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Atmospheric regime transitions are highly impactful as drivers of extreme weather events, but pose two formidable modeling challenges: predicting the next event (weather forecasting), and characterizing the statistics of events of a given severity (the risk climatology). Each event has a different duration and spatial structure, making it hard to define an objective "average event." We argue here that transition path theory (TPT), a stochastic process framework, is an appropriate tool for the task. We demonstrate TPT's capacities on a wave-mean flow model of sudden stratospheric warmings (SSWs) developed by Holton and Mass (1976), which is idealized enough for transparent TPT analysis but complex enough to demonstrate computational scalability. Whereas a recent article (Finkel et al. 2021) studied near-term SSW predictability, the present article uses TPT to link predictability to long-term SSW frequency. This requires not only forecasting forward in time from an initial condition, but also \emph{backward in time} to assess the probability of the initial conditions themselves. TPT enables one to condition the dynamics on the regime transition occurring, and thus visualize its physical drivers with a vector field called the \emph{reactive current}. The reactive current shows that before an SSW, dissipation and stochastic forcing drive a slow decay of vortex strength at lower altitudes. The response of upper-level winds is late and sudden, occurring only after the transition is almost complete from a probabilistic point of view. This case study demonstrates that TPT quantities, visualized in a space of physically meaningful variables, can help one understand the dynamics of regime transitions., Comment: 18 pages, 7 figures (main text), 19 pages, 1 figure (supplement). Accepted for publication in the Journal of the Atmospheric Sciences

Much of our conceptual understanding of midlatitude atmospheric motion comes from two-layer quasi-geostrophic (QG) models. Traditionally, these QG models don’t include moisture, which accounts for an estimated 30-60% of the available energy of the atmosphere. The atmospheric moisture content is expected to increase under global warming, and therefore a theory for how moisture modifies atmospheric dynamics is crucial. We use a two-layer moist QG model with convective adjustment as a basis for analyzing how latent heat release and large-scale moisture gradients impact the scalings of a midlatitude system at the synoptic scale. In this model, the degree of saturation can be tuned independently of other moist parameters by enforcing a high rate of evaporation from the surface. This allows for study of the effects of latent heat release at saturation, without the intrinsic nonlinearity of precipitation. At saturation, this system is equivalent to the dry QG model under a rescaling of both length and time. This predicts that the most unstable mode shifts to smaller scales, the growth rates increase, and the inverse cascade extends to larger scales. We verify these results numerically and use them to verify a framework for the complete energetics of a moist system. We examine the spectral features of the energy transfer terms. This analysis shows that precipitation generates energy at small scales, while dry dynamics drive a significant broadening to larger scales. Cascades of energy are still observed in all terms, albeit without a clearly defined inertial range.

Author(s): Li, X; Cai, W; Meehl, GA; Chen, D; Yuan, X; Raphael, M; Holland, DM; Ding, Q; Fogt, RL; Markle, BR; Wang, G; Bromwich, DH; Turner, J; Xie, SP; Steig, EJ; Gille, ST; Xiao, C; Wu, B; Lazzara, MA; Chen, X; Stammerjohn, S; Holland, PR; Holland, MM; Cheng, X; Price, SF; Wang, Z; Bitz, CM; Shi, J; Gerber, EP; Liang, X; Goosse, H; Yoo, C; Ding, M; Geng, L; Xin, M; Li, C; Dou, T; Liu, C; Sun, W; Wang, X; Song, C | Abstract: Over the modern satellite era, substantial climatic changes have been observed in the Antarctic, including atmospheric and oceanic warming, ice sheet thinning and a general Antarctic-wide expansion of sea ice, followed by a more recent rapid loss. Although these changes, featuring strong zonal asymmetry, are partially influenced by increasing greenhouse gas emissions and stratospheric ozone depletion, tropical–polar teleconnections are believed to have a role through Rossby wave dynamics. In this Review, we synthesize understanding of tropical teleconnections to the Southern Hemisphere extratropics arising from the El Nino–Southern Oscillation, Interdecadal Pacific Oscillation and Atlantic Multidecadal Oscillation, focusing on the mechanisms and long-term climatic impacts. These teleconnections have contributed to observed Antarctic and Southern Ocean changes, including regional rapid surface warming, pre-2015 sea ice expansion and its sudden reduction thereafter, changes in ocean heat content and accelerated thinning of most of the Antarctic ice sheet. However, due to limited observations and inherent model biases, uncertainties remain in understanding and assessing the importance of these teleconnections versus those arising from greenhouse gases, ozone recovery and internal variability. Sustained pan-Antarctic efforts towards long-term observations, and more realistic dynamics and parameterizations in high-resolution climate models, offer opportunities to reduce these uncertainties.

