Radiative Relaxation Time Scales Quantified from Sudden Stratospheric Warmings

Kevin Bloxam aMcGill University, Montreal, Quebec, Canada

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Yi Huang aMcGill University, Montreal, Quebec, Canada

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Abstract

Sudden stratospheric warmings (SSWs) are impressive events that occur in the winter hemisphere’s polar stratosphere and are capable of producing temperature anomalies upward of +50 K within a matter of days. While much work has been dedicated toward determining how SSWs occur and their ability to interact with the underlying troposphere, one underexplored aspect is the role of radiation, especially during the recovery phase of SSWs. Using a radiative transfer model and a heating rate analysis for distinct layers of the stratosphere averaged over the 60°–90°N polar region, this paper accounts for the radiative contribution to the removal of the anomalous temperatures associated with SSWs. In total 17 events are investigated over the 1979–2016 period. This paper reveals that in the absence of dynamical heating following major SSWs, longwave radiative cooling dominates and often results in a strong negative temperature anomaly. The polar winter stratospheric temperature change driven by the radiative cooling is characterized by an exponential decay of temperature with an increasing e-folding time of 5.7 ± 2.0 to 14.6 ± 4.4 days from the upper to middle stratosphere. The variability of the radiative relaxation rates among the SSWs was determined to be most impacted by the initial temperature of the stratosphere and the combined dynamic and solar heating rates following the onset of the events. We also found that trace-gas anomalies have little impact on the radiative heating rates and the temperature evolution during the SSWs in the mid- to upper stratosphere.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kevin Brian Bloxam, kevin.bloxam@mail.mcgill.ca

Abstract

Sudden stratospheric warmings (SSWs) are impressive events that occur in the winter hemisphere’s polar stratosphere and are capable of producing temperature anomalies upward of +50 K within a matter of days. While much work has been dedicated toward determining how SSWs occur and their ability to interact with the underlying troposphere, one underexplored aspect is the role of radiation, especially during the recovery phase of SSWs. Using a radiative transfer model and a heating rate analysis for distinct layers of the stratosphere averaged over the 60°–90°N polar region, this paper accounts for the radiative contribution to the removal of the anomalous temperatures associated with SSWs. In total 17 events are investigated over the 1979–2016 period. This paper reveals that in the absence of dynamical heating following major SSWs, longwave radiative cooling dominates and often results in a strong negative temperature anomaly. The polar winter stratospheric temperature change driven by the radiative cooling is characterized by an exponential decay of temperature with an increasing e-folding time of 5.7 ± 2.0 to 14.6 ± 4.4 days from the upper to middle stratosphere. The variability of the radiative relaxation rates among the SSWs was determined to be most impacted by the initial temperature of the stratosphere and the combined dynamic and solar heating rates following the onset of the events. We also found that trace-gas anomalies have little impact on the radiative heating rates and the temperature evolution during the SSWs in the mid- to upper stratosphere.

© 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Kevin Brian Bloxam, kevin.bloxam@mail.mcgill.ca

1. Introduction

Occasionally in the polar stratosphere during the extended winter period (November–March) impressive temperature anomalies can manifest within a matter of days reaching upward of +50 K above normal (Limpasuvan et al. 2004). These events, commonly referred to as sudden stratospheric warmings (SSWs), were first documented by Scherhag (1960) in the 1950s and have since become increasingly discussed in the atmospheric community due to their intriguingly complex nature. While SSWs manifest within the polar stratosphere, they are believed to originate in the troposphere whereby planetary waves (primarily wavenumbers 1 and 2) propagate upward from the troposphere and impart their energy in the stratosphere resulting in anomalous temperature and zonal winds (Matsuno 1971; Andrews et al. 1987; Polvani and Waugh 2004).

Those who study SSWs often make the distinction between minor and major events (e.g., Andrews et al. 1987). Major SSWs are not only associated with remarkable temperature anomalies but are also able to disrupt the climatological westerly winds in the upper stratosphere such that they reverse to an easterly flow. Minor events, on the other hand, do not reverse the flow of the wind. The zonal wind reversal associated with major SSWs has an important consequence on the upward wave activity to the stratosphere through what is known as the Charney–Drazin criterion. This condition stipulates that in order to have upward wave activity capable of reaching the stratosphere, the zonal winds must be westerly and not too strong (Charney and Drazin 1961). The common theme with all the SSWs discussed in this paper is that they were major events, resulting in a reversal of the westerly winds. Then, according to the Charney–Drazin criterion, this would inhibit the deposition of energy via wave activity into the stratosphere. While we do not test this hypothesis here, we refer to the work of Matsuno (1971), who provided a dynamical model of SSWs while utilizing the Charney–Drazin criterion. Mastsuno’s model successfully reproduced features similar to those exhibited by SSWs. This notion of the filtering of vertically propagating waves by easterly winds is also a well established idea and has been mentioned in a variety of papers including Liu et al. (2009), Tomikawa (2010), Tomikawa et al. (2012), and Hitchcock et al. (2013b), to name a few.

SSWs may be further classified according to whether they cause the stratospheric polar vortex to be displaced from its typical climatological position or cause the vortex to split into two smaller vortices (see Liu et al. 2014; Mitchell et al. 2013). An example of a vortex displacing major SSW occurred during the winter of 2006, as shown in Figs. 1a–c. From these figures one can begin to appreciate the magnitude of the temperature anomalies these events produce and the spatial scale they encompass and why SSWs are worth investigating. Following the onset of SSWs, the anomalous temperature and wind field characteristics of these events may then exhibit a downward influence on the underlying tropospheric circulation (Hitchcock and Simpson 2014; Baldwin and Dunkerton 2001; Karpechko et al. 2017) potentially leading to cold-air outbreaks felt at the surface in North America or Eurasia (Kolstad et al. 2010; Kidston et al. 2015; Mitchell et al. 2013). Some of those who study SSWs argue that for the development of certain SSWs such as vortex-splitting events or in order for the stratosphere to exhibit a downward control on the underlying troposphere relies on a preconditioned stratosphere thereby allowing for these events to take place (Albers and Birner 2014; Charlton and Polvani 2007; Zhou et al. 2002).


Fig. 1.
Fig. 1.

The SSW of 2006 captured at its starting date on 21 Jan. Shown at the 10 hPa height is (a) the 1979–2016 climatological temperature based on each calendar date, (b) the observed temperature, and (c) the resulting temperature anomaly. Noticeable is the large swath of warmer air situated over the Arctic leading to the approximate +50 K temperature anomaly in some regions. (d) The 60°–90°N averaged temperature anomaly (observed temperature minus the climatology) spanning the 1–450 hPa range during the same SSW—see section 2 for how the occurrence of an SSWs is determined.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

Those who research SSWs are typically interested in the dynamics leading up to and after their initiation, and rightly so considering the potential of these events to impact tropospheric weather. One often overlooked aspect associated with these events, however, is the role of radiation during the SSW lifespan, particularly during the recovery period. An implication of the Charney–Drazin criterion is that when the temperature perturbation is strong and there is a reversal of the zonal wind direction (as in the case of major SSWs), the supply of wave energy, i.e., the dynamical heating, might be cut off, which then leaves the atmospheric temperature evolution in the following period to be dominated by radiation. An understanding of the cooling effect radiation has on these events is important because it influences the duration of the temperature anomaly and as Hitchcock et al. (2013a) point out the duration of the SSW itself. Removing the thermal disturbance allows the stratosphere to reorganize itself into a more climatological state with the zonal wind reverting back to its typical westerly flow.

Detailed discussions regarding the suppression of wave activity to the stratosphere can be found in the works of Siskind et al. (2010), Tomikawa (2010), and Hitchcock et al. (2013a). The authors of these papers point out that events with extended recovery periods are characterized by a prolonged period of suppressed wave activity. The decrease in the supply of dynamical heating to the stratosphere is significant because the winter polar stratosphere, under normal conditions, can be thought of as being in a radiative–dynamical equilibrium whereby the heat supplied via solar radiation (minor) and advective processes are balanced with radiative cooling so as to maintain the observed vertical temperature structure of the stratosphere (Sasamori and London 1966; Andrews et al. 1987; Ramanathan et al. 1983). In a well known paper by Holton and Mass (1976) this interplay between radiative cooling and eddy heat fluxes is used to model the wave–mean flow interaction in the stratosphere and minor stratospheric warming cycles. In our paper, however, the focus is on the immediate recovery period following the onset of major SSWs when there is a sharp reduction in dynamical heating. Here the temperature enters a “free-fall” regime whereby the stratosphere cools via the emission of longwave radiation as the system tends toward a new equilibrium. In the majority of the major SSWs discussed here, by the time this new equilibrium has been established the temperature has decayed to a point well below the climatology, as demonstrated in Fig. 1d which depicts the evolution of the temperature anomaly in the stratosphere encompassing the SSW that began on 21 January 2006. This negative stratospheric temperature anomaly following the onset of SSWs has been noticed in several papers (see Tomikawa et al. 2012; Limpasuvan et al. 2012). Hitchcock and Shepherd (2013) analyzed the adiabatic and diabatic heating rates and how together they drive the temperature tendencies during the recovery phase of SSWs and found that the suppression of wave activity to the stratosphere permits radiative cooling to dominate resulting in a negative temperature anomaly. These previous works, however, did not explicitly compute the radiative cooling or the vertical structure of the relaxation time scales in the real atmosphere.

It is here that we take our motivation for this paper as we explore the distinct roles of the radiative and dynamical heating rates and how they instigate this cooling period following major SSWs. Expanding on the work performed by the previous studies, we will provide a composite of the temperature tendencies and heating rates averaged over the 60°–90°N polar region for distinct atmospheric layers during the recovery phase following the onset of SSWs. These composites, using reanalysis data, will break up the heating rate contributions from the vertical and meridional transport processes along with both the short and longwave radiative heating rates.

