## Mean meridional component of wind velocity in the atmospheric layers around 70°N

For any component of AMET, an essential variable is the northward wind velocity. Therefore, we first investigated the wind fields around the parallel 70°N (Fig. 1).

The three chosen layers represent the lower troposphere with a direct interaction with the Earth’s surface, the middle troposphere with a steering flow and the upper troposphere, where the main jet streams are located. The fields are very similar for both periods and so we focus on the present period, 1979–2019. The calculation of AMET through the latitude 70°N is consistent with the meridional wind fields, as this parallel crosses the large areas of increased wind velocity near their cores.

The results show that the meridional winds of both directions are the strongest over North America and Greenland. In the lower troposphere, the winds of both directions are weak over Eurasia, and there is a steady northward direction (Fig. 1b). The most clear picture of the alternating wind directions arises in the upper troposphere (Fig. 1e-f). It seems natural dividing the region into two hemispheres separated by the prime meridian 0°: 0°–179°E and 180°–1°W. The area-weighted average wind velocities support this division. In the lower troposphere of the Eastern Hemisphere the winds are directed towards the Arctic (0.23 m s− 1), whereas in the Western Hemisphere, the southward wind direction prevails (-0.34 m s− 1). In the middle and upper troposphere, the situation is reversed: the northward winds prevail in the Western Hemisphere and southward winds prevail in the Eastern Hemisphere (0.36 m s− 1 and 0.77 m s− 1 versus − 0.28 m s− 1 and − 0.65 m s− 1, respectively).

**Analysis of empirical orthogonal functions for the time series of sensible and latent heat transport components and the resulting large-scale regional division**

The time series of sensible and latent heat transports across 70°N (equations 1 and 2) were decomposed into empirical orthogonal functions (EOFs) (Fig. 2).

The leading modes of variability are nearly exactly divided into the Eastern and Western Hemispheres: variability of the sensible heat transport dominates in the Western Hemisphere, whereas that of the latent heat transport dominates in the Eastern Hemisphere. This division is more pronounced for the latent heat transport. The three EOFs in the figure explain about 50% of the variability for each heat transport component. The hemispheric pattern in the modes of variability is preserved if additional EOFs are added. For the sensible heat transport, the first eight EOFs explain 81% of the variance, and the first eight EOFs for the latent heat transport explain 79% of the variance. These results confirm the robustness of the identified hemispheric division for the components of the heat transport. The possible physical reasons are addressed further.

**Anti-phase pattern in the sensible and latent heat transports between the Eastern and Western Hemispheres**

In order to examine the vertical structure of sensible and latent heat transports, they were longitudinally averaged for the Eastern and Western Hemispheres. The noisy monthly time series were averaged to obtain annual means (Fig. 3a-d).

These time-altitude diagrams demonstrate the prevalence of sensible and latent heat transports into the Arctic in the lower troposphere (1000–800 hPa) and from the Arctic in the middle and upper troposphere for the Eastern Hemisphere. For the Western Hemisphere, the vertical distribution of the heat fluxes is opposite, which indicates a dipole anti-phase pattern between the hemispheres. According to the concept of the polar circulation cell19, heat transport should be directed into the Arctic in the upper troposphere and from the Arctic in the lower troposphere, which is true for the Western Hemisphere, but completely different in the Eastern Hemisphere. However, the anti-phase pattern is more stable for the sensible heat transport, because for the latent heat transport, there are layers with the same direction of fluxes in both hemispheres. For instance, these features are seen around 700–800 hPa (Fig. 3c-d).

