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Different climatic effects of the Arctic and Antarctic ice covers on land surface temperature in the Northern Hemisphere: application of Liang-Kleeman information flow method and CAM4.0

Ice covers in high latitudes play important role in the global atmospheric circulation and abnormal temperature distribution. The different inter-annual variabilities of the Arctic and Antarctic ice covers have been revealed, but their respective climate effects are not clear. The Liang-Kleeman information flow method is used to reveal the causal relationships from the sea ice to the surface air temperature. The results point out that the Arctic and Antarctic sea ice both have significant impacts on the global air temperature. Especially in East Asia and North America, the inter-annual variation of ice cover in the Antarctic has an even stronger impact than that of the Arctic. This causality is further proved by the General Atmospheric Circulation Model (CAM4.0). In the numerical experiments, the ice covers in Arctic and Antarctic are changed individually or simultaneously as the forcing fields, and then the corresponding climate effects are analyzed. The results show that the Arctic and Antarctic ice cover variations can change the intensity of atmospheric baroclinic disturbance in mid-high latitudes of individual hemisphere, generating wave energy transmission across the equator through the wave-train-window over the Eastern Equatorial Pacific, and eventually causing air temperature anomalies in another hemisphere. Furthermore, the Antarctic ice covers are closer to the mid-high latitude atmospheric jets in the southern hemisphere. Therefore, compared to the Arctic ice cover, the inter-annual changes of Antarctic ice cover lead to a larger atmospheric wave-activity flux response, quickly (less than two months) spreading to the northern hemisphere, and causing more significant air temperature anomalies over the East Asia and North America. However, the influence of the inter-annual variability of Arctic ice cover on the climate in the southern hemisphere requires a lag time of at least four months, and the intensity is relatively weak.


Introduction
As the "cold source" of the entire Earth system, the Antarctic and Arctic regions have significant climate effects and play vital roles in global heat balance. With global warming, the polar region plays a "magnifying glass" to the signal of abnormal climate change and is one of the climate change sensitive areas (Mare 1997;Wouters et al. 2015). The report of IPCC (The Intergovernmental Panel on Climate Change) pointed out that, at the current level of greenhouse gas emissions, the climate in high latitudes will change drastically in the next century, the sea ice will melt, and the temperatures will also continue to warm (Schiavon et al. 2007). The change cycle of Arctic (Antarctic) sea ice has remarkable seasonality, with the maximum (minimum) volume from February to March and the contrary value from August to September (Walsh and Johnson 1979;Cavalieri et al. 1997;Parkinson et al. 1999;Saba et al. 2004). Affected by the global warming, the Arctic has undergone tremendous changes in the past 30 years (IPCC 2007). Since satellite observations SSM/I (the Special Sensor Microwave/Imager)-SSMIS (the 1 3 Special Sensor Microwave Imager/Sounder) were available in the 1970s, the concentration and coverage of Arctic sea ice have shown a rapid decrease, and the rate has been even faster in recent years (Nghiem et al. 2007). The sea ice in the Arctic Ocean reached its minimum in September 2012, a 31% decrease from the average of the 1950 and 1970s . The melting of Arctic sea ice is closely related to the "Arctic amplification", which is a hot issue in recent years (Overland et al. 1996;Screen and Simmonds 2010). In recent decades, the temperature in the Arctic has increased twice as large as the global average rate, and this phenomenon is called the "Arctic amplification" (James and Ian 2010;Kim et al. 2016). A large number of simulation studies have pointed out that under a representative global warming scenario, the temperature increase will be amplified in the polar regions, and the rainfall increase will reduce the salinity of the upper Arctic ocean (Manabe and Stouffer 1994;Rind et al. 1995;Wu and Smith 2016). The Arctic amplification has also caused more frequent blocking patterns and extreme weather (Elizabeth 2013). In addition, ice cover in Antarctic has also changed significantly. Compared with Arctic sea ice, Antarctic sea ice has more movement freedom and has an important impact on atmospheric stability and precipitation in Antarctica (King and Turner 1997). Due to the thick snow and ice deposits on the Antarctic ice cap, the volume of snow and ice in the southern hemisphere is about 8.8 times than that of the northern hemisphere (Cavalieri et al. 1997(Cavalieri et al. , 2003. Unlike the rapid decrease in Arctic sea ice, the Antarctic sea ice has been growing slowly and lasting longer (Stammerjohn et al. 2012). The sea basin of the Arctic sea ice shrinks rapidly, while the Antarctic sea ice shows regional changes. Cavalieri et al. (2003) used several sea ice observations of satellite from 1972 to 2002 to analyze the changes in the sea ice extent of Antarctica. The study found that the sea ice area of Antarctica showed a decreasing trend from 1973 to 1977, but there was an increasing trend from 1977 to 2002. Further studies showed that the sea ice in the Ross Sea, Weddell Sea, and the eastern coast of the Antarctic continent has increased year by year, while the sea ice in the Bellinghausen Sea and Amundsen Sea has decreased (Cavalieri and Parkinson 2008;Comiso and Nishio 2008;Fan et al. 2014).
