The annual cycle of aerosol number concentration in the Amazon is characterized by extreme variations, from 250 particles cm⁻³ during the wet season to values as high as 30 000 particles cm⁻³ in the dry season . This contrast makes the Amazon region a natural laboratory for studying aerosol–cloud interactions. In this study, datasets obtained during the GoAmazon2014/5 campaign , carried out in 2014 and 2015 in the Brazilian Amazon, were used. The experimental sites of GoAmazon2014/5 were selected based on seasonal timing and the prevailing wind direction. The sites designated as “T0” were located north of the city of Manaus, a region undisturbed by the urban pollution plume due to the prevailing northeasterly winds. The Sites “T1” and “T2” were positioned south of Manaus. The “T3” and “T3u” sites were located southwest of the city, alternately influenced by clean and polluted air masses due to variations around the mean wind direction.

In this work, we used data collected from the T3 site (3.2° S, 60.6° W), which accommodated the largest number of instruments during both GoAmazon2014/5 campaign years. At T3, instruments operated by the U.S. Department of Energy (DoE) under the Atmospheric Radiation Measurement Program (ARM, https://www.arm.gov/, last access: 21 August 2026) were deployed, including the ARM Mobile Facility 1 (AMF-1) and the ARM Mobile Aerosol Observing System (MAOS; ). Furthermore, during the two intensive operational periods (IOP1 and IOP2, from 1 February to 31 March 2014, and from 15 August to 15 October 2014, respectively) of GoAmazon2014/5, other instrumental platforms were also employed, such as the Gulfstream-159 aircraft (“G1”; ) and the HALO aircraft (High Altitude and Long Range Research Aircraft; ). The HALO aircraft flew as part of a collaboration effort with the Brazilian-German project ACRIDICON-CHUVA .

The atmospheric and cloud properties obtained by ground-based remote sensing included the fc, the liquid water path (LWP), the cloud base height, and the cloud top height (CBH and CTH, respectively). All datasets were maintained and provided continuously by the ARM program. The data set fc originated from a Value-Added Product (RADiative FLUX ANALysis VAP, ) that combined measurements from different radiometers to derive total, direct and diffuse short- and longwave downward and upward irradiances, as well as fc for shortwave and longwave radiation. The fc values were retrieved at one-minute intervals and did not distinguish between different types of cloud.

The LWP values (sourced from the MicroWave Radiometer RETrievals VAP and with 1σ uncertainty, ) were derived through an algorithm that combines atmospheric thermodynamic state information – vertical profiles of air temperature, pressure, and relative humidity, used in independent steps of the method – with brightness temperature measurements at 23.8 and 31.4 GHz obtained by a surface-based microwave radiometer (MWR). The base and top heights of the observed cloud layers were derived from the Active Remote Sensing of Clouds VAP (ARSCL VAP, ) which combined measurements from a W-band ARM Cloud Radar (WACR, operating at 95.04 GHz) and a micropulse lidar system (MPL), with CBH and CTH values sampled every 5 s. An important observation is that the LWP data measured using the MWR could, in principle, be validated from in-situ LWC measurements made in clouds during flights over T3 (more on those LWC data in Sect. ), when co-located spatially and temporally with cloud radar and lidar (WACR + MPL) measurements, used to estimate CBH and CTH. However, there were no cases of simultaneous measurements from the three instruments at both IOPs and, for this reason, we were unable to cross-validate the LWP data.

The total aerosol scattering coefficient (βsct.), the total concentration of organic mass (“Total Organics” or “Org.”), the number concentration of cloud condensation nuclei (CCN) and the spectral aerosol optical depth (AOD) were the aerosol properties analyzed. The values of βsct. were derived using a pair of nephelometers measuring βsct. as a function of relative humidity at intervals of one-min, at three wavelengths λ (700, 550 and 450 nm), and for two cuts in particle size (1 and 10 µm). The values of Total Organics were obtained using an Aerosol Chemical Speciation Monitor (ACSM), a mass spectrometer based on thermal vaporization and subsequent ionization of aerosol particles smaller than 1 µm .

