Arctic as the ‘radiator fins’ of Earth in a warming climate

Earth radiates thermal radiation to balance the solar radiation it receives. Central to understanding climate change is how the radiation energy budget adjusts both globally and locally to external and internal forcing. In the past 18 years, satellite observations reveal a distinct positive trend of the Earth thermal radiation in the Arctic, which acts to radiate excess heating accumulating in the climate system to the space during global warming, i.e. a radiator fin region in a warming climate. Compared with other regions such as the tropics, the prominent trend in the Arctic results from a stronger surface and atmospheric warming and a less offsetting greenhouse effect of water vapor. Spectral decompositions further show the increase of thermal emission in the Arctic mainly originates from the far-infrared and mid-infrared window region and affirms the unbalanced radiative responses to temperature and humidity changes in these two spectral regions account for the unique thermal radiation trend in the Arctic.


Introduction
The Earth climate can in many ways be considered a 'furnace-radiator-fin' system [1], with excessive heat being produced in the furnace regions and radiated away in the radiator-fin regions.In terms of the mean climate, the 'furnace' and 'radiator fin' have been used to describe the convective and subsidence regions, respectively, in the tropics, where the unstable atmospheric condition leading a runaway greenhouse in the 'furnace' region is stabilized by exporting heat to the 'radiator fin' region [1].In the context of global warming, it has been of central interest in climate research to identify radiator fin regions and mechanisms facilitating the cycling and loss of energy to cool down the warming climate.For example, an Iris effect was hypothesized to modulate the outgoing longwave radiation (OLR) through changing water vapor and cloud amounts in analogy to an eye's iris [2], although no clear evidence has been found for such a negative climate feedback [3].Questions remain: does the Earth in a warming climate have radiator fins, and if it does, where do they exist?
The OLR is key to identifying radiator fins (e.g [4]).The earth climate is shaped by the balance between the OLR and the absorbed solar radiation at the top of the atmosphere (TOA) [5][6][7].Previous studies discovered an imbalance of the global mean radiation energy budget mainly caused by enhanced absorption of solar radiation [8][9][10][11].This makes it increasingly important to elucidate how the OLR responds at both global and regional scales to counteract more absorbed solar radiation.
In this letter, we report that, based on the start-ofthe-art earth satellite observations, the Arctic appears to be a prominent, if not the only, radiator-fin region to radiate increasing amount of OLR during global warming (figure 1), and, using radiative transfer modeling, we elucidate that this is due to an unparalleled effect of the surface and atmospheric warming and weak water vapor greenhouse effect, which leads to substantial OLR increase in the Arctic, distinguishing it from the rest of the globe.

Satellite-observed OLR trend
To identify the radiator-fin regions, we use the Balance and Filled dataset of the Clouds and Earth's Radiant Energy System Energy satellite (CERES EBAF) [12] to calculate the geographic distributions of OLR trends during January 2002-December 2019.The OLR trend at each location is calculated by a linear regression of deseasonalized OLR monthly anomaly time series.Figure 1(a) shows that satellite observed OLR trend over the globe and reveals that the Arctic region (70 N-90 N) shows a remarkable increase of OLR in this period, at a rate of 1.20 ±0.84 W m −2 decade −1 .The zonal mean OLR trend pattern (figure 1(b)) further affirms that the Arctic is exceptional in that this is the only region where the trend magnitude clearly exceeds the uncertainty, identifying the Arctic to be a radiator-fin region in a warming climate.In comparison, the global mean OLR trend is found to be 0.17±0.18W m −2 decade −1 , resulting from the nonrobust trends in other regions such as the tropics (table 1).The insignificant global mean trend found here is in consistency with several previous studies [8,13,14].Such comparison bears an interesting and important question-why does the Arctic region exhibit a strong OLR increase while the other regions do not?

