a. Model simulations

To investigate the contribution of sea ice loss to atmospheric variability, we employed a pair of two Community Earth System Model (CESM) (Hurrell et al. 2013) simulations with constrained sea ice. The model setup utilizes the Whole Atmosphere Community Climate Model (WACCM4), the Parallel Ocean Program version 2 (POP2), the Community Land Model version 4 (CLM4), and the Los Alamos Sea Ice Model (CICE4) component models. The atmosphere and land components both have horizontal resolutions of 1.9° × 2.5°, and the ocean and sea ice components have roughly 1° resolutions. The Whole Atmosphere Community Climate Model (WACCM4) is a high-top model with 66 vertical pressure levels reaching 5.96 × 10⁻⁶ hPa (approximately 140 km). The added vertical resolution and extension to higher heights leads to a better representation of the stratosphere. This is important for studying the impact of sea ice loss as troposphere–stratosphere interactions are known to be an important mechanism through which sea ice loss impacts the atmosphere (Sun et al. 2015). The model also includes a sophisticated stratospheric chemistry package that provides more realistic conditions in the upper-atmosphere (Marsh et al. 2013). The CICE4 model includes a thermodynamic component that calculates growth rates of snow and ice, an ice dynamics component that utilizes realistic ice physics based on ice mass and velocity, a thickness parameterization that quantifies ice strain and thickness, and a transport model that simulates ice advection (Hunke et al. 2015).

Both experiments are fully coupled with radiative forcing held constant at the year 2000. The control simulation (CTL) sea ice is nudged to the ensemble mean of the WACCM historical runs averaged over 1980–99 and the experiment simulation (EXP) is nudged to projected RCP8.5 values over 2080–99. The nudging method is described in Deser et al. (2015) and utilizes spatially and seasonally varying longwave radiative fluxes (LRF) in each grid cell of the sea ice model to force the sea ice to mimic historical and projected sea ice conditions. The LRF is applied only to the sea ice model where there is sea ice. The magnitude of the downward LRF is larger for months of greater ice thickness and coverage, and vice versa. Although energy is not conserved using this method, water is conserved between the sea ice and ocean model components. The experiments are both 300 years in duration, but we disregard the first 100 years for spinup time and retain only the last 200 years for the analysis.

One advantage of this coupled model configuration is that SSTs are free to vary. This allows for more realistic SSTs that are free to increase as the sea ice edge retreats and maintains dynamic atmosphere–ocean variability. Ocean–atmosphere coupling has been shown to be important for generating a more realistic response to sea ice loss that extends to lower latitudes and higher altitudes (Deser et al. 2015) and in producing a reduced summer storminess in the mid-to-late twenty-first century due to Arctic sea ice (Kang et al. 2023). Although the SSTs will differ between the simulations, they are still a direct biproduct of changes in sea ice as this is the only difference between the two model setups.

b. Self-organizing maps algorithm

There are three measures used to assess SOM map quality: topological error, quantization error, and the Sammon map. Quantization error is the average Euclidean distance between the input data and their associated BMU, thus describing how similar the map nodes are to the input data vectors. The topological error is defined as the percentage of input data vectors for whom the next best match unit is not a neighbor to the BMU and thus quantifies how well ordered the SOM is. The Sammon map is a nonlinear mapping that visually represents the relative locations of the SOM map nodes. Overtraining a SOM can result in a quantization error that continues to decrease at the expense of a twisted Sammon map and higher topological error. The SOM shown here is well constructed, meaning that it has a balance of low quantization error and low topological error (<15%) and a flat Sammon map (not shown). More information about the SOM method is available in Kohonen (2001). The SOM Program Package is publicly accessible at http://www.cis.hut.fi/research/som-research/.

c. Creation of final SOM

In this study, SOM is used to identify large-scale patterns of daily winter 500-hPa geopotential height anomalies ($Z_{500}^{\prime }$) over North America. Analysis is conducted over the winter (December–February) season when the impact of sea ice loss on atmospheric circulation is greatest. The data are also confined to the region of 25°–75°N, 180°–20°E to focus on the North American midlatitude response to sea ice loss and identify patterns of variability on synoptic spatial scales. We are interested in identifying changes in large-scale patterns separately from the mean response to sea ice loss. As such, anomalies are computed for each simulation (CTL and EXP) separately. A daily climatology is computed for each simulation by averaging each calendar day over all 200 model years. Anomaly fields are then created by subtracting the daily climatology, for the corresponding simulation and calendar day, from each day of the simulation. This procedure takes into account the seasonal cycle of Z₅₀₀ so that anomalies are identified across all months and effectively removes the seasonally varying mean response to sea ice loss. For subsequent analysis, the term “anomalies” will refer to the difference in any field relative to its seasonally varying climatology and these will be denoted with a prime, for example $Z_{500}^{\prime }$.

