a. Self-organizing maps

To understand what is driving the Arctic SAT trend over the 1990–2016 time period, the high-dimensional SAT dataset is reduced to a smaller number of representative patterns (Fig. 1) using SOM analysis (e.g., Kohonen 2001). SOM analysis is a clustering method that can identify patterns that recur in large datasets (e.g., Hewitson and Crane 2002; Johnson et al. 2008; Johnson and Feldstein 2010), similar to empirical orthogonal function (EOF) analysis (e.g., Kutzbach 1967). However, because the patterns identified by SOM analysis are not constrained to be orthogonal, as well as the property that SOM patterns arise from a minimization of the Euclidean distance with the observed fields, the patterns identified by SOM analysis are more likely to resemble the observed data than are EOF patterns (Yuan et al. 2015). Previous studies, such as that of Yuan et al. (2015), describe in detail the advantages of SOM analysis; therefore, we refrain from providing a more detailed discussion of SOM analysis below.

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Surface (2 m) air temperature anomaly patterns identified by SOM analysis using daily data from 1990 to 2016 during December–February. The value of p indicates the SOM pattern number. The frequency of occurrence of each SOM pattern is indicated above in each panel.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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In this study, we have chosen to use a SOM grid size of 3 × 3, as shown in Fig. 1. The SOM analysis is applied after the SAT anomaly fields are area weighted. To determine whether the results of this study are sensitive to the size of the SOM grid, the SOM analysis was repeated for SOM grids of comparable size. For example, SOM grid sizes of 4 × 5, 4 × 4, and 9 × 1 had similar results to those presented in this study. The number of SOM patterns we use is based upon having enough SOM patterns to accurately represent the daily fields, but not too many SOM patterns, to ensure that the same circulation pattern is not represented more than once. A detailed discussion of this perspective can be found in Johnson et al. (2008). The sensitivity of our results for different time periods (e.g., 1979 to 2016) and domains (e.g., poleward of 50°N) was also tested, finding that the results are not sensitive to either the period or the domain size.

Our aim is to determine how the resulting cluster patterns (Fig. 1) have contributed to Arctic amplification. This is accomplished by following a methodology that has been applied in previous studies to estimate the contribution to interdecadal trends by trends in the frequency of occurrence of intraseasonal SOM patterns of the same variable (as will be shown below, the variance of the SAT SOM patterns in this study are dominated by their intraseasonal contribution) (e.g., Johnson et al. 2008; Lee and Feldstein 2013; Feldstein and Lee 2014). First, each particular DJF day is assigned a best-matching SOM pattern, defined as the SOM pattern with the smallest Euclidean distance to the SAT anomaly field on that day. This leads to a binary time series δ_p,k,i for each SOM pattern p, where i is the day and k the DJF season, with i having 90 values (or 91 values on leap years) for each of the 26 DJF seasons. This binary time series δ_p,k,i is equal to 1.0 on days when SOM pattern p is the best-matching pattern, and zero otherwise. The DJF-mean SAT anomaly, for each DJF season, can then be approximated as a linear combination of the nine SOM patterns, where each SOM pattern is weighted by its frequency of occurrence, f_p,k, within each DJF season; that is,

$\widehat{\mathrm{SAT}}{\left(x,y\right)}_k\approx {\displaystyle \sum _{p=1}^{N\mathrm{pats}}{\displaystyle \sum _{k=1}^{26}{\displaystyle \sum _{i=1}^{N\mathrm{days}}{\displaystyle \frac{{\delta }_{p,k,i}}{N\mathrm{days}}}\mathrm{SA}{\mathrm{T}}_p\left(x,y\right)}}}={\displaystyle \sum _{p=1}^{N\mathrm{pats}}{\displaystyle \sum _{k=1}^{26}{f}_{p,k}\mathrm{SA}{\mathrm{T}}_p\left(x,y\right)}}.$(2)

In (2), Ndays denotes the number of days in each DJF season, Npats denotes the number of SOM patterns, and SAT_p(x, y) is SOM pattern p (Fig. 1). We use a “hat” in $\widehat{\mathrm{SAT}}$ to signify that the SAT field constructed from (2) is not the observed SAT; rather, it is an estimate of the SAT based on the time series of best-matching SOM patterns. The frequency of occurrence f_p,k, which has one value for each DJF season, is defined as follows:

$f_{p,k}\equiv {\displaystyle \sum _{i=1}^{N\mathrm{days}}{\displaystyle \frac{{\delta }_{p,k,i}}{N\mathrm{days}}}},$(3)

and is plotted in Fig. 2 as a function of DJF season for each pattern.

