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OPEN

Long‑term relationships
between summer clouds
and aerosols over mid‑highlatitudes of the Northern
Hemisphere
Akihisa Watari 1,2,6*, Yoshinori Iizuka 2*, Koji Fujita 3, Hirohiko Masunaga 4 &Kazuaki Kawamoto 5
While the short-term relationship between clouds and aerosols is well known, no adequate data isavailable to verify the longer-term, annual to decadal, relationship. It is important to quantify theaerosol–cloud interaction (ACI) for mitigating uncertainty in climate prediction. Here the long-term
ACI over the mid-to-high latitudes of the Northern Hemisphere was analyzed by using seasonallyresolved ion fluxes reconstructed from a southeastern Greenland ice core (SE-Dome ice core) as
aerosol proxies, and satellite-based summer cloud amount between 1982 and 2014. As a result, ­SO42−
flux in the ice core shows significant positive correlation with total cloud amounts (CC T ) and cloud
droplet concentration (Nd ) in the summer over the southeastern Greenland Sea, implying that thesulfate aerosols may contribute to the variability of CC T via microphysical cloud processes. Significant
positive correlations are persistent even under the constrained conditions when cloud formation
factors such as relative humidity, air temperature at cloud height, and summer North Atlantic
Oscillation are limited within ± 1σ variability. Hence sulfate aerosols should control the interannual
variability of summer CC T In terms of decadal changes, CC T was approximately 3–5% higher in the
1960s–1970s than in the 1990s–2000s, which can be explained by changes in the, SO4 2− flux preservedin the SE-Dome ice core.
Aerosol cloud-mediated radiative effects are thought to exert a significant cooling effect on the Earth’s climate.
However, quantifying the aerosol–cloud interaction (ACI) has been a major challenge despite scientific efforts
over the past few ­decades1,2. Estimation of aerosol-induced cloud amounts, called the “Albrecht effect”, is important in climate ­prediction3. In the past, ACI has been determined based on hourly to daily field measurements.
For example, a study showed that the arctic environment had a high sensitivity to light-absorbing aerosols, suchas black carbon, by heating the surrounding atmosphere and leading to the evaporation of low-level clouds, called
the semi-direct e­ ffect4. It was also reported that lightning density was enhanced by up to a factor of two overshipping lanes compared to adjacent areas due to the additional aerosols from s­ hips5. However, the annual todecadal ACI is poorly understood despite its crucial role in the climate system. Bellouin et al.6, reviewed aerosols
interact with radiation and clouds that substantial progress made over the past 40 years in observing, understanding, and modeling these processes helped quantify the imbalance in the Earth’s radiation budget caused byanthropogenic aerosols, called aerosol radiative forcing, but uncertainties remain large. Also, they pointed out
a necessary of local process studies that the lack of resolution of small scales by large-scale models means that
their integration of local processes into a globally averaged number is imperfect. Only model studies are used
for historical experiments from industrial revolution to present, primarily because of the lack of aerosol and1
Graduate School of Environmental Science, Hokkaido University, Sapporo 060‑0810, Japan. 2Institute of Low
Temperature Science, Hokkaido University, Sapporo 060‑0819, Japan. 3Graduate School of Environmental
Studies, Nagoya University, Nagoya 464‑8601, Japan. 4Institute for Space-Earth Environmental Research, Nagoya
University, Nagoya 464‑8601, Japan. 5Graduate School of Fisheries and Environmental Sciences, Nagasaki
University, Nagasaki 852‑8521, Japan. 6Present address: Nippon Koei Energy Solutions Co., Ltd, Tokyo 102‑8539,
Japan. *email: akiwatari1205@gmail.com; iizuka@lowtem.hokudai.co.jp