The vertical cross-sections (Fig. 3a-d) show visually notable differences in the variability between the hemispheres, especially for the latent heat transport. Indeed, the interannual standard deviation averaged over the height of the troposphere (1000–100 hPa) is 0.61 kW m− 2 for the latent heat transport in the Eastern Hemisphere and only 0.45 kW m− 2 in the Western Hemisphere. This means the interannual variability of latent heat transport is 1.36 times higher in the Eastern Hemisphere than in the Western Hemisphere. For the sensible heat transport, the interannual variability is comparable, being 68.45 kW m− 2 in the Western Hemisphere and 71.53 kW m− 2 in the Eastern Hemisphere, which is only 1.05 times higher. However, the temporal mean of the standard deviations over the isobaric surfaces reveals the dominance of sensible heat transport in the Western Hemisphere because it is 192.7 kW m− 2 here versus 130.97 kW m− 2 in the Eastern Hemisphere. This means the variability of sensible heat transport over the isobaric surfaces is 1.47 times higher in the Western Hemisphere than in the Eastern Hemisphere, which is also supported by a stronger vertical colour gradient in Fig. 3b than in Fig. 3a. The same estimates for the latent heat transport give a value of 1.35 kW m− 2 for the Western Hemisphere and 1 kW m− 2 for the Eastern Hemisphere. This means the variability of latent heat transport over the isobaric surfaces is 1.35 times higher in the Western Hemisphere than in the Eastern Hemisphere.

Thus, the hemispheric division based on the modes of variability in Fig. 2 corresponds to the highest ratios in the standard deviations (1.36 and 1.47). Whether the variability with time or height (isobaric surfaces) dominates the overall variability in latent heat transport and sensible heat transport depends upon the hemisphere. A more clear division into the Eastern and Western Hemispheres in Fig. 2 for the latent heat transport might be due to a higher overall importance of interannual standard deviations at different isobaric surfaces compared to standard deviations over isobaric surfaces for every year.

**Fully integrated sensible and latent heat transports in the lower and entire troposphere and their net values through the Arctic gate**

The monthly integral sensible and latent heat transports in the lower troposphere (1000–800 hPa) and the entire troposphere (1000–100 hPa) were studied (Fig. 4). The layers were identified based on the previous results on the mean directions of heat fluxes (Fig. 3).

The loess smoothing was applied to demonstrate the anti-phase pattern between the hemispheres (Fig. 4a-d) and the sign of the net fluxes (Fig. 4e-f). For the sensible heat transport in the entire troposphere (Fig. 4a and e), heat transport is mostly directed into the Arctic due to a stronger mean heat influx in the Western Hemisphere than heat outflux in the Eastern Hemisphere. The correlation coefficients for the unsmoothed time series used in the Fig. 4a are − 99.68% and − 99.56% for the smoothed time series displayed in the Fig. 4a. For the sensible heat transport in the lower troposphere (Fig. 4c and e), heat transport is mostly directed away from the Arctic due to a weaker mean heat influx in the Eastern Hemisphere than heat outflux in the Western Hemisphere. Thus, in the lower troposphere, the direction of heat fluxes in the hemispheres is flipped. The correlation coefficients for the unsmoothed time series used in the Fig. 4c are − 88.18% and − 79.85% for the smoothed time series displayed in the Fig. 4c.

For the latent heat transport in the entire troposphere (Fig. 4b and f), heat transport is mostly directed into the Arctic due to a combined effect of mean positive heat influxes in the Eastern and Western Hemispheres. This is also confirmed by a large area of intersection for the interquartile ranges in Fig. 4b and by significantly higher absolute values for the 75th percentiles than for the 25th percentiles. However, the clearly seen anti-phase pattern is preserved, and the correlation coefficients for the unsmoothed time series used in the Fig. 4b are − 82.07% and − 77.02% for the smoothed time series displayed in the Fig. 4b. For the latent heat transport in the lower troposphere (Fig. 4d and f), heat transport is also mostly directed into the Arctic, but due to a stronger mean heat influx in the Eastern Hemisphere than heat outflux in the Western Hemisphere. The correlation coefficients for the unsmoothed time series used in the Fig. 4d are − 65.65% and − 53.67% for the smoothed time series displayed in the Fig. 4d.

The internal energy budgets defined by the sums of sensible and latent heat fluxes between the hemispheres are − 0.65 ± 0.09 PW for the lower troposphere 1000–800 hPa and 4.28 ± 0.18 PW in the entire troposphere 1000–100 hPa. In both cases, the overall sign is defined by the several orders of magnitude higher absolute values of sensible heat flux than of latent heat flux. The mean values and corresponding uncertainties for the intermediate cases are shown in the Table 1.

Table 1. Mean heat fluxes of sensible heat transport (SHT) and latent heat transport (LHT) for the Eastern Hemisphere (EH) and Western Hemisphere (WH).