In this paragraph, we will present the effects of the GW hotspots, both single ones and in combination, on the development and propagation conditions of atmospheric waves. Therefore, we only capture the impact of the artificial GW forcing on the SPW activity but neglect the feedback mechanisms of the SPW changes on the GWD because those are small in comparison to the artificial GWD enhancement. We will concentrate on the SPWs in a specific altitude directly located above the artificial GW forcings by showing the SPWs amplitudes and Plumb fluxes. To see what is happening in the whole middle atmosphere we are mainly concentrating on the amplitudes and Eliassen–Palm (EP) fluxes of the SPW with wavenumber 1 (SPW 1), which is mainly affected by the GW hotspots.
4.1. Impact on the Atmospheric Wave Activity in the Region of the GW Hotspots
To get an overview of the included atmospheric waves during the different experiments, we performed a wavenumber-frequency analysis of the zonal wind of each experiment. This provides atmospheric waves with periods of 0 h, which are the SPWs with wavenumbers from 1–3 and additional atmospheric waves with periods of 12 h (wavenumber 2) and 24 h (wavenumber 1). The latter are the migrating diurnal (24 h) and semidiurnal (12 h) tides. Because we are mainly focusing on the stratospheric effects, the tidal amplitudes, which are maximizing in the thermosphere, are neglected in our analysis. This is justified because their amplitudes are small in the stratosphere. This shows that the GW hotspots do not create different PWs than SPWs, which is an effect of the constant GW forcing not varying in time. This may be different when using an intermittent GW forcing. To present the latitudinal variability of the SPW amplitudes,
Figure 5h shows latitude-wavenumber cross-sections of the SPW 1–3 zonal wind amplitudes in the Ref simulation for an altitude of 38 km, which is above the artificial GW forcing. The SPW 1 amplitude, which is ranging between 2.7 ms
and 21.2 ms
shows the largest amplitudes at lower to middle latitudes (30° N–50° N) and at higher latitudes (northward of 80° N). In between the amplitudes minimize at the border of the polar vortex, where the west wind is strongest. Compared to the SPW 1 amplitudes, the SPW 2 and particularly SPW 3 amplitudes are smaller having values between 1.6 ms
and 13.7 ms
. The latitudinal distribution of the maximum SPW 2 amplitudes is similar to the SPW 1 one, and they maximize between 40 and 50° N as well as around 75° N. SPW 3 amplitudes vary between 0 and 5.4 ms
and maximize at lower latitudes.
Panels (a–g) of
Figure 5 show zonal wind amplitude differences between each GW hotspot experiment and the Ref simulation. In all cases, around 60° N the SPW 1 amplitude is mainly increasing in connection with a local GW forcing. The positive anomalies range between 0.9 ms
HI GW hotspot—
Figure 5c and 6.6 ms
RM GW hotspot—
Figure 5a. This represents an increase of more than 20 up to 150% compared to the Ref SPW 1 amplitude in this region. For most of the experiments except for the RM (
Figure 5a) and EA simulation (
Figure 5b) there is only one, partly very narrow, latitudinal range, where the SPW 1 amplitude is increasing. This already leads us to the first hypothesis that especially the interference of the GW hotspots as well as the HI GW hotspot may decrease the SPW 1 activity at midlatitudes, especially around 40° N.
In the RM GW hotspot simulation (
Figure 5a) we observe an increase of the SPW 1 amplitude at the southern and northern flank of the GW hotspot as well as in the polar region. The same can be observed for the EA GW hotspot (
Figure 5b), when neglecting the increase at its southern flank. This indicates that the intensified SPW 1 activity leads to larger energy and momentum transfer induced by breaking SPWs 1 for these two experiments. This may cause a deceleration of the zonal mean flow, which is strongest for the RM and EA simulations. In the region between 30° N–50° N, where we observed a maximum SPW 1 amplitude for the Ref simulation, the SPW 1 amplitude anomalies are strongly negative for all simulations.
This negative anomaly is strongest for the RM + HI + EA simulation (
Figure 5g) with a decrease of −18.6 ms
. This shows that the propagation conditions significantly change owing to the combination of GW hotspots.