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cloud observations. Satellites are the best source of historical cloud observations since 1980s, and past aerosols
are preserved in polar ice cores. The direct comparison with satellite-based relationships of clouds and aerosols
has been difficult due to the lack of reliable long-term datasets, especially focused on aerosol species likely to
be cloud nuclei. In reanalysis of cloud data used in previous studies, it has been reported that there are large
uncertainties compared to satellite and field ­data7,8, thus the use of reanalysis data is not optimal for a detailed
comparison between clouds and aerosols.
The Arctic near-surface temperature continues to rise at double the rate of global average values, which havebeen reported by field observation and ­models9,10; a phenomenon called Arctic amplification. Ice cores drilledfrom the Greenland ice sheet can provide fluctuation records of past aerosols in the A­ rctic11,12. In particular,
an ice core from the southeastern dome of Greenland has well-preserved aerosols on a seasonal-scale with lesspost-depositional loss under high accumulation rates (~ 1.0 m w.e. a­ −1), and can track the variability of seasonal
aerosol fluxes for the long-term (1960–2014) atmospheric e­ nvironment13,14.
Here, long-term ACI was investigated using the new satellite-based cloud datasets (1982–2016), called Cloud_cci (CCI) data, and the SE-Dome ice core data over the mid-to-high latitudes of the Northern Hemisphere. The
historical variability of aerosol-driven cloud amounts in summer (Jun, July, and August; JJA) are evaluated overthe 33 year spanning 1982–2014. This period includes a time of high-pollution including significant emissionsof anthropogenic aerosols after the 1980s, some aerosol proxies decreased by the regulation of anthropogenic­activity15. The CCI is based on advanced very high-resolution radiometer (AVHRR) post meridiem version­316,17, which contained various cloud properties for the period from 1982 to 2016. The datasets are consistently
retrieved from AVHRR, which is one of the oldest cloud s­ atellites18, combined with some passive cloud datasets
to achieve increased temporal resolution with high spatial resolution covering the whole globe.

SO42− flux and cloud properties

First, the geographical distribution of correlation coefficients between the aerosol proxies ­(SO42−, ­NO3−, ­Cl−,­ a+, ­NH4+, ­Mg2+, ­Ca2+, and dust) and cloud properties (total cloud amounts (CC T ), low level (CC L ), middle
Nlevel (CC M ), and high level (CC H ), cloud optical depth (COD ), liquid water path ( LWP ), and cloud droplet
concentration ( Nd ) ) are analyzed for all seasons (spring (March, April, and May; MAM), summer (JJA), autumn(September, October, and November; SON), and winter (December, January, and February; DJF)) from 1982 to2014 (Figs. S1–S25). Among them, we focused on SO4 2− flux in the summer because (1) it has the most relevantcorrelations to cloud properties, (2) summer should be the season with the most solar radiation and also clouds,
and should influence the polar climate, and (3) sulfate aerosols are reported to be the highest cloud albedo effects
among the a­ erosols19. Figure 1a shows that the summer SO4 2− flux at the SE-Dome site significantly correlatedwith CC T over the southeast Greenland ocean where the probability of air mass to the SE-Dome site were morethan 50% (area surrounded by black line in Fig. S26 based on 14 days ­backtrajectory14, also see “Methods”),
implying that summer SO4 2− flux could be a proxy of CC T over the ocean.
In order to make clear the marine cloud over a target domain (blacklines in Fig. 1a, 25º–45ºW and 60º–68ºN,
modified from Fig. S26), the averaged correlation coefficients of the aerosol proxies and cloud properties over thetarget domain in all seasons from 1982 to 2014 (Fig. S27) are investigated to use ­SO42− flux as a proxy for the past

