Atmospheric Response to SST anomalies. Part 2: Background-state dependence, teleconnections and local effects in summer.

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1 Generated using the official AMS LATEX template two-column layout. FOR AUTHOR USE ONLY, NOT FOR SUBMISSION! J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S Atmospheric Response to SST anomalies. Part 2: Background-state dependence, teleconnections and local effects in summer. STEPHEN I. THOMSON, GEOFFREY K. VALLIS University of Exeter, UK. ABSTRACT The atmospheric response to SST anomalies is notoriously difficult to simulate, and may be sensitive to model details and biases, particularly in midlatitudes. In this paper and its companion we compare the response of models that have slightly different jet positions and modes of variability, in order to ascertain how much the response is affected by differences in models climatological states. In Part 1 we focussed on northern-hemisphere winter (DJF) whereas in this paper, Part 2 we focus on summer (JJA) and inter-seasonal comparisons. We use two different configurations of the same idealised atmospheric model, constructed using two different configurations of continents and topography. These configurations give rise to different background wind fields and variability within the same season, and therefore give a measure of how robust a response is to small changes in the background-state. We begin by characterising the types of responses that are found to SST anomalies in the midlatitudes and tropics in JJA, and compare these with the corresponding responses in DJF. We find that the responses to midlatitude SST anomalies in JJA are generally on a much smaller spatial scale than those in DJF. Responses in the tropics are much less dependent on season, although teleconnections between the tropical Pacific and the North Atlantic are not found in JJA as robustly as they are in DJF. Given insight from our model results, however, we find some summer periods in reanalysis data where there is a strong association between the tropical Pacific and the summer North-Atlantic Oscillation. Implications for seasonal prediction in JJA are discussed. 1. Introduction The response of the atmosphere to sea-surfacetemperature (SST) anomalies is a problem that has been studied extensively using a wide-range of techniques, ranging from analytical studies in simplified equation sets (e.g. Matsuno 1966; Gill 1980) to fully-coupled chemistry-climate models (e.g. Hurwitz et al. 2012). A significant difficulty with such studies is that the response of the atmosphere, particularly in midlatitudes, is thought to depend strongly on the background wind climatology and variability. In particular, Peng and Robinson (2001) showed that the response of the atmosphere to midlatitude SST anomalies depends strongly on when during winter the anomaly appeared, with their results showing the response in January having a very different character to the response in February. The focus of the present work is to investigate if this same kind of dependence is present in northern-hemisphere summer, and more generally to understand the circumstances under which SST anomalies Corresponding author address: Department of Mathematics, University of Exeter, UK stephen.i.thomson@gmail.com can have a robust affect on the atmosphere. A companion paper, Part 1, looked at similar issues in winter. The majority of previous work on the atmospheric response to SST anomalies focuses on the winter months. However, understanding the impact of SST anomalies on the atmosphere is arguably of equal importance in summer, with a role being played by the ocean in the climatological conditions (Dong et al. 2013), and also in extreme events, such as heat waves (McKinnon et al. 2016). Of related importance is the potential atmospheric predictability coming from SSTs, as is well established in winter (e.g. Scaife et al. 2016, and references therein). In Part 1 of this two-part study, an investigation was undertaken into the dependence of atmospheric responses to SST anomalies on the background climatological winds, focussing on northern-hemisphere winter (December-January-February, DJF). The investigations in Part 1 used the idealised general-circulation model (GCM) Isca (Vallis et al. 2017), with the response to SST anomalies compared across two different configurations of the model. The configurations were differentiated by having two different configurations of continents and topography. This resulted in the configurations having different climatological winds and modes of variability. It was Generated using v4.3.2 of the AMS L A TEX template 1

2 2 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S shown that the response of the atmosphere to tropical SST anomalies was robust to changes in background climatology, but that the response to midlatitude SST anomalies was highly dependent on the background climatology. Given the dependence on background climatology of some of the responses, it is of interest to study this dependence in northern-hemisphere summer, and this is the focus of the present work. To do this, we use the same method as in Part 1, but consider the atmospheric responses in northernhemisphere summer (June-July-August, JJA), comparing and contrasting it to the responses in winter. The outline of this paper is as follows. Section 2 describes the model and its two different configurations, and compares the model s climatologies and variability with reanalysis. Section 3 outlines our design for SST-anomaly experiments, section 4 discusses the response to tropical anomalies, section 5 discusses the response to midlatitude anomalies, section 6 compares the responses to tropical and midlatitude SST anomalies, section 7 compares the responses in JJA to those found in DJF in Part 1, and section 8 discusses the results and draws conclusions. 