Arctic weather variability and connectivity

Domain: earth_science
Published: 2023-10-18
Editorial outcome: major_revision

Abstract
The Arctic’s rapid sea ice decline may influence global weather patterns, making the understanding of Arctic weather variability (WV) vital for accurate weather forecasting and analyzing extreme weather events. Quantifying this WV and its impacts under human-induced climate change remains a challenge. Here we develop a complexity-based approach and discover a strong statistical correlation between intraseasonal WV in the Arctic and the Arctic Oscillation. Our findings highlight an increased variability in daily Arctic sea ice, attributed to its decline accelerated by global warming. This weather instability can influence broader regional patterns via atmospheric teleconnections, elevating risks to human activities and weather forecast predictability. Our analyses reveal these teleconnections and a positive feedback loop between Arctic and global weather instabilities, offering insights into how Arctic changes affect global weather. This framework bridges complexity science, Arctic WV, and its widespread implications.

Introduction
Arctic sea ice is declining and thinning at an accelerating rate due to anthropogenic climate change1,2. The overall warming trend is double in the Arctic compared to the global average and is even higher in some Arctic regions3 due to a phenomenon known as Arctic amplification (AA)4–8. Arctic sea ice conditions can affect the Arctic ecosystem, wildlife, hunting, shipping, natural resource exploration and more9–11. As one crucial component of the complex Earth system12,13, changes in Arctic sea ice are found to have statistically observable and dynamic connections with regional and remote climatic phenomena14–17 (as shown in Fig. 1) through both large-scale atmospheric and oceanic circulations18–22. The rapid shrinking of the ice cover has attracted much attention to the Arctic sea ice teleconnections and predictions on seasonal-to-decadal time scales in recent years23–26. However, our understanding of the Arctic sea ice variability on weather time scales is still in its infancy27,28, despite the importance that it has for weather forecasting, the safety of commercial and subsistence maritime activities, the survival of polar mammals and the benefit of polar economics. The impact of day-to-day Arctic sea ice variations has been underestimated in most of the climate models29. To resolve this knowledge gap, here we employ complexity-based approaches and the climate network framework to investigate the daily weather variability (WV) of Arctic sea ice and assess its connections in relation to climate phenomena on different spatiotemporal scales. This includes processes such as the Arctic Oscillation (AO), climate change, and weather conditions both locally and at remote locations.

Complexity science employs the mathematical representation used by network science and provides a powerful tool to study the structure, dynamics and function of complex systems30. The climate system is a typical complex adaptive system due to its nonlinear interactions and feedback loops between and within different layers and components. In recent years, network science has been applied to the climate system to construct the climate network (CN)31. The CN is an innovative tool used to reveal and predict various important climate mechanisms and phenomena32, including forecasting of the El Niño Southern Oscillation33,34, the Indian summer monsoon rainfall35,36, the global pattern of extreme-rainfall37, the changes in the global-scale tropical atmospheric circulation under global warming38, teleconnections among tipping elements in the Earth system39, the Indian Ocean Dipole40 and other phenomena.

The AO is one of the major modes of atmospheric circulation over the mid-to-high latitudes of the Northern Hemisphere (NH)41, which influences climate patterns in Eurasia, North America, Eastern Canada, North Africa, and the Middle East, especially during boreal winter42–44. The AO index is defined as the leading empirical orthogonal function of NH sea level pressure (SLP) anomalies from latitudes 20°N to 90°N and is characterized by the shifting of atmospheric pressure between the Arctic and the mid-latitudes.

During the positive AO phase, the SLP is below average in the Arctic region and above average in the mid-latitudes. The jet stream is zonal and shifts northward, accompanied by a poleward shift of the storm tracks45. In line with these dynamics, our recent findings demonstrate more rapid changes in sea ice and air temperature within the NH’s mid-to-high latitudes, as evidenced by a blue-shifted frequency spectrum. This stands in contrast to the relatively stable weather conditions observed in the further southern mid-latitudes, which are characterized by a red-shifted spectrum. These patterns diverge from those seen during the negative AO phase, which exhibits higher-than-normal Arctic SLP. To quantify the blue-shift/red-shift effect indicating increased/reduced WV and its geographic distribution, here we introduce two innovative mathematical techniques: the advanced weighted autocorrelation function method, i.e., W_ACF and the advanced weighted power spectrum method, i.e., W_PS (see “Methods”).

By employing these methods, we are able to demonstrate that the enhanced day-to-day variability in the ice cover across much of the Arctic can be attributed to substantial declines in sea ice area46. This has serious consequences, such as the increased risk of severe weather due to climate change47–50. Further, it is also possible that changes in the Arctic may have some role in affecting the likelihood of extreme weather conditions globally, although this is subject to ongoing research.

Finally, we statistically verify the existence of these teleconnections between Arctic sea ice and weather conditions in remote global regions via a multivariate climate network framework. These teleconnections can result in a positive WV feedback loop between the Arctic and other global locations. This improves our understanding of the mechanisms that link AA and mid-latitude weather51. The presented results and methodology not only encourage a quantitative assessment of the risks posed by extreme weather events but also reveal the existence of pathways that permit the interaction or synchronization among regional and global climate components. Unveiling the interconnections between different climatic elements advances our understanding of climate dynamics and enhances the potential predictability of the Earth’s climate system.

Results
Linkage of the weather variability and the AO
The WV refers to the irregularity/predictability of the climate data at weather time scales (i.e., hours—days). There are various ways to evaluate data variability/irregularity, such as entropy52–54, the detrended fluctuation analysis55,56, correlation dimension57, Lyapunov exponents analysis58, etc. However, most of them would be problematic, biased or invalid when dealing with short and noisy data, like weather data. The standard deviation (SD) is an effective metric for quantifying the dispersion of data, but is not a good way to measure irregularity, e.g., the SD of randomly shuffled data is the same as the original. In addition, the autocorrelation function describes the speed at which the self-similarity of a variable decays with time59, and power spectral analysis60 allows us to discover periodicity within data. However, a comprehensive evaluation of the autocorrelation and the power spectrum, as well as their dynamic evolution for nonstationary climate data, is still lacking.

Therefore, we present two mathematical methods, W_ACF and W_PS (refer to the “Methods” section for detailed explanations), to measure the WV within and near the Arctic region on a monthly basis. These methods are applied to the daily data spanning from 1979 to 2019. These functions allow us to quantify the dynamic behavior of the Arctic WV spanning from January 1980 to December 2019. For a given time series, the physical meaning of these metrics is as follows: higher W_ACF values indicate a weaker short-term memory; while higher W_PS values suggest faster changes (high-frequency variations).

In particular, to better understand their physical interpretations, we generate various nonlinear time series (illustrated in Fig. 2a) using the following dynamical equations, where t is measured in days and belongs to the interval [1000, 10000].

x_t = cos(2\pi t/20), (1)

y_t = cos(2\pi t/10), (2)

zx_t = 0.2x_t + 0.8u_t, (3)

zy_t = 0.2y_t + 0.8u_t, (4)

The function u_{t+1} = \mu u_t(1 - u_t) represents a nonlinear logistic function, where we have set the parameter \mu = 3.8 and u_0 = 0.01. This specific parameter configuration results in the generation of chaotic behavior61. Mathematically, Eqs. (1) and (2) are two periodic functions but with periods of 20 days and 10 days, respectively. On the other hand, Eqs. (3) and (4) consist of a combination of an aperiodic term and a chaotic term (as shown in Fig. 2a).

Therefore, strictly speaking, the value of W_ACF for zx_t (zy_t) is higher than x_t (y_t), indicating weaker short-term memory caused by the presence of the chaotic term u_t. The value of W_PS for y_t (zy_t) is higher than x_t (y_t), indicating faster changes attributed to the distinct periods of the periodic term. We analyzed 31 consecutive data points from each sample, representing one month of climate data, using W_ACF and W_PS methods. The results presented in Fig. 2b, c support our theory, demonstrating that W_ACF and W_PS effectively describe the variability (both disorder and frequency) of the given time series.

In this study, we assess the WV of Arctic sea ice by employing W_ACF and W_PS based on the sea ice extent dataset (daily data from 1979 to 2019, see “Data” section for details). The results of our analysis are presented in Fig. 2d–h. The positive correlation coefficient r, represented by blue shading in Fig. 2d or e, suggests a positive correlation between the annual mean of the W_ACF or W_PS values with the AO index. We observe that both W_ACF and W_PS exhibit higher values, implying faster and more irregular day-to-day changes in ice cover during the AO positive phases compared to AO negative phases. This is particularly true in certain Arctic regions such as the Canadian Archipelago, Beaufort Sea, and Central Arctic. To illustrate the effect of the AO on the W_PS, we show that the power spectrum for Arctic sea ice during the positive AO phase, e.g., Jan. 1989, is significantly blue-shifted compared to the negative AO phase, e.g., Jan. 2010 (see Fig. 2f). Similarly, to illustrate the effect of the AO on the W_ACF, we show that the time series for the AO index and W_ACF are significantly synchronized during the period 1980-2019 (as shown in Fig. 2g, h). Moreover, we reveal that the climatic effects of the AO are more prominent in the winter-spring seasons than in summer-autumn (see Supplementary Figs. S1 and S2).