The CCN number concentrations at the T3 site were measured using a cloud condensation nuclei particle counter (CCNC). This instrument measures aerosol concentrations by sampling air through a column with thermodynamically unstable supersaturated water vapor, which can condense on aerosol particles. The resulting grown particles are counted and sized by an Optical Particle Counter (OPC). Thus, CCNC quantifies the number concentration of particles activated as a function of the instrument's internal supersaturation .

Spectral AOD values constituted the final aerosol-related variable used in this study. Due to the limited availability of samples, two complementary datasets were employed. The first was obtained from a sun photometer belonging to AERONET (AErosol RObotic NETwork; https://aeronet.gsfc.nasa.gov/, last access: 21 August 2026), an instrument equipped with a 25 cm collimator system mounted on a robotic base that can be programmed to point either toward the sky or directly at the Sun. This photometer measures spectral solar and sky radiances at eight wavelengths (340, 380, 440, 500, 675, 870, 1020, and 1640 nm) and uses them to calculate AOD values and other quantities , after correcting for molecular scattering and absorption caused by ozone and other atmospheric gases. The AERONET-derived AOD values used here correspond to the 500 nm wavelength, being measured at variable sampling rates (ranging from 1.9 to 551.3 min).

The AERONET's data set was complemented with AOD values retrieved from solar irradiance measurements acquired by a MultiFilter Rotating Shadowband Radiometer (MFRSR) operated by ARM. These irradiances serve as input for a VAP that applies the algorithms described by , , and to derive spectral AOD values at six wavelengths (415, 500, 615, 673, 870, and 940 nm), with a sampling interval of 20 s.

In situ measurements of the liquid water content in clouds, total water content (TWC), total cloud droplet concentration (Nd), cloud droplet size distribution (N(D)), and effective cloud droplet diameter (Deff.) were performed using instruments onboard the G-1 and HALO aircraft.

Of the 35 flights conducted by the G-1 during IOP 1 and IOP 2, 29 flew over the retangular area (60.75° W, 3.3° S, 60.45° W, 3.1° S) of 0.2° × 0.3° centered at the T3 site and were used in this study. LWC and TWC measurements were carried out using the WCM-2000 instrument, a sensor composed of a scoop-shaped device equipped with several heated wires. Some of these wires are directly exposed to the airflow and cloud water droplets, while a separate reference wire is exposed only to the airflow. A power control system maintains constant voltage in one wire and constant temperature in the others. In the case of constant temperature operation, the “King-type” probe uses the system's power values, relative airspeed, ambient temperature, individual wire dimensions, and the latent heat of water vaporization to calculate LWC and TWC each second (for calculation details, see the user manual available at https://www.scieng.com/pdf/WCM2000User.pdf, last access: 21 August 2026).

The Nd and N(D) values measured during the G-1 flights were obtained using the Fast Cloud Droplet Probe (FCDP; manual available at https://www.arm.gov/publications/tech_reports/handbooks/doe-sc-arm-tr-238.pdf, last access: 21 August 2026), an instrument that employs a focused laser beam to size hydrometeors based on the amount of scattered light during particle–beam interaction. The FCDP has a resolution of 3 µm, measures droplet diameters between 1 and 50 µm, and divides them into 20 equally spaced size bins.

The HALO aircraft conducted 14 research flights between September and October 2014, during the GoAmazon2014/5 IOP 2. The flights were designed to cover five distinct mission types, focusing on different processes involving clouds, aerosols, chemistry, and radiation . The flights were numbered chronologically as ACXX, with X ranging from 07 to 20. Among these, only two flew over clean densely forested areas to the north and northwest of Manaus (AC09 and AC18, conducted on 11 and 28 September 2014, respectively). Those flights were conducted over two regions practically unaffected by biomass burning plumes from the deforestation arc in the Amazon, characterizing the cleanest possible atmosphere among all flights performed, as indicated in . Despite the low number of samples, these flights are representative of the cleanest possible atmospheric regime within the polluted season in the region, which is why they constitute the best available samples to characterize the second clean scenario used in this study. Given that the clouds measured during it were not directly affected by biomass-burning aerosols, those flights were selected to serve as a background reference.