Compared with the research on long-term trend changes accompanying global warming, the significant inter-annual changes of sea ice had attracted more attention, both in the local region and hemisphere (Parkinson and Cavalieri 1989;Lindsay and Zhang 2004;Screen et al. 2011). In 2007, the Arctic sea ice reached a new record low, and the extent of sea ice in the autumn of that year was reduced by 23% (Stroeve et al. 2008). This record was refreshed in September 2012, which was 12% lower than the lowest value in 2007 (Zhang et al. 2013). During the 2016/2017 icing period, the Arctic had 15 days of sea ice reduction, which was the most since 1979 (Hegyi and Taylor 2018). In February, the sea of Okhotsk experienced the largest inter-annual variability, while in July, the inter-annual variability in the Hudson Bay and northern Barents Sea was particularly large (Claire and Parkinson 1991). The Antarctic sea ice cover has a very significant annual change, and its smallest range is only 1/10 to 1/20 of the largest range, and different years show very different or even opposite trends (Cavalieri et al. 2003). Between 1973 and1977, Antarctic sea ice decreased dramatically, with an average annual decrease of about 2 × 10 6 km 2 , but from 1977 to 2002, the distribution range of sea ice gradually increased at a rate of (0. 10 ± 0. 05) × 10 6 km 2 /10 years (Zwally et al. 2002). The inter-annual variability of sea ice in the Arctic and Antarctica is complicated, and the inter-annual variability of ice cover in the Arctic and Antarctic regions is not synchronized. For example, the annual averages of the ocean ice surface area of the two polar regions are very similar over the period 1979-2012, but in fact the temporary evolution in sea ice in the two hemispheres are opposite (Pérez and González 2014). Furthermore, the inter-annual variabilities of ice covers in the Arctic and the Antarctic are significantly different (Gloersen and Campbell 1991;Gloersen et al. 1992;Stammerjohn et al. 2012). However, the mechanism and climate effects of the ice covers in polar regions are currently unclear.
The couple relationship between ice covers and the local atmosphere in polars has been concerned widely. For example, Francis and Hunter (2006) found that the location of the Arctic sea ice edge in summer has a strong correlation with the long-wave energy emitted by the atmosphere. Moreover, the greenhouse effect caused by downward long-wave radiation is amplified in the process of polar warming, which caused significant changes of the Arctic sea ice in summer from 1979 to 2004. In addition, temperature anomalies, local wind field anomalies , atmospheric circulation, polar cloud cover (Palm et al. 2010), and sea surface temperatures (Kay and Gettelman 2009;Alekseev et al. 2017) will have an impact on the thickness, coverage and intensity of the Arctic sea ice. Simmonds and Jacka (1995) discovered that the sea ice along the Antarctic continent, the Southwest Indian Ocean, the South Pacific, and the western Ross Sea interact with Southern Oscillation (SO). In addition, the Antarctic sea ice changes will also be affected by multiple factors such as temperature, carbon dioxide concentration, El Niño, and solar radiation (Gloersen 1995;Yuan and Martinson 2001;De Magalhães et al. 2012). In addition, the inter-annual changes of ice cover in the polar regions have been proved to change the energy balance of the ocean surface, local air temperature and atmospheric circulation (White and Peterson 1996;Allison et al. 2001;Francis and Vavrus 2012;Liu et al. 2013;Gao et al. 2015;Cheung et al. 2018). The reduction of Arctic ice cover makes the lower troposphere warmer and unstable, the cloud cover increases and the polar thickness gradient weakens, which weakens the polar jet (Francis et al. 2009). Researches (Liu and Yin 2001;Nakamura et al. 2015;Caian et al. 2017) pointed out the influences of Arctic sea ice on the phase and intensity of the North Atlantic Oscillation (NAO) and Arctic Oscillation (AO). The negative phase of NAO caused by the changes in sea ice in recent years has led to the cold winter in Europe (Cattiaux et al. 2010). In summer, the change of sea ice causes a positive phase of AO, which makes cold air shrink to the polar regions, and the temperature in most parts of the northern hemisphere is warmer (Jiang et al. 2019). At the same time, the transport of polar cold air to mid-latitudes and marine cold air outbursts (MCAOs) will change affect the climate of Eurasian continents at mid-high latitudes (Liu et al. 2006;Kolstad and Bracegirdle 2008). The ice cover in the Arctic will affect the local and northern hemisphere temperature by changing the NAO and AO, and the inter-annual variation of the ice cover in the Antarctic also has an impact on the climate in the southern hemisphere. Changes in the Antarctic sea ice will cause anomalies in regional atmospheric circulation, which will then propagate through wave trains or disperse energy to affect the weather and climate systems at the mid and low latitude areas in the southern hemisphere (Horel and Wallace 1981;Gloersen et al. 1992;Watkins and Simmonds 1998;Liu et al. 2004). It can be seen that the sea ice of the North and South Poles has been considered to be the main forcing factor of long-term climate change or abnormal temperature events on inter-annual time scales in their respective hemispheres. However, these previous studies only generally emphasized the influences of ice covers on their own hemisphere.