The underlying physical mechanism can be attributed to the characteristic atmospheric behavior of the AO and the close interactions between the Arctic sea ice and the surface atmosphere. During the positive phases of the AO, the northward shift of the jet stream and the displacement of storm tracks to higher latitudes62 (as illustrated in Supplementary Fig. S3) contribute to increased regional weather variability in the mid-to-high latitudes of the Northern Hemisphere (NH). Consequently, this leads to higher values of W_ACF and W_PS in the air temperature data, as depicted in Fig. 3 and Supplementary Fig. S3. Conversely, during negative AO phases, the Arctic region exhibits lower values of W_ACF and W_PS in air temperature, indicating higher predictability of weather63,64. Simultaneously, in the mid-latitudes of the NH, the W_ACF and W_PS of air temperature increase with the occurrence of significant weather events such as cold events, frozen precipitation, and blocking days62. This occurs as the zonal wind weakens during negative AO phases, as depicted in Fig. 3 and Supplementary Fig. S3.

In particular, as shown in Supplementary Fig. S4, we observe notable connections between the AO and WV within specific regions of the Southern Hemisphere (SH). These correlations between WV and the AO in the SH are noteworthy due to their significant seasonal fluctuations. A more detailed examination reveals a correspondence between these correlations and the position of the jet stream. Areas along the jet stream belt in the SH demonstrate significant correlation coefficients, and these coefficients display a marked seasonal divergence, especially between summer and winter. This pattern hints at a mutual influence between the positions and strengths of the jet streams in the northern and southern hemispheres, thereby underscoring the interconnectedness of atmospheric dynamics across hemispheres and the global implications of the AO. Moreover, the seasonality of these correlations emphasizes the importance of considering seasonal variations and their interaction with the AO when assessing the impacts of this atmospheric phenomenon on weather patterns.

Overall, the analysis of W_ACF and W_PS provides an additional quantitative approach to understanding the response of Arctic sea ice and the atmosphere to the AO. This methodology can be utilized to assess the risk of extreme events in the mid-to-high latitudes of the NH, enhancing our understanding of the relationships between the AO, weather variability, and the potential occurrence of extreme events in these regions.

Increased irregularity of Arctic sea ice cover
Using the past four decades (1980–2019) of data, our analysis reveals an evident upward trend in the weather variability linked to the day-to-day changes in the ice cover within a substantial region of the Arctic, with a specific concentration in and near the Central Arctic (see Fig. 4b, c). This increasing trend is supported by a notable rise observed in both the W_ACF and W_PS values. Figure 4 demonstrates that during this period, a significant proportion of Arctic nodes show a significant increase in the values of W_ACF or W_PS when comparing values for the same months in earlier years (see Fig. 4a).

The observed increasing trend in WV can be attributed to two main factors. First, advancements in remote sensing and data analysis technology have led to improved data resolution and accuracy throughout the observation record. Second, the rise in air temperature has played a substantial role in the thinning of sea ice65, with the rapid decline in multiyear ice cover being particularly influential in enhancing WV levels. The multiyear sea ice has been defined as the ice that survives at least one summer melt and represents the thick sea ice cover, while the first-year ice refers to the ice that has only one year of growth or less. As more perennial ice cover is replaced by younger and thinner ice cover, the regional ice cover becomes more fragile and vulnerable to fluctuations in air temperature or other forces46.

Supporting our findings, Supplementary Fig. S5 illustrates a substantial decline in sea ice thickness within the same period (1980–2019) in regions exhibiting a significant enhancing trend of WV. To further examine the relationship between increased WV and decreased multiyear sea ice cover in the Arctic, we conducted additional analysis (Supplementary Fig. S6). These results show that sub-regions of the Arctic with no significant trends in ice cover thinning also exhibit no significant trends in increasing weather variability. However, in most regions experiencing significant trends of ice cover thinning, there is a notable increase in weather variability. These findings provide further evidence for the connection between declining thick perennial ice cover and heightened WV in the Arctic region.

Moreover, we observe a higher occurrence of significant trends indicating enhanced instability during the melt season under global warming, as shown in Fig. 4a. This is because during the melt season (Apr.-Aug.), sea ice declines and fluctuates more dramatically than in other seasons. The distinct variability in weather patterns across different calendar months suggests the presence of a predictability barrier, particularly in June when both W_ACF and W_PS reach their peak values. The enhanced weather variability during this period makes weather prediction more challenging and less predictable. Additionally, an intensification of summer Arctic storm activity is also anticipated as the land-sea thermal contrast increases under global warming66–68. This could increase the WV in both the ocean and the atmosphere.

Arctic-global teleconnection patterns
Next, we propose the multivariate climate network approach to statistically reveal the potential teleconnection patterns between Arctic sea ice (Supplementary Fig. S7a) and the global air temperature field (Supplementary Fig. S7b); see more details in “Methods”. Unlike traditional climate network approaches that focus on single climate variables (see refs. 32, 69 and references therein), our approach constructs climate networks with links connecting nodes in the Arctic (Supplementary Fig. S7a) to nodes located elsewhere in the world (Supplementary Fig. S7b). Each link in the network quantifies the similarity of the temporal evolution between two different climate variables: Arctic sea ice and global air temperature. The statistical significance of each link is determined through a comparison with the null model (refer to “Methods” for specifics).

By applying the multivariate climate network, we are able to detect significant synchronizations between Arctic sea ice and global air temperature variations. In Fig. 5a, a typical link is observed, indicating a strong synchronization between the daily sea ice cover for one Arctic node and the air temperature for another remote global node during December 2018 (the corresponding time series are depicted in Supplementary Fig. S8). Specifically, Supplementary Fig. S8 illustrates that temperature changes at the node located in the Sichuan Province of Southwest China (30°N, 105°E) precede variations in sea ice at the Arctic node (77.5°N, 160°E) by a span of five days. This indicates that the evolution of air temperature in Southwest China can influence Arctic sea ice anomalies. To gain deeper insights into the relationship between sea ice and distant air temperature variability, we utilize the shortest path method (see “Methods” for more details) to identify the most likely teleconnection propagation path.

We discover a potential propagation path for this teleconnection, depicted in orange in Fig. 5a, which corresponds to negative wind anomalies from Southwest China to the Arctic. Additionally, we consider the feedback in the opposite direction. However, we observe a relatively weaker connection, specifically following a straight line from the Arctic to Southwest China via Eastern Russia and Mongolia. From a meteorological perspective, our analysis is highly consistent with wind climatology (refer to the background information in Fig. 5a). These two propagation paths form an interactive loop that suggests a large-scale atmospheric WV feedback between the Arctic and Southwest China. Remarkably, we have identified similar propagation paths in other months, such as February 1998 (Fig. 5b and Supplementary Fig. S9). To further substantiate the robustness of this feedback loop, we construct climate networks based on the similarity between Arctic and global air temperature variations during longer time durations. Specifically, we analyze time series spanning the past 40 years (1980–2019) (as shown in Fig. 5c), as well as time series spanning the most recent 30, 20, or 10 years (as illustrated in Supplementary Fig. S10a–c). Strikingly, these extended time series analyses consistently reveal that the propagation paths exhibit similar patterns akin to those observed during individual months. In particular, we observe a negative anomalous wind flow from Southwest China to the Arctic, followed by an early straight-line path from the Arctic back to Southwest China, thereby forming a feedback loop. This consistency across different time spans underscores the robust nature of these teleconnections between the Arctic and Southwest China, as they closely follow large-scale atmospheric circulation patterns.

Moreover, we observe another notable teleconnection (California and Arctic) as depicted in Fig. 5d–f. This teleconnection pathway, similar to the previous one observed between Southwest China and the Arctic, is characterized by negative zonal wind anomalies, indicating that fluctuations in air temperature in California can influence Arctic sea ice. Conversely, changes in Arctic sea ice can also impact temperature fluctuations in California, albeit to a lesser extent, along upper wind routes in the opposite direction (more details are shown in Supplementary Fig. S11). The teleconnection path between the Arctic and California, as depicted in Fig. 5d for March 2019, demonstrates similar patterns in other months, such as January 2000 (see Fig. 5e and Supplementary Fig. S12). These patterns remain consistent throughout the time spans of the past 40 years (see Fig. 5f), as well as 30, 20, and 10 years (Supplementary Fig. S10d–f). These teleconnections persist across different time periods and reinforce the potential for Arctic sea ice decline to contribute to droughts and wildfires in California70.

The synchronization of day-to-day weather between the Arctic and other regions can favor positive feedbacks in WV, whereby an increase in WV/instability of Arctic sea ice may amplify the risk of extreme weather conditions in distant global regions. Conversely, impacts from global regions can also induce unstable weather conditions in the Arctic. These mutual interactions emphasize the potential for cascading effects within the Earth’s climate system, where changes in one region can amplify weather variability and contribute to consequential weather events in remote areas.

