1. Introduction
Analysis of observations and output from numerical models has repeatedly shown that the middle atmosphere in the summer hemisphere responds to dynamical variability in the winter stratosphere. Two aspects of this problem have received attention. First, there are responses of the Brewer–Dobson circulation, the ozone concentration, and the temperature in the summer stratosphere to short-term variations, particularly those associated with sudden stratospheric warmings (e.g., Randel 1993). In this phenomenon, enhanced wave forcing in the winter leads to flow toward the pole and strong downwelling and warmer temperatures at the winter pole. Adjustments to maintain atmospheric mass and momentum balance produce a region of weak upwelling at low latitudes that, in some circumstances, has been observed to extend across the tropics and well into the midlatitudes of the summer hemisphere. A perturbation response can be observed or simulated in stratospheric ozone in the tropics and summer hemisphere, which responds to vertical transport and to the associated temperature perturbations (Randel 1993; Smith 1995; Tung and Kinnersley 2001). The response is also seen in the temperature itself (Fritz and Soules 1972; Yulaeva et al. 1994; Young et al. 2011) and in the strength of the Brewer–Dobson circulation (Abalos et al. 2014).
The second aspect of the response considered here is known by researchers of the middle atmosphere as interhemispheric coupling (IHC). This manifests as a correlation between dynamical activity in the winter stratosphere and that in the polar upper mesosphere of the summer hemisphere. The number of studies presenting observations of this coupling is not large and the mesospheric signal is weak. Nevertheless, the relationship is consistent across different observations; the sense of the coupling has anomalously warm temperatures in the polar summer upper mesosphere coinciding with anomalously warm temperatures in the polar winter stratosphere. The relation first received attention in the conclusion by Goldberg et al. (2004) that the July 2002 mesospheric temperatures at 69°N were anomalously warm, coincident with an unusually warm and active winter in the SH stratosphere. Modeling studies by Becker et al. (2004) and Becker and Fritts (2006) provided supporting evidence of the interhemispheric link and found that changes in gravity wave activity in the summer hemisphere played a role. Karlsson and Becker (2016) argue that climatological hemispheric differences in the mean temperatures of the northern and southern summer mesosphere can also be attributed to differences in the average state of the opposite (winter) mesosphere due to differences in gravity wave activity there.
Additional perturbations in the northern summer mesosphere in response to dynamical perturbations in the southern winter stratosphere have been seen for temperature itself (Espy et al. 2011) and for the presence or characteristics of polar mesospheric clouds (PMC) (Karlsson et al. 2007; Gumbel and Karlsson 2011; Siskind et al. 2011; France et al. 2018). PMC can be observed from the ground and from satellites in the months close to summer solstice; their formation and characteristics are very sensitive to the ambient conditions, especially the temperature around 82–85 km. The corresponding coupling in the opposite season, that is, the response of the southern summer mesosphere to variability in the northern winter stratosphere, has been reported for temperature (Xu et al. 2009; Tan et al. 2012), PMC (Karlsson et al. 2007, 2009b), and the meridional wind (Murphy et al. 2012).
Another coupling process that is relevant to the present investigation is vertical coupling from the winter stratosphere to the winter mesosphere. This is a strong relationship that has been well documented since the availability of extensive mesospheric observations (e.g., Lawrence and Randel 1996; Manney et al. 2005; Xu et al. 2009) and whole atmosphere models (e.g., Liu and Roble 2002; Becker and Fritts 2006; Karlsson et al. 2009a; Tan et al. 2012; Limpasuvan et al. 2016). Strong wave forcing in the stratosphere leads to poleward flow and warming of the polar stratosphere. This is accompanied by cooling in the upper stratosphere and mesosphere. The warming and cooling are respectively associated with downwelling and upwelling from the circulation that is driven by dissipation of both quasi-stationary planetary waves and gravity waves.
In this investigation, we document the links between perturbations in the winter stratosphere and zonal-mean responses throughout the tropical and summer middle atmosphere in a comprehensive whole atmosphere global model. Our goals are to show the details of the interhemispheric coupling in the simulations and to diagnose the processes responsible. In particular, we investigate how and on what time scales variations in driving by resolved and parameterized waves respond to and/or contribute to the coupling from the winter to the summer hemisphere.
2. Model simulations
Version 6 of the Whole Atmosphere Community Climate Model (WACCM6) is one of the atmospheric components of NCAR’s Community Earth System Model, version 2 (CESM2). Gettelman et al. (2019) describe the new features of this version of WACCM and present comparisons with observations. WACCM6 extends from Earth’s surface to about 140 km and is therefore especially appropriate for investigations of interactions across the whole atmosphere.
In the configuration of CESM2 used here, chemistry, dynamics, and radiation are fully coupled within the atmosphere and are coupled with CESM’s Community Land Model. New developments that are included in WACCM6 include a self-generated quasi-biennial oscillation (QBO) and interactive aerosols in the troposphere and middle atmosphere. The model has resolution of 1.25° longitude × 0.9° latitude; vertical resolution is variable and is approximately 2–3 km in the middle atmosphere. The time step is 30 min.
This investigation uses archived output from three “history” or Atmospheric Model Intercomparison Project (AMIP) simulations that were completed as part of phase 6 of the Coupled Model Intercomparison Project (CMIP6). They extend from 1950 to 2014 (65 years each). In all three realizations, the sea surface temperatures and sea ice are specified from the seasonally and annually varying observational record. Other external forcing, such as the solar flux, injection of volcanic aerosols into the stratosphere, and the emissions of anthropogenic greenhouse gases, sulfate, and ozone depleting chemical are based on observations and are the same in all three simulations.
