Overview of the Dependence of Atmospheric Tide Amplitudes on the Phases of Natural Tropical Oscillations based on MUAM simulations

Overview of the Dependence of Atmospheric Tide Amplitudes on the Phases of Natural Tropical Oscillations based on MUAM simulations | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Overview of the Dependence of Atmospheric Tide Amplitudes on the Phases of Natural Tropical Oscillations based on MUAM simulations Andrey V. Koval, Kseniia A. Didenko, Tatiana S. Ermakova, Alexey S. Fadeev, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6873106/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The dependence of atmospheric tide amplitudes on the phases of long-period tropical oscillations, specifically the Quasi-Biennial Oscillation (QBO) of zonal wind in the equatorial stratosphere and the El Niño–Southern Oscillation (ENSO), is examined. Numerical simulations of global atmospheric circulation are conducted using the MUAM nonlinear mechanistic atmospheric model under various scenarios incorporating different combinations of QBO/ENSO phases. The structures of migrating diurnal and semidiurnal tides with zonal wave numbers 1 and 2, respectively, as well as non-migrating diurnal and semidiurnal tides with zonal wave numbers 2 and 1, respectively, are calculated. The analysis is focused on the boreal winter season (January - February), the period of peak wave activity for planetary waves (PWs) that are involved in the nonlinear generation of non-migrating tides. The results demonstrate, in particular, that the migrating diurnal tide (DT1) is amplified during the westerly QBO phase (wQBO) and under La Niña conditions. For the semidiurnal migrating tide (SDT2), ENSO effects are found to be more pronounced than those of the QBO. During El Niño, the tide’s amplitude decreases in the equatorial region while increasing to the North and South of it, regardless of the QBO phase. Changes in non-migrating tides differ from those of migrating tides with similar periods, which is attributed to the altered wave activity of the stationary PW with zonal wave number 1 (SPW1). Nonlinear interactions between primary migrating tides and this wave generate non-migrating tides. The effect of strengthening/weakening of non-migrating diurnal tide (DT2) generation for different combinations of QBO/ENSO is demonstrated explicitly by considering the terms responsible for the nonlinear interaction of PW1 and DT1 in the balance equation of perturbed potential enstrophy. The numerical simulations performed under “idealized” conditions, isolating the effects of QBO and ENSO, allowed for the differentiation of the influences of these two oscillations. Such separation is challenging with observational data due to limited time series, which restricts sample size and thereby limits the statistical capacity needed to distinguish between these phenomena having close periods. general atmospheric circulation numerical modeling atmospheric tides planetary waves El Niño–Southern Oscillation Quasi-Biennial Oscillation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Introduction Global atmospheric waves, including solar thermal tides, significantly influence atmospheric dynamics, along with gravity waves playing a crucial role in shaping the thermodynamic regime of the atmosphere at mesospheric and lower thermospheric (MLT) altitudes (Forbes, 1982a , b ; 2008; Hagan et al., 1995 ; 1999 ; Jacobi et al., 1999 ; Pancheva et al., 2002 ; Smith, 2012 ). Solar tides are large-scale oscillations with periods matching a solar day (24 hours) and its harmonics (12, 8, and 6 hours, etc.), generated primarily by the absorption of solar radiation by water vapor in the troposphere, ozone in the stratosphere, and the ionization of oxygen by ultraviolet radiation in the thermosphere/ionosphere (Andrews et al., 1987 ; Xu et al., 2012 ). Due to decreasing atmospheric density and conservation of vertical wave energy flux, tidal amplitudes increase with altitude, peaking in the MLT region before continuing to grow in the thermosphere. In addition to directly transferring momentum to mean flow, tides play a vital role in the nonlinear interactions of planetary waves (PWs), modulating PW signals in the MLT region and thus aiding in PW propagation into the upper thermosphere (e.g., Laštovicka, 2006 ). Natural tropical oscillations such as the El Niño–Southern Oscillation (ENSO), the quasi-biennial oscillation (QBO) of the equatorial zonal wind in the stratosphere, along with solar activity cycles, influence both regional and global circulation, affecting conditions for the generation and propagation of atmospheric waves of various scales (e.g., Baldwin et al., 2001 ; Gan et al., 2017 ; Hitchman et al., 2021 ; Koval et al., 2019 ). These tropical oscillation signals can extend into the thermosphere (e.g., Echer, 2007 ; Koval et al., 2022a; 2024; Wang et al., 2018 ) and reach high latitudes, significantly impacting the stratospheric polar vortex through teleconnections (see also Garfinkel and Hartmann, 2007, Ermakova et al., 2024 , and references therein). The QBO, a key dynamic feature of the equatorial stratosphere, manifests as a periodic shift in zonal wind direction with an average period of about two years, exerting a considerable influence on global atmospheric circulation. During the QBO, the boundary between westerly and easterly winds gradually descends at a rate of approximately 1 km/month (Baldwin et al., 2001 ). A recent comprehensive review of QBO research advances was presented by Anstey et al. ( 2022 ). As Holton and Tan (1980) demonstrated, the QBO affects the width and position of extratropical waveguides, which carry PWs from the troposphere into the upper atmosphere. During the boreal winter, the polar vortex is generally weaker and more disturbed during the easterly QBO phase (eQBO) than during the westerly QBO phase (wQBO) due to increased PW activity. This is also supported by numerical modeling results (Koval et al., 2022b). Traveling along altered waveguides, PWs convey disturbances from the QBO into higher latitudes and upper atmospheric layers, including the thermosphere. In particular, Echer ( 2007 ) registered quasi-biennial oscillations in the ionosphere based in ionosonde data. Wang et al. ( 2018 ) studied QBO signal transmitting from the stratosphere to the thermosphere related to the propagation of atmospheric tides. The ENSO arises from ocean-atmosphere interactions in the tropical Pacific region. Positive temperature anomalies in the eastern or central equatorial Pacific, characteristic of El Niño (the positive ENSO phase), reduce temperature gradients in the ocean's surface layer. Consequently, trade winds weaken, the Southern Oscillation Index turns anomalously positive, and sea levels decrease in the west while rising in the east as the warming develops (e.g., Trenberth, 1997). Changes in extratropical circulation during different types of El Niño events are discussed in Ermakova et al. ( 2022 ). La Niña represents the opposite (negative) phase of the Southern Oscillation, where low pressure develops west of the dateline, and high pressure prevails to the east during periods of abnormally low sea surface temperatures along the equator. As was discussed by Coelho and Goddard ( 2009 ), ENSO is important factor effecting climate and weather anomalies, which influence through teleconnections spans up to the high latitudes and to the upper atmosphere (see also Larkin and Harrison 2005 ; Sanap et al. 2025 ). Significant attention is given to the effects of ENSO on global atmospheric dynamics, particularly at high latitudes (e.g., Ermakova et al., 2024 ; Kolennikova et al., 2021 ; Vyatkin et al., 2024 ; Wang et al., 2017 ). Interactions between the QBO and ENSO can induce substantial changes in winter stratospheric circulation and impact climate conditions in the Northern Hemisphere's troposphere. Therefore, at present, an increasing number of studies are focused on studying the features of the joint influence of the QBO and ENSO on the circulation of the stratosphere and troposphere. For instance, Xuan et al. (2022) investigated the joint effects of QBO and ENSO on the relationship between sea ice extent and Eurasian winter climate through PW activity and the stratospheric polar vortex. They found that mild winters in Europe are typically observed during La Niña + wQBO. Under these conditions, PW propagation from the troposphere to the stratosphere weakens, leading to a strengthened stratospheric polar vortex. This intensification of the polar vortex further contributes to isolating cold air masses within the polar region. Kumar et al. ( 2022 ) explored the combined impact of stratospheric QBO and ENSO on the polar vortex, subtropical westerly jets and wave structures. They also identified a strengthening of the stratospheric polar vortex during wQBO, with evidence suggesting that the influence of the QBO in the stratosphere is more pronounced under La Niña conditions. Using the Coupled Model Intercomparison Project (CMIP-5/6), Wang et al. ( 2024 ) investigated the joint impact of QBO and ENSO on polar stratospheric dynamics. They confirmed established views of a trend toward polar vortex weakening and warming during wQBO and El Niño, and additionally identified linearity in the superposed effects of these tropical oscillations on the winter stratosphere. A number of studies are focused on atmospheric tides and their relationship with natural tropical oscillations (e.g., Forbes et al., 2008 ; Hagan et al., 1999 ). Based on satellite data, Hagan et al. ( 1999 ) demonstrated that QBO-induced changes in the horizontal wind components in the stratosphere can lead to temperature variations of up to 10 K due to the diurnal tide. Forbes et al. ( 2008 ) showed quasi-biennial oscillations in migrating tidal amplitudes of up to ± 10–15%, modulated by the QBO. ENSO also significantly influences tidal structures. For example, Gurubaran et al. ( 2005 ) analyzed long-term radar observations in the MLT region and found that large-scale convective systems forming in the western Pacific in response to El Niño contribute to the excitation of non-migrating tides through latent heat release or water vapor redistribution. Additionally, Pedatella and Liu ( 2012 ) highlighted the significant dependence of the migrating diurnal tide on ENSO phases through numerical experiments conducted with the Whole Atmosphere Community Climate Model (WACCM). Correlation analysis is widely used to isolate the effects of ENSO, QBO, and solar activity on tidal variations (Wu et al., 2024 ). Warner and Oberheide ( 2014 ) dedicated their study to analyzing non-migrating tides during different ENSO phases using satellite data. The particular importance of studying the interaction of ENSO and tides is related to the fact that one of the sources of non-migrating tides is the latent heat release in the tropical troposphere, which depends on the phase of ENSO (e.g., Forbes et al., 1995; Gurubaran et al., 2005 ). Changes in atmospheric tidal amplitudes have also been studied at various stages of Sudden Stratospheric Warmings (SSWs), both using radar data (He et al., 2020 ; Hibbins et al., 2019 , and references therein), as well as through numerical modeling (Limpasuvan et al., 2016 ; Pedatella and Liu, 2013 ) and satellite measurements (Siddiqui et al., 2022 ). These studies highlight the significant variability of atmospheric tides. During recent SSW events, opposite trends were observed in the structure of tides in the mesosphere-lower thermosphere (MLT) region. For example, during the SSW events of 2006 and 2009, an enhancement of the migrating semidiurnal tide was noted (Sridharan et al., 2012 ), which the authors suggest may be associated with changes in stratospheric ozone. Conversely, He et al. ( 2020 ), using radar data, reported a weakening of the migrating semidiurnal tide in the mesosphere during the 2018 SSW. The difficulty of studying the effects of the QBO/ENSO is primarily due to the limited observational record of global atmospheric circulation. For example, in Ermakova et al. ( 2024 ), the MERRA2 reanalysis data in the “satellite” era (post-1980) allowed the identification of only three years for each four QBO/ENSO phase combination for January. Additionally, as discussed in Warner and Oberheide ( 2014 ), QBO and ENSO have similar periodicities, complicating the isolation of direct effects from each, especially in the MLT region, which is characterized by strong variability. Another complication in distinguishing the effects of these tropical oscillations arises from the fact that ENSO can influence the QBO period (Sun et al., 2018 ). This work aims to identify the main relationships between long-term tropical oscillations and the structure of atmospheric tides. Dominating the dynamics of the MLT region, tides transfer momentum and energy between atmospheric layers and, through nonlinear interactions, facilitate the propagation of planetary waves (PWs) from the lower to the upper atmosphere. In particular, being an important link in the dynamic coupling between atmospheric layers, they ensure the transmission of the signal from the QBO/ENSO to the upper atmosphere. However, the question arises: to what extent are they themselves subject to the influence of these oscillations? Our numerical modeling, conducted under "idealized" conditions using the 3D nonlinear Middle and Upper Atmosphere Model (MUAM), allowed us to obtain statistically significant estimates of tidal amplitude changes by isolating the effects of QBO and ENSO. The paper is organized as follows: Section 2 is dedicated to the description of data and methods used, including brief model description, nonlinear interaction theory, approach for assessing statistical significance; Section 3 presents results and their discussion in the context of recent studies; Section 4 contains brief summary and concluding remarks. Methods and Approaches The MUAM Model. To simulate the general atmospheric circulation in different phases of ENSO and QBO, a mechanistic nonlinear Middle and Upper Atmosphere Model (MUAM) is used (Pogoreltsev et al., 2007 ). MUAM has been widely applied to study large-scale wave processes (e.g., Koval et al., 2022a, b, 2024, and references therein). This finite-difference model is based on solving hydrodynamic equations in a spherical coordinate system, with a horizontal grid of 36×64 nodes in latitude and longitude, and 56 vertical levels from the Earth’s surface to about 300 km along a log-isobaric coordinate. To obtain averaged climate distributions for each QBO-ENSO combination, ensembles of 10 model calculations (runs) were computed. The ensemble generation methods in MUAM for producing averaged distributions, model initialization stages, and statistical processing are detailed in Koval ( 2019 ). The study focused on the boreal winter period (January-February), allowing for a detailed examination of non-migrating tides. The main mechanism for generating these tides lies in the nonlinear interactions of migrating tides with quasi-stationary PWs (e.g., Angelats i Coll and Forbes, 2002 ; Hagan and Forbes, 2002 , 2003 ; Hibbins et al., 2007 ), whose amplitudes peak during the winter months, increasing the