Another motivation for this paper is the relaxation behavior of temperature following the onset of major SSWs, particularly in the mid- to upper stratosphere. This exponential decay of temperature during the period of suppressed wave activity allows us to quantify the associated e-folding time scale of the thermal disturbances in the stratosphere. In their papers Newman and Rosenfield (1997) and Hitchcock et al. (2010) calculated this dampening rate by applying a linear regression of the temperature field. In this work, we instead provide an alternative method to determine the relaxation rate by means of fitting the longwave radiative cooling rates. Although they are equivalent under approximated conditions (see section 2 below), the use of the radiative cooling rate lets us focus on the temperature change component that is driven by the longwave radiative process, i.e., what the concept of radiative relaxation time scale is rooted in. Moreover, the radiative cooling rates which are computed using an accurate radiation model and are based on real atmospheric conditions take into consideration the vertical structure of the temperature anomalies in SSWs, accounting for not only the local temperature perturbations but also the remote effects from surrounding and remote layers, which is considered important (Fels 1982). Essentially the e-folding time calculated using our methodology provides a measure of how quickly thermal radiation is able to drive the temperature back to a new radiative–dynamic equilibrium.

2. Data and methodology

a. Atmospheric data

The analysis in this paper utilizes the 1979–2016 data provided by the European Centre for Medium-Range Weather Forecasts interim reanalysis (ERA-Interim, hereafter ERA-I) (Dee et al. 2011). These data, taken four times daily at a 1° × 1° grid spacing, provided the following variables used in this paper: wind (zonal, meridional, and vertical), temperature, skin temperature, specific humidity, ozone mass mixing ratio, surface level pressure, and surface albedo. The remaining atmospheric constituents (N2, O2, CO2, etc.) required for radiative transfer calculations are based on a model polar winter atmospheric profile using the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS; MIPAS 2001) retrievals. Note that all calculations in our analysis are based on the daily average of these variables and all climatologies are determined for each calendar date based on the 1979–2016 period.

b. The definition of a sudden stratospheric warming

To assess the role of radiation during SSWs a working definition must first be established. Though there are a variety of definitions used in the literature, the definition that will be implemented here is known to some as the Charlton and Polvani (CP) definition of SSWs. Based on the WMO’s definition (Andrews et al. 1987), Charlton and Polvani define an SSW as having occurred if the zonal mean wind at 10 hPa and 60°N reverses direction becoming easterly during the extended winter period (November–March) (Charlton and Polvani 2007). The first date in which the wind reverses is known as the central date of the event and at no time within 20 days of this date can another SSW be identified as to allow for a radiative relaxation of the stratosphere. In total 22 major SSWs were detected and their respective durations (measured as the length of time the zonal wind at 60°N remains easterly) were determined and are displayed in Table 1. The utility of using the CP definition is its simplicity in detecting the occurrence of major SSWs compared to other definitions and as such has been widely used in the scientific community that studies these warming events (e.g., Butler et al. 2015; Martineau et al. 2018; White et al. 2019) and suits the purposes of this study.

Table 1.

Summary of the occurrences of major SSWs during the 1979–2016 period based on the reversal of the zonal wind at 10 hPa and 60°N using the ERA-I dataset. Events with an asterisk were not included in this study.


Table 1.

c. Heating rates

Following Lateef’s (1964) treatment of the first law of thermodynamics, the temperature tendency equation can be expressed as
T t = V T ω T p + ω α c p + Q + ε ,
where T is the temperature, V the horizontal wind components, ω the vertical velocity in Pa s−1 (downward positive), α is the specific volume, and c p is the specific heat at constant pressure (1004 J K−1 kg−1). The terms Q and ε have been included in this equation to account for the effects of both the short and longwave radiative heating rates and any unaccounted residual heating. Based in pressure coordinates, Eq. (1) tells us that the rate of change of temperature is caused by the horizontal and vertical advection of temperature plus the effects of adiabatic expansion or compression through vertical motion (ωα/c p ), and by the diabatic heating/cooling done via radiation. To determine the average 60°–90°N heating rates throughout the stratosphere we use the following equation,
t p 1 p 2 A T d A d p p 1 p 2 A d A d p = p 1 p 2 A V T d A d p p 1 p 2 A d A d p p 1 p 2 A ω T p d A d p p 1 p 2 A d A d p + p 1 p 2 A ω α c p d A d p p 1 p 2 A d A d p + A Q d A A d A + p 1 p 2 A ε d A d p p 1 p 2 A d A d p ,
where A is the 60°–90°N polar cap area, p 1 the upper pressure level, and p 2 the lower pressure level boundary (based on the ERA-I’s 37 pressure levels). Note that Q represents the radiative heating rate for the pressure layer bound by p 1 and p 2 (see below) and as such we do not integrate along the pressure coordinate. Following a similar methodology to Lateef (1964), we can apply the two-dimensional form of the divergence theorem to Eq. (2) and obtain the following,
t p 1 p 2 A T d A d p p 1 p 2 A d A d p = p 1 p 2 60 °N υ T d L d p p 1 p 2 A d A d p + A ω T d A | p 1 A ω T d A | p 2 p 1 p 2 A d A d p + p 1 p 2 A ω α c p d A d p p 1 p 2 A d A d p + A Q d A A d A + p 1 p 2 A ε d A d p p 1 p 2 A d A d p ,
where υ is the meridional velocity (northward positive), and L is the 60°N circumference. Equation (3) now tells us that the average change in temperature for a volume of the atmosphere contained within the 60°–90°N polar cap region bound by two pressure levels is attributed to the meridional transport of temperature past 60°N and the net vertical transport into the volume past the upper and lower pressure levels, along with the adiabatic adjustment and effects of radiation. In calculating each respective term on the rhs of Eq. (3) we can determine the influence each heating rate has over the temperature during the recovery period of SSWs.
The Rapid Radiative Transfer Model for general circulation models (RRTMG) (Mlawer et al. 1997) was used to determine the longwave and shortwave radiative fluxes at each pressure level under clear-sky conditions. All-sky conditions were originally used in our analysis but due to the similar stratospheric radiative output in both cases (see appendix A), we opted for clear-sky conditions instead. Results from running the RRTMG for both longwave and shortwave radiation were then used to determine the net flux of radiation into/out of the respective pressure layers as determined by Eq. (4) with the downward direction being positive:
Δ F RAD NET = F RAD NET | p 1 F RAD NET | p 2 .
Note that prior to running the RRTMG we determined the 60°–90°N average of each atmospheric constituent required for running the model at each respective pressure level. It was found that treating this region as single column when performing the RRTMG calculations had a negligible impact on the results (see appendix B). Using the RRTMG radiative flux output one can determine the associated shortwave and longwave cooling rates through the following equation,
H RAD = T t RAD = g c p Δ F RAD NET Δ P ,
allowing us to define Q as
Q = H RAD LW + H RAD SW .

Alternatively, one may simply choose (as we have done) to use the RRTMG output of these heating rates instead of calculating the radiative heating rates directly.

d. Temperature fitting scheme and the determination of the e-folding time

In combining the first three terms on the rhs of Eq. (3) and calling this the dynamic heating rate, then together with the 60°–90°N averaged radiative and residual heating rates we can rewrite this equation as
T t = H DYN + H RAD LW + H RAD SW + ε .
Using Eq. (7) we will now explain how to determine the e-folding time of temperature following the onset of SSWs, specifically the period showing the longest continual temperature decay when there has been a suppression of wave activity. During this period, only events whereby the longwave radiative cooling rate is larger in magnitude than the sum of both the solar and dynamic heating rates for at least five days (as to allow for a proper fitting of the data) were considered. In addition to the 5-day criterion we also conduct an analysis of variance based on a simple linear regression to examine the amount of variance of the time rate of change of temperature that is explained by either thermal radiation or by the sum of the solar, dynamical, and residual heating rates. Using this analysis of variance we further stipulate that only periods whereby the longwave cooling explains the most amount of the variance of temperature can be used. In doing so this allows us to determine the e-folding time as attributed to the thermal radiative dampening rate. Taking the average of the dynamical and solar heating rates, along with the residual, during this period of temperature decay provides an approximate dynamical/solar heating rate that the longwave radiative cooling rate is converging toward in order to establish a new radiative–dynamical equilibrium (see appendix C as to why we associate the residual term with the dynamical heating). In other words, the radiative heating rate the system evolves to, H RAD LW ( ) , will be equal but opposite in sign to the sum of the dynamical heating rate (H DYN), the solar heating rate ( H RAD SW ) , and the residual heating rate (ε). Similar to the work of Cronin and Emanuel (2013), we use H RAD LW ( ) and the initial heating rate H RAD LW ( 0 ) to fit the radiative heating data, such that
H RAD LW = Δ H 0 exp ( t τ ) + H RAD LW ( ) ,
where ΔH 0 is determined by
Δ H 0 = H RAD LW ( 0 ) H RAD LW ( ) ,
and in doing so determine the e-folding time τ that best fits the data. The exponential fitting of the longwave radiative cooling rate is based on the expected evolution of the temperature field as dictated by radiation. When only considering the longwave radiative cooling rate of the atmosphere we know that the rate at which the temperature decreases will be directly related to the radiative cooling rate which itself is dependent upon the temperature (see appendix of Li et al. 2017) such that
T t T t RAD = H RAD LW T ,
which renders an exponential decay behavior of temperature. Since the longwave radiative cooling rate is a direct result of the temperature, it will also experience an exponential decay, as seen in Eq. (8). Using Eq. (7) together with Eq. (8) the total change in temperature with time can be expressed as
T t = Δ H 0 exp ( t τ ) + H RAD LW ( ) + H RAD SW + H DYN + ε .
Given H RAD LW ( ) = ( H DYN + H RAD SW + ε ) this leaves
T t = Δ H 0 exp ( t τ ) ,
or in an integral form,
T = Δ T 0 exp ( t τ ) + T ( ) ,
where
Δ T 0 = Δ H 0 * τ
and
T ( ) = T ( 0 ) Δ T 0 .

