Measurements of the wavelength-dependent aerosol absorption coefficient babs(λ) were obtained using a Magee Scientific AE-31 aethalometer. This allowed for multi-spectral measurements (7-λ: 370, 470, 520, 590, 660, 880 and 950 nm) in the wide UV–VIS–NIR (ultraviolet–visible–near-infrared) region, not available from other instruments (e.g. multi-angle absorption photometer, MAAP; particle soot absorption photometer, PSAP; and photoacoustic) (Virkkula et al., 2010; Petzold et al., 2005). This spectral range is needed for the HR determination (Sect. 2.2). The use of aethalometers also presents the advantage of global long-term data series (Ferrero et al., 2016; Eleftheriadis et al., 2009; Collaud Coen et al., 2010; Junker et al., 2006) that could allow for deriving historical data of the HR in the future.

To account for both the multiple-scattering enhancement (the elongation of the optical path induced by the filter fibres) and the loading effects (the non-linear optical path reduction induced by absorbing particles accumulating in the filter), the AE-31 data were corrected by applying the Weingartner et al. (2003) procedure (Ferrero et al., 2018, 2014, 2011b; Collaud Coen et al. 2010). As detailed by Collaud Coen et al. (2010), the Weingartner et al. (2003) procedure compensates for all the aethalometer artefacts (the backscattering is indirectly included within the multiple-scattering correction), showing a good robustness (negative values are not generated, and the results are in good agreement with other filter photometers), and, most importantly, it does not affect the derived aerosol absorption Ångström exponent (AAE) (fundamental for HR determination, Sect. 2.2). Overall, the multiple-scattering parameter C was 3.24 ± 0.03, as obtained by comparing the AE-31 data at 660 nm with an MAAP at a very similar wavelength (637 nm, Müller et al., 2011) (regression between AE-31 and MAAP in Fig. S2 in the Supplement). This value lies very close to that suggested by the Global Atmosphere Watch (GAW) programme (WMO/GAW, 2016), i.e. C = 3.5. The physical meaning of the similarity between the obtained C value (3.24 ± 0.03) and the GAW one implies that Milan (in the middle of the Po Valley) is characterized by continental-type aerosols (e.g. Carbone et al., 2010) and consistent with the global average. 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 AE-31 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 type of aerosol as follows: 1C=Cref+αω01-ω0, where α is the parameter for the Arnott et al. (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 computed C in Milan is 3.20 ± 0.35, in keeping with the experimental one (3.24 ± 0.03). Details concerning wavelength differences are discussed in the Supplement (“Measured and computed C factor”). The loading effects were dynamically determined following the Sandradewi et al. (2008b) approach, while the final equivalent BC (eBC) concentrations were obtained applying the AE-31 apparent mass attenuation cross section (16.6 m2g-1 at 880 nm).

The abovementioned compensation procedures introduce an uncertainty in the absorption coefficient measurements. Collaud Coen et al. (2010) tested these procedures in different locations and estimated the global accuracy of the Weingartner et al. (2003) correction (applied in the present work) to be ∼ 23 %. Moreover, Drinovec et al. (2015) showed a good agreement between AE-31 aethalometer data (corrected using Weingartner et al., 2003) and those of the new version, AE-33, with a slope close to unity and R2 > 0.90. Thus, the Collaud Coen et al. (2010) accuracy estimation is considered as the worst scenario.

As the spectral signature of the aerosol absorption coefficient babs(λ) reflects the different nature of absorbing aerosol (BC and BrC), once babs(λ) is obtained, it can be apportioned to determine the contributions of BC and BrC, respectively. This result can be achieved considering that BC aerosol absorption is characterized by an absorption Ångström exponent, AAE ≈ 1 (Massabò et al., 2015; Sandradewi et al., 2008a; Bond and Bengstrom, 2006). Conversely, BrC absorption is spectrally more variable, with an AAE from 3 to 10 (Ferrero et al., 2018; Shamjad et al., 2015; Massabò et al., 2015; Srinivas and Sarin, 2013; Yang et al., 2009; Kirchstetter et al., 2004). The wavelength dependence of the absorption coefficient of BrC can be described by the simple harmonic oscillator reported in Moosmüller et al. (2011): the much lower absorption in the IR (infrared) region (compared to UV) is a consequence of the resonances in the UV from which the IR region is far removed. This calculation also yields to decreasing AAE values with increasing wavelengths. This is equivalent to the band-gap model with the Urbach tail as detailed in Sun et al. (2007) and references in Moosmüller et al. (2011), where the key factor is the difference between the highest occupied and lowest unoccupied energy state of the molecules included in the BrC ensemble. In this study we determined AAEBrC following the innovative apportionment method proposed by Massabò et al. (2015). This allows for apportioning babs(λ) to BC and BrC and for determining, at the same time, the AAEBrC assuming that all BrC results from biomass burning. The method by Massabò et al. (2015) was previously applied to the Milan U9 measurements leading to an annual average of AAEBrC = 3.66 ± 0.03 (Ferrero et al., 2018).

