This study uses an ensemble of climate model experiments coordinated by the Quasi-Biennial Oscillation initiative (QBOi) to analyze the Madden-Julian Oscillation (MJO) in the presence of either perpetual El Ni & ntilde;o or La Ni & ntilde;a sea surface temperatures during boreal winter. In addition to the prescribed El Ni & ntilde;o Southern Oscillation (ENSO) conditions, the nine models internally generate QBOs, meaning each may influence the MJO. Objectives of our analyses are to assess the response of the MJO to strong idealized ENSO forcing and look for evidence of a QBO influence on the MJO in a multi-model context. The diagnostics used include wavenumber-frequency spectra of tropical convective and dynamical fields, measures of MJO lifetime, an evaluation of MJO diversity and visualization of MJO vertical structure, as well as an assessment of QBO morphology and the QBO's impact on tropical convection. Kelvin wave spectral power increases in the El Ni & ntilde;o simulations whereas equatorial Rossby waves power is stronger in the La Ni & ntilde;a simulations. All models simulate faster MJO propagation under El Ni & ntilde;o conditions. This change in speed is corroborated by the MJO diversity analysis, which reveals that models better reproduce the observed "fast propagating" and "standing" MJO archetypes given perpetual El Ni & ntilde;o and La Ni & ntilde;a, respectively. Regardless of ENSO, QBO descent into the lower stratosphere is underestimated and we detect little QBO influence on tropical tropopause stability and MJO activity. With little influence from the QBO on the MJO activity in these runs, we can be confident that the aforementioned changes in the MJO indeed arise from the different ENSO boundary conditions.

Parametrizations of subgrid-scale mountains are commonly used in numerical weather prediction and climate models. They try to represent quite separate processes; namely, the enhancement of the turbulent drag by orography, gravity-wave drag, and the effects of low-level flow blocking. Among the gravity wave schemes, some of them distinguish between upward-propagating waves and trapped lee waves. This article makes use of a recent theoretical methodology to propose a formalism that includes all these effects. This theory handles enhanced turbulent drag in the neutral case, gravity waves in the stratified case, and trapped lee waves in the transition. Mountain drag associated with all these processes is estimated analytically, as well as the fraction of the drag that stays within the boundary layer instead of being radiated in the far field. Although the theory used is adapted to gentle hills with small slope, we also try to evaluate the blocked layer depth by combining the sheltering effects that dominate when stratification is small and the blocking effects when stratification is strong.

Abstract. The equatorial resolved and parameterized wave forcing of the quasi-biennial oscillation (QBO) in models participating in phase 2 of the Atmospheric Processes and their Role in Climate (APARC) Quasi-Biennial Oscillation initiative (QBOi) is analyzed. We compare two experiments performed by the multi-model ensemble, NoNudge and ObsQBO, covering the period from 1979 to 2020. In this study, NoNudge designates experiments where the QBO is generated internally without nudging, whereas ObsQBO represents experiments in which the QBO is bias-corrected by nudging stratospheric zonal-mean zonal winds toward ERA5, allowing investigation of modelling uncertainties originating from biases in the background winds. While the NoNudge simulations exhibit QBO biases typically seen in models, including eastward wind bias in the mid-stratosphere and underestimation of the QBO amplitude in the lower stratosphere, these discrepancies are effectively mitigated by nudging in ObsQBO simulations. In the NoNudge experiments, the models reveal weaker Kelvin and gravity wave forcing in the tropical lower stratosphere than ERA5, but these forcings are enhanced in the ObsQBO experiment, suggesting that weak wave forcing of internally generated QBOs results from reduced critical-level filtering of waves due to unrealistically weak vertical wind shear at these levels. However, in ObsQBO experiments, the models still exhibit insufficient Kelvin and gravity wave forcing in the lower stratosphere. This suggests that the weak QBO amplitude in the lower stratosphere may stem from the inherent deficit in wave forcing in the models. One notable feature of the ObsQBO experiments is the excessive eastward wave forcing in the mid-to-upper stratosphere during the easterly QBO phase in the lower tropical stratosphere. The correlation coefficient between the 10 hPa eastward wave forcing and westerly QBO amplitude is 0.8, indicating that excessive westerly QBO is associated with strong eastward wave forcing in the mid-to-upper stratosphere.

