## 1. Introduction

The Arctic is warming faster than nearly any other region of the planet, and this rapid observed and projected warming has focused great attention on the dynamics of the Arctic climate system (Serreze and Barry 2011; Deser et al. 2010; Graversen et al. 2008; Holland and Bitz 2003). Most research on the Arctic climate has focused on the mean climate state (mainly the seasonal mean), while less consideration has been given to the transitions between seasons and the variability within each season. Seasonal transitions are, however, of equal if not greater significance than the mean climate especially in polar regions. The seasonal transition, especially from winter to spring, has great importance for human activities and for biological systems, as suggested by numerous phenological studies (Cayan et al. 2001; Høye et al. 2007; Linderholm 2006).

The strength of the seasonal cycle is greater in the Arctic than in any other region of the globe (Fig. 1a). In part this is due to the strong cycle in insolation and to local feedbacks associated with the cryosphere. In addition to its large amplitude, the Arctic seasonal cycle is asymmetric, with steeper warming in the spring and slower cooling in the fall (Fig. 1b), presumably because the relatively warm ocean continues to release heat to the atmosphere in fall as insolation decreases. Another prominent characteristic of the Arctic seasonal cycle, which appears to defy a simple explanation, is that the transition from winter to spring is abrupt (He and Black 2015), compared to the more gradual springtime transition observed in midlatitudes and to the fall transition in the Arctic (Fig. 1b). The sharp boundary between winter and spring suggests that different processes govern the Arctic climate in these two seasons, and this indicates a possibly significant role for atmospheric dynamics in the Arctic springtime transition. Indeed, a few studies conclude that large-scale atmospheric dynamics shapes the seasonal cycle and explains some of the observed changes in seasonal cycle. Stine and Huybers (2012) argued that the variability in the amplitude and phase of the annual cycle of surface temperature in the northern extratropics is related to the Northern Hemisphere atmospheric circulation as represented by the northern annular mode (NAM) and the Pacific–North America mode (PNA). Abatzoglou and Redmond (2007) found that, in western North America, changes in the atmospheric circulation produce an asymmetry in seasonal warming, which leads to the change in the amplitude of seasonal cycle. Paluš et al. (2005) found that the variability of seasonality in Europe is correlated with the NAO index and anticorrelated with an ENSO index. There is, therefore, increasing evidence that Arctic seasonality is strongly modulated by large-scale dynamics.

To the authors’ best knowledge, however, only He and Black (2015, 2016) have studied the abrupt transition in the Arctic from winter to spring and its possible dynamical mechanisms. In this paper we seek to understand and explain the dynamics of the unique features of the Arctic springtime transition. Section 2 describes the data used, the model setup, and the basic experimental design. Section 3 introduces the method used to define the Arctic spring onset, the general statistics of spring onset dates, and the feature of the spring transition. Section 4 presents diagnoses of the heating mechanisms that drive the abrupt transition focusing on the role of the eddy heat flux. Section 5 further explores the atmospheric circulation patterns responsible for the eddy heat flux, and the final section summarizes and discusses our results.

## 2. Data and model setup

We use reanalysis output to provide a dynamically self-consistent depiction of the observed Arctic climate. Lindsay et al. (2014) compared seven reanalysis products in the Arctic region over the period 1981 to 2010. They concluded that three reanalyses showed the greatest agreement with independent observations: the NOAA Climate Forecast System Reanalysis (CFSR), the NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA), and the European Centre for Medium-Range Weather Forecasts ERA-Interim. He and Black (2015) showed that there is little difference between MERRA and ERA-Interim in their representation of the Arctic springtime transition. Here we use 30 years of ERA-Interim reanalysis (Dee et al. 2011) data, from 1979 to 2008, with a T255 horizontal spectral truncation (this corresponds to a grid spacing of approximately 80 km) and a 6-hourly temporal resolution. The reanalysis output is downloaded from the NCAR–UCAR research data archive website (http://rda.ucar.edu/datasets/ds627.0/).