In addition to the influences of ice covers in polars in each hemisphere, the sea ice was proved to have a crossequator climate effect on the other hemisphere, which might affect the occurrence of local extreme climate events. Rogers and Loon (1979) found that sea ice affects planetary waves in the upper and middle troposphere, and pointed out that the location of large-scale sea ice anomalies is consistent with the inter-annual variation of large-scale planetary wave changes in the upper and middle troposphere. When Liu and Fedorov (2019) used climate models to study the impact of Arctic sea ice reduction, they found that the climate effect would change over time. During the initial period of Arctic sea ice reduction, the northern hemisphere became warmer and the southern hemisphere became colder, the tropical convergence zone moved northward, and the Antarctic sea ice expanded, but the opposite was true when the time scale became longer. The actual observation results also confirmed this. The satellite, ground-based, and reanalysis data over the past 40 years  show that since the end of the 1970 s, with the rapid decrease of Arctic sea ice, the temperature in the Southern Hemisphere has decreased regionally, but after 2016, the situation was reversed, and the Antarctic sea ice began to decrease sharply (Mokhov and Parfenova 2021). Antarctic sea ice was found to have a good connection with the atmospheric circulation in the northern hemisphere (Kwok and Comiso 2002;Douglas and Richard 2003). Furthermore, researches pointed out the abnormal cross-equatorial cold airflow in the South Indian Ocean and Australia in different years of Antarctic ice coverage (Christopher et al. 1996;Xue et al. 2003). Jie et al. (2009) pointed out that the Antarctic Oscillation (AAO) anomaly could trigger Pacific/North American teleconnection patterns (PNA) like quasi-stationary Rossby waves by affecting the tropical zonal wind. Therefore, the Antarctic sea ice anomaly had a good correlation with the East Asian monsoon and rainfall (Yang and Huang 1992;Qin et al. 2014). Regarding the steady Rossby wave propagation across the equator, Li et al. (2019) determined the obstacle area and corresponding waveguide as each window area in the northern hemisphere winter and summer tropospheric high-level wave propagation across the equator. These waveguides may be the main channels for energy exchange between the two hemispheres. The Eastern Pacific Ocean is the window area that exists in both winter and summer, and the Rossby waves can cross the equator through this window area. However, there remains several questions have not been well solved. Previous studies have emphasized that changes in sea ice can lead to significant climate effects, but there are significant different inter-annual variations for Arctic and Antarctic ice covers in actual observations. In the earth system, sea ice interacts with the atmosphere and ocean. How to extract the forcing signal of sea ice on air temperature in the complex earth coupling system? The Rossby wave across the equator are thought to be the possible causes of the polar sea ice forcing on the other hemisphere, but whether the intensity of the cross-equal forcing caused by Arctic or Antarctic ice cover is same? What are the specific impacts on the temperature distributions in the two hemispheres? In particular, what is the difference in the Rossby wave propagations triggered by the inter-annual changes of the two poles ice covers?
Based on the above questions, the Liang-Kleeman information flow (Liang 2013(Liang , 2014(Liang , 2015 method and model simulations will be used. A more specific introduction about the Liang-Kleeman information flow method will be explained in detail in the section of data and method. The method of Liang-Kleeman information flow is used to give the causal relationship from the Arctic or Antarctic sea ice to the air temperature, and then the Community Atmosphere Model version4.0 (CAM4.0) is used to discuss the influence mechanisms of Arctic and Antarctic ice covers on climate. The following are the section arrangements of this paper: Sect. 2 describes the data and method, including the calculation of the Liang-Kleeman information flow, T-N Wave-activity flux, Eady growth rate and introduction of the CAM4.0; Sect. 3 analyzes the influences of inter-annual variations of ice covers in two polars on temperature in observation and simulations; Sect. 4 analyzes the mechanisms of cross-equatorial climate effects of inter-annual variations of two poles ice covers on the other hemisphere; Sect. 5 summarizes and discusses.