Together Eqs. (11)(15) reveal how using the longwave radiative cooling rates, along with the initial temperature of the stratosphere, we can fit the temperature field following the onset of SSWs.

It is important to acknowledge here that taking the average of the solar and dynamic heating rates during the temperature decay period assumes that these rates are not changing in time. This provides a method of describing the temperature tendencies in the stratosphere during the periods of suppressed wave activity. Using the outlined methodology, 17 major SSWs that occurred during the 1979–2016 period were investigated. In total five events were not used from the list of identified major SSWs as they did not meet either the 5-day requirement or our analysis of variance check required to properly fit the temperature field.

3. Results

a. Composite of major sudden stratospheric warming heating rates

To begin our investigation into the dynamical and radiative heating rates that dictate the temperature during SSWs, we first show in Fig. 2 the average temperature anomaly and zonal wind pattern at 60°N. This figure serves to demonstrate how the composite figures have been organized. At lag zero this coincides with the reversal of the wind at 60°N and 10 hPa, i.e., the start of the SSW, at which point the zonal wind drops below 0 m s−1 (see Fig. 2a). Using this as our reference time we then juxtapose all the SSWs in this study at the same point in time so that we can showcase the first 20 days before the wind reversal and the following 60-day period. The average temperature anomalies for the 60°–90°N polar region seen in Fig. 2b, reveals that the maximum temperature anomaly typically coincides with the starting date of the SSWs, at lag zero, and is situated around 5–10 hPa reaching approximately 15 K above normal. A range of positive temperature anomalies exists from the top of the stratosphere down to roughly 350 hPa. After the onset of the SSWs we can see how the temperature anomalies in the lower stratosphere tend to persist for a much longer period of time, upward of 60 days, while the mid- to upper stratosphere positive temperature anomalies are much shorter lived. As we demonstrated in Fig. 1d, the temperature in this part of the stratosphere undergoes a decay process following the onset of the SSWs, resulting in the demonstrated pattern of negative temperature anomalies.


Fig. 2.
Fig. 2.

(a) Composite of the zonal wind at 60°N based on the SSWs used in this study for the 1–450 hPa region of the atmosphere. (b) Composite of the associated temperature anomalies (observed temperature minus the climatology) averaged over the 60°–90°N region. Note that lag 0 marks the start time of each SSW, based on the wind reversal at 60°N and 10 hPa.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

The heating rates that drive the temperature change during the life of an SSW are depicted in Fig. 3. In Fig. 3a the temperature tendency [lhs of Eq. (3)] shows a rapid temperature decay in the upper stratosphere (1–10 hPa) after the onset of the SSWs, while the mid- to lower stratosphere experiences a more subtle temperature decay which explains why the temperature anomaly persists for that region. In Fig. 3b we see that when we treat the 60°–90°N region as a single column, the heating rate due to meridional transport [first term on the rhs of Eq. (3)] acts to cool the stratosphere as it transports heat south past the 60°N boundary. The net heating rate from vertical transport [Fig. 3c/second term on the rhs of Eq. (3)] confirms that it is indeed the vertical transport-induced heating rate that is responsible for the sudden warming events as one can clearly see by the +20 K day−1 heating rates supplied to the upper stratosphere prior to the start of the SSW. After the onset of the SSW, when there is a reversal of the zonal wind, the heating due to vertical transport drops off noticeably allowing for the other heating rates to cool the stratosphere. The adiabatic heating rates [third term on the rhs of Eq. (3)] associated with vertical motion are displayed in Fig. 3d. Here we see that this heating rate acts to offset the overall rising motion typical of the 60°–90°N region cooling the air as it expands. If we had chosen to work in the transformed Eulerian mean (TEM) framework instead, the adiabatic motion would tell a very different story. The TEM framework would indicate that it is the residual downward and compressing motion that is responsible for the SSW (e.g., see Hitchcock and Shepherd 2013; de la Cámara et al. 2018). Working in this TEM framework would also reveal an enhancement of the poleward meridional residual circulation which acts to transport heat north past 60°N. However, since we are looking at the average motion and heating rates of the stratosphere, the residual circulation [not to be confused with the residual heating rates ε in Eq. (3) and Fig. 3e] and eddy heating rate components are masked. In Fig. 3e the residual heating rates (ε) can be seen and clearly indicate a nonclosure of the thermodynamic budget. This pattern of the residual heating rate suggests that it is the wind component of the ERA-I data (particularly the vertical wind) that may account for the nonclosure (see appendix C for more details). The sum of the long and shortwave heating rates Q shown in Fig. 3f demonstrate it is the thermal cooling of the stratosphere that dominates until around lag 40–60 after which the effects of solar radiation begin to become more important leading to a warming effect (see Fig. 5).


Fig. 3.
Fig. 3.

The 60°–90°N averaged composite of the (a) time rate of change of temperature, (b) meridional transport-induced heating rate across 60°N, (c) net vertical transport-induced heating rate into each respective atmospheric layer, (d) the adiabatic heating rate associated with vertical motions, (e) the residual heating rate, and (f) the sum of the thermal and solar heating rates. As in Fig. 2, the lag is based on the wind reversal at 60°N and 10 hPa. Note that H MERID|60°N, H VERT, and H ADIAB represent the first, second, and third terms on the right-hand side of Eq. (3).

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

In Fig. 4a the anomalous heating due to meridional transport indicates that after the onset of SSWs the southward heat transport, which acts to cool the stratosphere, is significantly reduced, dropping by up to 15 K day−1 showing up as a positive anomaly. Figures 4b and 4c demonstrate the effects of an enhancement of the upward wave activity to the stratosphere resulting in the +15 K day−1 heating rate anomaly prior to the start of the SSWs that is partially offset by the rise in adiabatic cooling. After the zonal winds have reversed the upward wave activity has been largely suppressed resulting in the negative vertical transport related heating rate anomaly throughout most of stratosphere. With this suppression of wave activity also comes a decrease in the amount of adiabatic cooling showing as a positive adiabatic heating rate anomaly during this period. The anomalous radiative heating rates in Fig. 4d show an enhanced cooling rate up to and after (for the lower parts of the stratosphere) the onset of the events followed by a period of positive heating rate anomalies. This switch to the positive heating rate anomaly is the result of the negative temperature anomaly that has developed (see Fig. 2b). With colder than normal temperatures the thermal cooling rate will diminish resulting in the positive radiative heating anomaly.


Fig. 4.
Fig. 4.

As in Fig. 3, but for the anomalous (a) meridional, (b) vertical, (c) adiabatic, and (d) radiative (thermal and solar) heating rates.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

To complete our heating rate composites, we now breakdown the radiative heating rates into the thermal (longwave) and solar (shortwave) components, as seen in Fig. 5. In the lower stratosphere both the thermal (Fig. 5a) and solar (Fig. 5b) heating rates are minimal while in the upper stratosphere the magnitude of these heating rates are significantly higher. Also note that in the upper stratosphere the longwave radiative cooling rate tends to play a more active role throughout the life of an SSW, considering that the longwave cooling rate is associated with the temperature itself. The solar heating rate only begins to play a more active role at later times coinciding with the Northern Hemisphere’s transition to spring and the increasing amount of solar radiation that it receives. The anomalous thermal heating rates seen in Fig. 5c follows the same trend as displayed in Fig. 4d and proves that the anomalous radiative heating rates during SSWs is for the most part controlled by the thermal component. We see in Fig. 5d that there are some minor anomalous solar heating rates in the stratosphere during SSWs; however, these are only fractional compared to the magnitude of the thermal contribution. See section 4 below for a brief analysis of the impact trace-gas anomalies have on the thermal and solar heating rates during SSWs.


Fig. 5.
Fig. 5.

The 60°–90°N averaged composite of the (a) thermal and (b) solar radiative heating rates, along with (c),(d) their anomalies relative to the 1979–2016 climatology.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

b. Radiative relaxation time-scale determination—Example using the major sudden stratospheric warming of 2006

In this section, the SSW that occurred in 2006 is used to provide an example of applying the fitting scheme described in section 2 to determine the radiative relaxation time scale (the e-folding time) for the 7–10 hPa layer. This SSW was chosen not only because of the impressive temperature anomalies that ensued but because this event has a prolonged period of suppressed wave activity providing an excellent case study to examine radiation’s dominance over the temperature in the absence of dynamical heating.

To begin we plot the 60°–90°N averaged temperature in Fig. 6a. Also indicated (in red) is the focus period for this pressure layer which met the outlined criteria for choosing events (see section 2). During this period the temperature drops exponentially from 235 K on 25 January to 208 K on 16 February. The longwave radiative cooling rates during this period can be seen in Fig. 6b and similar to the temperature field they also exhibit an exponential decay from its lowest value of −3.7 K day−1 increasing to approximately −1.5 K day−1. The sum of the solar, dynamical, and residual heating rates are depicted in Fig. 6c. Note that here and going forward we group the dynamic heating rate with the residual and refer to this as the adjusted dynamic heating rate H DYN * (see appendix C). With the solar heating rate remaining approximately constant during this period, this figure demonstrates the transition of the dynamical heating rate from anomalously large values prior to the start of the SSW to below average following the central date on 21 January during the period of suppressed wave activity. With such a sharp cutoff in the dynamic energy transported to this region of the stratosphere it is undoubtedly the longwave radiative cooling that controls the evolution of the temperature during this time.


Fig. 6.
Fig. 6.