For our simulations we use the Community Earth System Model (CESM 1.0.5). CESM is a coupled climate model for simulating Earth’s climate system, composed of five separate models, capable of simultaneously simulating Earth’s atmosphere, ocean, land, land ice, and sea ice, together with a central coupler component. For the present study, the model is configured as an **F** components set [equivalent to CAM5 (Community Atmosphere Model version 5) in a stand-alone configuration]. This includes active atmosphere and land models forced with a data ocean and sea ice model. The grid spacing is 0.9° × 1.25° realized in a finite-volume grid. The parameterization schemes are set to the CAM5 defaults (see detailed descriptions of these schemes at http://www.cesm.ucar.edu/models/cesm1.0/).

A 30-yr control simulation is conducted. The stand-alone atmosphere model is forced by a repeating monthly mean climatology of SST and sea ice. The SST and sea ice dataset is a combination of NCAR and Hadley Center SST and sea ice data, for the 30-yr period 1940–69. These are the default data used as boundary conditions in the CESM community.

In addition to the simulations with a full seasonal cycle, three perpetual-season simulations are carried out, corresponding to the dates 31 January, 16 March, and 30 April. As is shown in the next section, the average spring onset date is around 16 March, so these dates represent midwinter, spring onset, and spring. In each perpetual simulation, the solar radiation is fixed to the value for that date, while its diurnal cycle is retained. The remaining boundary conditions—SST, sea ice, and aerosol—are also set to fixed values for the same date. Each perpetual-season simulation is run for 1825 days.

## 3. Arctic springtime transition

The seasonal cycle in the Arctic is most pronounced in the lower troposphere and at the surface. Here the surface air temperature (SAT) is chosen as the index to represent the seasonal march of Arctic climate. The areal average of SAT north of 70°N (Arctic SAT) is used to characterize the seasonality of the Arctic region.

As is shown in Fig. 1, a salient feature of the Arctic seasonal cycle is the abrupt onset of spring. In the climatology, Arctic SAT is quasi-steady in middle to late winter (January–February). At the end of this season, SAT abruptly begins its springtime rise, and spring onset occurs. Metrics commonly used to define seasonal transitions (Thomson 1995; Qian et al. 2009) are not appropriate for the purposes of this study, as they do not capture the “kink” in the SAT evolution at spring onset. Instead, we use a modified version of a two-phase linear regression model (LRM) (Cook and Buckley 2009) to define the spring onset date. The model is applied to the Arctic SAT series spanning the period from 1 January to 31 May. The first segment is constrained to be a flat line, representing the wintertime quasi-steady state, and the second segment starts from the end point of the first segment. The date of the intersection between the flat and rising lines is defined as the spring onset date. The three model parameters (the wintertime temperature, the date of spring onset, and the rising slope of the springtime temperatures) are determined by minimizing the root-mean-square deviation of this model from the full Arctic SAT time series from 1 January to 31 May. The LRM is used, instead of the ROC (radius of curvature) method employed by He and Black (2015), because the LRM represents the entire transition from quasi-steady winter temperatures to the rapid warming of spring, while the ROC method places more emphasis on the temperature evolution in the weeks surrounding spring onset.

An example of the application of the model to a single year of observed Arctic SAT is shown in Fig. 2a. The LRM effectively represents the spring transition from relatively flat winter temperatures to rapid warming spring.