Geophysical variable trends
To answer the question above, we first investigate the factors that control the OLR from radiative transfer point of view.We use the reanalysis data from the fifth generation of European Center for Medium-Range Weather Forecasts atmospheric reanalysis (ERA5) [15] to examine the trends in surface temperature, air temperature, atmospheric water vapor (figure 1) and cloud cover (figure S1) in three regions: the global, tropics (30 N-30 S), and Arctic (70 N-90 N).The global and tropical means are used to make comparison with the Arctic and to better illustrate the cause of unique OLR trend in the Arctic, with one representing the averaged change over the globe (global mean) and another representing the region with much different atmospheric state (the tropics).
In contrast to the OLR which shows a significant trend only in the Arctic, we find significant trends in the state variables not only in the Arctic but also in the tropics and for the global mean (figures 1(c)-(f) and S1).The surface temperature change exhibits a well-known amplified warming in the Arctic [16][17][18], although statistically significant warming also emerges in the middle latitudes and the south pole (figure 1(d)), which suggests that the surface warming alone cannot explain the distinct OLR increase in the Arctic.The air temperature and specific humidity increases in the Arctic manifest a bottom-heavy feature, while their increases in the other two regions show a vertically more uniform pattern (figure 1(e)).Compared with the global or tropical mean, the lower troposphere in the Arctic experiences a much stronger warming (figure 1(e)).In terms of water vapor concentration change, although the fractional changes in the Arctic are 3-4 times stronger than that in the tropics and global mean, especially in the lower troposphere, it is worth noting that the absolute water vapor concentration in the Arctic atmosphere is about one to two orders of magnitude smaller than that in the tropics and the global mean, meaning that the Arctic is still much drier than the tropics in the warming climate.For the clouds, the total cloud cover changes mostly occur in the tropics, with increasing cloudiness in the Eastern Pacific and reduction in the Western Pacific (figure S1(a)), which correspond well to the regional OLR changes in these regions (figure 1(a)) but their compensation neutralizes the change in the tropical mean OLR (table 1).The findings here are consistent with [19], which investigated the clearsky OLR trend in the Arctic.
In short, significant changes in surface and atmospheric state variables are found in the Arctic, as well as other regions globally.This suggests that the distinct OLR increase in the Arctic region cannot be attributed to the changes in any variable (such as surface temperature or air temperature) alone.Therefore, the respective contributions of multiple factors to the OLR change warrant further investigations.

Quantifying the causes of OLR increase
To measure the respective contributions of different surface and atmospheric variables to the OLR change and identify the reason for a unique OLR increase in the Arctic region, we use the Rapid Radiative Transfer Model (GCM version, RRTMG) [21] to simulate the OLR changes of the same period as the CERES observation.
Conceptually, the OLR change can be decomposed to the contributions of the radiative forcing of Greenhouse-Gases (GHGs) and other radiative responses [22][23][24][25]: In this decomposition, the radiative forcing term ∆R GHG includes the contributions of wellmixed GHGs such as CO 2 , CH 4 , N 2 O (∆R WMG ), and the nonuniform GHG: O 3 (∆R O3 ).The radiative response term is contributed by the changes in surface temperature (∆R ts ), air temperature (∆R ta ), atmospheric water vapor (∆R q ) and clouds (∆R c ). Radiative forcing ∆R GHG is calculated by the difference of two RRTMG simulations with and without GHGs changes, and radiative responses are calculated using the kernel method [26][27][28] (see data and methods section).The RRTMG simulations are validated against the CERES (figure S2).It is worth noting that the overall OLR change, radiative forcing and radiative responses in equation ( 1) are respectively regressed on their timeseries to obtain the corresponding trends.For simplicity, we use the terms in equation ( 1) to directly represent their trends in the following and denote them as radiative forcing contribution and radiative response contribution.Uncertainties are calculated by the Weatherhead method [20] (see data and methods section).Positive (negative) trend means OLR increase (decrease).
For radiative forcing contribution, the global mean value is around −0.30 W m −2 decade −1 (figure 2(a)), consistent with previous estimations [14].The contribution in the tropics and Arctic is relatively stronger and weaker compared with the global mean value, due to the atmospheric state dependency of the forcing [29,30].Compared to the overall OLR change, the radiative forcing contribution is much less and of the opposite sign in the Arctic.While in the tropics or for global mean, the fractional contribution of radiative forcing is much stronger due to small total OLR change.
The non-cloud radiative responses in the Arctic make substantial contributions to the OLR increase, which is consistent with previous findings [19].Among all non-cloud variables, the surface temperature and air temperature increase contribute most to the OLR increase, with the contribution of air temperature slightly higher than that of surface temperature (figure 2(b)).The greenhouse effect of the moistening in the atmosphere is much weaker compared with the temperature contribution (figure 2(b)).As noticed earlier in figure 1(b), this is due to the low water vapor concentration in the Arctic even in a warmer climate, despite the much stronger local moistening trend.The findings here are consistent with [19], that the temperature effect makes a major contribution to the OLR trend in the Arctic.But different from their finding that the surface temperat- ure contributes the most in clear sky, we find that it is the air temperature that makes the strongest contribution in all sky, due to clouds masking the surface contribution.
In comparison, the contributions of surface temperature and water vapor in the tropics and for global mean are much different from those in the Arctic.Taking the tropics as an example, high climatological water vapor concentration (figure 1(f)) and relatively weaker surface warming trend (figure 1(b)) lead to a weak positive contribution of surface temperature.Meanwhile, the increase of tropical water vapor concentration strongly dampens the OLR increase and offsets the temperature effect, leading to a small OLR trend (figure 2(b)).The sum of air temperature and water vapor contributions in figure 2(b) shows a shear contrast between the tropics and Arctic.
Clouds make no prominent contribution to OLR change in the Arctic and a weak negative contribution for the tropics and global mean.In the Arctic, this results from compensating effects of a cover increase in the near-surface layer and decrease in the mid-tohigh troposphere (figure S1(c)), while in the tropics this results from geographically compensating cloud changes noted earlier.
In summary, the decomposed contributions of radiative forcing and responses to OLR change evidence that the robust OLR increase in the Arctic region is due to an unparalleled temperature warming effect and a weak dampening effect of water vapor compared with other regions, i.e. the distinct, unbalanced radiative responses to the temperature and humidity change.