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The frequency of occurrence (y axis) of each self-organizing map pattern (the value of p indicates the SOM pattern number) as a function of the December–February (DJF) season (x axis). Panels correspond to the patterns shown in Fig. 1. The blue bars show the fraction of days that any particular pattern was the best-matching pattern (see text) to the daily surface air temperature anomaly field for the corresponding DJF season. The red line is the linear fit to the blue bars and the slope of the linear fit is indicated above the top-right corner of each panel. The slopes for patterns 1, 3, 5, and 8 are statistically significant at the 5% level based on a two-tailed Student’s t test, as indicated by the asterisks.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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To determine the contribution of each individual SOM pattern toward the SAT trend, in Fig. 3 the product of Δf_p,k and SAT_p(x, y) is displayed for all patterns p. The estimated DJF SAT trend using (4), defined as the sum over all panels in Fig. 3, is shown in Fig. 4b. As can be seen by comparing Fig. 4a (the observed SAT trend) and Fig. 4b, a substantial fraction of the SAT trend is captured by (4) (the difference between Figs. 4a and 4b is shown in Fig. 4c). The implication of the similarity between Figs. 4a and 4b will be discussed more in section 3. Any discrepancies between Figs. 4a and 4b reflect the fact that SAT observations on any particular day are being “forced” to fit one of nine SOM patterns.

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The contribution to the surface (2 m) air temperature trend by each SOM pattern identified in daily data from 1990–2016 during December–February. The value of p indicates the SOM pattern number. As indicated in the top label for each panel, these contributions are calculated by multiplying the linear trend in the frequency of each pattern (Fig. 2) by the SOM patterns in Fig. 1.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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(a) The observed 1990–2016 DJF surface air temperature trend. (b) The approximated (see text) 1990–2016 DJF surface air temperature trend using self-organizing maps. (c) The difference between the observed and approximated surface air temperature trends [(a) minus (b)]. (d) The values of the 1990–2016 DJF surface air temperature trends averaged in the domains outlined by boxes overlaid in (a)–(c). The average values in (d) are area weighted.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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b. The composite method

To determine the physical processes that drive the growth and decay of the SOM patterns on intraseasonal time scales, we generate composites based on the Euclidean distance between the SOM patterns and observations. (This composite approach does not contribute to Figs. 1–5.) For the days that comprise these composites, the SAT anomaly fields have an excellent match with the SOM patterns (Fig. 1). We calculate lagged composites of each term in the thermodynamic energy equation, and then integrate this equation forward in time to determine the terms that make the largest contributions to SAT anomaly growth/decay associated with each SOM pattern. As discussed below, each SOM pattern shown in Fig. 1 can be accurately estimated by a composite of the SAT anomalies based on days when the Euclidean distance between that SOM pattern and the observed SAT anomaly field is small. (The threshold criteria for these composites will also be discussed below.)

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Autocorrelation functions of the projection time series associated with each SOM pattern. The projection time series are obtained by calculating the dot product between the daily SAT anomaly data and the SOM patterns shown in Fig. 1.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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The days with particularly small Euclidean distances, which comprise our composites, are termed events. To select these events, we first generate candidate events for each SOM pattern p. A candidate event is any day for which SOM pattern p is the best-matching SOM pattern to the daily SAT anomaly field. To be considered an event, however, this candidate must satisfy several additional constraints. These constraints are applied to ensure that the resulting composites both resemble the SOM patterns and comprise statistically independent events.

To guarantee a good match between the SOM patterns and the composite patterns, any candidate event for SOM pattern p must be a day for which the Euclidean distance between SOM pattern p and the daily SAT anomaly field is a local minimum (i.e., a day when the time derivative of the Euclidean distance changes sign from negative to positive). This local minimum is also constrained to have a value of less than 0.5 standard deviations of the mean Euclidean distance associated with all candidate events for SOM pattern p. To ensure statistical independence, any pair of candidate events for SOM pattern p that satisfy the above constraints must also be separated from each other by more than 12 days, unless a different SOM pattern occurs on a date between them. If a pair of candidates are too close to each other, the candidate with the smaller Euclidean distance is considered to be an event and the other candidate event is discarded. This final constraint ensures that the events comprising our composites are statistically independent because teleconnection patterns typically have a decorrelation time scale of about 10 days (e.g., Feldstein 2000), as is the case for the SOM patterns in our study (Fig. 5). In Fig. 6, the event selection method is illustrated for two individual years, where the events are marked by yellow asterisks. In general, we find that the results of this study are not sensitive to how strictly an event is defined, but we choose to utilize strict constraints in order to maximize the resemblance between the composite SAT anomalies and the corresponding SOM patterns in Fig. 1 and to ensure statistical independence.