Liang-Kleeman information flow and time series causal analysis
Analyzing the causal relationship between events is an important topic in many disciplines, and it is the direct purpose of many scientific researches. In meteorology, most methods use time lag correlation analysis to infer the causality between series. However, correlation analysis does not distinguish the directionality, and for a periodic process, we cannot judge whether a phase difference is time lag or time advance. For example, in a fluctuation period of T, the lag t is the same as the lead T-t. The sequence constructed by Liang (2014) is an example, which proves that the cause and effect given by the lead-lag correlation is completely opposite to the actual situation. Liang proposed the theory of information flow, and analyzed the causal relationship between events through the method of Liang-Kleeman information flow (Liang 2014(Liang , 2015. Compared with traditional data analysis methods such as correlation analysis and lead-lag correlation, this method of present study is more innovative. This method has been widely used since it was proposed (Stips et al. 2016;Liang 2018;Jiang et al. 2019). The causality of a given two time series can be judged by the Liang-Kleeman information flow theory. The information flow has always been considered as an appropriate measure of causality, as the exchange of information between two events, not only indicates the quantity, but also the direction of the causality (Liang 2014). Liang (2014Liang ( , 2015Liang ( , 2016 proved that if the development of X 1 is independent of X 2 , then the information flow from X 2 to X 1 is 0. For linear systems, given two time series of X 1 and X 2 , Liang proves that the maximum likelihood estimator (mle) of information flowing from X 2 to X 1 per unit time is is the sample covariance between X i and a series derived from X j using the Euler forward differencing scheme, , Δt is the time step and k ≥ 1 (integer). If T 2→1 = 0 , X 2 does not cause X 1 ; if it is not equal to zero, it is causal (statistical significance test must be performed). The calculation program of this information flow can be downloaded through http:// www. ncoads. cn/ artic le/ show/ 63. aspx. This method has been widely recognized and applied (Vaid and Liang 2015, 2018, 2019a, b, 2020Vaid and Kripalani 2021). Jiang et al. (2019) used the Liang-Kleeman information flow and CAM4.0 to analyze the climate effect of multi-source forcing.

T-N Wave-activity flux
The TN wave-activity flux is a three-dimensional waveactivity flux derived by Nakamura (1997, 2001) based on the Plumb wave flux, making it more suitable for complex background airflow, such as the background circulation in the middle and high latitude. The background field takes the average monthly climate field for many years, which can better describe the energy dispersion characteristics of the stationary Rossby wave and the propagation anomaly of the Rossby wave. The three-dimensional expression of the T-N wave-activity flux is as follows: (1) where the superscript " ′ " is zonal deviation, ϕ, λ, Φ, f = 2Ω sin ϕ, a, Ω are latitude, longitude, potential, Coriolis parameter, earth radius and earth rotation rate, � = � f is the perturbation of the quasi-ground transfer function relative to the climate field, and the basic flow field U = (U, V) represents the climate field. It is widely used to analyze the propagation of Rossby waves in atmospheric dynamics (Nakamura et al. 2010).

Eady growth rate
In the classical theory of atmospheric stability, the baroclinicity of the atmosphere is defined by the horizontal temperature gradient, the Coriolis force on the vertical shear and vertical stability of the horizontal velocity. In the original situation, the growth rate of baroclinic pressure, which characterizes the instability of atmospheric baroclinic pressure, is defined as When Hoskins and Valdes (1990) researched the storm track in the northern hemisphere, simplified it to: In which, U is the zonal wind, θ is the potential temperature, α = T θT p=1000 , N 2 = −gα θ p . N 2 is the Brunt-Vaisala frequency of atmosphere, also called buoyancy frequency, which indicates the frequency at which the gas block oscillates when it is vertically disturbed. N 2 can be used to measure stability. In recent years, this simplified version has been widely used ). This paper uses (3) to calculate the eady growth rate, represented the baroclinicity of the atmosphere.

Model introduction
In addition to statistical analysis of observational data, model simulations can provide a more detailed description of the physical processes in climate change. CAM4.0 (Community Atmosphere Model version 4.0) is a global atmospheric circulation model developed by NCAR (National Center for Atmospheric Research) (Neale et al. 2010;Gent et al. 2011). Existing research results show that CAM4.0 has good simulation capabilities for global atmospheric circulation and climate change, and has also been widely used (Neale et al. 2013;Chen et al. 2016;Kumar et al. 2016). CAM4.0 also includes the land surface model (CLM4.0), which provides the land surface conditions and lower boundary conditions such as energy, momentum, and water vapor exchange between land and air (Oleson et al. 2010). Three power cores are optional: the Euler spectrum core, the finite volume core and the half Lagrangian core. The Euler spectrum is be used in this paper, and the horizontal resolution of the model used is T85 (128 × 256, about 1.5°). In the vertical direction, the coordinates used from bottom to top are the σ coordinates, the σ-p transition coordinates, and the pure p coordinate, covering 26 layers. The deep convection process is used a parametric scheme developed by Zhang and McFarlane (1995) and corrected by Richter and Rasch (2008). Compared with CAM3.0, CAM4.0 has significantly improved on deep convection scheme, Arctic cloud simulation, radiated interface and computational scalability. What's more, its default power core has been changed from the original spectral core to a finite volume core, and improves simulation capabilities for ENSO (Neale et al. 2008).