Spectral irradiance measurements were collected using a multiplexer–radiometer–irradiometer (MRI; Fig. S1; details in Cogliati et al., 2015) which resolves the UV–VIS–NIR spectrum (350–1000 nm) in 3648 spectral bands (3648-element linear CCD array detector; charge-coupled device; Toshiba TCD1304AP, Japan) for both the downwelling and the upwelling radiation fluxes. The instrument was developed at the University of Milano-Bicocca using an optical switch (MPM-2000-2x8-VIS, Ocean Optics Inc., USA) to sequentially select between different input fibres fixed to up- and down-facing entrance fore-optics. The configuration used in the present work connects each spectrometer to three input ports: (1) the CC-3 cosine-corrected irradiance probes to collect the downwelling irradiance, (2) the bare fibre optics with a 25∘ field of view to measure the upwelling radiance from the terrestrial surface and (3) the blind port that is used to record the instrument dark current. A 5 m long optical fibre with a bundle core with a diameter of 1 mm is used to connect the entrance fore-optics to the multiplexer input, while the connection between the multiplexer output ports and the spectrometers is obtained with 0.3 m long optical fibres. The set-up allows for sequentially measuring dark current and both up- and downwelling spectra simultaneously with the two spectrometers. The two spectrometers used are high-resolution HR4000 holographic grating spectrometers (Ocean Optics Inc., USA). Finally, the multiplexer–radiometer–irradiometer was equipped with a rotating shadow band to measure separately the spectra of the direct, diffuse and reflected irradiance (Fdir(λ), Fdif(λ), Fref(λ)). The reflected irradiance originated from a Lambertian concrete surface (due to its flat and homogeneous characteristics which represents the average spectral reflectance of the Milan urban area well; Ferrero et al, 2018).

Broadband (300–3000 nm) downwelling (global and diffuse) and upwelling (reflected) irradiance measurements were also collected using LSI Lastem radiometers (DPA154 and C201R, class 1, ISO 9060, 3 % accuracy). Diffuse broadband irradiance was measured using the DPA154 global radiometer equipped with a shadow band whose effect was corrected (Ferrero et al., 2018) to determine the true amount of both diffuse and direct (obtained after subtraction from the global) irradiance. Next, MRI spectra were normalized and completed with normalized literature spectra (Ferrero et al., 2018) to cover the broadband range (300–3000 nm) and irradiance intensity measured by standard LSI Lastem pyranometers, allowing for the HR to be evaluated over the whole short-wave range (babs(λ) was estimated outside the AE-31 range using its AAE). The approach was previously validated (Ferrero et al., 2018): the HR in the strict UV–VIS–NIR range (350–950 nm of the AE31 and the MRI) accounted on average for 86.4 ± 0.4 % of the total broadband values.

In addition to radiation measurements, temperature, relative humidity, pressure and wind parameters were measured using the following LSI Lastem sensors: DMA580 and DMA570 for thermo-hygrometric measurements (for T and RH: range of -30– +70 ∘C and 10 %–98 %, accuracy of ± 0.1 ∘C, and ± 2.5 % sensibility of 0.025 ∘C and 0.2 %), the CX110P barometer model for pressure (range of 800–1100 hPa and accuracy of 1 hPa) and the CombiSD anemometer (range of 0–60 ms-1 and 0–360∘) for wind measurements.