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The best-matching self-organizing map pattern (blue bars) and corresponding Euclidean distance to the daily surface air temperature anomaly field (red lines) for the (a) 1995/96 and (b) 2012/13 DJF seasons. The green line shows the threshold determined by the candidate events associated with the best-matching self-organizing map pattern (see section 2). Yellow asterisks are overlaid on the red line for days that were determined to be an event (see section 2).

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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Over all of the years between 1990 and 2016, the event selection criteria described above result in between 19 and 34 events for all SOM patterns. The resulting composite SAT anomaly fields for each SOM pattern are very similar to those displayed in Fig. 1 (not shown). Therefore, the SAT anomaly composites can be substituted in place of SAT_p(x, y) in (4) with little impact on the accuracy of the estimate for $\Delta \widehat{\mathrm{SAT}}\left(x,y\right)$ (not shown).

Excellent correspondence is found between the SAT anomaly SOM patterns in Fig. 1 and composites of the temperature anomalies calculated on the lowest hybrid sigma–pressure level of the ECWMF reanalysis model (see Fig. 7), which corresponds to a height of about 10 m (Berrisford et al. 2009). Therefore, to investigate the processes that drive the SAT anomalies, for each SOM pattern, as discussed above, we integrate the thermodynamic energy equation, that is,

${\displaystyle \frac{\partial T^{\prime }}{\partial t}}=-{\left(u{\displaystyle \frac{\partial T}{\partial x}}\right)}^{\prime }-{\left(\upsilon {\displaystyle \frac{\partial T}{\partial y}}\right)}^{\prime }-{\left(\dot{\eta }{\displaystyle \frac{\partial T}{\partial \eta }}\right)}^{\prime }+{\left({\displaystyle \frac{\kappa T\omega }{p}}\right)}^{\prime }+Q_1^{\prime }+Q_{\mathrm{2}}^{\prime }+Q_3^{\prime }+Q_4^{\prime },$(5)

on the lowest hybrid sigma–pressure level, where primes signify anomalies. We calculate lagged composites of each term on the rhs of (5) for each SOM pattern. (Note that the primes on bracketed quantities apply to the product within the brackets.) We examine the thermodynamic energy equation on the lowest hybrid sigma–pressure level for a practical reason, namely that wind and diabatic heating data are not available at a height of 2 m. However, wind and diabatic heating data are available at the lowest hybrid sigma–pressure level. Therefore, we assume that the terms that drive the temperature anomalies on this lowest hybrid sigma–pressure level are the same as those that drive the SAT anomalies.

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Temperature anomaly composites (colors) on the lowest model level and sea level pressure anomaly composites (contours) for the self-organizing map events (see section 2). Solid (dashed) contours denote positive (negative) sea level pressure anomalies. Alphabetically labeled green boxes outline the major anomalies examined in this study (also see Fig. 8). Stippling indicates statistical significance of the surface air temperature anomaly composites for p < 0.10.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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The diabatic terms in (5)—which, as described above, comprise radiational heating (shortwave and longwave), vertical mixing, and latent heat release—are downloaded explicitly from ERA-Interim as 12-h accumulated fields for both 0000 and 1200 UTC. The daily mean heating is then obtained by adding the 0000 and 1200 UTC 12-h accumulations. The horizontal temperature advection terms represent daily means, calculated with 6-hourly wind data and temperature data on the lowest model level, and applying the gradient operator in spherical form (an NCAR Command Language built-in function, gradsf, was utilized). The adiabatic warming term is also a daily mean calculated with 6-hourly data. A detailed discussion for the calculation of vertical temperature advection on the lowest model level is included in the appendix section of Clark and Feldstein (2020a). All terms in (5) and (6) are domain averaged in the green boxes outlining the dominant anomalies shown in Fig. 7. The motivation for choosing the domains in Fig. 7 will be discussed in the next section.