Figure 1.  Relationships of aerosol proxies in the SE-Dome ice core and cloud properties. (a) Geographicaldistribution of correlation coefficients between ­SO42− flux and CC T in summer with a resolution of 0.5º from1982 to 2014. The black line shows the target domain for the correlation analysis. An asterisk denotes the
SE-Dome site where the ice core was ­drilled13. (b) The area-averaged correlation coefficients between aerosol
proxies preserved in the SE-Dome ice core and cloud and atmospheric properties in the target domain.
The vertical axis shows the cloud properties (red text); total cloud amounts (CC T ), low level (CC L), middle
level (CC M ), and high level (CC H ), cloud optical depth (COD), liquid water path (LWP ), and cloud droplet
concentration (Nd ), and the atmospheric properties (black text); wind components at 10 m height (U10m andV10m), 2 m height air temperature (T2m), sea ice concentration (Csi), sea surface temperature (Tss), downward
solar radiation at the surface (Rsd ), total precipitation (Pt ), and relative humidity (Hr ), respectively. The
horizontal axis shows the aerosol proxies reconstructed in the SE-Dome ice core. White asterisks in panel b
denote p < 0.05.
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cloud amounts in summer. Although most aerosols proxies have no significant correlation with cloud properties,some significant correlations are found (asterisks in Fig. S27). For instance, a negative correlation between dust
flux and CC L due to the suppression of dust nucleation when a certain amount of dust aerosol is present in theatmosphere is found. These correlations were reported in previous ­studies20. Among aerosols, summer SO4 2−flux is the most relevant to CC T in the target domain (Fig. 1b). The SO4 2− flux also significantly correlates withthe downward solar radiation at the surface (Rsd , r = –0.49, p < 0.01), cloud optical depth (COD, r = 0.42, p < 0.05),
and liquid water path ( LWP , r = 0.34, p < 0.05) (Fig. 1b). A previous study suggested that polluted marine clouds
could increase in LWP due to growth in optically thick clouds by analyzing stratocumulus along shipping l­ anes21.
Other studies have shown that sulfate aerosol particles could act as cloud condensation nuclei (CCN) in the cloudformation ­processes22,23. SO4 2− flux in the SE-Dome ice core is highly correlated with cloud amounts which varies with the COD, suggesting that summer S­ O42− flux contributes to marine cloud formation over the domain.
The correlation plots among the aerosol proxies show that SO4 2− and NO3 − fluxes highly correlate in summer(Fig. S28b, r = 0.76, p < 0.001), which is roughly consistent with emission sources and deposition processes, while
the correlation coefficient between the N­ O3− flux but CC T in the target domain was not significant (r = 0.22,
p = 0.37)24. These results and discussion suggest that SO4 2− flux is cloud-related more than the ­NO3− flux by
efficiently serving as CCN 22.
For reference, SO4 2− flux also shows significant correlation with the cloud amounts in the ERA5 reanalysis
data for the same domain (r = 0.36, p < 0.05 for CC L and r = 0.38, p < 0.05 for CC T , Fig. S29) and their distributions
are qualitatively similar to the satellite-based results (Fig. 1a).

SO4 2− flux and cloud droplet concentration

The satellite-based Nd (also see “Methods”)25 is calculated to investigate the cloud formation influenced bysulfate aerosols. Figure 2a shows the spatial distribution of correlation coefficients between SO4 2− flux and Nd
for low-level warm clouds. Positive correlations were observed in a portion of the target domain, even though
the area-averaged correlation coefficients were not significant. This positive correlation is consistent with thatbetween the SO4 2− flux and CC T (Fig. 1a). The variability of sulfate aerosol leads to changing Nd loads in thetarget domain. Nd has been used as a proxy for CCN concentrations and has a remarkable power-law relation to
the corresponding aerosol optical depth ( AOD)25,26. For instance, cloud amounts over the ocean increase withboth LWP and Nd until reaching nearly total cloud amounts for a given cloud geometrical ­thickness27. The clouds
precipitate substantially, whereas precipitation in clouds is mostly suppressed as a result of the smaller cloud
droplet size when Nd increases. Figure 2b shows the dependence of CC T on Nd in the target domain. Therefore,
significantly positive correlations between SO4 2− flux and Nd suggest a physically persistent process of ACI,
which is clarified through a series of SO4 2− aerosol, Nd , and CC T in the target domain.