This study quantifies differences among four widely used atmospheric reanalysis datasets (ERA5, JRA-55, MERRA-2, and CFSR) in their representation of the dynamical changes induced by springtime polar stratospheric ozone depletion in the Southern Hemisphere from 1980 to 2001. The intercomparison is undertaken as part of the SPARC (Stratosphere–troposphere Processes and their Role in Climate) Reanalysis Intercomparison Project (S-RIP). The reanalyses are generally in good agreement in their representation of the strengthening of the lower stratospheric polar vortex during the austral spring–summer season, associated with reduced radiative heating due to ozone loss, as well as the descent of anomalously strong westerly winds into the troposphere during summer and the subsequent poleward displacement and intensification of the polar front jet. Differences in the trends in zonal wind between the reanalyses are generally small compared to the mean trends. The exception is CFSR, which exhibits greater disagreement compared to the other three reanalysis datasets, with stronger westerly winds in the lower stratosphere in spring and a larger poleward displacement of the tropospheric westerly jet in summer. The dynamical changes associated with the ozone hole are examined by investigating the momentum budget and then the eddy heat and momentum fluxes in terms of planetary- and synoptic-scale Rossby wave contributions. The dynamical changes are consistently represented across the reanalyses and support our dynamical understanding of the response of the coupled stratosphere–troposphere system to the ozone hole. Although our results suggest a high degree of consistency across the four reanalysis datasets in the representation of these dynamical changes, there are larger differences in the wave forcing, residual circulation, and eddy propagation changes compared to the zonal wind trends. In particular, there is a noticeable disparity in these trends in CFSR compared to the other three reanalyses, while the best agreement is found between ERA5 and JRA-55. Greater uncertainty in the components of the momentum budget, as opposed to mean circulation, suggests that the zonal wind is better constrained by the assimilation of observations compared to the wave forcing, residual circulation, and eddy momentum and heat fluxes, which are more dependent on the model-based forecasts that can differ between reanalyses. Looking forward, however, these findings give us confidence that reanalysis datasets can be used to assess changes associated with the ongoing recovery of stratospheric ozone.

Extreme weather events have significant consequences, dominating the impact of climate on society. While high-resolution weather models can forecast many types of extreme events on synoptic timescales, long-term climatological risk assessment is an altogether different problem. A once-in-a-century event takes, on average, 100 years of simulation time to appear just once, far beyond the typical integration length of a weather forecast model. Therefore, this task is left to cheaper, but less accurate, low-resolution or statistical models. But there is untapped potential in weather model output: despite being short in duration, weather forecast ensembles are produced multiple times a week. Integrations are launched with independent perturbations, causing them to spread apart over time and broadly sample phase space. Collectively, these integrations add up to thousands of years of data. We establish methods to extract climatological information from these short weather simulations. Using ensemble hindcasts by the European Center for Medium-range Weather Forecasting (ECMWF) archived in the subseasonal-to-seasonal (S2S) database, we characterize sudden stratospheric warming (SSW) events with multi-centennial return times. Consistent results are found between alternative methods, including basic counting strategies and Markov state modeling. By carefully combining trajectories together, we obtain estimates of SSW frequencies and their seasonal distributions that are consistent with reanalysis-derived estimates for moderately rare events, but with much tighter uncertainty bounds, and which can be extended to events of unprecedented severity that have not yet been observed historically. These methods hold potential for assessing extreme events throughout the climate system, beyond this example of stratospheric extremes., 28 pages, 6 figures. Resubmitted for publication

