The Arctic sea ice-cloud radiative negative feedback in the Barents and Kara Sea region

Abstract

Shortwave cloud radiative effect (SWCRE), known as the cooling effect triggered by cloud, plays a vital role in adjusting the global radiation budget. As the Arctic gets warmer, it may become a more indispensable factor curbing this warming tendency. Research has pointed out a significant relationship between sea ice cover (SIC) and SWCRE over the Arctic during summer (June–August). Although no evidence has been found on cloud response to SIC during summer on the average of the Arctic, this study regards cloud as an inter-connection which can regulate SIC and SWCRE in a particular place: Barents and Kara Sea region (15°E–85°E, 70°N–80°N). Its SWCRE and SIC vary significantly, with their trends being 5.85 w∙m⁻² and − 5.87% per decade compared to those of the Arctic mean (2.93 w∙m⁻² and − 4.65% per decade). In this area, we find that the growing number of low-level cloud which is resulted from the loss on SIC may be accountable for the increase in SWCRE, as is shown in the correlation coefficient between low-level cloud and SIC reaches − 0.4. The correlation coefficient between low-level cloud and SWCRE is 0.6. It reflects a SIC-cloud-SWCRE negative feedback. Moreover, a regression fitting model is being established to quantify the contribution of Arctic cloud in the process of slowing down the Arctic warming. It reveals that this specific region would turn into an ice-free region with sea surface temperature (SST) 1.5 °C higher than reality during 2001 if we stop the increase in SWCRE. This result presents how fascinating the contribution cloud has been making in its way slowing down the warming pace.

Appendix

Regression fitting model.

The example of regression fitting model is as follows, ${{{x}}}_{{{t}}}$ stands for independent variable, ${{{y}}}_{{{t}}}$ stands for dependent variable. If we want to build a linear connection between ${{{x}}}_{{{t}}}$ and ${{{y}}}_{{{t}}}$, we can use the ordinary least squares approach.

$$x_t\rightarrow y_t\;\left(t=1,\;2\dots,n\right)$$

$$b=\frac{\sum_{t=1}^n=x_ty_t-nx^\ast y^\ast}{\sum_{t=1}^n\;x_t\;x_t-nx^\ast x^\ast},\;a=y^\ast-bx^\ast\;,\;y'_t=\;bx_t\;+\;a\;\left(x^\ast={\textstyle\sum_{t=1}^n}\;x_t/n\;y^\ast\;=\;{\textstyle\sum_{t=1}^n}\;Y_t/n\right)$$

The formula above is just a basic example on implementing the linear regression progress. The specific formualtion on the talked data is as follows, ${\mathrm{ASR}}_t$ is the independent variable while ${\mathrm{SIC}}_t$ and ${\mathrm{SST}}_t$ are the dependent variables.This model is designed to justify the relationship between ASR and the dependent variables: SIC and SST by comparing the fitting regression result $\mathrm{SIC}'_t\;\mathrm{and}\;\mathrm{SST}'_t$ to the oringnal data $SIC_t\;\mathrm{and}\;SST_t$.

$$ASR_t\rightarrow SIC_t\;\left(t=1,\dots,42\right)$$

$$b_{sic}=\frac{\sum_{t=1}^n=ASR_t\;SIC_t-nASR^\ast SIC^\ast}{\sum_{t=1}^n\;ASR_t\;ASR_t\;-nASR^\ast\;ASR\ast},\;a_{sic}=\;SIC^\ast\;-\;b_{sic}\;ASR^\ast,\;SIC'_t\;=\;b_{sic}ASR_t\;+\;a_{sic}$$

$$ASR_t\rightarrow SIT_{t\;}\left(t=1,\dots,42\right)$$

$$b_{sst}\;=\;\frac{\sum_{t=1\;}^nASR_tSST_t-nASR^\ast SST^\ast}{\sum_{t=1}^n\;ASR_tASR_t-nASR^\ast ASR^\ast}\;,\;a_{sst}\;=\;SST^\ast-\;b_{sst}ASR^\ast,\;SST'_t\;=\;b_{sst}ASR_t+\;a_{sst}$$

$$\left(ASR^\ast=\sum\nolimits_{t=1}^nASR_t/n\;SIC^\ast=\sum\nolimits_{t=1}^nSIC_t/n\;SST^\ast\;=\sum\nolimits_{t=1}^nSST_t/n\right)$$

CONSTANT-SWCRE method is the same as the method used above but keep SWCRE as a constant figure. It is worth noting that it shares the same ${{{b}}}_{{{s}}{{i}}{{c}}}$, ${{{b}}}_{{{s}}{{s}}{{t}}}$, ${{{a}}}_{{{s}}{{i}}{{c}}}$, $a_{sst}$ with the abovementioned. However, it ignores the rise in SWCRE from 1979 to 2020 and maintains SWCRE as it is in 1979 as time passes. This approach is designed to test the effect of SWCRE by comparing the CONSTANT-SWCRE result $\mathrm{SIC}''_t$ and ${\mathrm{SST}''}_t$ to the oringnal data ${SIC}_t\;\mathrm{and}{\;SST}_t$.

$$\mathrm{SIC}''_t\;=\;b_{sic}\;\left({\mathrm{ASR}}_t\;+\;S\left(\mathrm t-1979\right)\right)\;+\;a_{sic}\;,\;\mathrm{SST}''_t\;=\;b_{sst}\;\left({\mathrm{ASR}}_t\;+\;\mathrm S\left(\mathrm t-1979\right)\right)\;+\;a_{sst}$$

S: Annually mean slope on SWCRE in both regions (Arctic and Novaya) from 1979 to 2020.