Methods
Data
This study primarily utilizes two variables: the daily sea ice cover and the air temperature at the 850 hPa pressure level at 0 hr (UTC). The sea ice cover refers to the fraction of a grid box that is covered by sea ice. It provides information on the extent of sea ice within each grid box. The air temperature at the 850 hPa pressure level represents the atmospheric temperature at a specific vertical level above the Earth’s surface. This pressure level is chosen because it is just above the boundary layer, which helps avoid direct interactions between the sea ice and the surface atmosphere26. These data were extracted from the ERA5 reanalysis datasets, which can be obtained from the European Centre for Medium-Range Weather Forecasts (ECMWF) website80. The spatial resolution of the data is 2.5° in both the zonal (latitude) and meridional (longitude) directions.

To ensure global coverage, we selected a total of 8040 grids from the air temperature datasets, distributing them approximately equally across the globe (refer to Supplementary Fig. S7b for further details). Within these selected grids, we identified 377 grids located in the Arctic region over the ocean, which exhibited non-zero sea ice cover for at least one day (refer to Supplementary Fig. S7a for visualization). For each calendar year y and for each grid point, we calculated the anomalous value for each calendar day t by subtracting the original value from the corresponding climatological average and then dividing by the climatological standard deviation. The calculations for the climatological average and standard deviation were based on data spanning the period from 1979 to 2019. Leap days were excluded to maintain consistency in the calendar year duration and simplify the analysis.

The wind data at 500 hPa pressure level was extracted from ERA5 reanalysis datasets, with a temporal resolution of daily and monthly. The AO index data was obtained from the following URL: https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/monthly.ao.index.b50.current.ascii [Accessed in Sep. 2021].

The Arctic Sea Ice extent, sourced from the National Snow and Ice Data Center (NSIDC) and depicted as the blue curve in Fig. 4a, was acquired from the URL: https://nsidc.org/data/g02135/versions/3 [Accessed in Jan. 2021]. The Sea Ice extent data product is based on gridded fields of sea ice concentration data derived from passive microwave radiometers and is commonly used for monitoring and analyzing changes in Arctic sea ice extent over time81.

The dataset used to analyze the thinning of ice cover in the Arctic is sourced from NSIDC and obtained from the URL: https://nsidc.org/data/nsidc-0611/versions/4. It provides weekly estimates of sea ice age for the Arctic Ocean, which are derived from remotely sensed sea ice motion and sea ice extent. The dataset covers the time period from January 1984 to December 2021, with a spatial resolution of 12.5 km by 12.5 km. In our analysis, the ratio of thin ice cover refers to the fraction of the area within a specific Arctic sub-region (as illustrated in Supplementary Fig. S6) that is covered by first-year ice or has a sea ice concentration of less than 15%. A rising proportion of thin ice signifies the melting of the Arctic’s ice cover under global warming.

Assessing weather variability
The autocorrelation function (ACF) is widely used to measure the memory of a time series and reveal how the correlation between any two values of the signal changes as their time lag59. For a given time series denoted as x_t, the ACF is defined as follows:

C(\tau) = Cov(x_t, x_{t+\tau}) / \sqrt{Var(x_t) Var(x_{t+\tau})}, (5)

where Cov(X,Y) = E[(X - E[X])(Y - E[Y])] and Var(X) = E[X^2] - E[X]^2. If x_t is completely uncorrelated, for example, a white noise process, C(\tau) is zero at all lags except a value of unity at lag zero (\tau = 0). A correlated process, on the other hand, has nonzero values at lags other than zero, which indicates a correlation between different lagged observations. In particular, the short-range memory of x_t is described by C(\tau), which declines exponentially

C(\tau) \sim exp(-\tau/\tau*), (6)

with a characteristic time scale, \tau*. For long-range memory, C(\tau) declines as a power-law

C(\tau) / \tau^{-\gamma}, (7)

with an exponent 0 < \gamma < 1. However, a direct calculation of C(\tau), \tau* and \gamma is usually not appropriate due to noise superimposed on the collected data x_t and due to underlying trends of unknown origin82. To overcome these challenges, we propose an advanced weighted autocorrelation function, W_ACF, to quantify the memory strength, encompassing both short and long-range correlations in the time series. It is defined as follows:

W_ACF = max(|C(\tau)|) - mean(|C(\tau)|) / Var(|C(\tau)|) - mean(|C(\tau)|) / Var(|C(\tau)|), (8)

Here, max(|C(\tau)|) and mean(|C(\tau)|) represent the maximum and mean values of the absolute autocorrelation function |C(\tau)|, respectively. \tau belongs to the interval [-\tau_{max}, \tau_{max}], which represents the range of time lags considered. In the present work, we consider a maximum time lag of \tau_{max} = 10 days since we are considering the day-to-day changes in data at the time scale of weather forecasting, i.e., within two weeks. Equation (8) describes the fluctuations of the ACF, and its values reveal the strength of memory, i.e., a higher (smaller) W_ACF indicates a weaker (stronger) correlation and results in a weak (strong) memory. For example, white noise has a maximum value W_ACF = \sqrt{(2\tau_{max} + 1)} / (2\tau_{max} + 1). Other examples are described in Fig. 2.

An essential advantage of our method is that it captures the memory strength of the data and provides a robust measure of irregularity, even with limited data points. In contrast, many other methods, such as entropy-based measures and detrended fluctuation analysis (DFA), suffer from reduced accuracy or validity when applied to shorter time series. This aspect makes our method particularly advantageous in situations where data availability is limited, enabling meaningful analysis and assessment of irregularity despite the shorter time series. This also enables the examination of how irregularity evolves and changes over time, uncovering potential trends or patterns in the data. Another significant advancement of our method is its ability to address problematic nonstationarities.

To demonstrate the effectiveness of the W_ACF method in eliminating the influence of data length and nonstationarity, we apply our method to artificial model data with known properties, the MIX(p) stochastic processes52 and the Logistic map. The MIX(p) time series, with p ranging between 0 and 1, can be informally described as a sine wave with random noise, where N \times p randomly selected points are replaced with random noise values. This substitution introduces irregularity, which escalates as the p increases. On the other hand, the irregularity of a Logistic map, given by the equation x_{t+1} = \mu x_t(1 - x_t), is controlled by the parameter \mu. Both the MIX(p) time series and the Logistic maps provide controlled different irregularity levels.

Subsequently, we calculated the W_ACF for time series of varying lengths (i.e., N = 30 and 100) and different types of trends. Specifically, we generated multiple sets of MIX(p) time series and logistic maps, to which we added strong monotonous trends (1000t^b) with varying power b = 1/2, 1 and 2, or oscillatory trends (10 sin(2\pi tf)) with different frequencies f = 1/500 and 1/1000, following the approach outlined in ref. 82. The results, as depicted in Supplementary Fig. S13, clearly illustrate that the W_ACF accurately reflects the irregularity of the data, regardless of strong and slow (monotonic or periodic) trends being superimposed on the raw data. This substantiates the robustness and reliability of our method in managing nonstationarities and capturing the inherent data irregularity.

Additionally, our approach remains effective even for shorter data series with N = 30, enabling us to capture and scrutinize patterns of variability effectively. By partitioning the time series into smaller portions, we gain the ability to monitor shifts in data variability over time. This process affords us valuable insight into the dynamic nature of the system under investigation. However, it is important to note that the shortest length that makes the W_ACF method valid may vary for different real-world systems, depending on the intrinsic characteristics of the system under study. It is therefore essential to carefully consider the specific properties and dynamics of the data when determining the appropriate segment length for analysis.

The advanced autocorrelation function W_ACF sufficiently quantifies the memory for an arbitrary time series but does not reveal any information about the frequency content. For example, Eqs. (1) and (2) are two functions with different periods. Their W_ACF values are almost the same, as shown in Fig. 2. To fill this gap, we further develop an advanced power spectrum (PS) method. Based on Welch’s method83, we define the advanced weighted power spectral density W_PS as,

W_PS = \int P(f) \times f df, (9)

where P(f) is the normalized spectral density and f stands for the frequency. Notably, a relatively higher value of the W_PS indicates a larger ratio of the high-frequency components (i.e., blue shift), see examples shown in Fig. 2.

Climate networks
Unlike the classical climate network, which only uses single node classification, see refs. 32, 84 and references therein, here, we define two types of nodes: global nodes i with the air temperature variable T_i(t) and Arctic nodes j with the Arctic sea ice cover variable I_j(t). We thus have 8040 global nodes (as shown in Supplementary Fig. S7b) and 377 Arctic nodes (as shown in Supplementary Fig. S7a).