effectiveness of this mechanism. MUAM accurately reproduces the structure of atmospheric tides and has been used extensively to study various modes of migrating (Geißler et al., 2020 ; Lilienthal et al., 2018 ; Lilienthal and Jacobi, 2019 ) and non-migrating (Suvorova and Pogoreltsev, 2011 ) tides. In MUAM, tide generation is self-consistent, occurring through parameterized solar heating and nonlinear interactions between gravity waves and PWs. The spatial structure of the simulated tides in MUAM aligns well with observations, although amplitudes may be underestimated, as in many other models (Lilienthal and Jacobi, 2019 ). This study focuses on relative changes in tidal amplitudes. ENSO Phases. In MUAM, ENSO phases are taken into account through the parameterization of latent heat release following the method proposed by Ermakova et al. ( 2019 ). Several specialized indices are used to identify ENSO phases. One of them, the Multivariate ENSO Index (MEI), is employed in this study. MEI is based on a set of six primary observable variables in the tropical Pacific Ocean: sea-level pressure, sea surface temperature, air temperature near the surface, zonal and meridional surface winds, and total sky cloudiness (Wolter and Timlin, 2011 ). Years corresponding to El Niño and La Niña phases are selected based on MEI values, and the seasonal average fields of temperature and geopotential height for those years are used as initial conditions in MUAM. Phases of QBO. To define the QBO phase, a specific pressure level is typically selected, such as in the classic work by Holton and Tan (1980), where the zonal flow is considered at the 50 hPa level. Analysis of UK Met Office data reveals (Pogoreltsev et al., 2014 ; 2015 ) that the highest interannual variability of the mean zonal flow occurs around an altitude of 30 km (10 hPa level). Therefore, it was suggested to determine the QBO phase based on the direction of the mean zonal flow at this level. However, this approach introduces ambiguity due to the vertical structure of the QBO and the gradual descent of the oscillation from the upper to the lower stratosphere, which may lead to opposing QBO phase designations depending on the pressure level referenced. Thus, in this study, we use a method not tied to a specific pressure level, examining the vertical evolution of the QBO through an approach proposed by Wallace et al. ( 1993 ) and implemented in previous research (Koval et al., 2022a). This method relies on decomposing observed zonal flow oscillations using empirical orthogonal functions. Employing this approach allowed us to select years corresponding to the easterly and westerly QBO phases, with criteria that align closely with the commonly used Singapore QBO index at 10 hPa (see https://cmr.earthdata.nasa.gov/search/concepts/C1214598833-SCIOPS ). When discussing results and comparing them with other studies, we consider that different studies define the QBO at different levels and adapt these results accordingly to our terminology. In the numerical calculations, QBO is represented in the MUAM by nudging the modeled mean zonal flow in the equatorial stratosphere towards corresponding average distributions from MERRA2 reanalysis data for different QBO phases. Numerical Experiment Setup. MUAM modeling begins with a windless atmosphere based on a set global temperature profile. During the initial 120–129 days, MUAM applies daily averaged solar heating rates. After day 120–129, diurnal variations of heating and PW sources are introduced. From model day 300, seasonal changes in the solar zenith angle are activated, with days 300–390 corresponding to the December–February period. To ensure statistically significant data for analyzing dynamic interactions, MUAM employs ensemble calculations. Ensembles are formed from different model runs, representing distinct phases of vacillations between mean flow and PWs in the middle atmosphere (Holton and Mass, 1976 ). These phases in MUAM are controlled by varying the start date of daily solar heating variations and PW generation between model days 120 and 129 in one-day increments, producing an ensemble of 10 members. Initial and background conditions remain identical across all runs. It is essential to note that monthly mean PW amplitudes, mean flow intensity, and winter stratospheric temperatures can vary substantially across ensemble members. This variability in model calculations is interpreted as interannual one (Pogoreltsev, 2007 ). With MUAM, we examine average "climate" distributions of hydrodynamic fields obtained by ensemble averaging for all four ENSO/QBO combinations. Calculation of Tidal Amplitudes. The hydrodynamic fields from each ensemble member are decomposed into zonal harmonics through Fourier decomposition. Tidal amplitudes and phases are then calculated using a least-squares fitting. To investigate the variation of tidal amplitudes under different QBO/ENSO combinations, the calculated amplitudes are averaged across respective ensembles. To improve statistical significance, tide and PW amplitudes were calculated for the 4 fifteen-day subintervals (for January – February) for each member of ensemble simulations as it was proposed by Koval et al. ( 2019 ). Statistical significance of the changes in the amplitudes was then calculated based on the paired Student’s t-test, applied to 40 pairs of data in each model grid node (10 model nuns within each ensemble × 4 fifteen-days subintervals). The analysis is focused on the following tidal modes: migrating diurnal and semidiurnal tides with zonal wave numbers of 1 and 2, respectively, as well as non-migrating diurnal and semidiurnal tides with zonal wave numbers of 2 and 1, respectively. Tidal amplitude changes are examined as deviations from the mean "climate" data, averaged over all 40 numerical simulations, i.e., across all QBO/ENSO combinations. Interactions of tides with the mean flow and with the stationary PWs. To interpret the interaction between tides and the mean flow and to demonstrate features of tidal propagation in the MLT area, Eliassen-Palm (EP) fluxes were calculated using standard formulas (e.g., Jucker, 2021 ). In this context, EP flux represents momentum and heat flux for each tidal component, providing insights into how these fluxes contribute to atmospheric dynamics and energy distribution in the MLT region. To describe the nonlinear interaction of a migrating tide with the stationary PW leading to the generation of a non-migrating tide, the perturbed potential enstrophy analysis is used. This method was successfully applied in the study of interactions between stationary PWs during the boreal winter and during the development of SSWs (Didenko et al., 2022 ; Smith, 1983 ), between atmospheric migrating tides (Didenko and Pogoreltsev, 2022), and also to demonstrate the effect of generating a 16-day westward traveling PW as a result of the interaction of 4- and 5-day PWs (Didenko et al., 2024 ). These works present formulas for calculating the perturbed potential enstrophy, which is the square of the potential vorticity. In the case of a secondary non-migrating tide (we will consider the example of a diurnal tide, zonal wavenumber m = 2 ), the balance equation of perturbed potential enstrophy is written as follows: where P is the Ertel’s potential vorticity, \(\:\overrightarrow{V}\) is the wind speed vector, S includes terms describing the additional contribution to the momentum equation and the diabatic sources and sinks, and ρ 0 is density. Overbars denote zonal averaging, and primes denote deviations from the zonally averaged values, with the subscripts characterizing the wave type: 2/24 is the diurnal non-migrating tide ( m = 2 ), 1/24 is the diurnal migrating tide ( m = 1 ), and SPW1 is the stationary planetary wave ( m = 1 ). The change in the wave activity of the non-migrating diurnal tide (the term on the left-hand side) is determined by the nonlinear interactions of the diurnal migrating tide with the SPW1 (the first two terms on the right-hand side of Eq. ( 1 )), the divergence and advection of the potential enstrophy flux (the third and fourth terms), the interaction of the non-migrating tide with the mean flux and dissipation (the last two terms on the right-hand side of the equation, respectively). The terms responsible for the nonlinear interactions between the PWs take into account the method of generating secondary PWs, which is described in detail in Pogoreltsev ( 2001 ) and Didenko et al. ( 2024 ). Results and discussion 3.1 Migrating Solar Tides Figure 1 a shows the average "climate" amplitude of the diurnal migrating tide (DT1) in the temperature field, calculated for January-February based on MUAM simulations incorporating all four QBO-ENSO combinations (i.e., based on 40 model simulations). The structure of the diurnal tide is typical for boreal winter, with a peak amplitude near the equator and secondary maxima in the tropical latitudes, where the amplitude in the Southern Hemisphere is greater than in the Northern Hemisphere. In general, as previously mentioned, MUAM accurately reproduces tidal patterns: the amplitude and overall structure of the diurnal and semidiurnal tides can be compared favorably with satellite data (Cen et al., 2022 ; Forbes et al., 2008 ; Jin et al., 2012 ; Manson et al., 1989 ; Singh and Gurubaran, 2017 ; Smith et al., 2012; Sun et al., 2018 ). Changes in tidal amplitudes under different QBO and ENSO phases are shown in Figs. 1 b-e. In the equatorial region, under El Niño + eQBO, the diurnal tide weakens by 10–13% (Fig. 1 b), while under La Niña + eQBO, the weakening is slightly smaller, up to 10% (Fig. 1 d). The most substantial changes, represented by an amplitude increase of up to 25%, are recorded under La Niña + wQBO conditions (Fig. 1 e), whereas under El Niño + wQBO (Fig. 1 c), the amplitude is closest to the mean value shown in Fig. 1 a. In this case, statistically significant increments are minimal and can be negative in the Northern Hemisphere below 100 km and positive in the Southern Hemisphere. Above 100 km in Fig. 1 c, the changes are also weak and vary with latitudes. In summary, Fig. 1 suggests that tidal amplitudes increase under wQBO and La Niña conditions (and, accordingly, weakens under eQBO and El Niño), with Figs. 1 b and 1 e illustrating the combined influence of both oscillations. The enhancement of the diurnal tides under wQBO has been discussed in other studies, such as those based on Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite data (Liu et al., 2024a ; Wu et al., 2024 ) at altitudes around 100 km. Additionally, Forbes et al. ( 2008 ) noted an increase in the diurnal migrating tide during years associated with the wQBO phase. Conversely, tidal changes related to shifts in tropical convection, heating processes, and mean zonal wind changes due to ENSO are more complex to interpret. For example, Gurubaran et al. ( 2005 ) also marked weakening of diurnal tide during peak El Niño phase in 1997-98 using meteor wind radar data. On the other hand, Pedatella and Liu ( 2012 ), based on numerical experiments, indicated a slight increase in the diurnal tide during El Niño, which contradicts our calculations. However, studies by Cen et al. ( 2022 ) and Wu et al. ( 2024 ) report an anti-correlation between diurnal tide amplitude and ENSO, where the cold La Niña phase corresponds to an increase in tide amplitude, aligning with our results. There are two possible reasons for these discrepancies. First, significant tidal variability in the MLT region is driven by multiple factors, including the influence of gravity waves, which actively dissipate in these layers, and solar cyclicity. Second, a discovered time lag between ENSO phase changes and tidal activity fluctuations, reaching up to 5 months (Wu et al., 2024 ), also plays a role. This time lag, presumably due to the response of tropospheric infrared absorption to ENSO, needs to be considered in observational data analysis, while in our experiment, it is inherently absent as the ENSO phase is parameterized within the MUAM model during initialization. As discussed in the following subsection, an additional contribution to the weakening of the tide under La Niña + eQBO (Fig. 1 d) and in the polar thermosphere under El Niño + wQBO (Fig. 1 c) may come from enhanced PW1 wave activity, which promotes the generation of non-migrating diurnal tide DT2 and, accordingly, the redistribution of wave momentum towards the secondary tide. The reverse process of DT1 strengthening, PW1 weakening, and DT2 reduction characterizes La Niña + wQBO (Fig. 1 e). Arrows in Fig. 1 b-e indicate the increments of EP fluxes. It is notable that in the equatorial region, the weakening/strengthening of the diurnal tide is accompanied by a decrease/increase in the upward EP flux, which can be interpreted as a reduction/enhancement of wave activity propagation from lower atmospheric layers. This suggests that changes in the background circulation in the equatorial region are the primary reason for the alteration of tidal structures. Additionally, tidal strengthening is accompanied by meridional EP fluxes converging toward the equator, in the area of tidal maximum, which is particularly noticeable in Fig. 1 e, while weakening, as shown in Figs. 1 b and 1 d, is associated with diverging EP fluxes away from the equator. Figure 2 presents the same values as Fig. 1 , but for the semidiurnal migrating tide (SDT2) with a zonal wave number of m = 2 . Above 90 km, the semidiurnal tide amplitude, similar to the diurnal tide, exhibits three peaks in equatorial and tropical regions. Notably, in the equatorial region, the semidiurnal tide amplitudes in Fig. 2 a are comparable to those of the diurnal tide shown in Fig. 1 a. Outside the equatorial region, the semidiurnal tide amplitudes exceed those of the diurnal tide. Additionally, in the summer (southern) hemisphere, the tide amplitude is greater than in the winter hemisphere. Such characteristics of semidiurnal migrating tide structures have been extensively discussed before (e.g., He et al., 2020 ; Liu et al., 2024b ; Pancheva et al., 2009 ; Pedatella and Liu, 2013 ; Wu et al., 2011 ). The observed changes in the amplitude of the semidiurnal migrating tide (Figs. 2 b-e) exhibit a more complex structure than that of the diurnal tide, with relatively smaller increment values. The influence of ENSO is more apparent than that of the QBO: during the "warm" El Niño phase (Figs. 2 b, 2 c), similar trends are observed across all latitudes except in the 30°-90° S range. This includes a decrease in tidal amplitude in the equatorial region and an increase to the north and south of this area, regardless of the QBO phase. In the "cold" La Niña phase, on the contrary, there is an intensification of the semidiurnal tide in the equatorial thermosphere and a weakening at other latitudes. In Fig. 2 e, there is a region South of 30° S with an intensified tide, which is the opposite of what is observed in Fig. 1 b and appears to be associated with the QBO. A similar effect of an intensified semidiurnal tide during the wQBO phase over Halley, Antarctica, was discussed by Hibbins et al. ( 2007 ) based on radar data. Pancheva et al. ( 2009 ) identified quasi-biennial modulation of the semidiurnal