2. Model setup and comparison of model climatologies and reanalysis As in Part 1, we construct our models using Isca (Vallis 2017), a framework for the construction of idealised models. The configuration of Isca used in the present work, and in Part 1, uses GFDL s spectral, primitive-equation dynamical core, run at T42 horizontal resolution, and performs radiative transfer using the Rapid Radiative Transfer code RRTM (Clough et al. 2005), as used in the MiMA model of Jucker and Gerber (2017). In its present configuration, Isca uses a Monin-Obukhov boundary layer scheme, and a mixed-layer ocean, as in the model of Frierson et al. (2006), and the Betts-Miller convection scheme (Betts and Miller 1986). The mixed-layer has a constant depth in time, and has a seasonally-varying horizontal heat transport in the form of a Q-flux, so that the model s SSTs remain close to a seasonally-varying SST climatology calculated from the AMIP SST dataset (Taylor et al. 2000). A simple representation of land-sea contrast is added by modifying the mixed-layer s properties in regions of land. Details of the simple land model, and other aspects of our configuration of Isca, are given in Part 1. In both Part 1 and the present study, Isca is run with two different configurations of land and topography in order to generate slightly different climatological states. The first of the two configurations is a simple configuration of continents and simplified topography, which are shown in figure 1. The continent shapes and topography are an extended version of the simplified continents found in Saulière et al. (2012). By contrast, the complex configuration uses realistic continent shapes and topography, which are taken from the ERA-interim invariants (Dee et al. 2011). This continental configuration is shown for comparison in figure 1. In order for our comparison of atmospheric responses to SST anomalies in these two configurations to make sense, it is required that the climatologies of the two configurations are somewhat similar to one another, but not identical. If their climatologies were either very different or identical, then the comparison would be meaningless. It is also desired that these climatological states are somewhat similar to the real world, in order that qualitative conclusions drawn from Isca s results may be qualitatively applicable to real-world problems. Figures 1(d) and (e) show the 20-year time-mean zonal wind at 850 hpa in JJA in the simple and complex configurations, respectively, with panel (f) showing the same field in the JRA-55 reanalysis, averaged between (Kobayashi et al. 2015). Broadly speaking, the two model configurations are similar to each other in terms of their wind structure and magnitudes. Some small differences are apparent, however, particularly in the strength of the jet in the west Pacific, and the position of the maximum winds in the jet over the north Atlantic. A comparison between the two configurations and JRA-55 shows that, again broadly-speaking, our model wind distributions and magnitudes look quite like reanalysis. Some notable differences are in the latitude of the jet stream over the north Pacific, and the south-westnorth-east tilt of the jet stream over the north Atlantic, with the models jet streams being too zonal. A similar comparison can be made between the two model configurations and JRA-55 at other vertical levels, and similar conclusions apply. For example, figures (g), (h) and (i) are equivalent plots to (d), (e) and (f) at 250 hpa. As an additional measure of the similarity of the configurations to each other and to reanalysis, figure 2 shows the time-mean JJA sea-level pressure fields, minus their zonal-means, in the simple and complex configurations, and JRA-55 (c). These JJA stationary waves are remarkably similar in all three plots, including over the north Atlantic. The latter is a relative surprise, given the simple configuration s lack of Greenland, which had a significant negative impact on the realism of the stationary wave pattern in the simple configuration in DJF, as discussed in Part 1. The southern-hemisphere JJA stationary-wave patterns are significantly different across the configurations and JRA-55, which suggest that our configurations may not be similar enough to apply this method to any southern-hemisphere SST anomalies in JJA. Possible reasons for these significant differences in the southern hemisphere include the simple configuration s lack of southernhemisphere mountain ranges and its lack of Antarctica. Given the broad similarity of the model configurations with each other and reanalysis, but with details being different, we deem our two model configurations to be both

3 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S 3 m (c) m m (d) (e) (f) ms 1 (g) (h) (i) ms 1 FIG. 1: A comparison of the topographic height (panels, and (c)) and the zonal wind at 850 hpa in JJA (panels (d), (e) and (f)) and at 250 hpa (panels (g), (h) and (i)) in the simple configuration (left column), the complex configuration (middle column) and JRA-55 (right column). different enough and similar enough for our comparison of their responses to be meaningful. Having compared two time-mean quantities, it is also important to compare the modes of variability found in the two configurations and in JRA-55. This is important because the projection of the atmospheric response onto internal modes of variability is often seen in DJF (see e.g. Part 1 or Peng and Robinson 2001). Therefore an understanding of how different these modes are is important for interpreting any responses that project onto internal modes. Figure 3 shows EOF1 of the zonal-wind at 250 hpa in JJA, calculated separately over two latitudelongitude regions. These regions are the North Atlantic 1 (80 W-40 E, N) and the North Pacific (120 E- 240 E, N). One of the clearest features of this comparison is that the modes over the North Pacific are very similar in structure and magnitude in all three cases. However, over the North Atlantic the complex configuration s mode looks relatively similar to the mode in JRA- 55, albeit with the positive jet feature being too far south in the complex configuration. The simple configuration s mode is rather different to both the complex configuration and JRA-55. However, all of these modes correspond to a latitudinal shift of the jet stream, and so the modes are indeed describing the same physical mode of the system. Having made this comparison, we regard our two configurations as being similar and different enough to each other and to JRA-55 to make a comparison meaningful. 3. Experiment design In order to study the atmospheric responses to SST anomalies in our two model configurations, we follow the same procedure as in Part 1, by running each configuration in its control state and keeping the final 20 years of a 60 year run. We then run separate experiments with different Q-flux anomalies added to the seasonally-varying Q-flux. Each Q-flux anomaly is constant in time, and has the spatial form 1 The EOFs calculated over the Atlantic correspond to the summer NAO (North Atlantic Oscillation) mode of variability, although the sign of the EOF is opposite to the definition found in Folland et al. (2009), meaning that a positive projection onto our EOF corresponds to a state of negative summer NAO. { Q Aγ(θ,φ), γ > 0 = δ, elsewhere, (1)