SO42− flux and cloud amount under the constrained condition

Primary cloud formation depends on a variety of atmospheric variables such as temperature (Tcloud_height ) andrelative humidity ( Hr)28,29. Atmospheric circulation represented by climate indices (e.g., North Atlantic Oscillation (NAO), Arctic Oscillation (AO), Atlantic Multidecadal Oscillation (AMO)) is also important for cloudformation and distribution in mid-high latitudes of the Northern ­Hemisphere30. To avoid these effects from
implicitly overriding the correlation between SO4 2− flux and CC T , the meteorological conditions which could
affect atmospheric circulation ( Hr , Tcloud_height , and NAO index in summer; sNAO, Fig. S30 and see “Methods”) are constrained by limiting all variables within ± 1 standard deviation (14 of 33 years remained). Figure 3
shows the geographical distribution of the significant correlation between the SO4 2− flux and CC T (r > 0.49,
p < 0.05) under the constrained conditions. Similar distributions of correlations with CCI and ERA5 data, andFigure 2.  Nd have positive correlation with ­SO42− flux and CC T in the target domain. (a) Geographicaldistribution of correlation coefficients between ­SO42− flux and Nd for low-level warm clouds with a resolutionof 0.5º from 1982 to 2014. (b) Dependence of CC T on Nd in the target domain (black polygon in panel a). Error
bars represent 1 standard deviation of the monthly CC T .
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Figure 3.  Relationships between CC T and ­SO42− flux under the constrained atmospheric conditions for cloudformation. Geographical distributions of the correlation coefficients between S­ O42− flux and CC T of (a) CCI and(b) ERA5 datasets under the constrained atmospheric conditions (Tcloud_height , Hr , and sNAO within <  ± 1σ) inthe target domain.
the persistent positive correlations in the target domains (Figs. 1a, 2a and 3). These results suggest cloud amountin the target domain varied positively with the sulfate aerosol flux to the SE-Dome site regardless of atmosphericconditions for main cloud formation ( Hr , Tcloud_height , and sNAO).

Past cloud amounts reconstruction

In this research, SO4 2− flux showed a positive correlation with satellite-based Nd in the target domain, which also
supports a physically persistent process of ACI (Fig. 2). The sulfate aerosol preserved in the SE-Dome ice core in
1984 (17.32 mgm−2 season−1) and 1987 (10.82 mgm−2 season−1) was more than two standard deviations higher
between 1982 and 2014 (Fig. S31, 3.74 ± 3.23 mg ­m−2 ­season–1). Figure S32 shows the distributions of CC T and
Nd anomalies in 1984 and 1987 against the means (1982–2014). The mean CC T and Nd in the target domain from1982 to 2014 were 82.7 ± 7.8% and 94.0 ± 14.7 ­cm−3, respectively, while the CC T and Nd anomalies were observed
to be up to 8.9% and 59.1 ­cm−3. The observed changes in CC T and Nd can be attributed to the increased SO4 2−flux at the SE-Dome site. The atmospheric transport processes from the emission sources to the SE-Dome siteshould have accounted for the higher SO4 2− fluxes. During the air mass transportation, the higher SO4 2− could
have increased the cloud amount.
The relationship between 11 year-averaged SO4 2− flux ( FSO4 ) and satellite-based CC T (%) are obtained forthe 33 year period from 1982 to 2014 (Fig. 4a) to reconstruct past cloud amounts:2
CCT = −0.025FSO+ 1.272FSO4 + 71.100 FSO4 < 25.44(1)
4

Figure 4.  Reconstruction of CCT from the ­SO42− flux in ice-core. (a) The scatter plot of the CC T and ­SO42−
flux from 1982 to 2014 with a quadratic approximation (black line). The dashed red line indicates the value of
15.28 mg ­m−2 ­season−1 in ­SO42− flux. (b) An 11 year running mean of reconstructed CC T from the SE-Dome icecore (blue line) and satellite-based CC T in the CCI dataset averaged for the target domain (red line).
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CCT = 87.280 FSO4 ≥ 25.44(2)