tide, most prominent in the Northern Hemisphere, and attributed it to QBO influence. It was shown that during years with the eQBO phase, the semidiurnal tide intensifies within the 100–120 km range. Similar trends, although in horizontal wind component fields, are discussed by Laskar et al. ( 2016 ) based on radar data. QBO modulation of the semidiurnal tide is also discussed in Forbes et al. ( 2008 ). However, as with Pancheva et al. ( 2009 ), the limited timeframe of satellite observations does not allow for confidently distinguishing QBO effects from other large-scale processes, including ENSO. The impact of ENSO on tropospheric tidal sources was recently reviewed by Li et al. ( 2020 ), who demonstrated in particular a weakening of SDT2 sources during El Niño, which may be related to our observed trends in the weakening of SDT2 in the equatorial region during El Niño. 3.2 Non-migrating Tides The amplitude of the diurnal non-migrating tide with zonal wave number 2 (DT2) and its changes under various QBO/ENSO combinations are shown in Fig. 3 . The structure of this tide resembles that of the migrating diurnal tide shown in Fig. 1 , which can be explained by the primary mechanism of its generation through nonlinear interactions between the diurnal tide and the stationary PW with zonal wave number 1 (Angelats i Coll and Forbes, 2002 ; Hagan and Forbes, 2002 , 2003 ). A second significant mechanism behind the formation of non-migrating tides involves zonally asymmetric thermal forcing, driven by surface topography, geographically variable heat sources, and changes in solar heating with longitude (Pancheva et al., 2020 ). The most substantial differences in the behavior between DT1 and DT2 are observed during El Niño + wQBO and La Niña + eQBO (Figs. 1 c, d and 3 c, d). The non-migrating tide intensifies during El Niño + wQBO in Fig. 3 c, while the migrating tide does not experience such a strengthening in Fig. 1 c. On the contrary, during La Niña + eQBO the non-migrating tide is maximally weakened in Fig. 3 d. This phenomenon can be explained by differences in stationary planetary wave activity with zonal wavenumber m = 1 (SPW1) during dese combinations. The behavior of SPW1 under different QBO/ENSO combinations is illustrated in Fig. 4 . The SPW structure for all QBO/ENSO combinations (Fig. 4 a) is typical for boreal winter conditions: a maximum in the stratosphere in the Northern Hemisphere, accompanied by strong upward EP fluxes. Starting from the mesosphere, SPW propagates upward and southward along the direction of EP fluxes. During wQBO, the equatorial wind profile creates conditions favorable for SPW1 propagation in low latitudes, while during eQBO, the SPW1 waveguide shifts to higher latitudes, weakening the stratospheric polar vortex and in many cases contributing to the formation of SSW (Garfinkel et al., 2012 ; Holton and Tan, 1980; Koval et al., 2022a, b). This behavior under different QBO phases and the same cold ENSO phase is clearly shown in Figs. 4 d and 4 e. It can be assumed that the weakened SPW1 wave activity during La Niña + eQBO leads to a reduction in the nonlinear interaction between DT1 and SPW1, resulting in a weaker DT2 generation in Fig. 3 d. Conversely, during El Niño + wQBO, increased SPW1 (Fig. 4 c) enhances the process of DT2 generation in Fig. 3 c. In particular, if we consider the region of the maximum diurnal tides (near-equatorial region, altitude range from 90 to 120 km), the amplitude of SPW1 increases under the El Niño + wQBO phase in Fig. 4 c and decreases under the La Niña + eQBO phase in Fig. 4 d. A similar intensification of the non-migrating tide with increased SPW1 forcing was discussed by Pedatella and Liu ( 2013 ) in a study on the effects of global atmospheric waves and tides on ionospheric disturbances during SSW. To check our hypothesis about the enhancement of DT2 generation (Fig. 3 c) under El Niño + wQBO due to the enhancement of the nonlinear interaction between DT1 and SPW1 (and the weakening of the interaction under La Niña + eQBO), we calculated the terms in the balance equation of the perturbed potential enstrophy for DT2 using formula (1) and concentrated on considering the terms responsible for the interaction between DT1 and SPW1 (the first two terms on the right-hand side of Eq. ( 1 )) as well as on the changes in DT2 wave activity (terms on the left-hand side of Eq. ( 1 )). Since we are interested in the absolute contribution of these terms to the equation, in Fig. 5 we plotted the 10-day running mean of the absolute values of these terms averaged over two ensembles of model runs (i.e., 10 runs for El Niño + wQBO and for La Niña + eQBO). As can be seen from Fig. 5 , the expected strengthening of the interaction of DT1 and SPW1 under El Niño + wQBO (red dashed curve) relative to La Niña + eQBO (blue dashed curve) is observed for most of the considered 2-month time interval. To be more precise, we see that the "DT1-SPW1" interaction in the first case is stronger from the beginning of January to February 20. The average values ​​of the interaction for two months are demonstrated by the corresponding horizontal lines. In the period from the beginning of January to February 20, an increase in the wave activity of DT2 under El Niño + wQBO is also observed (solid curves in Fig. 5 ). Our calculations showed that the difference in wave activity and, as a consequence, in the amplitude of DT2 during this period is determined precisely by the difference in the interaction of the primary tide and SPW1, while the other terms in Eq. ( 1 ) are close in magnitude or compensate each other. Thus, we explicitly demonstrate the generation of DT2: its strengthening under El Niño + wQBO leads to a redistribution of wave momentum and, consequently, to a weakening of the primary diurnal tide DT1. In the opposite case, under La Niña + eQBO, a weakening of the generation of the secondary tide occurs, which is accompanied by a decrease in its amplitude in Fig. 3 e and an increase in the amplitude of the primary tide (Fig. 1 e). Figures 3 b and 3 e demonstrate weaker changes in DT2 during El Niño + eQBO and La Niña + wQBO, than the observed above ones, and in Fig. 3 b, statistical significance is reduced due to high variability. The amplitudes of the SPW1 for these combinations in the region of maximum wave activity of the DT1 are close to zero, which is reflected in the weakening of nonlinear interactions. Here, however, one can distinguish the region of amplification of DT2 northward from the equator in Fig. 3 e, which corresponds to the amplification of SPW1 in Fig. 4 e. The spatial variability of atmospheric tides, which reduces the statistical significance of the observed increments, has been widely discussed. For example, in Pancheva et al. ( 2020 ), tidal structures were analyzed using radar data from two stations in Norway located relatively close to each other. It was shown that even a small distance between the stations significantly affects the recorded tidal oscillations. In Fig. 6 a, the amplitude of the semidiurnal non-migrating tide ( SDT1) with m = 1 is shown. Similar to the diurnal migrating and non-migrating tides (as seen in Figs. 1 and 3 ), the structure of the semidiurnal tide in Figs. 2 and 6 is largely comparable due to the primary generation mechanism of SDT1 — the nonlinear interaction between the primary semidiurnal migrating tide SDT2 and SPW1, as discussed above (see also Hibbins et al., 2007 ). The amplitudes of non-migrating tides are smaller than those of migrating ones. The dependence on SPW1 wave activity, as discussed earlier, is also characteristic of SDT1 structure. This is especially evident in the La Niña phase (Figs. 6 d, e): a decrease in wave activity during wQBO (Fig. 4 e) leads to a reduction in SDT1 across all latitudes, while an increase in PW1 during eQBO (Fig. 4 d) enhances the non-migrating SDT1 (Fig. 6 d) and reduces the migrating SDT2 (Fig. 2 d). In the El Niño + eQBO phase (Fig. 6 b), the overall structure of the tide reflects that of the migrating tide in Fig. 2 b, which can be explained by the lack of significant PW1 amplitude increments above 100 km (except for a minor increase in the mid-latitudes of the Northern Hemisphere). Pedatella and Forbes (2010), in their study of total electron content variations, suggested that the interaction between the migrating semidiurnal tide and strong PW activity during SSW events contributes to the enhancement of the non-migrating semidiurnal tide during such events. This is due to the fact that, in the initial phase of an SSW, an increase in polar temperature and a decrease in zonal wind may coincide with a strengthening of PW activity (namely, SPW1 – in case of vortex-displacement SSWs; and SPW2 – in case of vortex-split SSWs, e.g., Charlton and Polvani, 2007 ), which in turn intensifies the nonlinear interactions between SPW1 and the primary migrating tide. The enhancement of the semidiurnal non-migrating tide in the lower Northern Hemisphere thermosphere during SSW events was also demonstrated by Hibbins et al. ( 2019 ). An interesting feature of SDT1 is the absence of the previously noted correlation between tidal amplitude increments and the direction of EP fluxes. Across all panels in Fig. 6 , in the southern thermosphere, an increase in SDT1 is accompanied by descending EP fluxes, whereas a decrease is associated with ascending fluxes, indicating no direct relationship between the upward propagation of the tide and changes in its structure, in other words, indicating the in-situ generation of a secondary non-migrating tide. Conclusion This study is dedicated to examining the dependence of atmospheric tides on the phases of long-period tropical oscillations: the quasi-biennial oscillation (QBO) of zonal wind in the equatorial stratosphere and the El Niño–Southern Oscillation (ENSO). To achieve this, a series of numerical simulations were performed, modeling global atmospheric circulation under various QBO/ENSO combinations using the nonlinear mechanistic Middle and Upper Atmosphere Model (MUAM). The study focuses on migrating diurnal and semidiurnal tides with zonal wave numbers 1 and 2, respectively, as well as non-migrating diurnal and semidiurnal tides with zonal wave numbers 2 and 1, respectively. The analysis was conducted for boreal winter (January–February), the season of maximum planetary wave activity, which plays a key role in the generation of non-migrating tides. The main findings of this research can be summarized as follows: The migrating diurnal tide (DT1) tends to strengthen in the thermosphere during wQBO and La Niña phases. A reduction or increase in DT1 is accompanied by a corresponding decrease or increase in the upward EP flux, which can be interpreted as a modulation of wave activity propagation from lower atmospheric layers. For the semidiurnal migrating tide (SDT2), the impact of ENSO is more pronounced than that of QBO. During the El Niño phase, there is a decrease in tide amplitude in the equatorial region and an increase to the South and North of this area, regardless of the QBO phase. The effect is generally opposite during La Niña. An additional contribution to the change in the amplitude of migrating tides is made by the increase in the wave activity of the SPW1, which helps to strengthen the process of generating secondary non-migrating tides and, accordingly, the transfer of momentum to the secondary oscillation. Increased spatial variability of non-migrating atmospheric tides, caused by the variability of primary migrating tides and SPWs, leads to reduced statistical significance of observed tide amplitude changes. The non-migrating diurnal tide (DT2), in contrast to the migrating DT1, intensifies during El Niño + wQBO. This is explained by the change in the wave activity of SPW1, the nonlinear interaction of DT1 with which generates DT2. In particular, the strengthening of SPW1 during El Niño + wQBO in the area of primary DT1 maximum strengthens the generation of DT2 in this region and vice versa, the weakening of SPW1 weakens the generation of DT2 during La Niña + eQBO. The effect of strengthening/weakening the generation of DT2 under different combinations of QBO/ENSO is demonstrated explicitly when considering the terms responsible for the interaction of SPW1 and DT1 in the balance equation of perturbed potential enstrophy. The dependence on SPW1 wave activity is also characteristic of the structure of the non-migrating semidiurnal tide (SDT1). This is well illustrated during the La Niña phase: reduced wave activity during wQBO leads to a decrease in SDT1 across all latitudes, while increased PW1 during eQBO enhances non-migrating SDT1 and weakens migrating SDT2. Comparison of the calculated tide amplitudes with observational data, including various QBO–ENSO combinations, confirms that MUAM accurately reproduces the examined tidal oscillations. The importance of studying the interaction of tides with long-period atmospheric oscillations lies in the fact that, in addition to directly exchanging momentum with the mean flow, tides engage in nonlinear interactions with PWs, serving as a crucial factor in the formation of large-scale dynamics in the mesosphere and lower thermosphere. In particular, the tides are modulated by the PWs according to the mechanism proposed by Laštovička et al. (2006) and thus facilitate the passage of PWs through critical levels in the lower thermosphere, penetrating into the upper atmosphere. A brief overview of this mechanism is presented also in Koval et al. (2022). It can be assumed that the enhancement of DT1 during the wQBO should contribute to more efficient regeneration of SPW1, and, accordingly, to larger amplitudes of SPW1 in the thermosphere. It is precisely this, the enhancement of SPW1 during the wQBO up to altitudes of 300 km, that was demonstrated in the work of Koval et al. (2022), based on model simulations. Therefore, further studies of the regeneration of secondary/tertiary PWs, capable of significantly affecting the dynamics of the upper atmosphere, including from the point of view of space exploration, seem promising. Our numerical modeling conducted under "idealized" conditions — isolating the effects of QBO and ENSO — allowed us to obtain statistically significant estimates of tidal amplitude changes and to separate the influence of both oscillations. This separation is difficult to achieve through observational data analysis due to limited time series and, consequently, insufficient sample size required for the necessary statistics to distinguish between these closely related phenomena, which are capable of mutually influencing each other. Declarations Funding : Development of the scenarios and performing numerical simulations under different QBO/ENSO combinations were supported by the Russian Science Foundation: grant #25-47-00122; processing data, calculating tidal structures and EP fluxes, statistical analysis were supported by Saint Petersburg State University (research grant #124032000025-1). Competing interests. The authors declare no competing interests. Availability of data and materials. All rights to the MUAM computer code belong to the Russian State Hydrometeorological University (RSHU). To gain access to computer codes and acquire the right to use them, permission from the Rector of the RSHU in needed. The authors will provide the necessary assistance in obtaining the appropriate permission. All datasets presented in the article are archived in https://disk.yandex.ru/d/Eu1WTOvUxAgk8A Zenodo ( all materials will be archived to Zenodo after revision ). All graphs in this study were generated using the Grid Analysis and Display System (GrADS), a free software developed by NASA's Advanced Information Systems Research Program. Authors' contributions. All authors made valuable contributions to data analysis, visualization of the results, writing and editing the text. A.V. Koval: funding acquisition, conceptualization, processing and interpretation of modeling results; K.A. Didenko: numerical modeling, nonlinear interactions; T.S. Ermakova: statistical processing; A.S. Fadeev and A.V. Sokolov: visualization and discussion of results. References Angelats i Coll, M., Forbes, J.M., 2002. Nonlinear interactions in the upper atmosphere: the s=1 and s=3 nonmigrating semidiurnal tides. J. 