4 4 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S (c) hpa FIG. 2: Panels, and (c) show the JJA mean SLP minus its zonal-mean The left hand column shows the simple configuration, the central column shows the complex configuration, and the right-hand column shows JRA-55. (c) ms 1 FIG. 3: Panel shows the first EOFs of the 250 hpa zonal wind in JJA in the simple configuration, calculated separately in the Atlantic and Pacific basins. Dark lines mark the domain over which the EOF was calculated. Panels and (c) are the same quantity, but for the complex configuration and JRA-55, respectively. The EOFs are calculated from data north of 20 N. Here A = 200Wm 2 is the amplitude of the anomaly, γ is the paraboloid function γ(θ,φ) = 1 ((φ φ 0 ) 2 + (θ θ 0 ) 2 ), where φ 0 and θ 0 are the central longitude and latitude of the anomaly, respectively. The constant δ is applied over the entire ocean outside of the paraboloid such that the area integral of Q over the ocean is equal to zero. It has been verified that the SST outside the paraboloid region changes very little as a result of δ 0 (not shown). This anomalous Q-flux divergence is added to the seasonally-varying Q-flux climatology in equation (1) of Part 1. SST anomalies arise from anomalous ocean heat transport, as in reality, and we maintain the significant advantages (and realism) of using a oceanic mixed layer rather than a specified SST distribution, as discussed by Bretherton and Battisti (2000). SST anomalies are colocated spatially with the Q-flux anomaly, unlike in Sutton and Mathieu (2002). In order to calculate the atmospheric response to each SST anomaly, we run the model with each anomaly for 24 years. We then discard the first 4 years as a spin-up phase, whilst the model adjusts to the anomaly. The remaining 20 years are then compared with 20 years from the control simulation for the relevant configuration, and time-averages are taken of the differences in various model fields. The statistical significance of any response is measured using the Student s t-test, with responses considered significant at the 95% confidence limit. Throughout this paper, we will be concerned with whether the responses to particular SST anomalies are robust. In order for a response to be deemed robust, we require that it meets two criteria: 1. The response in a particular quantity must be similar across the two configurations. 2. The responses within the two configurations must both be statistically significant, as judged by the t- test with a 95% confidence limit. In order to get an understanding of how the circulation responds to Atlantic and Pacific SST anomalies at both mid- and tropical latitudes, we have chosen 31 different locations for our Q-flux anomalies. These are shown in figure 4. Each of these locations is run separately for each configuration, giving a total of 62 experiments. The anomaly locations were chosen to give the Pacific and Atlantic a reasonable coverage, and many equatorial locations were chosen in the Pacific to identify whether any El Niño-type responses were produced by the model. 4. Responses to tropical anomalies Figure 4 summarises the main results to be presented in this section. A clear result is that robust responses are found to all the tropical SST anomalies in JJA, as was the case in DJF This is in clear contrast to the responses to the

5 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S 5 FIG. 4: Figure reproduced from Part 1. Circles show the outer edge of the positive Q-flux anomalies in each of the 31 locations considered in the present work. As in Part 1, the circles are colour-coded by the season in which their responses are robust. Green circles indicate that the response is robust in both DJF and JJA. Blue circles indicate that the response is robust in JJA only, and red circles indicate that the response is robust in neither DJF nor JJA. In all the cases considered in the present work, the responses are robust in both DJF and JJA. The letter labels are used for reference throughout the text. midlatitude anomalies, where only 7 of the 15 cases produce a robust response in JJA. Focussing on JJA, we now consider the responses in each case, giving detailed explanations in a few example cases. Our reason for presenting the responses in different individual cases is to give an idea of the types of responses found in different locations within the tropics, and therefore to show the variety and similarity of the responses across the locations considered. a. Tropical response to tropical Pacific SST anomalies We begin by considering the response of the tropical atmosphere to tropical SST anomalies, which we refer to as the local responses to the tropical anomalies. The first subset of cases to be considered are those at 10 N in the Pacific, i.e. cases P1W-P1E. At 850 hpa, the atmospheric response is a local positive wind anomaly over and to the west of the SST anomaly, which is robust across both configurations in all four cases. The example of case P1E is shown in figure 5 and. This response is also remarkably similar to the response to these SST anomalies in DJF, although they generally extend over a greater area in JJA than in DJF. At 250 hpa, the responses are more diverse across these four cases. In cases P1CE and P1E, the latter of which is displayed in figure 5(c) and (d), the local response over the SST anomaly is an anticylonic circulation, with a positive zonal-wind anomaly to the north of the SST anomaly, and a negative zonal-wind anomaly to the south of the SST anomaly. The negative zonal-wind anomaly extends down to the equator. To the south of the equator, there is also a positive zonal-wind anomaly, implying the presence of anomalous anticyclonic circulation on both sides of the equator. This response bears some similarity to the response to these SST anomalies in DJF, but is significantly stronger than the responses in DJF. The responses at both levels imply