Liang-Kleeman information flow and observation results
In order to discuss the influences of sea ices in the Arctic and Arctic on the temperature in different regions, we calculate the spatial distribution of the information flow from sea ice to temperature by the Liang-Kleeman information flow method. In the calculation of the information flow from sea ice to temperature, the time series is from 1982 to 2017. We average the Arctic and Antarctic sea ice coverage and calculate the information flow from sea ice coverage to temperature for each grid point. Figure 1 shows that there are obvious causal relationships from the Arctic and Antarctic sea ice to the temperature, the temperature change is closely related to the sea ice anomaly. Changes in Antarctic and Arctic sea ice have an impact on the temperature in the other hemisphere. Temperature changes in Asia and North America are also closely related to Antarctic sea ice, and the response to Antarctic sea ice in East Asia is even more pronounced than that of Arctic sea ice. Whether Antarctic sea ice has a greater impact on the above areas is also analyzed from observations. From 1982 to 2017, the years 1987 and 1990 are selected as the Arctic sea ice anomaly years, in which the Arctic sea ice changes significantly but the Antarctic sea ice is almost unchanged. Similarly, the years 2003 and 2005 are selected as the Antarctic sea ice anomaly years (Fig. 2). We analyze the temperature changes in these years to discuss the climate response of sea ice reduction. Figure 3 shows the different spatial distribution of temperature between the sea ice decreasing and increasing anomalous years.
In different seasons (summer and winter) of the anomaly years of sea ice, the temperature changes have obviously different spatial distributions (Fig. 3). Considering that sea ice has a tendency to decrease, we do not discuss temperature changes in the polar regions, but mainly discuss the temperature changes in Eurasia and North America. When the Arctic sea ice decreases abnormally, the temperature of Eurasian increases significantly in summer, but in winter it heats up in the north and cools down in the south. For North America, it's warm up in summer, but in winter the north (Canada) cools, while the south (USA) warms. In addition, the temperature in the southern hemisphere is also affected, and there are cooling trends in Oceania and southern South America. When the Antarctic sea ice decreases abnormally, there is no doubt that it will bring about a significant temperature change in the southern hemisphere, and it will affect the temperature of the northern hemisphere. In the year of Antarctic sea ice abnormal decrease, the most regions of East Asia have a clear warming trend, but the north regions have a cooling trend, which is consistent in summer and winter. Regardless of summer or winter, North America shows a trend of decreasing temperature in the north and increasing temperature in the south. Through the actual observation, the Arctic and Arctic sea ice have obvious cross-equatorial climate effects, and the effects of the two are quite different in some areas. Therefore, it is meaningful to discuss the individual climate effect of ice cover in the Arctic or Antarctic region by using the CAM4.0 model.  1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Temperature changes in the simulation
The experiments using the CAM4.0 are designed to study the climate response of Arctic and Antarctic ice cover. Therefore, we set up a control experiment and several contrast experiments by changing the forcing field, and Table 1 shows the specific experiment settings. The time scale of the observation data used in this article is from 1948 to 2017. The difference between the periods 1948-1982 and 1983-2017 represents the actual observational changes. Therefore, we use the situation in 2000 (the middle year of 1983-2017) as the forcing field for the control experiment, and the situation in 1965 (the middle year of  as the forcing field for the contrast experiments. There are twenty samples, which persists for 1 year in each experiment group, and the ensemble averages for four groups are analyzed in the subsequent discussion. Compared with the control experiment, the ice cover in the contrast test is significantly reduced (Fig. 4). We change the ice cover of the forcing field at the Arctic and Antarctic separately to distinguish the climate effects they bring. In addition, the experiments of changing the ice cover of the Arctic or Antarctic separately are compared with that of changing the ice cover of the two poles at the same time to assess whose influence is more important.