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A., Fröhlich, K., Jacobi, Ch. Planetary waves in coupling the lower and upper atmosphere // J. Atmos. Solar-Terr. Phys. 69, 2083−2101, 2007. https://doi.org/10.1016/j.jastp.2007.05.014 Pogoreltsev, A. I., Savenkova, E. N., Aniskina, O. G., Ermakova T. S., Chen, W., Wei, K., 2015. Interannual and intraseasonal variability of stratospheric dynamics and stratosphere–troposphere coupling during northern winter // J. Atmos. Solar-Terr. Phys. 136, 137-200. Sanap, S.D., Priya, P., Chowdary, J.S. et al. On the dynamics of ENSO linked contrasting heat wave patterns over the Indian region. Clim Dyn 63, 183 (2025). https://doi.org/10.1007/s00382-025-07662-3 Siddiqui, T.A., Chau, J.L., Stolle, C., Yamazaki, Y. Migrating solar diurnal tidal variability during Northern and Southern Hemisphere Sudden Stratospheric Warmings // Earth, Planets and Space, 2022, 74:101 https://doi.org/10.1186/s40623-022-01661-y Singh, D., and S. Gurubaran (2017) Variability of diurnal tide in the MLTregion over Tirunelveli (8.7°N), India:Consistency between ground- andspace-based observations, J. Geophys.Res. Atmos., 122, 2696–2713,doi:10.1002/2016JD025910 Smith, A.K. (1983) Observation of wave-wave interactions in the stratosphere. J Atmos Sci 40:2484–2493 Smith, A.K. (2012) Global Dynamics of the MLT. Surv Geophys, 33:1177–1230. DOI 10.1007/s10712-012-9196-9 Sridharan, S., Sathishkumar, S., & Gurubaran, S. (2012). Variabilities of mesospheric tides during sudden stratospheric warming events of 2006 and 2009 and their relationship with ozone and water vapour. Journal of Atmospheric and Solar-Terrestrial Physics, 78-79, 108–115. https://doi.org/10.1016/j.jastp.2011.03.013 Sun, Y.Y., Liu, H., Miyoshi, Y., Liu, L., Chang, L.C. (2018) El Niño–Southern Oscillation effect on quasi-biennial oscillations of temperature diurnal tides in the mesosphere and lower thermosphere // Earth, Planets and Space, 70:85 https://doi.org/10.1186/s40623-018-0832-6 Suvorova, E. V., and Pogoreltsev, A. I., 2011. Modeling of nonmigrating tides in the middle atmosphere // Geomagmetizm and Aeronomy. 51(1), 105-115. Trenberth. K. E. The Definition of El Niño. Bulletin of the American Meteorological Society, 1997, Volume 78, Issue 12, pp. 2771–2778; DOI:10.1175/1520-0477(1997)0782.0.CO;2. Vyatkin, A.N., Zorkaltseva, O.S., Mordvinov, V.I. (2024) Influence of EL-NIÑO on Parameters of the Middle and Upper Atmosphere Over Eastern Siberia According to Reanalysis and Model Data in Winter. Solar-Terrestrial Physics, 10(1), 40–48. DOI: 10.12737/stp-101202406 Wallace, J. M., R. L. Panetta, and J. Estberg, 1993: Representation of the equatorial stratospheric quasi-biennial oscillation in EOF phase space. J. Atmos. Sci., 50, 1751–1762. Wang, J. C., Tsai-Lin, R., Chang, L. C., Wu, Q., Lin, C. H., Yue, J. Modeling study of the ionospheric responses to the quasi-biennial oscillations of the sun and stratosphere. J. Atmos. Solar Terr. Phys. 171, 119–130 (2018) Wang, C., Deser, C., Yu, JY., DiNezio, P., Clement, A. El Niño and Southern Oscillation (ENSO): A Review. Coral Reefs of the Eastern Tropical Pacific, 2017, vol 8, pp. 85–106; DOI: 10.1007/978-94-017-7499-4_4. Wang, H., Rao, J., Guo, D., Liu, Y., Lu, Y (2024) A revisit of the linearity in the combined effect of ENSO and QBO on the stratosphere: model evidence from CMIP5/6 // Climate Dynamics DOI: 10.1007/s00382-024-07430-9 Warner, K., and J. Oberheide (2014), Nonmigrating tidal heating and MLTtidal wind variability due to the ElNiño–Southern Oscillation, J. Geo-phys. Res. Atmos., 119, 1249–1265,doi:10.1002/2013JD020407. Wolter, K., & Timlin, M. S. (2011). El Niño/Southern Oscillation behaviour since 1871 as diagnosed in an extended multivariate ENSO index (MEI.ext). International Journal of Climatology, 31(7), 1074–1087. https://doi.org/10.1002/joc.2336 Wu, Q., Ortland, D.A., Solomon, S.C., Skinner, W.R., Niciejewski, R.J. (2011) Global distribution, seasonal, and inter-annual variations of mesospheric semidiurnal tide observed by TIMED TIDI. Journal of Atmospheric and Solar-Terrestrial Physics, V. 73, Issues 17–18, P. 2482-2502 Wu, C., Ridley, A. J., & Cullens, C. Y. (2024). Seasonal dependency of the solar cycle, QBO, and ENSO effects on the interannual variability of the wind DW1 in the MLT region. Journal of Geophysical Research: Space Physics, 129, e2024JA032472. https://doi.org/10.1029/2024JA032472 Xu, J., Smith, A. K., Jiang, G., Yuan, W., and Gao, H.: Features of the seasonal variation of the semidiurnal, terdiurnal and 6-h components of ozone heating evaluated from Aura/MLS observations, Ann. Geophys., 30, 259–281, https://doi.org/10.5194/angeo-30-259-2012, 2012. Xuan Ma; L. Wang; D. Smith; L. Hermanson; R. Eade; N. Dunstone; S. Hardiman and J. Zhang. ENSO and QBO modulation of the relationship between Arctic sea ice loss and Eurasian winter climate. Environmental Research Letters, 2022, Volume 17, Number 12. DOI 10.1088/1748-9326/aca4e9. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6873106","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":471620312,"identity":"c1f5ce80-3d30-4d4c-9566-d557bdbb33f5","order_by":0,"name":"Andrey V. Koval","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAwUlEQVRIiWNgGAWjYJACxgYgwcfewMBMmhY2ngMka5FIIFILfwOPAeOMisPybJLPnz0ubGPINzhAQIvEAaCWDWcOG7ZJ55gbz2xjsNxASAvDAbYExodtaYxALWzSvG0MBgRtkYdqsW+TPP6MOC0GB5gPMG5ss0lsk2AwI06L4WHmAwdnnLFJbuMB+mXGOQkDSUJa5I43Nj7sqZCw7Wc//uxxQZmNAR8hLaC4gKlhA2IJQupRARtpykfBKBgFo2DEAACJ9Tk9kNz1iAAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0001-6446-1808","institution":"Saint Petersburg University: Sankt-peterburgskij gosudarstvennyj universitet","correspondingAuthor":true,"prefix":"","firstName":"Andrey","middleName":"V.","lastName":"Koval","suffix":""},{"id":471620313,"identity":"c9cd3113-3590-48c2-a74e-bf0c3468afb9","order_by":1,"name":"Kseniia A. Didenko","email":"","orcid":"","institution":"Pushkov Institute of Terrestial-Magnetism Ionosphere and Radiowave Propagation RAS: FGBUN Institut zemnogo magnetizma ionosfery i rasprostranenia radiovoln imeni N V Puskova Rossijskoj akademii nauk","correspondingAuthor":false,"prefix":"","firstName":"Kseniia","middleName":"A.","lastName":"Didenko","suffix":""},{"id":471620314,"identity":"79e60239-fea6-45fa-bdcb-a1b310e29ced","order_by":2,"name":"Tatiana S. Ermakova","email":"","orcid":"","institution":"Russian State Hydrometeorological University: Rossijskij gosudarstvennyj gidrometeorologiceskij universitet","correspondingAuthor":false,"prefix":"","firstName":"Tatiana","middleName":"S.","lastName":"Ermakova","suffix":""},{"id":471620315,"identity":"dc4a7fcb-0f12-4068-87f0-52d83f9f7ad5","order_by":3,"name":"Alexey S. Fadeev","email":"","orcid":"","institution":"Saint Petersburg State University: Sankt-peterburgskij gosudarstvennyj universitet","correspondingAuthor":false,"prefix":"","firstName":"Alexey","middleName":"S.","lastName":"Fadeev","suffix":""},{"id":471620316,"identity":"6f799753-079c-48f2-8f70-07b0ff558901","order_by":4,"name":"Elena N. Savenkova","email":"","orcid":"","institution":"Russian State Hydrometeorological University: Rossijskij gosudarstvennyj gidrometeorologiceskij universitet","correspondingAuthor":false,"prefix":"","firstName":"Elena","middleName":"N.","lastName":"Savenkova","suffix":""},{"id":471620317,"identity":"a00331bf-0678-4d13-bf04-01537c2ecc87","order_by":5,"name":"Arseniy Sokolov","email":"","orcid":"","institution":"Saint Petersburg State University: Sankt-peterburgskij gosudarstvennyj universitet","correspondingAuthor":false,"prefix":"","firstName":"Arseniy","middleName":"","lastName":"Sokolov","suffix":""}],"badges":[],"createdAt":"2025-06-11 15:02:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6873106/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6873106/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84786046,"identity":"76561dfe-f8e7-4936-9d41-cd55bb55edcc","added_by":"auto","created_at":"2025-06-17 10:27:56","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":806329,"visible":true,"origin":"","legend":"\u003cp\u003eAltitude-latitude distribution of temperature variation amplitude (K) caused by the diurnal migrating tide (m=1), averaged across all QBO/ENSO combinations (a); tidal amplitude changes under El Niño + eQBO, El Niño + wQBO, La Niña + eQBO, and La Niña + wQBO phases (b-e, respectively). Statistically significant (95%) increments in figures (b-e) are marked by the gray background. Arrows indicate corresponding EP fluxes and their increments (m²/s², with the vertical component scaled by 100).\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/e67f833cb252357cd982c56f.png"},{"id":84786047,"identity":"06e53be8-a5d7-4616-8e7c-85aa1f2a246c","added_by":"auto","created_at":"2025-06-17 10:27:56","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":734533,"visible":true,"origin":"","legend":"\u003cp\u003eAltitude-latitude distribution of temperature variation amplitude (K) induced by the semidiurnal migrating tide (m=2), averaged across all QBO/ENSO combinations (a); tidal amplitude changes under El Niño + eQBO, El Niño + wQBO, La Niña + eQBO, and La Niña + wQBO phases (b-e, respectively). Statistically significant (95%) increments in figures (b-e) are marked by the gray background. Arrows indicate corresponding EP fluxes and their increments (m²/s², with the vertical component scaled by 100).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/45e5a2fdebffdbe54f67bdaa.png"},{"id":84786052,"identity":"31feac4e-f8de-4548-9151-6a4c15ad95ad","added_by":"auto","created_at":"2025-06-17 10:27:56","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":717119,"visible":true,"origin":"","legend":"\u003cp\u003eAltitude-latitude distribution of temperature variation amplitudes (K) caused by the diurnal non-migrating tide (m=2), averaged over all QBO/ENSO combinations (a); tidal amplitude changes during El Niño + eQBO, El Niño + wQBO, La Niña + eQBO, and La Niña + wQBO (b-e, respectively). Statistically significant (95%) increments in figures (b-e) are marked by the gray background. Arrows indicate corresponding EP fluxes and their increments (m²/s², with the vertical component multiplied by 100).\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/c2a6fffb74fec26fbacf5767.png"},{"id":84786674,"identity":"6b717eb4-3ead-42e7-8f72-db1f6f4fab37","added_by":"auto","created_at":"2025-06-17 10:35:56","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":754735,"visible":true,"origin":"","legend":"\u003cp\u003eAltitude-latitude distributions of the amplitude of geopotential height variations for the SPW with m=1 (gpm), averaged over all QBO/ENSO combinations (a); tidal amplitude changes during El Niño + eQBO, El Niño + wQBO, La Niña + eQBO, and La Niña + wQBO (b-e, respectively). Statistically significant (95%) increments in figures (b-e) are marked by the gray background. Arrows indicate corresponding EP fluxes and their increments (m²/s², with the vertical component multiplied by 100).\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/86823efeccbe3ca947e36277.png"},{"id":84786053,"identity":"9ac9e1d5-4ef3-4097-b1a3-3baaa2ca8842","added_by":"auto","created_at":"2025-06-17 10:27:56","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":220133,"visible":true,"origin":"","legend":"\u003cp\u003eThe change in the wave activity of the non-migrating diurnal tide (solid lines); the terms responsible for nonlinear DT1-SPW1 interactions (dashed lines) in the balance equation of the perturbed potential enstrophy at 7.5°S-2.5°N, 90-120 km during January-February. 10-days running mean values. Red / blue curves correspond to El Niño + wQBO / La Niña + eQBO combinations, reaspectively. Horizonlal lines show time-averaged values. Units are 10\u003csup\u003e12 \u003c/sup\u003e(kg∙m\u003csup\u003e–3\u003c/sup\u003e)\u003csup\u003e2\u003c/sup\u003e∙PVU\u003csup\u003e2\u003c/sup\u003e/day, where 1PVU= 10\u003csup\u003e–6\u003c/sup\u003eK∙m\u003csup\u003e2\u003c/sup\u003e∙kg\u003csup\u003e–1\u003c/sup\u003e∙s\u003csup\u003e–1\u003c/sup\u003e\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/944cead76d2b76ed37d2e573.png"},{"id":84786054,"identity":"75d9340a-c19b-47d3-9ff9-c67916f4d2ba","added_by":"auto","created_at":"2025-06-17 10:27:56","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":763873,"visible":true,"origin":"","legend":"\u003cp\u003eAltitude-latitude distribution of temperature variation amplitudes (K) caused by the semidiurnal non-migrating tide (m=1), averaged over all QBO/ENSO combinations (a); tidal amplitude changes during El Niño + eQBO, El Niño + wQBO, La Niña + eQBO, and La Niña + wQBO (b-e, respectively). Statistically significant (95%) increments in figures (b-e) are marked by the gray background. Arrows indicate corresponding EP fluxes and their increments (m²/s², with the vertical component multiplied by 100).