Figure 4b shows the trends of the satellite-based CC T reconstruction from 1960 to 2014. The anthropogenic
SO2 during the highly polluted period should have contributed to the increases of sulfate aerosol ­particles31.
The reconstructed CC T in the 1960s and 1970s was approximately 3–5% higher than after 1991, which issimilar to the CC T trends observed in Italy though the authors assumed that the trends should correlate with
the NAO driven atmospheric circulation p­ attern30. Decreasing trends during the 1990s and a rather stable
twenty-first century are consistent with those of satellite-based CC T 30,32. Thus, the relationship between averaged
SO4 2− flux and reconstructed CC T suggests that the cloud amount over the ocean may have increased during
1960–80 via the aerosol Albrecht e­ ffect3. Also, the absence of a clear correlation for small values of SO4 2− fluxin the relationship between averaged SO4 2− flux and satellite-based CC T for 55 years suggests a threshold of
15.28 mg ­m−2 ­season−1 due to the highest correlation to increases cloud amount effectively. This implies thatan increase in aerosols does not directly cause an increase in amount of cloud, but that a certain amount ofaerosols is required for a substantial increase in cloud amount. The concept of a threshold may be importantin reconstructing cloud amounts over a wide area, which is required for further comparison between ice coredata and satellite (or reanalysis) measurements, and would lead to improvement of physical mechanisms inaerosol-climate models.
The second ice core in the SE-Dome region is drilled in 2021, and the ice core cover pre-industrial revolution
to ­present33,34, so that the new ice core will extend the interpretation obtained in this study to pre-industrial times.
Bellouin et al.6, pointed out in the review that the degree to which human activities affect natural aerosol levels,and the response of clouds, and especially ice clouds, to aerosol perturbations remain particularly uncertain. The
present paper reconstructs CC T during 1960–70 in Greenland, when the SOx emission maximum from aroundcountries. The relationship between SO4 2−- aerosols and Nd (and CC T ) during the SOx emission maximum will
help to reduce the uncertainty in projections of future aerosols interacting with radiation and clouds throughan improvement of climate models.

Conclusions

The historical variability of aerosol-driven cloud amounts in summer were evaluated over a 33 year period from1982 to 2014. Although most aerosol proxies have no significant correlation with cloud properties, SO4 2− flux
has a highly positive correlation with cloud amount in the target domain. Positive correlations between ­SO42− flux
and Nd were observed in a part of the target domain. The analyses suggest a physically persistent process of ACI,
which is clarified through a series of SO4 2− aerosol, Nd and CC T in the target domain. Then, the meteorologicalconditions which could affect the atmospheric circulation (Hr, T_cloud_height, and sNAO) were constrained for
detailed analysis of the relationships between SO4 2− flux and CC T . Regardless of the atmospheric conditions forcloud formation, SO4 2− has significant correlation with both satellite-based and reanalysis CC T . Thus, SO4 2−flux preserved in the SE-Dome ice core cloud be a proxy of past cloud amounts. From significant correlations
between SO4 2− flux and the cloud amounts from 1960 to 2014, it is estimated that CC T in the 1960s and 1970s
was approximately 3–5% higher than that after 1991, which is similar to trends observed in I­ taly30. These results
supported the Twomey effects, which implied the aerosols have driven the cloud microphysics process, especiallyin cloud a­ mounts3.

Methods

Backward trajectory analysis

The transport pathways of air masses in the SE-Dome were analyzed according to Iizuka et al.14, who used
the hybrid single-particle Lagrangian integrated trajectory (HYSPLIT model), which is distributed by NOAA(National Oceanic and Atmospheric Administration)35. The probability was weighted by the daily precipitation
rate when the air mass arrived at the SE-Dome, because aerosols preserved in the ice core were wet ­deposited14.
Figure S26 shows the probability distribution of air mass arriving at the SE-Dome site over 14 days for 1500 m
above ground level in JJA from 1982 to 2014. The black line shows the area where the integrated probability of
air mass at the SE-Dome was more than 50%.