Abstract. As part of the Quasi-Biennial Oscillation initiative (QBOi) phase 1, a model-intercomparison study explored the representation of the semi-annual oscillation (SAO) in participating models and found a common easterly bias of several tens of m/s compared to observations, mostly with weaker westerly phases and stronger easterly phases. QBOi phase 1 results also reported biases in model representations of the QBO, which dominates the region below the SAO, with most models displaying a westerly time mean wind bias, and generally weaker QBO easterly phases. Given that the SAO forcing terms can be influenced by the QBO, in this paper we explore the influence of these QBO biases on the representation of the SAO. A multi-model analysis is conducted here using QBOi phase 2 data from current state-of-the-art climate models to examine changes in representation of the SAO in response to corrections in zonal-mean zonal wind QBO biases. Most models show an improvement with a reduced easterly SAO bias in response to the corrected QBO bias. The extent of this response is found to vary significantly across models with SAO time-mean winds changing by 6 % to 403 % in simulations with a bias-corrected QBO relative to the control simulations. Changed gravity wave drag in response to the improved QBO is attributed as the forcing term having the largest overall impact.

Abstract. Observations suggest that the stratospheric Quasi-biennial Oscillation (QBO) modulates the Madden-Julian Oscillation (MJO) in the tropical troposphere, where the MJO is stronger with a smoother eastward propagation in the boreal winter seasons with a QBO easterly (QBOE) than that with a QBO westerly (QBOW) phase. Such connection is not captured by current climate models through their internally generated QBO and MJO. The QBO initiative (QBOi) phase 2 project included climate models from global modeling centers and conducted simulations with the tropical zonal-mean zonal wind in the model stratosphere nudged towards the observations. This paper investigates the potential connection between the nudged QBO and the internally generated MJO in 12 participating climate models. Results show that the stratospheric QBO and its associated impacts on the upper troposphere and lower stratosphere stability around the equator are realistically represented in all models through the nudging although a smaller amplitude is found for the temperature responses. However, there is no significant connection between the QBO and MJO in any of the participating models. Further diagnostics suggest this likely result from the biases in the internally generated MJO by the models where the simulated MJO convective variation is constantly underestimated so that the intense MJO OLR and precipitation anomalies are inadequately induced. However, the QBOi phase 2 models show no systematic bias in the MJO cloud-radiative feedback strength, with individual models spanning the full range from underestimation to overestimation of the observed values. These findings emphasize the importance of accurate representation of the MJO convective system in capturing the QBO-MJO connection by climate models. This paper also underscores the urgency of new theoretical understandings for the observed QBO-MJO connection.

Abstract. We describe the protocol for coordinated experiments in phase-2 of the Quasi-Biennial Oscillation initiative (QBOi) and the participating models. The experiments involve nudging tropical stratospheric zonal-mean zonal winds in the models toward observations, enabling analysis of the impact of QBO biases on simulated teleconnections. Additionally, nudging the tropical winds allows investigation of the origins of QBO biases by examining the behaviour of resolved and parameterized equatorial waves under realistic equatorial wind shear conditions. We document here the scientific rationale and design of the nudging experiments, summarize the QBOi data request, and provide an overview of participating models. An initial evaluation is given of tropical stratospheric winds simulated by the multi-model ensemble for both nudged and free-running cases, and the overall impact of nudging on climatological aspects of the atmospheric circulation is examined.

Most operational gravity-wave parameterizations use single-column and steady-state approximations, thus neglecting horizontal propagation and transience. Recent studies indicate that these simplifications can lead to inaccurate predictions. Orographic gravity waves, e.g., can propagate over substantial horizontal distances, leading to the deposition of momentum far from their sources. The neglect of this could be a cause of regional momentum-flux deficits in atmospheric models, e.g. downstream of the Andes. Moreover, the variability of low-level winds can make mountain-wave generation a highly transient process, challenging the legitimacy of the steady-state approximation. This motivates the development of more complex models. MS-GWaM is a Lagrangian gravity-wave parameterization that is based on a multi-scale WKB theory allowing for both transience and horizontal propagation. In a previous study (Jochum et al., 2025), it was used in simulations within the idealized atmospheric flow solver PincFlow to investigate its ability to correctly describe the interaction between orographic gravity waves and a large-scale flow. 2D flows over periodic monochromatic orographies were considered, using MS-GWaM either in its fully transient implementation or in a steady-state implementation that represents classic mountain-wave parameterizations. Comparisons of wave-resolving simulations (not using MS-GWaM) and coarse-resolution simulations (using MS-GWaM) showed that allowing for transience leads to a significantly more accurate forcing of the resolved mean flow. The present study supplements MS-GWaM (within PincFlow's successor PinCFlow.jl) with a new blocked-layer scheme and continues the investigation with the more realistic case of an isolated 2D mountain range, where the impact of upstream blocking and horizontal propagation increases substantially, resulting in a more complex wave-mean-flow interaction. The blocked-layer scheme uses a relatively simple approach to blocking that is consistent with MS-GWaM's spectral representation of the unresolved orography. Its two parameters are calibrated via Ensemble Kalman Inversion, using a wave-resolving simulation as reference. The results show that the inclusion of this scheme yields a slightly improved forcing of the mean flow.ReferencesJochum, F., Chew, R., Lott, F., Voelker, G. S., Weinkaemmerer, J., and Achatz, U. (2025). The impact of transience in the interaction between orographic gravity waves and mean flow. Journal of the Atmospheric Sciences.