There are several options for preprocessing input data depending on the research question. In this study, the $Z_{500}^{\prime }$ fields are normalized by removing the mean of the time series and dividing by the standard deviation at each grid point prior to training. This ensures that locations that experience greater variability do not have a larger impact on the SOM classification. The data are then multiplied by the cosine of the latitude to account for grid box area changes with latitude. Input data for the SOM consist of model output from both the CTL and EXP simulations to ensure all patterns of variability present in each simulation are represented in the final SOM.

The SOM algorithm includes several user-defined parameters, the most notable being the number of map nodes (archetypal patterns). Here the number of map nodes is determined through testing a variety of different SOM sizes. A final SOM size is chosen that is the smallest size that is able to identify all patterns that are physically relevant to the research question. After testing different SOM sizes, a 5 × 3 grid of map nodes for a total of 15 nodes was chosen for this study. For well-constructed SOMs, such as that presented here, Gervais et al. (2016) found that changes in other user-defined parameters (e.g., neighborhood function and learning rate parameter) made little difference in the final SOM.

d. SOM analysis

Once a SOM is trained, the final nodes or LSMPs are no longer modified and each input data vector (or day of data in this case) is compared to the final SOM and assigned a BMU. This enables a multitude of additional analyses to explore the LSMPs. The frequency of occurrence of each LSMP is computed as the total number of BMUs for a given node divided by the total number of input days for the entire SOM. This can provide information about which LSMPs are most common. We can also obtain a more complete understanding of the physical processes associated with each node through compositing of any variable of interest. These composites (S) are computed for a given node by averaging all days that are assigned as a BMU for that node. For both the frequency (f) and composite, calculations can include all of the input data or only the BMUs associated with either the CTL (f_CTL or S_CTL) or EXP (f_EXP or S_EXP).

Differences in atmospheric variability between experiments can arise from either differences in the frequency of SOM nodes (Δf = f_EXP − f_CTL) or differences in their pattern (ΔS = S_EXP − S_CTL). The relative importance of changes in frequency versus change in pattern will depend on the SOM size. With a smaller SOM we would expect changes in pattern to be greater and for a larger SOM we would expect to see more changes in frequency. Examining both metrics together provides a complete view of changes in the variability (Gervais et al. 2020). Throughout the paper, these differences will be described as the impact of sea ice loss on the either the frequency or pattern.

Significant differences in frequency are evaluated using a permutation test. Here BMUs from both simulations are randomly assigned to new “CTL” and “EXP” labels and a new Δf is computed. This process is repeated 1000 times in order to create a null distribution of Δf values. If the true Δf lies outside the 2.5th or 97.5th percentile, the frequency differences are deemed significant. This process is repeated for each node. Statistical significance for ΔS at each grid point is determined using Student’s t test at a 95% confidence level with a null hypothesis of zero.

a. Winter atmospheric response to sea ice loss

The atmospheric response to future sea ice loss will be defined in this study as the difference between the CTL and EXP simulations (EXP − CTL). The differences in sea ice cover between the simulations are seasonally varying with the greatest differences in September coinciding with the seasonal sea ice minimum (Fig. 1a). Although sea ice loss is greatest in September, the mean impact on atmospheric circulation is greatest in the winter, consistent with previous studies (Vihma 2014). This seasonality of the atmospheric response can be seen in the monthly mean differences in 500-hPa geopotential height (Z₅₀₀) and sea level pressure (SLP) between the simulations (Fig. S1 in the online supplemental material.). The winter mean atmospheric response to future sea ice loss shows a clear signal of Arctic amplification with warmer potential temperatures at 850 hPa (Θ₈₅₀) that are greatest at the high latitudes (Fig. 2a). Consistent with an increase in mean column temperature, we find a similar pattern in the geopotential heights in the midtroposphere (Z₅₀₀; Fig. 2b).

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(a) Monthly mean sea ice extent (millions of km²) defined as the total area of grid boxes having at least 15% sea ice concentration for the CTL (green) and EXP (purple) experiments. (b) Mean difference in winter sea ice (December–February) concentration (%) between the EXP and CTL experiments.

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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Mean winter differences between simulations (EXP − CTL) in color and climatology in black contours for (a) Θ₈₅₀ with climatology contoured every 5 K, (b) Z₅₀₀ with climatology contoured every 100 m, (c) wind speed on the dynamic tropopause (DT WIND) with climatology contoured every 5 m s⁻¹, (d) 50-hPa geopotential height (Z₅₀) with climatology contoured every 100 m, (e) SLP with climatology contoured every 4 hPa, (f) turbulent heat flux (THFLX) with climatology contoured every 10 W m s⁻², (g) surface longwave radiation (LW) with climatology contoured every 5 W m s⁻², (h) surface shortwave radiation (SW) with climatology contoured every 2 W m s⁻², (i) total cloud cover (CLDT) with climatology contoured every 5%, and (j) precipitation (PCP) with climatology contoured every 2 mm day⁻¹. Insignificant differences at the 5% significance level according to a resampling test are stippled.