We constructed a multivariate climate network for each month from Jan. 1980 to Dec. 2019. To obtain the strength of the links between each pair of nodes i and j, we computed, for each month m, the time-delayed, cross-correlation function

C_m(\tau) = <T_m^i(t) I_m^j(t-\tau)> - <T_m^i(t)> <I_m^j(t-\tau)> / \sqrt{Var(T_m^i(t)) Var(I_m^j(t-\tau))}, (10)

C_m(-\tau) = <T_m^i(t-\tau) I_m^j(t)> - <T_m^i(t-\tau)> <I_m^j(t)> / \sqrt{Var(T_m^i(t-\tau)) Var(I_m^j(t))}, (11)

where the bracket < > denotes an average over consecutive days during a given month m, and \tau \in [0, \tau_{max}] is the time lag. Since we mainly focus on the dynamic WV in the Arctic, here we chose the maximal time lag \tau_{max} = 20 days for Eqs. (10) and (11).

We identified the time lag \theta at which the absolute value of the cross-correlation function |C_m(\tau)| reached its maximum. The weight of link (i,j)_m was defined as the corresponding value of the cross-correlation function, i.e., C_m^{i,j} = C_m(\tau = \theta). Therefore, the weight of each link could be either positive or negative, but with the maximum absolute value. The sign of \theta indicates the direction of each link; that is, when the time lag is positive (\theta > 0), the direction of this link is from j to i, and vice versa85.

Next, we investigated the statistical significance of the link weights in the real networks by comparing them to the shuffled surrogate networks. In the surrogate networks, we calculated the link weights by utilizing two data segments, each consisting of 30 consecutive days. These segments were randomly selected from the period between Jan. 1980 and Dec. 2019. The purpose of this selection was to ensure that there were no actual correlations between the nodes in the temporal dimension.

We constructed 100 surrogate networks using this strategy and established a significance threshold, denoted as q, for each link. This threshold for a specific link was determined as the 95th percentile of the absolute weights for the same link in the surrogate networks. For the real network, specifically for a particular month m, we classified the link (i,j)_m as significant if its weight exceeded q or fell below -q. Mathematically, this can be represented as |C_m^{i,j}| > q.

Constructing climate networks spanning longer time spans involves calculating time-delayed cross-correlation functions (Eqs. (10) and (11)) between pairs of nodes using data records ranging from 10 to 40 years. To assess the significance of the links connecting Arctic nodes to global nodes, null model is created by shuffling the order of years in the original climate data. This approach allows for the examination of long-term relationships between climate variables and the identification of robust connections between the Arctic and the globe.

Teleconnection path mining
To identify the teleconnection path, we apply the shortest path method to complex networks to find the optimal paths in our climate networks. A path is a sequence of nodes in which each node is adjacent to the next one, in particular, in a directed network, the path can follow only one direction. Here, our climate network is based on only one climate variable—air temperature at the 850 hPa pressure level, and we select 726 nodes from the 10,512 nodes36,39. This selection is made to manage computational complexity. For each climate network link (i,j)_m, we define its cost function value as

E_m^{i,j} = 1 / |C_m^{i,j}|, (12)

The Dijkstra algorithm86 was used to determine the directed optimal path between a source node i and a sink node j with the following constraints39,87: (1) the distance for each step is limited to less than 1000 km. However, should we fail to identify a path, the distance is then adjusted to 1500 km; (2) the link time delay \theta \ge 0, ensuring that all steps have the same direction; (3) the sum cost function value for a collection of links through path i -> j is minimal. In this way, we identify the optimal paths that information/energy/matter follow in two-dimensional space.

Data availability
The ERA5 reanalysis data used here are publicly available at: https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels. The Arctic Oscillation data used here are publicly available at: https://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/monthly.ao.index.b50.current.ascii. The Arctic Sea Ice extent data used here are publicly available at: https://nsidc.org/data/g02135/versions/3 and https://nsidc.org/data/nsidc-0611/versions/4. All other data that support the plots within this paper and other findings are provided as a Source Data file and in a Zenodo repository88.