This study investigates Quasi-Biennial Oscillation (QBO) teleconnections and their modulation by the El Niño–Southern Oscillation (ENSO) using a multi-model ensemble from the Atmospheric Processes And their Role in Climate (APARC) QBO initiative (QBOi). Analyzing observed QBO–ENSO teleconnections is challenging because it is difficult to separate the respective influences of QBO and ENSO outside the QBO region due to aliasing in the historical record. To isolate these signals, simulations were conducted with annually repeating prescribed sea-surface temperatures (SSTs) representing idealized El Niño and La Niña conditions (the QBOi EN and LN experiments, respectively), and results are compared with the QBOi control experiment (CTL) under ENSO-neutral conditions. The strength of the Holton-Tan relationship between the phase of the QBO and the strength of the polar vortex seen in observations is reproduced in fewer than three models in CTL and by one model in EN. In LN, three out of nine models reproduce the observed Holton–Tan relationship, but with less than half of the observed amplitude. In the Arctic winter climate, sudden stratospheric warmings (SSWs) occur more frequently in EN than in LN; however, unlike in observations, there is no discernible difference in SSW frequency between QBO westerly (QBO-W) and QBO easterly (QBO-E) phases. The Asia-Pacific subtropical jet (APJ) shifts significantly equatorward during QBO-W compared to QBO-E in observations, but this shift is not robust across models, regardless of ENSO phases. In the tropics, the sign and spatial pattern of the QBO precipitation response vary widely across models and experiments, indicating that any potential QBO signal is strongly modulated by the prevailing ENSO phases. Overall, the QBOi models exhibit unrealistically weak QBO wind amplitudes in the lower stratosphere, which may explain the weak polar vortex and APJ responses, as well as the weak precipitation signals in the tropics. In contrast, the QBO teleconnection with the Walker circulation during boreal summer and autumn shows consistent signals in both observations and most models. Specifically, the QBO-W phase is characterized by upper-level westerly and lower-level easterly anomalies over the Indian Ocean–Maritime Continent relative to QBO-E, although the amplitude and timing of these anomalies remain model-dependent. Notably, the influence of QBO phase on the Walker circulation appears insensitive to the ENSO phase.

The Atmospheric Processes And their Role in Climate (APARC) Quasi-Biennial Oscillation initiative (QBOi) has conducted new experiments to explore the modulation of the QBO by El Ni & ntilde;o-Southern Oscillation (ENSO). This paper provides an overview of the experimental design and investigates the modulation of the QBO by ENSO using nine climate models used in QBOi. A key finding is a consistent lengthening of the QBO period during La Ni & ntilde;a compared to El Ni & ntilde;o across all models, aligning with observational evidence. Although several models simulate QBO periods that deviate from the observed mean of approximately 28 months, the relative difference between La Ni & ntilde;a and El Ni & ntilde;o remains interpretable within each model. The simulated QBO periods during La Ni & ntilde;a tend to be longer than those during El Ni & ntilde;o, although, in most models, the differences are small compared to that observed. However, the magnitude of this lengthening shows large inter-model differences. By contrast, even the sign of the ENSO effect on QBO amplitude varies among models. Models employing variable parameterized gravity wave sources generally exhibit greater sensitivity of the QBO amplitude to the presence of ENSO than those models using fixed sources. The models capture key observed ENSO-related characteristics, including a weaker Walker circulation and increased equatorial precipitation during El Ni & ntilde;o compared to La Ni & ntilde;a, as well as a characteristic response in zonal mean zonal wind and temperature. All models also simulate stronger equatorial tropical upwelling in El Ni & ntilde;o compared to La Ni & ntilde;a up to similar to 10 hPa, consistent with ERA5 reanalysis. These modulations influence the propagation and filtering of gravity waves. Notably, models with variable parameterized gravity wave sources show stronger wave forcing during El Ni & ntilde;o, potentially explaining the shorter QBO period modulation in these models. Further investigation into the complex interplay between ENSO, gravity waves, and the QBO can contribute to improved model formulations.