\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/82dc6318230cbefa55451029.png"},{"id":86816143,"identity":"29af2af7-f0b0-49b6-bce0-157b8f086cab","added_by":"auto","created_at":"2025-07-16 00:37:51","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":4703016,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6873106/v1/a6c2548d-4782-4dfb-b876-9de5979124cf.pdf"}],"financialInterests":"","formattedTitle":"Overview of the Dependence of Atmospheric Tide Amplitudes on the Phases of Natural Tropical Oscillations based on MUAM simulations","fulltext":[{"header":"Introduction","content":"\u003cp\u003eGlobal atmospheric waves, including solar thermal tides, significantly influence atmospheric dynamics, along with gravity waves playing a crucial role in shaping the thermodynamic regime of the atmosphere at mesospheric and lower thermospheric (MLT) altitudes (Forbes, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1982a\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003eb\u003c/span\u003e; 2008; Hagan et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Jacobi et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Pancheva et al., \u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Smith, \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Solar tides are large-scale oscillations with periods matching a solar day (24 hours) and its harmonics (12, 8, and 6 hours, etc.), generated primarily by the absorption of solar radiation by water vapor in the troposphere, ozone in the stratosphere, and the ionization of oxygen by ultraviolet radiation in the thermosphere/ionosphere (Andrews et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Xu et al., \u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Due to decreasing atmospheric density and conservation of vertical wave energy flux, tidal amplitudes increase with altitude, peaking in the MLT region before continuing to grow in the thermosphere. In addition to directly transferring momentum to mean flow, tides play a vital role in the nonlinear interactions of planetary waves (PWs), modulating PW signals in the MLT region and thus aiding in PW propagation into the upper thermosphere (e.g., Laštovicka, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eNatural tropical oscillations such as the El Ni\u0026ntilde;o\u0026ndash;Southern Oscillation (ENSO), the quasi-biennial oscillation (QBO) of the equatorial zonal wind in the stratosphere, along with solar activity cycles, influence both regional and global circulation, affecting conditions for the generation and propagation of atmospheric waves of various scales (e.g., Baldwin et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2001\u003c/span\u003e; Gan et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Hitchman et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Koval et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). These tropical oscillation signals can extend into the thermosphere (e.g., Echer, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Koval et al., 2022a; 2024; Wang et al., \u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) and reach high latitudes, significantly impacting the stratospheric polar vortex through teleconnections (see also Garfinkel and Hartmann, 2007, Ermakova et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e, and references therein).\u003c/p\u003e \u003cp\u003eThe QBO, a key dynamic feature of the equatorial stratosphere, manifests as a periodic shift in zonal wind direction with an average period of about two years, exerting a considerable influence on global atmospheric circulation. During the QBO, the boundary between westerly and easterly winds gradually descends at a rate of approximately 1 km/month (Baldwin et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2001\u003c/span\u003e). A recent comprehensive review of QBO research advances was presented by Anstey et al. (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). As Holton and Tan (1980) demonstrated, the QBO affects the width and position of extratropical waveguides, which carry PWs from the troposphere into the upper atmosphere. During the boreal winter, the polar vortex is generally weaker and more disturbed during the easterly QBO phase (eQBO) than during the westerly QBO phase (wQBO) due to increased PW activity. This is also supported by numerical modeling results (Koval et al., 2022b). Traveling along altered waveguides, PWs convey disturbances from the QBO into higher latitudes and upper atmospheric layers, including the thermosphere. In particular, Echer (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) registered quasi-biennial oscillations in the ionosphere based in ionosonde data. Wang et al. (\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) studied QBO signal transmitting from the stratosphere to the thermosphere related to the propagation of atmospheric tides.\u003c/p\u003e \u003cp\u003eThe ENSO arises from ocean-atmosphere interactions in the tropical Pacific region. Positive temperature anomalies in the eastern or central equatorial Pacific, characteristic of El Ni\u0026ntilde;o (the positive ENSO phase), reduce temperature gradients in the ocean's surface layer. Consequently, trade winds weaken, the Southern Oscillation Index turns anomalously positive, and sea levels decrease in the west while rising in the east as the warming develops (e.g., Trenberth, 1997). Changes in extratropical circulation during different types of El Ni\u0026ntilde;o events are discussed in Ermakova et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). La Ni\u0026ntilde;a represents the opposite (negative) phase of the Southern Oscillation, where low pressure develops west of the dateline, and high pressure prevails to the east during periods of abnormally low sea surface temperatures along the equator. As was discussed by Coelho and Goddard (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2009\u003c/span\u003e), ENSO is important factor effecting climate and weather anomalies, which influence through teleconnections spans up to the high latitudes and to the upper atmosphere (see also Larkin and Harrison \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Sanap et al. \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). Significant attention is given to the effects of ENSO on global atmospheric dynamics, particularly at high latitudes (e.g., Ermakova et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Kolennikova et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Vyatkin et al., \u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Wang et al., \u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eInteractions between the QBO and ENSO can induce substantial changes in winter stratospheric circulation and impact climate conditions in the Northern Hemisphere's troposphere. Therefore, at present, an increasing number of studies are focused on studying the features of the joint influence of the QBO and ENSO on the circulation of the stratosphere and troposphere. For instance, Xuan et al. (2022) investigated the joint effects of QBO and ENSO on the relationship between sea ice extent and Eurasian winter climate through PW activity and the stratospheric polar vortex. They found that mild winters in Europe are typically observed during La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;wQBO. Under these conditions, PW propagation from the troposphere to the stratosphere weakens, leading to a strengthened stratospheric polar vortex. This intensification of the polar vortex further contributes to isolating cold air masses within the polar region. Kumar et al. (\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) explored the combined impact of stratospheric QBO and ENSO on the polar vortex, subtropical westerly jets and wave structures. They also identified a strengthening of the stratospheric polar vortex during wQBO, with evidence suggesting that the influence of the QBO in the stratosphere is more pronounced under La Ni\u0026ntilde;a conditions. Using the Coupled Model Intercomparison Project (CMIP-5/6), Wang et al. (\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) investigated the joint impact of QBO and ENSO on polar stratospheric dynamics. They confirmed established views of a trend toward polar vortex weakening and warming during wQBO and El Ni\u0026ntilde;o, and additionally identified linearity in the superposed effects of these tropical oscillations on the winter stratosphere.\u003c/p\u003e \u003cp\u003eA number of studies are focused on atmospheric tides and their relationship with natural tropical oscillations (e.g., Forbes et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Hagan et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). Based on satellite data, Hagan et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) demonstrated that QBO-induced changes in the horizontal wind components in the stratosphere can lead to temperature variations of up to 10 K due to the diurnal tide. Forbes et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) showed quasi-biennial oscillations in migrating tidal amplitudes of up to \u0026plusmn;\u0026thinsp;10\u0026ndash;15%, modulated by the QBO. ENSO also significantly influences tidal structures. For example, Gurubaran et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) analyzed long-term radar observations in the MLT region and found that large-scale convective systems forming in the western Pacific in response to El Ni\u0026ntilde;o contribute to the excitation of non-migrating tides through latent heat release or water vapor redistribution. Additionally, Pedatella and Liu (\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) highlighted the significant dependence of the migrating diurnal tide on ENSO phases through numerical experiments conducted with the Whole Atmosphere Community Climate Model (WACCM). Correlation analysis is widely used to isolate the effects of ENSO, QBO, and solar activity on tidal variations (Wu et al., \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Warner and Oberheide (\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) dedicated their study to analyzing non-migrating tides during different ENSO phases using satellite data. The particular importance of studying the interaction of ENSO and tides is related to the fact that one of the sources of non-migrating tides is the latent heat release in the tropical troposphere, which depends on the phase of ENSO (e.g., Forbes et al., 1995; Gurubaran et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2005\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eChanges in atmospheric tidal amplitudes have also been studied at various stages of Sudden Stratospheric Warmings (SSWs), both using radar data (He et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Hibbins et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e, and references therein), as well as through numerical modeling (Limpasuvan et al., \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Pedatella and Liu, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) and satellite measurements (Siddiqui et al., \u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). These studies highlight the significant variability of atmospheric tides. During recent SSW events, opposite trends were observed in the structure of tides in the mesosphere-lower thermosphere (MLT) region. For example, during the SSW events of 2006 and 2009, an enhancement of the migrating semidiurnal tide was noted (Sridharan et al., \u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), which the authors suggest may be associated with changes in stratospheric ozone. Conversely, He et al. (\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), using radar data, reported a weakening of the migrating semidiurnal tide in the mesosphere during the 2018 SSW.\u003c/p\u003e \u003cp\u003eThe difficulty of studying the effects of the QBO/ENSO is primarily due to the limited observational record of global atmospheric circulation. For example, in Ermakova et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), the MERRA2 reanalysis data in the \u0026ldquo;satellite\u0026rdquo; era (post-1980) allowed the identification of only three years for each four QBO/ENSO phase combination for January. Additionally, as discussed in Warner and Oberheide (\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), QBO and ENSO have similar periodicities, complicating the isolation of direct effects from each, especially in the MLT region, which is characterized by strong variability. Another complication in distinguishing the effects of these tropical oscillations arises from the fact that ENSO can influence the QBO period (Sun et al., \u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThis work aims to identify the main relationships between long-term tropical oscillations and the structure of atmospheric tides. Dominating the dynamics of the MLT region, tides transfer momentum and energy between atmospheric layers and, through nonlinear interactions, facilitate the propagation of planetary waves (PWs) from the lower to the upper atmosphere. In particular, being an important link in the dynamic coupling between atmospheric layers, they ensure the transmission of the signal from the QBO/ENSO to the upper atmosphere. However, the question arises: to what extent are they themselves subject to the influence of these oscillations? Our numerical modeling, conducted under \"idealized\" conditions using the 3D nonlinear Middle and Upper Atmosphere Model (MUAM), allowed us to obtain statistically significant estimates of tidal amplitude changes by isolating the effects of QBO and ENSO. The paper is organized as follows: Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e is dedicated to the description of data and methods used, including brief model description, nonlinear interaction theory, approach for assessing statistical significance; Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e presents results and their discussion in the context of recent studies; Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e4\u003c/span\u003e contains brief summary and concluding remarks.\u003c/p\u003e"},{"header":"Methods and Approaches","content":"\u003cp\u003e\u003cstrong\u003eThe MUAM Model.\u003c/strong\u003e To simulate the general atmospheric circulation in different phases of ENSO and QBO, a mechanistic nonlinear Middle and Upper Atmosphere Model (MUAM) is used (Pogoreltsev et al., \u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e). MUAM has been widely applied to study large-scale wave processes (e.g., Koval et al., 2022a, b, 2024, and references therein). This finite-difference model is based on solving hydrodynamic equations in a spherical coordinate system, with a horizontal grid of 36×64 nodes in latitude and longitude, and 56 vertical levels from the Earth’s surface to about 300 km along a log-isobaric coordinate. To obtain averaged climate distributions for each QBO-ENSO combination, ensembles of 10 model calculations (runs) were computed. The ensemble generation methods in MUAM for producing averaged distributions, model initialization stages, and statistical processing are detailed in Koval (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). The study focused on the boreal winter period (January-February), allowing for a detailed examination of non-migrating tides. The main mechanism for generating these tides lies in the nonlinear interactions of migrating tides with quasi-stationary PWs (e.g., Angelats i Coll and Forbes, \u003cspan class=\"CitationRef\"\u003e2002\u003c/span\u003e; Hagan and Forbes, \u003cspan class=\"CitationRef\"\u003e2002\u003c/span\u003e, \u003cspan class=\"CitationRef\"\u003e2003\u003c/span\u003e; Hibbins et al., \u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e), whose amplitudes peak during the winter months, increasing the effectiveness of this mechanism. MUAM accurately reproduces the structure of atmospheric tides and has been used extensively to study various modes of migrating (Geißler et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Lilienthal et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e; Lilienthal and Jacobi, \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e) and non-migrating (Suvorova and Pogoreltsev, \u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e) tides. In MUAM, tide generation is self-consistent, occurring through parameterized solar heating and nonlinear interactions between gravity waves and PWs. The spatial structure of the simulated tides in MUAM aligns well with observations, although amplitudes may be underestimated, as in many other models (Lilienthal and Jacobi, \u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). This study focuses on relative changes in tidal amplitudes.