With respect to the SPW 2 amplitude, we mainly observe an increase of the SPW 2 activity at lower latitudes, where the SPW 1 activity is reduced. This is more pronounced for the EA GW hotspot in
Figure 5b with SPW 2 maximum amplitude anomalies of 1.7 ms
, and less pronounced for the RM in
Figure 5a and HI GW hotspots in
Figure 5c. While all three single GW hotspot simulations show the increase at lower latitudes, not all of the simulations including the interference of two GW hotspots correspond to these results. The combination of the RM and HI GW hotspots (HI + RM,
Figure 5e) does not lead to larger SPW 2 amplitudes. Also, when the EA GW hotspot is added to these two GW hotspots (HI + EA + RM,
Figure 5g the SPW 2 amplitude anomalies do not change at lower latitudes.
The SPW 3 amplitude anomalies are mainly negative for the RM and EA hotspots, but positive for the HI hotspot. For the RM and EA GW hotspot the SPW 3 activity is nearly completely dampened, while for the HI GW hotspot the SPW 3 amplitude has partly doubled. The interference of two GW hotspots partly lead to an increase of the SPW 3 amplitude, which is strongest for the HI + EA hotspot combination shown in
Figure 5f. But the EA GW hotspot dampens the constructive effect of the HI GW hotspot on the SPW 3 activity, especially near the borders of the EA GW hotspot (blue lines). Thus, the SPW 3 amplitude anomalies are smaller compared to those caused by the single HI GW hotspot. These two GW hotspots in combination with the third RM GW hotspot cause again a weaker increase in some regions.
To investigate the wave behavior in detail,
Figure 6 shows the three-dimensional wave activity flux (Plumb flux, [
58]) at 38 km. It includes the wave activity flux of all SPWs. In
Figure 6 the direction and the strength of the horizontal wave activity flux is illustrated by the colored arrows, while the vertical component is given by the edge color of the arrows. Blue (red) color indicates downward (upward) propagation. From the horizontal wave activity we observe one large area of strong wave activity, located above East Asia, Alaska and Canada, from where the horizontal wave activity flux is directed towards the tropical region. In the region of the maximized horizontal wave activity flux there is also an upward directed wave activity flux around 50° N. Above the Atlantic and Europe the wave activity flux is less pronounced. SPW 1 is the dominating wave in our experiments, therefore, the Plumb flux is mainly determined by SPW 1, and the Plumb flux characteristics correspond to the properties of the SPW 1 EP flux reported by Samtleben et al. [
16]. They analysed the same reference simulation and have shown that the SPW 1 is mainly propagating via the midlatitudes towards the tropical stratosphere.
Figure 7 shows the Plumb flux differences between each experiment including single and combined GW hotspots and the Ref simulation.
Blue (red) edged arrows indicate negative (positive) Plumb flux differences of the vertical component. In general, the horizontal wave activity flux is strongly decreasing above North America and the West Pacific region, which means that the single as well as the combined GW hotspots are acting as a block preventing wave propagation, i.e., energy transport. In this region the anomalies of the vertical component are also negative around 50° N. For the RM run in
Figure 7a the apparent absence of the enhanced Plumb flux above North America is partly compensated by an increase above Eurasia, which, however, is mainly limited to higher latitudes. The vertical component of the wave activity flux over the Eurasian region around 60° N turns positive as well. Compared to the RM GW hotspot, the EA GW hotspot is not directly located in the region of maximum wave activity flux (in the Ref simulation) but on the left-hand side. This GW hotspot also reduces the wave activity flux above North America but not as strong as the RM GW hotspot does (
Figure 7b). Also the increase of the horizontal wave activity flux over Eurasia is visible, but it is weak and is not connected with an increase in the vertical component.
While the HI GW hotspot Figure in
Figure 7c is not located near the maximum wave activity flux above North America in the Ref simulation, the wave activity is strongly decreasing. Especially, the horizontal wave activity density is strongly decreasing above East Asia as well as the vertical component around 40° N (less positive) and 50° N (less negative). Thus, the vertical transport of energy nearly vanishes and the wave activity has significantly weakened (see also
Figure 5c). This GW hotspot also shows more often an SPW amplitude decrease (
Figure 5) than the other two GW hotspots.