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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During the winter, differences in sea ice between the CTL and EXP are concentrated in the marginal sea ice zone with reductions of up to 100% sea ice cover (Fig. 1b). The local response to sea ice loss can be clearly seen in the surface fluxes and SLP. Over the marginal seas where sea ice loss is greatest and the atmosphere is exposed to more open ocean, there is a substantial increase in turbulent heat flux (defined as the sum of the sensible and latent heat flux) from the ocean to the atmosphere (Fig. 2f). Over the Bering–Beaufort Seas and Hudson Bay this change in turbulent heat flux reaches 100 W m⁻². Consistent with a large decrease in surface albedo with a greater fraction of ice free ocean there is a large increase in net absorbed shortwave radiation at the surface with sea ice loss (Fig. 2h). The warmer surface temperatures of an ice-free ocean are associated with a larger net surface outgoing longwave radiation (Fig. 2g). Finally, there is a local reduction in SLP concentrated near regions of sea ice loss (Fig. 1e) consistent with a thermal low response (Fig. 2e). For example, over the Hudson Bay there are large negative SLP anomalies that reach −5 hPa. Over and downstream of these regions of newly open ocean in the Bering–Beaufort Seas and Hudson Bay there is enhanced total cloud cover (Fig. 2i) and precipitation (Figs. 2f,j) consistent with enhanced sensible and latent heat flux associated with a transition to ice-free conditions (Fig. 2f).

In the midlatitudes, negative anomalies in the winter mean Z₅₀₀ and SLP response indicate a deepening of the Aleutian low in the North Pacific (Figs. 2b,e). This is dynamically consistent with an intensification and elongation of the Pacific jet, where we would expect a corresponding eastward displacement of an enhanced secondary circulation favoring a more intense troposphere-deep cyclonic circulation. Here we identify the jet using the wind speed on the dynamic tropopause, where the dynamic tropopause is defined as the 2 potential vorticity unit (PVU; 1 PVU = 10⁻⁶ K kg⁻¹ m² s⁻¹) surface (Fig. 2c). The dynamic tropopause is an ideal surface upon which to examine midlatitude jets as this is where the jet is maximized and it rises with the increasing column temperature (Hoskins et al. 1985) thus ensuring that the differences are due to changes in the jet rather than the height of the tropopause. Coinciding with the elongated North Pacific jet and deeper Aleutian low, we see an increase in precipitation that extends to the west coast of North America (Fig. 2j).

Over the Atlantic, the response to sea ice loss includes an increase in Z₅₀₀ (Fig. 2b) over Greenland and an equatorward shift of the North Atlantic jet, as seen in the dipole of wind speed on the dynamic tropopause (Fig. 2c), consistent with several previous studies (Deser et al. 2015; Sun et al. 2015; Blackport and Kushner 2017, 2018; Screen et al. 2018; Ronalds et al. 2020). Furthermore, we find a dipole in precipitation over the North Atlantic as would be expected from an equatorward shift of the storm track along with the jet (Fig. 2j). The winter mean SLP response shows no clear change in the Icelandic low (Fig. 2e).

b. Identification of large-scale patterns

To understand the impact of sea ice loss on LSMPs, we begin by first identifying dominant large-scale patterns of $Z_{500}^{\prime }$ using SOM (Fig. 3). Figure 3 shows the $Z_{500}^{\prime }$ SOM nodes (LSMPs) in color and composites of Z₅₀₀ in the control simulation (S_CTL) in black lines. In general, LSMPs on the left side of the SOM have amplified climatological ridges (troughs) over western (eastern) North America and vice versa on the right side of the SOM. Enhancement of the ridge/trough patterns shifts from being farther east in LSMPs at the top of the SOM (e.g., LSMP [1, 1]) to farther west at the bottom (e.g., LSMP [5, 1]). Similarly, negative (positive) anomalies over the climatological ridge (trough) shift from being to the west in LSMP [1, 3] to farther east in LSMP [5, 3].

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SOM of DJF $Z_{500}^{\prime }$(color; m) over North America with the DJF climatological mean Z₅₀₀ (black contours every 100 m).