Slight differences in the initial conditions cause the simulations to diverge within the first few weeks, especially with regard to short-term variations (weather). The quasi-biennial oscillation (self-generated in these simulations) also has different phases in the three simulations. Longer-term variations, such as trends due to increasing greenhouse gases, are similar in the three realizations, as are forced perturbations due to volcanic eruptions.
Gettelman et al. (2019) show comparisons of WACCM6 variables with available observations. The simulated climatology of winds and temperature in the middle atmosphere and the simulated trends of temperature and ozone agree well with observations for the most part. Although not specifically addressed by Gettelman et al. (2019), the altitude and minimum temperature of the summer mesopause are well simulated in WACCM. WACCM6 has several discrepancies worth noting: the QBO does not extend to as low an altitude as observed, the semiannual oscillation in tropical mesospheric winds is poorly simulated, and the timing of sudden stratospheric warmings within the seasonal cycle is shifted compared with observations.
Daily average quantities for determining the Eliassen–Palm (EP) flux are used in the analysis. These do not enable the separation of the wave fluxes into the contributions from different wavenumbers or periods, and we are therefore not able to evaluate the WACCM6 climatology of short-period waves such as the 2- and 5-day waves.
With the output from these simulations, we have a total of 195 years to investigate dynamical interactions. Key dynamical fields have been zonally averaged and archived at daily and monthly time scales and give the opportunity to explore the characteristics of the interhemispheric coupling in WACCM6 and the processes that connect the far distant regions. WACCM6 does not have the capability of simulating PMCs so we cannot evaluate their responses; instead we focus on the temperature of the summer polar mesosphere.
In our analysis, model output from individual months have been combined together irrespective of the phase of the QBO. Since there is some earlier evidence from Espy et al. (2011) and Murphy et al. (2012) that the phase of the QBO could affect aspects of the summer mesosphere response, we also investigated the impact of the QBO phase on the responses. The QBO impact was found to be small and is not considered further in this study.
For correlation or other analysis, it is necessary to first remove any trends that could give spurious correlations. To determine the long-term trend of monthly mean output, time series are constructed for each calendar month using the average of the three realizations. Averaging over the realizations gives an estimate of the long-term change in the temperature that is similar to those for the individual realizations but smoother in time. Then a second-order polynomial is fit to the time series at each latitude and pressure; these fits are then removed from the individual monthly values. The fit is approximately linear since changes in greenhouse gases since 1950 are the leading source of the trend.
For analysis of daily output within a single year, the apparent trends are the result of the seasonal cycle. The seasonal cycle at each latitude and pressure is defined as the average over all years and all realizations for each calendar date. The seasonal cycle is then removed for each calendar year. Since our analysis of daily fields treats each year separately, it is not necessary to also remove a long-term trend based on multiyear time series.
Previous investigations of interhemispheric coupling have used various quantities to represent the dynamical perturbation in the winter stratosphere: temperature near the winter pole, zonal-mean zonal wind in the high latitudes, or a representation of wave processes (eddy heat flux, EP flux divergence, etc.). The available WACCM6 output includes all of these. These variables are related to one another since perturbations to EP flux, zonal wind speed, and polar cap temperature are closely linked in the winter stratosphere (Andrews et al. 1987). However, they are not interchangeable, as discussed in section 4. Looking more closely at the available observational studies, we find that the published analyses that focus on monthly mean, rather than short-term, relations between the winter stratosphere and summer mesosphere use the temperature in the winter polar stratosphere to represent variability. Following these examples, the perturbation from the detrended mean temperature averaged over the pressure range 10–1 hPa and latitudes greater than 60° in the winter stratosphere is used as an index of winter dynamical activity in the analysis of monthly mean output. In analysis of the time evolution using daily output, we use the EP flux divergence in the middle to high latitudes of the winter stratosphere as a direct measure of the wave driving. The impact of the different measures of stratospheric perturbations are discussed in section 4.
3. Coupling in WACCM6
Some previous studies of IHC have used monthly averages. The use of monthly averages implies that the time scale of the perturbation of interest is sufficiently long that it will influence the average over approximately 30 days. It also implies that the time needed for a signal to propagate from the winter pole to the global middle atmosphere is short compared to a month. Observations over many decades have shown that dynamical activity in the winter hemisphere has strong interannual variability that is associated with rapid changes on shorter time scales. Monthly averages will often reflect one or two large dynamical events that occur during the month such as major or minor sudden stratospheric warmings.
We begin with monthly mean fields as a way to combine a large amount of output in a concise way and to identify locations and periods showing an indication of the interhemispheric response that we are looking for.
a. Signals from binning monthly mean temperatures
To determine whether WACCM6 reproduces the monthly mean signal of IHC, we bin the monthly model results based on an indicator of dynamical activity in the winter stratosphere. For this binning, dynamical activity is defined using as an index the detrended temperature averaged over 60°–90° latitude and 10–1 hPa (area weighted in latitude but not mass weighted in pressure). Results are binned according to whether this temperature is above or below the multiyear average. Figure 1 shows how the detrended temperature in those bins differs from the multiyear-mean temperature for January and September. These two months were chosen because they show the highest variability in the winter stratosphere for the Northern and Southern Hemispheres, respectively. The differences in the right column indicate the temperature difference of the two panels to the left; that is, it gives the full range of the difference between years that are warmer and cooler in the winter stratosphere.