(a) An example of applying the two-phase linear regression model to the Arctic SAT series. The blue curve is the original SAT time series and the red line is the two-phase linear regression model. This calculation uses the ERA-Interim reanalysis for 2008. (b) Composite of SAT based on the spring onset date calculated using ERA-Interim reanalysis (red) and the CTRL simulation (blue). The climatology of ERA-Interim SAT (black) is shifted in time axis so that day 73 in the climatology aligns with day 0 in this plot. The mean value for each curve over the 101 day composite period is subtracted.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

(a) An example of applying the two-phase linear regression model to the Arctic SAT series. The blue curve is the original SAT time series and the red line is the two-phase linear regression model. This calculation uses the ERA-Interim reanalysis for 2008. (b) Composite of SAT based on the spring onset date calculated using ERA-Interim reanalysis (red) and the CTRL simulation (blue). The climatology of ERA-Interim SAT (black) is shifted in time axis so that day 73 in the climatology aligns with day 0 in this plot. The mean value for each curve over the 101 day composite period is subtracted.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

(a) An example of applying the two-phase linear regression model to the Arctic SAT series. The blue curve is the original SAT time series and the red line is the two-phase linear regression model. This calculation uses the ERA-Interim reanalysis for 2008. (b) Composite of SAT based on the spring onset date calculated using ERA-Interim reanalysis (red) and the CTRL simulation (blue). The climatology of ERA-Interim SAT (black) is shifted in time axis so that day 73 in the climatology aligns with day 0 in this plot. The mean value for each curve over the 101 day composite period is subtracted.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Applying this model to the ERA-interim data for the years 1979 to 2009, it is found that the average date of spring onset is day 77. The average onset date in the control simulation is day 73. The standard deviations of the spring onset dates are 11.3 days in ERA-Interim and 10.7 days for the control simulation. This similarity in the mean and variability in the onset date between the model and reanalysis data suggests that our model is suitable for addressing the dynamics of spring onset. Further, it suggests that variations in the timing of spring onset are primarily controlled by dynamical variability intrinsic to the atmosphere.

Composite averages for spring onset are constructed by shifting the temporal evolution of a quantity so that the onset dates (nominally composite day 0) coincide. Composites of Arctic SAT for ERA-Interim and the control simulation are shown in Fig. 2b, together with the climatological evolution of the Arctic SAT in ERA-Interim. The control simulation closely matches the salient features of the Arctic springtime transition in reanalysis. The composites of SAT show rapid warming following the onset day, in contrast to the more gradual transition in the climatology.

Surface warming during the spring transition is not spatially uniform (Fig. 3). The initial warming occurs around the Barents and Kara Seas and then spreads eastward and into the deep Arctic. Composites based on reanalysis (not shown) are similar. These maps are computed using anomaly fields with the climatological seasonal cycle removed, although composites of the full temperature field (not shown) are very similar, supporting the idea that the evolution of the transition is primarily dynamical.

Composite of change in SAT between each day and day 0. The unit is K. The calculation uses CTRL simulation outputs. Climatology is subtracted before compositing, and composites are based on the Arctic springtime onset dates.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of change in SAT between each day and day 0. The unit is K. The calculation uses CTRL simulation outputs. Climatology is subtracted before compositing, and composites are based on the Arctic springtime onset dates.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of change in SAT between each day and day 0. The unit is K. The calculation uses CTRL simulation outputs. Climatology is subtracted before compositing, and composites are based on the Arctic springtime onset dates.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

## 4. Dynamical heating

### a. Heat budget

*A*is the area of polar cap. The term on the left is the temperature tendency, which is expected to have large positive values following the transition. The first term on the right is the horizontal advection of temperature (HADV), and the second term includes the vertical advection of temperature and the temperature change due to adiabatic expansion or compression due to vertical motion (S-OMEGA). The final term on the right represents the temperature tendency from physics and other factors not included (RESI). The HADV term can be related to the heat flux across the Arctic boundary after applying the divergence theorem and the chain rule of differentiation:

*L*is the perimeter of the latitude circle at 70°N, and the asterisk (*) represents the deviation of a quantity from its zonal mean. Also,

The composite heat budget for spring onset in the ERA-Interim reanalysis is shown in Fig. 4. As expected, the temperature tendency (dT) is strongly positive during the early springtime transition (lag 0–lag 15). Although the term dT has noticeable year-to-year variability, strong positive dT following the springtime onset is apparent in each year (shaded region in Fig. 4).

Composite of heat budget terms in Eq. (1), averaged over the Arctic region, based on the Arctic springtime onset date from 1979 to 2008. All curves are smoothed using a 5-day running mean. The shading region is bounded by the composite mean of dT plus its one standard deviation (upper bound) and the mean minus one standard deviation (lower bound). The unit is K day^{−1}. The calculation uses the ERA-Interim reanalysis data.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of heat budget terms in Eq. (1), averaged over the Arctic region, based on the Arctic springtime onset date from 1979 to 2008. All curves are smoothed using a 5-day running mean. The shading region is bounded by the composite mean of dT plus its one standard deviation (upper bound) and the mean minus one standard deviation (lower bound). The unit is K day^{−1}. The calculation uses the ERA-Interim reanalysis data.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of heat budget terms in Eq. (1), averaged over the Arctic region, based on the Arctic springtime onset date from 1979 to 2008. All curves are smoothed using a 5-day running mean. The shading region is bounded by the composite mean of dT plus its one standard deviation (upper bound) and the mean minus one standard deviation (lower bound). The unit is K day^{−1}. The calculation uses the ERA-Interim reanalysis data.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Variations in dT are determined largely by variations in horizontal advection, while the vertical motion (S-OMEGA) term is weakly anticorrelated with dT and HADV. This is consistent with the large-scale atmospheric response to anomalous heating in the framework of the quasigeostrophic omega equation (Holton 2004). When there is anomalously strong warm advection into the Arctic, the resulting secondary circulation adiabatically cools the atmosphere. The HADV closely follows the eddy heat flux. The zonal heat flux and mass divergence (MDV) are anticorrelated (not shown), and their sum makes little contribution to the variation of temperature tendency (dT). These relationships apply equally to the original heat budget prior to any compositing and to the results of the perpetual season simulations. Thus, the abrupt warming in the early springtime transition corresponds to a period of strong temperature tendency, caused by the horizontal advection, and thus the eddy flux, of sensible heat. It is, therefore, necessary to determine the mechanisms that drive the eddy heat flux into the Arctic in order to understand the dynamical Arctic springtime transition. Similarly, Adams et al. (2000) show that the transient eddy heat flux is important in the energy budget in the Arctic in the transition from fall to winter.

### b. Eddy heat flux

It was shown in Fig. 4 that the EHF explains much of the variation in the temperature tendency over the Arctic. Further inspection of Fig. 4 reveals the source of rapid warming during the springtime transition. Given an initial value, the integral of dT (blue curve) gives the trajectory of *T*. Prior to the onset day (day 0), dT varies around its mean value of zero, so that its time integral, the Arctic SAT, similarly varies around its initial value. This corresponds to the quasi-steady winter state. Immediately following spring onset, a pulse of strong positive EHF causes rapid warming. Subsequently, dT is persistently positive, but with less variability. The persistently positive tendency is then driven by solar heating, and the reduced variability is due to the diminished role of a dynamically varying EHF.

The climatology of EHF variance in 11-day windows is shown in Fig. 5 (blue curve). The three dots are calculated using a similar method for each perpetual simulation, namely dividing the simulations into 11-day segments, computing the variance within each such segment, and taking the mean across the segments. The variance of eddy heat flux in the perpetual season simulations follows the seasonal trend in the control simulation, with the strongest variance in the winter, decreasing with time to a summer minimum. The seasonal decrease is more stepwise than gradual, however, and contributes significantly to the abrupt appearance of spring onset.

Variance of the zonal mean eddy heat flux

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Variance of the zonal mean eddy heat flux

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Variance of the zonal mean eddy heat flux

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

The spatial distribution of the eddy heat flux changes markedly as the season advances. In the winter (Fig. 6a), the eddy heat flux is concentrated over the Greenland Sea. It exhibits a similar pattern in early spring but with reduced magnitude (Fig. 6b), consistent with its decreasing variance. By midspring, there is only weak EHF over the Greenland Sea, and the center of strong EHF is shifted to Siberia (Fig. 6c).

Shading indicates the regression of the eddy heat flux onto the its zonal mean at 70°N [unit: K (m s^{−1})^{−1}]. Contours represent the mean air temperature at 850 hPa (units: K); the contour interval for the temperature is 4 K. The calculation uses the perpetual simulation in (a) January, (b) March, and (c) April.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Shading indicates the regression of the eddy heat flux onto the its zonal mean at 70°N [unit: K (m s^{−1})^{−1}]. Contours represent the mean air temperature at 850 hPa (units: K); the contour interval for the temperature is 4 K. The calculation uses the perpetual simulation in (a) January, (b) March, and (c) April.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Shading indicates the regression of the eddy heat flux onto the its zonal mean at 70°N [unit: K (m s^{−1})^{−1}]. Contours represent the mean air temperature at 850 hPa (units: K); the contour interval for the temperature is 4 K. The calculation uses the perpetual simulation in (a) January, (b) March, and (c) April.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

The mean air temperature at 850 hPa (contours in Fig. 6) suggests that the spatial distribution of the EHF is largely controlled by the lower boundary thermodynamic forcing. In other words, the EHF collocates with the temperature ridge at lower levels, which, on a seasonal time scale, is a consequence of the land–sea thermal contrast. In the winter and early spring, the SAT over the Greenland Sea is warmer than over northern Europe, Russia, or the Canadian sub-Arctic at the same latitude. In middle to late spring, however, increasing insolation warms the air over the continents, and the thermal ridge over the Greenland Sea disappears. This seasonal variation in the strength of the thermal wave is also likely important in the variations of the moisture flux into the Arctic (Dufour et al. 2016).

Three terms contribute to the variance of the eddy heat flux: the variance of the transient meridional wind fluxing the climatological temperature, the variance of climatological meridional wind fluxing the transient temperature, and the cross-interaction between them. For January and March (Figs. 7a,b), the main factor is

Decomposition of the variance of EHF into three terms as shown in Eq. (2), for the perpetual simulation in (a) January, (b) March, and (c) April. See detailed description in text.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Decomposition of the variance of EHF into three terms as shown in Eq. (2), for the perpetual simulation in (a) January, (b) March, and (c) April. See detailed description in text.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Decomposition of the variance of EHF into three terms as shown in Eq. (2), for the perpetual simulation in (a) January, (b) March, and (c) April. See detailed description in text.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Thus, the seasonal change of EHF variance comes primarily from the change in

Comparison of (a) the variance of ^{2} s^{−2}) and (b)

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Comparison of (a) the variance of ^{2} s^{−2}) and (b)

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Comparison of (a) the variance of ^{2} s^{−2}) and (b)

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

## 5. Dynamical mechanism

As shown above, variability in the eddy heat flux comes mainly from variability in the transient eddy meridional wind

### a. Anomalous flow pattern

To isolate the dynamical features associated with EHF, composite analyses are based on the 32 strongest EHF events in the perpetual January simulation. Because the distribution of heat flux events is strongly skewed, with the strongest tenth of events contributing approximately 40% of the cumulative heat flux into the Arctic, these strong events are representative of those most responsible for the variability of Arctic climate.

The evolution of geopotential height at 500 hPa (Z500) composited around the dates of strongest heat flux is shown in Fig. 9. The most prominent pattern at lag 0 (the time of strongest flux) is a dipole-like pattern spanning the North Atlantic and the Greenland Sea. This is consistent with anomalous southerly geostrophic flow

Composite of geopotential height anomaly at 500 hPa (Z500) based on 32 strong EHF events. Unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height anomaly at 500 hPa (Z500) based on 32 strong EHF events. Unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height anomaly at 500 hPa (Z500) based on 32 strong EHF events. Unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height along 70°N based on EHF events at (a) lag −12, (b) lag 0, and (c) lag 12. Shading is based on the anomaly field (time mean removed); contours are based on the full field (including the time mean). The unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height along 70°N based on EHF events at (a) lag −12, (b) lag 0, and (c) lag 12. Shading is based on the anomaly field (time mean removed); contours are based on the full field (including the time mean). The unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height along 70°N based on EHF events at (a) lag −12, (b) lag 0, and (c) lag 12. Shading is based on the anomaly field (time mean removed); contours are based on the full field (including the time mean). The unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

A Hovmöller diagram (Fig. 11a) confirms this westward propagation, with an approximate period of 25 days. This is consistent with the phase speed of Hough mode

Composite of geopotential height anomaly at 500 hPa along 70°N, based on EHF events: (a) the full geopotential height field, (b) the sum of the wavenumber-1 and wavenumber-2 components, (c) the wavenumber-1 component only, and (d) the wavenumber-2 component only. Unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height anomaly at 500 hPa along 70°N, based on EHF events: (a) the full geopotential height field, (b) the sum of the wavenumber-1 and wavenumber-2 components, (c) the wavenumber-1 component only, and (d) the wavenumber-2 component only. Unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Composite of geopotential height anomaly at 500 hPa along 70°N, based on EHF events: (a) the full geopotential height field, (b) the sum of the wavenumber-1 and wavenumber-2 components, (c) the wavenumber-1 component only, and (d) the wavenumber-2 component only. Unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Previous studies have shown evidence for regularly propagating large-scale waves in the middle and high latitudes (Madden 1978; Lindzen et al. 1984; Deland 1964). Following the method in Madden (1978), cross-spectra between the sine and cosine components of the geopotential height at 500 hPa at 70°N reveal the following. For wavenumber 1, there is significant coherence squared with a phase of −90 across a wide range of frequencies, with periods of 12–50 days, and with maximum strength of coherence at a period of 16 days, confirming the presence of westward propagating wavenumber 1. For wavenumbers 2 and 3, significant coherence squared at a phase of 90 indicates eastward propagation, and the period is much shorter than observed in the heat-flux composite.

As shown in Fig. 11c, the amplitude of wavenumber 1 fluctuates with time and amplifies at phases −90 and 90. A natural question arises whether this feature is an artifact of the heat-flux composite or is intrinsic to the behavior of planetary wavenumber 1. A scatterplot of the phase and amplitude of wavenumber 1 of Z500 at 70°N, across all times, is shown in Fig. 12. Large amplitudes of wavenumber 1 cluster around the phases −90 and 90. How wavenumber 1 amplifies and gains energy at these two phases is addressed in the next subsection.

Scatterplot of the amplitude and phase of the wavenumber-1 component of Z500 at 70°N. Only data points with amplitudes greater than one standard deviation above the mean are retained. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Scatterplot of the amplitude and phase of the wavenumber-1 component of Z500 at 70°N. Only data points with amplitudes greater than one standard deviation above the mean are retained. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Scatterplot of the amplitude and phase of the wavenumber-1 component of Z500 at 70°N. Only data points with amplitudes greater than one standard deviation above the mean are retained. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

### b. Energetics

When the geopotential dipole spans the North Atlantic, anomalous

The terms are defined as follows: ZAPE is zonal available potential energy, EAPE is eddy available potential energy, EKE is eddy kinetic energy, BC is baroclinic conversion, BT is barotropic conversion; TOT ENERGY is the sum of zonal and eddy available potential energy and kinetic energy, GZAPE is the generation rate of ZAPE, GEAPE is the generation of EAPE, and DISS is the dissipation of energy by boundary and radiative processes. The generation rates are multiplied by 24 × 3600 in order to convert the units to energy generation per day. The results are shown in Fig. 13.

Domain average of energetics composite based on EHF events; see text for the meaning of each term. The calculation uses the perpetual January simulation. The time mean of each term is subtracted before compositing.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Domain average of energetics composite based on EHF events; see text for the meaning of each term. The calculation uses the perpetual January simulation. The time mean of each term is subtracted before compositing.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Domain average of energetics composite based on EHF events; see text for the meaning of each term. The calculation uses the perpetual January simulation. The time mean of each term is subtracted before compositing.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

The composite energetics has an apparent periodicity of about 25 days. The conversion between ZAPE and EAPE is consistent with the classical theory of baroclinic growth. When the anomalous

### c. Geopotential tendency

*χ*is the geopotential tendency, and

*f*and

*ζ*are the vertical components of planetary vorticity and relative vorticity;

*f*at 45°N. We choose

To construct a budget of the geopotential tendency from the different terms, the tendencies are areally averaged over two boxes (colored rectangular boxes in Fig. 9). Both boxes range from 60° to 80°N. The west box extends from 90°W to 0° while the east box covers 0° to 90°E. These two boxes correspond to the two centers of the anomalous dipole pattern. Figure 14 shows the composite geopotential height anomaly averaged over these two boxes at 850 hPa and at 300 hPa. The west average and east average are out of phase with each other, consistent with the traveling wavenumber-1 mechanism. The 300-hPa curves are in phase with the 850-hPa curves, indicating that the structures associated with EHF events are quasi-barotropic. Again, this is consistent with linear Rossby wave theory.

Geopotential height anomaly composite averaged over the west box and east box at (a) 850 hPa and (b) 300 hPa. The west box covers 60°–80°N, 90°W–0°; the east box covers 60°–80°N, 0°–90°E. The unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Geopotential height anomaly composite averaged over the west box and east box at (a) 850 hPa and (b) 300 hPa. The west box covers 60°–80°N, 90°W–0°; the east box covers 60°–80°N, 0°–90°E. The unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Geopotential height anomaly composite averaged over the west box and east box at (a) 850 hPa and (b) 300 hPa. The west box covers 60°–80°N, 90°W–0°; the east box covers 60°–80°N, 0°–90°E. The unit is m. The calculation uses the perpetual January simulation.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

The contribution from longwave radiation forcing is small, so, in the following results, this term is omitted. Figure 15 shows the inverted tendencies from different forcing terms averaged over the west and east boxes. The largest contribution is from the linear term (Linear; red curve). The linear term includes the phase propagation and group propagation of linear Rossby waves. The role of the linear term is different in the west and east centers of the dipole. In the west, the linear term damps the height anomaly, such that the tendency is most positive when the height anomaly is negative (lag 0) and vice versa. In the east, the linear term reinforces the height anomaly, and its peak is located between the ridge and trough of the geopotential height anomaly (about lag −5).

Inverted geopotential tendency averaged over the west and east boxes at 850 and 300 hPa. The unit is 10^{−3} m^{2} s^{−3}. The calculation uses the perpetual January simulation. See text for details of each term.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Inverted geopotential tendency averaged over the west and east boxes at 850 and 300 hPa. The unit is 10^{−3} m^{2} s^{−3}. The calculation uses the perpetual January simulation. See text for details of each term.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

Inverted geopotential tendency averaged over the west and east boxes at 850 and 300 hPa. The unit is 10^{−3} m^{2} s^{−3}. The calculation uses the perpetual January simulation. See text for details of each term.

Citation: Journal of Climate 30, 23; 10.1175/JCLI-D-17-0333.1

The contribution from high-frequency eddies (Hi-Hi) tends to correlate with the height anomaly itself. This can be explained by the interaction between the high-frequency eddies and the low-frequency mean flow. For example, at lag 0, there is a low in the west, and the westerly flow on its southern flank is strengthened. Consequently, anomalously strong synoptic eddies originate there, and they flux heat and vorticity northward, converging into the west center. These convergences of heat and vorticity fluxes reinforce the negative height anomaly and produce a positive feedback (Lau and Nath 1991). The roles of the heat flux and the vorticity flux differ, however. The anomalous vorticity flux reinforces the negative height anomaly barotropically, while the heat flux reinforces the height anomaly at lower levels and damps the height anomaly at higher levels. The results shown here indicate that the vorticity flux forcing dominates, because the high-frequency term has the same sign at higher and lower levels. The condensation forcing is most important in the lower troposphere, because moisture is concentrated at low levels. When there is an anomalously strong EHF, warm, moist air is fluxed into the Arctic increasing condensation and precipitation near the east coast of Greenland. This release of latent heat intensifies the negative height anomaly in the lower troposphere (Fig. 15c), which also acts as a positive feedback and reinforces the western low at lower levels.

The contribution from low-frequency eddies has a comparable magnitude with the linear terms in some locations. This is consistent with the results in Blackmon et al. (1977), who found that time scales between 2.5 to 6 days and motions with periods longer than 10 days contribute comparable amounts of transient-eddy heat transport, with the high-frequency eddies dominating in the storm-track region and the low-frequency motions at higher latitudes.

## 6. Conclusions and discussion

Reanalysis data and model simulations are used to investigate the dynamical mechanisms of the abrupt springtime transition in the Arctic and the associated variations in the dynamical heating of the Arctic. Spring onset in the Arctic features an abrupt transition from quasi-steady winter to rapid warming in the spring. The onset date varies from year to year, with an average date in mid-March and a range from late February to mid-April. The similarity in the variability of onset dates between observations and a model with fixed repeating seasonal cycle of boundary conditions suggests that this variability is driven primarily by atmospheric internal variability.

Analysis of the heat budget indicates that the rapid warming at spring onset is caused by an anomalously strong positive eddy heat flux into the Arctic. The eddy heat flux varies greatly within the winter but its variability decreases sharply after spring onset. This rapid decrease in dynamical heating, combined with the rapid increase in insolation, creates the abrupt appearance of the springtime transition. The spatial distribution of EHF also changes with seasons. It is concentrated in the Greenland Sea in the winter, and spreads zonally with a reduced magnitude after the seasonal transition.

Decomposition of the EHF variance reveals that the change of EHF variance across seasons is mainly caused by changes in transient meridional winds and the stationary wave of low-level temperatures, with the latter term contributing more than half of the change in EHF variance. Thus, the primary reason for the decrease from winter to spring in the variability of the eddy heat flux is the weakening of the thermal ridge over the North Atlantic/Greenland Sea in spring, as increased insolation warms the continents and erodes the strong land–sea thermal contrast that was present in winter.

Through composite analyses of strong EHF events, we identify planetary wavenumber 1 as playing a key role in heat flux events. This wave generally propagates westward, and it fluxes heat into the Arctic when the phase of its southerly winds coincides with the stationary thermal ridge east of Greenland. An analysis of the energetics of these events reveals that wavenumber 1 is maintained and amplified by a baroclinic process, yet this feature is clearly not an unstable baroclinic growing mode, as indicated by its westward propagation, its predominantly barotropic structure, and the importance of the stationary thermal wave.

The analysis of geopotential tendencies confirms the importance of an approximately linear planetary wave as the source of heat flux events. The linear terms, which represent the phase and group propagation of a linear Rossby wave, dominate the tendencies, although there are also significant contributions from low-frequency eddies. High-frequency eddies and latent heating also contribute to the intensification of the anomalous wave, but with relatively less importance.

While we have identified the dynamical features associated with the Arctic springtime transition and explained its abrupt appearance, some questions remain. The composite energetics explains why planetary wavenumber 1 amplifies at phase +90, leading to strong fluxes of heat into the Arctic, but does not explain why this feature also amplifies at phase −90. Composites based on wavenumber-1 life cycles may provide more insight into the dynamics of this feature. In addition, our results suggest that variability in North Atlantic/Nordic Sea SST should have a significant impact on the Arctic springtime transition, and this, too, warrants further investigation.

## Acknowledgments

We thank the three anonymous reviewers for their insightful comments and suggestions. We also thank the CESM community for the model code and general assistance in the use of the model. This material is based upon work supported by the National Science Foundation under Grant ARC-1107651.

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