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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The LSMPs [1, 1] and [2, 1] in the upper-left corner have a pattern similar to the positive phase of the Pacific–North American pattern (PNA; Wallace and Gutzler 1981) with negative anomalies in the Pacific and eastern North America and positive anomalies over Alaska and the Pacific Northwest. Conversely, LSMP [5, 3] in the bottom-right corner resembles the negative PNA. LSMPs [1, 1], [1, 2], and [1, 3] include anomalies over the North Atlantic that are consistent with a negative Arctic Oscillation (AO; Thompson and Wallace 1998) or North Atlantic Oscillation (NAO)-like (Hurrell 1995) pattern. LSMPs [1, 1] and [1, 2] have positive $Z_{500}^{\prime }$ near Iceland while LSMP [1, 3] has a center of action shifted farther west. LSMPs [1, 2] and [1, 3] have negative anomalies over the subtropical North Atlantic. In contrast, LSMPs [3, 2] and [4, 2] have weak positive AO/NAO-like anomalies. Although the NAO is an important feature of the Northern Hemisphere climate variability and exerts an impact on North American weather, our SOM is trained with data over North America and therefore we expect variability over the North Atlantic will have a limited presence as compared to other sources. LSMPs [4, 1] and [5, 1] have a strong positive anomaly over Alaska that acts to amplify and shift the climatological ridge over the Rockies farther east, while LSMPs [3, 3], [4, 3], and [5, 3] have a negative anomaly over Alaska. LSMPs [1, 1], [1, 2], [2, 1], and [2, 2] exhibit a strengthened Aleutian low, while LSMPs [4, 3], [5, 1], [5, 2], and [5, 3] exhibit a weakened Aleutian low. Nodes in the center of the SOM have weaker patterns overall.

To obtain further understanding of the synoptic conditions associated with each map LSMP and their sensible weather impacts, we compute control simulation composites (S_CTL) for additional variables. LSMPs in the top left of the SOM (namely, LSMPs [1, 1], [1, 2], [2, 1], [2, 2]) have deeper Aleutian lows as shown in their sea level pressure anomalies (SLP′; Figs. 4 and 5) consistent with the negative values in $Z_{500}^{\prime }$ SOM (Fig. 3). Those on the right side of the SOM (viz., LSMPs [3, 3], [4, 3], [5, 3]) have Aleutian lows that are shifted farther east toward the continent and coupled with a high over the subtropics (Figs. 4 and 5). This high/low pressure couplet of SLP′ over the Gulf of Alaska and west coast of North America acts to generate westerly lower-tropospheric winds through geostrophic balance arguments. This in turn can act to enhance the transport of warm maritime air into the continent, which is seen in the positive ${\mathrm{\Theta }}_{850}^{\prime }$ values over western North America associated with these LSMPs (Fig. 4). LSMPs on the top and left side of the SOM are generally colder, specifically nodes [1, 1], [1, 2], [3, 1], and [4, 1]. These are associated with either an enhancement of the climatological high pressure and ridge over western North America (LSMPs [1, 1], [2, 1], [3, 1], [4, 1]) and/or a weakened Iceland low (LSMPs [1, 1] and [2, 1]) consistent with the negative phase of the NAO (Fig. 4). LSMPs [1, 2] and [4, 1] are associated with particularly deep cold anomalies down to −2°C.

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CTL composites of ${\mathrm{\Theta }}_{850}^{\prime }$ (color; °C), SLP′ (black contours every 4 hPa; dashed negative from 2 hPa), and wind speed on the dynamic tropopause (green contours every 5 m s⁻¹ from 35 m s⁻¹).

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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CTL composites of total precipitation (color; mm day⁻¹), SLP (black contours every 4 hPa), and wind speed on the dynamic tropopause (magenta contours; every 5 m s⁻¹ from 35 m s⁻¹).

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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Circulation patterns can also play a key role in the precipitation over the continental United States. LSMPs with strong Aleutian lows that are closer to the continent ([2, 2], [2, 3], [3, 2], [3, 3]) are associated with enhanced precipitation along the west coast, whereas nodes with weaker Aleutian lows ([4, 1], [5, 1], [4, 2], [5, 2]) have less precipitation along the west coast (Fig. 5 and contours in Fig. 9). Enhanced precipitation in the southeastern United States is found in LSMPs [5, 1], [5, 2], [5, 3], and [1, 3], all of which are characterized by a trough over the southeastern United States (Fig. 5 and contours in Fig. 9). In contrast, precipitation is reduced in LSMPs [2, 1], [3, 1], and [3, 2] where the trough is located offshore (Fig. 5 and contours in Fig. 9).

Figures 6a and 6b show the associated frequency of each map node in the CTL and EXP simulations. All LSMPs in Fig. 3 are present in both the CTL and EXP simulations. In the CTL simulation, LSMPs [3, 2], [4, 2], and [4, 3] occur most often. The LSMPs that occur least often are [1, 1] and [1, 2], both of which are characterized a deepened Aleutian low, cold ${\mathrm{\Theta }}_{850}^{\prime }$ over North America, and high SLP′ over northeastern Canada and Greenland. In the EXP simulation, LSMPs [2, 2], [4, 2], and [4, 3] occur most often, while LMSPs [1, 1], [2, 1], and [3, 1] occur least often. The mean residency time, defined as the number of consecutive days spent in a given map node, are shown in Figs. 6d and 6e for the CTL and EXP simulations respectively. Mean residency times range from 3.2 to 4.3 days with LSMP [5, 1] having the highest and LSMP [4, 2] the lowest residency time for both the CTL and EXP simulations. It should be noted that for both the frequency and residency time the values will change depending on the SOM size (decreasing with increasing SOM size), therefore the actual values are less meaningful than how they might change between the CTL to the EXP simulations.