Differences in the monthly mean temperature from the long-term average over three realizations. The months are sorted by the perturbation temperature in the high-latitude winter stratosphere, specifically the region poleward of 60° and between 10 and 1 hPa [(left) warmer than average and (center) cooler than average]. (right) Differences of left and center columns. (top) NH winter in January and (bottom) SH winter in September. The contour interval is 2 K; the zero contour is not shown; and contours for +1 and −1 K are shown as dashed lines. The numbers in parentheses show the number of months contributing to the average.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Differences in the monthly mean temperature from the long-term average over three realizations. The months are sorted by the perturbation temperature in the high-latitude winter stratosphere, specifically the region poleward of 60° and between 10 and 1 hPa [(left) warmer than average and (center) cooler than average]. (right) Differences of left and center columns. (top) NH winter in January and (bottom) SH winter in September. The contour interval is 2 K; the zero contour is not shown; and contours for +1 and −1 K are shown as dashed lines. The numbers in parentheses show the number of months contributing to the average.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Differences in the monthly mean temperature from the long-term average over three realizations. The months are sorted by the perturbation temperature in the high-latitude winter stratosphere, specifically the region poleward of 60° and between 10 and 1 hPa [(left) warmer than average and (center) cooler than average]. (right) Differences of left and center columns. (top) NH winter in January and (bottom) SH winter in September. The contour interval is 2 K; the zero contour is not shown; and contours for +1 and −1 K are shown as dashed lines. The numbers in parentheses show the number of months contributing to the average.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Differences shown in the right column of Fig. 1 indicate that the temperatures in the winter mesosphere vary strongly out of phase with those in the winter stratosphere. This relationship has previously been reported many times from observational and modeling analysis; see the introduction for citations and discussion. There is an indication of a perturbation temperature signal curving up from the tropical middle mesosphere toward the summer polar mesosphere. In January, the magnitude is weak (~1 K) and the altitude of the positive perturbation at the summer pole (~0.003 hPa) is above the location of the summer mesopause and the altitudes of PMC. A similar weak extension of perturbation temperature to the high-latitude summer upper mesosphere is seen for other NH winter months November–February (not shown). In September (SH winter), differences due to perturbations in the winter stratosphere have a similar pattern to those seen for NH winter in January. Likewise, perturbation temperatures extending into the summer hemisphere have a similar shape to those during NH winter but the magnitude in the summer mesosphere is larger and the altitude of the perturbation is lower and extends farther poleward; at the summer pole the maximum difference is 2–3 K at 0.002 hPa. Similar binning for other months during SH winter indicates that this pattern is present during the period July–October.
Figure 2 shows scatterplots of the monthly mean perturbation temperature (difference from the long-term average over all realizations) in the polar summer mesosphere against that in the polar winter stratosphere averaged for each January and September. There is no obvious correlation in January, consistent with the negligible differences seen in Fig. 1 if one looks specifically at the summer mesosphere at the pressure range 0.01–0.001 hPa. A positive correlation can be clearly seen by eye for September. To compare other dynamical fields, we average the model results for the 20 years with warmest stratosphere (right of the red lines in the respective panels) and the 20 with coolest stratosphere (left of the blue lines). The averages and the differences between them are given in Fig. 3 for January. The top four rows are averages of zonal-mean quantities: zonal wind, temperature, transformed Eulerian-mean meridional wind, and transformed Eulerian-mean vertical wind. As expected, since we use stratospheric winter temperature as the criterion for separating the two sets, the differences are largest near the winter pole. A warm middle stratosphere is accompanied by a cool upper stratosphere and mesosphere, weaker zonal wind speed in the winter midlatitudes, and downward mean circulation. The differences in transformed Eulerian meridional wind in the mesosphere, however, extend into the summer hemisphere. The latitudinal extent of the meridional wind is similar to that seen in correlation patterns found by Tan et al. (2012), who analyzed an earlier version of WACCM. The differences in the forcing (m s−1 day−1) by EP flux divergence (∇ ⋅ F) from resolved waves and by parameterized gravity waves are strong in the winter middle and high latitudes but weak in the summer hemisphere.
Scatterplots showing the relationship between the monthly average temperature in the winter stratosphere [(top) 70°–80°N for January and (bottom) 70°–80°S for September] for the pressure range 10–1 hPa and the monthly average temperature in the summer mesosphere [(top) 70°–90°S for January and (bottom) 70°–90°N for September] for the pressure range 0.01–0.001 hPa. The blue and red lines delineate the 20 coldest and the 20 warmest months in the stratosphere. The dashed red lines are linear fits.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Scatterplots showing the relationship between the monthly average temperature in the winter stratosphere [(top) 70°–80°N for January and (bottom) 70°–80°S for September] for the pressure range 10–1 hPa and the monthly average temperature in the summer mesosphere [(top) 70°–90°S for January and (bottom) 70°–90°N for September] for the pressure range 0.01–0.001 hPa. The blue and red lines delineate the 20 coldest and the 20 warmest months in the stratosphere. The dashed red lines are linear fits.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Scatterplots showing the relationship between the monthly average temperature in the winter stratosphere [(top) 70°–80°N for January and (bottom) 70°–80°S for September] for the pressure range 10–1 hPa and the monthly average temperature in the summer mesosphere [(top) 70°–90°S for January and (bottom) 70°–90°N for September] for the pressure range 0.01–0.001 hPa. The blue and red lines delineate the 20 coldest and the 20 warmest months in the stratosphere. The dashed red lines are linear fits.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