In observations, the 2 m temperature generally shows an increasing trend, and some regions in Europe, Asia and North America have cooled (Fig. 5a, b). It can be seen from the simulation results that when the Arctic ice cover and Antarctic ice cover are changed at the same time (the  experiment SIC), the temperature in winter changes drastically, and the temperature in Asia obviously increases, while the temperature in North America and Europe decreases (Fig. 5c, d). After changing the Antarctic ice cover and Arctic ice cover, it can be seen that compared to NSIC (Fig. 5e,  f), the simulation results of SSIC (Fig. 5g, h) is closer to the simulation results of SIC (Fig. 5c, d), including the warming in East Asia and the cold winter in North America. Changes in Arctic ice cover have caused more pronounced cooling in winter in Europe, and also brought winter warming in parts of South America (the warming is even wider than the temperature increase caused by changes in Antarctic ice cover) (Fig. 5e, f). It can be seen that whether changes in Arctic ice cover or Antarctic ice cover will affect the other hemisphere across the equator. Antarctic ice cover has a greater impact on East Asia and North America than Arctic ice cover. Why does the Arctic/Antarctic ice cover change have a huge impact on the temperature in the southern/northern hemisphere, bringing about a cross-equator climate effect? Why the cross-equatorial climate effect of Antarctic ice cover is stronger than that of Arctic ice cover? We will analyze the mechanism of this cross-equator climate response below.

Mechanism of cross-equatorial climate effect of inter-annual variation of ice cover
The previous sections analyzed the temperature changes caused by the Arctic and Antarctic ice cover, but what is the mechanism of this cross-equatorial climate effect? The existence of the window area allows the Rossby wave to propagate across the equator, and these waveguides may be the main channels for energy exchange between the two hemispheres (Li et al. 2019). Similar to the method of Li et al. (2019), we first set fixed points, and then perform the lead-lag correlation between their stream-function time series and the global field. We set the base points at 60° N, 90° E when analyzing the results of NSIC (the experiment of Arctic ice cover changes) and 60° S, 135° W when analyzing the results of SSIC (the experiment of Antarctic ice cover changes). When the Arctic ice cover decreases, the temperature in the polar regions increases, the zonal temperature gradient decreases, and the baroclinity of the atmosphere weakens, resulting in a reduction in wave-activity flux (Fig. 6a). Therefore, the obvious wave-activity flux reduction appeared in the North Pole in the first month, and the area where the wave-activity flux changed most drastically corresponds to the area where the ice cover changed drastically. At this time, because the Antarctic ice cover has not changed, it can be seen that there is almost no change in wave-activity flux in the southern hemisphere, and the wave-activity flux will gradually pass to the south over time (Fig. 6b, c). As can be seen from the spatial distribution of the 300 hPa height anomaly field (Fig. 7), when the ice cover in the Arctic changes, the height field anomaly (Fig. 7a) first appears in Eurasia, causing baroclinic fluctuations. The atmospheric wave train gradually passes southward and spread across the equator to the southern hemisphere through the window area over the Eastern Equatorial Pacific, then divides into two eastward and southward branches ( Fig. 7b and c). The change of ice cover first causes the change of the temperature gradient of the lower layer, causing the abnormal atmospheric baroclinic instability, resulting in the generation and propagation of atmospheric baroclinic fluctuation anomalies. This anomalous signal of ice coverage interacts with the wave current of high-altitude  1983-2017 and 1948-1982. Difference between control and contrast experiments. c, d SIC, e, f NSIC, g, h SSIC (filling, unit: K; left column: annual average, right column: winter average). All shading areas exceed 95% significance level atmospheric jets through the baroclinic wave flux and further amplifies, generating meridional waves and even transmitting Rossby waves across the equator. When analyzing the changes in wave-activity flux caused by Antarctic ice cover, we will start from June (corresponding to the winter in the southern hemisphere). When we only change the Antarctic ice cover, we can notice that at the first time (Fig. 8a), the wave-activity flux changes in both Antarctic and Arctic regions, although the waveactivity flux changes in the northern hemisphere are not as strong as those in the southern hemisphere. That is to say, after the change of Antarctic ice cover, it got a rapid response in the northern hemisphere, which is strange and thought-provoking. The sea-land distribution in the northern and southern hemispheres is very different, and there is more land in the northern hemisphere, so the prevailing westerlies are split and its intensity is weak. In the southern hemisphere, the ocean area accounts for the majority, so the prevailing westerlies are complete and stronger. Changes in ice cover will bring changes in north-south temperature Fig. 6 Vertical section of the difference in meridional mean a-c baroclinic eddy growth rate (filling, unit: 10 -6 m/s 3 ) and changes in Arctic ice cover in the forced field by month (polyline: ice cover change with latitude, superscript: month, unit : fraction) d-f wave-activity flux between CTRL and NSIC (filling, unit: m 2 /s 2 ), wave-activity flux distribution in CTRL (contour line, unit: m 2 /s 2 ). All shading areas exceed 95% significance level gradients, affecting the location and intensity of the prevailing westerlies. Therefore, in the process of ice cover affecting the climate, the location of ice cover and the westerly jet stream plays an important role, which may be the reason why changes in Antarctic ice cover can quickly affect the northern hemisphere. It can be seen from the anomalous spatial distribution of the 300 hPa height field (Fig. 9). After the ice cover changes in the Antarctic, due to the change in temperature gradient, the baroclinicity of the atmosphere changes, and a baroclinic fluctuation rapidly occurs in the southern hemisphere. Over time, the wave passed north and crossed the equator to reach the northern hemisphere. At the same time, it divided into two branches, one of which continued to pass north, and the other spread eastward through the North American region. The entire northward transmission process of the wave is also faster than the wave transmission process when the Arctic ice cover changes.