Many operational gravity wave parameterizations rely on the single column and steady state approximations, thus neglecting horizontal propagation and transience. Recent studies indicate that these assumptions can lead to faulty predictions, motivating the development of more complex models. MS-GWaM, a Lagrangian gravity wave parameterization that has been in development for about a decade, is one such model that is based on a multi-scale WKB theory allowing for both transience and horizontal propagation. So far, it has been validated mainly for non-orographic gravity waves, however, a simple orographic source has already been implemented in a test version of the model, which is coupled to a pseudo-incompressible flow solver (PincFlow). The present study investigates that source in an idealized setting. For this purpose, the model is adjusted to PincFlow's recently implemented terrain-following coordinate system. In addition, the orographic source is supplemented with a blocked flow drag and a wave amplitude reduction that accounts for blocked layer formation. These are derived from background flow tendencies and gravity wave momentum fluxes in highly idealized, wave-resolving simulations. The model is then tested against the latter, using both the transient configuration and a newly implemented steady state mode. The comparison shows that allowing for transience results in a more accurate forcing of the resolved mean flow, especially when the orographic source is changing in time.

Parameterizations of subgrid scale mountains are commonly used in large scale numerical weather prediction and climate models. They try to represent quite separate processes: the enhancement of the turbulent drag by orography, gravity waves and low level flow blocking. Among the gravity waves some schemes eventually separate between the upward propagating waves and the trapped lee waves. Using a recent theoretical methodology that addresses the interaction of stratified boundary layers with mountains, a theory that handles the transition from neutral to stratified dynamics and trapped waves, we propose a formalism that can include all these effects. As in most parameterizations it separates the flow between a linear part and a blocked part. Here the linear part handles enhanced turbulent drag in the neutral case and gravity waves in the stratified case, trapped lee waves in the transition. In this presentation we evaluate the mountain drag associated to all these processes as well as the fraction of the drag that stays within the boundary layer instead of being radiated in the far field. We also try to evaluate the blocked part by combining the sheltering effects that dominate when stratification is small and the blocking effects that dominate when stratification is large.

The transfer of momentum due to non‐orographic Gravity Waves (GWs) significantly regulates the Martian middle‐upper atmospheric dynamics. Thus, these waves influence the transport of tracers and escape in the thermosphere. However, models assume that the non‐orographic GWs are emitted from a constant source level that approximates the averaged Planetary Boundary Layer (PBL). We move on to impose that the emission of the waves follows the top of a real‐time evaluated PBL to account for the diurnal cycle of the waves' source altitudes and implement this improvement in the Mars Planetary Climate Model (Mars PCM). In the absence of the PBL during the night, the non‐orographic GWs are assumed to be launched at altitudes near the surface following Hinson and Wilson (2023, https://doi.org/10.1016/j.icarus.2022.115420 )'s results. Sensitivity tests with the Mars PCM show that non‐orographic GWs are built up efficiently during the (polar) night. With the new scheme, the angular momentum in the upper atmosphere is enhanced. Additionally, simulations recover the “cold pockets” in temperature observed by the Mars Climate Sounder at 80–100 km and capture “deep drops” of the atmospheric species recorded by the Neutral Gas and Ion Mass Spectrometer in the polar night.

This paper presents a formalism of mixing induced by non-orographic gravity waves (GWs) to integrate with the stochastic GWs scheme in the Mars Planetary Climate Model. We derive the formalism of GWs and their mixing under the same assumptions, integrating the two schemes within a unified framework. Specifically, a surface-to-exosphere parameterization of GW-induced turbulence has been derived in terms of the eddy diffusion coefficient. Simulations show that the coefficient is on the order of to and a turbopause is at altitudes of 70-140 km, varying with seasons. The triggered mixing has minor effects on model temperatures, yet it substantially impacts upper atmospheric abundances. Simulations are consistent with observations from the Mars Climate Sounder and the Neutral Gas and Ion Mass Spectrometer. Mixing enhances the tracer transports in the middle and upper atmosphere, governing the dynamics of these regions. The scheme reveals how non-orographic GW-induced turbulence can regulate upper atmospheric processes, such as tracer escape.

A Lagrangian gravity-wave parameterization (MS-GWaM, Multi-Scale Gravity-Wave Model) that allows for fully transient wave-mean-flow interaction and horizontal propagation is applied to orographic gravity waves for the first time. Both linear and nonlinear mountain waves are modeled in idealized simulations within the pseudo-incompressible flow solver PincFlow. Two-dimensional flows over monochromatic orographies are considered, using MS-GWaM either in its fully transient implementation or in a steady-state implementation that represents classic mountain-wave parameterizations. Comparisons of wave-resolving simulations (not using MS-GWaM) and coarse-resolution simulations (using MS-GWaM) show that allowing for transience leads to a significantly more accurate forcing of the resolved mean flow. The model is able to reproduce the transient forcing of linearly generated mountain waves that slowly propagate upwards, in contrast to the instantaneous distribution of wave energy in classic parameterizations. At high altitudes, wave breaking induces a wind reversal that is captured by the transient model but inhibited in steady-state simulations, due to the assumption of critical level formation. This shows that transience can have a substantial impact in the interaction between mountain waves and mean flow.