The main factors of cloud formation in the target domain

To exclude the influence of factors other than aerosols, the correlation coefficients between CC T and atmosphericenvironment (i.e. atmospheric pressure (Ps), Hr, Tcloud_height, Csi, Rsd, wind direction (DW), wind speed (SW), sNAO,
GBI, and AMO) are investigated. Due to the relative correlation among each variable, CC T in the target region
have a high correlation with all atmospheric environments. For further analysis, the atmospheric environmentsthat affect CCT from previous ­research28,29 are considered. As a result, Hr , Tcloud_height in the cloud height(300–900 hpa), and sNAO indices are most relevant to cloud amount (Fig. S30). Next, the standard deviation of
Hr , Tcloud_height and sNAO index are calculated over 33 years in the target domain where the relationship between
SO4 2− flux and CC T was significant. To exclude the influence of factors other than aerosols, the period during
which the all variables were within ± 1σ (dots in Fig. S30) are constrained. If the correlation coefficient between
SO4 2− flux and cloud amount is still significant even under the constrained conditions of cloud formation factors(14-period), the variability of cloud amounts can be explained by the variability of aerosol concentrations.

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SE‑Dome ice core data

The ice core used in this research was obtained at SE-Dome (67.18°N, 36.37°W, 3160 m a.s.l.) in southeast
Greenland in ­201514. Due to its high accumulation rate (1.01 m w.e. ­a−1), the time scale of the SE-Dome ice core
was determined to be from 1960 to 2014 with a measurement error of ± 2 months using the oxygen-isotope
matching ­method13,14. The high temporal resolution of the aerosol proxies was reconstructed with better quality
than any other ice cores drilled inside the ice ­sheets14. The high accumulation rate also allows aerosols to bepreserved without post-depositional ­alternation14. The fluxes of ­SO42−, ­NO3−, ­Cl−, ­Na+, ­NH4+, ­Mg2+, and ­Ca2+
as proxies for past aerosols were obtained with ion chromatography, and the dust was observed by a Beckman
Coulter Counter Multisizer ­313,14. The measurement errors were reported to be 10% for the ions, and 15% forthe ­dust36. In this research, aerosol fluxes are obtained using the accumulation rate of the SE-Dome ice coremultiplied by the ion concentration.

Cloud and meteorological data

Cloud datasets were obtained from the latest version of the advanced very high resolution radiometer post
meridiem (AVHRR-PM) cloud data record (CDR), generated within the cloud component of the European Space
Agency’s (ESA) climate change initiative programme (CCI) (i.e. Cloud_cci project). In the ESA Cloud_cci project,long-term and coherent cloud property datasets have been provided by exploiting the synergic capabilities of different earth passive satellites. Cloud detection and cloud property retrieval are done using the community cloud
retrieval for climate (CC4CL) ­algorithm17,18. The CCI datasets from 1982 to 2014 were used in this research, providing sufficient samples to obtain statistically significant results of long-term ACI. The advantage of the CC4CL
algorithm is that the visible infrared imager (AVHRR) has a proven track record of long-term observations andis useful for climate research. On the other hand, the disadvantage is that it is a passive sensor, so informationon the vertical structure of clouds is limited, and so estimation of overlapping clouds is subject to large errors.
The meteorological data were used from ERA5 provided by the European Centre for Medium-Range Weather
Forecasts (ECMWF). The ERA5 datasets are well-suited to understand the interactions of meteorological factors
over the target region, due to the long time period and high spatial resolution. Supplementary Table 1 summarizes
cloud properties in CCI and ERA5 used in this research.

