APEdir), diffuse (APEdiff) and reflected (APEref) irradiance measured at the U9 site for different cloudiness are presented in Figure S9 and can explain why HRBrC values in Figure 16 were always greater or equal to the corresponding ones of BC. This results from the combination of the different spectral absorption of BC and BrC and of the different influence of clouds on the direct, reflected and diffuse components of the spectral irradiances.
As the BrC has the capacity to absorb much more radiation in the UV-blue region (featuring AAE of 3.49±0.01, compared to ~1 of BC) it follows that, depending on sky conditions BrC behavior can deviate from that of BC.
This can be related to the different APE of the direct, diffuse and reflected irradiance in different sky conditions. Figure   S9 shows that while APEdir and APEref slightly increases towards overcast conditions, APEdif strongly decreased with similar ( Figure S9).
As the BrC has the capacity to absorb much more radiation in the UV-blue region (featuring higher APE) it follows that, depending on sky conditions BrC can deviate from the BC behavior. In this respect, when APE for the total sky irradiance (APEtot) was determined as a weighted average with respect to the absolute amount of direct, diffuse and reflected component ( Figure S9) it showed an increasing APEtot from CS to cloudy conditions, approaching APEdif at okta=8. This APEtot feature explain the counter-intuitive property that cloudy conditions suppress slightly more the normalized HRBC with respect to the normalized HRBrC, as shown in Figure 16. Figure S8. Average photon energy of different shape of radiation spectra for a) the direct and b) the diffuse and c) reflected irradiance . Figure S9. Direct, diffuse and reflected average photon energy of the radiation (APEdir, APEdif and APEref) together with the total one (APEtot). were finally normalized and completed with normalized literature spectra to cover the complete 300-3000 nm band measured by standard radiometers (section 2.2 of the manuscript). Figure S8 reports a normalized spectra measured by the MRI for a clear sky ( Figure S58a) and cloudy ( Figure   S8b