Code availability
The analysis codes used in this study have been deposited in Zenodo88.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper by Meng et al “Dynamic Arctic weather variability and connectivity” applies several techniques to datasets of Arctic sea ice and Arctic Oscillations to establish patterns and dependencies in the region.\nI think the paper has interesting results, but it requires further improvement in a major revision. The English language of the paper need to be improved in many aspects, so I would recommend service of a professional editor.\nThe title of the paper contains a tautology: variability is already dynamic, so word “dynamic” has to be omitted, and the title should be “Arctic weather variability and connectivity”.\nIn several places there are contradictions between weather scale (up to 2 weeks) and longer climatic scale (page 6). This should be corrected, as speaking of weather variability is possible only in short-term scale.\nThe introduced “advanced autocorrelation function method”, according to Equation 8, is not really a function but a single value for each time series. Introducing such a technique in a small supplement section without thorough testing on artificial data is not convincing, in my opinion. The technique requires clear illustration on data with known properties. Claiming that it removes effect of trends (page 16) should be supported by analytical derivation or numerical simulations.\nThe proposed “advanced power spectrum method” integrates over a range of frequencies. Why then, in Figure 2, panel c, the units in the legend for W_{PS} are 1/day? Was it calculated for a frequency band around 1/day? If so, this should be clearly explained and justified.\nIt is not clear what the authors mean by ice cover: extent or volume? Please check the dataset documentation. In page 15, the authors say that they use daily sea ice cover of ERA5, but then mention NSIDC sea ice extent – so what sea ice data was actually analysed?\nIn Figure 4, panel (a) clearly shows monthly data, but the caption discusses daily weather variability – how can this be explained?\nIn page 8, first line of 2nd paragraph, “its” – whose?\nIn figure 3, period 1980-2019 – is this period of average or does it mean that two columns correspond to two years, 1980 and 2019?", "reviewer_2": "Review of Meng et al 2023\n“Dynamic Arctic weather variability and connectivity”\nNature Communications\nThis paper uses statistical techniques to examine Arctic weather variability and teleconnections from the Arctic. The statistical approaches are interesting and provide a new perspective on some of these problems but I don’t think the current study is coherent and suffers from looking at a few things in little detail. Here are some of the specific conclusions from the paper:\n• “Weather variability” is correlated with the Arctic Oscillation: I think this is well supported by the paper.\n• Variability is decreasing due to thinner ice cover: The authors demonstrate the decrease in variability but do not show the link between thinner ice cover, they just point to other papers.\n• Identify Arctic teleconnections: The authors use an interesting technique here but only apply to it two months from the 40+ year record so it is hard to estimate whether this is robust and representative. I think for the paper to be accepted, I would suggest a much more thorough analysis throughout the entire record.\n• Identify feedback loops through Arctic teleconnections: This is the weakest part of the paper. It is hard for me to understand how robust these linkages are, how much of an impact they have and whether this feedback is stabilising or destabilising.\nOverall the study presents interesting complexity science approaches as applied to understanding the Arctic but does not present a strong story or advance our understanding significantly. I suggest the authors think about presenting one component of the story in a more robust and detailed way, or submit to a journal which accepts longer papers so that each component of the story can be developed fully.\nI note that I do not feel qualified to assess the use of the statistical approaches in this study. I will focus on the climate response which is more in the domain of my expertise.\nLine numbers would be appreciated to enable easy reviewing.\nP1: “disrupting the balance of nature” is subjective and should be rephrased\nP2: Other recent references which may be of interest:\nEngland, M., I. Eisenman, N. Lutsko and T. Wagner (2021), The recent emergence of Arctic Amplification, Geophysical Research Letters, 48, e2021GL094086, doi: 10.1029/2021GL094086\nChylek, P., Folland, C., Klett, J. D., Wang, M., Hengartner, N., Lesins, G., & Dubey, M. K. (2022). Annual mean Arctic Amplification 1970–2020: Observed and simulated by CMIP6 climate models. Geophysical Research Letters, 49, e2022GL099371. https://doi.org/10.1029/2022GL099371\nFigure 1: It is hard for the reader to assess the accuracy of the schematic on the left. The graphic is visually appealing but it is hard to evaluate how scientifically relevant it is. The authors repeatedly point to this figure as evidence or an explanation but it is unconvincing.\nP5: I am skeptical that the reported Southern Hemisphere impacts of the AO are robust. Can the authors present some mechanism to explain this regional signature?\nP7: Choosing two months from the whole record to explore Arctic teleconnections doesn’t seem a robust approach."}, "author_response": "Reviewer #1:\nThe paper by Meng et al “Dynamic Arctic weather variability and connectivity”\napplies several techniques to datasets of Arctic sea ice and Arctic Oscillations to\nestablish patterns and dependencies in the region.\nResponse: We appreciate the referee's accurate summary of our study.\nI think the paper has interesting results, but it requires further improvement in a\nmajor revision.\nResponse: We are grateful for the referee's positive remarks on our manuscript and\nhis/her constructive suggestion for a major revision. We have worked diligently to\nincorporate these improvements in our revised manuscript.\nThe English language of the paper need to be improved in many aspects, so I would\nrecommend service of a professional editor.\nResponse: We thank the reviewer for their insightful recommendation regarding the\nlanguage quality of our manuscript. To address this, we have sought the expertise of\nprofessional editors to ensure clarity, precision, and readability throughout our\nmanuscript.\nThe title of the paper contains a tautology: variability is already dynamic, so word\n“dynamic” has to be omitted, and the title should be “Arctic weather variability and\nconnectivity”.\nResponse: We thank the referee for pointing out the redundancy in the title. We\nappreciate this feedback and have revised the title to \"Arctic weather variability and\nconnectivity.\"\nIn several places there are contradictions between weather scale (up to 2 weeks) and\nlonger climatic scale (page 6). This should be corrected, as speaking of weather\nvariability is possible only in short-term scale.\nResponse: We are grateful to the referee for identifying this potential source of\nconfusion. Our sincere apologies for any confusion caused by the contradictory\nreferences to weather and climate scales in our paper.\nTo clarify, our investigation of weather variability employs measures of (cid:1849) and\n(cid:3002)(cid:3004)(cid:3007)\n(cid:1849) on a monthly basis. Each of these metrics represents the irregularity of daily\n(cid:3017)(cid:3020)\nweather fluctuations within a specified month for each grid point, enabling us to track\nand analyze the changes in weather variability over time, and interpret the impact of\nthe Arctic Oscillation (AO), as shown in Fig.2g in the main text.\nThe annual indices were computed by averaging the monthly values of (cid:1849) and\n(cid:3002)(cid:3004)(cid:3007)\n(cid:1849) over a year (refer Fig. 2 and 3 in the main text). This average provides a\n(cid:3017)(cid:3020)\nconsolidated measure of weather variability for the entire year, effectively reducing\nspurious correlations introduced by seasonality.\nMoreover, we explored the correlation between weather variability and AO on a\nseasonal basis, ensuring we compared months from the same season for accurate\nanalysis (refer Fig. S1-S4 in the supplementary information).\nWe sincerely hope that this response clarifies our approach and provides a better\nunderstanding of the ways we differentiated between weather and climatic scales.\nThe introduced “advanced autocorrelation function method”, according to Equation\n8, is not really a function but a single value for each time series. Introducing such a\ntechnique in a small supplement section without thorough testing on artificial data is\nnot convincing, in my opinion. The technique requires clear illustration on data with\nknown properties. Claiming that it removes effect of trends (page 16) should be\nsupported by analytical derivation or numerical simulations.\nResponse: We sincerely appreciate the referee's valuable feedback and acknowledge\nthe importance of validating new methodologies. We understand the concerns raised\nregarding the \"advanced autocorrelation function method\" and its validation.\nTo address this, we have conducted further analysis on artificial model data with\nknown properties to demonstrate the effectiveness of the (cid:1849) method in removing\n(cid:3002)(cid:3004)(cid:3007)\nthe influence of trends and capturing the inherent irregularity.\nSpecifically, we applied our technique to two distinct types of time series with known\nirregularity patterns: the MIX(p) stochastic processes [1] and the Logistic map. The\nMIX(p) time series, characterized by a length of N and p ranging from 0 to 1, can be\ninformally depicted as a sine wave contaminated with random noise. Here (cid:1840)×(cid:1868)\npoints selected randomly are replaced with noise values. This substitution introduces\nirregularity, which escalates as the p increases. Conversely, the irregularity of the\nLogistic map, described by the equation (cid:1876) = (cid:2020)(cid:1876) (1−(cid:1876) ), is controlled by the\n(cid:3047)(cid:2878)(cid:2869) (cid:3047) (cid:3047)\nparameter (cid:2020). Both MIX(p) time series and Logistic map provide controlled\nparameters to adjust the level of irregularity, allowing for a comprehensive evaluation\nof the (cid:1849) method across different irregularity levels.\n(cid:3002)(cid:3004)(cid:3007)\nSubsequently, we calculated the (cid:1849) for time series of different lengths ((cid:1840) =\n(cid:3002)(cid:3004)(cid:3007)\n30 (cid:1853)(cid:1866)(cid:1856) 100) and various types of trends. Specifically, we generated multiple sets of\nMIX(p) time series and Logistic map and imposed strong monotonous trends of\n1000(cid:1872)(cid:3029) with varying powers (cid:1854) = (cid:2869) ,1,2 , or oscillatory trends of 10sin2(cid:2024)(cid:1872)(cid:1858) with\n(cid:2870)\n(cid:2869) (cid:2869)\ndifferent frequencies (cid:1858) = , , following the approach outlined in Ref. [2]. The\n(cid:2873)(cid:2868)(cid:2868) (cid:2869)(cid:2868)(cid:2868)(cid:2868)\nresults depicted in Fig. 1 in this letter (corresponding to Fig. S13 in the supplementary\ninformation) distinctly illustrate the (cid:1849) method's capability to accurately portray\n(cid:3002)(cid:3004)(cid:3007)\ndata irregularity, regardless of strong and slow (monotonic or periodic) trends being\nsuperimposed on the raw data. This substantiates the robustness and reliability of our\nmethod in managing non-stationarities and capturing the inherent data irregularity.