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Heatmaps of frequency of occurrence of each node in the (a) CTL and (b) EXP, and (c) their difference, and mean residency time for each node in the (d) CTL and (e) EXP, and (f) their difference. Differences are only shown when significant at the 95% level using a permutation test.

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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c. Impact of sea ice loss on LSMP frequency and residency

To understand the impact of sea ice loss on LSMPs, we will first discuss the impact on their frequency of occurrence and residency. Figure 6c demonstrates the difference in frequency of each LSMP between the CTL and EXP. LSMP [3, 2] decreases in frequency by −0.6% while LSMPs [1, 2] and [2, 2] increase in frequency by 0.7% and 0.9%, respectively. These changes may seem small; however, relative to the CTL frequency of 6.4% in LSMP [2, 2], for example, the fractional increase is 14%. All of these LSMPs ([1, 2], [2, 2], and [3, 2]) have anomalously strong Aleutian lows but LSMPs [1, 2] and [2, 2] are stronger than LSMP [1, 3] (Figs. 3 and 4); therefore, these changes in frequency imply that patterns with deepened Aleutian lows become more common with sea ice loss. It should be noted that here we have already removed the seasonal mean difference between the experiments that was characterized by a mean deepening of the Aleutian low and that this result shows further changes in how often these deepened Aleutian low patterns occur. We also see that LSMP [5, 1] decreases in frequency while LSMP [4, 1] increases in frequency with sea ice loss. Since node [5, 1] has a larger positive $Z_{500}^{\prime }$ over Alaska than node [4, 1] (Fig. 3), this can be interpreted as the positive anomaly over Alaska becoming de-amplified.

Unlike the frequency, only LSMP [2, 2] experiences a significant change in mean residency time, with an increase of 0.3 days. This LSMP also exhibited an increase in frequency, indicating that some of the increase in frequency is due to enhanced persistence. Since these LSMPs capture synoptic spatial scale variability, they include patterns associated with Rossby wave propagation across North America. The overall lack of change in residency times across the SOM implies that there is no general change in the speed of wave propagation owing to sea ice loss.

d. Impact of sea ice loss on LSMP pattern

To complete our investigation of sea ice impacts on LSMPs, we examine differences in LSMP composite mean (ΔS) for a variety of atmospheric variables. The impact of Arctic sea ice loss is to weaken the $Z_{500}^{\prime }$ in many LSMPs, which can be interpreted as a reduction in variability (Fig. 7). The best example of this is LSMP [1, 2], where the magnitude of the gradient associated with the −NAO-like dipole in $Z_{500}^{\prime }$ between the Icelandic low and subtropical high is reduced by approximately 15% with sea ice loss. In many cases, the ΔS of $Z_{500}^{\prime }$ are not centered on the CTL composites $Z_{500}^{\prime }$ and thus are better characterized as a shift in location; for example, the anomalous ridging along the west coast in LSMPs [4, 1], [5, 1], and [5, 2] is shifted farther south. A few LSMPs are amplified with sea ice loss; for example, the positive $Z_{500}^{\prime }$ in the subtropical Pacific in LSMPs [4, 3] and [5, 3] are deepened and in [5, 3] extended farther east toward the continent. LSMP [1, 3] also has negative ΔS of $Z_{500}^{\prime }$ in the North Pacific consistent with a deepened Aleutian low. In all cases, the ΔS of $Z_{500}^{\prime }$ are smaller than the CTL composites and so there is no change in the sign of the patterns. This is necessarily true for $Z_{500}^{\prime }$ since the SOM is trained and BMUs are assigned based on this field. However, for other fields, LSMP composites may see larger changes if the conditions associated with these $Z_{500}^{\prime }$ patterns change.

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CTL Composites of $Z_{500}^{\prime }$ (contours; every 50 m from ±50 m; dashed negative) and difference in composites (EXP − CTL) of $Z_{500}^{\prime }$ (color; stippled insignificant using Student’s t test).

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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To understand the impact of sea ice loss on the sensible weather associated with these circulation patterns, we examine ΔS of ${\mathrm{\Theta }}_{850}^{\prime }$ (Fig. 8) and precipitation anomalies (Fig. 9). The most striking impact of sea ice loss on ${\mathrm{\Theta }}_{850}^{\prime }$ is in LSMP [1, 2] (Fig. 8). This LSMP was associated with deep cold anomalies up to −1.75°C in the CTL simulation. However, the impact of sea ice loss far exceeds this at up to +4°C in ΔS of ${\mathrm{\Theta }}_{850}^{\prime }$, resulting in a change in sign of ${\mathrm{\Theta }}_{850}^{\prime }$ associated with this LSMP in the CTL relative to the EXP. LSMP [4, 1] that is also associated with strong cold anomalies over North America reaching −2°C in the CTL simulation experiences a large decrease in magnitude with sea ice loss of up to +1.5°C. Both LSMPs [4, 1] and [1, 2] increase in frequency with sea ice loss, so the circulation patterns typically associated with deep cold anomalies become more common with sea ice loss; however, they are much less cold or, in the case of [1, 2], now associated with a warm ${\mathrm{\Theta }}_{850}^{\prime }$.