a slow-down of the JJA Walker circulation, although it is noted that the JJA Walker circulation is stronger in the model than in reanalysis (not shown), and so this aspect may not be realistic. By contrast, cases P1W and P1CW have similar local robust responses, but they are much weaker, and are on a smaller scale than those in cases P1CE and P1E. This contrast between cases P1W and P1CW and cases P1CE and P1E implies some sensitivity of the response to the longitude of the SST anomaly. Such a sensitivity may be expected, however, given that there is a gradient in climatological SST from west to east across the equatorial Pacific, with the west Pacific being warmer in the mean. Therefore anomalies on the east edge of the Pacific might be expected to enhance the climatological west-east gradient, where anomalies on the western edge of the Pacific might be expected to decrease the climatological west-east gradient. This argument is consistent with the eastern-pacific anomalies leading to a slow-down in the Walker circulation. The local responses to anomalies along the equator, i.e. cases P0W1-P0E4 in JJA at 850 hpa are positive zonalwind anomalies extending over and to the west of the SST anomaly (not shown). Some cases have this zonal-wind anomaly extending to the north-west (e.g. case P0W1), but most have the anomaly extending along the equator itself. The responses in the four east-pacific cases (P0E1-P0E4) strongly resemble the responses in those same cases in DJF. Those in the west-pacific are weaker and less robust in DJF compared with JJA, and so the similarity across seasons is not as strong. At 250 hpa, the behaviour is more complicated, as was the case for these anomalies in DJF. The robust part of the response is a negative zonal wind anomaly that sits over the SST anomaly, and has various strengths and east-west extensions, which depend on the

6 6 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S ms 1 (c) (d) ms 1 FIG. 5: Time-mean responses to Q-flux anomaly in case P1E. Figure is the response in JJA for the simple configuration at 850 hpa, and is the response in DJF for the complex configuration at 850 hpa. Figures (c) and (d) are like and, but are at 250 hpa. longitude of the SST anomaly. The example of case P0E2 is shown in figure 7. As these extensions are not the same across configurations, we do not consider them to be part of the robust response. In addition to this negative wind anomaly response over the equator, there is also a robust positive zonal-wind anomaly at the northern edge of the SST anomaly, implying anticyclonic circulation similar to that seen at 250 hpa for the cases at 10 N. With the exception of cases P0E3 and P0E4, which have weaker responses in the complex configuration, all of the responses at 250 hpa look remarkably similar to the responses to these same SST anomalies in DJF. b. Extra-tropical responses to tropical Pacific SST anomalies In terms of remote responses, which we define to be responses in regions of the atmosphere away from the location of the SST anomaly, there are significantly fewer cases of significance compared with DJF. In terms of the remote response over the north Pacific, there are no cases with significant responses. This is in stark contrast with the same cases in DJF, where all but two of the twelve tropical-pacific cases produced a robust strengthening of the Aleutian low in midlatitudes. The lack of Aleutian low response in JJA is, at least in part, due to the lack of the Aleutian low itself during the JJA season (compare figure 2 to figure 2 from Part 1). To demonstrate the lack of response in the midlatitude Pacific, we calculate correlation coefficients between the responses and EOF1 of zonal wind at 250 hpa over the North Pacific in the two configurations separately. We then plot the correlation coefficient in the simple configuration against the correlation coefficient in the complex configuration for each case. This plot is shown in figure 6, with the coefficients from the simple configuration on the x-axis and the coefficients from the complex configuration on the y-axis. Any cases that have both high correlation coefficients, and similar coefficients in the two configurations are deemed to have a robust projection of the response onto EOF1. The fact that none of the cases plotted in figure 6 produce a high correlation in both configurations suggests that no cases robustly project onto EOF1 over the North Pacific in JJA. This contrasts significantly with the equivalent figure 6 for DJF in Part 1, which shows a significant clustering of points near ( 1, 1). This clustering near ( 1, 1) indicated a robust strengthening of the Aleutian low in nearly all cases. c. Atlantic responses to tropical Pacific SST anomalies In addition to the lack of response to tropical-pacific SST anomalies in the midlatitude Pacific, there is also a lack of response to tropical-pacific SST anomalies in the north Atlantic. This lack of significant remote response

7 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S 7 (c) (d) FIG. 6: Panel compares correlation coefficients in the simple configuration, on the x axis, with correlation coefficients in the complex configuration, on the y axis. The correlation coefficients are calculated between the zonal-wind response in JJA at 250 hpa in cases with tropical SST anomalies, and the EOF of zonal-wind in JJA over the Pacific basin (120 E to 240 E). The dashed line is y = x. The colours denote the basin in which the anomaly is placed, with red being in the Pacific, and black being in the Atlantic. The code used at each point correspond with those in figure 4 without the letter denoting the basin. Panel is like panel, but correlates the responses with the EOF confined over the Atlantic basin (80 W to 40 E). Panels (c) and (d) are the same as plots and, respectively, but use the zonal-wind responses in cases with midlatitude SST anomalies. can be seen in the lack of high correlation coefficients between the responses and the summer EOF1s in the North Atlantic in figure6. The only cases that have some appreciable response over the midlatitude North Atlantic are cases P0W1, P0W2, and P0E2, but these remote responses are only seen in the simple configuration. The responses in case P0E2 can be seen in figure 7, where the response in the simple configuration over the north Atlantic in (c) is not reflected in the complex