The monthly average (top to bottom) zonal wind (contour interval: 10 m s−1), temperature (contour interval: 10 K), transformed Eulerian-mean meridional wind (contour interval: 1.5 m s−1), transformed Eulerian-mean vertical wind (contour interval: 0.5 cm s−1), wave forcing from resolved waves (contour interval: 6 m s−1 day−1), and gravity wave drag (contour interval: 10 m s−1 day−1) averaged for (left) the 20 warmest Januaries and (center) the 20 coolest Januaries. (right) Differences between the left and center columns, with contours at ±0.5 and ±0.25 times the interval indicated with dashed lines and zero contours not shown.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
The monthly average (top to bottom) zonal wind (contour interval: 10 m s−1), temperature (contour interval: 10 K), transformed Eulerian-mean meridional wind (contour interval: 1.5 m s−1), transformed Eulerian-mean vertical wind (contour interval: 0.5 cm s−1), wave forcing from resolved waves (contour interval: 6 m s−1 day−1), and gravity wave drag (contour interval: 10 m s−1 day−1) averaged for (left) the 20 warmest Januaries and (center) the 20 coolest Januaries. (right) Differences between the left and center columns, with contours at ±0.5 and ±0.25 times the interval indicated with dashed lines and zero contours not shown.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
The monthly average (top to bottom) zonal wind (contour interval: 10 m s−1), temperature (contour interval: 10 K), transformed Eulerian-mean meridional wind (contour interval: 1.5 m s−1), transformed Eulerian-mean vertical wind (contour interval: 0.5 cm s−1), wave forcing from resolved waves (contour interval: 6 m s−1 day−1), and gravity wave drag (contour interval: 10 m s−1 day−1) averaged for (left) the 20 warmest Januaries and (center) the 20 coolest Januaries. (right) Differences between the left and center columns, with contours at ±0.5 and ±0.25 times the interval indicated with dashed lines and zero contours not shown.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Figure 4 is similar to Fig. 3 but for the warmest and coolest stratospheres in the SH in September. Again, the variable that most clearly shows an extension into the summer hemisphere is the transformed Eulerian-mean meridional wind. Note that the September average still has characteristics of winter in the Southern Hemisphere (see, e.g., the strong westerly zonal wind) but is transitional in the Northern Hemisphere (weak westerly zonal winds at all levels; no evidence of a cold summer mesopause). Consistent with the transitional status, the wave forcing by both resolved and parameterized waves is weak in the northern latitudes (last two rows, left and center columns). Positive temperatures in the summer hemisphere extend from the tropical mesosphere to the north (summer to early fall) pole. The occurrence of higher than average summer mesopause temperatures coinciding with higher winter stratosphere temperatures is a signature of interhemispheric coupling, similar to that seen in other investigations.
As in Fig. 3, but for Septembers.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 3, but for Septembers.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 3, but for Septembers.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
The differences shown in Figs. 1–4, based on monthly mean output, confirm that WACCM6 simulates interannual differences in the summer middle atmosphere that are coincident in time with, and have a consistent phase relationship to, differences in the high-latitude winter stratosphere. The following subsection uses the daily model output to assess the actual correlations on short time scales.
b. Correlations of daily data
We focus on two periods: NH winter from 1 December to 28 February (DJF) and SH winter from 1 August to 31 October (ASO). These dates encompass the periods of highest wave activity, as measured by ∇ ⋅ F in the winter stratosphere of the respective hemisphere. Time series correlations between various sets of dynamical variables are calculated separately for the respective 90- or 92-day periods in each of the 195 years in the dataset and then the correlation coefficients are averaged. Before the analysis, output fields are averaged into bins of 10° latitude and about 6 km in the vertical. The time series for the index derived from stratospheric EP flux divergences covers the entire 90- or 92-day period. To account for positive and negative lags, the time series for global temperature and other variables extend to earlier and later times.
Figure 5 shows the correlation coefficients of daily zonal average temperature with the EP flux divergence averaged over the latitude band 60°–70°N and the pressures 3–0.3 hPa for DJF. Note that EP flux divergence is more strongly negative for perturbed conditions so the pattern has the opposite sign of that in Figs. 1, 3, and 4. The lags on the individual figure panels indicate the number of days by which the EP flux divergence in the winter stratosphere leads temperature at the respective point in pressure and latitude. The figure shows that the correlation coefficients are small (absolute value less than 0.1) for negative lags before −2 days. The highest correlations are seen in the winter polar mesosphere for positive lags of 2–4 days. The patterns in the northern high latitudes (negative correlation below; positive correlation above) are matched by pronounced correlations of the opposite sign extending from midlatitudes of the winter into the summer hemispheres. Figure 6 gives a similar plot for ASO correlating ∇ ⋅ F averaged over the latitude band 60°–70°S and the pressures 3–0.3 hPa with the global temperatures.
Correlation of daily temperature for DJF with the EP flux divergence averaged over 60°–70°N and 3–0.3 hPa. Each panel shows correlation for a different lag in increments of 1 day. Contour interval is 0.05; the zero contour is not shown.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Correlation of daily temperature for DJF with the EP flux divergence averaged over 60°–70°N and 3–0.3 hPa. Each panel shows correlation for a different lag in increments of 1 day. Contour interval is 0.05; the zero contour is not shown.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Correlation of daily temperature for DJF with the EP flux divergence averaged over 60°–70°N and 3–0.3 hPa. Each panel shows correlation for a different lag in increments of 1 day. Contour interval is 0.05; the zero contour is not shown.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 5, but for correlation with the EP flux divergence averaged over 60°–70°S and 3–0.3 hPa during ASO.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 5, but for correlation with the EP flux divergence averaged over 60°–70°S and 3–0.3 hPa during ASO.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 5, but for correlation with the EP flux divergence averaged over 60°–70°S and 3–0.3 hPa during ASO.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
The pattern seen in Figs. 5 and 6 indicates that wave forcing by resolved waves (negative ∇ ⋅ F) in the winter high latitude is followed closely by temperature perturbations extending across the equator to about 60° or more in the summer hemisphere. This pattern has been seen in other investigations using satellite data (Xu et al. 2009; Tan et al. 2012) or global models (Tan et al. 2012; Limpasuvan et al. 2016).