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CTL Composites of ${\mathrm{\Theta }}_{850}^{\prime }$ (contours; every 0.25°C from ±0.25°C; dashed negative) and difference in composites (EXP − CTL) of ${\mathrm{\Theta }}_{850}^{\prime }$ (color; stippled insignificant using Student’s t test).

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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CTL Composites of precipitation anomalies (contours; every 1 mm day⁻¹ from ±1 mm day⁻¹; dashed negative) and difference in composites (EXP − CTL) of precipitation anomalies (color; stippled insignificant using Student’s t test).

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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Looking across the entire SOM, we see that a reduction in the amplitude of ${\mathrm{\Theta }}_{850}^{\prime }$ associated with these $Z_{500}^{\prime }$ LSMPs is ubiquitous (Fig. 8). Other LSMPs associated with large cold anomalies (LSMPs [1, 1], [2, 1], [5, 1], and [2, 3]) become warmer and those associated with warmer anomalies become colder. Several of these LSMPs (namely, [3, 3], [4, 3], and [5, 3]), are not associated with significant changes in frequency (Fig. 6), so their contribution to changes in variability is solely through a change in pattern. This de-amplification of ${\mathrm{\Theta }}_{850}^{\prime }$ is consistent with the general reduction in $Z_{500}^{\prime }$ across the SOM owing to sea ice loss. One explanation is that the reduction of horizontal temperature gradients owing to AA may lead to a reduction in anomalous temperature advections occurring in these nodes, even though the mean impact of AA is already removed by virtue of computing the anomalies. This can result in reduced ${\mathrm{\Theta }}_{850}^{\prime }$ and through hypsometric arguments in a corresponding reduction in $Z_{500}^{\prime }$.

The impact of sea ice loss on precipitation anomalies associated with these LSMPs is less robust and more localized (Fig. 9). LSMPs [3, 1], [4, 1], and [4, 2] all experience a small decrease in precipitation along the California coast, acting to amplify the precipitation anomalies values typically associated with these LSMPs (Fig. 9). This is consistent with a positive SLP′ that acts to further reduce the transport of moist air to the region (Fig. S2). The opposite is true for LSMPs [1, 1] and [2, 2] (Fig. 9 and Fig. S2). LSMP [1, 3] experiences an increase in ΔS of precipitation anomalies in the southeastern United States (Fig. 9) consistent with the enhanced troughing (Fig. 7 and Fig. S2) occurring in proximity to the Gulf of Mexico and Atlantic Basin, well-known moisture sources for the region. The opposite is true for LSMP [3, 3].

e. Mechanisms responsible for LSMP [1, 2] pattern changes

Given the striking changes in LSMP [1, 2] and in particular the associated ${\mathrm{\Theta }}_{850}^{\prime }$, a deeper investigation into mechanisms operating in this node is warranted. First, it is important to recognize that the LSMPs identified in this study are from anomalous Z₅₀₀ fields relative to the respective climatologies of each simulation (i.e., $Z_{500}^{\prime }$). Thus, these patterns represent atmospheric variability separate from mean impacts of sea ice loss. However, when it comes to understanding the impacts of these LSMPs on fields such as Θ₈₅₀, the mean impacts of sea ice loss can still be important. As such, in the ensuing analysis we will be examining both composites of total fields (e.g., Z₅₀₀) and anomaly fields (e.g., $Z_{500}^{\prime }$).

Figure 10 shows the CTL and EXP composite of Θ₈₅₀ and SLP. In the CTL simulation, high SLP over the center of the continent and low SLP over the North Atlantic implies a north-northeasterly geostrophic wind. Coupled with the strong meridional background temperature gradient between the pole and the midlatitudes, there is implied geostrophic cold air advection over northeastern North America. Furthermore, the anticyclonic circulation around the high pressure system would aid in transporting this cold air throughout North America. This helps explain why LSMP [1, 2] is associated with deep cold continental temperatures.

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Node [1, 2] composites of Θ₈₅₀ (color) and SLP (black contours; every 4 hPa) for (a) CTL, (b) EXP, and (c) their difference (EXP − CTL). For (a) and (b). SLP contours are every 4 hPa and for (c), SLP contours are every 1 hPa with dashed negative values and the 0 contour omitted.