The RM + EA hotspot combination presented in
Figure 7d leads to a strong Plumb flux decrease, which is even larger than for the single RM and EA GW hotspots. The horizontal wave activity flux anomalies are not only negative above North America but also in the West Pacific region, which is not the case in any of the single GW hotspot simulations. The positive horizontal wave activity flux anomalies above Eurasia are now more located above Scandinavia and are less (more) pronounced than in the RM (EA) single GW hotspot simulation. In this region there is also an increase in the vertical component of the wave activity flux, in contrast to any other simulations. Panels (e–g) show the HI + RM, HI + EA, and HI + EA + RM hotspot combinations. They all show similar patterns with a wave activity flux decrease above North America and East Asia, while the anomalies are strongest for HI + EA + RM.
To briefly summarize, the combined GW hotspots mainly lead to a decrease of the wave activity in connection with decreasing (i) amplitudes, especially at midlatitudes and (ii) fluxes above East Asia and North America, which means that the flux towards lower latitudes as well as the upward transport of energy is strongly dampened. This effect is partly compensated by the single RM and EA GW hotspot as well both GW hotspots in combination leading to an enhanced Plumb flux above Eurasia. Thus, the impact of the atmospheric waves, SPWs 1–3, is reduced and partly blocked by the respective GW hotspots and their interactions. As for the constructive and destructive interference at lower and higher latitudes this effect is caused by the meridional tilt of the SPW phases induced by the additional GWD forcing and the climatological eddies.
4.2. Impact on the SPW 1 Activity in the Middle Atmosphere
Because the SPW 1 shows the strongest amplitudes, we analyse here zonal wind SPW 1 amplitudes and the differences between each experiment and the Ref simulation as well as EP flux and EP flux divergence differences. Samtleben et al. [
17] already analysed the SPW 1 anomalies induced by localized GW hotspots in detail. Owing to the broad consistency of some single GW hotspots to our experiments we briefly summarize the effects of the single RM, EA and HI GW hotspots. The contour lines in
Figure 8 represent the SPW 1 amplitude distribution of the RM, EA, and HI experiment, resp., while the color shading illustrates the differences with the Ref simulation. For the RM hotspot in
Figure 8a the SPW 1 anomalies are changing between positive and negative values, which are arranged in bands slightly tilted towards the polar region with increasing height. These results correspond to those in
Figure 5a at 38 km.
As already reported by Samtleben et al. [
16], the EA hotspot
Figure 8b leads to a decrease of the SPW 1 amplitude at lower latitudes southward of 40° N and around 70° N. The positive SPW 1 amplitude anomalies of about 8 ms
see also
Figure 5b are restricted in altitude and only occur around 30 km at 60 and 80° N.
This positive anomaly may be induced by horizontally propagating SPWs 1 seen in the Plumb flux in
Figure 7b. Overall the EA GW hotspot mainly leads to a SPW1 amplitude decrease [
16]. The HI GW hotspot in
Figure 8c shows strongly negative SPW 1 amplitude anomalies in the middle atmosphere turning positive only above 70 km and partly below 30 km. Consequently the SPW 1 amplitudes are very small and vary mostly between 0 and 5 ms
, only in few altitude ranges the SPW 1 amplitude exceeding 10 ms
. According to Samtleben et al. [
17], the SPW 1 activity is mostly dampened because (i) the localized GW forcings prevent wave propagation at midlatitudes and (ii) the GW forcing interacts destructively with the original SPW 1, which is highly depending on the position of the GW hotspot with respect to the original SPW 1 phase. All three GW hotspots dampen the propagation at midlatitudes but the RM GW hotspot (similar to the H5 GW hotspot in Samtleben et al. [
17]), which can be interpreted as an additional wave 1, interferes constructively with the original SPW 1 leading to increased SPW 1 amplitudes [
17].
To investigate in how far the arrangement of the GW hotspots influences the interference of the respective GW hotspot effects, we now analyze the effect of the combined GW hotspots, EA + RM, HI + RM, HI + EA, and HI + EA + RM, and compare this with the linearly summed effect of each GW hotspot alone.