Through the above analysis, the following conclusions can be drawn. When change in the Arctic ice cover, the significant high-level height field anomalies are first produced just over the sea ice areas. Subsequently, the waves partly propagates zonally and partly propagates towards the equator. After about four months, the equatorial wave crosses the equator through the wave-train-window over Eastern Equatorial Pacific to reach the mid-high latitudes of the South Pacific, and causes a weak response in the southern hemisphere (Fig. 7). However, after the Antarctic sea ice changes (Fig. 9), the height field anomaly mainly propagates meridionally towards the equator. Only after 1 month (which is faster than what happened after the Arctic ice cover changed), it quickly propagates to the westerlies in the mid-high latitudes of the northern hemisphere, forming a significant zonal wave train with a significant impact on the atmospheric circulations over the North America and Eurasia (Fig. 8). This process has also been verified in the diagnostic calculations of zonal averaged baroclinicity and atmospheric wave activity flux in Figs. 6 and 8. This shows that compared to the Arctic sea ice, the inter-annual variability of Antarctic sea ice will cause stronger anomaly in local baroclinic energy and a faster transmission to the other hemisphere.
Due to the difference in the distribution of land and sea, the atmospheric circulation patterns in the northern and southern hemispheres are different. The prevailing westerlies in the southern hemisphere is wider than that in the northern hemisphere, and the upper westerly jet stream is stronger and wider (Fig. 10). Arctic ice cover and Antarctic ice cover are mainly reduced, and marginal ice cover has increased, but Antarctic ice cover has increased more significantly and is closer to the location of upper jets. In other words, changes in Antarctic ice cover have a more pronounced effect on the upper jets, which are more closely related to high-altitude westerly jets than Arctic ice cover. Therefore, the location of Antarctic ice cover and the westerly jet may affect the climate effect of Antarctic ice cover. A new set of experiments (SSIC_South_Movement) is added. In the SSIC_South_Movement, we shifts the change of the ice cover in the SSIC to the south by five degrees, and then superimposed on the 2000 Antarctic ice cover of CTRL as the ice cover forced field (Fig. 11). Other settings are consistent with SSIC. The distance between the region of the ice cover change and the atmospheric jets is increased, so the hypothesis of the effect of ice cover on the jet stream mentioned above is examined. In this case, ice cover changes do not correspond to high-altitude jets, that is, the direct effects of ice cover changes on the jets have weakened.
After shifting the change of Antarctic ice cover in the forcing field five latitudes to the south, it can be seen that the temperature response has become significantly weaker. In general, the warming caused by changes in Antarctic ice cover has significantly weakened in East Asia (Fig. 12). For North America, the temperature decrease has decreased, including the reduction of the range and the decrease in amplitude. In addition, the magnitude of wave-activity flux changes has also decreased ( Fig. 13). After the Antarctic ice cover change field shifting five latitudes to the south, the response of the waveactivity flux in the southern hemisphere in the earlier period decreased significantly. Therefore, the climate effect weakened in the result of the SSIC_ South_Movement.

Summary and discussion
In previous studies, the influence of Arctic (Antarctic) ice cover on the northern (southern) hemisphere is generally studied (Cattiaux et al. 2010;Raphael et al. 2011, Vihma 2014). However, this study reveals the crossequatorial climate effects of the two ice covers and their mechanisms. According to the Liang-Kleeman information flow method, it is found that the information flows from Arctic and Antarctic sea ices to the 2 m temperature are obvious. Furthermore, the influence of Antarctic sea ice on the temperature in East Asia is greater than that of Arctic sea ice. Previous studies have also shown that changes in Antarctic sea ice will affect the climate of East Asia (Fan and Wang 2006;Zhu 2009). However, whether the influence of Antarctic ice cover on the climate of East Asia is greater than that of the Arctic ice cover requires further research.