As will be discussed in section 3, 15 days approximates two decorrelation time scales of each SOM pattern; however, it is found that the results are not sensitive to the day at which the integration is initiated. Statistical significance is tested with a Monte Carlo approach, by randomly generating 250 composites.

a. The causes of surface air temperature trends: Thermodynamic energy budget at the lowest model level

Comparing Figs. 1 and 2, it is evident that warm Arctic SOM patterns are increasing in frequency and cold Arctic SOM patterns are decreasing in frequency. This result is unsurprising and guaranteed because the underlying data have a positive trend. Based on (4) and the results shown in Figs. 1 and 2, we expect the approximated Arctic SAT trend to be characterized by warming much like that shown in Fig. 4a. Indeed, over the Arctic, Fig. 4b shows that the approximated SAT trend strongly resembles the observed SAT trend. In fact, the approximated SAT trend in Fig. 4b is characterized not only by broad warming over the Arctic but also by a local maximum of warming over the Barents and Kara Seas, much like that seen for the observed Arctic SAT trend (Fig. 4a). Specifically, the estimated Arctic SAT trend can explain about one-half of the trend over the Barents and Kara Seas, one-third of the trend over Baffin Bay, and two-thirds of the trend over the Chukchi Sea (Fig. 4d). As discussed below, on average, about 85% of the variance of each SOM pattern comes from intraseasonal time scales. Therefore, these results indicate that in addition to an interannual-time-scale contribution to the interdecadal Arctic SAT trend, intraseasonal-time-scale weather patterns also likely make an important contribution to the driving of the trend. The SOM patterns that most strongly contribute to the SAT trend pattern shown in Fig. 4b are patterns 1, 3, 5, and 8, as seen in Fig. 3.

The fact that the estimate for the interdecadal Arctic SAT trend in Fig. 4b is a good match to the observed Arctic SAT trend in Fig. 4a has important implications. Noting that the decorrelation time scale of each SOM pattern is found to be less than about 10 days (Fig. 5), as measured by the number of days that it takes for the autocorrelation function of each SOM pattern to decay by a factor of e, the match between Figs. 4a and 4b suggests that a substantial fraction of the interdecadal Arctic SAT trend can be explained by the interdecadal trend in the frequency of occurrence of spatial patterns that have a large contribution from intraseasonal-time-scale weather. However, as will be discussed below, there is a contribution to the estimated SAT trend shown in Fig. 4b from interannual-time-scale variability that projects onto the intraseasonal-time-scale patterns. Nonetheless, the intraseasonal decay of the autocorrelations in Fig. 5 suggest that intraseasonal variability is important for driving the Arctic SAT trend. (The time series for the amplitude of each SOM pattern were obtained by projecting the daily SAT onto the SOM pattern, i.e., calculating the dot product between the daily SAT anomaly field and each SOM pattern. Note that these projections are not part of the SOM analysis.) As discussed in the introduction, these results, on their own, do not indicate whether or not the trends in the frequency of each SOM pattern arise from natural variability.

Next, we quantify the intraseasonal and interannual contribution to the SOM patterns. We use two approaches. In the first approach we remove the interannual variability from the projection time series by subtracting the DJF mean from each season. For the SOM patterns, we find that the variance of the resulting time series varies between 66% and 82% (with a median of 76%) of the corresponding time series that includes interannual variability. The actual variance due to intraseasonal-time-scale processes is larger than these values, because seasonal-mean sampling of an intraseasonal AR(1) process can account for a substantial fraction of the interannual variance. This relationship between intraseasonal-time-scale fluctuations and interannual variance is known as climate noise (e.g., Madden 1976; Madden and Shea 1978; Feldstein 2002; Franzke 2009). A climate noise calculation was performed by computing 1000 synthetic time series, each using the lag-1-day autocorrelation of the corresponding SOM projection time series. As the median interannual variance from climate noise was found to be 44% of the total interannual variance, these results imply that, on average, intraseasonal time scales account for about 87% of the total variance. In the second approach, we reconstruct the daily SAT fields by assigning each day to the SOM pattern with the minimum Euclidean distance (as discussed in section 2a). Removing the interannual variability from the resulting SAT field, by subtracting the DJF mean from each season, shows that about 84% of the variability in the SAT is generated on intraseasonal time scales. Although these results indicate that intraseasonal-time-scale processes dominate the variance of the SOM patterns, the SOM method cannot quantify the exact fraction of the Arctic amplification trend that is explained by intraseasonal-time-scale processes. Nevertheless, these results are strongly suggestive that intraseasonal-time-scale processes play an important role in Arctic amplification.

In spite of these results, however, we recognize the importance for future research to further examine the relative importance of intraseasonal and interannual variability on Arctic amplification. It is important to note that our method is targeted toward understanding the intraseasonal contribution to Arctic warming.

To determine the processes that are contributing to the Arctic SAT trend, we next examine the thermodynamic energy budget of the SAT anomalies that characterize each SOM pattern. However, because the large number of SAT anomalies (labeled by green boxes in Fig. 7) make the examination of the thermodynamic energy budget cumbersome, for the remainder of this study, we focus only on the SOM patterns with statistically significant increasing or decreasing trends (Fig. 2). These trending SOM patterns that form the focus of the remainder of this study are patterns 1, 3, 5, and 8. SOM patterns 2, 4, 6, 7, and 9 are also examined, but are deferred to the online supplemental material.