The experimental station U9 is also equipped with an automatic lidar–ceilometer operated by ISAC-CNR in the framework of the Italian Automated LIdar-CEilometer network (ALICEnet, http://www.alice-net.eu, last access: 22 March 2021) and contributes to the EUMETNET (European meteorology network) E-Profile network (https://www.eumetnet.eu/, last access: 22 March 2021). This is a Jenoptik Nimbus 15k biaxial lidar–ceilometer operating 24 hd-1, 7 d per week. It is equipped with an Nd:YAG (neodymium-doped yttrium aluminium garnet) laser that emits light pulses at 1064 nm with an energy of 8 µJ per pulse and a repetition rate of 5 kHz. The backscattered light is detected by an avalanche photodiode in the photon-counting mode (Wiegner and Geiß, 2012; Madonna et al., 2015). The vertical and temporal resolution of the raw signals are 15 m and 30 s, respectively. In order to improve the signal-to-noise ratio of the backscatter signal, the signal is processed with temporal averages of 2 min. The full overlap is obtained at an altitude of some hundred metres above the observation site, and overlap correction functions are applied in the first layers. The Nimbus 15k lidar–ceilometer is able to determine cloud base height (CBH), penetration depth, and with specific processing mixing layer height and vertical profiles of aerosol optical and physical properties (e.g. Diemoz et al., 2019a, b; Dionisi et al., 2018). We used the U9 ceilometer data for cloud layering and relevant cloud base height, as the system can reliably detect multiple cloud layers and cirrus clouds (Wiegner et al., 2014; Boers et al., 2010; Martucci et al., 2010) within its operating vertical range (up to 15 km). Given the vertical resolution of the instrument, expected uncertainty of the cloud base height derived by the lidar–ceilometer is less than ± 30 m.

Global and diffuse irradiance measurements, coupled with the ceilometer data, were used to determine the sky cloud fraction and to classify the cloud types by following the methodology presented in the Sect. 2.3.

The cloudiness was determined following the approach reported in Ehnberg and Bollen (2005) that enables calculating the fraction of the sky covered by cloud in terms of oktas (N), overall leading to nine classes, corresponding to the values of N ranging from 0 (clear-sky conditions) to 8 (completely overcast situation). As reported by Ehnberg and Bollen (2005), the amount of global irradiance (Fglo) is related to the solar elevation angle (π/2-θz) and to the cloudiness following the Nielsen et al. (1981) equation: 4Fglo(N)=a0(N)+a1(N)sin⁡π2-θz+a3(N)sin⁡3π2-θz-L(N)a(N), where N represents one of the nine possible classes of sky conditions expressed in oktas (from 0 for clear-sky conditions to 8 for completely overcast) and a, a0, a1, a3 and L are empirical coefficients that enable computing the expected global irradiance for each okta class (Fglo(N)), at a fixed solar elevation angle (π/2-θz). Their values, extracted from the original work of Ehnberg and Bollen (2005), are summarized in Table S1 in the Supplement. Overall, Eq. (4) allows for determining the unique okta value N by comparing the measured global irradiance (Fglo) with Fglo(N) at any given time.

With this approach, the cloudiness can be used to evaluate the interaction between incoming radiation and LAA in cloudy conditions but does not provide the opportunity to discriminate between cloud type. The following section describes the methods applied to overcome this limitation by implementing a cloud classification scheme.

The identification of clouds classes is by common practice still largely performed by human observations based on the reference standard defined by the World Meteorological Organization (WMO; https://cloudatlas.wmo.int/en/home.html, last access: 22 March 2021). However, these observations lack the required time resolution which was needed in the present work to couple highly time-resolved HR data with cloud type. Cloud classification literature reports a huge quantity of papers and reviews aimed at classifying clouds by means of different techniques and their integration to avoid the limits of a simple human inspection. Most of these rely on different ensemble of instruments: (1) ground-based, (2) remote-sensing- or satellite-based, or (3) installed on meteorological balloons (Tapakis and Charalambides, 2013). Some examples are reported in Singh and Glennen (2005), Ricciardelli et al. (2008), Calbó and Sabburg (2008), and Tapakis and Charalambides (2013).

To exploit the full potential of our measurements, we needed a cloud type classification method able to follow the high temporal resolution of the observations including the high spatial and temporal variability of clouds.