\nAdditionally, our approach remains effective even for shorter data series with (cid:1840) =\n30, enabling us to capture and scrutinize patterns of variability effectively. By\npartitioning the time series into smaller portions, we gain the ability to monitor shifts\nin data variability over time. This process affords us a valuable insight into the\ndynamic nature of the system under investigation. However, it is important to note\nthat the shortest length that makes the (cid:1849) method valid may vary for different\n(cid:3002)(cid:3004)(cid:3007)\nreal-world systems, depending on the intrinsic characteristics of the system under\nstudy. It is therefore essential to carefully consider the specific properties and\ndynamics of the data when determining the appropriate segment length for analysis.\nWe have incorporated a detailed description of these analyses and their results in the\nMethod Section (lines 369-395) to provide a comprehensive understanding of the\nmethod's validation using artificial data.\nWe would like to express our sincere gratitude to the referee for the valuable feedback\nand constructive criticism. Your insights have significantly contributed to the\nimprovement and strengthening of our manuscript.\nFig.1: An intuitive demonstration of the effectiveness of (cid:1849) in quantifying the\n(cid:3002)(cid:3004)(cid:3007)\nvariability of non-stationary data. The (cid:1849) values are calculated for the MIX(p)\n(cid:3002)(cid:3004)(cid:3007)\nmodel (a,b) and Logistic models (c,d), which exhibit strong monotonous trends of the\nform 1000(cid:1872)(cid:3029) with varying power values (b=2, 1, and 0.5), as well as superimposed\noscillatory trends of the form 10sin2(cid:2024)(cid:1872)(cid:1858) with different frequencies (f=1/500,\n1/1000). The (cid:1849) consistently changes with parameters (p and μ) that control the\n(cid:3002)(cid:3004)(cid:3007)\nchaotic behavior of the data. N represents the length of the time series, and each\n(cid:1849) value is obtained by averaging over 100 realizations.\n(cid:3002)(cid:3004)(cid:3007)\nThe proposed “advanced power spectrum method” integrates over a range of\nfrequencies. Why then, in Figure 2, panel c, the units in the legend for W_{PS} are\n1/day? Was it calculated for a frequency band around 1/day? If so, this should be\nclearly explained and justified.\nResponse: We appreciate the referee for bringing this issue to our attention. The units\nfor (cid:1849) in Figure 2, panel c, are indeed 1/day, which represents that it was\n(cid:3017)(cid:3020)\ncalculated for a frequency band around 1/day. The choice of this specific frequency\nband was determined by the nature of our data, which consists of daily measurements.\nThis alignment ensures compatibility and facilitates meaningful comparisons within\nthe same timescale.\nTo clarify, in our analysis, we employed time series data measured in days, which\naligns with the units of the climate data used in our study.\nThe time series were generated according to the equations provided:\n(cid:1876) = cos(2(cid:2024)(cid:1872)/20) (1)\n(cid:3047)\n(cid:1877) = cos(2(cid:2024)(cid:1872)/10) (2)\n(cid:3047)\n(cid:1878)(cid:3051) = 0.2(cid:1876) +0.8(cid:1873) (3)\n(cid:3047) (cid:3047) (cid:3047)\n(cid:3052)\n(cid:1878) = 0.2(cid:1877) +0.8(cid:1873) (4)\n(cid:3047) (cid:3047) (cid:3047)\nwhere t is measured in days and belongs to the interval [1000, 10000]. The\nfunction(cid:1873) = (cid:2020)(cid:1873) (1−(cid:1873) ) represents the nonlinear logistic function, where we\n(cid:3047)(cid:2878)(cid:2869) (cid:3047) (cid:3047)\nhave set the parameter (cid:2020) = 3.8 and (cid:1873) = 0.01. This specific parameter\n(cid:2868)\nconfiguration leads to the emergence of chaotic behavior.\nIt is not clear what the authors mean by ice cover: extent or volume? Please check the\ndataset documentation.\nResponse: Thank you for this important clarification. The term \"ice cover\" used in\nour study refers to the fraction of a grid box covered by sea ice in the ERA5 dataset.\nTherefore, it reflects the extent, rather than the volume, of sea ice within each grid\nbox. We have carefully reviewed the dataset documentation and amended the text.\nIn page 15, the authors say that they use daily sea ice cover of ERA5, but then\nmention NSIDC sea ice extent – so what sea ice data was actually analysed?\nResponse: We apologize for any confusion arising from the mention of different\ndatasets in our manuscript. In our analysis, we indeed used both the daily sea ice\ncover data from ERA5 and the monthly sea ice extent indices from NSIDC. The daily\ndata from ERA5 was used to analyze weather variability, as it provides\ncomprehensive information by combining model data with observations from various\nsources. This choice ensures that the daily data of sea ice and air temperature are from\nthe same source, enhancing consistency in our analysis, while the monthly data from\nNSIDC was used to assess the longer-term trend of Arctic sea ice extent. We opted for\nthe NSIDC data for convenience, as it is readily available for download and widely\nused for monitoring and analyzing changes in Arctic sea ice extent over time.\nWe have revised the manuscript to clarify the use of each dataset in the revised Data\nsection.\nIn Figure 4, panel (a) clearly shows monthly data, but the caption discusses daily\nweather variability – how can this be explained?\nResponse: We appreciate the referee's attention to detail. In Figure 4, panel (a), the y-\naxis indeed represents monthly data. However, this monthly data is derived from the\nanalysis of day-to-day weather variability ((cid:1849) and (cid:1849) ) within each specific\n(cid:3002)(cid:3004)(cid:3007) (cid:3017)(cid:3020)\nmonth. By comparing the same month, for instance, June, across all years from 1980\nto 2019, we can determine the ratio of Arctic nodes where the weather variability\nexhibits significant increasing (or decreasing) trends over time. In Figure 4(a), the y-\naxis index of each grey/purple point represents the proportion of nodes with\nstatistically significant increasing trends for the specific month indicated on the x-\naxis.\nIn the revised manuscript, we have clarified this point by stating that the weather\nvariability is quantified on a monthly basis using the daily data from 1979 to 2019\n(lines 104-106).\nIn page 8, first line of 2nd paragraph, “its” – whose?\nResponse: We apologize for any confusion caused by this unclear reference. In the\nsection 'Arctic-global teleconnection patterns,' we have revealed the potential\npropagation path through which changes in the temperature in Southwest China can\naffect sea ice variations in the Arctic. Furthermore, we have observed the influence of\nArctic sea ice on weather conditions in Southwest China in the opposite direction\nthrough large-scale atmospheric circulations. We refer to this phenomenon as a\nfeedback loop.\nTo provide further clarification, in the revised manuscript, we have improved the\nsentence as follows: We discover a potential propagation path for this teleconnection,\ndepicted in orange in Fig.5a, which corresponds to negative wind anomalies from\nSouthwest China to the Arctic. Additionally, we consider the feedback in the opposite\ndirection. However, we observe a relatively weaker connection, specifically follows a\nstraight line from the Arctic to Southwest China via Eastern Russia and Mongolia .\n(lines 219-223)\nIn figure 3, period 1980-2019 – is this period of average or does it mean that two\ncolumns correspond to two years, 1980 and 2019?\nResponse: We apologize for any confusion caused. In Figure 3, the period \"1980-\n2019\" refers to the time span of the data used for the analysis. It does not mean that\neach column corresponds to a specific year. The colors in the heatmap indicate the\ncorrelation between the annual mean of (cid:1849) or (cid:1849) and the Arctic Oscillation\n(cid:3002)(cid:3004)(cid:3007) (cid:3017)(cid:3020)\nindex over the entire period from 1980 to 2019. In the revised manuscript, we have\nclarified this to avoid any misunderstanding.\nReference:\n[1] Pincus, S. Approximate entropy (ApEn) as a complexity measure. Chaos 5, 110–\n117 (1995).\n[2] Kantelhardt, J. W., Koscielny-Bunde, E., Rego, H. H. A., Havlin, S. & Bunde, A.\nDetecting long-range correlations with detrended fluctuation analysis. Physica A:\nStatistical Mechanics and its Applications 295, 441–454 (2001).\nReviewer #2 :\nThis paper uses statistical techniques to examine Arctic weather variability and\nteleconnections from the Arctic. The statistical approaches are interesting and\nprovide a new perspective on some of these problems but I don’t think the current\nstudy is coherent and suffers from looking at a few things in little detail. Here are\nsome of the specific conclusions from the paper:\nResponse: We are grateful for the reviewer's positive comment on our statistical\nmethods and their potential to offer fresh perspectives. We acknowledge the concerns\nraised about the coherence and depth of our study and have made significant efforts to\naddress these points in the revised manuscript.\n• “Weather variability” is correlated with the Arctic Oscillation: I think this is well\nsupported by the paper.\nResponse: We appreciate reviewer's positive feedback regarding our analysis.\n• Variability is decreasing due to thinner ice cover: The authors demonstrate the\ndecrease in variability but do not show the link between thinner ice cover, they just\npoint to other papers.\nResponse: We appreciate the referee for raising this point. We think the referee\nmeant that: Variability is increasing due to ice cover being thinner. In response to this\nconcern, we have conducted further analysis to substantiate the correlation between\nthe thickness sea ice cover and weather variability (WV). In our study, we used the\nsea ice age (SIA) data to represent the sea ice thickness, higher (lower) SIA means\nthicker (thinner) ice cover. In Fig. 2 of this letter (which corresponds to Fig. S5 in the\nsupplementary information), we provided a depiction of the considerable decline in\nSIA by comparing 1985 and 2019 in regions, where we notice a marked increasing\ntrend in WV (denoted by the pink circles in Figs. 2a and 2b).\nTo further unveil the relationship between increased WV and decreased SIA in the\nArctic (12 sub-regions were chosen as shown in Fig. 2c), we conducted an additional\nanalysis, by plotting the temporal evolution of the ratio of area covered by thin ice\n(i.e. first year ice or ice concentration less than 15%), the averaged (cid:1849) and (cid:1849) ,\n(cid:3002)(cid:3004)(cid:3007) (cid:3017)(cid:3020)\nas depicted in Fig. 3 (corresponding to Fig. S6 in the supplementary information). In\nArctic sub-regions without significant thinning ice cover trends, we also observed no\nsignificant trends of increasing weather variability. However, notably, in most regions\ndemonstrating significant thinning ice cover trends, there was a pronounced increase\nin weather variability.\nThese findings suggest a potential relationship between changes in sea ice cover and\nthe variability in Arctic weather patterns. We have impended the above\naforementioned into the revised manuscript (lines 181-188).\nFig. 2: Decline of the multi-year sea ice cover. a, A sample image displaying sea ice\nage for the week of Jun. 3-10, 1985 (https://doi.org/10.5067/UTAV7490FEPB.