Spectral contributions to OLR change
Spectral decompositions provide further insights on how the OLR changes.Figure 3 shows the spectral OLR trend in the Arctic.The Arctic total spectral trend is validated against the Atmospheric Infrared Sounder (AIRS) Level 3 spectral observation [31] (figure 3(a)) and is mainly from the contributions in the far-infrared (FIR) band (10-500 cm −1 ) and the window region (700-1080 cm −1 ).
The GHG increase reduces the OLR mainly at the wings of the 667 cm −1 (15 µm) CO 2 absorption band (figure 3(b)).While in the CO 2 absorption center, the OLR shows an increasing trend.This is because the OLR in the CO 2 absorption center mainly originates from the stratosphere and with CO 2 increase, the emitting layer is elevated to a higher and warmer altitude [32] and thus leads to an OLR increase.The spectral OLR signatures of the GHG forcing quantified here corroborate the CO 2 effects postulated in earlier studies [33,34].In addition, another noteworthy finding for the OLR change is the O 3 increase during this period, without which one cannot explain the decrease of OLR in its absorption band at 1040 cm −1 (9.6 µm).
The spectral results also vividly illustrate the contrasting behaviors in the Arctic and Tropics in terms of the compensation between the temperature and water vapor effects noted earlier (figures 3 and S3).In the Arctic, not only does the surface and air temperature warming lead to a greater increase of OLR in the H 2 O absorption band in the far-infrared (FIR, <500 cm −1 ), but the temperature effect is much less offset by increased trapping (reduction) of OLR caused by the atmospheric moistening (figure 3(c)).The spectral signals disclosed here indicate the usefulness of FIR measurements for detecting and attributing climate change, which can be observationally validated by the planned FIR satellite missions [35][36][37] to fly in near future.The spectral trends detected in this section agree well with the findings of [19], where the spectral trend of clear-sky OLR was analyzed in different seasons.
If organizing the water vapor and temperatureinduced spectral OLR changes to Planck, lapse rate (LR) and relative humidity change (RH) effects (figure 3(d)), according to the decomposition Method [38] (see Data and Method section) and using the aid of spectral kernels [39], it is clear that the prominent increase of OLR in Arctic compared to tropics is largely contributed by the Planck term, which further affirms that the unique increase of OLR in the Arctic region is due to the distinct radiative sensitivity of OLR to temperature and water vapor changes in this region and not caused by different vertical patterns or non-thermodynamicallyconstrained (varying RH) changes of them.