configuration over the north Atlantic in (d). d. Responses to tropical Atlantic SST anomalies Concerning the responses to SST anomalies in the tropical Atlantic, we begin by considering the two cases at 10 N, i.e. cases A1W and A1E. Both of these cases produce similar local responses at 850 hpa as cases P1W- P1E did in the tropical Pacific, with a positive zonalwind anomaly over and to the west of the SST anomaly (not shown). In addition, there is also a robust negative zonal-wind anomaly to the east of the SST anomaly, and a robust southern-hemisphere response in the south Atlantic. At 250 hpa, the response is most similar to cases P1CE and P1E, with a negative zonal-wind anomaly over the southern-end of the SST anomaly, and a positive zonal-wind anomaly over the northern-end of the SST anomaly, implying a local anticyclonic circulation (not shown). These responses are similar in strength to those in P1CE and P1E, and extend longitudinally, although this extension is not robust. For example, in case A1W, the

8 8 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S ms 1 FIG. 7: Time-mean responses to Q-flux anomaly in case P0E2. Figure is the response in JJA for the simple configuration, and is the response in JJA for the complex configuration. simple case extends to the east, where the complex case extends to the west. For the two cases considered on the equator in the tropical Atlantic, i.e. cases A0W and A0E, the responses at 850 hpa are much less robust than the responses in the cases at 10 N. In case A0W a positive zonal-wind anomaly over the SST anomaly is visible in the complex configuration, but is hardly visible in the simple configuration. In case A0E a positive zonal-wind anomaly is not visible at all in the simple configuration, but is visible in the complex configuration. This lack of consistency over the equator suggests some dependence on the background wind field over the equator in the Atlantic that is not present at 10 N. At 250 hpa, both cases have a robust positive zonal-wind anomaly over and to the east of the anomaly, but do not have a robust negative zonal-wind anomaly to the west, as was seen in all cases on the equator in the Pacific. The example of case A0E is shown in figure 8. This lack of negative zonal-wind anomaly appears to be seasonal, as it is robustly present in all other seasons in both of these cases (not shown). In terms of remote responses, none of the Atlantic cases stand out as having high correlations with the EOFs in figure 6 and. However, in terms of the response of the zonal-wind itself in the Atlantic cases, case A0E does produce a robust response over the north Atlantic, as can be seen in figure 8 and. The responses do not look like EOF1 in either configuration, and hence do not have high correlation coefficients. The responses do look relatively similar to each other, however, producing a cyclonic circulation over the North Atlantic. Case A1E looks somewhat similar to A0E, but the robustness of the response is slightly less convincing than in case A0E. These results suggest that a remote connection from the tropical Atlantic to the midlatitude Atlantic may well be physically plausible. 5. Responses to midlatitude anomalies Concerning the responses to midlatitude SST anomalies in JJA, 7 of the 15 locations tested in this work produce robust responses. The geographic distribution of the anomalies that produce robust responses is shown in figure 4. In common with DJF, all three of the cases at 30 N in the Pacific, i.e. cases P3W-P3E, produce robust responses. The robust part of the response in these JJA cases is a local baroclinic response, with a local anticyclone aloft, as in figure 9 (c) and (d), and a near-surface cyclone (not shown). This is consistent with the linear response to surface heating discussed in e.g. Kushnir et al. (2002). At 40 N in the Pacific, a notably different set of responses occurs. Cases P4W and P4C produce robust baroclinic responses local to the anomaly, consisting of a negative wind anomaly at 250 hpa to the south and east of the SST anomaly, and a positive wind anomaly to the north of the SST anomaly, thus implying an anticyclonic circulation aloft, as can be seen for case P4C in figure 10 and. However, unlike cases P3W-P3E at 30 N, there are no corresponding anomalies at 850 hpa. Case P4E does not produce a local response at either 250 hpa or 850 hpa. However, cases P4C and P4E produce robust remote responses over the North Atlantic, in contrast to both case P4W and those at 30 N. The robust remote response in case P4C over the north Atlantic is barotropic and of reasonable amplitude, as can be seen in figure 10 and. This response correlates strongly with EOF1 over the Atlantic in both configurations, having correlation coefficients that are close to the y = x line in figure 6(d). The responses in the two configurations, although similar to their EOF1s, are somewhat different to each other in spatial structure, with the simple configuration responding most strongly in the western Atlantic, and the complex configuration responding mostly in the eastern Atlantic. This structure reflects the spatial patterns of EOF1 of zonal wind over this region, with the simple configuration s EOF having the largest amplitudes over the western Atlantic (as in figure 3), and the complex configuration s EOF hav-

9 9 JOURNAL OF THE ATMOSPHERIC SCIENCES Ϭ ms 1 Ϳ Ϭ F IG. 8: Time-mean responses to Q-flux anomaly in case A0E. Figure is the response in JJA for the simple configuration, and is the response in JJA for the complex configuration. Ϭ ms 1 Ϳ Ϭ F IG. 9: Time-mean responses to Q-flux anomaly in case P3E. Figure is the response in JJA for the simple configuration, and is the response in JJA for the complex configuration. ing the largest amplitudes over the UK (see figure 3), with the latter reflecting the structure of the EOF found in JRA-55 (see figure 3(c)). Case P4E produces a similar response to case P4C in both configurations, with the response being barotropic and centred on the western edge and eastern edge of the Atlantic in the simple and complex configurations, respectively. The responses in case P4E do look slightly less like the EOFs than in case P4C s complex configuration, which is reflected in the lower correlation coefficients found for case P4C in figure 6(d). Other cases that have reasonably high correlation coefficients in figure 