The correlation patterns in Figs. 5 and 6 have four-lobed structures: values are negative in the winter stratosphere and in the tropical and summer mesosphere. The opposite correlation appears for the winter mesosphere and the tropical and summer stratosphere. Changeover pressure in this four-lobed pattern is at about 1 hPa or a little above that level (~48–50 km) at high winter latitudes but then tilts toward higher altitude in the summer hemisphere. The latitude of the transition in NH winter (Fig. 5) is at 50° in the winter stratosphere while the transition in the SH winter stratosphere is around 40°. The higher latitude of the transition in northern winter reflects the more poleward location of peak planetary wave dissipation and the weaker vortex than seen in southern winter. In northern winter, the latitude of the transition then shifts toward the tropics in the mesosphere; a similar shift is only weakly apparent in southern winter. The transition from negative to positive correlation in the winter middle and high latitudes is consistent with observation (e.g., Manney et al. 2005) and modeling studies (e.g., Limpasuvan et al. 2016) of the NH winter that show that dynamical activity in the winter leads to perturbations in the mesosphere that are opposite to those in the stratosphere. For example, sudden stratospheric warmings are accompanied by cooling in the high-latitude mesosphere. These same events lead to oppositely signed temperature perturbations at lower winter latitudes as the vertical component of the residual mean circulation has opposite sign. What is seen in Figs. 5 and 6 but has not been commonly noted is the extension of this lower-latitude winter response deep into the summer hemisphere.
4. Mechanisms
In this section, we first discuss the short-term global responses with respect to two (not mutually exclusive) possible mechanisms for the mesospheric component of the summer response to winter perturbations. Next, we discuss the relation between the monthly mean responses and the short-term responses based on daily model output.
a. Comparisons of model response to mechanistic models
The perturbations to the zonal-mean state of the stratosphere and/or mesosphere could affect wave driving of the mesosphere. This could occur by several processes: the waves that are able to propagate to the mesosphere may be affected by perturbed winds or temperatures in the stratosphere, the breaking and/or dissipation of waves within the mesosphere may vary because of perturbations to the background conditions, or the generation of waves by unstable flow configurations might vary if the background conditions vary. By any of these wave mechanisms, dissipation associated with these waves could then directly affect the driving of zonal-mean perturbations in the summer mesosphere. An alternative mechanism is that the mesospheric circulation could, like that in the stratosphere, be a zonal-mean response to mass imbalance associated with strong impulsive upwelling and downwelling events in the midlatitude winter.
Since we use output from existing simulations, we cannot control the wave processes in the model for mechanistic simulations. However, with the extensive detailed output available, we can examine the day-by-day responses of the global middle atmosphere to dynamical perturbations.
Figures 7 and 8 show global correlations of several fields with the EP flux divergence (∇ ⋅ F) in the winter stratosphere for the northern and southern winters, respectively. Results are shown for lags of −3, 0, +3 and +6 days. The left columns repeat temperature correlation results from Figs. 5 and 6 for comparison with the lag correlations of υ*, ∇ ⋅ F, and gravity wave drag. At zero and subsequent lags (second row), the correlation of υ* in the upper stratosphere extends well into the summer hemisphere. The correlations with variability of the resolved and parameterized wave activity in the summer hemisphere are negligible at zero lag. Weak correlations with wave forcing in the summer occur after several days. This analysis indicates that the υ* response occurs before there are any correlated changes in the wave activity in the summer hemisphere.
Lag correlations between the daily EP flux divergence in the winter stratosphere and several dynamical variables for DJF. The rows give different lag times and the columns show (left to right) the temperature, the transformed Eulerian-mean meridional wind, the wave forcing from resolved waves, and gravity wave drag. The contour interval is irregular, as indicated on the color bar.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Lag correlations between the daily EP flux divergence in the winter stratosphere and several dynamical variables for DJF. The rows give different lag times and the columns show (left to right) the temperature, the transformed Eulerian-mean meridional wind, the wave forcing from resolved waves, and gravity wave drag. The contour interval is irregular, as indicated on the color bar.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Lag correlations between the daily EP flux divergence in the winter stratosphere and several dynamical variables for DJF. The rows give different lag times and the columns show (left to right) the temperature, the transformed Eulerian-mean meridional wind, the wave forcing from resolved waves, and gravity wave drag. The contour interval is irregular, as indicated on the color bar.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 7, but forASO.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 7, but forASO.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
As in Fig. 7, but forASO.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
We can quantify the strength of the correlation patterns in the summer hemisphere using a quantitative assessment of the spatial features of the correlation fields. The method is described in the appendix. In essence, this analysis uses spatial statistics in a latitude × pressure domain as a way to draw conclusions about the size and nature of the observed correlations. The analysis determines a variable called the sill; a higher value of the sill indicates a stronger spatial signal. Figure 9 shows the results for the summer hemispheres for the variables included in Figs. 7 and 8 over a wide range of lag times. The analysis includes the summer hemisphere for the pressure range 100–0.003 hPa. The values for global temperature (including both summer and winter hemispheres) are also shown as dashed lines. The sequence in the response shows up clearly. The meridional and vertical residual winds peak simultaneously with the EP flux divergence in the opposite (winter) hemisphere, that is, at lag 0. The temperature signal in the summer hemisphere peaks several days later (lag 3–4 days) and persists for another 30 days. The magnitudes of the wave patterns are near zero at lags of zero or negative and then show small values. The EP flux divergence from resolved waves is maximum at lag of about two days. The gravity wave drag is somewhat different in the two hemispheres but for both shows a broader response over lag times extending from 1 to about 15 days. The hemispheric differences in the gravity wave drag response may be due to the differences in background wind conditions: during January there is a strong westerly jet in the Southern Hemisphere while during September the Northern Hemisphere winds are weak.