We begin our discussion of the thermodynamic energy budget with the SAT anomaly labeled “A” (indicated by a green box over Siberia) associated with SOM pattern 1 (Fig. 7, top left). For SOM pattern 1, the SAT anomaly labeled “A” is referred to as “SOM P1: A” in Fig. 8. Although SOM P1: A is characterized by colder than average temperatures within the interior of Asia, poleward of this anomaly, within the Arctic, warmer than average temperatures are observed (Fig. 7, top left). Therefore, SOM P1 is reminiscent of the warm Arctic–cold continent SAT trend pattern observed in recent decades (e.g., Cohen et al. 2014). As discussed in the previous section, to determine what terms are driving SOM P1: A, each term in the thermodynamic energy equation, (5), is integrated forward in time using (7). The box-averaged SAT values calculated from this integration, as well as the box-averaged composite SAT anomaly itself, are shown in Fig. 8 (top left).

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(top to bottom) Thermodynamic energy budgets of the alphabetically labeled surface air temperature (SAT) anomalies shown in Fig. 7 for patterns 1, 3, 5, and 8, respectively. Each panel corresponds to a different surface air temperature anomaly boxed in green in Fig. 7. The curves in each panel correspond to different terms in the thermodynamic energy equation (see legend). The thick gray line corresponds to the domain (area-weighted)-average SAT anomaly composite minus the lag day −15 SAT anomaly. The remaining terms (also domain averaged) are $-\mathbf{u}\cdot \nabla T+\overline{\mathbf{u}\cdot \nabla T\hspace{0.17em}}$ (thick red), $\hspace{0.17em}-{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}+\overline{{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}}$ (thin red), $\hspace{0.17em}-\overline{\mathbf{u}}\cdot \nabla T^{\prime }+\overline{\overline{\mathbf{u}}\cdot \nabla T^{\prime }}$, (dashed red) $-{\mathbf{u}}^{\prime }\cdot \nabla T^{\prime }+\overline{{\mathbf{u}}^{\prime }\cdot \nabla T^{\prime }}$ (dotted red), anomalous adiabatic warming/cooling (green), anomalous vertical advection (yellow), anomalous diabatic heating (thick blue), longwave heating/cooling (thin blue), vertical mixing + latent heating (dashed blue), and the sum of diabatic term with the advection terms and adiabatic warming (thin gray). The gray lines correspond to the right y axis, while the remaining terms correspond to the left y axis. Note that all terms that appear on the right-hand side of the thermodynamic energy equation, (5), are integrated using the composite values at each lag (x axis). Statistical significance at p < 0.10 is indicated with × marks.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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Upon examination of SOM P1: A (Fig. 8, top left), we can see that the SAT anomaly (thick gray line) reaches a peak value of about −4.0 K at lag day +1 (right y axis). The term in the thermodynamic energy equation that most strongly contributes to this SAT anomaly over Siberia is the anomalous horizontal temperature advection (thick red line; left y axis), which is dominated by the contribution from the anomalous wind, $\left(-{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}+\overline{{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}}\right)$, shown by the thin red line. This term, which corresponds to the advection of the climatological temperature by the anomalous wind, contributes about −10 K of temperature change over the 30-day integration period for SOM P1: A. This finding, and the fact that SOM P1 has been occurring more frequently, supports the idea that changes in the large-scale circulation, and the accompanying changes in horizontal temperature advection, have contributed to the emergence of the warm Arctic–cold continent SAT pattern (Clark and Lee 2019).

The driving of the negative SAT anomaly of SOM P1: A by the term $\left(-{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}+\overline{{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}}\right)$ is consistent with the fact that the SAT anomaly is located in a region where the anomalous sea level pressure gradient is maximized (see the contours in Fig. 7, top left). In addition, the vertical mixing + latent heat release term (dashed blue line) also contributes to the negative SAT anomaly of SOM P1: A. However, the contribution to the SAT anomaly by vertical mixing + latent heat release is overall much weaker than that by horizontal temperature advection.