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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In the EXP simulations, the background temperature gradient from equator to pole is weakened, as is expected with AA (Fig. 10). This in and of itself would cause a reduction in cold air advection in this LSMP. However, we also see that the high pressure over Hudson Bay is weakened, resulting in a slackening of the SLP gradient over eastern Canada and a weakening of the implied north-northeasterly geostrophic wind by roughly 30%. Furthermore, the overall reduction in the strength of the high pressure system would reduce the typical transport of this cold air into the interior of North America. This can be seen, for example, in the slacking of the meridional pressure gradient from Hudson Bay to the Gulf of Mexico coast. Therefore, though we could ascribe the changes in cold air advection to mean AA and the weakened temperature gradient (a thermodynamic impact), these changes in SLP also imply a large role for dynamical impacts.

As discussed previously, there is an increase in mean winter turbulent heat flux and decrease in mean winter SLP between the two simulations over Hudson Bay (Fig. 2), consistent with a local thermal low pressure response to sea ice loss. The difference in CTL and EXP LSMP [1, 2] composites of SLP′ are insignificant over much of the North American continent (Fig. 11c). Furthermore, the effect of turbulent heat flux is smaller in LSMP [1, 2] (Fig. 11d) potentially owing to the warmer ${\mathrm{\Theta }}_{850}^{\prime }$ reducing the ocean–atmosphere temperature gradients (Fig. 11a). This implies that much of the difference in the SLP gradients discussed above is owing to differences in the mean climatology between the CTL and EXP simulations and how this projects onto the LSMP [1, 2] circulation pattern rather than changes in SLP that are specific to this LSMP. For this node in particular, where the high pressure in this region is an important factor, this mean change acts to reduce the zonal SLP gradient and consequently the strong cold air advection in northeastern North America that characterizes the LSMP.

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Node [1, 2] CTL composites (contours) and differences (EXP − CTL) in composites (color) for (a) ${\mathrm{\Theta }}_{850}^{\prime }$ (contours every 0.25°C from ±0.25°C; dashed negative), (b) $Z_{500}^{\prime }$ (contours every 50 m from ±50 m; dashed negative), (c) SLP′ (contours every 2 hPa from ±2 hPa; dashed negative), (d) turbulent heat flux anomalies (THFLX′; contours every 20 W m s⁻² from ± 20 W m s⁻²; dashed negative), (e) total cloud cover anomalies (CLDT′; contours every 5% from ±5%; dashed negative), (f) precipitation anomalies (PCP′; contours every 1 mm day⁻¹ from ±1 mm day⁻¹; dashed negative), (g) incoming shortwave radiation anomalies (SW′; positive down; contours every 5 W m s⁻² from ±5 W m s⁻²; dashed negative), and (h) outgoing longwave radiation anomalies (LW′; positive up; contours every 5 W m s⁻² from ±5 W m s⁻²; dashed negative). In all panels insignificant differences at the 5% level computed using Student’s t test are stippled.

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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In addition to changes in temperature advection, diabatic processes may also play a role in the increased ${\mathrm{\Theta }}_{850}^{\prime }$ associated with LMSP [1, 2]. There is an increase in total cloud cover anomalies and precipitation anomalies downstream (south) of Hudson Bay with sea ice loss (Figs. 11e,f). This is expected given the mean increase in moisture and heat flux (Fig. 2f) from the ice-free surface with sea ice loss (Fig. 1b). This increase in clouds and precipitation relative to other LSMPs is associated with less incoming net shortwave radiation and less upward longwave radiation (Figs. 11g,h). Furthermore, we would expect an increase in diabatic heating to be associated with cloud and precipitation generation, though this cannot be directly confirmed with the variables saved in these model simulations. These results imply a role of diabatic processes in addition to temperature advection in producing the large differences in ${\mathrm{\Theta }}_{850}^{\prime }$ in LSMP [1, 2].

f. Contributions of changes in LSMPs to mean DJF response to sea ice loss

AA is one of the most notable impacts of Arctic sea ice loss. In Fig. 2a we can see this reflected in the DJF seasonal mean difference between the CTL and EXP (ΔΘ₈₅₀). As described above, some LSMPs are associated with greater changes ${\mathrm{\Theta }}_{850}^{\prime }$ than others (e.g., LSMP [1, 2]). Decomposing the DJF mean ${\mathrm{\Theta }}_{850}^{\prime }$ response by LSMP contribution can provide an avenue into better understanding of how synoptic-scale processes relate to mean ${\mathrm{\Theta }}_{850}^{\prime }$ response and elucidate additional mechanisms responsible for AA that might otherwise be obscured.