\n[Accessed in Sep. 2021].). b, The same as a for the year 2019. Nodes with a\nsignificant trend of enhancing (cid:1849) or (cid:1849) as shown in Fig. 4 of the main text, are\n(cid:3002)(cid:3004)(cid:3007) (cid:3017)(cid:3020)\nmarked by pink circles. c, Depicts the 12 sub-regions of the Arctic. The colored points\nindicate grid points with non-zero sea ice cover for at least one day during the years\nfrom 1979 to 2019, according to ERA5 datasets.\nFig. 3: Temporal evolution of the ratio of area covered by thin ice (i.e., first year ice\nor ice concentration less than 15%), the averaged (cid:1849) and (cid:1849) for 12 subregions\n(cid:3002)(cid:3004)(cid:3007) (cid:3017)(cid:3020)\nshown in Fig. 2c. The dashed lines are the best fitting lines with significant trends.\n• Identify Arctic teleconnections: The authors use an interesting technique here but\nonly apply to it two months from the 40+ year record so it is hard to estimate whether\nthis is robust and representative. I think for the paper to be accepted, I would suggest\na much more thorough analysis throughout the entire record.\nResponse: We appreciate the referee's insightful feedback. In our study, we have\naddressed this issue by providing a more detailed analysis of the teleconnections over\nthe entire 40-year record, emphasizing the robustness and representativeness of our\nfindings, covering the period from 1980 to 2019. We apologize if our initial\nsubmission did not sufficiently highlight this.\nTo underscore the robustness of these teleconnections, we have provided a more\ncomprehensive depiction of their persistence across the record. As illustrated in Figs.\n4-5, we demonstrate recurring teleconnections between the Arctic and Southwest\nChina, and between the Arctic and California. Additionally, we have examined\nclimate networks spanning the most recent 40, 30, 20, and 10 years. These analyses\nreveal consistent teleconnection patterns, thereby underscoring their persistent nature.\nWe appreciate the referee's insightful feedback, as it has helped us to improve the\nclarity, comprehensiveness, and rigor of our work. We added the above discussions in\nlines 227-254.\nFig. 4: Visualization of the propagation pathway of teleconnection in the climate\nnetwork. a, illustrates the teleconnection pathway (dashed curves with arrows)\nbetween an Arctic node (77.5°N, 160°E) and a global node at (30°N, 105°E) in\nSouthwest China, as observed in December 2018. b, depicts the same pathway but\nfor the month of February 1998. c, presents the same teleconnection, but spans a\nlonger period, covering the recent 40 years (1980-2019). The colours and white\narrow represent the magnitudes and directions of the 500 hPa winds on a specific day\nwithin the network period in a and b, while in c, they represent the temporal average\nover the recent 40 years. Panels d-f showcase analogous information as a-c, but for\nanother teleconnection link between California, United States (35°N, 115°W) and the\nArctic (87.5°N, 165°W).\nFig. 5: a-c, The shortest path method identifies propagation pathways in climate\nnetworks constructed from global air temperature data over the most recent 30, 20 and\n10 years. These pathways are between a node in Southwest China (30°N, 105°E) and\nan Arctic node (77.5°N, 160°E). d-e, Similar to a-c, but for another teleconnection\nbetween California (35°N, 115°W) and Arctic (87.5°N, 165°W). The visualization\nof these pathways features background colors representing the averaged wind speed\n(500 hPa), with white arrows indicating the prevailing wind direction over the\ncorresponding periods\n• Identify feedback loops through Arctic teleconnections: This is the weakest part of\nthe paper. It is hard for me to understand how robust these linkages are, how much of\nan impact they have and whether this feedback is stabilising or destabilising.\nResponse: We sincerely appreciate the referee's constructive comments and\nunderstand the concerns raised about the robustness, impact, and stability of the\nidentified feedback loops through Arctic teleconnections. In response, we have\nconducted further investigations and made significant improvements to better clarify\nthese aspects.\nFor the robustness of the feedback loops, we chose the teleconnection paths between\nthe Arctic and Southwest China/California as representative examples. We have\nrepeatedly identified similar feedback paths in multiple instances within a one-month\nperiod, as shown in Fig. 4a, b, and d, e. These paths closely coincide with wind routes\nfor individual months, as is evident from the background coloration in the figures.\nTo further demonstrate the robustness of the feedback loops, we expanded our\nanalysis to consider longer time scales. We constructed climate networks based on the\nsimilarity between Arctic and global air temperature variations, and examined time\nseries spanning the past 40 years (1980-2019), as presented in Fig. 4c and f.\nAdditionally, we analyzed time series over the most recent 30, 20, and 10 years, as\ndisplayed in Fig. 5 (Fig. S10 in the supplementary information).\nRemarkably, our analyses over these extended time periods consistently reveal that\nthe propagation paths exhibit similar patterns to those observed during individual\nmonths. In particular, we observe a negative anomalous wind flow from Southwest\nChina/California to the Arctic, followed by a nearly straight-line path from the Arctic\nback to outside, thereby forming a feedback loop.\nAdditionally, a wavier jet stream may serve as a potential mechanism that can\nincrease the exchange of air masses between high and low latitudes, establishing a\nlinkage between the Arctic and lower latitudes. Moreover, the variations observed in\nthe teleconnection routes at shorter time scales, such as monthly, may be influenced\nby the inherent chaotic nature of the jet stream on weather time scales.\nWe have incorporated these improvements and discussions in the revised manuscript\n(lines 227-254).\nOverall the study presents interesting complexity science approaches as applied to\nunderstanding the Arctic but does not present a strong story or advance our\nunderstanding significantly. I suggest the authors think about presenting one\ncomponent of the story in a more robust and detailed way, or submit to a journal\nwhich accepts longer papers so that each component of the story can be developed\nfully.\nResponse: We greatly value the referee's constructive suggestions and recognize the\nimportance of delivering a robust, detailed narrative that significantly advances our\nunderstanding of the Arctic.\nIn light of the referee's comments, we have carried out extensive revisions to bolster\nthe comprehensiveness and depth of our analysis, particularly focusing on the Arctic\nteleconnections. We have incorporated additional figures and extended our\nexamination to longer time scales, highlighting the persistence and reliability of the\nidentified teleconnection patterns.\nWe concur with the referee that a more robust and in-depth presentation of our work\nwould enhance its impact. Hence, we have strived to present a clear and coherent\nnarrative that systematically unveils the Arctic complexities, applying complexity\nscience approaches. We thank the referee for his/her valuable guidance throughout the\nrevision process. It has been instrumental in refining our work and enhancing its\noverall quality and impact. We earnestly hope that the revised manuscript will meet\nNature Communications standards and contribute significantly to advancing our\ncollective understanding of the Arctic.\nI note that I do not feel qualified to assess the use of the statistical approaches in this\nstudy. I will focus on the climate response which is more in the domain of my\nexpertise.\nLine numbers would be appreciated to enable easy reviewing.\nResponse: As the referee's suggestion, we have incorporated line numbers in our\nrevised manuscript. We are thankful for this valuable recommendation.\nP1: “disrupting the balance of nature” is subjective and should be rephrased\nResponse: We appreciate the referee's comment and understand the importance of\nobjectivity in scientific writing.\nP2: Other recent references which may be of interest:\nEngland, M., I. Eisenman, N. Lutsko and T. Wagner (2021), The recent emergence of\nArctic Amplification, Geophysical Research Letters, 48, e2021GL094086, doi:\n10.1029/2021GL094086\nChylek, P., Folland, C., Klett, J. D., Wang, M., Hengartner, N., Lesins, G., & Dubey,\nM. K. (2022). Annual mean Arctic Amplification 1970–2020: Observed and simulated\nby CMIP6 climate models. Geophysical Research Letters, 49,\ne2022GL099371. https://doi.org/10.1029/2022GL099371\nResponse: We greatly appreciate the referee's recommendations and have diligently\nreviewed the suggested references. We found them to be particularly informative and\nbeneficial to our work. Accordingly, we have integrated these references into our\nrevised manuscript, enriching our discussion on Arctic Amplification. We thank the\nreferee for their constructive contribution to enhancing our study.\nFigure 1: It is hard for the reader to assess the accuracy of the schematic on the left.\nThe graphic is visually appealing but it is hard to evaluate how scientifically relevant\nit is. The authors repeatedly point to this figure as evidence or an explanation but it is\nunconvincing.\nResponse: We greatly appreciate the referee's feedback on Figure 1. We understand\nthe concerns about the accuracy and scientific relevance of the figure. The figure was\nindeed intended to be a visual representation of the complexity and interconnectivity\nwithin the Arctic climate system, rather than a precise diagram of the processes\ninvolved.\nIn response to your comment, we have revised the caption of Figure 1 to better clarify\nits purpose, emphasizing its role as an illustrative schematic, and not a data-driven\ndiagram. The figure now serves to visually communicate the broad concept of the\nArctic system and its teleconnections with the global climate system. We have also\nmodified references to this figure in the manuscript, ensuring we do not cite it as\nconcrete evidence or as a scientific explanation.\nWe genuinely value your critique and acknowledge that the emphasis of our work\nshould be on the robust scientific analysis and findings presented throughout the\nmanuscript. Although Figure 1 has been retained in the revised version primarily to\nmaintain the overall structure, we are open to the possibility of removing it if you\nbelieve it would be more appropriate. We believe that these revisions will alleviate\nany confusion surrounding the role and interpretation of Figure 1.\nYour feedback has been invaluable in refining our work, and we thank you for\nbringing this matter to our attention.\nP5: I am skeptical that the reported Southern Hemisphere impacts of the AO are\nrobust. Can the authors present some mechanism to explain this regional signature?\nResponse: We appreciate the referee's skepticism and his/her request for a\nmechanism to explain the reported Southern Hemisphere impacts of the Arctic\nOscillation (AO).