Methodology for calculating cloud droplet concentration◦◦

For each 0.5 × 0.5 grid, the Nd over the ocean was calculated using cloudy pixels with COD greater than the90th percentile of cloud optical thickness (τ ) in 10 × 10 ­pixels25. Nd was used as a proxy of CCN concentrations
which depends on the aerosol loads and the updraft v­ elocity37.
1

1

Nd = C 2 τ 2 (

C=

re −5
2
)
k

5·A
Cw
A= 4
3 · π · Qext·
3 π · ρw

k is assumed to be 1.08, which relates r­ e to the mean volume r­ adius25. The extinction efficiency factor (Qext )is approximated to be ­225, and ρw is the density of water. Values for C are ­calculated35, and the condensation
rate (Cw ) is calculated using parcel model with ERA5 datasets as follows. The adiabatic liquid water content at
different cloud base temperatures for a given 900 hPa is calculated using ERA5 data. The altitude at 900 hPa is
defined as the cloud base pressure in this research. Then, the dependence of Cw on the cloud base temperature(Tc ) was obtained in order to perform a regression analysis between calculated water condensation and liquidwater content. The maximum and minimum temperatures in the target domain are 265.8 (K) and 298.7 (K), thus
the relationships within this temperature range are investigated. As a result,

CW = 1.01e−4 Tc + 5.90e−4
between 265.8 (K) and 298.7 (K) was calculated which gives Cw for each cloud base temperature. Daily data
were used to calculate Nd . Some thresholds are used to obtain the low-level warm cloud as follows. (1) cloudphase(θ) is water (2) Cloud top pressure is above 680 hPa (3) Pixels whose COD are the highest 90th p­ ercentiles21.
Figure S33a shows the geographical distribution of calculated Nd in summer over the 33 year period from 1982
to 2014. The Nd over the oceans close to North America and Europe are higher than that over any other regions
by emitting anthropogenic aerosols. The probability of Nd in the same region in summer over the 33 year period
from 1982 to 2014 is investigated for verification of the calculation method (Fig. S33b). As a result, the mode Ndvalue is 60 ­cm−3 and 70% of Nd is calculated within the 150 ­cm−3, consistent with previous field ­observations38,39.
We evaluated the quality of the satellite data, particularly regarding the calculation of droplet number
concentration ( Nd ) as bellow. Mcgarragh et al.18, shows the relative uncertainty associated with cloud optical
thickness and cloud particle size are both less than 20%. Nd is proportional to 1/2 power of cloud optical thickness
and − 5/2 power of cloud particle size (assuming that the uncertainties of these other variables are sufficiently
small), so the relative uncertainty of Nd is calculated as less than 60% (< 21 (20%) + 52 (20%)) ).

Data availability

The cloud data for this research is publicly available. CCI cloud data was obtained from the European Space
Agency https://​clima​te.​esa.​int/​en/​proje​cts/​cloud/​data/. ERA5 data is available from the European Centre for
Medium-Range Weather Forecasts at https://​cds.​clima​te.​coper​nicus.​eu/. The AOD provided by advanced very
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www.nature.com/scientificreports/high resolution radiometer (AVHRR) was collected from the National Centers for Environmental Information
https://​www.​ncei.​noaa.​gov/​produ​cts/​clima​te-​data-​recor​ds/​avhrr-​aeros​ol-​optic​al-​thick​ness. The ice core data isavailable at https://​eprin​ts.​lib.​hokud​ai.​ac.​jp/​dspace/​handle/​2115/​67127. Code for calculations and data processing are available from the corresponding author upon request.
Received: 27 November 2023; Accepted: 15 April 2024

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Acknowledgements

We are grateful to the drilling and initial analysis teams of the SE-Dome ice core project. This work was supported
by JSPS KAKENHI Grant Numbers 18H05292 and 23H00511, and the Joint Research Program and Readershipprogram of the Institute of Low Temperature Science, Hokkaido University. This study was a part of ArCS II(Arctic challenge for sustainability II, program Grant Number JPMXD1420318865).

Author contributions

Y. I. and K. F. designed the research. A. W. and K. F. analyzed the data with help of H. M. and K. K. A. W. wrote
the paper. All authors contributed to revising the paper.

Funding

This work was supported by Japan Society for the Promotion of Science, 18H05292, Arctic Challenge for Sustainability II Program, 1420318865.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary Information The online version contains supplementary material available at https://​doi.​org/​
10.​1038/​s41598-​024-​59817-7.
Correspondence and requests for materials should be addressed to A.W. or Y.I.
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