Figure 9a–d shows the SPW 1 amplitude differences between each experiment and the Ref simulation in color coding. In addition, the contour lines represent the sum of the differences between the respective single GW hotspots and the Ref simulation (e.g., (RM − Ref) + (EA − Ref) in
Figure 9a). Thus, differences between contours and shading indicate destructive or constructive interference between the combined GW hotspots, i.e., deviations from a linear superposition of the GW hotspot effects. The right column (e–h) illustrates the difference between the combined GW hotspot differences (color coding) and the added up differences (contour lines), e.g., (RM + EA − Ref) − ((RM − Ref) + (EA − Ref)). Dark red (blue) areas indicate a stronger increase (decrease) of the SPW 1 amplitude by the combination of the GW hotspots and therefore, a constructive interference of the combined GW hotspots with respect to the SPW 1 activity. Red (blue) indicates a less stronger decrease (increase) of the SPW 1 amplitude by the combined GW hotspots compared to the added up differences. Light red (blue) indicates a change in sign from negative (positive) anomalies for the added up differences to positive (negative) anomalies for the combined GW hotspots differences. To summarize, regions colored in blue show a stronger decrease of the SPW 1 amplitude induced by the combination of the GW hotspots, which means that there is a stronger destructive effect on the SPW amplitude induced by the combined GW hotspots than expected from linear interference. We also introduce a linearity factor defined as the ratio of the effect of combined hotspots and the sum of single hotspot effects, e.g., for the combination of the RM and EA hotspots:
If the differences (RM + EA) − Ref and (RM − Ref) + (EA − Ref)) are both either positive or negative, L (i) is positive and (ii) indicates an additive or rather linear interference when it is equal or larger than 1. In some cases both differences have an opposite sign, i.e., L (i) is negative and (ii) indicates a subtractive or destructive interference because the combined GW hotspots effect differs from the linear sum resulting from the respective single GW hotspots. In connection to the color coding, this means that dark red/blue regions in
Figure 9 stand for constructive interference between the GW hotspots, while the other colored gradations represent destructive interference.
Starting with the SPW 1 amplitude differences between each experiment and the Ref simulation (
Figure 9a–d color coding), it can be generally seen that the SPW 1 amplitude is strongly decreasing between 30 and 70 km, with the largest negative anomalies around 40 and 70° N. The effect is strongest for the experiment including all three GW hotspots. In parts of the lower stratosphere, southward of 20° N and northward of 60° N as well as above 70 km, the SPW 1 amplitude is mostly increasing. The enhanced amplitudes around 60° N, which is largest for the RM and EA combination, may be caused by horizontally propagating SPW 1 according to the increase of the horizontal component of the Plumb flux, which we observed in case of the EA and RM GW hotspots. The summed up single GW hotspot differences and the combined GW hotspot differences mutually vary and need to be discussed in more detail.
By comparing the values of the combined EA and RM GW hotspots differences to the added up differences, it can be seen that the negative SPW 1 amplitude changes at midlatitudes and in the polar region above 30 km are more pronounced (more negative = dark blue) for the combined GW hotspots simulation (
Figure 9e). Thus, with respect to the SPW 1 activity we observe a destructive effect caused by the combined GW hotspots. According to the linear superposition of the single GW hotspots the combined GW hotspots lead to similar differences or even exceed those, i.e., we observe an additive or linear interference between both GW hotspots in these regions colored in dark blue also indicated by the linearity factor being strongly positive. Around 60° N, where the added up differences of the single EA and RM GW hotspots are strongly positive above 30 km (
Figure 9a, contour lines), the SPW 1 amplitude differences in
Figure 9e show that the SPW 1 amplitude changes are less positive (blue) or even negative (light blue) for the combined GW hotspots in this region. Thus, above 30 km we mainly observe an intensified decreasing SPW 1 amplitude owing to the combination of the EA and RM GW hotspots. In this case, both GW hotspots interfere destructively emphasized by the negative and slightly positive (<1) L in this region. Solely, the positive SPW 1 anomalies at the northern flank of the EA GW hotspot seen in (
Figure 9a, red regions) are more positive as they would be if we sum up the differences of the single GW hotspots. In this region the linear interference of both GW hotspots (linearity factor larger than 1) lead to a constructive effect on the SPW 1 amplitude. Because of the negative SPW forcing originating from the combination of the RM and EA GW hotspots, most of the regions (77% of the presented latitude-height plot) are colored in blue in
Figure 9e.