In order to study the specific temperature changes bring about by the sea ice changes, the observation data is analyzed. Based on the observed sea ice data, the years 1987 Fig. 8 Vertical section of the difference in meridional mean a-c baroclinic eddy growth rate (filling, unit: 10 −6 m/s 3 ) and changes in Antarctic ice cover in field by month (polyline: ice cover change with latitude, superscript: month, unit: fraction), d-f wave-activity flux between CTRL and SSIC (filling, unit: m 2 /s 2 ), wave-activity flux distribution in CTRL (contour line, unit: m 2 /s 2 ). All shading areas exceed 95% significance level (in which the Arctic sea ice anomaly increased) and 1990 (in which the Arctic sea ice anomaly decreased) are selected as the Arctic sea ice anomaly years, and there is almost no variance of Antarctic sea ice in these 2 years. According to these 2 anomaly years, we discuss the different interannual responses of air temperature when the Arctic sea ice is abnormal. Likewise, the years 2003 (Antarctic sea ice anomaly increased) and 2005 (Antarctic sea ice anomaly decreased) are selected to discuss the inter-annual variations in the Antarctic sea ice anomaly years. The decrease in Arctic sea ice brings the warming in most parts of East Asia, cooling in Europe, warming in North America (Canada), and cooling in the South (USA). When the Antarctic sea ice is abnormally decreased, most regions of China Fig. 9 Lead-lag correlation coefficients between the 300-hPa height anomaly at the basepoint (60° S, 135° W) and the global field (filling, black dot: the base point and branch point, subscript: month, black curves indicate the wave propagation path through the window area in Eastern Pacific). All shading areas exceed 95% significance level have a warming anomaly, while the temperature in Europe decreases. At the same time, the temperature in the south of North America is rising, while in the north part, there is a cooling anomaly. Similarly, this cross-equatorial forcing relationship of sea ice covers in the Arctic and Antarctic regions can be obtained from the results of the information flow, in which the anomaly of Antarctic ice covers has also led to the significant temperature changes in Eurasia and North America. In conclusion, changes in ice covers produce a cross-equatorial climate effects, affecting the temperature in the other hemisphere, especially the Antarctic ice covers.
In the observation, changes in temperature are simultaneously affected by multiple forcing factors. In order to analysis the mechanism of the cross-equatorial climate effect of ice covers, we conduct multiple sets of numerical experiments. In the results of the CAM4.0 simulations, the temperature anomalies in SSIC simulation (in which only the Antarctic ice cover changed) are closer to that of SIC simulation (changing both Arctic and Antarctic ice cover), which is characterized by an obvious cooling in European winter. However, a warming in East Asia and a cooling in North America in winter are mainly caused by the changes in the Antarctic ice cover. In the simulations, both Arctic and Antarctic ice covers affect the other hemisphere across the equator. Previous researches have shown that Rossby waves can propagate across the equator through the "window area", which is over the Eastern Equatorial Pacific all the year (Li et al., 2019). Liu et al. (2018) proposed the South-North Pacific (SNP) teleconnection pattern, and proved that SNP can act as an "atmospheric bridge" to propagate wave energy across the equator. Therefore, we further study the crossequatorial effects caused by the propagation of atmospheric wave-activity fluxes. After the change of Arctic (Antarctic) ice covers, the local temperature of the Arctic (Antarctic) with the intensity of atmospheric baroclinicity at mid-high latitudes increases or decreases firstly. As a result, the local baroclinic wave-activity fluxes over the Arctic (Antarctic) change (Fig. 14). As time progresses, the wave energy transmission gradually travels across the equator in the meridional direction through the wave-train-window area over the Eastern Equatorial Pacific, affecting the climate in the other hemisphere. However, the prevailing mid-latitude westerly jet in the southern hemisphere is stronger and wider than that in the northern hemisphere, which is also closer to the edge of ice cover. The intensity of the cross-equatorial climate effect caused by the Antarctic ice cover is much stronger than that by Arctic ice. In order to verify the relationship between the cross-equatorial climate effect and the position All shading areas exceed 95% significance level of the Antarctic ice cover, a new experiment with a southward shifting the Antarctic ice cover by 5° of latitudes is set. After shifting the Antarctic ice cover, there is a much weakened locally response in the southern hemisphere and weak cross-equatorial effect in the north hemisphere.
Compared with the Arctic ice cover, the Antarctic ice covers are closer to the mid-latitude westerly jet. Therefore, the Antarctic ice cover changes the low-level atmospheric temperature gradient and the process of atmospheric baroclinic wave uploading, and causes more significant changes in the upper atmospheric height field and jet stream. The stronger height field anomaly in the southern hemisphere then causes the obvious Rossby fluctuation anomaly propagation across the equator, leading to significant temperature changes in the northern hemisphere, especially over the Eurasia and North America. In the Liang-Kleeman information flow and numerical model results, the cross-equatorial effects of the Antarctic ice cover on the northern hemisphere are even more significant than the effects of the Arctic ice cover. It indicates that the variation of Antarctic ice cover is Fig. 13 Vertical section of the difference in meridional mean baroclinic growth rate and wave-activity flux between SSIC and SSIC_ South_Movement, changes in Antarctic ice cover in the forced field by month (filling, contour line: wave-activity flux distribution in SSIC, polyline: sea ice change with latitude, superscript: month). All shading areas exceed 95% significance level indispensable in the medium-and long-terms weather and climate predictions of the northern hemisphere.