For SOM P1: A, the sum of all the integrated terms in the thermodynamic energy equation (thin gray line in Fig. 8) is almost equal to the temperature change (thick gray line). This confirms that our breakdown of the thermodynamic energy equation is reasonable at this location. However, for other regions examined in Fig. 8, there are often discrepancies between the thick and thin gray lines, most likely due to the fact that the temperature changes associated with individual terms in the thermodynamic energy equation can be an order of magnitude greater than the observed change in temperature. As a result, small numerical errors in the calculations of the dominant terms on the rhs of (5) can lead to larger errors in the summation curve (thin gray line) relative to the observed temperature change (thick gray line). Sources of error in the calculation of the dominant terms include the following:

• The use of a 24-h time step in our integration of daily mean quantities, which is significantly larger than the reanalysis time step of about 12 min (ECMWF 2014).

• The use of a horizontal resolution (2.5°) that is significantly coarser than that of the reanalysis model, which integrates the thermodynamic equation with the spectral transform method (ECMWF 2014).

• The lack of a horizontal diffusion term in our analysis, which is present in the reanalysis model but is not available for download from ECMWF or easily applied to observations (ECMWF 2014).

• The absence in our budgets of an analysis increment that is generated by ECMWF from 12-hourly data assimilation.

• The use of diabatic heating terms that represent the daily average of 12-min time steps, which differs from the daily average of 6-hourly data that was used in the other terms.

Considering these sources of error, which are often insurmountable or unavoidable, a balanced budget is not expected to occur over most regions. Nevertheless, it is still useful to examine the dominant terms in the thermodynamic budgets with these sources of error in mind.

Upon examination of the remaining panels in Fig. 8, a similar picture to that seen for SOM P1: A emerges. Specifically, the advection of the climatological temperature by the anomalous wind plays a central role in driving the growth of each SAT anomaly shown in Fig. 7, while longwave heating/cooling plays a crucial role in the decay of each SAT anomaly. This can be seen in Fig. 8 by the fact that the sign of the temperature curve (thick gray line) is usually the same as the sign of the horizontal temperature advection curve (thick red line). Furthermore, for all domains, vertical advection and adiabatic warming are unimportant contributors to the SAT anomalies relative to the other terms in the thermodynamic energy equation. However, unlike that seen for SOM P1: A, vertical mixing + latent heat release does not consistently contribute to the growth of SAT anomalies. In fact, vertical mixing + latent heat release more often contributes to the decay of SAT anomalies. For example, for SOM P1: B, SOM P3: A, SOM P8: A, and SOM P8: D, vertical mixing + latent heat release plays an even more important role in the decay of the SAT anomalies than does longwave heating/cooling. Vertical mixing + latent heat release only contributes to the growth of four SAT anomalies: SOM P1: A, SOM P5: A, SOM P8: B, and SOM P8: E.

The finding that vertical mixing contributes to the growth of only four SAT anomalies is in contrast with the sea ice albedo feedback mechanism for Arctic amplification, which predicts the growth of SAT anomalies to be dominated by vertical mixing in regions of pronounced sea ice decline. In addition, inspection of the location of these four SAT anomalies in Fig. 7 (SOM P1: A, SOM P5: A, SOM P8: B, and SOM P8: E) indicates that vertical mixing contributes to the driving of SAT changes only over continents and open ocean, where sea ice is not present climatologically.

In all but one instance (SOM P5: A), advection of the climatological temperature by the anomalous wind is the dominant contributor to SAT anomaly growth. As discussed for SOM P1: A, this finding is consistent with the fact that the SAT anomalies shown in Fig. 7 tend to be largest in regions where the amplitude of the anomalous sea level pressure gradient maximizes. In the one instance where temperature advection does not dominate the driving of the SAT anomaly, for SOM P5: A, it is vertical mixing + latent heat release that dominates the driving of the SAT anomaly.

According to the ice albedo feedback mechanism, as discussed in section 1, the melting of Arctic sea ice will result in an upward sensible and latent heat flux, in addition to an upward longwave radiative flux, followed by widespread warming over much of the Arctic. Since the sea ice melting will be confined to a relatively small region within the Arctic, the corresponding warming must be initially confined to the same small region, and the widespread warming over the Arctic that follows the sea ice melting must be accomplished by horizontal temperature advection. If this scenario has been taking place, however, we would expect to see strong contributions to the horizontal temperature advection from$\hspace{0.17em}\left(-\overline{\mathbf{u}}\cdot \nabla T^{\prime }+\overline{\overline{\mathbf{u}}\cdot \nabla T^{\prime }}\right)$ and/or $\left(-{\mathbf{u}}^{\prime }\cdot \nabla T^{\prime }+\overline{{\mathbf{u}}^{\prime }\cdot \nabla T^{\prime }}\right)$ (i.e., horizontal temperature advection associated with the SAT anomalies). However, our findings show that advection of the climatological temperature by the anomalous wind $\left(-{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}+\overline{{\mathbf{u}}^{\prime }\cdot \nabla \overline{T}}\right)$ dominates the SAT changes. This finding provides further support to the perspective that surface heat fluxes are not important contributors to the fraction of the Arctic SAT trend shown in Fig. 4b.