Among the abovementioned instrumental ensembles, ground-based instruments provide measurement of the incident solar irradiance for detecting the effect of clouds (Calbò et al., 2001). The concept of using irradiance measurements to estimate cloud types was first introduced in the work of Duchon and O'Malley (1999), which is based on the fact that clouds with different velocities and optical depths cross the slowly changing path of the solar beam over different time durations. Given the available irradiance data (Sect. 2.1), in the present work, the cloud classification starts from the Duchon and O'Malley (1999) method which was successfully applied in the geographical context of the Po Valley (Galli et al., 2004). In particular, we used irradiance measurements (Fglo) to compute two parameters, Rt and SDt, as follows: 5Rt=120∑i=t-10i=t+10Fglo(i)Fglo_CS(i),6SDt=σt±10(Fglo(t±10)⋅Sft±10), where Rt is the 20 min moving average ratio between the observed global irradiance (Fglo) and the modelled clear-sky irradiance (Robledo and Soler, 2000) expected at the same place (Fglo_CS) at time t. Rt describes the time-dependent cloud efficiency in reducing the incoming solar radiation (Rt = 1 in perfect clear-sky conditions, while Rt ∼ 0 in completely overcast conditions). SDt represents the 20 min SD (standard deviation) of the scaled global irradiance (Fglo⋅Sf) centred at the time t and describes the temporal stability of clouds in the atmosphere (e.g. persistent stratus clouds are characterized by SDt ∼ 0, while cumulus clouds in good weather are characterized by higher values of SDt).

The scaling factor Sft (Duchon and O'Malley, 1999) is given by 7Sft=1400Wm-2Fglo_CS(t).

Visualization of the SD vs. R (SD–R plot) results thus represents a first tool in distinguishing different cloud categories as a function of their efficiency in reducing the incoming solar radiation (R) and their persistency (SD). The potential of the SD–R plot is presented in Fig. 2a–h; it shows four examples of the temporal evolution of the observed Fglo, Fglo_CS andFdif (left column) and the corresponding SD–R diagrams (right column). Explored more in detail are the following:

The first case (Fig. 2a) shows Fglo following Fglo_CS without any significant temporal deviation, thus leading to a cluster of data in the SD–R diagram (Fig. 2b) characterized by R ∼ 1 and SD ∼ 0 Wm-2. These conditions are those associated with clear-sky (CS) conditions by Duchon and O'Malley (1999).

Overall, Fig. 2a–h shows the potential (and limits) of the SD–R plots for a preliminary broad sky–cloud classification. As mentioned, the SD–R diagram alone leaves margins of misclassification, especially because it is impossible to retrieve the required information when different cloud types at different levels are present simultaneously.

In the present work, we attempted a further refinement of cloud classification, including the information of the cloud base height (CBH) and the number of cloud layers obtained from the automated lidar–ceilometer measurements. The cloud base height is a key parameter in the characterization of clouds (Hirsch et al., 2011), since its estimation limits the number of potential cloud classes (that the SD–R classifier has to discriminate between), thus maximizing the efficiency of the Duchon and O'Malley (1999) classification algorithm. In fact, ceilometer instruments were developed and are commonly used in airports to operationally detect cloud layers, and their use for aerosol-related studies is more recent. Furthermore, the use of ceilometer data for cloud classification and cloud study purposes does not represent an absolute novelty in the scientific literature as demonstrated by recent works by Huertas-Tato et al. (2017) and Costa-Surós et al. (2013). The availability of CBH information allows for dividing cloud types in three fundamental categories (Tapakis and Charalambides, 2013): low-level clouds ( < 2 km), mid-altitude clouds (2–7 km) and high-altitude clouds ( > 7 km). From a general perspective the high-altitude cloud category includes cirrus (Ci), cirrocumulus (Cc) and cirrostratus (Cs); mid-altitude clouds include altocumulus (Ac), altostratus (As) and nimbostratus (Ns); low-level clouds include cumulus (Cu), stratocumulus (Sc), stratus (St) and cumulonimbus (Cb) (Tapakis and Charalambides, 2013; Ahrens, 2009; Cotton et al., 2011).

We colour-coded the SD–R diagram in Fig. 3 using the ceilometer-based information on cloud altitude. The plot shows that, on average, low-level clouds are located on the left side of the SD–R diagram (stratiform clouds), while high-altitude clouds are conversely on the opposite side (Ci and Cu clouds); finally, mid-altitude clouds mostly cover the central part, describing all the possible transitions and combinations from St to Cu and Ci, e.g. altostratus (As) and altocumulus (Ac).

Overall, adding the CBH information to the SD–R plot enabled us to identify eight cloud types: St (stratus), Cu (cumulus) and Sc (stratocumulus) as low-level clouds; As (altostratus) and Ac (altocumulus) as mid-altitude clouds; Ci (cirrus) and Cc–Cs (cirrocumulus and cirrostratus merged in one single class) as high-altitude clouds.

A summary of the threshold values of R, SD and cloud level used here to the final cloud classification is given in Table 1, with the R and SD limits being based on the works of Duchon and O'Malley (1999) and Harrison et al. (2008) and those of the CBH being derived considering the cloud properties at midlatitudes.

Finally, to avoid misclassification due to the presence of multiple cloud layers, the analysis was limited to those cases where only one cloud layer was detected by the ceilometer (8405 single layer cases, representing 61 % of all measurements). Another reason for limiting the analyses to one cloud layer is due to the main aim of this work: to quantify the effects of different cloudiness and cloud types on the LAA HR. We wanted to avoid conditions with multiple-layer clouds, as this would result in confounding information for the purpose of the present study.

Figure 4 shows the SD–R diagram of all data (grey) with superimposed R and SD mean values and a 99 % confidence interval for each of the eight identified cloud classes, plus clear-sky (CS) conditions. The final cloud classification was obtained for the period from November 2015 to March 2016, during which all necessary parameters were available (Sect. 3).

Since this methodology is applied for the first time in the Po Valley, a complete validation of the aforementioned approach is reported in Appendix B (“Cloud type validation”). It includes two validation exercises: the first was carried out comparing the present automatized cloud classification with a visual cloud classification based on sky images collected during 1 month of the wintertime field campaign; the second was carried out comparing the present automatized cloud classification with the one discussed by Ylivinkka et al. (2020). In fact, simultaneously to the submission of our work, Ylivinkka et al. (2020) proposed a classification based on the coupling of irradiance and CBH measurements. Overall, based on these comparisons, agreement with our classification is 80 % with the visual approach and 90 % with the Ylivinkka et al. (2020) methodology, with these results further demonstrating the reliability of the cloud classification algorithm used in our study.

Figure 6a already provided the first indication of the important influence of clouds on the total HR. In fact, it shows the magnitude of the absolute (and relative) contribution of the diffuse component (HRdif) with respect to the total HR revealing that, on a monthly basis, the diffuse contribution accounted on average for 40 ± 1 % (of the total HR). In most cases this was comparable or even higher than the HRdir. The only exception was in November 2015 when the lower HRdif (Fig. 6a) and Fdif (Fig. 6b) fractions in the total HR and Fglo were measured (30.4 ± 1.4 % and 34.3 ± 2.6 % of the total, respectively), with this also being the month with the lowest average cloudiness (2.91 ± 0.06 oktas). The aforementioned data demonstrate the importance of the diffuse component of radiation. Therefore, the absolute values of the HR and its components were firstly investigated as a function of cloudiness (clear-sky and completely overcast situations, seasonal averages, Fig. 9a). In the wintertime clear sky, the direct component of the HR (HRdir) was higher than the HRdif and HRref, accounting for 1.35 ± 0.04 Kd-1 and explaining on average 60 ± 5 % of the total HR. Similarly, in the springtime clear sky, HRdir was 0.47 ± 0.01 Kd-1, again higher than the HRdif and HRref. Conversely, in a completely overcast condition (7–8 oktas), the HRdif dominated (84 ± 1 % of the total HR) and accounted for 0.33 ± 0.01 and for 0.19 ± 0.01 Kd-1 during winter and spring, respectively.

In order to further investigate the role of cloudiness, we decoupled the variability of the HR induced by radiation from that due to LAA concentrations. Thus, the HR values and those of its components (HRdir, HRdif and HRref) were normalized to the unit mass of eBC (Km3d-1µg-1) and reported as a function of cloudiness in Fig. 9b together with the measured irradiance (Fglo, Fdir, Fdif and Fref): this parameter (HR/eBC) reports the efficiency of warming per mass concentration of eBC at different cloudiness levels. Overall, Fig. 9b shows the general decease of HR/eBC for increasing cloud cover, a pattern also observed for both HRdir/eBC and HRref/eBC, which follow the respective decrease of direct and reflected irradiance. Note that at okta values of 7–8, HRdir/eBC reached values close to 0 (due to the suppression of Fdir by clouds), while HRref/eBC was 0.03 ± 3 × 10-4 Km3d-1µg-1 due to the presence of surficial albedo effect on the diffuse irradiance (Fdif). HRdif/eBC increased with increasing cloudiness up to intermediate cloudiness conditions (5–6 oktas), reaching a maximum (0.16 ± 0.01 Km3d-1µg-1). This is in line with the behaviour of the diffuse irradiance: maximum of 147 ± 6 Wm-2 (at 5–6 oktas), doubling the value in overcast conditions (74 ± 3 Wm-2; 7–8 oktas) and exceeding 150 % of that for clear-sky conditions (91 ± 2 Wm-2). In the overcast condition (7–8 oktas) both HRdif/eBC and the diffuse irradiance reached their minimum due to the capability of clouds to effectively attenuate the incoming radiation. However, in these conditions, HRdif/eBC was still not null (0.08 ± 0.01 Km3d-1µg-1), dominating the total atmospheric HR, with a contribution of 84 ± 1 %.