Estimated sill parameters for spatial correlation fields of temperature (T), meridional (υ*) and vertical (w*) residual velocity, resolved wave EP flux divergence (delF), and gravity wave drag (GWD) over the summer hemisphere with the EP flux divergence in the winter polar stratosphere as a function of lag for (top) DJF and (bottom) ASO. The dashed lines show the spatial correlations of global temperature. See text for details.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Estimated sill parameters for spatial correlation fields of temperature (T), meridional (υ*) and vertical (w*) residual velocity, resolved wave EP flux divergence (delF), and gravity wave drag (GWD) over the summer hemisphere with the EP flux divergence in the winter polar stratosphere as a function of lag for (top) DJF and (bottom) ASO. The dashed lines show the spatial correlations of global temperature. See text for details.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
Estimated sill parameters for spatial correlation fields of temperature (T), meridional (υ*) and vertical (w*) residual velocity, resolved wave EP flux divergence (delF), and gravity wave drag (GWD) over the summer hemisphere with the EP flux divergence in the winter polar stratosphere as a function of lag for (top) DJF and (bottom) ASO. The dashed lines show the spatial correlations of global temperature. See text for details.
Citation: Journal of the Atmospheric Sciences 77, 3; 10.1175/JAS-D-19-0253.1
A mechanism proposed by Karlsson et al. (2009a) is a potential pathway by which variations in the winter stratosphere will affect the summer mesopause region. This mechanism, which was demonstrated in steady-state simulations with a two-dimensional model of the middle atmosphere by Körnich and Becker (2010), has the following steps:
EP flux divergence from planetary waves causes large perturbations to the circulation, temperature and zonal wind of the winter stratosphere.
Filtering by the perturbed zonal wind affects propagation of planetary and gravity waves and, when the waves dissipate, leads to perturbations of the opposite sign in the winter middle mesosphere.
Mass balance gives residual circulation cells extending to low latitudes.
The resulting temperature perturbations near the equator affect the equator-to-pole temperature gradient in the summer hemisphere.
Through the thermal wind relation, the zonal wind in the summer midlatitude mesosphere is perturbed in response to the equatorial temperature. This affects gravity wave breaking and dissipation in the summer midlatitudes.
Perturbation to the gravity wave drag in the midlatitudes shift the altitude profile of the normal gravity wave forcing of upwelling seen in the summer mesosphere. This in turn modifies the upwelling and temperature near the pole.
Comparison of the Karlsson et al. (2009a) mechanism with the processes occurring in WACCM6 indicates qualitative differences. The mechanisms diverge at their step 3: the mass balance flow in response to winter wave events in WACCM6, as in many observations, is not confined to the winter hemisphere but extends across the equator to middle and high latitudes of the summer hemisphere. Gravity wave perturbations are clearly associated with the coupling between the stratosphere and mesosphere in the winter midlatitudes (see the right columns in Figs. 7 and 8). However, the WACCM6 correlation analyses do not indicate that there is a role for gravity waves in extending the response to the summer hemisphere. The primary discrepancy may stem from an underestimate by Karlsson et al. (2009a) and Körnich and Becker (2010) of the strength and latitudinal extent of the mass balance circulation; their underestimate may in part be due to their assumption that perturbations to the winter stratosphere can be represented as steady state.
Another possible mechanism to carry a perturbation signal across wide range of latitudes is the generation of unstable waves in response to changes in the zonal-mean winds and temperature (France et al. 2018). Planetary-scale wave activity in the mesosphere during the summer solstice and fall equinox seasons is dominated by traveling waves that are generated by instabilities of the zonal-mean background atmosphere; these include the quasi-2-day wave (Q2DW) (e.g., McCormack et al. 2014; France et al. 2018), the 5-day wave, and the 6.5-day wave (Lieberman et al. 2003). A potential mechanism by which these waves could contribute to interhemispheric coupling is this: perturbations to the winds and temperatures in the tropical region occur through the circulation driven by the dynamical perturbations in the winter stratosphere and mesosphere, as described in the mechanism of Körnich and Becker (2010). Changes in the zonal winds affect the location and intensity of the unstable conditions that contribute to the generation of waves. These waves contribute to momentum transport and perturbations in the mesosphere near solstices (Lieberman 1999; Lieberman et al. 2003) and could therefore impact the summer polar temperature (Pendlebury 2012; Siskind and McCormack 2014). France et al. (2018) showed observations from the SH winter of 2014 indicating that strong magnification of the 2-day wave affected PMCs in the summer high latitudes during that year. They linked the wave amplification to changes in the zonally averaged zonal wind in the summer mesosphere that was associated with dynamical activity in the winter hemisphere.
Figures 7–9 show that, when averaged over many years, the planetary wave response in the summer mesosphere in WACCM6, like that of the gravity wave drag response, is weak and is delayed compared to the response of υ* and w*. If variations in the presence of the Q2DW, 5-day wave, or 6.5-day wave in the summer mesosphere were instrumental in transferring the perturbation signal from the equator to summer midlatitudes and/or from midlatitudes to the summer pole on a day-by-day basis, then there should be a correlation between ∇ ⋅ F in the winter stratosphere and that in the summer mesosphere. The lack of such a correlation argues against an important role for these planetary waves in interhemispheric coupling. Note that the available WACCM6 output for the simulations allows us to determine only the daily mean ∇ ⋅ F. While this includes any wave forcing from waves generated by instability, it also includes divergence from any other resolved waves that are present.