b. The causes of skin temperature trends: The surface energy budget

In section 2 and section 3a, we showed that a substantial fraction of the SAT trend is driven by the trend in the frequency of occurrence of the nine SOM patterns (Fig. 2). In Fig. 9b, we show that the trend in the frequency of the nine SOM patterns (Fig. 2) can also explain a substantial fraction of the total SKT trend, since substitution of the SKT anomaly composites (Fig. 10 and Fig. S2 in the online supplemental material, leftmost column) in place of SAT_p(x, y) in (4) leads to a good match with the observed SKT trend (Fig. 9a). To determine what processes are contributing to the SKT trend shown in Fig. 9b, we derive an equation for the evolution of SKT anomalies.

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(a) The observed 1990–2016 DJF skin temperature trend. (b) The approximated (see text) 1990–2016 DJF SKT trend using self-organizing maps.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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(top to bottom) Composite surface energy budget for self-organizing map patterns 1, 3, 5, and 8, respectively. (left to right) Lag-day-0 composites of the skin temperature anomaly, surface downward longwave radiation anomaly, surface (latent + sensible) heat flux anomaly, residual, and the 2-m temperature anomaly minus the skin temperature anomaly, respectively. The pattern correlation with the corresponding skin temperature anomaly pattern is indicated in the top-left corner of each panel (except for the rightmost column, which does not appear in the surface energy budget equation). Each quantity of the surface energy budget represents a daily mean. Statistical significance at p < 0.10 is indicated by the stippling.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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Compared to all other terms in (11), the surface DLR anomalies most strongly resemble the SKT anomalies (Fig. 10), with a pattern correlation of about 0.90 for all SOM patterns. The pattern correlations between the SKT and all other terms in the surface energy budget (i.e., the surface heat fluxes and residual) are substantially smaller. In light of the strong correlation between the DLR and SKT anomaly patterns, one can ask whether the SKT anomalies are caused by the DLR anomalies or vice versa. We can gain insight into this question by considering the other terms in the surface energy budget. For regions where there are positive SKT anomalies, if the SKT were to increase the DLR, a flux of heat from the surface to the atmosphere must occur. Therefore, if such a process were occurring in observations, we would expect to see upward (negative) surface heat fluxes in regions of positive SKT anomalies. However, for all four SOM patterns in Fig. 10, the correlations between the SKT field and the surface heat fluxes are positive (downward surface heat fluxes over regions with positive SKT anomalies). In addition, if the SKT were not driven by the fluxes from the atmosphere, then the SKT would be driven by residual processes. Contrastingly, for all four SOM patterns in Fig. 10, the residual is negatively correlated with the SKT anomaly pattern. These results imply that the surface DLR anomalies likely drive the SKT anomalies, not the other way around. In addition, these results also indicate that DLR is the primary driver of the SKT trend shown in Fig. 9b. However, we must emphasize that, although DLR is driving the SKT anomalies, DLR is not driving the SAT anomalies. As discussed in the previous subsection, SAT anomalies are driven primarily by horizontal temperature advection.

One may ask why longwave radiation drives temperature anomaly growth at the surface (Fig. 10), but the temperature anomaly decays at only 2 m above the surface (Fig. 8). The reason is illustrated schematically in Fig. 11. At the surface, as seen in Fig. 11, longwave radiation contributes to temperature changes solely through absorption of downward longwave radiation (DLR). In contrast, above the surface, the longwave radiation Q₁ has contributions from the absorption of both downward and upward longwave radiation, as well as from the emission of downward and upward longwave radiation.

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Idealized schematic illustrating how longwave radiative fluxes impact the surface air temperature (SAT) and skin temperature (SKT). At a height of 2 m, a layer of depth D is depicted with a temperature (SAT) that is impacted by downward longwave fluxes entering the top of the layer (FDA) and exiting the bottom of the layer (FD2). The temperature of the layer at 2 m is also impacted by upward longwave fluxes entering the layer from the bottom (FUB) and exiting from the top (FU2). The SKT is impacted by only one longwave flux, which is the downward longwave flux at the surface (FDS). The SAT is a fluid and is impacted also by horizontal temperature advection, as indicated, while the SKT can only be impacted by upward or downward fluxes, or other residual processes, as discussed in the text.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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We examine what is driving the longwave radiation at both the surface and 2 m above the surface using the Rapid Radiative Transfer Model (RRTMG; Mlawer et al. 1997; Iacono et al. 2008). In particular, we follow Clark and Feldstein (2020b) and conduct two types of clear-sky radiative transfer calculations. The aim of the first (second) calculation is to determine the contribution that atmospheric temperature (moisture) anomalies have on both the surface DLR and the radiative heating rates on the lowest model level. The first (second) calculation is conducted by inputting the observed temperature and climatological water vapor concentrations (climatological temperature and observed water vapor concentrations) for the entire depth of the atmosphere into RRTMG. For more details about configuring the data for these calculations, see Clark and Feldstein (2020b) and their supplementary material.