The SPW 1 amplitude changes of the combined HI and RM GW hotspots correspond well to the summed up differences of the single HI and RM GW hotspots. The difference between these two differences in
Figure 9f shows that the SPW 1 amplitude differences caused by the combined GW hotspots are less negative than taken from linear addition in most of the regions between 30 and 70 km (colored in red). Thus, the combination of both GW hotspots has a less destructive effect on the SPW 1 activity than expected from linear assumption. In the red region the linearity factor ranges between 0 and 1 indicating destructive interference between both GW hotspots because the combined GW hotspots difference is less negative.
There are only a few regions, in which the negative SPW 1 amplitude anomalies are more pronounced and both GW hotspots interfere constructively. The positive SPW 1 amplitude changes around 60° N caused by the combined GW hotspots are slightly enhanced compared to those obtained from the linear sum of the single GW hotspots, while the SPW 1 amplitude changes of the combined GW hotspots in the polar region are less intense. Comparing the SPW 1 changes induced by the combined RM and HI GW hotspots in
Figure 9b with the single RM and HI GW hotspots, it can be seen that the impact on the SPW 1 activity is less destructive. The negative SPW 1 amplitude changes caused by the combined HI and RM GW hotspots are less intense than those of the summed up differences of the single GW hotspots in connection with linearity factors smaller than 1 standing for destructive interference. This means that the combination of these two GW hotspots leads to a weaker decrease of the SPW 1 activity compared to the sum of the respective single GW hotspots. Only 45% of the area in
Figure 9f is blue (destructive effect on SPW 1). The results of the experiment including all three hotspots are similar to those of the combined RM and HI GW hotspots. Solely around 60° N, the positive SPW 1 anomalies induced by the combination of all three hotspots is not as strong as the sum of the anomalies based on the respective single GW hotspots. Thus, the addition of the EA GW hotspots leads to a destructive interference between all three GW hotspots in this region.
Compared to all the other experiments, the combined EA and HI GW hotspots shown in
Figure 9f lead to a large extent to smaller negative (positive) anomalies than expected from the linear assumption of the respective single EA and HI GW hotspots. Thus, the combined GW hotspots (i) have a less destructive (constructive) effect on the SPW 1 activity and (ii) their interactions are nonlinear or rather non-additive underlined by the positive L < 1. The less negative SPW anomalies caused by the combined GW hotspots predominate. The effect on the SPW 1 activity is less destructive for the EA and HI combination than for the other experiments. Therefore, this combinations also has the largest percentage of nonlinear interference between these two GW hotspots. In this experiment only 31% of the area in
Figure 9g is blue (destructive interference). Up to 30 km northward of 60° N the SPW 1 differences caused by the combined GW hotspots are more negative or less positive. Thus, the combination has a destructive effect on the SPW 1 amplitude in this region.
To summarize, the combinations of the different GW hotspots mainly lead to a decrease of the SPW 1 activity. The combined EA and RM GW hotspots have a more destructive effect on the SPW 1 activity because of their additive interference. The SPW 1 amplitude differences of the combined EA and RM GW hotspots are more negative than those of the summed up SPW 1 amplitude differences based on the single GW hotspots. Compared to the EA and RM GW hotspots combination, the combined RM and HI GW hotspots have a less destructive effect on the SPW 1 activity owing to the nonlinear interference. In longitude, the RM and HI are displaced by 170° against each other; this is the reason, why a nearly complete counteracting of these two GW hotspots might be expected. The longitudinal distance between the EA and RM GW hotspots is only 105°. Furthermore, the EA GW hotspot is placed 10° further North, while the HI GW hotspots is located 5° further South than the RM GW hotspot. This spatial distribution explains, why the interference between the EA and RM GW hotspots is more constructive than the one between the RM and HI GW hotspots. The HI and the EA GW hotspots are located next to each other, however, this combination has the most constructive effect on the SPW 1 activity owing to the nonlinear interference. Thus, the zonal displacement between both GW hotspots of 20° leads to the non-additive interference. Another factor is the interference of the GW forcing with the original SPW 1. Samtleben et al. [
17] showed that that the RM is mainly in phase with the original SPW 1, while the HI GW hotspot is mostly out of phase. We observe a weakening (strengthening) of the GW hotspot effects, which is more in (out) phase with the original SPW 1, when it is combined with a GW hotspot being more out (in) of phase with the original SPW 1. This also indicates destructive interference between the GW hotspots.