A number of investigators have used simple models to explore the global response to a body force, such as that due to the EP flux divergence in the winter middle atmosphere. Dickinson (1968) showed that the response depends on the presence of damping, such as diabatic processes (represented in his model by Newtonian cooling). Garcia (1987) used a two-dimensional model to show that the response to a middle atmosphere perturbation depends on the time scale of the perturbation. Haynes et al. (1991) mostly limit their simulation to one hemisphere but also emphasize that the response is confined to the vicinity of the forcing only when the time scale is long enough to be represented as steady state. Dunkerton (1989) and Tung and Kinnersley (2001) discuss in detail the roles played by nonconservative processes (diabatic heating and friction) originally introduced by Dickinson (1968). Plumb and Eluszkiewicz (1999) show that, in steady-state conditions, damping is involved in the shift of the location of wave-driven upwelling from the winter hemisphere to the equatorial region. A consistent feature of these models is that the induced circulation appears at and below the altitude of the imposed forcing.
Tung and Kinnersley (2001) showed that the circulation response in the opposite hemisphere is stronger for winter wave forcing that is in the upper rather than lower stratosphere and whose spatial extent stretches farther into the subtropics. Plumb and Eluszkiewicz (1999) also note the importance of the latitude of the wave forcing that drives the circulation. The larger response seen in WACCM6 for the southern winter case (cf. Figs. 3 and 4) may be a result of the climatological location of maximum wave driving, which is at higher altitude and farther from the pole than that in the NH. Garcia (1987) also showed that the circulation response for an episodic EP flux in the winter stratosphere with a time scale of 15 days extends farther into the opposite hemisphere than does that for a steady-state EP flux. In a mechanistic model that also included interactive parameterized gravity waves, Becker and Fritts (2006) found that the cross-equator circulation response to perturbations in the winter preceded the response of waves in the summer hemisphere.
While WACCM6 is much more complex than the mechanistic models described here, both types of model should capture the key physical situation of a broad latitudinal response to strong impulsive forcing. WACCM6 includes various processes that can dissipate zonal-mean angular momentum, such as diabatic heating and cooling, wave–mean flow interactions from resolved and parameterized waves, and numerical diffusion. In that sense, the model dynamical processes conform with the conclusions of Dickinson (1968) and Plumb and Eluszkiewicz (1999), and other model studies that dissipative processes are necessary for a far reaching cross-equatorial response to a localized body force. Based on the rapid response of the meridional circulation to perturbations in the winter middle atmosphere, together with the weak response of waves everywhere except the midlatitude winter, the conclusion that the climatological interhemispheric coupling in WACCM6 is driven by a mean circulation response is the one that fits best with our analysis.
b. Time scales of stratospheric perturbations
This study shows that WACCM6 simulates interhemispheric coupling signals on both short time scales (lagging the winter wave forcing by a few days) and in the monthly mean. In this section we give arguments supporting our interpretation that the rapid but short-lived global circulation response found on time scales of less than a week is also responsible for the temperature correlations seen in the monthly mean analyses (Fig. 1). As noted in section 2, we follow the lead of previous studies and use temperature in the high-latitude winter stratosphere as the index for winter stratospheric variability in our analysis of monthly mean data. Analyses of the short-term responses use the EP flux divergence in the winter stratosphere.
It is readily seen from Fig. 9 that the temperature perturbations in the summer hemisphere and globally (both hemispheres) persist for weeks following perturbations in EP flux divergence. Figures 7 and 8 also show that the temperature perturbations in the winter stratosphere persist for longer than do the perturbations in EP flux divergence. The latter are relatively short lived, as seen by the rapid disappearance of the correlations over lag periods of less than a week.
All of the temperature curves on Fig. 9 indicate that the spatial correlation signal has not decayed completely even after 30 days. This indicates that the types of wave events that lead to a global circulation and temperature response are associated with global temperature perturbations that persist for tens of days. The extended nature of these perturbations means that they will appear in monthly averages, indicating that the correlations found in monthly mean data have the same cause as those on shorter time scales. In both cases, the circulation response to wave forcing in the winter is responsible for a perturbation in temperature and these temperature perturbations persist even after the wave forcing perturbations decay. Note that the monthly averaged results presented in Figs. 1–5 use temperature in the winter polar region to separate monthly periods into warm and cool categories.
The long duration of the temperature response to wave forcing can be explained by the time scale needed for the temperature perturbation to relax back toward climatology. The time scale for the change in middle atmosphere temperature due to infrared radiative processes (cooling due primarily to CO2), as calculated by Newman and Rosenfield (1997) and Mlynczak et al. (1999), reaches a minimum of about 6–7 days in the vicinity of the stratopause. The time scale quantifies the rate that diabatic processes damp perturbations in temperature.
We can calculate the time scale for the decay of the temperature perturbation represented in Fig. 9 by fitting an exponential form to the decay in the signal with increasing lag. For a time series beginning at a lag of 4 days, the decay times are 9.6 days for the values in the summer hemisphere of both seasons (the solid black curves on both panels of Fig. 9) and 8.5 and 7.4 days, respectively, for global values during NH winter and SH winter (dashed curves). These time scales are within the range of thermal decay times for the middle and upper portions of the middle atmosphere. The consistency between the radiative cooling rate and the time scale for the global temperature response to a wave forcing pulse in the winter hemisphere would be expected if radiative forcing is involved in the return from perturbed conditions to climatology.
5. Conclusions
We investigate the simulation of interhemispheric coupling that links the winter stratosphere with the summer middle atmosphere using WACCM6. We find clear evidence that winter perturbations extend to about 50°–60° into the summer stratosphere and can extend somewhat farther toward the summer pole in the mesosphere. There is no evidence that feedback between wind perturbations in the summer hemisphere and wave drag is making a significant contribution to the correlation on time scales of a few weeks or less. Instead, the results are consistent with the interpretation that the summer response is due to circulation induced to restore zonal-mean balance to the atmosphere. The patterns that we identify are strong and spatially broad; the interpretation is not sensitive to which particular latitude band or pressure level is viewed.