(a) The 60°–90°N averaged temperature (blue line) for the 7–10 hPa layer during the SSW of 2006. The focus period (red line) which encompasses the largest temperature decline during this period (based on the event data criteria—see section 2) and the respective climatology (black dashed line) are also displayed. (b) As in (a), but for the longwave radiative cooling rates. (c) As in (a), but for the sum of the solar and adjusted dynamic (i.e., H DYN + ε) heating rates.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

In addition to the 5-day criterion for the longwave cooling rates to be larger in magnitude than the combined heating rates, we also stipulated that the time periods used in our analysis must meet the criterion that the variance of the time rate change of temperature, ∂T/∂t, must be predominately explained by thermal radiation. In Fig. 7 we break up the January–March time frame into three periods: 1–25 January (top row), 25 January–16 February (middle row), and 16 February–31 March (bottom row). These periods represent the time before, during, and after the period of interest. In the 1–25 January period the most amount of the variance of ∂T/∂t is explained by the adjusted dynamical heating rate. Because this is a time of heightened wave activity to the stratosphere, the dynamic heating rate dictates the temperature evolution during this period. During our focus period for determining the e-folding time, i.e., 25 January–16 February, most (83%) of the variance of ∂T/∂t is explained by thermal cooling. In the following 16 February–31 March period, we find that the temperature is being driven predominately by solar radiation. The dynamic heating rate, which has been significantly reduced, plays virtually no role in the temperature evolution during the last two periods.


Fig. 7.
Fig. 7.

The relationship between the temperature tendency (∂T/∂t) and heating rate components: (left) H DYN * , (center) H RAD SW , and (right) H RAD LW , which correspond to the adjusted dynamical (H DYN + ε), shortwave, and longwave heating rates, respectively. Shown in the rows are the periods (top) before (1–25 Jan), (middle) during (25 Jan–16 Feb), and (bottom) after (16 Feb–31 Mar) the stage of the SSW when the longwave radiation dominates the temperature change. The R 2 is the amount of variance that is explained by each respective heating rate and the p-val is the p value for the F test on the significance of the linear regression model.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

Next, we examine more closely the focus period during which the longwave radiative cooling dominates the temperature evolution and determine the associated e-folding time. First, we take the average of the combined solar, dynamic, and residual heating rates during our period of interest, yielding a value of ~1.1 K day−1. The average is taken since there is no clear trend in the dynamic heating rate during this period. Using this average we then stipulate that to achieve radiative–dynamical equilibrium, the longwave radiative cooling rate must converge to the negative of this value, i.e., −1.1 K day−1. Since we know the initial radiative heating rate on 25 January, we can determine the overall change in the heating rate [ΔH 0 in Eq. (9)]. Then we fit the data according to Eq. (8). The result of the fitted radiative heating rate is demonstrated in Fig. 8a which shows a good agreement between the data and the fitted line. Also note that the e-folding time (determined through the fitting of the data) associated with the 7–10 hPa layer during the SSW of 2006 is ~11.5 days. Using this e-folding time and Eq. (13) we fit the temperature field as seen in Fig. 8b. Again, there is a good agreement between the fitted line and the data demonstrating the validity of using a radiative–dynamical equilibrium to explain the evolution of the temperature field.


Fig. 8.
Fig. 8.

(a) The 60°–90°N averaged longwave radiative cooling rates during the period of interest for the 7–10 hPa stratospheric layer is shown along with the fitted line representing the evolution of the thermal cooling rate as it converges to a new radiative–dynamic equilibrium. The respective e-folding time of the thermal cooling rates was determined to be 11.5 days. (b) The average temperature for the same region and period of time as the longwave cooling rates. Also displayed is the fit of the temperature field constructed using the associated heating rates.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

The example above demonstrated the concept of our analysis method and quantified the radiative relaxation time scale for one event (the 2006 major SSW) at one atmospheric layer (7–10 hPa), but how do other pressure levels and other SSWs compare? In the following section we will investigate the typical behavior of the 17 SSWs investigated in terms of their dynamic and radiative heating rates, beginning and ending temperatures, and their respective e-folding times from one pressure layer to another.

c. Summary features for 17 major sudden stratospheric warmings

Applying the same methodology outlined in the previous section to other pressure layers of the stratosphere and other sudden warmings we aim to uncover the characteristic behavior of the stratosphere’s temperature and heating rates following the onset of the SSWs. First, the 17 event average of the starting and converging temperature anomalies during the major SSWs are plotted in Fig. 9a. There are several prominent features in this figure, the first being the range of the starting and converging anomalies. Notice that in the upper stratosphere the range of the temperature anomalies is larger than subsequent layers below suggesting that the upper levels of the stratosphere experience enhanced cooling periods following the start of the SSW. In the upper stratosphere the temperature during an SSW follows the pattern of transitioning from a period of being well above normal to well below normal whereas in the lower layers the temperature converges to a value much closer to the climatology.


Fig. 9.
Fig. 9.

(a) The 17-event average of the 60°–90°N average starting (red line) and converging (blue line) temperature anomalies associated with the temperatures used in our thermal damping rate determination. The pressure layers shown range from 1–2 hPa to the 20–30 hPa layer. (b) As in (a), but for thermal cooling rate anomalies . (c) As in (a), but for the adjusted dynamical heating rate anomalies (H DYN + ε). The prior dynamical heating rate refers to the value taken just before the period of interest. This value was chosen to provide the reader with an idea of strength of the dynamical heating rate before its abrupt cutoff. (d) The 17-event averaged e-folding time of the fitted temperature field following the SSWs as determined based on the radiative and dynamical heating rates. Shading in all panels indicate the standard deviation of the events.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

Figure 9b shows that the radiative heating rate anomaly exhibits a similar pattern to that of temperature. In the upper portions of the stratosphere the radiative cooling is stronger (more negative) than the climatology and transitions to a magnitude lower than the climatology (positive anomaly) at that level of the atmosphere. In the lower layers, similar to the temperature field, the converging longwave radiative cooling rate (now in equilibrium with the solar and dynamical heating rates) deviates less from the climatology. The overall change in the radiative cooling rates (ΔH 0) in the upper stratosphere is larger compared to lower levels since the temperature field itself dictates the initial radiative heating rate.

The average of the converged adjusted dynamic heating rate anomalies following the 17 SSWs are displayed in Fig. 9c. Noticeable is the stark departure from the climatology in the upper stratosphere which become less pronounced as one descends toward the middle stratosphere. The transition of the dynamic heating from above to below average following the SSWs emphasizes that when the stratosphere loses its heat source (i.e., dynamical heating) the radiative cooling then dominates over the temperature field until the radiative and dynamical heating return to equilibrium.

Finally the 17 event averaged e-folding times that establish the thermal damping time scale of the stratosphere are demonstrated in Fig. 9d. This figure reveals that the e-folding time increases as one descends through the stratosphere. The increasing time scale implies that the time for the stratosphere to readjust itself to a new radiative–dynamical equilibrium is more expeditious in nature at 5.7 ± 2.0 days at the top of the stratosphere (1–2 hPa), increasing to 14.6 ± 4.4 days in the middle stratosphere (20–30 hPa). These results are in agreement with our expectation for the e-folding time to increase as one descends through the stratosphere due to radiation’s ability to cool the atmosphere via longwave emissions to space. This cooling rate diminishes in the lower stratosphere due to the increasing atmospheric thickness in the layers above which effectively absorb and reemit the radiation to the layers below dampening the ability to radiate energy to space. The cooling rate also slows as one approaches the tropopause because of the decrease in temperature since the amount of radiation emitted is directly related to the temperature itself. Note that the majority of the longwave radiation that is absorbed and reemitted in the stratosphere is done via carbon dioxide with smaller contributions from ozone and water vapor (see Clough and Iacono (1995) for more details). These results are also consistent with the work of Hitchcock et al. (2010), who found that the typical January damping rates averaged over the 70°–90°N region increase from approximately 6 days at 1 hPa to about 12.5 days at the 30 hPa level.

4. Discussion

Important to the discussion of the radiative–dynamical equilibrium is the determination of H RAD LW ( ) , i.e., the thermal radiative cooling rate that the system is evolving toward. The lack of any discernible trend following the onset of the SSWs (see Fig. 6c) is the justification for using the combined heating rate during this period. Uncertainty in this value may result in uncertainties in the converging radiative heating rate, the converging temperature, and the e-folding time.

The decision to incorporate the residual heating rate with the dynamic and solar heating rates played a significant role in the determination of the e-folding times. The variability introduced when omitting this value resulted in nonnegligible changes to the calculation of H RAD LW ( ) . Taking the 2006 major SSW as an example, we determined that if we omit the residual heating rate this would increase the average dynamic + solar heating rate in the 7–10 hPa layer by ~73% during the period of interest (see Fig. 6c), which also effectively decreases H RAD LW ( ) by the same amount. In turn, this had an impact on the calculated ΔH 0 value, which influences the fitting of the longwave radiative cooling rates, the temperature, and the e-folding time. For example, this 73% discrepancy resulted in an e-folding time of 5.4 days, under half the value previously determined. This bias created through the exclusion of the residual heating is further influenced by the choice of H RAD LW ( 0 ) . For instance, if we had chosen the starting date to be two days earlier, the thermal cooling rate would have been stronger at −4.3 K day−1, effectively increasing the value of ΔH 0, and decreasing the e-folding time to 4.9 days. The 7–10 hPa layer was not the only layer susceptible to the variability associated with the calculated dynamic heating rates, in fact the overall fitting of both the longwave radiation and temperature fields when omitting the residual heating rate resulted in a poor match to the data in general. It is for this reason that the residual heating rate was incorporated with the solar and dynamical heating rates to fit the data and to determine the respective e-folding times of the stratosphere.