LWC and Deff. HALO measurements were obtained using the Cloud and Aerosol Spectrometer with Detector for Polarization (CAS-DPOL), a spectrometer that also measures the cloud droplet size distribution from 0.5 to 50 µm . Filtering of LWC and Deff. for low-level liquid clouds was performed using flight altitude data (above sea level, ASL) from the Basic HALO Measurement and Sensor System (BAHAMAS), considering a maximum flight height of 3 km.

Table  compiles the atmospheric, cloud and aerosol variables used in this study. The table also shows the corresponding instrument, measurement unit, experimental platform, and sampling interval for each variable. For CBH, CTH, and LWP, 1 min averages were calculated to facilitate the derivation of microphysical parameters for subsequent low-level liquid-cloud modeling. For AOD, βsct., Total Organics, CCN, and fc, daily and/or diurnal averages were calculated. The mathematical formulations of the variables presented in Table  are provided in Sect. .

Periods with lower and higher average aerosol number concentration during the GoAmazon2014/5 campaign will be referred to as “clean” and “polluted” scenarios, respectively. The term “clean” does not imply a complete absence of anthropogenic aerosols in the atmosphere, but rather a distinctly lower concentration compared to the “polluted” scenario. The latter corresponds to episodes in 2014 and 2015 with a higher frequency of biomass-burning events and advection of the Manaus pollution plume over the T3 site.

The identification of clean and polluted scenarios during GoAmazon2014/5 was based on a visual analysis of daily means of βsct., Org., CCN, and AOD together. Among these quantities, βsct. and AOD are directly proportional to aerosol loading and result from the interaction between aerosols and incident electromagnetic radiation, particularly at wavelengths between approximately 0.3 and 4 µm – the solar spectrum range. This interaction is described by Mie scattering , which applies Maxwell's electromagnetic theory to describe radiation scattered by spherical particles with radius r comparable to or greater than the incident wavelength. Macroscopically, βsct. at position s′ along an optical path s for aerosols with refractive index n(λ) is given by Eq. (), where Np(r,s′) is the number of aerosol particles per unit air volume per size interval at position s′, and Qsct. is the scattering efficiency factor. Spectral AOD is related to the amount of optically active aerosols in the atmospheric column. To derive it, one must consider the solar zenith angle (θ0, formed between the vertical direction and the propagation path of the incident radiation beam) and the linear absorption coefficient βabs. (Eq. ), resulting in the formulation shown in Eq. (). 1βsct.(λ,s′)=πr2Qsct.2πrλ,n(λ)∫0∞Np(r,s′)dr2βabs.(λ,s′)=πr2Qabs.2πrλ,n(λ)∫0∞Np(r,s′)dr3AOD(λ)=∫0sβsct.(λ,s)+βabs.(λ,s)cos⁡(θ0)ds

Daily means of βsct., Org., and CCN for 2014 are displayed in Fig. . The period between days 10 and 90 of 2014 was selected as representative of the clean scenario, whereas the intervals between days 210–277 and 300–345 were chosen to represent polluted periods. For 2015, the same procedure was applied to the daily time series of βsct., Org., and AOD. Figure , which presents these series, shows that aerosol influence peaked during the second half of the year. During the polluted period of 2015, the βsct. and Org. peaks were greater than those observed in 2014, which exhibited a shorter clean period compared to 2015. From the time series shown in Figs.  and , the start and end days of the clean and polluted scenarios for 2014 and 2015 were determined. Table  summarizes these intervals and the weighted means of βsct., Org., CCN, and AOD calculated for them. This reference will be extensively used in the calculation and analysis of IRFaci.

The clean scenarios of 2014 and 2015 define the periods within which the cleanest days were used as the basis for the determination of the first atmospheric reference state. The selection of these cleanest days proceeded as follows: first, all days sharing common data for the variables βsct., Org., CCN, and AOD (for AOD, since the AERONET dataset had many empty data points, only data derived from the MFRSR were considered) were identified. For these days, daytime medians (06:00–18:00 LT) were calculated for each of the four variables. After normalizing these medians, the K-Means clustering algorithm was applied using 2, 3, and 4 clusters. For each cluster and each variable, a characteristic median was assigned. Comparing the medians across different cluster counts helped determine the optimal number of clusters, corresponding to cases in which no overlap occurred between the characteristic medians of distinct groups.

From the identification of optimal cluster counts for 2014 and 2015, the minimum characteristic median values were obtained, allowing the identification of the cleanest days within each clean scenario. For 2014, six days in February (11, 17, 23, 24, 26, and 28) and ten in March (2, 6, 7, 8, 12, 20, 21, 22, 25, and 28) were selected. For 2015, the cleanest days were 25 February and 3–4 May. The mean upward irradiance values at the top of the atmosphere (TOA) simulated for these days were later used as a fixed reference for the IRFaci calculations.

Upward irradiance values at the TOA were calculated by the libRadtran radiative transfer code , which uses only LWC and reff. values of modeled clouds as input. Although shown here, the theoretical formulation of LWC (Eq. , , with the density of water ρ, the cloud droplet radius r, and N(D) given by Eq. ) and of reff. (Eq. , ) were not used to calculate the LWC and reff.. Instead of that, the measured LWC values were used, and the reff. was calculated as will be explained ahead in this section. Given that in situ values of LWC, TWC, N(D), Nd, and Deff.=2reff. were obtained only during G1 flights, the availability of these measurements was limited. Therefore, a procedure was established to increase this availability for the entire GoAmazon2014/5 period. This procedure consisted of the following:

Deriving empirical relationships between measured LWC and the values of reff., which were calculated from Eq. ();

The first step to derive empirical relationships between reff. and in situ LWC was to consider only positive simultaneous measurements of Nd and LWC, ensuring that the aircraft was within a cloud. Subsequently, only cases with zero ice water content (IWC = TWC - LWC) were retained, thereby filtering liquid clouds. During data screening, cases where Nd<0.3 particles cm⁻³ and LWC < 0.02 g m⁻³ were excluded, removing experimental points associated with fog or extremely tenuous clouds. These filters were applied for both IOP's, with the aim of ensuring consistency of data selection for two intensive periods. Finally, reff. was computed according to Eq. (), where <rj> represents the jth mean of one of the 20 size intervals (bins) in which N(D) values were classified. 4LWC=4π3ρ∫0∞r3N(D)dr5N(D)=N0rme-Λr 6areff.=∫0∞r3N(D)dr∫0∞r2N(D)dr6breff.=∑j=120<rj>3N(D)jdr∑j=120<rj>2N(D)jdr

The scatterplot of calculated reff. versus measured LWC for IOP 1 did not show patterns that could be easily fitted by simple functions (e.g., linear or quadratic). To address this, the data were divided into 20 equally spaced LWC bins (with a width of 0.05 g m⁻³, between 0.02 and 1.02 g m⁻³), within which the LWC and reff. medians were calculated. The pairs of these medians were plotted and showed a particular trend, similar to that obtained by . Like this study, those authors explored the relationship between LWC and reff. of liquid clouds in the Brazilian Amazon. Using in situ aircraft measurements of liquid stratiform and cumuliform clouds with bases located within the planetary boundary layer, concluded that after testing several fitting functions, the hyperbolic arc cosine function provided the best fit. This motivated its adoption to adjust the median pairs for IOP 1 here (Fig. ).

For IOP 2, the scatterplot of the calculated reff. versus the measured LWC not showed any easily identifiable pattern also. Given that, other approach was consider LWC / Nd ratios instead of N(D). In addition to this, rather than using Eq. (), these ratios were applied to Eqs. () and (), relative to the cumulus and stratocumulus clouds, respectively . All the resulting values of reff. were considered together, without distinguishing the two types of clouds. Like in the IOP 1, the resulting data set were divided into 20 equally spaced LWC bins, and the corresponding medians were calculated. The final scatter plots for IOP 2 presented the same pattern as medians relative to IOP 1, and the hyperbolic arc cosine function provided the best fit again (Fig. ). 7reff.=6.67LWCNd0.318reff.=7.50LWCNd0.33

Following the procedure to derive new reff. and LWC values, the second step was to use surface-derived values of CBH, CTH, and LWP to compute LWCground. These LWCground values were then inserted into the empirical relationships shown in Fig. , generating new reff. estimates for liquid clouds during IOPs 1 and 2. This procedure enabled the construction of an expanded database, covering all days within the clean and polluted periods defined by the intervals listed in Table , thus increasing data availability across 2014 and 2015.

For transition periods, hybrid adjustments were made using weighted averages that combined both empirical functions. For instance, during the first transition days of 2014, the calculated reff. values had a greater weight from the clean-period equation, while the last days were progressively influenced by the polluted-period function. This approach enabled the generation of reff. values as a function of LWCground for nearly every day of the GoAmazon2014/5 campaign, consequently allowing the modeling of liquid clouds for almost the entire observation period.

The selection of low-level liquid clouds was also performed by filtering the LWCground and CTH datasets. The interval [0.2–0.4] g m⁻³ for LWCground encompasses typical values of cumulus and stratiform clouds in clean and polluted continental environments , and was therefore applied as a filter to the LWCground data. Additionally, only clouds with CTH less than or equal to 3 km were considered to ensure that the final results represented low-level clouds exclusively. Added to the filters previously applied to the reff. and LWC values, the filters applied to the LWCground and the corresponding calculated reff. data justify the term “low-level liquid”, which includes both shallow cumulus and low stratiform cloud types in this work.

The effective radius of liquid clouds increases with altitude in the atmosphere , justifying the selection of this as a conceptual model to simulate characteristic low-level liquid clouds for each day of GoAmazon2014/5. To represent the vertical increase of reff. with altitude, the clouds were configured with two horizontal layers, ensuring that the reff. and LWC values in the models were higher in the upper layer. The base height of the modeled clouds was set according to the 12.5th percentile of CBH values, while the top height corresponded to the 87.5th percentile of the CTH data distribution. The central height was defined as the arithmetic mean between the base and top heights. The 12.5th and 87.5th percentiles of the daily reff. and LWCground distributions were similarly selected to describe the reff. and LWC values at the base and top, respectively, while the middle layer was represented by the median of the same distributions. Although these statistics are insufficient to explicitly capture intraday variability or transient processes, constituting a low-dimensional description, they are adequate to characterize the central tendency and dispersion of the variables mentioned. Table  summarizes the statistical parameters used to simulate representative low-level liquid clouds for most days of the GoAmazon2014/5 campaign.

The integrated upward irradiance values (hereafter referred to as F) at the TOA were obtained using the libRadtran radiative transfer model, which applies the DISORT method (DIScrete Ordinate Radiative Transfer solver; ) to solve the radiative transfer equation after accounting for adjustments to atmospheric boundary conditions. In addition, libRadtran uses the “medium” spectral resolution mode (bandwidth = 5 cm⁻¹) of the REPTRAN parameterization as the standard spectral configuration. The wavelength interval selected for the simulations ranged from 300 to 1000 nm, encompassing the entire visible spectrum and a small portion of the near-infrared region. The solar spectrum used extended from 250 to 10 000 nm, with a resolution of 0.1 nm.

REPTRAN is also the default method employed by libRadtran to represent atmospheric molecular scattering, applicable to both the solar and terrestrial spectra. For this, vertical profiles of the main atmospheric gases (O₂, O₃, NO₂, CO₂, and water vapor) must be provided. The “standard tropical atmosphere” file available in libRadtran already includes vertical profiles for these gases, along with profiles of air density, temperature, and pressure. The profiles of less abundant trace gases such as N₂O, CO, and CH₄ were taken from the “standard U.S. atmosphere” dataset. Considering this, the tropical atmosphere data provided by the Earth Observation Data Group (EODG) of the University of Oxford (http://eodg.atm.ox.ac.uk/RFM/atm/minor.atm, last access: 21 August 2026) were used here to generate new vertical profiles for these gases. All the profiles mentioned were used equally in all simulations, seeking to follow the definition of “instantaneous” forcing, namely, forcings obtained with the tropospheric and stratospheric profiles of constant T.