After performing RRTMG calculations to determine the anomalous surface DLR and radiative heating rates, composites of surface DLR and radiative heating rate anomalies are calculated for the events discussed in section 2 (Fig. 12 and Fig. S4). The leftmost three columns of Fig. 12, respectively, show the water vapor–driven contribution to the surface DLR anomalies, the temperature-driven contribution to the surface DLR anomalies, and their summation (column 1 + column 2). The summation of column 1 and 2 is an excellent match with the ERA-Interim clear-sky DLR anomalies (cf. Fig. 12, column 3, to the corresponding SOM patterns in Fig. S3), indicating that the contributions from temperature and water vapor anomalies to the surface DLR anomalies can be linearly separated. As shown in Fig. 12, the dominant contributor to the clear-sky surface DLR is temperature, but water vapor is certainly also important.

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The contribution to the skin temperature anomalies from (column 1) water vapor–driven DLR and (column 2) temperature-driven DLR. (column 3) The sum of columns 1 and 2. Also shown are (column 4) the water vapor–driven and (column 5) the temperature-driven longwave radiative heating rates at the lowest reanalysis model level.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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To quantify the impact that cloud liquid water and ice have on the surface DLR patterns shown in Fig. 9 and Fig. S2, in Fig. 13 we show the difference between the ERA-Interim all-sky and clear-sky surface DLR anomalies (i.e., subtracting the surface DLR anomalies in Fig. S3 from those in column 2 of Fig. 9 and Fig. S2). The result shows that clouds overall amplify the surface DLR anomalies; compare Fig. 13 to the corresponding patterns in Fig. 11 and Fig. S4, column 3. The impact of clouds on surface DLR identified here may also be underestimated due to inaccurate parameterizations of ice nuclei over the Arctic (e.g., Prenni et al. 2007).

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The difference between surface clear-sky downward longwave radiation and surface all-sky downward longwave radiation, using ERA-Interim data.

Citation: Journal of Climate 34, 8; 10.1175/JCLI-D-19-0937.1

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As was seen for the surface DLR, the contribution to the heating rates by water vapor and temperature anomalies can be linearly separated, because the sum of the rightmost two columns is almost exactly equal the total longwave heating rates calculated by ERA-Interim (not shown). Because longwave radiation drives the decay of the lowest-model-level temperature anomalies (Fig. 8), anomalous emission must exceed anomalous absorption. Therefore, as evidenced by Fig. 12 (rightmost two columns), the emission of longwave radiation at the lowest model level is driven primarily by temperature anomalies, providing further justification for the conceptualization using (8). Interestingly, the water vapor–driven contribution to the longwave heating rate sometimes contributes to SAT anomaly growth, but the amplitude is small (Fig. 12, column 4).

Returning to the remaining panels of Fig. 10, we conclude this subsection by considering the surface heat fluxes, which have been implicated as potential contributors to Arctic amplification due to amplified sea ice decline. Apart from showing that the SKT anomalies of each SOM pattern are driven by anomalies in surface DLR, Fig. 10 also shows that the surface heat fluxes are driven in large part by the difference between the SKT and SAT anomalies (cf. Fig. 10, columns 3 and 5). This implies that the surface heat flux anomaly patterns shown in Fig. 10 can be explained by horizontal temperature advection because the SAT anomalies are driven directly by horizontal temperature advection, as shown in Fig. 8, and the SKT anomalies are, in large part, driven indirectly by horizontal temperature advection through the changes in surface DLR. Changes in moisture also impact the SKT through changes in surface DLR (Figs. 11 and 12) and although we did not examine what drives the moisture changes, it is likely that the circulation plays a prominent role here as well. The circulation changes associated with the SOM patterns would presumably also act to advect the climatological moisture field, which has a similar gradient field to that of the climatological temperature. All of these results highlight the prominent role that the circulation has on Arctic SKT variability.