\nAs a prominent pattern of climate variability, the AO primarily influences weather\npatterns in the Northern Hemisphere. The direct impact of the AO on Southern\nHemisphere weather and climate patterns is generally not expected to be robust due to\nthe geographical separation. However, the AO might have indirect impacts on the\nSouthern Hemisphere through complex atmospheric and oceanic teleconnections\nwithin the global climate system [1]. As the AO modulates the strength and location\nof the polar jet stream, it can indirectly influence atmospheric circulation patterns\nglobally. For example, during the positive phase of the AO, the polar vortex is\nstronger and more stable, which can lead to more zonal (east-to-west) wind patterns\nand a faster, more confined jet stream. These changes can influence atmospheric wave\npropagation, potentially altering the transfer of energy and momentum between\ndifferent latitudes and between the troposphere and stratosphere. In turn, these\nchanges in atmospheric circulation can influence oceanic circulation patterns. For\ninstance, changes in wind patterns can alter surface ocean currents and upwelling\npatterns, influencing the distribution of heat and nutrients in the oceans. Through\nthese mechanisms, changes in the AO can potentially have effects on climate and\nweather patterns in the Southern Hemisphere.\nTo better understand the Southern Hemisphere impacts of the AO in our study, we\nhave included additional analyses, showing the statistical relationship between AO\nand atmospheric conditions in the Southern Hemisphere (lines 148-159). In Fig. 6\n(corresponding to Fig. S4 in the supplementary information), we observe notable\nconnections between the AO and WV within specific regions of the Southern\nHemisphere (SH). These correlations between WV and the AO in the SH are\nnoteworthy due to their significant seasonal fluctuations.\nA more detailed examination reveals a correspondence between these correlations and\nthe position of the jet stream. In particular, areas along the jet stream belt in the SH\ndemonstrate significant correlation coefficients, and these coefficients display a\nmarked seasonal divergence, especially between summer and winter. This pattern\nhints at a mutual influence between the positions and strengths of the jet streams in\nthe Northern and Southern hemispheres, thereby underscoring the interconnectedness\nof atmospheric dynamics across hemispheres and the global implications of the AO.\nConsidering the seasonality of these correlations is also crucial. The observed changes\nin correlation coefficients accentuate the need to consider seasonal dynamics and their\ninteraction with the AO when evaluating its influence on weather patterns.\nOur findings offer a feasible explanation for the documented impacts of the AO in the\nSouthern Hemisphere. We appreciate the referee's insightful comment, which has\nspurred a more in-depth exploration and elucidation of this regional characteristic.\nFig. 6: Visualization of the AO's seasonal influences on Southern Hemisphere local\nweather variability patterns. a, Heatmaps depicting correlations between the AO and\n(cid:1849) , considering only values from the same season Only (i.e., Dec.-Feb for winter,\n(cid:3002)(cid:3004)(cid:3007)\nMar.-May for spring, Jun.-Jul. for summer, and Sep.-Nov. for autumn). b, Analogous\nto a but for (cid:1849) . c, Similar to a but for the monthly averaged zonal wind speed at\n(cid:3017)(cid:3020)\n250 hPa pressure level (U250). d, The mean speed of U250 during the period from\nJan. 1980 to Dec. 2019. Correlation values with 95% or higher significance are\nindicated by an “x”.\nP7: Choosing two months from the whole record to explore Arctic teleconnections\ndoesn’t seem a robust approach.\nResponse: We understand the referee's concern about the robustness of our results\nbased on the examination of a two-month span. In response, we have expanded our\nanalysis to cover the entire period from 1980 to 2019. To demonstrate robustness, we\nhave pinpointed recurring teleconnections between the Arctic and specific regions\nacross multiple individual months. Further, by comparing these teleconnection\npathways with the wind trajectories of the corresponding months, we have observed a\nremarkable congruity between them.\nBy incorporating these analyses, we have strengthened the robustness and reliability\nof our approach in exploring Arctic teleconnections.\nWe appreciate the referee's critical insight, which has guided us to perform a more\ncomprehensive analysis and enhanced the robustness of our findings.\nReference:\n[1] Clara Deser (2000), On the teleconnectivity of the “Arctic Oscillation”,\nGeophysical Research Letters, 27(6), 779-782, doi: 10.1029/1999GL010945"}, {"round": 2, "reviewer_comments": {"reviewer_1": "I am satisfied with the revision and recommend the revised paper for publication.", "reviewer_2": "The authors have substantially addressed many of my concerns from the original manuscript,\nhowever a few issues remain.\nL78-79: This sentence about global extreme weather is exaggerated\nL107-108: So WACF and WPS are in the same direction (high values mean shorter memory in\nsystem?). I don't understand the term 'faster changes'.\nL165-167: Point to which figure you are referring to in particular.\nFigS6: I find this somewhat difficult to interpret. Could you report the trend numbers somewhere in\nthe figure? ie the slope coefficients.\nL249-251: I think the mention of wavier jet stream is not necessary here. This is a hotly debated\ntopic which I personally do not think is very strong, and I do not think the mechanisms suggested by\nthe authors rely on it. Therefore I think including this discussion may weaken the argument.\nL254-256: Overstated.\nOn a side note, I think the authors need to understand that not all changes in the Arctic are driven by\nclimate change, and some can be attributed to internal climate variability. I think the authors should\ndiscuss this and what this means for their results.\nDörr, J. S., Bonan, D. B., Årthun, M., Svendsen, L., and Wills, R. C. J.: Forced and internal components\nof observed Arctic sea-ice changes, The Cryosphere Discuss. [preprint],\nhttps://doi.org/10.5194/tc-2023-29, in review, 2023.\nEngland, M., A. Jahn, and L. Polvani (2019), Non-uniform contribution of internal variability to recent\nArctic sea ice loss, Journal of Climate, 32, 4039-4053, doi: 10.1175/JCLI-D-18-0864.1"}, "author_response": "Reviewer #1\nI am satisfied with the revision and recommend the revised paper for publication.\nResponse: We thank the referee for his/her fully support publication of our work.\nReviewer #2\nThe authors have substantially addressed many of my concerns from the original manuscript,\nhowever a few issues remain.\nResponse: We are grateful for the reviewer's constructive feedback and are pleased to hear that our\nrevisions have substantially addressed many of the initial concerns. We have made additional\nrevisions to specifically address the remaining concerns, and these changes are clearly marked and\nexplained in the revised manuscript.\nL78-79: This sentence about global extreme weather is exaggerated\nResponse: We appreciate the reviewer's attention to detail and the concern raised about the original\nphrasing. In the revised manuscript, we have modified the sentence as, “It is also possible that\nchanges in the Arctic may have some role in affecting the likelihood of extreme weather conditions\nglobally, although this is subject to ongoing research.”\nL107-108: So WACF and WPS are in the same direction (high values mean shorter memory in system?). I don't\nunderstand the term 'faster changes'.\nResponse: We appreciate the reviewer's insightful question. Indeed, both W and W values are in\nACF PS\nthe same direction—higher values indicate higher variability or irregularity within the system. W\nACF\nprimarily focuses on the memory of the time series, while W is concerned with its frequency\nPS\ncontent. When we refer to \"faster changes,\" we mean changes occurring at a higher frequency. We\nhave clarified this point in the revised manuscript by explicitly stating that \"faster changes\" refer to\nhigh-frequency variations.\nL165-167: Point to which figure you are referring to in particular.\nResponse: We appreciate the reviewer's suggestion. The text in lines 165-167 is referring to Figure 4\nb and c. We have clarified this in the revised manuscript.\nFigS6: I find this somewhat difficult to interpret. Could you report the trend numbers somewhere in\nthe figure? ie the slope coefficients.\nResponse: Thank you for your insightful suggestion. We apologize for any difficulties our initial\npresentation of Fig. S6 may have caused. To clarify, this figure displays the temporal evolution of the\narea covered by thin ice, as well as the averaged W and W for the 12 subregions shown in Fig.\nACF PS\nS5. Based on your recommendation, we have added best-fitting lines that denote significant trends to\nthe figure. Specifically, we've included the slope coefficients for ice cover (m ), WACF (m ), and\nice acf\nWPS (m ) to make the data easier to interpret. These amendments are now reflected in the revised\nps\nmanuscript.\nL249-251: I think the mention of wavier jet stream is not necessary here. This is a hotly debated topic\nwhich I personally do not think is very strong, and I do not think the mechanisms suggested by the\nauthors rely on it. Therefore I think including this discussion may weaken the argument.\nResponse: Thank you for your thoughtful feedback. We recognize the contentious nature of the\ndiscussion around a 'wavier jet stream' and agree that its inclusion in this context could potentially\nweaken our argument. Accordingly, we have removed the relevant paragraph from the revised\nmanuscript to focus on the core findings and implications of our study.\nL254-256: Overstated.\nOn a side note, I think the authors need to understand that not all changes in the Arctic are driven by\nclimate change, and some can be attributed to internal climate variability. I think the authors should\ndiscuss this and what this means for their results.\nDörr, J. S., Bonan, D. B., Årthun, M., Svendsen, L., and Wills, R. C. J.: Forced and internal\ncomponents of observed Arctic sea-ice changes, The Cryosphere Discuss. [preprint],\nhttps://doi.org/10.5194/tc-2023-29, in review, 2023.\nEngland, M., A. Jahn, and L. Polvani (2019), Non-uniform contribution of internal variability to\nrecent Arctic sea ice loss, Journal of Climate, 32, 4039-4053, doi: 10.1175/JCLI-D-18-0864.1\nResponse: Thank you for your thoughtful feedback. We think the reviewer means the L269-271\nregarding the climate change's role in Arctic variability: “the variability of Arctic sea ice on weather\ntime scales has significantly increased due to the melting of thick perennial sea ice. This finding\nunderscores the profound impact of climate change on the Arctic region.”\nWe totally agree that not all changes in the Arctic are driven by climate change, and some can be\nattributed to internal climate variability. In line with your suggestion, we have revised the text as, “The\nvariability of Arctic sea ice on weather time scales has increased, partially attributable to the melting\nof thick perennial sea ice. This finding underscores both the profound impact of climate change and\nthe role of internal climate variability on the Arctic region [1,2].”\n1. Dörr, J. S., Bonan, D. B., Årthun, M., Svendsen, L., and Wills, R. C. J.: Forced and internal\ncomponents of observed Arctic sea-ice changes, The Cryosphere Discuss. [preprint],\nhttps://doi.org/10.5194/tc-2023-29, in review, 2023.\n2. England, M., A. Jahn, and L. Polvani (2019), Non-uniform contribution of internal variability to\nrecent Arctic sea ice loss, Journal of Climate, 32, 4039-4053, doi: 10.1175/JCLI-D-18-0864.1"}]

Decision letter