The files used to simulate representative daily low-level liquid clouds considered the exact geographic location and elevation of the T3 site. Since T3 was situated in a forested region, a surface albedo of 14 % was adopted. The mean CO₂ mixing ratios estimated for 2014 and 2015 according to the Keeling curve were also taken into account. All simulations were configured to represent upward irradiance at TOA for 16:00 UTC (12:00 LT), ensuring that the Sun was near zenith at the simulation time. Moreover, the fc was set to 100 % for all simulations, assuming that the simulated clouds completely covered the sky at 12:00 LT. Typical examples of input files (extension .inp) used in libRadtran can be found at the link 10.5281/zenodo.20610494 .

The upward integrated irradiance values at the TOA obtained from libRadtran (hereafter FlibRadtran) do not account for variations in the Earth–Sun distance (d). The necessary correction was made using Eq. (), which assumes a plane-parallel atmosphere. The values of d and the solar zenith angle (θ0) used in Eq. () were calculated using spreadsheets provided by NOAA's Earth System Research Laboratories (https://gml.noaa.gov/grad/solcalc/calcdetails.html, last access: 21 August 2026). These spreadsheets compute various astronomical parameters for any location on Earth; therefore, the d and θ0 data were obtained specifically for the T3 site. With these parameters and the FlibRadtran outputs, the corrected irradiance values (Fcorr.) were computed, accounting for temporal variations in d throughout 2014 and 2015 at T3. 9Fcorr.=d2FlibRadtrancos⁡(θ0)

Instantaneous radiative forcings (IRF) were then calculated as the difference between Fcorr. in the reference state and Fcorr. in the anthropogenically perturbed state (Eq. ()). Moreover, since the IRF calculations were based on integrated irradiances simulated for 12:00 LT at T3, the estimation of daily radiative forcing (IRFdaily, corresponding to 00:00 to 23:59 LT) required consideration of the variation of the θ0 throughout the day. This correction was implemented using Eq. (), which incorporated 120 values of θ0 sampled every 6 min during daylight hours. Because T3 is located near the Equator, the durations of daytime and nighttime were considered nearly identical, and the morning and afternoon periods were approximately equal in length. For this reason, IRFdaily corresponds to either the morning or afternoon interval, justifying the division by 2 in Eq. (). 10IRF=Fcorrreference-Fcorrperturbed11IRFdaily=12IRF∑n=06:0018:00cos⁡(θ0)n120

As previously discussed, two clean atmospheric reference values were used in Eq. (). The first, a fixed value of 689.9 Wm-2, corresponds to the mean of the corrected irradiances obtained from the cleanest days of the GoAmazon2014/5 campaign. This reference represents natural background atmospheric conditions during the 19 cleanest days of 2014 and 2015, which may differ from those characterizing the polluted periods of the same years. To account for seasonal variability in cloud microphysical properties, a second reference with variable irradiance was implemented. This approach, which consists of a first approximation to account for the natural variation in the microphysical characteristics of clouds, involved generating low-level liquid cloud models (example shown in Table ) based on LWC data (within the [0.2–0.4] g m⁻³ interval) and reff. values corresponding to the cleanest conditions identified during IOP 2. The measurements used came from HALO aircraft flights AC09 and AC18, which represents the cleanest cases available among HALO flights made during the polluted period of 2014.

For these models, libRadtran simulated upward integrated irradiances at TOA for θ0=0 and an Earth–Sun distance of 1 AU. The resulting irradiances, 766.7 Wm-2 and 769.1 Wm-2, yielded a mean value of 767.9 Wm-2, which was considered representative of the cleanest possible atmospheric conditions for September 2014. This mean was used as the reference for IRF calculations only during the polluted periods of 2014 and 2015. For the transitional days, reference irradiances were calculated to vary linearly (Fig. ) between the clean and polluted reference values (689.9 Wm-2 and 767.9 Wm-2, respectively). The assumption of this linear variation between the cleanest days of the clean period and the cleanest days within the polluted period of 2014 came after an analysis of the evolution of reff. between these two scenarios, which occurs in an approximately linear manner throughout 2014, justifying the approximation used.