The Quasi-Biennial Oscillation (QBO) is the leading natural model of interannual variability of the zonal mean wind in the equatorial stratosphere, consisting of alternating regions of easterly and westerly zonal wind that descend through the equatorial stratosphere with a mean period of approximately 28 months. Its dominant influence on the dynamical structure of the equatorial stratosphere raises the prospect of teleconnections to the extratropical atmosphere. For example, the QBO has been linked to variability in the Northern Hemisphere winter stratospheric polar vortex, the timing and frequency of sudden stratospheric warmings, the phase of the North Atlantic Oscillation, and the modulation of tropospheric mid-latitude waves in the Pacific region. However, the reproduction of these extratropical teleconnections in free-running models relies upon on a quantitatively realistic internally-generated QBO, and the ability of the model dynamics to respond to this QBO. To isolate the dynamical response, a new experiment protocol, defined by the Atmospheric Processes and their Role in Climate (APARC) Quasi-Biennial Oscillation initiative (QBOi), describes how the observed equatorial stratospheric zonal winds can be imposed in model experiments. This allows the dynamical response across different models with similar and realistic QBOs to be analysed. Using a multi-model ensemble generated by QBOi modelling centres, we present an assessment of the extratropical teleconnections in comparison with observations.

We compare the parameterization schemes that represent gravity waves in the Atmospheric Component of the IPSL Climate Model (LMDZ6A) and the high-resolution ICOsahedral Nonhydrostatic Weather and Climate Model (ICON). Our focus lies in assessing the capabilities of the gravity wave drag schemes to predict zonal momentum fluxes derived from ICON. The parameterization is run offline using ICON meteorological fields coarse grained to a healpix grid with size representative of an ESM grid (around 100km x 100km). We then examine the temporal mean, horizontal mean, and zonal mean gravity wave stresses predicted by the parameterizations and compare them to the zonal momentum fluxes associated with the ICON subgrid scale fields (e.g. the motions that are filtered out during the coarse-graining). The investigation reveals that in the stratosphere, the parameterizations have some skill at predicting zonal momentum fluxes of ICON, and this without prior tuning. More specifically, the parameterized gravity wave stresses due to mountains, convection and fronts align reasonably well with the zonal momentum fluxes from ICON in the stratosphere, each scheme consistently playing a dominant role where it should (frontal waves dominating in the midlatitude storm tracks, convective waves in the tropics, and mountain waves over orography). This permits physical interpretations of the origin of the gravity waves predicted by ICON, but raises challenges when extending this comparison to the troposphere. There, the agreement between the parameterized stress and the ICON subgrid scale stress is much weaker, which is likely attributable to the fact that in the troposphere subgrid scale forced motions like convective cells produce stresses much larger than the gravity wave stresses.

Sudden stratospheric warmings (SSWs) show a large spread across climate models in characteristics such as frequency of occurrence, seasonality and strength. This is reflective of inherent model biases. A well-known source of inter-model variability is the parameterized gravity wave forcing, as the parameterization schemes vary from model to model. This work compares the simulation of boreal SSWs in historical runs for seven high-top Climate Model Intercomparison Project Phase 6 models and in two reanalyses. The analysis is focused on the evolution of the different terms in the transformed Eulerian mean zonal mean zonal momentum equation. A large spread is found between models and with reanalyses in the mean magnitude of the resolved and parameterized wave forcing and the responses (wind deceleration and anomalous residual circulation). The results reveal that, in the stratosphere, both the wind deceleration and the strengthening of the residual circulation during SSWs correlate linearly across the models with anomalies in the resolved wave forcing. In the mesosphere, the forcing is a combination of resolved waves and, predominantly, parameterized gravity waves. Models with larger gravity wave forcing anomalies produce larger changes in the residual circulation, while models with larger resolved wave forcing anomalies produce stronger wind deceleration, which we attribute to differences in the spatial shape of resolved and parameterized wave forcing. Although the forcing–response relation across individual SSW events is similar for each model in the stratosphere, this does not hold in the mesosphere. Our results are useful for interpreting the spread in projections of the dynamical forcing of SSWs in a changing climate.