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eENSO Phases.\u003c/strong\u003e In MUAM, ENSO phases are taken into account through the parameterization of latent heat release following the method proposed by Ermakova et al. (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). Several specialized indices are used to identify ENSO phases. One of them, the Multivariate ENSO Index (MEI), is employed in this study. MEI is based on a set of six primary observable variables in the tropical Pacific Ocean: sea-level pressure, sea surface temperature, air temperature near the surface, zonal and meridional surface winds, and total sky cloudiness (Wolter and Timlin, \u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e). Years corresponding to El Niño and La Niña phases are selected based on MEI values, and the seasonal average fields of temperature and geopotential height for those years are used as initial conditions in MUAM.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePhases of QBO.\u003c/strong\u003e To define the QBO phase, a specific pressure level is typically selected, such as in the classic work by Holton and Tan (1980), where the zonal flow is considered at the 50 hPa level. Analysis of UK Met Office data reveals (Pogoreltsev et al., \u003cspan class=\"CitationRef\"\u003e2014\u003c/span\u003e; \u003cspan class=\"CitationRef\"\u003e2015\u003c/span\u003e) that the highest interannual variability of the mean zonal flow occurs around an altitude of 30 km (10 hPa level). Therefore, it was suggested to determine the QBO phase based on the direction of the mean zonal flow at this level. However, this approach introduces ambiguity due to the vertical structure of the QBO and the gradual descent of the oscillation from the upper to the lower stratosphere, which may lead to opposing QBO phase designations depending on the pressure level referenced. Thus, in this study, we use a method not tied to a specific pressure level, examining the vertical evolution of the QBO through an approach proposed by Wallace et al. (\u003cspan class=\"CitationRef\"\u003e1993\u003c/span\u003e) and implemented in previous research (Koval et al., 2022a). This method relies on decomposing observed zonal flow oscillations using empirical orthogonal functions. Employing this approach allowed us to select years corresponding to the easterly and westerly QBO phases, with criteria that align closely with the commonly used Singapore QBO index at 10 hPa (see \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://cmr.earthdata.nasa.gov/search/concepts/C1214598833-SCIOPS\u003c/span\u003e\u003c/span\u003e). When discussing results and comparing them with other studies, we consider that different studies define the QBO at different levels and adapt these results accordingly to our terminology. In the numerical calculations, QBO is represented in the MUAM by nudging the modeled mean zonal flow in the equatorial stratosphere towards corresponding average distributions from MERRA2 reanalysis data for different QBO phases.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eNumerical Experiment Setup.\u003c/strong\u003e MUAM modeling begins with a windless atmosphere based on a set global temperature profile. During the initial 120–129 days, MUAM applies daily averaged solar heating rates. After day 120–129, diurnal variations of heating and PW sources are introduced. From model day 300, seasonal changes in the solar zenith angle are activated, with days 300–390 corresponding to the December–February period. To ensure statistically significant data for analyzing dynamic interactions, MUAM employs ensemble calculations. Ensembles are formed from different model runs, representing distinct phases of vacillations between mean flow and PWs in the middle atmosphere (Holton and Mass, \u003cspan class=\"CitationRef\"\u003e1976\u003c/span\u003e). These phases in MUAM are controlled by varying the start date of daily solar heating variations and PW generation between model days 120 and 129 in one-day increments, producing an ensemble of 10 members. Initial and background conditions remain identical across all runs. It is essential to note that monthly mean PW amplitudes, mean flow intensity, and winter stratospheric temperatures can vary substantially across ensemble members. This variability in model calculations is interpreted as interannual one (Pogoreltsev, \u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e). With MUAM, we examine average \"climate\" distributions of hydrodynamic fields obtained by ensemble averaging for all four ENSO/QBO combinations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCalculation of Tidal Amplitudes.\u003c/strong\u003e The hydrodynamic fields from each ensemble member are decomposed into zonal harmonics through Fourier decomposition. Tidal amplitudes and phases are then calculated using a least-squares fitting. To investigate the variation of tidal amplitudes under different QBO/ENSO combinations, the calculated amplitudes are averaged across respective ensembles. To improve statistical significance, tide and PW amplitudes were calculated for the 4 fifteen-day subintervals (for January – February) for each member of ensemble simulations as it was proposed by Koval et al. (\u003cspan class=\"CitationRef\"\u003e2019\u003c/span\u003e). Statistical significance of the changes in the amplitudes was then calculated based on the paired Student’s t-test, applied to 40 pairs of data in each model grid node (10 model nuns within each ensemble × 4 fifteen-days subintervals). The analysis is focused on the following tidal modes: migrating diurnal and semidiurnal tides with zonal wave numbers of 1 and 2, respectively, as well as non-migrating diurnal and semidiurnal tides with zonal wave numbers of 2 and 1, respectively. Tidal amplitude changes are examined as deviations from the mean \"climate\" data, averaged over all 40 numerical simulations, i.e., across all QBO/ENSO combinations.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eInteractions of tides with the mean flow and with the stationary PWs.\u003c/strong\u003e To interpret the interaction between tides and the mean flow and to demonstrate features of tidal propagation in the MLT area, Eliassen-Palm (EP) fluxes were calculated using standard formulas (e.g., Jucker, \u003cspan class=\"CitationRef\"\u003e2021\u003c/span\u003e). In this context, EP flux represents momentum and heat flux for each tidal component, providing insights into how these fluxes contribute to atmospheric dynamics and energy distribution in the MLT region.\u003c/p\u003e\n\u003cp\u003eTo describe the nonlinear interaction of a migrating tide with the stationary PW leading to the generation of a non-migrating tide, the perturbed potential enstrophy analysis is used. This method was successfully applied in the study of interactions between stationary PWs during the boreal winter and during the development of SSWs (Didenko et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Smith, \u003cspan class=\"CitationRef\"\u003e1983\u003c/span\u003e), between atmospheric migrating tides (Didenko and Pogoreltsev, 2022), and also to demonstrate the effect of generating a 16-day westward traveling PW as a result of the interaction of 4- and 5-day PWs (Didenko et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e). These works present formulas for calculating the perturbed potential enstrophy, which is the square of the potential vorticity. In the case of a secondary non-migrating tide (we will consider the example of a diurnal tide, zonal wavenumber \u003cem\u003em = 2\u003c/em\u003e), the balance equation of perturbed potential enstrophy is written as follows:\u003c/p\u003e\n\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\n \u003cdiv class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\u003cimg 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\"\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cp\u003ewhere \u003cem\u003eP\u003c/em\u003e is the Ertel’s potential vorticity, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\overrightarrow{V}\\)\u003c/span\u003e\u003c/span\u003e is the wind speed vector, \u003cem\u003eS\u003c/em\u003e includes terms describing the additional contribution to the momentum equation and the diabatic sources and sinks, and \u003cem\u003eρ\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is density. Overbars denote zonal averaging, and primes denote deviations from the zonally averaged values, with the subscripts characterizing the wave type: \u003cem\u003e2/24\u003c/em\u003e is the diurnal non-migrating tide (\u003cem\u003em = 2\u003c/em\u003e), \u003cem\u003e1/24\u003c/em\u003e is the diurnal migrating tide (\u003cem\u003em = 1\u003c/em\u003e), and SPW1 is the stationary planetary wave (\u003cem\u003em = 1\u003c/em\u003e). The change in the wave activity of the non-migrating diurnal tide (the term on the left-hand side) is determined by the nonlinear interactions of the diurnal migrating tide with the SPW1 (the first two terms on the right-hand side of Eq.\u0026nbsp;(\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e)), the divergence and advection of the potential enstrophy flux (the third and fourth terms), the interaction of the non-migrating tide with the mean flux and dissipation (the last two terms on the right-hand side of the equation, respectively). The terms responsible for the nonlinear interactions between the PWs take into account the method of generating secondary PWs, which is described in detail in Pogoreltsev (\u003cspan class=\"CitationRef\"\u003e2001\u003c/span\u003e) and Didenko et al. (\u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e"},{"header":"Results and discussion","content":"\u003ch2\u003e3.1 Migrating Solar Tides\u003c/h2\u003e\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea shows the average \"climate\" amplitude of the \u003cstrong\u003ediurnal migrating tide\u003c/strong\u003e (DT1) in the temperature field, calculated for January-February based on MUAM simulations incorporating all four QBO-ENSO combinations (i.e., based on 40 model simulations). The structure of the diurnal tide is typical for boreal winter, with a peak amplitude near the equator and secondary maxima in the tropical latitudes, where the amplitude in the Southern Hemisphere is greater than in the Northern Hemisphere. In general, as previously mentioned, MUAM accurately reproduces tidal patterns: the amplitude and overall structure of the diurnal and semidiurnal tides can be compared favorably with satellite data (Cen et al., \u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e; Forbes et al., \u003cspan class=\"CitationRef\"\u003e2008\u003c/span\u003e; Jin et al., \u003cspan class=\"CitationRef\"\u003e2012\u003c/span\u003e; Manson et al., \u003cspan class=\"CitationRef\"\u003e1989\u003c/span\u003e; Singh and Gurubaran, \u003cspan class=\"CitationRef\"\u003e2017\u003c/span\u003e; Smith et al., 2012; Sun et al., \u003cspan class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eChanges in tidal amplitudes under different QBO and ENSO phases are shown in Figs. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb-e. In the equatorial region, under El Niño + eQBO, the diurnal tide weakens by 10–13% (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb), while under La Niña + eQBO, the weakening is slightly smaller, up to 10% (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed). The most substantial changes, represented by an amplitude increase of up to 25%, are recorded under La Niña + wQBO conditions (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee), whereas under El Niño + wQBO (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec), the amplitude is closest to the mean value shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea. In this case, statistically significant increments are minimal and can be negative in the Northern Hemisphere below 100 km and positive in the Southern Hemisphere. Above 100 km in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec, the changes are also weak and vary with latitudes. In summary, Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e suggests that tidal amplitudes increase under wQBO and La Niña conditions (and, accordingly, weakens under eQBO and El Niño), with Figs. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb and \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee illustrating the combined influence of both oscillations. The enhancement of the diurnal tides under wQBO has been discussed in other studies, such as those based on Thermosphere-Ionosphere-Mesosphere Energetics and Dynamics (TIMED) satellite data (Liu et al., \u003cspan class=\"CitationRef\"\u003e2024a\u003c/span\u003e; Wu et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e) at altitudes around 100 km. Additionally, Forbes et al. (\u003cspan class=\"CitationRef\"\u003e2008\u003c/span\u003e) noted an increase in the diurnal migrating tide during years associated with the wQBO phase.\u003c/p\u003e\u003cp\u003eConversely, tidal changes related to shifts in tropical convection, heating processes, and mean zonal wind changes due to ENSO are more complex to interpret. For example, Gurubaran et al. (\u003cspan class=\"CitationRef\"\u003e2005\u003c/span\u003e) also marked weakening of diurnal tide during peak El Niño phase in 1997-98 using meteor wind radar data. On the other hand, Pedatella and Liu (\u003cspan class=\"CitationRef\"\u003e2012\u003c/span\u003e), based on numerical experiments, indicated a slight increase in the diurnal tide during El Niño, which contradicts our calculations. However, studies by Cen et al. (\u003cspan class=\"CitationRef\"\u003e2022\u003c/span\u003e) and Wu et al. (\u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e) report an anti-correlation between diurnal tide amplitude and ENSO, where the cold La Niña phase corresponds to an increase in tide amplitude, aligning with our results. There are two possible reasons for these discrepancies. First, significant tidal variability in the MLT region is driven by multiple factors, including the influence of gravity waves, which actively dissipate in these layers, and solar cyclicity. Second, a discovered time lag between ENSO phase changes and tidal activity fluctuations, reaching up to 5 months (Wu et al., \u003cspan class=\"CitationRef\"\u003e2024\u003c/span\u003e), also plays a role. This time lag, presumably due to the response of tropospheric infrared absorption to ENSO, needs to be considered in observational data analysis, while in our experiment, it is inherently absent as the ENSO phase is parameterized within the MUAM model during initialization.\u003c/p\u003e\u003cp\u003eAs discussed in the following subsection, an additional contribution to the weakening of the tide under La Niña + eQBO (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed) and in the polar thermosphere under El Niño + wQBO (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec) may come from enhanced PW1 wave activity, which promotes the generation of non-migrating diurnal tide DT2 and, accordingly, the redistribution of wave momentum towards the secondary tide. The reverse process of DT1 strengthening, PW1 weakening, and DT2 reduction characterizes La Niña + wQBO (Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee).\u003c/p\u003e\u003cp\u003eArrows in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb-e indicate the increments of EP fluxes. It is notable that in the equatorial region, the weakening/strengthening of the diurnal tide is accompanied by a decrease/increase in the upward EP flux, which can be interpreted as a reduction/enhancement of wave activity propagation from lower atmospheric layers. This suggests that changes in the background circulation in the equatorial region are the primary reason for the alteration of tidal structures. Additionally, tidal strengthening is accompanied by meridional EP fluxes converging toward the equator, in the area of tidal maximum, which is particularly noticeable in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee, while weakening, as shown in Figs. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb and \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed, is associated with diverging EP fluxes away from the equator.\u003c/p\u003e\u003cp\u003eFigure \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003e presents the same values as Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003e, but for the \u003cstrong\u003esemidiurnal migrating tide\u003c/strong\u003e (SDT2) with a zonal wave number of \u003cem\u003em = 2\u003c/em\u003e. Above 90 km, the semidiurnal tide amplitude, similar to the diurnal tide, exhibits three peaks in equatorial and tropical regions. Notably, in the equatorial region, the semidiurnal tide amplitudes in Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea are comparable to those of the diurnal tide shown in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea. Outside the equatorial region, the semidiurnal tide amplitudes exceed those of the diurnal tide. Additionally, in the summer (southern) hemisphere, the tide amplitude is greater than in the winter hemisphere. Such characteristics of semidiurnal migrating tide structures have been extensively discussed before (e.g., He et al., \u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e; Liu et al., \u003cspan class=\"CitationRef\"\u003e2024b\u003c/span\u003e; Pancheva et al., \u003cspan class=\"CitationRef\"\u003e2009\u003c/span\u003e; Pedatella and Liu, \u003cspan class=\"CitationRef\"\u003e2013\u003c/span\u003e; Wu et al., \u003cspan class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe observed changes in the amplitude of the semidiurnal migrating tide (Figs. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb-e) exhibit a more complex structure than that of the diurnal tide, with relatively smaller increment values. The influence of ENSO is more apparent than that of the QBO: during the \"warm\" El Niño phase (Figs. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb, \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec), similar trends are observed across all latitudes except in the 30°-90° S range. This includes a decrease in tidal amplitude in the equatorial region and an increase to the north and south of this area, regardless of the QBO phase. In the \"cold\" La Niña phase, on the contrary, there is an intensification of the semidiurnal tide in the equatorial thermosphere and a weakening at other latitudes. In Fig. \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee, there is a region South of 30° S with an intensified tide, which is the opposite of what is observed in Fig. \u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb and appears to be associated with the QBO. A similar effect of an intensified semidiurnal tide during the wQBO phase over Halley, Antarctica, was discussed by Hibbins et al. (\u003cspan class=\"CitationRef\"\u003e2007\u003c/span\u003e) based on radar data. Pancheva et al. (\u003cspan class=\"CitationRef\"\u003e2009\u003c/span\u003e) identified quasi-biennial modulation of the semidiurnal tide, most prominent in the Northern Hemisphere, and attributed it to QBO influence. It was shown that during years with the eQBO phase, the semidiurnal tide intensifies within the 100–120 km range. Similar trends, although in horizontal wind component fields, are discussed by Laskar et al. (\u003cspan class=\"CitationRef\"\u003e2016\u003c/span\u003e) based on radar data. QBO modulation of the semidiurnal tide is also discussed in Forbes et al. (\u003cspan class=\"CitationRef\"\u003e2008\u003c/span\u003e). However, as with Pancheva et al. (\u003cspan class=\"CitationRef\"\u003e2009\u003c/span\u003e), the limited timeframe of satellite observations does not allow for confidently distinguishing QBO effects from other large-scale processes, including ENSO. The impact of ENSO on tropospheric tidal sources was recently reviewed by Li et al. (\u003cspan class=\"CitationRef\"\u003e2020\u003c/span\u003e), who demonstrated in particular a weakening of SDT2 sources during El Niño, which may be related to our observed trends in the weakening of SDT2 in the equatorial region during El Niño.\u003c/p\u003e\n\u003ch3\u003e3.2 Non-migrating Tides\u003c/h3\u003e\n\u003cp\u003eThe amplitude of the \u003cb\u003ediurnal non-migrating tide\u003c/b\u003e with zonal wave number 2 (DT2) and its changes under various QBO/ENSO combinations are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The structure of this tide resembles that of the migrating diurnal tide shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, which can be explained by the primary mechanism of its generation through nonlinear interactions between the diurnal tide and the stationary PW with zonal wave number 1 (Angelats i Coll and Forbes, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2002\u003c/span\u003e; Hagan and Forbes, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2002\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). A second significant mechanism behind the formation of non-migrating tides involves zonally asymmetric thermal forcing, driven by surface topography, geographically variable heat sources, and changes in solar heating with longitude (Pancheva et al., \u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe most substantial differences in the behavior between DT1 and DT2 are observed during El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO and La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec, d and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec, d). The non-migrating tide intensifies during El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec, while the migrating tide does not experience such a strengthening in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ec. On the contrary, during La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO the non-migrating tide is maximally weakened in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed. This phenomenon can be explained by differences in stationary planetary wave activity with zonal wavenumber \u003cem\u003em\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e (SPW1) during dese combinations. The behavior of SPW1 under different QBO/ENSO combinations is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. The SPW structure for all QBO/ENSO combinations (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea) is typical for boreal winter conditions: a maximum in the stratosphere in the Northern Hemisphere, accompanied by strong upward EP fluxes. Starting from the mesosphere, SPW propagates upward and southward along the direction of EP fluxes. During wQBO, the equatorial wind profile creates conditions favorable for SPW1 propagation in low latitudes, while during eQBO, the SPW1 waveguide shifts to higher latitudes, weakening the stratospheric polar vortex and in many cases contributing to the formation of SSW (Garfinkel et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Holton and Tan, 1980; Koval et al., 2022a, b). This behavior under different QBO phases and the same cold ENSO phase is clearly shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed and \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee.\u003c/p\u003e \u003cp\u003eIt can be assumed that the weakened SPW1 wave activity during La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO leads to a reduction in the nonlinear interaction between DT1 and SPW1, resulting in a weaker DT2 generation in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ed. Conversely, during El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO, increased SPW1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec) enhances the process of DT2 generation in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec. In particular, if we consider the region of the maximum diurnal tides (near-equatorial region, altitude range from 90 to 120 km), the amplitude of SPW1 increases under the El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO phase in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec and decreases under the La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO phase in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed. A similar intensification of the non-migrating tide with increased SPW1 forcing was discussed by Pedatella and Liu (\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) in a study on the effects of global atmospheric waves and tides on ionospheric disturbances during SSW.\u003c/p\u003e \u003cp\u003eTo check our hypothesis about the enhancement of DT2 generation (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec) under El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO due to the enhancement of the nonlinear interaction between DT1 and SPW1 (and the weakening of the interaction under La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO), we calculated the terms in the balance equation of the perturbed potential enstrophy for DT2 using formula (1) and concentrated on considering the terms responsible for the interaction between DT1 and SPW1 (the first two terms on the right-hand side of Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)) as well as on the changes in DT2 wave activity (terms on the left-hand side of Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e)). Since we are interested in the absolute contribution of these terms to the equation, in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e we plotted the 10-day running mean of the absolute values of these terms averaged over two ensembles of model runs (i.e., 10 runs for El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO and for La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO). As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the expected strengthening of the interaction of DT1 and SPW1 under El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO (red dashed curve) relative to La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO (blue dashed curve) is observed for most of the considered 2-month time interval. To be more precise, we see that the \"DT1-SPW1\" interaction in the first case is stronger from the beginning of January to February 20. The average values ​​of the interaction for two months are demonstrated by the corresponding horizontal lines. In the period from the beginning of January to February 20, an increase in the wave activity of DT2 under El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO is also observed (solid curves in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Our calculations showed that the difference in wave activity and, as a consequence, in the amplitude of DT2 during this period is determined precisely by the difference in the interaction of the primary tide and SPW1, while the other terms in Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) are close in magnitude or compensate each other. Thus, we explicitly demonstrate the generation of DT2: its strengthening under El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO leads to a redistribution of wave momentum and, consequently, to a weakening of the primary diurnal tide DT1. In the opposite case, under La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO, a weakening of the generation of the secondary tide occurs, which is accompanied by a decrease in its amplitude in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee and an increase in the amplitude of the primary tide (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ee).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigures\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee demonstrate weaker changes in DT2 during El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;eQBO and La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;wQBO, than the observed above ones, and in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb, statistical significance is reduced due to high variability. The amplitudes of the SPW1 for these combinations in the region of maximum wave activity of the DT1 are close to zero, which is reflected in the weakening of nonlinear interactions. Here, however, one can distinguish the region of amplification of DT2 northward from the equator in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ee, which corresponds to the amplification of SPW1 in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee. The spatial variability of atmospheric tides, which reduces the statistical significance of the observed increments, has been widely discussed. For example, in Pancheva et al. (\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), tidal structures were analyzed using radar data from two stations in Norway located relatively close to each other. It was shown that even a small distance between the stations significantly affects the recorded tidal oscillations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ea, the amplitude of the \u003cb\u003esemidiurnal non-migrating tide (\u003c/b\u003eSDT1) with \u003cem\u003em\u0026thinsp;=\u0026thinsp;1\u003c/em\u003e is shown. Similar to the diurnal migrating and non-migrating tides (as seen in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), the structure of the semidiurnal tide in Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e is largely comparable due to the primary generation mechanism of SDT1 \u0026mdash; the nonlinear interaction between the primary semidiurnal migrating tide SDT2 and SPW1, as discussed above (see also Hibbins et al., \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). The amplitudes of non-migrating tides are smaller than those of migrating ones. The dependence on SPW1 wave activity, as discussed earlier, is also characteristic of SDT1 structure. This is especially evident in the La Ni\u0026ntilde;a phase (Figs.