Using the seasonal reference based on aerosol availability aimed to reduce the seasonal contamination of thermodynamic variables (temperature, pressure, and water vapor profiles were the same for all simulations) and to isolate the effect of aerosols on forcings. Given that the seasonality of atmospheric dynamics affecting LWP, CBH and CTH was already embedded in the statistics of these variables, the second approach allowed the calculation of new daily forcing values less affected by the seasonal variability of natural atmospheric conditions in the T3 region.

The IRFdaily values were obtained assuming a cloud fraction of 100 %. However, to regionalize the results according to the actual cloudiness observed at T3, each daily value was also multiplied by the corresponding daytime mean fc for that specific day. Figure , which presents the IRFdaily values for the first clean-atmosphere reference, shows that the results incorporating the fc measured at T3 generally display smaller absolute magnitudes compared to those associated with fc=100 %. The observed daily oscillation arises from the way the low-level liquid-cloud models were configured – that is, based on the percentiles and medians of reff. and LWC. Figure  also clearly reveals the mean reduction in IRFdaily magnitude as the more polluted periods approach, with values becoming increasingly negative during those episodes.

To evaluate the relative behavior of IRFdaily values across different aerosol-loading scenarios, boxplots were generated for each case. Figure  displays the results for 2014, along with the means and medians for each scenario. Overall, IRFdaily values that do not account for the measured fc at T3 exhibit distributions shifted toward more negative values compared to those incorporating fc variability, indicating that a constant fc=100 % produces markedly stronger negative instantaneous radiative forcings. The statistics show progressively more negative values as the clean days give way to polluted ones, with results for the second 2014 transition period showing an increasing trend consistent with the decreasing aerosol parameters displayed in Fig. . It is also noteworthy that, although positive values occur only under the clean scenario (at the upper limit of the seventy-fifth percentile), both the means and medians for all scenarios remain negative.

The IRFdaily values computed for the polluted period of 2015 (Fig. ) exhibit means, medians, and percentiles that are more negative than those of the clean and transitional periods of the same year. While mean and median values range from 0 to −8 Wm-2 during the clean period, the values associated with the polluted scenario lie between approximately −15 and −30 Wm-2. An important observation is that the mean IRFdaily values for fc=100 % and for the measured cloud fraction at T3 are nearly identical under cleaner atmospheric conditions, which is not the case for the polluted scenario. This is noteworthy because – even with elevated aerosol concentrations and reduced cloud cover during polluted periods – the instantaneous radiative forcing associated with the few existing clouds is more negative than that produced by the more numerous clouds in the clean season.

The boxplots discussed above were complemented by histograms of the annual IRFdaily distributions for 2014 and 2015, shown in Figs.  and . The results in Fig.  indicate that the overall statistics for 2014 are more negative than those for 2015: the 2015 median corresponds to about 47 % of that for 2014, whereas the mean represents 66% of the 2014 mean. The results scaled by the daytime mean fc (Fig. ) display more homogeneous distributions approaching normality, with the lower and upper quartiles of the corresponding boxplots confined to narrower intervals than those for the distributions that ignore fc variability at T3. This outcome suggests that multiplying by the daytime mean fc effectively selects and constrains the final dataset, removing extreme values and producing probability density functions with reduced kurtosis magnitude.

The IRFdaily values obtained using a variable irradiance value for a clean-atmosphere reference are presented here. It is important to recall that this seasonal irradiance reference approach aimed to reduce the likelihood that the results would be influenced by the natural atmospheric variability over T3, thus better isolating the aerosol effect on low-level liquid clouds. As shown in Fig. , the IRFdaily values in this case fluctuate around zero, unlike the forcings computed using the fixed irradiance reference value (Fig. ). Nevertheless, the results are, on average, nearly constant throughout 2014 and 2015, with most data points exhibiting negative values. Subtle variations can also be observed that may or may not be associated, on average, with aerosol properties.