We will now discuss the e-folding times determined from the 17 major SSWs that were investigated. As seen in Fig. 9 the e-folding time increases from 6 days in the upper stratosphere (1–2 hPa) to around 15 days by 30 hPa. Also increasing from the top to the middle of the stratosphere is the degree of variability. The cause behind this variability and what impacts the e-folding time the most was investigated by exploring the correlation between the e-folding time with various metrics such as: starting temperature, starting temperature anomaly, heating rates, heating rate anomalies, ΔH 0, and zonal wind (see Table 2). These findings indicate that there are two factors that impact the damping rate of the stratosphere the most, the first being the starting temperature, T(0), and the second being the converging longwave radiative cooling rate, H RAD LW ( ) . In looking at Fig. 10a, which demonstrates the relationship between the radiative relaxation time scale and the stating temperature, we find that higher values of T(0) are associated with faster damping times. While not surprising, this affirms the dependence of the damping rates on temperature mentioned by Hitchcock et al. (2010). Though the initial thermal cooling rate, H RAD LW ( 0 ) , also explains a significant proportion of the variability of the e-folding time, this cooling rate is a direct result of temperature [see Eq. (10)] and as such does not provide much further information other than at higher initial temperatures the longwave cooling rate will also be higher which results in faster damping times. Regarding the amount of variance explained by H RAD LW ( ) we remind the reader that H RAD LW ( ) = ( H DYN * + H RAD SW ) which means that it is the underlying heating rates (shortwave, dynamical, and residual), that the thermal cooling rate is converging toward, that is responsible for this variability. This relationship between the e-folding time and H DYN * + H RAD SW is shown in Fig. 10b. Here we see that when the sum of these heating rates is higher, the time it takes for the thermal cooling rate to match this supply of heat will be faster, resulting in a shorter e-folding time. To see where this dependency of the radiative relaxation time scale on the supply of heat via dynamics and solar radiation comes from we refer to Eqs. (8) and (9). These equations indicate that determining the radiative relaxation time scale requires us to first establish ΔH 0, which itself is dependent on H RAD LW ( 0 ) and H RAD LW ( ) . As we mentioned before any dependency on H RAD LW ( 0 ) is instead the result of T(0), while the dependency on H RAD LW ( ) instead stems from the underlying supply of heat from H DYN * and H RAD SW . So, in varying the solar and dynamic heating rates this will cause the value of ΔH 0 to change which in turn influences the fitting of the thermal cooling rates and ultimately the e-folding time. To further highlight some of these key points we refer to Fig. 11 which showcases the e-folding time (Fig. 11a), T(0) (Fig. 11b), and H DYN * + H RAD SW (Fig. 11c) for the 17 SSWs used in this study and which of these major warmings met the outlined criteria for choosing events at each pressure layer. In comparing these events we see that in general those events with a shorter e-folding time corresponds to either a higher starting temperature, a larger heating rate ( H DYN * + H RAD SW ), or a combination of the two. For instance, looking at the 1–2 hPa layer we find that the SSW of 2001 (purple square) has an e-folding time of 3.4 days and correspondingly has an initial temperature of 270 K and a heating rate of 7.8 K day−1. On the other hand, at the same level the SSW of 2006 (black diamond) has an e-folding time of 8.9 days, an initial temperature of 241 K, and a heating rate of 3.2 K day−1. Using Fig. 11 we can attribute the higher degree of variability of the e-folding time in the middle stratosphere (20–30 hPa) to the fact that the spread among the heating rate values at this level is smaller than higher up in the stratosphere. A smaller spread of the heating rate supplied by H DYN * and H RAD SW implies that the heating rate that the thermal cooling rate is converging toward [ H RAD LW ( ) ] tends to be similar in magnitude among the events. In turn this means that despite some events beginning with a larger initial temperature and consequently a smaller (more negative) initial thermal cooling rate, having a relatively constant thermal cooling rate that the system is evolving toward results in a large spread of ΔH 0 values at that level and among the thermal damping rates. Furthermore, we stipulate that to fit the data, we require the longwave radiative cooling rate to be larger in magnitude than both the solar and dynamic heating rates for a minimum of five days, along with the criterion of the thermal heating rate explaining the most amount of the variance of ∂T/∂t. Together this has an impact on the number of events we can use in our analysis since the heating rates are similar in magnitude at this level thereby leading to the enhanced uncertainty found in the middle stratosphere.

Table 2.

Summary of the correlation coefficients (R), coefficients of determination (R 2), and the associated p values for the F test on the significance of the linear regression model that describe the relationship between the e-folding times of the SSWs used in this study for all pressure layers and various metrics. Here u 60°N(0)|10hPa refers to the zonally averaged zonal wind at 60°N and 10 hPa when it first switches direction. Note that primes indicate the departure from the 1979–2016 climatology for each calendar date.


Table 2.

Fig. 10.
Fig. 10.

(a) The e-folding times associated with each of the 17 SSWs used in this study and the associated 60°–90°N averaged starting temperature T(0). (b) As in (a), but with the sum of the adjusted dynamic and solar heating rates (i.e., H DYN * + H RAD SW ), which represents the heating rate that the thermal cooling rate is converging toward to reestablish a radiative–dynamic equilibrium. Note that the results from all pressure layers used in our analysis are displayed here.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1


Fig. 11.
Fig. 11.

(a) The e-folding times associated with each of the 17 SSWs used in this study for the pressure layers ranging from 1–2 to 20–30 hPa. (b) As in (a), but for the 60°–90°N averaged starting temperature T(0) of each event. (c) As in (a), but for the sum of the adjusted dynamic and solar heating rates (i.e., H DYN * + H RAD SW ). Note that each pressure layer is only populated by events that met the outlined requirements for selecting events. The SSWs are referenced by the year in which the central date of each event occurred.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

Another important note about the thermal damping rates determined in our work is that they have been generalized to the 60°–90°N Arctic region during the winter months only. As pointed out by Newman and Rosenfield (1997) and Hitchcock et al. (2010) there is also a seasonal and latitudinal dependency of the e-folding time. In the future a more thorough analysis of the e-folding time at each latitude and month will be performed to assess how much these results may vary from one latitude to another and from season to season.

While this work offers a novel way of determining the radiative damping rates of the stratosphere there are certain limitations. The most obvious limitation is that our methodology can only be applied to instances whereby there is a prolonged period of suppressed wave activity to the stratosphere, i.e., long duration SSWs. Furthermore, the value of ΔH 0 [Eq. (9)] during these events must be large enough to allow sufficient time for the thermal radiation to control the temperature and cool the stratosphere. Another limitation is the range of stratospheric layers that meet our criteria for calculating the thermal damping rate. For instance, none of the layers of the stratosphere below 50 hPa met our explained variance criterion while only two of the SSWs investigated in our study met this criterion at the 30–50 hPa layer and thus were not included in our results. The reason why these levels of the stratosphere below 30 hPa failed our variance test was because there was not enough separation between the radiative cooling rate and the combined heating rates, i.e., the ΔH 0 value was too small.

We conclude this discussion with a note regarding the sensitivity of the thermal and solar heating rates to trace-gas anomalies during SSWs. For instance, changes in water vapor and particularly ozone concentrations, which are known to vary during SSWs (e.g., see Kuttippurath and Nikulin 2012; Scheiben et al. 2012; Cámara Illescas et al. 2018), may have an impact on these heating rates and in turn influence the radiative relaxation time scales previously determined. During the SSW of 2006, for example, we determined that the ozone concentrations in some regions of the stratosphere reached upward of 20% above their 1979–2016 climatological value while water vapor concentrations dropped by over 5%. To test the impact water vapor and ozone has on the heating rates a simple experiment was performed whereby we first replaced the water vapor concentration at specific layers of the stratosphere, e.g., 7–10 hPa, with the climatological concentration while all other layers were allowed to vary. Performing both longwave and shortwave RRTMG calculations the results were compared to the unaltered output. We then performed the same experiment for ozone and for all layers of the stratosphere with the results for the 7–10 hPa layer seen in Fig. 12. From this figure we see that despite the changes in water vapor and ozone concentrations during this event, the radiative impact on the 7–10 hPa layer’s thermal cooling rates (Fig. 12a) and solar heating rates (Fig. 12b) were negligible. Together the explicit and accurate radiative heating rates of this experiment reveals that in the mid- to upper stratosphere, the focus region of this work, the heating rate anomalies during the SSWs are dominated by temperature and are insensitive to trace-gas anomalies. Note, however, that this insensitivity may not necessarily be the case in the lower stratosphere.


Fig. 12.
Fig. 12.

(a) The 60°–90°N averaged longwave radiative heating rate for the 7–10 hPa region during the stratospheric warming of 2006. The black line indicates the reanalysis values of ozone (O3) and water vapor (q) during the event while the red and blue lines correspond to the associated heating rate when ozone and water vapor concentrations have been replaced by their 1979–2016 climatological values. (b) As in (a), but for the shortwave heating rates. Any deviation of the red or blue line from the black line indicates the influence water vapor or ozone has on the respective heating rate.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

5. Conclusions

This paper investigated 17 major SSWs during the 1979–2016 period and highlighted the importance of radiation in removing anomalous heat from the stratosphere through the means of a heating rate analysis generalized for the 60°–90°N polar region. Using the thermodynamic equation we developed composites of the dynamical (due to meridional transport, vertical transport, and adiabatic cooling due to vertical motion) and radiative (both thermal and solar) heating rates, along with their associated anomalies to depict the typical characteristics of the stratospheric warmings. These composites demonstrate how the vertical motions are responsible for the warming of the stratosphere contributing a heating rate anomaly in excess of 15 K day−1 on average to the upper stratosphere. Following the onset of the SSWs when the zonal winds at 60°N have reversed to an easterly direction there is suppressed wave activity to the stratosphere resulting in a reduction of the amount of heat supplied throughout much of the stratosphere by vertical motions. During this period there is a tendency for the stratospheric temperature to transition from a positive anomaly to an equally impressive negative anomaly. It is during this time of suppressed dynamic heating that the thermal radiative cooling asserts its dominance over the temperature. The cooling of the region continues until a new radiative–dynamical heating rate equilibrium is reached and the temperature plateaus.