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed, e): a decrease in wave activity during wQBO (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ee) leads to a reduction in SDT1 across all latitudes, while an increase in PW1 during eQBO (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed) enhances the non-migrating SDT1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003ed) and reduces the migrating SDT2 (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed). In the El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;eQBO phase (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003eb), the overall structure of the tide reflects that of the migrating tide in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb, which can be explained by the lack of significant PW1 amplitude increments above 100 km (except for a minor increase in the mid-latitudes of the Northern Hemisphere). Pedatella and Forbes (2010), in their study of total electron content variations, suggested that the interaction between the migrating semidiurnal tide and strong PW activity during SSW events contributes to the enhancement of the non-migrating semidiurnal tide during such events. This is due to the fact that, in the initial phase of an SSW, an increase in polar temperature and a decrease in zonal wind may coincide with a strengthening of PW activity (namely, SPW1 \u0026ndash; in case of vortex-displacement SSWs; and SPW2 \u0026ndash; in case of vortex-split SSWs, e.g., Charlton and Polvani, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2007\u003c/span\u003e), which in turn intensifies the nonlinear interactions between SPW1 and the primary migrating tide. The enhancement of the semidiurnal non-migrating tide in the lower Northern Hemisphere thermosphere during SSW events was also demonstrated by Hibbins et al. (\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAn interesting feature of SDT1 is the absence of the previously noted correlation between tidal amplitude increments and the direction of EP fluxes. Across all panels in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, in the southern thermosphere, an increase in SDT1 is accompanied by descending EP fluxes, whereas a decrease is associated with ascending fluxes, indicating no direct relationship between the upward propagation of the tide and changes in its structure, in other words, indicating the in-situ generation of a secondary non-migrating tide.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThis study is dedicated to examining the dependence of atmospheric tides on the phases of long-period tropical oscillations: the quasi-biennial oscillation (QBO) of zonal wind in the equatorial stratosphere and the El Ni\u0026ntilde;o\u0026ndash;Southern Oscillation (ENSO). To achieve this, a series of numerical simulations were performed, modeling global atmospheric circulation under various QBO/ENSO combinations using the nonlinear mechanistic Middle and Upper Atmosphere Model (MUAM). The study focuses on migrating diurnal and semidiurnal tides with zonal wave numbers 1 and 2, respectively, as well as non-migrating diurnal and semidiurnal tides with zonal wave numbers 2 and 1, respectively. The analysis was conducted for boreal winter (January\u0026ndash;February), the season of maximum planetary wave activity, which plays a key role in the generation of non-migrating tides.\u003c/p\u003e \u003cp\u003eThe main findings of this research can be summarized as follows:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe migrating diurnal tide (DT1) tends to strengthen in the thermosphere during wQBO and La Ni\u0026ntilde;a phases. A reduction or increase in DT1 is accompanied by a corresponding decrease or increase in the upward EP flux, which can be interpreted as a modulation of wave activity propagation from lower atmospheric layers.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eFor the semidiurnal migrating tide (SDT2), the impact of ENSO is more pronounced than that of QBO. During the El Ni\u0026ntilde;o phase, there is a decrease in tide amplitude in the equatorial region and an increase to the South and North of this area, regardless of the QBO phase. The effect is generally opposite during La Ni\u0026ntilde;a.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAn additional contribution to the change in the amplitude of migrating tides is made by the increase in the wave activity of the SPW1, which helps to strengthen the process of generating secondary non-migrating tides and, accordingly, the transfer of momentum to the secondary oscillation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eIncreased spatial variability of non-migrating atmospheric tides, caused by the variability of primary migrating tides and SPWs, leads to reduced statistical significance of observed tide amplitude changes.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe non-migrating diurnal tide (DT2), in contrast to the migrating DT1, intensifies during El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO. This is explained by the change in the wave activity of SPW1, the nonlinear interaction of DT1 with which generates DT2. In particular, the strengthening of SPW1 during El Ni\u0026ntilde;o\u0026thinsp;+\u0026thinsp;wQBO in the area of primary DT1 maximum strengthens the generation of DT2 in this region and vice versa, the weakening of SPW1 weakens the generation of DT2 during La Ni\u0026ntilde;a\u0026thinsp;+\u0026thinsp;eQBO. The effect of strengthening/weakening the generation of DT2 under different combinations of QBO/ENSO is demonstrated explicitly when considering the terms responsible for the interaction of SPW1 and DT1 in the balance equation of perturbed potential enstrophy.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eThe dependence on SPW1 wave activity is also characteristic of the structure of the non-migrating semidiurnal tide (SDT1). This is well illustrated during the La Ni\u0026ntilde;a phase: reduced wave activity during wQBO leads to a decrease in SDT1 across all latitudes, while increased PW1 during eQBO enhances non-migrating SDT1 and weakens migrating SDT2.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eComparison of the calculated tide amplitudes with observational data, including various QBO\u0026ndash;ENSO combinations, confirms that MUAM accurately reproduces the examined tidal oscillations.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThe importance of studying the interaction of tides with long-period atmospheric oscillations lies in the fact that, in addition to directly exchanging momentum with the mean flow, tides engage in nonlinear interactions with PWs, serving as a crucial factor in the formation of large-scale dynamics in the mesosphere and lower thermosphere. In particular, the tides are modulated by the PWs according to the mechanism proposed by Laštovička et al. (2006) and thus facilitate the passage of PWs through critical levels in the lower thermosphere, penetrating into the upper atmosphere. A brief overview of this mechanism is presented also in Koval et al. (2022). It can be assumed that the enhancement of DT1 during the wQBO should contribute to more efficient regeneration of SPW1, and, accordingly, to larger amplitudes of SPW1 in the thermosphere. It is precisely this, the enhancement of SPW1 during the wQBO up to altitudes of 300 km, that was demonstrated in the work of Koval et al. (2022), based on model simulations. Therefore, further studies of the regeneration of secondary/tertiary PWs, capable of significantly affecting the dynamics of the upper atmosphere, including from the point of view of space exploration, seem promising.\u003c/p\u003e \u003cp\u003eOur numerical modeling conducted under \"idealized\" conditions \u0026mdash; isolating the effects of QBO and ENSO \u0026mdash; allowed us to obtain statistically significant estimates of tidal amplitude changes and to separate the influence of both oscillations. This separation is difficult to achieve through observational data analysis due to limited time series and, consequently, insufficient sample size required for the necessary statistics to distinguish between these closely related phenomena, which are capable of mutually influencing each other.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e: Development of the scenarios and performing numerical simulations under different QBO/ENSO combinations were supported by the Russian Science Foundation: grant #25-47-00122; processing data, calculating tidal structures and EP fluxes, statistical analysis were supported by Saint Petersburg State University (research grant\u0026nbsp;#124032000025-1).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests.\u0026nbsp;\u003c/strong\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAvailability of data and materials.\u0026nbsp;\u003c/strong\u003eAll rights to the MUAM computer code belong to the Russian State Hydrometeorological University (RSHU). To gain access to computer codes and acquire the right to use them, permission from the Rector of the RSHU in needed. The authors will provide the necessary assistance in obtaining the appropriate permission. All datasets presented in the article are archived in https://disk.yandex.ru/d/Eu1WTOvUxAgk8A Zenodo (\u003cem\u003eall materials will be archived to Zenodo after revision\u003c/em\u003e). All graphs in this study were generated using the Grid Analysis and Display System (GrADS), a free software developed by NASA\u0026apos;s Advanced Information Systems Research Program.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions.\u0026nbsp;\u003c/strong\u003eAll authors made valuable contributions to data analysis, visualization of the results, writing and editing the text. A.V. Koval: funding acquisition, conceptualization, processing and interpretation of modeling results; K.A. Didenko: numerical modeling, nonlinear interactions; T.S. Ermakova: statistical processing; A.S. Fadeev and A.V. Sokolov: visualization and discussion of results.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAngelats i Coll, M., Forbes, J.M., 2002. Nonlinear interactions in the upper atmosphere: the s=1 and s=3 nonmigrating semidiurnal tides. J. Geophys. Res. 107, A8. https://doi.org/10.1029/2001JA900179.\u003c/li\u003e\n\u003cli\u003eAndrews DG, Holton JR, Leovy CB (1987) Middle atmosphere dynamics. Academic Press, New York \u003c/li\u003e\n\u003cli\u003eAnstey, J.A., Osprey, S.M., Alexander, J., Baldwin, M.P., Butchart, N., Gray, L., Kawatani, Y., Newman, P.A., Richter, J,H. (2022) Impacts, processes and projections of the quasi-biennial oscillation // Nature Reviews Earth \u0026amp; Environment, 3, 588\u0026ndash;603. https://doi.org/10.1038/s43017-022-00323-7\u003c/li\u003e\n\u003cli\u003eBaldwin, M. P., Gray, L. J., Dunkerton, T. J., Hamilton, K., Haynes, P. H., Randel, W. J., Holton, J. 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International Journal of Climatology, 31(7), 1074\u0026ndash;1087. https://doi.org/10.1002/joc.2336\u003c/li\u003e\n\u003cli\u003eWu, Q., Ortland, D.A., Solomon, S.C., Skinner, W.R., Niciejewski, R.J. (2011) Global distribution, seasonal, and inter-annual variations of mesospheric semidiurnal tide observed by TIMED TIDI. Journal of Atmospheric and Solar-Terrestrial Physics, V. 73, Issues 17\u0026ndash;18, P. 2482-2502 \u003c/li\u003e\n\u003cli\u003eWu, C., Ridley, A. J., \u0026amp; Cullens, C. Y. (2024). Seasonal dependency of the solar cycle, QBO, and ENSO effects on the interannual variability of the wind DW1 in the MLT region. Journal of Geophysical Research: Space Physics, 129, e2024JA032472. https://doi.org/10.1029/2024JA032472\u003c/li\u003e\n\u003cli\u003eXu, J., Smith, A. K., Jiang, G., Yuan, W., and Gao, H.: Features of the seasonal variation of the semidiurnal, terdiurnal and 6-h components of ozone heating evaluated from Aura/MLS observations, Ann. Geophys., 30, 259\u0026ndash;281, https://doi.org/10.5194/angeo-30-259-2012, 2012.\u003c/li\u003e\n\u003cli\u003eXuan Ma; L. Wang; D. Smith; L. Hermanson; R. Eade; N. Dunstone; S. Hardiman and J. Zhang. ENSO and QBO modulation of the relationship between Arctic sea ice loss and Eurasian winter climate. Environmental Research Letters, 2022, Volume 17, Number 12. DOI 10.1088/1748-9326/aca4e9.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"general atmospheric circulation, numerical modeling, atmospheric tides, planetary waves, El Niño–Southern Oscillation, Quasi-Biennial Oscillation","lastPublishedDoi":"10.21203/rs.3.rs-6873106/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6873106/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe dependence of atmospheric tide amplitudes on the phases of long-period tropical oscillations, specifically the Quasi-Biennial Oscillation (QBO) of zonal wind in the equatorial stratosphere and the El Ni\u0026ntilde;o\u0026ndash;Southern Oscillation (ENSO), is examined. Numerical simulations of global atmospheric circulation are conducted using the MUAM nonlinear mechanistic atmospheric model under various scenarios incorporating different combinations of QBO/ENSO phases. The structures of migrating diurnal and semidiurnal tides with zonal wave numbers 1 and 2, respectively, as well as non-migrating diurnal and semidiurnal tides with zonal wave numbers 2 and 1, respectively, are calculated. The analysis is focused on the boreal winter season (January - February), the period of peak wave activity for planetary waves (PWs) that are involved in the nonlinear generation of non-migrating tides. The results demonstrate, in particular, that the migrating diurnal tide (DT1) is amplified during the westerly QBO phase (wQBO) and under La Ni\u0026ntilde;a conditions. For the semidiurnal migrating tide (SDT2), ENSO effects are found to be more pronounced than those of the QBO. During El Ni\u0026ntilde;o, the tide\u0026rsquo;s amplitude decreases in the equatorial region while increasing to the North and South of it, regardless of the QBO phase. Changes in non-migrating tides differ from those of migrating tides with similar periods, which is attributed to the altered wave activity of the stationary PW with zonal wave number 1 (SPW1). Nonlinear interactions between primary migrating tides and this wave generate non-migrating tides. The effect of strengthening/weakening of non-migrating diurnal tide (DT2) generation for different combinations of QBO/ENSO is demonstrated explicitly by considering the terms responsible for the nonlinear interaction of PW1 and DT1 in the balance equation of perturbed potential enstrophy. The numerical simulations performed under \u0026ldquo;idealized\u0026rdquo; conditions, isolating the effects of QBO and ENSO, allowed for the differentiation of the influences of these two oscillations. Such separation is challenging with observational data due to limited time series, which restricts sample size and thereby limits the statistical capacity needed to distinguish between these phenomena having close periods.\u003c/p\u003e","manuscriptTitle":"Overview of the Dependence of Atmospheric Tide Amplitudes on the Phases of Natural Tropical Oscillations based on MUAM simulations","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-17 10:27:51","doi":"10.21203/rs.3.rs-6873106/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"364dfc52-a3d0-45f6-8d23-883b225c740e","owner":[],"postedDate":"June 17th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-16T00:29:42+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-17 10:27:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6873106","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6873106","identity":"rs-6873106","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}