Discussion
Satellite observations analyzed here reveal the Arctic to be a unique 'radiator fin' region in the warming climate, which shows a robust increasing trend of OLR in the past eighteen years and acts to radiate away the excessive heat in the climate system accumulated by an increase of the net solar radiation absorbed by Earth.
Our modeling analyses suggest that the unparalleled increase of OLR in the Arctic is mainly caused by a strong surface and atmosphere warming and a low background water vapor concentration in the past 18 years.The temperature warming effect leads to a substantial increase in OLR in the Arctic and the low background water vapor concentration allows transmission of increased thermal radiation to space, both of which contribute to a distinct OLR increase in the Arctic.In comparison, the abundant water vapor and stronger greenhouse effect in the tropics neutralize the OLR increase caused by temperature warming.
The spectral decomposition of the OLR trend discloses that the increase of Arctic OLR mainly occurs in the mid-infrared atmospheric window and far-infrared region, both of which are observationally verifiable.This warrants the observation of OLR and its spectrum, to monitor whether the continued warming and moistening in the Arctic will reduce the effectiveness of the 'radiator fin' , which may have important implications for both the local and global radiation energy budget.are interpolated to the horizontal grids with resolution of 2.5 deg × 2.5 deg (the same as ERA5 reanalysis data used in RRTMG simulations).CERES only provides broadband OLR values and AIRS data contains the spectral OLR value with the band interval of 10 cm −1 from wavenumber 15 cm −1 -1995 cm −1 .
Monthly mean OLR values are used and the anomalies are calculated as the deviations from the climatological monthly value (i.e.deseasonalized timeseries) to calculate the OLR trend.
Trend and Uncertainty: Consider a linear regression model, where ŷ is the estimated anomalous timeseries of the variable of interest (e.g.OLR anomaly, or its radiative forcing or response component).t is the time span of the timeseries.a and b are the linear regression coefficient and y-intercept, respectively.As the autocorrelation of a timeseries can affect the detection of linear trends, we adopt the method proposed by [20] to calculate the standard deviation of linear regression coefficient a as, where y i and y i are the truth and estimated value at the ith time instance.n is the total time instances (the length of y timeseries).t i is the ith time instance and t is the mean value of t.Φ is the auto-correlation coefficient of y.Hence, using a 95% confidence level, we consider the trend to be significant if the trend magnitude of a is over 2σ; otherwise insignificant.Models: we use the rapid-radiative-transfer-model GCM version (RRTMG) and 4-times daily instantaneous ERA5 profiles to simulate the OLR for the same period as CERES observations.The required inputs such as surface temperature, air temperature, water vapor, ozone concentration, cloud cover and cloud water path are from ERA5, and the required effective radii of cloud droplets are from the 3-hourly synoptic TOA and surface fluxes and cloud product of CERES [42].A random cloud overlapping scheme is adopted for all-sky simulations.
The RRTMG can not only output broadband OLR but also 16 spectral band-integrated values, spanning from 10 cm −1 to 3250 cm −1 .To validate the RRTMG spectral results, we convert the AIRS data to the same band limits as RRTMG (figures 3 and S3).

Radiative forcing:
The total OLR trend can be decomposed into contributions of radiative forcing and radiative responses (equation ( 1)).To quantify the radiative forcing induced by GHGs emissions, we run RRTMG simulations of OLR with and without changes in GHGs and use the difference between these two simulations to calculate the radiative forcing.The GHG concentrations are taken from the National Oceanic and Atmospheric Administration Global Monitoring Laboratory [43,44].

Radiative responses and kernel method:
The noncloud radiative responses in equation ( 1) are diagnosed by the kernel method, ∆R x is the response variable x change induced OLR change.K x is the broadband radiative kernel of variable x, which represents the radiative sensitivity of OLR to x perturbation.∆x is the deseasonalized anomaly of x.The cloud response is calculated using the adjusted cloud radiative effect method [27], where the superscript o represents quantities in clear sky.∆R and ∆R o are the deseasonalized OLR timeseries simulation by RRTMG in all sky and clear sky, respectively.Σ∆R x and Σ∆R o x are the sum of non-cloud radiative responses in all sky and clear sky, respectively.∆R GHG and ∆R o GHG are the radiative forcings in all sky and clear sky, receptively.In this work, the broadband ERA5 kernels developed by [28] are used for the calculation.
The spectral radiative response can be calculated using similar method but with spectral radiative kernel.Here we use a set of spectral radiative kernel based on ERA5 reanalysis [39], which is also generated by RRTMG and has the same band configurations as the simulations used in this study.The spectral noncloud radiative responses are calculated as, where K i x is the spectral radiative kernel of variable x in the ith band and ∆R i x is the corresponding responses of x in the ith band.The broadband response ∆R x is the sum of spectral responses in all 16 bands ( 16 i =1 ∆R i x ).Based on Held and Shell [38], the radiative responses induced by the temperature and water vapor changes can be organized using the relative humidity as a state variable, ∆R PL = K ts + K ta + K q * dts (M6) ∆R LR = K ta + K q * (dta − dts) (M7) in which ∆R PL is the Planck contribution, i.e. the contribution to OLR change by a vertically uniform temperature change.∆R LR is the lapse rate contribution, i.e. the contribution to OLR change due to the vertically non-uniform temperature change.∆R RH is the contribution to OLR due to relative humidity change.Following equation (M5), these contributions can also be decomposed into spectral bands (figure 3(d)).