Using the notion of a radiative–dynamical equilibrium the temperature field for distinct stratospheric layers between 1 and 30 hPa during the period when the temperature displays the longest period of continual decrease following the onset of the SSW was reconstructed. To do so the longwave radiative cooling rates were fit such that the value these heating rates converge toward is the same magnitude but opposite in sign as the sum of the average solar and dynamical heating rates for the same period. Using this fitted longwave cooling rate, all the heating rates were then added together and integrated producing a fitted temperature curve that matched the data reasonably well.

In the development of the fitted temperature curves during major SSWs, the associated e-folding times for distinct stratospheric layers were also determined providing a quantification of the length of time required to remove thermal disturbances from the atmosphere via longwave radiation. As expected, the e-folding time was the smallest at the top of the stratosphere (1–2 hPa) with a value of 5.7 ± 2.0 days increasing to 14.6 ± 4.4 days in the middle stratosphere (20–30 hPa). The variability among the e-folding times of the SSWs used in this study was also briefly discussed. It was found that the initial temperature, T(0), and the heating rate supplied by dynamics and solar radiation, H DYN * + H RAD SW , following the onset of the SSWs, i.e., the heating rate that the thermal cooling rate is converging toward, H RAD LW ( ) , explain the most amount of the variability of the radiative relaxation rates of these events. SSWs with a higher initial temperature or those with a larger heating rate are associated with faster e-folding times. The spread in the heating rates was also found to decrease as one approaches the middle stratosphere meaning that the heat supplied to that level of the stratosphere following the onset of SSWs does not vary much from one SSW to another, unlike the upper levels of the stratosphere. Together, the knowledge of the initial temperature of the stratosphere and the heating rates involved provide a deeper understanding of the variability among SSWs and why it takes longer for some SSWs to reestablish a radiative–dynamic equilibrium than others. Furthermore, as is the case with the SSWs discussed here, during the period of wave suppression the supply of heat via dynamics is often below its climatological value. As such, relying only on the knowledge of the climatological heating rates will not provide as accurate of account of the radiative relaxation rate or temperature tendencies following the onset of SSWs.

With SSWs undoubtedly representing such a strong source of internal variability of the stratosphere from year to year it is important to better understand how the system reacts to such intense periods of anomalous temperatures through the process of radiative cooling. In studying major SSWs, this research has provided unique case study examples in which to better constrain the thermal damping rates of the stratosphere to these anomalous disturbances. Moreover, this paper has highlighted the necessity to incorporate the radiation field when discussing SSWs as longwave radiative cooling directly influences the temperature evolution and length of time the stratosphere remains in a perturbed state.

The complex nature associated with SSWs underlines the need for further work to be conducted to better understand and constrain their unique characteristics and for that matter what differentiates one SSW from another. The variability among the major SSWs investigated here and their associated dynamical heating rates, radiative heating rates, temperature, and the e-folding times also requires further investigation. In doing so an improved understanding of the mechanisms behind the supply (removal) of heat to (from) the stratosphere will be developed. While additional research on these events is required, we have demonstrated, however, the importance of radiation during these events. Furthermore, we have highlighted the importance of the radiative–dynamic equilibrium in the polar winter stratosphere and when the system is perturbed there will always be a tendency for the stratosphere reestablish this equilibrium. In the case of major SSWs, however, when this equilibrium is reached it will likely be at a temperature well below normal.

Acknowledgments

We wish to thank the three anonymous reviewers of this paper and the McGill Atmospheric Radiation Research Group for all the fruitful conversations and feedback during the course of this work. This research has been made possible through the Natural Sciences and Engineering Research Council of Canada’s Postgraduate Scholarship—Doctoral program (R249404C0G) and we also acknowledge the grants from the National Sciences and Engineering Research Council of Canada (NSERC, RGPIN-2019-04511) and the Canadian Space Agency (G&C, 16SUASURDC) that supported this research.

APPENDIX A

Comparison of Net Clear-Sky and All-Sky Longwave Radiative Fluxes and Heating Rates

The choice of using clear-sky conditions instead of all-sky is rooted in the similar net longwave radiative output and heating rates found throughout the stratosphere. Figure A1 depicts an identical radiative output and heating rate for the 7–10 hPa layer while for the 70–100 hPa layer only a slight separation appears between the two outputs. It is this similarity which provides the foundation for our choice in using clear-sky conditions throughout this paper. Furthermore, running RRTMG under all-sky conditions required the use of liquid and ice droplet radii data which are provided by Clouds and the Earth’s Radiant Energy System (CERES) (Wielicki et al. 1996). This dataset, however, does not provide the same temporal coverage as the ERA-I, limiting the number of SSWs that could be used in our analysis.


Fig. A1.
Fig. A1.

(top) The net 60°–90°N longwave radiation emitted from the (a) 7–10 and (b) 70–100 hPa layers during the SSW in 2006 under all-sky (blue) and clear-sky (red) conditions. (bottom) The 60°–90°N averaged heating rate over the same period for the (c) 7–10 and (d) 70–100 hPa layers.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

APPENDIX B

Validation of Treating the 60°–90°N Region as a Single Column While Using RRTMG

The treatment of the 60°–90°N region as a single column was done to save computational resources and as seen for the heating rates at the 7–10 and 70–100 hPa layers in Fig. B1, this had a negligible impact. The only noticeable difference occurs during the period leading up to the onset of the SSW. However, since this work focuses on the period of temperature decay, this difference does not affect our results.


Fig. B1.
Fig. B1.

The 60°–90°N averaged thermal cooling rates for the (a) 7–10 and (b) 70–100 hPa layers during the SSW in 2006. The dashed line in both panels represents this average taken after the RRTMG calculations were performed at each grid point over the 60°–90°N region. The solid lines are the cooling rates determined when treating the 60°–90°N region as a single column, i.e., taking the 60°–90°N average of the temperature and atmospheric constituents first and then running RRTMG.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

APPENDIX C

The Adjusted Dynamic Heating Rate

The residual heating rates used in our calculations for the thermal damping rate and temperature fitting scheme are the result of the inability to close the thermodynamic budget completely. This term contains errors associated with the radiative transfer model, our calculations, and the data themselves which also include any biases introduced through data assimilation increments. To check whether the radiative heating rates (determined using RRTMG) or the dynamical heating rates were most impacted by the inclusion of the residual heating rate, we performed an analysis of variance like the one seen in Fig. 7. In this test, however, we investigated the amount of variance of ∂T/∂t that is explained by either the thermal heating rate, the solar heating rate, or the dynamical heating rate during the same periods used in Fig. 7. We then performed the same test but added the residual heating to each of the heating rates individually (see Fig. C1). We reason that the residual heating rate should improve the amount of explained variance by the term that contains the highest error associated with it. We find that during the 1–25 January period, when there is enhanced wave activity to the stratosphere, the inclusion of the residual heating rate with the dynamical heating rate (first column of Fig. C1) led to a significant improvement in the amount of variance that is explained by the dynamic heating rate. For example, in the 7–10 hPa layer this led to an ~60% increase in the amount of the variance of ∂T/∂t that is explained by the dynamic heating rate, increasing from 60% to 95%. When we included the residual heating rate with the thermal heating rate the result was a decrease in the amount of explained variance for the 1–25 January and 25 January–16 February (middle column of Fig. C1) periods and only a slight increase of 3% for the 16 February–31 March period. For the solar heating rate the result was a decrease in the amount of explained variance for all periods, including 16 February–31 March when the solar heating rate explains the most amount of the variance of ∂T/∂t (see the third column of Fig. C1). These results indicate that it is likely the dynamic heating rate that contains the highest amount of error. While we do not test if the vertical or meridional heating rate component is the predominate source of the error, we assume the vertical heating rate components are the culprit since the vertical wind measurements provided by reanalysis data are known to suffer from excessive noise and errors (see Wohltmann and Rex (2008) for more details). For these reasons, the authors felt justified in grouping the residual and dynamic heating rates together and calling this the adjusted dynamic heating rate.


Fig. C1.
Fig. C1.

As in Fig. 7, except with the focus on the impact of the residual heating rate (ε) on (left column) the dynamic heating rate (H DYN) during the 1–25 Jan period, (center) the thermal cooling rate ( H RAD LW ) from 25 Jan to 16 Feb, and the (right) solar heating rate ( H RAD SW ) during the 16 Feb–31 Mar period.

Citation: Journal of the Atmospheric Sciences 78, 1; 10.1175/JAS-D-20-0015.1

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  • Charlton, A. J. , and L. M. Polvani , 2007: A new look at stratospheric sudden warmings. Part I: Climatology and modeling benchmarks. J. Climate, 20, 449469, https://doi.org/10.1175/JCLI3996.1.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Clough, S. A. , and M. J. Iacono , 1995: Line-by-line calculation of atmospheric fluxes and cooling rates: 2. Application to carbon dioxide, ozone, methane, nitrous oxide and the halocarbons. J. Geophys. Res., 100, 16 51916 535, https://doi.org/10.1029/95JD01386.

    • Search Google Scholar
    • Export Citation
  • Cronin, T. W. , and K. A. Emanuel , 2013: The climate time scale in the approach to radiative-convective equilibrium. J. Adv. Model. Earth Syst., 5, 843849, https://doi.org/10.1002/jame.20049.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P. , and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • de la Cámara, A. , M. Abalos , and P. Hitchcock , 2018: Changes in stratospheric transport and mixing during sudden stratospheric warmings. J. Geophys. Res. Atmos., 123, 33563373, https://doi.org/10.1002/2017JD028007.