HR/eBC and cloudiness data were linearly related, showing a high level of correlation (R2 = 0.935, Fig. S5b). Cloudiness could thus be used as good predictor (in modelling activity) for HR/eBC.

As from Fig. S5a (Sect. 3.1), the CBH appeared related to the cloudiness, and an additional linear correlation was tested between HR/eBC and the CBH (Fig. S5c; R2 = 0.857); this relationship is weaker than that between HR/eBC and cloudiness. Cloudiness, describing the fraction of sky covered by clouds, is a better predictor of the capability to suppress the incoming radiation (and thus the HR promoted by LAA). The relationship between the CBH and cloudiness should be also investigated in other monitoring sites around the world to explore the possibility of using the CBH (together with cloudiness) as a promising prognostic variable for the HR of LAA in future studies.

Overall, our experimental HR data enabled us to estimate the degree of error introduced by improperly assuming clear-sky conditions in radiative-transfer calculations. Particularly, we found that the simplified assumption of clear-sky conditions leads to an overestimation of the LAA-induced HR by a factor ranging from 50 % to 470 % (50 % in low cloudiness: 1–2 oktas; 109 % in moderate cloudiness: 3–4 oktas; 148 % in intermediate cloudiness: 5–6 oktas; and 470 % in cloudy conditions: 7–8 oktas). These results clearly highlight that clouds are responsible for an important feedback on the aerosol HR that needs to be carefully quantified, pointing to the need to correctly include and model cloudy conditions in radiative-transfer calculations aimed at evaluating the real contribution of aerosol forcing on the atmospheric HR on a global scale.

The presence of clouds can also alter the HR diurnal pattern. Figure 10a–d show the mean diurnal pattern of eBC, wind speed, Fglo and the HR in both clear-sky (0 oktas) and cloudy conditions (7–8 oktas). In clear-sky conditions, the eBC peaked at 08:00 LST (6.41 ± 0.31 µgm-3) during the rush hour (Fig. 10a); then eBC decreased until its minimum in the early afternoon (1.07 ± 0.10 µgm-3) when the wind speed reached its maximum (1.5 ± 0.1 ms-1, Fig. 10b). The incoming Fglo in clear-sky conditions peaked as expected at midday with 497 ± 10 Wm-2 (Fig. 10c). This caused an asymmetric HR diurnal pattern, being characterized by a fast increase to the maximum at 10:00 LST (3.60 ± 0.18 Kd-1) and a subsequent slower decrease by sunset (Fig. 10d). This pattern was not present in cloudy conditions (Fig. 10d). First, eBC showed a moderate peak at 10:00 LST (4.09 ± 0.20 µgm-3) being quite stable during the afternoon – remaining above 3 µgm-3 until 16:00 LST (Fig. 10a). The eBC behaviour was consistent with that of wind speed, which only slightly rose during the day but was however always below 1 ms-1 (on average 0.64 ± 0.03 ms-1, Fig. 10b). The incoming Fglo in cloudy conditions peaked again as expected at midday with 103 ± 4 Wm-2 with a much slower increase during the day (Fig. 10c). The Supplement (“Wind speed, cloudiness and clouds”) and Fig. 7b show that cloudy conditions were mostly associated with stratus and very low windy conditions (0.64 ± 0.02 ms-1), explaining the flat diurnal behaviour of eBC differing from the clear-sky case. Moreover, the absence of any direct irradiance in cloudy conditions (Fig. 9b; Sect. 3.1) determines that Fglo was essentially due to the diffuse irradiance whose symmetrical bell-shaped curve drove the HR behaviour (Fig. 10d), peaking at midday with a value of 0.74 ± 0.01 Kd-1 (much lower than in CS).