6(d) are cases A5C and A5E, i.e. the eastern-most cases in the Atlantic at 50 N. The responses in case A5E can be seen in figure 10(c) and (d). The responses in case A5C are similar, but are weaker in the complex configuration and stronger in the simple configuration (not shown). The weakness in the complex configuration in case A5C is enough for us to not deem the response to be robust in this case. The response in cases A5C and A5E somewhat resemble those in case P4C, particularly in the simple configuration, which has a strong EOF-like barotropic response. The complex configuration s response is much weaker than in the simple configuration, and is present at 250 hpa but not at 850 hpa, suggesting that any surface response is hidden by the high background variability. Both cases A5C and A5E produce an anticyclonic circulation over the UK in the complex configuration that is similar to that seen in cases P4C and P4E. That a surface response is seen in cases P4C and P4E but not in cases A5C and A5E perhaps suggest that cases P4C and P4E produce a true projection onto the model s internal modes, but that A5C and A5E s response is more of a local baroclinic-type response, consistent with cases P3W-P3E. One of the clear features of figure 6(d) is that many of the responses in the simple configuration in JJA project negatively onto EOF1 of the zonal wind in the Atlantic sector at 250 hpa. Despite these strong projections in the simple configuration, little projection onto the EOF is seen in many of the complex configuration cases. That the responses in the simple configuration project more strongly onto the summer EOF1 than do the responses in the complex configuration is an interesting difference. One possible explanation for this difference is that the summer EOF1 over the Atlantic in the simple configuration explains 32.0% of the monthly variance, where the summer

10 10 JOURNAL OF THE ATMOSPHERIC SCIENCES (c) Ϭ ms 1 Ϳ Ϭ (d) Ϭ ms 1 Ϳ Ϭ F IG. 10: Unlike previous figures, is the response in JJA for the simple configuration in case P4C, and is the response in JJA for the complex configuration in case P4C. Figure (c) is the response in JJA for the simple configuration in case A5E, and (d) is the response in JJA in the complex configuration in case A5E. EOF1 over the Atlantic in the complex configuration explains only 23.6% of the monthly variance. It might be expected, therefore, that a model response would project more strongly onto an EOF if it explains more of the variance. The lower percentage in the complex configuration is the more realistic of the two, however, with the same EOF in JRA-55 explaining 23.3% of the monthly variance2. Equally, the EOF s spatial pattern in the simple case is arguably less realistic than that in JRA-55, particularly in high latitudes. Both of these factors suggests that the projection onto the summer NAO (North Atlantic Oscillation Folland et al. 2009) in the simple cases may well be unrealistic. The lack of significant local responses to the anomalies at 30 N in the Atlantic (A3W-A3E), at 50 N (P5W-P5E) in the Pacific, and in two of the three cases at 50 N in the Atlantic is an intriguing contrast to the significant local response in the Pacific at 30 N in cases P3W-P3E and the weak responses over the UK from cases at 50 N in the Atlantic in cases A5C-A5E. One potential reason for this difference is the atmospheric variability in the basic state in the Pacific at 30 N is small compared with the atmospheric variability at other anomaly locations, including 2 Similar conclusions to these can be drawn from EOFs calculated using daily data, where the fractions of variance explained are 14.5%, 10.6% and 11.1% in the simple configuration, complex configuration and JRA-55, respectively. 30 N in the Atlantic, and at latitudes further north. This contrast in variability means that the signal-to-noise ratio will be much better in the Pacific cases at 30 N than at any of the other midlatitude locations, making the linear-type response more likely to be visible. JRA-55 also reflects these contrasts in variability. The daily variance of geopotential height at 250 hpa in JRA55 is smaller at 30 N in the mid-pacific (180 W) than at 30 N in the mid-atlantic (330 W) and is smaller than the variance in either basin at 40 N or 50 N due to the presence of the midlatitude storm tracks. It therefore seems that 30 N in the Pacific is the only place outside of the tropics where a linear response might be expected to be visible compared with the variability. Unlike the winter case, there are no significant summer responses in the NH s stratosphere. This is to be expected, however, given the lack of vertically-propagating waves propagating through the stratosphere, as explained by the Charney-Drazin criterion (Charney and Drazin 1961). 6. Comparison of tropical and midlatitude responses The results described above show a clear contrast between responses to tropical SST anomalies and midlatitude SST anomalies in JJA. This result is consistent with a similar contrast found in DJF in Part 1. One prevalent explanation for why the atmosphere responds differently

11 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S 11 to tropical and midlatitude SST anomalies is that the response of the atmosphere to anomalous heating is predominantly vertical advection of anomalous temperature in the tropics, and horizontal advection in the midlatitudes, as discussed in e.g. Hoskins and Karoly (1981); Frankignoul (1985). A useful way to see this contrast is by applying the linearized advection equation for temperature to our results, as in equation (39) of Frankignoul (1985), u T acos(φ) λ + v T T + ω a φ p R C p p ω T = q (2) C p Here the primed quantities are departures from zonal means, R is the gas constant, C p is the heat capacity at constant pressure, q is the combined diabatic heating and any effects from boundary-layer frictional heating. We calculate explicitly all the terms on the left-hand side, and find the right-hand side terms as the sum of the terms on the left-hand side. Applying this decomposition directly to our anomaly experiments captures the response to our SST anomalies, but also captures the balances already in place in the climatology. We therefore calculate the terms in the anomaly experiments and the control experiments separately, and look at differences in each of the terms between the anomaly and control experiments. It is these differences that we refer to as the responses of each term to our SST anomalies. In the corresponding analysis for DJF in Part 1, a typical contrast between tropical and midlatitude responses to anomalous heating was shown in Part 1 s figure 12 and. The contrast between the tropics and the midlatitudes was due to differences in which terms were balancing the anomalous diabatic heating over the centre of the SST anomaly. In the tropics, the dominant terms were seen to be the two terms involving ω, whereas all the terms, including horizontal advection, were seen to be important to the balance in the midlatitudes. The same picture is found to apply in JJA, except that the latitude at which the horizontal advection terms become important lies between 30 N and 40 N, rather than between 10 N and 30 N in DJF. To show this distinction, we show the anomalous temperature budgets in cases P0W4, P3W and P4W in figure 11, panels, and (c), respectively. The first two of these are the same two cases shown for DJF in Part 1. A comparison between the three JJA cases in figure 11 - (c) shows that the tropical case in is again dominated by the balance of the two ω terms, indicating a key role for vertical advection, and very little role for horizontal advection, in agreement with the tropical cases in DJF. Case P3W at 30 N in is very like the tropical cases in JJA and DJF, with very little role played by horizontal advection above 500 hpa. The significant role played by advection below 500 hpa is somewhat more midlatitudelike, but the overall character of the profile is more tropical than case P3W in DJF. In contrast, case P4W at 40 N in (c) shows a balance that involves all of the terms, including horizontal advection, and looks very like the cases at 30 N and poleward in DJF. This change in character between 30 N and 40 N in JJA may well be one of the reasons why the responses discussed in section 5 at 40 N in JJA in the Pacific are more similar to those at 30 N in the Pacific in DJF than they are to those at 40 N in DJF. One additional feature of this comparison between cases is that the size of the ω terms in case P0W4 in are significantly smaller than those in case P3W in. These small ω terms are, however, seen only in case P0W4 out of the cases along the equator in JJA, with large values of the vertical advection found in other cases along the equator. We therefore do not think the low values seen in case P0W4 are especially significant. Also included in figure 11(d) and (e) are anomalous temperature profiles over the central gridpoints of 5 cases at 195 W in the Pacific at the 5 different latitudes considered. These profiles show similar features to those in DJF, with the height attained by temperature anomalies increasing for anomalies further towards the equator. However, a significant difference is the anomaly at 30 N looks much more similar to the tropical profiles than it did in DJF, again supporting the conclusion that the transition from a tropical-type response to a midlatitude response happens further north in JJA compared with DJF. 7. Comparison of winter and summer a. Response to tropical anomalies There is a large degree of similarity between DJF and JJA in the local responses to tropical anomalies. For example, the responses in case P1E can be compared in figure 5 for JJA, and figure 7 of Part 1 for DJF. The character of the responses close to the SST anomalies are broadly similar across the seasons, suggesting that the same Matsuno-Gilltype responses are similarly at work in DJF as in JJA. The main difference in these two responses is their magnitude, which is much larger in JJA. This implies a dependence of the response on the background state of the tropical atmosphere across the seasons, even though some of these background-state differences are rather small. This point can be verified through a comparison of figure 1(d)-(i) and the same figure in Part 1. In terms of the remote responses to tropical SSTs, there is a clear lack of significant responses in JJA compared with DJF, particularly in terms of responses to tropical- Pacific SSTs over the north Atlantic. For example, case P0W4 produced a response over the North-Atlantic in DJF, but does not produce a similar response in JJA. To assess the cause of this difference, we have performed ray-tracing calculations on the climatological zonal winds in JJA in both the complex model configuration and the JRA-55 reanalysis. Details of the ray-tracing methods are given in the appendix of Part 1. The main result of this

12 12 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S u acos( ) T v a T (hpa) (hpa) T p R Cpp T q Cp + F T (c) (hpa) (10 4 Ks 1 ) (d) (hpa) (10 4 Ks 1 ) (e) (hpa) (10 4 Ks 1 ) (K) (K) FIG. 11: Figures, and (c) show a decomposition of equation (2), which is the linearized temperature-advection equation, into its different terms. Figure shows the decomposition for a single horizontal gridpoint at the centre of the SST anomaly in case P0W4 in the complex configuration. Figure shows the decomposition in case P3W, which displays a similar balance to that shown in. In contrast, figure (c) shows the same decomposition over the central gridpoint in case P4W in the complex configuration. As a reference point for these profiles, figure (d) shows the anomalous temperature profiles in midlatitude cases P5E, P4E and P3E, and (e) shows the anomalous temperature profiles in tropical cases P1CE and P0W3. All five of the cases in (d) and (e) lie at 195 W and are typical of the profiles at each of these latitudes. Crosses on the temperature profiles indicate that this datapoint is not statistically different from 0, which is again calculated using a t-test with a 95% confidence interval. ray-tracing in JJA is that no stationary Rossby waves are able to propagate out of the equatorial regions in JJA in either the complex configuration or JRA-55. This lack of propagation out of the equatorial regions in JJA is due to the westward climatological zonal winds over the equatorial regions throughout the depth of the troposphere in JJA. This contrasts with the situation in DJF, where stationary Rossby waves are able to propagate out of the equatorial regions, as shown in figure 13 of Part 1. Propagation out of the tropics is possible in DJF due to the positive zonal winds that exist near the tropopause in the equatorial regions in DJF. This contrast in background winds between JJA and DJF can be seen by comparing the JRA-55 plots at 250 hpa in JJA in figure 1(i), and the equivalent plot in figure 1(i) of Part 1. It is, however, possible to find Rossby waves that propagate from the Pacific into the north Atlantic during JJA, with an example of waves started from 235 E and 30 N shown in figure 12. Still, the area of the Pacific from which rays are able to propagate into the north Atlantic is significantly smaller than in DJF, and is confined to much higher latitudes. One intriguing possibility from our experiments is that there is a connection between the tropical Atlantic and the north Atlantic during JJA. For example, case A0E, shown in figure 8, shows a robust response over the North Atlantic. However, ray-tracing calculations again imply that no stationary waves are able to propagate out of the tropical Atlantic, given the negative background winds. Investigating this particular case will form part of our future work. Further evidence for the general lack of tropical effect on the midlatitudes in JJA can be seen using linear regression. In the following, we regress SSTs onto the principal component timeseries of the EOF1 of zonal wind at 250 hpa over the Atlantic basin. The EOF used in this analysis is the same as that plotted in figure 3. Linear regression is applied separately in each of the two model configurations and in the HadISST SST data (Rayner et al. 2003), the latter of which is combined with the PC1 timeseries from JRA-55. Maps of the regression coefficients are shown in figure 13. Focussing first on the map of the HadISST and JRA-55 regression in panel (c) a tripole SST

13 J O U R N A L O F T H E A T M O S P H E R I C S C I E N C E S 13 ms 1 FIG. 12: The results of a ray-tracing calculation on the climatological zonal wind at 200hPa in our complex configuration in and in JRA-55 in. The contours show this zonal wind after a 60 zonal running mean has been applied. Three ray paths are shown emanating from the point 235 W and 30 N. The three rays correspond to different values of the x-wavenumber. Wave-1 is in black, wave-2 in green and wave-3 in purple. pattern is clear in the North Atlantic, consistent with previous SST regressions onto an summer NAO-like EOF (see e.g. figure 4a of Dong et al. (2013)). This tripole is like the NAO-associated SST tripole in DJF, as seen in figure 14(c) of Part 1. Both model configurations also show this tripole in JJA, although the southern maxima is not statistically significant in the complex configuration. Considering the connection between the tropics and the midlatitudes as seen in this analysis, the regression coefficients in the tropics in figure 13 are generally small in the complex configuration in panel and in HadISST in panel (c). The smallness of the coefficients in the tropics is consistent with the results of our SST anomaly experiments and ray-tracing calculations, which both indicate a lack of effect of tropical SSTs on the circulation over the north Atlantic in JJA. By contrast with the complex configuration and HadISST, large regression coefficients are found in the tropics in the simple configuration, implying a connection between the SST and the circulation over the North Atlantic. This connection appears to be possible in the simple configuration as there are positive zonal winds around 250 hpa over the mid-pacific that extend from the tropics up to the midlatitudes. This can be seen in figure 1(g). Applying the ray-tracing code to the control state of the simple configuration (not shown) confirms that stationary Rossby waves can, in fact, propagate into the midlatitudes from this region, unlike in either the complex configuration or JRA-55. Given the apparent connection between the tropics and midlatitudes during JJA in the simple configuration, it appears that a connection between the tropics and midlatitudes might be possible in the real world, but only if the variability in the tropical zonal winds is high enough that there are periods of robustly positive zonal winds over a reasonably-large longitude range in the Pacific during JJA. To test this idea, we looked at the zonal-wind along the equator in monthly JRA-55 data at 250 hpa, and took sector averages of 60 width centred on 170 W, thus giving a single equatorial zonal-wind timeseries for the central Pacific. We then re-calculated the linear regression between the SST and the north-atlantic EOF s PC1, but calculated the regression separately for summer months when the zonal-wind timeseries was negative, as is normal, and for those summer months when the zonal-wind timeseries was positive. The regression map in the case of negative equatorial winds (not shown) looks very like the map calculated using all summer months in figure 13(c). However, the regression map in the case of positive equatorial winds is significantly different, and is shown in figure 14, alongside a composite of the zonal wind conditions during the summer months with a positive zonalwind index in. It is clear from panel that there is now a much stronger association between the SSTs off the west coast of South America and the EOF in JJA, with this pattern of SSTs resembling an El Niño-like SST anomaly (see e.g. figure 22.13(c) of Vallis 2017). It therefore appears that some summer months could have a strong association between tropical SSTs and the circulation over the North Atlantic, potentially leading to increased seasonal predictability for the North Atlantic during these periods. However, these periods are the exception, rather than the norm. Of the 174 summer months between in our JRA-55 and HadISST datasets, there are only 42 months (24%) with positive equatorial winds over our pre-defined longitude range, with 132 months (76%) having the standard negative equatorial winds. Using different longitude widths and central longitudes for our zonal-wind timeseries changes these numbers somewhat, especially as the number of months where a negative zonal wind occurs decreases when the central longitude of our sector average is moved away from the central Pacific 3. However, the general pattern of the regression maps stayed the same 3 Using a central longitude of 150 W and a sector width of 60 gives 41 months with positive equatorial zonal winds, rather like the case centred on 170 W. Taking a central longitude of 130 W has only 10 months