    • Search Google Scholar
    • Export Citation
  • Fels, S. B. , 1982: A parameterization of scale-dependent radiative damping rates in the middle atmosphere. J. Atmos. Sci., 39, 11411152, https://doi.org/10.1175/1520-0469(1982)039<1141:APOSDR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , and T. G. Shepherd , 2013: Zonal-mean dynamics of extended recoveries from stratospheric sudden warmings. J. Atmos. Sci., 70, 688707, https://doi.org/10.1175/JAS-D-12-0111.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , and I. R. Simpson , 2014: The downward influence of stratospheric sudden warmings. J. Atmos. Sci., 71, 38563876, https://doi.org/10.1175/JAS-D-14-0012.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , T. G. Shepherd , and S. Yoden , 2010: On the approximation of local and linear radiative damping in the middle atmosphere. J. Atmos. Sci., 67, 20702085, https://doi.org/10.1175/2009JAS3286.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , T. G. Shepherd , and G. L. Manney , 2013a: Statistical characterization of Arctic polar-night jet oscillation events. J. Climate, 26, 20962116, https://doi.org/10.1175/JCLI-D-12-00202.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , T. G. Shepherd , M. Taguchi , S. Yoden , and S. Noguchi , 2013b: Lower-stratospheric radiative damping and polar-night jet oscillation events. J. Atmos. Sci., 70, 13911408, https://doi.org/10.1175/JAS-D-12-0193.1.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R. , and C. Mass , 1976: Stratospheric vacillation cycles. J. Atmos. Sci., 33, 22182225, https://doi.org/10.1175/1520-0469(1976)033<2218:SVC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Karpechko, A. Y. , P. Hitchcock , D. H. W. Peters , and A. Schneidereit , 2017: Predictability of downward propagation of major sudden stratospheric warmings. Quart. J. Roy. Meteor. Soc., 143, 14591470, https://doi.org/10.1002/qj.3017.

    • Search Google Scholar
    • Export Citation
  • Kidston, J. , A. A. Scaife , S. C. Hardiman , D. M. Mitchell , N. Butchart , M. P. Baldwin , and L. J. Gray , 2015: Stratospheric influence on tropospheric jet streams, storm tracks and surface weather. Nat. Geosci., 8, 433440, https://doi.org/10.1038/ngeo2424.

    • Search Google Scholar
    • Export Citation
  • Kolstad, E. W. , T. Breiteig , and A. A. Scaife , 2010: The association between stratospheric weak polar vortex events and cold air outbreaks in the Northern Hemisphere. Quart. J. Roy. Meteor. Soc., 136, 886893, https://doi.org/10.1002/qj.620.

    • Search Google Scholar
    • Export Citation
  • Kuttippurath, J. , and G. Nikulin , 2012: A comparative study of the major sudden stratospheric warmings in the Arctic winters 2003/2004–2009/2010. Atmos. Chem. Phys., 12, 81158129, https://doi.org/10.5194/acp-12-8115-2012.

    • Search Google Scholar
    • Export Citation
  • Lateef, M. A. , 1964: The energy budget of the stratosphere over North America during the warming of 1957. J. Geophys. Res., 69, 14811495, https://doi.org/10.1029/JZ069i008p01481.

    • Search Google Scholar
    • Export Citation
  • Li, Y. , D. W. Thompson , and Y. Huang , 2017: The influence of atmospheric cloud radiative effects on the large-scale stratospheric circulation. J. Climate, 30, 56215635, https://doi.org/10.1175/JCLI-D-16-0643.1.

    • Search Google Scholar
    • Export Citation
  • Limpasuvan, V. , D. W. J. Thompson , and D. L. Hartmann , 2004: The life cycle of the Northern Hemisphere sudden stratospheric warming. J. Climate, 17, 25842596, https://doi.org/10.1175/1520-0442(2004)017<2584:TLCOTN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Limpasuvan, V. , J. H. Richter , Y. J. Orsolini , F. Stordal , and O.-K. Kvissel , 2012: The roles of planetary and gravity waves during a major stratospheric sudden warming as characterized in WACCM. J. Atmos. Sol.-Terr. Phys., 78–79, 8498, https://doi.org/10.1016/j.jastp.2011.03.004.

    • Search Google Scholar
    • Export Citation
  • Liu, C. , B. Tian , K. F. Li , G. L. Manney , N. J. Livesey , Y. L. Yung , and D. E. Waliser , 2014: Northern Hemisphere mid-winter vortex-displacement and vortex-split stratospheric sudden warmings: Influence of the Madden-Julian oscillation and quasi-biennial oscillation. J. Geophys. Res. Atmos., 119, 12 59912 620, https://doi.org/10.1002/2014JD021876.

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    • Export Citation
  • Liu, Y. , C. Liu , H. Wang , X. Tie , S. Gao , D. Kinnison , and G. Brasseur , 2009: Atmospheric tracers during the 2003–2004 stratospheric warming event and impact of ozone intrusions in the troposphere. Atmos. Chem. Phys., 9, 21572170, https://doi.org/10.5194/acp-9-2157-2009.

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    • Export Citation
  • Martineau, P. , S. W. Son , M. Taguchi , and A. H. Butler , 2018: A comparison of the momentum budget in reanalysis datasets during sudden stratospheric warming events. Atmos. Chem. Phys., 18, 71697187, https://doi.org/10.5194/acp-18-7169-2018.

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    • Export Citation
  • Matsuno, T. , 1971: A dynamic model of the stratospheric sudden warming. J. Atmos. Sci., 28, 14791494, https://doi.org/10.1175/1520-0469(1971)028<1479:ADMOTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • MIPAS, 2001: RFM atmospheric profiles—MIPAS model atmospheres (2001). University of Oxford Earth Observation Data Group, accessed 18 November 2019, http://eodg.atm.ox.ac.uk/RFM/atm/.

  • Mitchell, D. M. , L. J. Gray , J. Anstey , M. P. Baldwin , and A. J. Charlton-Perez , 2013: The influence of stratospheric vortex displacements and splits on surface climate. J. Climate, 26, 26682682, https://doi.org/10.1175/JCLI-D-12-00030.1.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J. , S. J. Taubman , P. D. Brown , M. J. Iacono , and S. A. Clough , 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 66316 682, https://doi.org/10.1029/97JD00237.

    • Search Google Scholar
    • Export Citation
  • Newman, P. A. , and J. E. Rosenfield , 1997: Stratospheric thermal damping times. Geophys. Res. Lett., 24, 433436, https://doi.org/10.1029/96GL03720.

    • Search Google Scholar
    • Export Citation
  • Polvani, L. M. , and D. W. Waugh , 2004: Upward wave activity flux as a precursor to extreme stratospheric events and subsequent anomalous surface weather regimes. J. Climate, 17, 35483554, https://doi.org/10.1175/1520-0442(2004)017<3548:UWAFAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Scheiben, D. , C. Straub , K. Hocke , P. Forkman , and N. Kämpfer , 2012: Observations of middle atmospheric H2O and O3 during the 2010 major sudden stratospheric warming by a network of microwave radiometers. Atmos. Chem. Phys., 12, 77537765, https://doi.org/10.5194/acp-12-7753-2012.

    • Search Google Scholar
    • Export Citation
  • Scherhag, R. , 1960: Stratospheric temperature changes and the changes in pressure distribution. J. Meteor., 17, 575583, https://doi.org/10.1175/1520-0469(1960)017<0575:STCATA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
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    • Search Google Scholar
    • Export Citation
  • Tomikawa, Y. , 2010: Persistence of easterly wind during major stratospheric sudden warmings. J. Climate, 23, 52585267, https://doi.org/10.1175/2010JCLI3507.1.

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    • Export Citation
  • Tomikawa, Y. , K. Sato , S. Watanabe , Y. Kawatani , K. Miyazaki , and M. Takahashi , 2012: Growth of planetary waves and the formation of an elevated stratopause after a major stratospheric sudden warming in a T213l256 GCM. J. Geophys. Res., 117, D16101, https://doi.org/10.1029/2011JD017243.

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  • White, I. , C. I. Garfinkel , E. P. Gerber , M. Jucker , V. Aquila , and L. D. Oman , 2019: The downward influence of sudden stratospheric warmings: Association with tropospheric precursors. J. Climate, 32, 85108, https://doi.org/10.1175/JCLI-D-18-0053.1.

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  • Cámara Illescas, Á. , M. Ábalos Álvarez , P. Hitchcock , N. Calvo Fernández , and R. R. Garcia , 2018: Response of Arctic ozone to sudden stratospheric warmings. Atmos. Chem. Phys., 18, 16 49916 513, https://doi.org/10.5194/acp-18-16499-2018.

    • Search Google Scholar
    • Export Citation
  • Charlton, A. J. , and L. M. Polvani , 2007: A new look at stratospheric sudden warmings. Part I: Climatology and modeling benchmarks. J. Climate, 20, 449469, https://doi.org/10.1175/JCLI3996.1.

    • Search Google Scholar
    • Export Citation
  • Charney, J. G. , and P. G. Drazin , 1961: Propagation of planetary-scale disturbances from the lower into the upper atmosphere. J. Geophys. Res., 66, 83109, https://doi.org/10.1029/JZ066i001p00083.

    • Search Google Scholar
    • Export Citation
  • Clough, S. A. , and M. J. Iacono , 1995: Line-by-line calculation of atmospheric fluxes and cooling rates: 2. Application to carbon dioxide, ozone, methane, nitrous oxide and the halocarbons. J. Geophys. Res., 100, 16 51916 535, https://doi.org/10.1029/95JD01386.

    • Search Google Scholar
    • Export Citation
  • Cronin, T. W. , and K. A. Emanuel , 2013: The climate time scale in the approach to radiative-convective equilibrium. J. Adv. Model. Earth Syst., 5, 843849, https://doi.org/10.1002/jame.20049.