Figure 1 .
Figure 1.Climate trends in OLR and other surface and atmospheric variables.(a) Geographic distribution and (b) zonal mean pattern of OLR trend from CERES; (c) and (d) the same as (a) and (b) but for surface temperature from ERA5, (e) regional mean vertical distribution of air temperature (ta) trend (black line) and its climatological value (red line); (f) the same as (e), but for atmospheric water vapor (q).The dotted areas in panels (a) and (c) indicate the regions with trends significant at the 95% confidence level; the pink shadings in panels (b) and (d), and grey shadings in panels (e) and (f) indicate the uncertainty interval of the trends at the same confidence level (see data and methods section).Black (grey) lines in (b), (d), (e) and (f) represent significant (insignificant) trends.OLR = outgoing longwave radiation, CERES = Cloud and Earth's Radiant Energy System.ERA5 = the fifth generation of European Center for Medium-Range Weather Forecasts atmospheric reanalysis.OLR is defined as upward positive and positive trend means OLR increase.Atmospheric water vapor is presented as the logarithm of specific humidity, log (q).

∆R
CERES = OLR trend from CERES observations, ∆R RRTMG = OLR trend from RRTMG simulations, ∆R GHG = OLR trend due to Greenhouse-Gas change, non∆R c = OLR trend due to non-cloud component changes, ∆R c = OLR trend due to cloud change, ∆R ts = OLR trend due to surface temperature change, ∆R ta + ∆R q = OLR trend due to both atmospheric temperature and water vapor changes.CERES = Cloud and Earth's Radiant Energy System, RRTMG = Rapid Radiative Transfer Model-GCM version, global mean = averaged over the whole globe with area weights, tropical mean = averaged from 30 N to 30 S, Arctic mean = from 70 N to 90 N.

Figure 2 .
Figure 2. Decomposition of the OLR trend.(a) Component contributions to OLR trend calculated by RRTMG and kernel method; (b) further decomposed non-cloud contributions.Global mean is the area-weighted average value across the globe.Tropical mean is averaged from 30 N to 30 S. Arctic mean is from 70 N to 90 N. Grey vertical bars are the uncertainties calculated by the Weatherhead method [20] (see data and methods section).∆R RRTMG = OLR trend from RRTMG simulations, ∆RGHG = OLR trend due to Greenhouse-Gas change, non∆Rc = OLR trend due to non-cloud component changes, ∆Rc = OLR trend due to cloud change = OLR trend due to surface temperature change, ∆Rta = OLR trend due to atmospheric temperature change, ∆Rq = OLR trend due to water vapor change, ∆Rta + ∆Rq = OLR trend due to both atmospheric temperature and water vapor changes, OLR = outgoing longwave radiation, RRTMG = rapid radiative transfer model-GCM version.Upward positive is defined for all terms.

Figure 3 .
Figure 3. Spectrally-decomposed OLR trends in the Arctic.(a) total spectral trend, (b) GHG forcing contributions, (c) atmospheric and surface response contributions, (d) similar to (c) but recombined to quantify Planck, lapse rate and relative humidity effects.The lightened color bars in each panel represent statistically insignificant trends and the normal color bars, significant trends.∆R RRTMG = OLR trend from RRTMG simulations, ∆RAIRS = OLR trend from AIRS observation, ∆RGHG = OLR trend due to GHG change, ∆RWMG = OLR trend due to well-mixed GHGs change, ∆RO3 = OLR trend due to ozone change, ∆Rc = OLR trend due to cloud change, ∆Rts = OLR trend due to surface temperature change, ∆Rta = OLR trend due to air temperature change, ∆Rq = OLR trend due to atmospheric water vapor change, ∆RPL = OLR trend due to Planck effect, ∆RLR = OLR trend due to lapse rate change, ∆RRH = OLR trend due to relative humidity change.OLR = outgoing longwave radiation, AIRS = Atmospheric Infrared Sounder, RRTMG = rapid Radiative Transfer Model GCM version, GHG = Greenhouse-Gas, AIRS = Atmospheric Infrared Sounder.Upward positive is defined for all terms.

Table 1 .
OLR trends in the global mean, tropical mean and Arctic mean from CERES observations and RRTMG simulations.