The IRFdaily boxplots for the different aerosol-loading scenarios in 2014 and 2015 (Figs.  and , respectively) indicate that the distributions multiplied by the measured fc at T3 are more homogeneous and less skewed than those that do not account for this parameter. The distributions for all scenarios in both years show central values (between the twenty-fifth and seventy-fifth percentiles) between −10 Wm-2 and approximately +8.0 Wm-2. The means and medians for the clean and polluted scenarios of the two years are negative, with greater magnitudes for the clean periods. This behavior, associated with a larger dispersion of IRFdaily values during cleaner conditions, can be explained – at least for the distributions that do not include the T3's cloud fraction – by greater variability in the reff. values of the modeled clouds in clean periods. For the results multiplied by fc, this effect may also occur, as higher fc values during clean conditions make the means and medians even more negative than those observed during polluted periods.

The results derived from the variable irradiance reference allow the derivation of annual statistics in which the first indirect aerosol effect is more clearly isolated. The resulting statistics for 2014 and 2015 (Figs.  and ) show that, compared to the values obtained using the fixed irradiance reference, the IRFdaily magnitudes are smaller. The effect of seasonal variations in atmospheric conditions on the low-level liquid cloud droplet size is illustrated by the percentage variations in the mean reff. during the clean periods of 2014 and 2015 relative to the mean reff. of the clean reference state. These differences were 21.6 % and 20.7 %, respectively, while the polluted periods exhibited reductions of 18.7 % for both years. The percentage variations in TOA flux were 1.62 % and 0.50 % for the clean intervals, while for the polluted intervals, there were increases of 0.82 % and 0.34 %, even though LWC was assumed to be the same for both clean and polluted periods.

According to , aerosol optical depth (AOD) is widely recognized as a critical indicator to understand atmospheric physics and regional air quality due to its ability to quantify aerosol loading in the atmosphere. Considering this, one way to assess the sensitivity of daily instantaneous forcings to aerosol availability is via AOD.

In this study, the sensitivity of IRFdaily to AOD was assessed as follows: first, we calculated the daily medians of AOD for the clean and polluted scenarios of each year, and for each of these scenarios, we selected the 10 d with the lowest medians. Then, all days of a given scenario were used to calculate the average AOD (for the clean scenario of 2014, for example, we called this average “Tclean14”), while another average was calculated only for the 10 cleanest days selected previously (“tclean14” for the clean scenario of 2014, for example). Finally, we used Eq. () to obtain the percentage variation of AOD within each scenario, taking “t” as the clean reference and seeking to determine by what percentage the average “T” is greater than “t”. To test the hypothesis that ΔAOD%clean<ΔAOD%polluted for a given year, we applied a bootstrap test and obtained the statistical significance (5 % level) of the percentage variations for each year. The results (IC = [-67.8, -23.4], p-value = 0.00 and [-16.1, 21.9], p-value = 0.92 for 2014 and 2015, respectively) show that the hypothesis was confirmed only for 2014. As with AOD, the average IRFdaily values for each scenario and for the 10 cleanest days within each scenario were calculated (TIRFpolluted14 and tIRFpolluted14, for example). The difference between these averages (ΔIRFdaily=TIRF-tIRF) was used to calculate sensitivity S (Eq. , with units of Wm-2%-1), for each scenario of each year. The final step consisted of performing a new statistical significance test, considering the hypothesis that S in the clean scenario is greater than in the polluted scenario. The results (p-value = 0.00 and 0.39 for 2014 and 2015, respectively) for the confidence level of 5 % showed that this occurred only in 2014.

Table  presents the calculated sensitivities for the clean and polluted periods of 2014 and 2015, derived from the results based on the seasonal irradiance reference while assuming fc=100 %. The 2014 results indicate that the sensitivity of low-level liquid clouds to variations in aerosol load may be greater under cleaner atmospheric conditions than in already highly polluted environments. 12ΔAOD%=100⋅T-tt13S=ΔIRFdailyΔAOD%