In this analysis, we use wintertime data from a span of 3 months without regard for the magnitude of wave forcing events. While major perturbations such as sudden stratospheric warmings are included, the majority of variations have smaller amplitude. Lag correlation plots indicate that the EP flux divergence does not remain coherent beyond 5 days (Figs. 7 and 8) but the temperature perturbation that follows it persists for much longer in both the winter and summer hemispheres. Observational analyses have primarily used temperature perturbations in the high-latitude winter stratosphere as an indication of dynamical events. Our analysis suggests that the persistence of the temperature in both hemispheres is a factor in the detection of the coupling signal over time scales of weeks or a month.
A balance explanation would suggest that a strong wave-driven pattern of upwelling and downwelling in the winter middle and high latitudes gives rise to global downwelling and upwelling to maintain mass balance (Garcia 1987; Tung and Kinnersley 2001). This argument has been discounted on theoretical grounds that it is inconsistent with the dynamics described by the downward control principle presented by Haynes et al. (1991). However, the downward control argument should not constrain the IHC discussion since steady-state arguments do not apply for the short-time-scale perturbations found in this analysis. The mass balance circulation extending into the summer hemisphere is known for the stratosphere, where it has a measurable impact on the variability of lower-stratospheric ozone (Randel 1993).
The IHC signal in WACCM6 is weak at the summer pole during January (Figs. 1 and 3) and other months during NH winter (not shown) and the location of the temperature response at the summer pole is well above the altitude where PMC are observed. This is an apparent discrepancy with the pole-to-pole coupling outlined in other investigations. However, a closer look at the published observational studies indicates that this may not indicate an actual discrepancy. To consider this, refer to Figs. 1 and 5, which indicate that there is actually a response at middle to high latitudes even though the response exactly at the South Pole is small and is not at the altitude where PMCs form. A close look at the observations indicates that they, also, are not always taken at the very highest latitudes. In the SH summer, observations finding an IHC signal have used latitudes equatorward of 53°S (Tan et al. 2012) and at 68°S (Murphy et al. 2012) or were averaged over latitude bands 50°–83°S (Karlsson et al. 2007), poleward of 70°S (Karlsson et al. 2009b), and 60°–85°S (Xu et al. 2009). NH summer observations were at 59° or 57°N (Espy et al. 2011), were averaged over the latitude bands 65°–70°N and 50°–58°N (both analyzed by Siskind et al. 2011), or were for the latitude band 70°–80°N (France et al. 2018). Even the observations described by Goldberg et al. (2004), which triggered the recent interest in interhemispheric coupling and its impact on the summer mesosphere, were from 69°N. The absence of a response at PMC altitudes at the summer pole in WACCM6 is thus not inconsistent with the observations.
A survey of observational studies of interhemispheric coupling indicate that the results are often presented in the form of correlations between some variable in the winter stratosphere and the same or another variable in the global atmosphere. Correlation analysis is a powerful technique, but it must be borne in mind that it can indicate strong correlation coefficients even if the variations themselves have only weak amplitude. The temperature amplitudes in the summer hemisphere are indeed weak in these simulations (only 1–3 K on average, but reaching 5 K for the largest events; see Fig. 2); this may also be true in some of the other studies cited. Even though temperature is one of the best observed quantities in the middle atmosphere, variations of only a few kelvins are difficult to verify. As a result, the weak temperature perturbations may be hard to observe although the relatively long persistence time of temperature perturbations can help in detecting a signal. However, interhemispheric coupling affecting observations of ozone perturbations in the summer stratosphere, which are very sensitive to small variations in temperature and/or vertical transport, have been detected (Randel 1993). Likewise, variation in PMC presence or characteristics, which are highly sensitive to temperature and humidity and therefore to the upwelling velocity, may give a more reliable signal of a weak dynamical perturbation in the summer upper mesosphere (e.g., Karlsson et al. 2009b; France et al. 2018).
Acknowledgments
The CESM project is supported primarily by the National Science Foundation. This material is based upon work supported by the National Center for Atmospheric Research, which is a major facility sponsored by the National Science Foundation under Cooperative Agreement 1852977. Computing and data storage resources, including the Cheyenne supercomputer (https://doi.org/10.5065/D6RX99HX), were provided by the Computational and Information Systems Laboratory (CISL) at NCAR. The simulation output used in this investigation is archived in the CMIP6 repository (https://esgf-node.llnl.gov/projects/cmip6/). AKS and NMP acknowledge support from NSF Grant 1552153 through Coupling, Energetics, and Dynamics of Atmospheric Regions (CEDAR). The authors thank Astrid Maute and Rolando Garcia for helpful discussions and comments on the manuscript.
APPENDIX
Quantitative Diagnostic of Spatial Correlations
This appendix describes the mathematical method used to derive values that captures the degree of correlation between two fields as a function of lag. This is applied to the correlation coefficients in Figs. 7 and 8 but extending the range of lag times beyond those shown in the figures. The resulting spatial correlation values are shown in Fig. 9.
The method we adopt to measure the aggregated correlation in the opposite hemisphere is to model the observed spatial correlations as an isotropic, stationary Gaussian process. The parameters of the covariance function used for the process provide a numerical summary to compare one correlated field to another and ascertain which field represents a stronger signal.
Var[ε(s)] = τ2 is classically referred to as the nugget effect, and σ2 the sill, where the sill corresponds to the variance of the field attributed to spatial patterns (Cressie 2015). Further reading on the role of the sill and other spatial parameters of the Gaussian process model can be found in section 3.2 of Cressie (2015); section 2.6 of the same work gives a discussion of alternative methods of parameter estimation. In short, comparing the sills between spatial fields provides a measure for the strongest correlations observed in each field when accounting for some amount of measurement error or noise τ2.
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