    • Search Google Scholar
    • Export Citation
  • Dee, D. P. , and Coauthors, 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Search Google Scholar
    • Export Citation
  • de la Cámara, A. , M. Abalos , and P. Hitchcock , 2018: Changes in stratospheric transport and mixing during sudden stratospheric warmings. J. Geophys. Res. Atmos., 123, 33563373, https://doi.org/10.1002/2017JD028007.

    • Search Google Scholar
    • Export Citation
  • Fels, S. B. , 1982: A parameterization of scale-dependent radiative damping rates in the middle atmosphere. J. Atmos. Sci., 39, 11411152, https://doi.org/10.1175/1520-0469(1982)039<1141:APOSDR>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , and T. G. Shepherd , 2013: Zonal-mean dynamics of extended recoveries from stratospheric sudden warmings. J. Atmos. Sci., 70, 688707, https://doi.org/10.1175/JAS-D-12-0111.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , and I. R. Simpson , 2014: The downward influence of stratospheric sudden warmings. J. Atmos. Sci., 71, 38563876, https://doi.org/10.1175/JAS-D-14-0012.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , T. G. Shepherd , and S. Yoden , 2010: On the approximation of local and linear radiative damping in the middle atmosphere. J. Atmos. Sci., 67, 20702085, https://doi.org/10.1175/2009JAS3286.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , T. G. Shepherd , and G. L. Manney , 2013a: Statistical characterization of Arctic polar-night jet oscillation events. J. Climate, 26, 20962116, https://doi.org/10.1175/JCLI-D-12-00202.1.

    • Search Google Scholar
    • Export Citation
  • Hitchcock, P. , T. G. Shepherd , M. Taguchi , S. Yoden , and S. Noguchi , 2013b: Lower-stratospheric radiative damping and polar-night jet oscillation events. J. Atmos. Sci., 70, 13911408, https://doi.org/10.1175/JAS-D-12-0193.1.

    • Search Google Scholar
    • Export Citation
  • Holton, J. R. , and C. Mass , 1976: Stratospheric vacillation cycles. J. Atmos. Sci., 33, 22182225, https://doi.org/10.1175/1520-0469(1976)033<2218:SVC>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Karpechko, A. Y. , P. Hitchcock , D. H. W. Peters , and A. Schneidereit , 2017: Predictability of downward propagation of major sudden stratospheric warmings. Quart. J. Roy. Meteor. Soc., 143, 14591470, https://doi.org/10.1002/qj.3017.

    • Search Google Scholar
    • Export Citation
  • Kidston, J. , A. A. Scaife , S. C. Hardiman , D. M. Mitchell , N. Butchart , M. P. Baldwin , and L. J. Gray , 2015: Stratospheric influence on tropospheric jet streams, storm tracks and surface weather. Nat. Geosci., 8, 433440, https://doi.org/10.1038/ngeo2424.

    • Search Google Scholar
    • Export Citation
  • Kolstad, E. W. , T. Breiteig , and A. A. Scaife , 2010: The association between stratospheric weak polar vortex events and cold air outbreaks in the Northern Hemisphere. Quart. J. Roy. Meteor. Soc., 136, 886893, https://doi.org/10.1002/qj.620.

    • Search Google Scholar
    • Export Citation
  • Kuttippurath, J. , and G. Nikulin , 2012: A comparative study of the major sudden stratospheric warmings in the Arctic winters 2003/2004–2009/2010. Atmos. Chem. Phys., 12, 81158129, https://doi.org/10.5194/acp-12-8115-2012.

    • Search Google Scholar
    • Export Citation
  • Lateef, M. A. , 1964: The energy budget of the stratosphere over North America during the warming of 1957. J. Geophys. Res., 69, 14811495, https://doi.org/10.1029/JZ069i008p01481.

    • Search Google Scholar
    • Export Citation
  • Li, Y. , D. W. Thompson , and Y. Huang , 2017: The influence of atmospheric cloud radiative effects on the large-scale stratospheric circulation. J. Climate, 30, 56215635, https://doi.org/10.1175/JCLI-D-16-0643.1.

    • Search Google Scholar
    • Export Citation
  • Limpasuvan, V. , D. W. J. Thompson , and D. L. Hartmann , 2004: The life cycle of the Northern Hemisphere sudden stratospheric warming. J. Climate, 17, 25842596, https://doi.org/10.1175/1520-0442(2004)017<2584:TLCOTN>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Limpasuvan, V. , J. H. Richter , Y. J. Orsolini , F. Stordal , and O.-K. Kvissel , 2012: The roles of planetary and gravity waves during a major stratospheric sudden warming as characterized in WACCM. J. Atmos. Sol.-Terr. Phys., 78–79, 8498, https://doi.org/10.1016/j.jastp.2011.03.004.

    • Search Google Scholar
    • Export Citation
  • Liu, C. , B. Tian , K. F. Li , G. L. Manney , N. J. Livesey , Y. L. Yung , and D. E. Waliser , 2014: Northern Hemisphere mid-winter vortex-displacement and vortex-split stratospheric sudden warmings: Influence of the Madden-Julian oscillation and quasi-biennial oscillation. J. Geophys. Res. Atmos., 119, 12 59912 620, https://doi.org/10.1002/2014JD021876.

    • Search Google Scholar
    • Export Citation
  • Liu, Y. , C. Liu , H. Wang , X. Tie , S. Gao , D. Kinnison , and G. Brasseur , 2009: Atmospheric tracers during the 2003–2004 stratospheric warming event and impact of ozone intrusions in the troposphere. Atmos. Chem. Phys., 9, 21572170, https://doi.org/10.5194/acp-9-2157-2009.

    • Search Google Scholar
    • Export Citation
  • Martineau, P. , S. W. Son , M. Taguchi , and A. H. Butler , 2018: A comparison of the momentum budget in reanalysis datasets during sudden stratospheric warming events. Atmos. Chem. Phys., 18, 71697187, https://doi.org/10.5194/acp-18-7169-2018.

    • Search Google Scholar
    • Export Citation
  • Matsuno, T. , 1971: A dynamic model of the stratospheric sudden warming. J. Atmos. Sci., 28, 14791494, https://doi.org/10.1175/1520-0469(1971)028<1479:ADMOTS>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • MIPAS, 2001: RFM atmospheric profiles—MIPAS model atmospheres (2001). University of Oxford Earth Observation Data Group, accessed 18 November 2019, http://eodg.atm.ox.ac.uk/RFM/atm/.

  • Mitchell, D. M. , L. J. Gray , J. Anstey , M. P. Baldwin , and A. J. Charlton-Perez , 2013: The influence of stratospheric vortex displacements and splits on surface climate. J. Climate, 26, 26682682, https://doi.org/10.1175/JCLI-D-12-00030.1.

    • Search Google Scholar
    • Export Citation
  • Mlawer, E. J. , S. J. Taubman , P. D. Brown , M. J. Iacono , and S. A. Clough , 1997: Radiative transfer for inhomogeneous atmospheres: RRTM, a validated correlated-k model for the longwave. J. Geophys. Res., 102, 16 66316 682, https://doi.org/10.1029/97JD00237.

    • Search Google Scholar
    • Export Citation
  • Newman, P. A. , and J. E. Rosenfield , 1997: Stratospheric thermal damping times. Geophys. Res. Lett., 24, 433436, https://doi.org/10.1029/96GL03720.

    • Search Google Scholar
    • Export Citation
  • Polvani, L. M. , and D. W. Waugh , 2004: Upward wave activity flux as a precursor to extreme stratospheric events and subsequent anomalous surface weather regimes. J. Climate, 17, 35483554, https://doi.org/10.1175/1520-0442(2004)017<3548:UWAFAA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Ramanathan, V. , E. J. Pitcher , R. C. Malone , and M. L. Blackmon , 1983: The response of a spectral general circulation model to refinements in radiative processes. J. Atmos. Sci., 40, 605630, https://doi.org/10.1175/1520-0469(1983)040<0605:TROASG>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Sasamori, T. , and J. London , 1966: The decay of small temperature perturbations by thermal radiation in the atmosphere. J. Atmos. Sci., 23, 543554, https://doi.org/10.1175/1520-0469(1966)023<0543:TDOSTP>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Scheiben, D. , C. Straub , K. Hocke , P. Forkman , and N. Kämpfer , 2012: Observations of middle atmospheric H2O and O3 during the 2010 major sudden stratospheric warming by a network of microwave radiometers. Atmos. Chem. Phys., 12, 77537765, https://doi.org/10.5194/acp-12-7753-2012.

    • Search Google Scholar
    • Export Citation
  • Scherhag, R. , 1960: Stratospheric temperature changes and the changes in pressure distribution. J. Meteor., 17, 575583, https://doi.org/10.1175/1520-0469(1960)017<0575:STCATA>2.0.CO;2.

    • Search Google Scholar
    • Export Citation
  • Siskind, D. E. , S. D. Eckermann , J. P. McCormack , L. Coy , K. W. Hoppel , and N. L. Baker , 2010: Case studies of the mesospheric response to recent minor, major, and extended stratospheric warmings. J. Geophys. Res., 115, D00N03, https://doi.org/10.1029/2010JD014114.

    • Search Google Scholar
    • Export Citation
  • Tomikawa, Y. , 2010: Persistence of easterly wind during major stratospheric sudden warmings. J. Climate, 23, 52585267, https://doi.org/10.1175/2010JCLI3507.1.

    • Search Google Scholar
    • Export Citation
  • Tomikawa, Y. , K. Sato , S. Watanabe , Y. Kawatani , K. Miyazaki , and M. Takahashi , 2012: Growth of planetary waves and the formation of an elevated stratopause after a major stratospheric sudden warming in a T213l256 GCM. J. Geophys. Res., 117, D16101, https://doi.org/10.1029/2011JD017243.

    • Search Google Scholar
    • Export Citation
  • White, I. , C. I. Garfinkel , E. P. Gerber , M. Jucker , V. Aquila , and L. D. Oman , 2019: