Publications by Lesley Gray

Forecasting extreme stratospheric polar vortex events

Nature Communications Springer Nature 11 (2020) 4630

LJ Gray, M Brown, J Knight, M Andrews, H Lu, C O'Reilly, J Anstey

Extreme polar vortex events known as sudden stratospheric warmings can influence surface winter weather conditions, but their timing is difficult to predict. Here, we examine factors that influence their occurrence, with a focus on their timing and vertical extent. We consider the roles of the troposphere and equatorial stratosphere separately, using a split vortex event in January 2009 as the primary case study. This event cannot be reproduced by constraining wind and temperatures in the troposphere alone, even when the equatorial lower stratosphere is in the correct phase of the quasi biennial oscillation. When the flow in the equatorial upper stratosphere is also constrained, the timing and spatial evolution of the vortex event is captured remarkably well. This highlights an influence from this region previously unrecognised by the seasonal forecast community. We suggest that better representation of the flow in this region is likely to improve predictability of extreme polar vortex events and hence their associated impacts at the surface.

The Evaluation of the North Atlantic Climate System in UKESM1 Historical Simulations for CMIP6


J Robson, Y Aksenov, TJ Bracegirdle, O Dimdore-Miles, PT Griffiths, DP Grosvenor, DLR Hodson, J Keeble, C MacIntosh, A Megann, S Osprey, AC Povey, D Schroder, M Yang, AT Archibald, KS Carslaw, L Gray, C Jones, B Kerridge, D Knappett, T Kuhlbrodt, M Russo, A Sellar, R Siddans, B Sinha, R Sutton, J Walton, LJ Wilcox

Historical Simulations With HadGEM3-GC3.1 for CMIP6


MB Andrews, JK Ridley, RA Wood, T Andrews, EW Blockley, B Booth, E Burke, AJ Dittus, P Florek, LJ Gray, S Haddad, SC Hardiman, L Hermanson, D Hodson, E Hogan, GS Jones, JR Knight, T Kuhlbrodt, S Misios, MS Mizielinski, MA Ringer, J Robson, RT Sutton

On the role of Rossby wave breaking in the quasi-biennial modulation of the stratospheric polar vortex during boreal winter

Quarterly Journal of the Royal Meteorological Society Wiley 146 (2020) 1939-1959

H Lu, MH Hitchman, LJ Gray, JA Anstey, SM Osprey

<br>The boreal‐winter stratospheric polar vortex is more disturbed when the quasi‐biennial oscillation (QBO) in the lower stratosphere is in its easterly phase (eQBO), and more stable during the westerly phase (wQBO). This so‐called “Holton‐Tan effect” (HTE) is known to involve Rossby waves (RWs) but the details remain obscure.</br> <br>This tropical‐extratropical connection is re‐examined in an attempt to explain its intra‐seasonal variation and its relation to Rossby wave breaking (RWB). Reanalyses in isentropic coordinates from the National Center for Environmental Prediction Climate Forecast System for the 1979 – 2017 period are used to evaluate the relevant features of RWB in the context of waveguide, wave mean‐flow interaction, and the QBO‐induced meridional circulation. During eQBO, the net extratropical wave forcing is enhanced in early winter with ~25% increase in upward propagating PRWs of zonal wavenumber 1 (wave‐1). RWB is also enhanced in the lower stratosphere, characterized by convergent anomalies in the subtropics and at high‐latitudes and strengthened waveguide in between at 20‐40°N, 350‐650 K. In late winter, RWB leads to finite amplitude growth, which hinders upward propagating PRWs of zonal wavenumber 2 and 3 (wave‐2‐3). During wQBO, RWB in association with wave‐2‐3 is enhanced in the upper stratosphere. Wave absorption/mixing in the surf zone reinforces a stable polar vortex in early to middle winter. A poleward confinement of extratropical waveguide in the upper stratosphere forces RWB to extend downward around January. A strengthening of upward propagating wave‐2‐3 follows and the polar‐vortex response switches from reinforcement to disturbance around February, thus a sign reversal of the HTE in late winter.</br>

Uncertainty in the response of sudden stratospheric warmings and stratosphere‐troposphere coupling to quadrupled CO2 concentrations in CMIP6 models

Journal of Geophysical Research: Atmospheres American Geophysical Union 125 (2020) e2019JD032345

B Ayarzagüena, AJ Charlton-Perez, AH Butler, P Hitchcock, IR Simpson, LM Polvani, N Butchart, EP Gerber, L Gray, B Hassler, P Lin, F Lott, E Manzini, R Mizuta, C Orbe, S Osprey, D Saint-Martin, M Sigmond, M Taguchi, EM Volodin, S Watanabe

Major sudden stratospheric warmings (SSWs), vortex formation and final breakdown dates are key highlight points of the stratospheric polar vortex. These phenomena are relevant for stratosphere‐troposphere coupling, which explains the interest in understanding their future changes. However, up to now, there is not a clear consensus on which projected changes to the polar vortex are robust, particularly in the Northern Hemisphere, possibly due to short data record or relatively moderate CO2 forcing. The new simulations performed under the Coupled Model Intercomparison Project, Phase 6, together with the long daily data requirements of the DynVarMIP project in preindustrial and quadrupled CO2 (4xCO2) forcing simulations provide a new opportunity to revisit this topic by overcoming the limitations mentioned above. In this study, we analyze this new model output to document the change, if any, in the frequency of SSWs under 4xCO2 forcing. Our analysis reveals a large disagreement across the models as to the sign of this change, even though most models show a statistically significant change. As for the near‐surface response to SSWs, the models, however, are in good agreement as to this signal over the North Atlantic: there is no indication of a change under 4xCO2 forcing. Over the Pacific, however, the change is more uncertain, with some indication that there will be a larger mean response. Finally, the models show robust changes to the seasonal cycle in the stratosphere. Specifically, we find a longer duration of the stratospheric polar vortex, and thus a longer season of stratosphere‐troposphere coupling.

Evaluation of the Quasi‐Biennial Oscillation in global climate models for the SPARC QBO‐initiative

Quarterly Journal of the Royal Meteorological Society Wiley (2020) qj.3765

AC Bushell, JA Anstey, N Butchart, Y Kawatani, SM Osprey, JH Richter, F Serva, P Braesicke, C Cagnazzo, H Chun, RR Garcia, LJ Gray, K Hamilton, T Kerzenmacher, Y Kim, F Lott, C McLandress, H Naoe, J Scinocca, AK Smith, TN Stockdale, S Versick, S Watanabe, K Yoshida, S Yukimoto

The equatorial stratospheric semiannual oscillation and time‐mean winds in QBOi models

Quarterly Journal of the Royal Meteorological Society Wiley (2019)

AK Smith, LA Holt, RR Garcia, JA Anstey, F Serva, N Butchart, S Osprey, AC Bushell, Y Kawatani, Y Kim, F Lott, P Braesicke, C Cagnazzo, C Chen, H Chun, L Gray, T Kerzenmacher, H Naoe, J Richter, S Versick, V Schenzinger, S Watanabe, K Yoshida

The Quasi‐Biennial Oscillation initiative (QBOi) is a model intercomparison programme that specifically targets simulation of the QBO in current global climate models. Eleven of the models or model versions that participated in a QBOi intercomparison study have upper boundaries in or above the mesosphere and therefore simulate the region where the stratopause semiannual oscillation (SAO) is the dominant mode of variability of zonal winds in the tropical upper stratosphere. Comparisons of the SAO simulations in these models are presented here. These show that the model simulations of the amplitudes and phases of the SAO in zonal‐mean zonal wind near the stratopause agree well with the information derived from available observations. However, most of the models simulate time‐average zonal winds that are more westward than determined from observations, in some cases by several tens of m·s–1. Validation of wave activity in the models is hampered by the limited observations of tropical waves in the upper stratosphere but suggests a deficit of eastward forcing either by large‐scale waves, such as Kelvin waves, or by gravity waves.

Extreme weather events in early summer 2018 connected by a recurrent hemispheric wave-7 pattern

Environmental Research Letters IOP Publishing 14 (2019) 054002

K Kornhuber, S Osprey, D Coumou, S Petri, V Petoukhov, S Rahmstorf, L Gray

The summer of 2018 witnessed a number of extreme weather events such as heatwaves in North America, Western Europe and the Caspian Sea region, and rainfall extremes in South-East Europe and Japan that occurred near-simultaneously. Here we show that some of these extremes were connected by an amplified hemisphere-wide wavenumber 7 circulation pattern. We show that this pattern constitutes an important teleconnection in Northern Hemisphere summer associated with prolonged and above-normal temperatures in North America, Western Europe and the Caspian Sea region. This pattern was also observed during the European heatwaves of 2003, 2006 and 2015 among others. We show that the occurrence of this wave 7 pattern has increased over recent decades.

The effects of a well-resolved stratosphere on the simulated boreal winter circulation in a climate model

Journal of the Atmospheric Sciences American Meteorological Society 76 (2019) 1203-1226

Y Kawatani, K Hamilton, LJ Gray, S Osprey, S Watanabe, Y Yamashita

The impact of stratospheric representation is investigated using the Model for Interdisciplinary Research on Climate Atmospheric General Circulation Model (MIROC-AGCM) run with different model-lid heights and stratospheric vertical resolutions, but unchanged horizontal resolutions (~1.125°) and subgrid parameterizations. One-hundred-year integrations of the model were conducted using configurations with 34, 42, 72, and 168 vertical layers and model-lid heights of ~27 km (L34), 47 km (L42), 47 km (L72), and 100 km (L168). Analysis of the results focused on the Northern Hemisphere in winter. Compared with the L42 model, the L34 model produces a poorer simulation of the stratospheric Brewer–Dobson circulation (BDC) in the lower stratosphere, with weaker polar downwelling and accompanying cold-pole and westerly jet biases. The westerly bias extends into the troposphere and even to the surface. The tropospheric westerlies and zone of baroclinic wave activity shift northward; surface pressure has negative (positive) biases in the high (mid-) latitudes, with concomitant precipitation shifts. The L72 and L168 models generate a quasi-biennial oscillation (QBO) while the L34 and 42 models do not. The L168 model includes the mesosphere, and thus resolves the upper branch of the BDC. The L72 model simulates stronger polar downwelling associated with the BDC than does the L42 model. However, experiments with prescribed nudging of the tropical stratospheric winds suggest differences in the QBO representation cannot account for L72 − L42 differences in the climatological polar night jet structure. The results show that the stratospheric vertical resolution and inclusion of the full middle atmosphere significantly affect tropospheric circulations.

Slowdown of the Walker circulation at solar cycle maximum

Proceedings of the National Academy of Sciences National Academy of Sciences 116 (2019) 7186-7191

S Misios, L Gray, M Knudsen, C Karoff, H Schmidt, J Haigh

The Pacific Walker Circulation (PWC) fluctuates on interannual and multidecadal timescales under the influence of internal variability and external forcings. Here, we provide observational evidence that the 11-y solar cycle (SC) affects the PWC on decadal timescales. We observe a robust reduction of east–west sea-level pressure gradients over the Indo-Pacific Ocean during solar maxima and the following 1–2 y. This reduction is associated with westerly wind anomalies at the surface and throughout the equatorial troposphere in the western/central Pacific paired with an eastward shift of convective precipitation that brings more rainfall to the central Pacific. We show that this is initiated by a thermodynamical response of the global hydrological cycle to surface warming, further amplified by atmosphere–ocean coupling, leading to larger positive ocean temperature anomalies in the equatorial Pacific than expected from simple radiative forcing considerations. The observed solar modulation of the PWC is supported by a set of coupled ocean–atmosphere climate model simulations forced only by SC irradiance variations. We highlight the importance of a muted hydrology mechanism that acts to weaken the PWC. Demonstration of this mechanism acting on the 11-y SC timescale adds confidence in model predictions that the same mechanism also weakens the PWC under increasing greenhouse gas forcing.

Observed and Simulated Teleconnections Between the Stratospheric Quasi-Biennial Oscillation and Northern Hemisphere Winter Atmospheric Circulation

Journal of Geophysical Research: Atmospheres 124 (2019) 1219-1232

MB Andrews, JR Knight, AA Scaife, Y Lu, T Wu, LJ Gray, V Schenzinger

©2019 Crown copyright. This article is published with the permission of the Controller of HMSO and the Queen's Printer for Scotland. The Quasi-Biennial Oscillation (QBO) is the dominant mode of interannual variability in the tropical stratosphere, with easterly and westerly zonal wind regimes alternating over a period of about 28 months. It appears to influence the Northern Hemisphere winter stratospheric polar vortex and atmospheric circulation near the Earth's surface. However, the short observational record makes unequivocal identification of these surface connections challenging. To overcome this, we use a multicentury control simulation of a climate model with a realistic, spontaneously generated QBO to examine teleconnections with extratropical winter surface pressure patterns. Using a 30-hPa index of the QBO, we demonstrate that the observed teleconnection with the Arctic Oscillation (AO) is likely to be real, and a teleconnection with the North Atlantic Oscillation (NAO) is probable, but not certain. Simulated QBO-AO teleconnections are robust, but appear weaker than in observations. Despite this, inconsistency with the observational record cannot be formally demonstrated. To assess the robustness of our results, we use an alternative measure of the QBO, which selects QBO phases with westerly or easterly winds extending over a wider range of altitudes than phases selected by the single-level index. We find increased strength and significance for both the AO and NAO responses, and better reproduction of the observed surface teleconnection patterns. Further, this QBO metric reveals that the simulated AO response is indeed likely to be weaker than observed. We conclude that the QBO can potentially provide another source of skill for Northern Hemisphere winter prediction, if its surface teleconnections can be accurately simulated.

The importance of stratospheric initial conditions for winter North Atlantic Oscillation predictability and implications for the signal‐to‐noise paradox

Quarterly Journal of the Royal Meteorological Society John Wiley and Sons, Ltd. 145 (2018) Part A, 131-146

C O'Reilly, A Weisheimer, T Woollings, L Gray, D Macleod

This study investigates the influence of atmospheric initial conditions on winter seasonal forecasts of the North Atlantic Oscillation (NAO). Hindcast (or reforecast) experiments – which differ only in their initial conditions – are performed over the period 1960–2009, using prescribed sea surface temperature (SST) and sea‐ice boundary conditions. The first experiment (“ERA‐40/Int IC”) is initialized using the ERA‐40 and ERA‐Interim reanalysis datasets, which assimilate upper‐air, satellite and surface observations; the second experiment (“ERA‐20C IC”) is initialized using the ERA‐20C reanalysis dataset, which assimilates only surface observations. The ensemble mean NAO skill is largest in ERA‐40/Int IC (r = 0.54), which is initialized with the superior reanalysis data. Moreover, ERA‐20C IC did not exhibit significantly more NAO hindcast skill (r = 0.38) than in a third experiment, which was initialized with incorrect (shuffled) initial conditions. The ERA‐40/Interim and ERA‐20C initial conditions differ substantially in the tropical stratosphere, where the quasi‐biennial oscillation (QBO) of zonal winds is not present in ERA‐20C. The QBO hindcasts are highly skilful in ERA‐40/Int IC – albeit with a somewhat weaker equatorial zonal wind amplitude in the lower stratosphere – but are incorrect in ERA‐20C IC, indicating that the QBO is responsible for the additional NAO hindcast skill; this is despite the model exhibiting a relatively weak teleconnection between the QBO and NAO. The influence of the QBO is further demonstrated by regressing out the QBO influence from each of the hindcast experiments, after which the difference in NAO hindcast skill between the experiments is negligible. Whilst ERA‐40/Int IC demonstrates a more skilful NAO hindcast, it appears to have a relatively weak predictable signal; this is the so‐called “signal‐to‐noise paradox” identified in previous studies. Diagnostically amplifying the (weak) QBO–NAO teleconnection increases the ensemble‐mean NAO signal with negligible impact on the NAO hindcast skill, after which the signal‐to‐noise problem seemingly disappears.

Preindustrial Control Simulations With HadGEM3-GC3.1 for CMIP6


MB Menary, T Kuhlbrodt, J Ridley, MB Andrews, OB Dimdore-Miles, J Deshayes, R Eade, L Gray, S Ineson, J Mignot, CD Roberts, J Robson, RA Wood, P Xavier

Recent observed changes in the North Atlantic climate system with a focus on 2005-2016

International Journal of Climatology John Wiley & Sons, Inc. 38 (2018) 5050-5076

J Robson, A Archibald, F Cooper, M Christensen, L Grey, NP Holliday, C Macintosh, M McMillan, B Moat, K Carslaw, O Embury, D Feltham, D Grosvenor, S Josey, B King, A Lewis, GD McCarthy, C Merchant, AL New, C O'Reilly, S Osprey, K Read, A Scaife, A Shepherd

Major changes are occurring across the North Atlantic climate system, including in the atmosphere, ocean and cryosphere, and many observed changes are unprecedented in instrumental records. As the changes in the North Atlantic directly affect the climate and air quality of the surrounding continents, it is important to fully understand how and why the changes are taking place, not least to predict how the region will change in the future. To this end, this article characterizes the recent observed changes in the North Atlantic region, especially in the period 2005–2016, across many different aspects of the system including: atmospheric circulation; atmospheric composition; clouds and aerosols; ocean circulation and properties; and the cryosphere. Recent changes include: an increase in the speed of the North Atlantic jet stream in winter; a southward shift in the North Atlantic jet stream in summer, associated with a weakening summer North Atlantic Oscillation; increases in ozone and methane; increases in net absorbed radiation in the mid‐latitude western Atlantic, linked to an increase in the abundance of high level clouds and a reduction in low level clouds; cooling of sea surface temperatures in the North Atlantic subpolar gyre, concomitant with increases in the western subtropical gyre, and a decline in the Atlantic Ocean's overturning circulation; a decline in Atlantic sector Arctic sea ice and rapid melting of the Greenland Ice Sheet. There are many interactions between these changes, but these interactions are poorly understood. This article concludes by highlighting some of the key outstanding questions.

Preconditioning of Arctic Stratospheric Polar Vortex Shift Events

Journal of Climate American Meteorological Society 31 (2018) 5417-5436

J Huang, W Tian, L Gray, J Zhang, Y Li, J Luo, H Tian

This study examines the preconditioning of events in which the Arctic stratospheric polar vortex shifts toward Eurasia (EUR events), North America (NA events), and the Atlantic (ATL events) using composite analysis. An increase in blocking days over northern Europe and a decrease in blocking days over the Bering Strait favor the movement of the vortex toward Eurasia, while the opposite changes in blocking days over those regions favor the movement of the vortex toward North America. An increase in blocking days over the eastern North Atlantic and a decrease in blocking days over the Bering Strait are conducive to movement of the stratospheric polar vortex toward the Atlantic. These anomalous precursor blocking patterns are interpreted in terms of the anomalous zonal wave-1 or wave-2 planetary wave fluxes into the stratosphere that are known to influence the vortex position and strength. In addition, the polar vortex shift events are further classified into events with small and large polar vortex deformation, since the two types of events are likely to have a different impact at the surface. A significant difference in the zonal wave-2 heat flux into the lower stratosphere exists prior to the two types of events and this is linked to anomalous blocking patterns. This study further defines three types of tropospheric blocking events in which the spatial patterns of blocking frequency anomalies are similar to the blocking patterns prior to EUR, NA, and ATL events, respectively, and our reanalysis reveals that the polar vortex is indeed more likely to shift toward Eurasia, North America, and the Atlantic in the presence of the above three defined tropospheric blocking events. These shifts of the polar vortex toward Eurasia, North America, and the Atlantic lead to statistically significant negative height anomalies near the tropopause and corresponding surface cooling anomalies over these three regions.

Surface impacts of the quasi biennial oscillation

Atmospheric Chemistry and Physics European Geosciences Union 18 (2018) 8227-8247

L Gray, JA Anstey, Y Kawatani, H Lu, S Osprey, V Schenzinger

Teleconnections between the Quasi Biennial Oscillation (QBO) and the Northern Hemisphere zonally averaged zonal winds, mean sea level pressure (mslp) and tropical precipitation are explored. The standard approach that defines the QBO using the equatorial zonal winds at a single pressure level is compared with the empirical orthogonal function approach that characterizes the vertical profile of the equatorial winds. Results are interpreted in terms of three potential routes of influence, referred to as the tropical, subtropical and polar routes. A novel technique is introduced to separate responses via the polar route that are associated with the stratospheric polar vortex, from the other two routes. A previously reported mslp response in January, with a pattern that resembles the positive phase of the North Atlantic Oscillation under QBO westerly conditions, is confirmed and found to be primarily associated with a QBO modulation of the stratospheric polar vortex. This mid-winter response is relatively insensitive to the exact height of the maximum QBO westerlies and a maximum positive response occurs with westerlies over a relatively deep range between 10 and 70 hPa. Two additional mslp responses are reported, in early winter (December) and late winter (February/March). In contrast to the January response the early and late winter responses show maximum sensitivity to the QBO winds at  ∼  20 and  ∼  70 hPa respectively, but are relatively insensitive to the QBO winds in between ( ∼  50 hPa). The late winter response is centred over the North Pacific and is associated with QBO influence from the lowermost stratosphere at tropical/subtropical latitudes in the Pacific sector. The early winter response consists of anomalies over both the North Pacific and Europe, but the mechanism for this response is unclear. Increased precipitation occurs over the tropical western Pacific under westerly QBO conditions, particularly during boreal summer, with maximum sensitivity to the QBO winds at 70 hPa. The band of precipitation across the Pacific associated with the Inter-tropical Convergence Zone (ITCZ) shifts southward under QBO westerly conditions. The empirical orthogonal function (EOF)-based analysis suggests that this ITCZ precipitation response may be particularly sensitive to the vertical wind shear in the vicinity of 70 hPa and hence the tropical tropopause temperatures.

Overview of experiment design and comparison of models participating in phase 1 of the SPARC Quasi-Biennial Oscillation initiative (QBOi)

Geoscientific Model Development Copernicus Publications 11 (2018) 1009-1032

N Butchart, J Anstey, K Hamilton, S Osprey, C McLandress, A Bushell, Y Kawatani, Y-H Kim, F Lott, J Scinocca, T Stockdale, M Andrews, O Bellprat, P Braesicke, C Cagnazzo, C-C Chen, H-Y Chun, M Dobrynin, R Garcia, J Garcia-Serrano, L Gray, L Holt, T Kerzenmacher, H Naoe, H Pohlmann

The Stratosphere–troposphere Processes And their Role in Climate (SPARC) Quasi-Biennial Oscillation initiative (QBOi) aims to improve the fidelity of tropical stratospheric variability in general circulation and Earth system models by conducting coordinated numerical experiments and analysis. In the equatorial stratosphere, the QBO is the most conspicuous mode of variability. Five coordinated experiments have therefore been designed to (i) evaluate and compare the verisimilitude of modelled QBOs under present-day conditions, (ii) identify robustness (or alternatively the spread and uncertainty) in the simulated QBO response to commonly imposed changes in model climate forcings (e.g. a doubling of CO2 amounts), and (iii) examine model dependence of QBO predictability. This paper documents these experiments and the recommended output diagnostics. The rationale behind the experimental design and choice of diagnostics is presented. To facilitate scientific interpretation of the results in other planned QBOi studies, consistent descriptions of the models performing each experiment set are given, with those aspects particularly relevant for simulating the QBO tabulated for easy comparison.

Changing response of the North Atlantic/European Winter Climate to the 11-year solar cycle

Environmental Research Letters IOP Publishing 13 (2017) 1-10

H Ma, H Chen, L Gray, L Zhou, X Li, R Wang, S Zhu

Recent studies have presented conflicting results regarding the 11-year solar cycle (SC) influences on winter climate over the North Atlantic/European region. Analyses of only the most recent decades suggest a synchronized North Atlantic Oscillation (NAO)-like response pattern to the SC. Analyses of long-term climate data sets dating back to the late 19th century, however, suggest a mslp response that lags the SC by 2-4 years in the southern node of the NAO (i.e. Azores region). To understand the conflicting nature and cause of these time dependencies in the SC surface response, the present study employs a lead/lag multi-linear regression technique with a sliding window of 44-years over the period 1751-2016. Results confirm previous analyses, in which the average response for the whole time period features a statistically significant 2-4-year lagged mslp response centered over the Azores region. Overall, the lagged nature of Azores mslp response is generally consistent in time, with stronger and statistically significant SC signals tend to appear in the periods when the SC forcing amplitudes are relatively larger. Individual month analysis indicates the consistent lagged response in December-January-February average arises primarily from early winter months (i.e. December and January), which is associated with ocean feedback processes that involve reinforcement by anomalies from the previous winter. Additional analysis suggests that the synchronous NAO-like response in recent decades arises primarily from the late winter month (February), possibly reflecting a result of strong internal noise.

Atlantic Multidecadal Variability and the UK ACSIS Program


RT Sutton, GD McCarthy, J Robson, B Sinha, AT Archibald, LJ Gray

Stratospheric Response to the 11-Yr Solar Cycle: Breaking Planetary Waves, Internal Reflection, and Resonance

JOURNAL OF CLIMATE 30 (2017) 7169-7190

H Lu, LJ Gray, IP White, TJ Bracegirdle