According to Samtleben et al. [
17], single GW hotspots lead to a blocking of SPW 1 propagation at midlatitudes.
Figure 10 shows the differences of the EP flux and its divergence between the respective experiment and the Ref run, in order to see if this is also the case for the combined GW hotspots. Changes in the direction and strength of the EP flux difference is illustrated by the colored arrows, while the changes of the EP divergence are given in color coding. Areas of negative EP divergence in the Ref simulation are hatched to be able to interpret the EP divergence differences. From observations and also previous publications we know that there is one major branch of SPW 1 propagation originating at midlatitudes and from there going further upward and heading towards the equatorial stratosphere. And a second branch heading from the midlatitudes towards the polar lower stratosphere is less well-developed [
16].
In all cases, the EP flux and, for large areas also its divergence, is decreasing as a result of the hotspot effect. An exception is the RM hotspot (
Figure 10a), where the EP flux is increasing, especially at higher latitudes up to 60 km. In this region SPWs do normally not propagate owing to the strong polar vortex. Because of its displacement or even weakening, which is strongest for the RM GW hotspot (strong decrease in zonal mean flow and geopotential height), in this simulation the SPWs 1 are also propagating via the polar region into the middle atmosphere.
Also more SPWs 1 are breaking in the polar region indicated by the negative EP divergence, which means that more energy and momentum is transferred leading to the deceleration of the west wind, and thus, to the destabilization of the polar vortex. In the polar upper mesosphere there is a strong positive EP divergence anomaly and therefore, represents a source of SPWs 1. But because of the wind reversal in the mesosphere, these SPWs 1 are not able to propagate further upward.
According to Samtleben et al. [
17] the EA GW hotspot (
Figure 10b) shows a decrease in the EP flux amplitude and the difference arrows are pointing downward. Thus, also the EP divergence is less negative or even positive, which explains the positive EP divergence anomalies, especially in the middle atmosphere at lower latitudes. This decrease of energy transfer normally induced by breaking SPWs leads to the acceleration of the zonal mean flow in this region observed in
Figure 3b. In the upper mesosphere the EP flux is slightly increasing originating from a region of positive EP divergence (60° N, 70 km), a sink of SPWs 1. These SPWs 1 are mainly generated by local instabilities [
16]. They propagate upward, but they break nearly immediately and lead to the negative EP divergence in the mesosphere. While the vertical propagation conditions changed dramatically, we observed positive SPW 1 amplitude anomalies around 30 km at midlatitudes and in the polar region lower stratosphere in
Figure 8b. These positive anomalies are probably induced by horizontally propagating SPWs 1 observed in the increased Plumb flux above Eurasia (
Figure 7b), which are not able to propagate further upward and therefore, are confined to specific altitude ranges. The HI GW hotspot effects in
Figure 10c show a similar structure as the one for the EA GW hotspot. Also, the combinations of several GW hotspots show nearly the same behaviour in the EP flux and its divergence like the HM GW hotspot.
Thus, we may briefly summarize that the analysed GW hotspots both as single ones or in combination mainly lead to a dampening of the SPW 1 activity by preventing them from propagating upwards at midlatitudes. Thus, the GW hotspots act like a blockade. Owing to the suppressed propagation of SPWs 1 we observe a decrease in the EP flux in connection with a decreasing transfer of momentum and energy indicated by positive EP flux divergence anomalies. As an exception, in case of the RM GW hotspot the SPWs 1 are able to propagate via the higher latitudes into the middle atmosphere and compensate the damping. This is possible because of the stronger weakening of the polar vortex in the RM experiment, compared to the other experiments.