We use the latest reanalysis from the European Centre for Medium-Range Weather Forecasts (ECMWF), ERA5 (Hersbach et al., 2020), in this study. For the detection and Eulerian analysis of WaMAIs in the 40 recent winters (DJF from 1979 to 2018), we use the reanalysis dataset at a 6-hourly temporal and 0.75∘ horizontal resolution. This includes the vertically integrated northward water vapor flux (fw), sea-ice concentration (SIC), 500 hPa geopotential height (GH500), 2 m air temperature (T2m), 850 hPa temperature (T850), total water path (TWP), liquid water path (LWP), ice water path (IWP), and precipitation rate (PRCP). For the Lagrangian analysis, we also use ERA5 3D wind field at a 6-hourly resolution for the calculations of air-mass trajectories during WaMAIs, in the same way as described in You et al. (2020, 2021). We additionally interpolate energy-budget terms with forecast data from ERA5 at the higher temporal resolution (1-hourly). This includes surface net solar (Fsw) and thermal (Flw) irradiances, the surface sensible (Fsh), and latent heat fluxes (Flh), as well as the 1-hourly temperature tendencies due to different model physics extracted at model levels.

Utilizing the ERA5 reanalysis introduces uncertainty, especially for anything that comes from parameterized model physics such as cloud parameters and the energy budget. Large upward residual heat flux biases exist among all reanalyses, and turbulent heat fluxes over the sea ice are also poorly simulated in all seasons (Graham et al., 2019). ERA5 has a larger warm bias in winter, especially when the surface temperature is under -25∘C. Sea-ice thickness is thinner in ERA5 because of the larger warm bias and higher precipitation (Wang et al., 2019). In the data assimilation, the main variables in a reanalysis are constrained by observations, and in situ observations over the central Arctic Ocean are sparse, especially in winter. The loss of all visible wavelengths in passive remote sensing in winter also makes many satellite products less trustworthy. However ERA-Interim, the predecessor of ERA5, generally performs best among the available reanalysis datasets, especially for the wind (Lindsay et al., 2014), and substantial progress has been made in data quality and diagnostic techniques during last few decades (Mayer et al., 2019). However, it would be not possible to analyze air mass transformation climatologically on the energy budgets along the trajectories of winter WaMAIs in any other way than relying on a reanalysis. Here, we alleviate uncertainty in two ways: first by averaging over a large number of cases and second by considering anomalies rather than actual mean values. Avoiding single case studies reduces random errors, while considering anomalies reduces systematic errors.

Clouds and moisture are integral and important parts of the Arctic surface and boundary-layer energy budgets, and relative humidity in the Arctic boundary layer is almost always high (Andreas et al., 2002; Persson et al., 2002). A particular warm air intrusion may carry less moisture than a typical moist intrusion, but a typical moist intrusion will certainly carry warm air into the Arctic. We therefore name these events as “warm and moist air intrusions”, and we identify and quantify them with the vertically integrated northward moisture flux, fw, separately over the ocean sectors of Barents, Kara, Laptev, East Siberian, Chukchi, and Beaufort (Fig. 1). Among these sectors, winter SIC only varies substantially with time over the Barents Sea and Kara Sea. North of 80∘ N in the Barents Sea, SIC has a statistically significant regression with fw (Fig. 2a). Locations that pass a p<0.05 Student's t test (stippled in Fig. 2a) are considered the sensitive region. For the remaining sectors, all sea-ice-covered locations are considered sensitive regions since they do not display winter variability in SIC. The mean fw values over each sensitive region, fw‾, are approximately normally distributed (Fig. 2b and d). We define a WaMAI as a continuous period when fw‾>0 (red lines in Fig. 2c and e) with a maximum larger than the 95th percentile of the distribution of all values of fw‾. The portions of WaMAIs when fw‾ is larger than the 95th percentile are moreover considered extreme moist intrusions (EMIs; blue line in Fig. 2c and e); note that each WaMAI can only include one EMI. The onset and terminal time of a WaMAI is taken at the nearest minimum values of fw‾ or zero of fw‾.

Similar to You et al. (2021, 2020), ensembles of 2 d forward and backward trajectories at different altitudes are calculated for each WaMAI over all ocean basins, using the trajectory algorithm from Woods et al. (2013). Over each ocean sector and for each WaMAI, we select a launch point along a latitude circle where the T850 is the largest. The latitude circle of 75∘ N (blue lines in Fig. 2a) is used for all ocean sectors, except for the Barents Sea where 80∘ N (red line in Fig. 2a) is used. Forward (backward) trajectories are also terminated where they start to track southward (northward) (requirement 1). Hence, we only capture the part of each trajectory that continuously tracks northwards. Finally, the terminal points of selected trajectories have to be at least 5∘ north of the sea-ice edge (requirement 2), defined as where SIC exceeds 15 % and reaches 80∘ N (requirement 3; 85∘ N for the Barents sector). Taking the Barents sector as an example, we have checked how strict requirement 1 is by counting how many trajectories turn southward before they reach 85∘ N. According to our calculation, there are 45 (8.2 %) trajectories tracking southward before they reach 85∘ N. Similarly, we have also checked how strict requirement 2 is by calculating the number of trajectories which are all the way north and reach 85∘ N, but the terminal point is less than 5∘ north of the sea-ice edge. The results show that only 28 (5 %) trajectories are in this case. Actually the strictest requirements is requirement 3. Around 59 % of trajectories cannot meet this requirement, but this requirement is necessary since we want to look at how the air column evolves on its way to the central Arctic over the sea ice.

Trajectories are calculated at several different heights, every 100 m, from 300 to 800 m, and vertical profiles of the various variables are then extracted from ERA5, from the surface to 2 km, by interpolation in time and space along each of these trajectories. The final vertical cross-section for each WaMAI is the ensemble average of the results along all trajectories initialized at different heights. For the 40 winters in this study, 87 (124) WaMAIs are detected over the ocean sectors with open ocean (land-locked sea ice) for a total of 211 WaMAIs. Their launch time and launch longitudes are listed in Tables S1 and S2, respectively.

It is to be noted that both the temporal and spatial resolutions may increase the accuracy of the trajectory calculation (Draxler, 1987; Kahl and Samson, 1986; Stohl et al., 1995). However, it is less effective to only improve the temporal resolution if the spatial resolution is very low (Stohl et al., 1995). Minimally, a 6 h temporal resolution is needed to resolve diurnal variations in the wind field (Stohl et al., 1995), supporting the temporal resolution used in this paper. As the error of trajectory calculation increases exponentially with time, in this study, we calculate the trajectories 2 d forward and backward, instead of calculating 4 d trajectory at once. Errors are also introduced by the vertical interpolation from pressure level to geometric height. The vertical interpolation of vertical velocity produces larger errors than the vertical interpolation of horizontal components (Stohl et al., 1995).

As shown in Eq. (1), total surface energy-budget (Ftotal) is contributed by surface net solar irradiance (Fsw), surface net thermal irradiance (Flw), surface turbulent sensible heat fluxes (Fsh), and surface turbulent latent heat fluxes (Flh). Note that all surface net energy fluxes contributing to a surface warming are considered positive. Individual terms in Eq. (1) are also interpolated from ERA5 at each 0.5∘ interval in latitude along the trajectories. 1Ftotal=Fsw+Flw+Fsh+Flh We also evaluate the cloud longwave radiative effects (CREs) (Flw_CRE=Flw_all_sky-Flw_clear_sky), using the same method. Flw_all_sky is the surface net thermal irradiance, considering the actual clouds' presence, while Flw_clear_sky is the clear-sky counterpart, assuming clouds were not present.

For the atmospheric energy-budget calculations, we also extract the temperature tendencies due to different model physics from ERA5, where we can resolve all terms in the thermal equation (Eq. 2). As shown in Eq. (2), the total temperature tendency Tt of an air mass in a WaMAI is contributed by heating/cooling from the divergence of shortwave irradiance (∂T∂tsw), longwave irradiance (∂T∂tlw), vertical turbulent heat flux (∂T∂tTH), and the latent heat of condensation in cloud formation (∂T∂tLH). In a Lagrangian view, the advection tendencies are by definition zero, while in an Eulerian view the total tendencies would additionally be balanced by temperature advection. All these terms are also interpolated along the trajectories as previously discussed (also see You et al., 2020, 2021). 2Tt=∂T∂tsw+∂T∂tlw+∂T∂tLH+∂T∂tTH Note that while the surface energy-budget depends on the surface fluxes, the atmospheric energy-budget depends on the vertical gradient of fluxes.

EMIs were identified in the Arctic Ocean basins of Barents Sea, Kara Sea, Laptev Sea, East Siberian Sea, Chukchi Sea, and Beaufort Sea. Figure 3 (Fig. 4) shows the composite of all EMIs over the Barents Sea (Beaufort Sea), representing the large-scale features of winter EMIs over ocean sectors with open ocean (land-locked sea ice). Both Figs. 3a and 4a show one pair of negative and positive GH500 anomalies with a large geopotential height gradient in between, generating an intensive fw anomaly directed into the Arctic (Figs. 3c, 4c), enhancing temperature advection (Figs. 3b, 4b) and cloud formation (Figs. 3d, 4d), consistent with previous studies (Tjernström et al., 2015; Overland and Wang, 2016; Gong and Luo, 2017; Johansson et al., 2017; Sedlar and Tjernström, 2017; Messori et al., 2018; Cox et al., 2019; You et al., 2021). Unlike over the Barents Sea, where the TWP anomaly is dominated by LWP (Fig. 4d and e), TWP over the Beaufort Sea is dominated by IWP. These features in the GH500, T850, and TWP anomalies are also found in all other ocean basins (Figs. S1, S3, S5, S7 in the Supplement).

As warm and moist air is advected into the Arctic over the Barents Sea, it interacts with the cool ice surface through turbulence and radiation, enforcing positive Fsh, Flh, and Flw anomalies at the surface (Fig. 5c, d and e). The Fsh anomaly reaches >60 W m-2 over open water near the Norwegian coast, tapering off northward over the ice all the way to the pole. The pattern of Flh anomaly is similar to that of Fsh south of 80∘ N but decreases to nearly zero over the sea ice north of 80∘ N. Positive LWP and IWP anomalies in Fig. 3d and e, extending from the coast to the north pole along the path of the EMIs, also affect the surface energy-budget with a positive Flw anomaly (Fig. 5c). This relation between Flw anomaly and winter EMIs over the Barents Sea is also discussed in other climatological analyses (Gong et al., 2017; Gong and Luo, 2017). In total, these anomalies in the surface energy fluxes sum up to a positive Ftotal anomaly, inducing decreased SIC (Fig. 5b).

A similar surface energy-budget pattern is also found over the Beaufort Sea (Fig. 6) and other ocean sectors with land-locked sea ice (Figs. S2, S4, S6, S8) but with some differences. The anomaly in Ftotal over the Barents Sea is dominated by Fsh, while Ftotal anomaly over the Beaufort Sea is dominated by Flw. The magnitudes of Fsh, Flh, and Ftotal anomalies over the Beaufort Sea are less than half the magnitude of those over the Barents Sea, especially south of 80∘ N and hence induce 4 times less SIC decrease. As EMIs occur over the Beaufort Sea, positive Fsh, Flh, Ftotal, Flw, LWP, and IWP anomalies and negative SIC anomaly is found. However, negative Fsh, Flh, Ftotal, Flw, LWP, and IWP anomalies and positive SIC anomalies could also be found over the Barents Sea sector, while some WaMAIs from the Beaufort Sea pass through the pole and become cold spells over the Barents Sea (Figs. 4 and 6).

Table 1 summarizes the averaged surface energy-budgets over sea ice across the six basins. Except for the Barents Sea, Flw anomalies are almost twice larger than Fsh anomalies. Since Fsw anomalies can be ignored in winter, the Flw anomalies dominate Ftotal. However, over the Barents Sea, Fsh anomalies are almost twice larger than Flw anomalies and contribute to more than 50  % of Ftotal anomalies. Over the Barents Sea and Chukchi Sea, positive Fsh anomalies are statistically significant, which is not the case for any of the other sectors. Except for the Laptev Sea, positive Ftotal and Flw anomalies are statistically significant. Here, if the mean values of these surface energy-budget terms are positive and they are still greater than 0 after deducting their standard deviation, then we consider that they are statistically significantly positive. This definition is quite lax, since it only passes 0.32 for Student's significance test.

The composites of large-scale pattern discussed above are extracted from the stronger EMI events to generate a clear signal; however, these may not necessarily represent the general pattern of all WaMAIs. Therefore, linear regressions of daily averaged GH, T850, SIC, Ftotal, Fsh, Flh, Fsw, and Flw anomaly against the time series of daily averaged fw‾ over the sensitive regions in 40 recent winters were calculated separately for all the examined ocean basins. All the regressed fields have a similar pattern as their counterparts in Figs. 3–6, implying a similar relationship for all days but at smaller magnitudes. Since the regressions confirm the conclusions, we will consider only the Barents Sea and Beaufort Sea as an example of ocean sector with open ocean and land-locked sea ice, respectively (Figs. 7 and 8).

In this section, we will explore the transformation of temperature inversion, cloud formation, and surface energy-budget along the trajectories of warm-and-moist air masses over ocean basins with open water and land-locked sea ice, respectively, by compositing the heights to the maximum specific humidity (hsh), temperature (ht), and vertical temperature gradient (htz), along with TWP, LWP, IWP, precipitation rate (PRCP), and surface energy-budget terms (Fsh, Flh, Ftotal, Flw) from all detected WaMAIs.

Over the completely ice-covered sea sectors such as the Laptev Sea, East Siberian Sea, Chukchi Sea, and Beaufort Sea, strong temperature inversion develops with cloud formation below, as the warm-and-moist air propagates over the sea ice. In this case, hsh is higher than ht, and both are higher than htz (Fig. 9a). From the ice edge and onward up to 10∘ north of the ice edge, hsh, ht, and htz increase almost linearly, by 30–40 m per degree latitude (Fig. 9a) as the inversion is lifted. TWP and PRCP also increase northward, although more slowly for the first 2∘, in total by 6 g m-2 and 0.4 mm d-1 per degree latitude, respectively, implying that stratocumulus develops continuously along the trajectories (Fig. 9b, c). The increasing TWP is mainly due to the increase in IWP since LWP is almost constant along the trajectories (Fig. 9b). The increase of htz is comparable to that of summer WaMAIs, while the increase in TWP is about half that of summer WaMAIs (You et al., 2021), since less moisture is available for cloud development in winter (Fig. 4c). The gradual increase of htz, a manifestation of increased boundary-layer mixing, leads to a reduction in near-surface gradients. Since the turbulent heat fluxes at the surface depend on these gradients, the Fsh anomaly decreases gradually at a rate of 1.5 W m-2 per degree latitude (Fig. 10a). Simultaneously, the Flw anomaly increases almost linearly by 2.5 W m-2 per degree latitude, while Flh, the smallest contributor to Ftotal, is almost constant along the trajectories (Fig. 10a). The increase in Flw along trajectories is due to increasing cloud radiative effects by the evolving stratocumulus clouds; Flw_CRE increases at a similar rate as Flw (Fig. 10b). From 0 to 2∘ north of the sea-ice edge, the Ftotal anomaly is dominated by the Fsh anomaly, while farther north it is dominated by Flw anomaly (Fig. 10a). Generally, Ftotal anomaly increases with distance from the sea-ice edge at a rate of 1 W m-2 per degree latitude, and this increasing trend is dominated by Flw anomaly (Fig. 10a).

Over the Barents Sea, with open warm water south of the ice edge, ht and hsh also increase nearly linearly but at a 1.6 times larger rate than those over ocean sectors with land-locked sea ice but starting at considerably smaller values (Fig. 9d). The maximum values of ht and hsp here are comparable to the minimum values over the completely ice-covered sectors, implying that WaMAIs over the Barents Sea develop a shallower well-mixed layer and hence bring the moist and warm air closer to the surface. However, the temperature inversion over the Barents Sea is too weak to be easily identified with the metrics used above. Unlike for the sectors with land-locked sea ice, TWP and PRCP are constant with downwind distance from the ice edge, varying slightly around 150 g m-2 and 7 mm d-1 (Fig. 9e, f). As a consequence, Flw anomaly and Flw_CRE along the trajectories (Fig. 10c, d) are nearly constant with northward distance. Although TWP remains quasi-constant, LWP (IWP) decreases (increases) at a rate of -6 g m-2 (+6 g m-2) along the trajectories (Fig. 9e). From 0 to 4∘ north of the sea-ice edge, TWP is contributed by LWP and IWP in about equal parts, while from 4∘ north of the sea-ice edge and onward, TWP gradually becomes dominated by IWP. The Fsh anomaly decreases fast by nearly 50 % over the first 2∘ from the sea-ice edge (Fig. 10c). From 2 to 10∘ north of the sea-ice edge, the decrease is more moderate at a rate of 4 W m-2 per degree latitude (Fig. 10c), which is still faster than that over the completely frozen ocean sectors. However, the Fsh anomaly is still larger than the largest corresponding value for the completely frozen ocean sectors, even 10∘ north of the ice edge (Fig. 10a). This is likely due to the much warmer upstream conditions over the open ocean. The large thermal contrast between open ocean and sea-ice surface contributes to the stable atmospheric layer over the sea-ice surface and rapidly reducing Fsh anomaly, while the decrease of Fsh anomaly with downstream distance is due to the slowly reducing temperature gradient resulting from the turbulent mixing. Similar decreasing trends are also present for Flh and Ftotal anomaly (Fig. 10c). From 2 to 10∘ north of the sea-ice edge, they decrease at a rate of 1 and 5 W m-2 per degree latitude, respectively (Fig. 10c). Within 5∘ north of the sea-ice edge, Ftotal anomaly is dominated by Fsh, while downstream the turbulent heat flux (Fsh+Flh) anomaly becomes comparable to Flw anomaly and contributes almost equally to Ftotal anomaly (Fig. 10c).

Without the presence of solar radiation in winter, the variation of Ftotal anomaly over the Barents Sea is dominated by Fsh anomaly (Fig. 10a), while it is dominated by Flw anomaly over ocean sectors with land-locked sea ice (Fig. 10c). This distinction between ocean sectors with and without open ocean upstream can be explained by the stronger air–sea interaction over the Barents Sea (Kim et al., 2019). Before the air mass is advected in over the sea ice, it is heated and moistened by the ocean and consequently exerts greater turbulent heat fluxes on the surface as it suddenly enters over the sea ice (Fig. 10c). Cloud

Cloud formation happens already upstream in a typical cloud-topped marine boundary layer (Lemone et al., 2018) and is hence not much affected by the advection over sea ice. Instead a much shallower well-mixed layer forms as the air enters over the ice, and the larger vertical gradients resulting from the large temperature difference across the ice edge gives rise to larger Fsh. This dominance of turbulent heat fluxes remains until halfway along the trajectories.

As discussed in previous sections, cloud formation as part of the air-mass transmission can exert large variability on the surface energy-budget. Here, we focus on the cloud effects on the boundary-layer energy budget. For each WaMAI, the boundary-layer energy-budget terms are evaluated and interpolated along the trajectory and analyzed on a case-by-case basis, categorizing patterns into four main categories: (a) lifting temperature inversion (INV), (b) radiation-dominated (RAD), (c) turbulence-dominated (TBL), and (d) turbulence-dominated with cold dome (TCD). Some typical cases are shown in Figs. 11–14, respectively, for these four categories, illustrating different boundary-layer energy budgets in each category, while conceptual summary graphs of all the different categories are summarized in Fig. 15. The boundary-layer energy-budget pattern is very variable from case to case, mainly because the northward component of the advection is different from case to case. Additionally, the location of the ice edge is also different from case to case. Some trajectories are long but reach less far north, while others are shorter but still reach further north. In the vertical, the cases are also subject to different subsidence, affecting the boundary-layer growth. We therefore have not yet come up with a workable idea that would allow for an ensemble average of all the cases.

Almost all WaMAIs over ocean sectors with land-locked sea ice feature a boundary-layer energy-budget pattern of category INV. Similar to category TBL for summer WaMAIs (You et al., 2021), category INV is characterized by increasingly lifting temperature inversion and continuously stratocumulus development near the inversion. Different from the ocean sectors with land-locked sea ice, clouds during WaMAIs over the ocean sector with an upstream open ocean (e.g., Barents Sea) form at the altitude of ∼1 km, above the warm-and-moist air masses. The boundary-layer energy budget here is categorized into three categories (RAD, TBL, TCD). Category RAD is characterized by stronger cloud-top radiative cooling and related buoyant mixing, while category TBL is characterized by more intensive surface turbulent mixing. Category TCD is similar to category TBL excluding a cold dome over the high Arctic. The boundary-layer energy-budget patterns are categorized by manually checking case by case if they have the typical characteristics of each category. Their launch time and launch longitudes are listed in Table S1 in the Supplement. WaMAIs over the Kara Sea sectors are characteristic of both ocean sector with land-locked sea ice and open ocean. Some WaMAIs behave as typical for the Barents Sea, while some behave like those for the other sectors with land-locked sea ice.

Note that unlike radiation and condensation/evaporation, turbulence does not generate heating/cooling by itself. Instead, it heats/cools air locally by redistributing heat from one altitude to another through mixing within the column. Also, note that the temperature tendencies discussed below are only those that are due to model physics in a Lagrangian view, while in an Eulerian framework they would be balanced by advection (not shown). In an absolute sense the boundary layer always undergoes a gradual cooling during the advection over the sea ice.