As a conclusion, in different cloudiness conditions, not only the absolute magnitude of the HR but also its diurnal pattern are different. This also changes the related atmospheric feedbacks, such as the influence on the liquid water content (Jacobson, 2002), planetary boundary layer dynamics (Wang et al., 2018; Ferrero et al., 2014), regional circulation systems (Ramanathan and Feng, 2009; Ramanathan and Carmichael, 2008), and finally the cloud dynamic and evolution itself (Koren et al., 2008; Bond et al., 2013). Thus, an inappropriate use of the clear-sky assumption in models will also reflect on the modelled HR-triggered feedbacks. These results also acquire relevance in the context of the counterintuitive semi-direct effect proposed by Perlwitz and Miller (2010) and referred to in Sect. 1: the atmospheric heating induced by tropospheric absorbing aerosol could lead to a cloud cover increase (especially low-level clouds). Such a feedback stresses the need for a proper inclusion of sky conditions into radiative-transfer calculations.

The previous sections showed the effect of cloudiness on the total LAA HR. The impact of each cloud type on the HR is addressed here, as not all clouds have the same effect on irradiance (Tapakis and Charalambides, 2013). As previously done, we refer to HR values normalized to eBC unit mass (HR/eBC) to decouple radiation and aerosol effects. Figure 11a–d show the total HR/eBC and Fglo together with the corresponding components (HRdir/eBC and Fdir, HRdif/eBC and Fdif, and HRref/eBC and Fref; Fig. 11b–d). The figure shows a prefect agreement between cloud type, irradiance and the corresponding HR/eBC component (R2 > 0.93; not shown). It also highlights how critical it is, for radiative-transfer calculations and HR determination, to take into account the role of each cloud type. Only the cloud influence on the HRdif/eBC is markedly different from the other components.

In terms of absolute values (not normalized for eBC), Fig. 12 reveals that the HRdir was only dominant during periods of CS and Ci clouds (HRdir of 1.11 ± 0.04 and 0.92 ± 0.05 Kd-1, respectively), explaining 66 ± 3 % and 57 ± 4 % of the total atmospheric HR. In the cases of other clouds (St, As and Sc) HRdif dominates, reaching the highest absolute contribution of 84.4 ± 3.8 %, 83.0 ± 10.7 % and 76 ± 4 % (HRdif of 0.25 ± 0.01, 0.34 ± 0.03 and 0.66 ± 0.02 Kd-1), respectively.

Given this impact of cloud type, the ability of cloudiness to be a good predictor for the HR (as detailed in Sect. 3.2.1), and the relationship (over the investigated site) between cloudiness and cloud type (Sect. 3.1, Fig. 7b), the synergic impact of cloudiness and cloud type on the HR was investigated and presented in Fig. 13. In the figure, we summarize the HR results in terms of percent difference from the clear-sky (CS) case by averaging the cloudiness (in oktas) for each cloud type (as detected in Sect. 3.3). Overall, the derived linear regression indicates an HR decrease of -11.9 ± 1.2 % per okta. The regression R2 (0.963) was slightly higher than that reported in Fig. S5b (R2 = 0.935; relationship with the cloudiness only) suggesting the need (for precise calculations) to account for the cloud types responsible for any sky coverage in agreement with a recent work of Bartoszek et al. (2020). Figure 13 also allowed us to associate the HR decrease with each specific cloud type over Milan. Particularly, Ci clouds produced a modest impact on cloudiness (0.50 ± 0.05 oktas), decreasing the HR by ∼ 3 %, while Cu clouds (1.76 ± 0.09 oktas) decreased the HR by -26 ± 8 %. Cc–Cs clouds (3.56 ± 0.14 oktas) were responsible for a -49 ± 6 % decrease of the HR. Their impact was comparable to that of Sc clouds (4.68 ± 0.10 oktas, -48 ± 4 % of the HR). Ac clouds (4.11 ± 0.18 oktas) had a higher impact, decreasing the HR by -59 ± 6 %. The highest impact was due to As (6.57 ± 0.15 oktas; -76 ± 4 % of the HR) and by St (7.19 ± 0.04 oktas) that suppressed the HR by a factor of -83 ± 4 %.