As discussed in the methods section (section 2), the mean difference between experiments can be approximated as those arising due to changes in frequency versus pattern of the LSMPs [Eq. (4)]. For Θ₈₅₀ the contribution from changes in frequency are much smaller than from changes in pattern (not shown). On the left side of Eq. (4), Δ(fS) is an approximation of the seasonal mean difference between experiments for a given variable (e.g., ΔΘ₈₅₀). Substituting these assumptions, we can rewrite Eq. (4) for Θ₈₅₀ as

$\mathrm{\Delta }{\mathrm{\Theta }}_{850}\approx {\displaystyle \sum _{i=1}^n{f}_{\text{avg},i}\mathrm{\Delta }{S}_i},$(8)

where f_avg,i is the mean frequency of occurrence over the CTL and EXP simulations and ΔS_i is the composite mean Θ₈₅₀ of EXP minus that of CTL for a given node i. Expanding out the summation, dividing both sides by ΔΘ₈₅₀ and multiplying by 100 we can obtain the percent contribution of each node to ΔΘ₈₅₀:

$100\approx \frac{f_{\text{avg},1}\mathrm{\Delta }{S}_1}{\mathrm{\Delta }{\mathrm{\Theta }}_{850}}\times 100+\frac{f_{\text{avg},2}\mathrm{\Delta }{S}_2}{\mathrm{\Delta }{\mathrm{\Theta }}_{850}}\times 100+\cdots +\frac{f_{\text{avg},15}\mathrm{\Delta }{S}_{15}}{\mathrm{\Delta }{\mathrm{\Theta }}_{850}}\times 100.$(9)

In Fig. 12, each of the terms of the right-hand side is plotted, showing the percent contribution of each node to the mean DJF Θ₈₅₀ response. The sum of all the percent contributions over all nodes is approximately equal to 100 (±5%) at each grid point location, confirming that changes in composite are indeed the greatest contributor to the mean Θ₈₅₀ response.

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Percentage contribution of changes in each LSMP composite pattern to mean Θ₈₅₀ in DJF (color). For reference, the DJF mean difference between CTL and EXP (ΔΘ₈₅₀) is provided in contours every 0.5°C beginning at 0.5°C, as shown in Fig. 2a in color. Locations where ΔΘ₈₅₀ is not significantly different at the 95% confidence level as determined using a permutation test are masked out. Stippling shows regions where the percentage contribution of changes in LSMP composite are not significant at a 95% level as determined using a permutation test.

Citation: Journal of Climate 37, 3; 10.1175/JCLI-D-23-0389.1

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To avoid the creation of artificially high values of percent contribution where ΔΘ₈₅₀ is very small, grid points where ΔΘ₈₅₀ is not statistically significant are masked out in Fig. 12. This is computed using a permutation test applied at each grid point to determine if the mean of DJF days used for the SOM analysis in the CTL are different from the EXP simulation with a significance level of 95%. This is similar to the test used in Fig. 2 except there the DJF seasonal mean is computed first and the null hypothesis is that the seasonal means are the same.

If each of these nodes contributed equally to the mean Θ₈₅₀ response, we would expect the percent contribution over 15 nodes to be 6.6% at each grid point. To test this, we compute a null distribution of percent contributions using a permutation test. Here the percent contributions are computed as in Eq. (9) but using an average frequency of 6.6% and the number of days per composites equal to the frequency times the number of input data vectors. We then shuffle the SOM node labels and choose a new set of CTL and EXP randomly without replacement and compute the difference in their composites. This process is repeated 500 times and if the actual percent contribution to the mean Θ₈₅₀ response is greater than the 97.5th percentile or less than the 2.5th percentile of this null distribution, it is considered significant at the 95% level.

The results show that there are indeed nodes that contribute much more significantly to mean Θ₈₅₀ response than others. LSMP [1, 2] stands out for its significant contributions to mean DJF Θ₈₅₀ response over the majority of North America ranging from 20% to 50%. Over northern Canada (including the Northwest Territories, Nunavut, and northern Quebec) where mean Θ₈₅₀ response is greatest, LSMP [1, 2] contributes up to 20% of the total mean Θ₈₅₀ response. This is more than double the rate if there was an equal distribution across nodes. LSMP [4, 1] also has a notable increase in contribution to the mean Θ₈₅₀ response of up to 15% over the Yukon and Northwest Territories. It should be noted that these two LSMPs were associated with deep cold anomalies in the CTL simulations (Fig. 4) in these regions. This implies that processes specific to these LSMPs, such as those outlined in section 3c, are important for creating the mean Θ₈₅₀ response and can occur on synoptic time scales.

In the midlatitudes, the mean Θ₈₅₀ response is much smaller and the contributions of LSMPs are larger. LSMP [1, 2] contributes up to 50% to the mean Θ₈₅₀ response in the southern United States. This implies that LSMP [1, 2] plays an important role in propagating the mean Θ₈₅₀ response into the midlatitudes. There are also notable positive contributions to the mean Θ₈₅₀ response in the southern United States from LSMPs [1, 1], [2, 3], and [4, 2] as well as negative contribution other LSMPs including [2, 1], [2, 2], [3, 1], [3, 2], [3, 3], [4, 1], and [4, 3]. This is consistent with the general reduction in intensity in Θ₈₅₀ across LSMPs identified in Fig. 8. It should be noted that in these regions where ΔΘ₈₅₀ is smaller, the percent contribution will be much larger for the same ΔS_i. One interpretation of these results is therefore that when the mean signal is smaller the impact of internal variability will be larger.