Climate models in phase 5 of the Coupled Model Intercomparison Project (CMIP5) vary significantly in their ability to simulate the phase and amplitude of atmospheric stationary waves in the midlatitude Southern Hemisphere. These models also suffer from a double intertropical convergence zone (ITCZ), with excessive precipitation in the tropical eastern South Pacific, and many also suffer from a biased simulation of the dynamics of the Agulhas Current around the tip of South Africa. The intermodel spread in the strength and phasing of SH midlatitude stationary waves in the CMIP archive is shown to be significantly correlated with the double-ITCZ bias and biases in the Agulhas Return Current. An idealized general circulation model (GCM) is used to demonstrate the causality of these links by prescribing an oceanic heat flux out of the tropical east Pacific and near the Agulhas Current. A warm bias in tropical east Pacific SSTs associated with an erroneous double ITCZ leads to a biased representation of midlatitude stationary waves in the austral hemisphere, capturing the response evident in CMIP models. Similarly, an overly diffuse sea surface temperature gradient associated with a weak Agulhas Return Current leads to an equatorward shift of the Southern Hemisphere jet by more than 3° and weak stationary wave activity in the austral hemisphere. Hence, rectification of the double-ITCZ bias and a better representation of the Agulhas Current should be expected to lead to an improved model representation of the austral hemisphere.

The transport of trace gases by the atmospheric circulation plays an important role in the climate system and its response to external forcing. Transport presents a challenge for Atmospheric General Circulation Models (AGCMs), as errors in both the resolved circulation and the numerical representation of transport processes can bias their abundance. In this study, two tests are proposed to assess transport by the dynamical core of an AGCM. To separate transport from chemistry, the tests focus on the age‐of‐air, an estimate of the mean transport time by the circulation. The tests assess the coupled stratosphere–troposphere system, focusing on transport by the overturning circulation and isentropic mixing in the stratosphere, or Brewer–Dobson Circulation, where transport time‐scales on the order of months to years provide a challenging test of model numerics. Four dynamical cores employing different numerical schemes (finite‐volume, pseudo‐spectral, and spectral‐element) and discretizations (cubed sphere versus latitude–longitude) are compared across a range of resolutions. The subtle momentum balance of the tropical stratosphere is sensitive to model numerics, and the first intercomparison reveals stark differences in tropical stratospheric winds, particularly at high vertical resolution: some cores develop westerly jets and others easterly jets. This leads to substantial spread in transport, biasing the age‐of‐air by up to 25% relative to its climatological mean, making it difficult to assess the impact of the numerical representation of transport processes. This uncertainty is removed by constraining the tropical winds in the second intercomparison test, in a manner akin to specifying the Quasi‐Biennial Oscillation in an AGCM. The dynamical cores exhibit qualitative agreement on the structure of atmospheric transport in the second test, with evidence of convergence as the horizontal and vertical resolution is increased in a given model. Significant quantitative differences remain, however, particularly between models employing spectral versus finite‐volume numerics, even in state‐of‐the‐art cores., The climatological and zonal mean zonal wind ū (m·s−1), as simulated by two different dynamical cores, (left) pseudospectral (GFDL‐PS) and (right) finite‐volume (CAM‐FV), with (top) 40 vertical levels and (bottom) 80 vertical levels. With higher vertical resolution, the pseudospectral core develops westerlies in the tropical stratosphere between 20 and 80 hPa, while the finite‐volume core consistently simulates easterlies at both vertical resolutions. Both cores have comparable horizontal resolution. The contour interval is 10 m·s−1., US National Science Foundation

An intermediate-complexity moist general circulation model is used to investigate the forcing of stationary waves in the Northern Hemisphere boreal winter by land–sea contrast, horizontal heat fluxes in the ocean, and topography. The additivity of the response to these building blocks is investigated. In the Pacific sector, the stationary wave pattern is not simply the linear additive sum of the response to each forcing. In fact, over the northeast Pacific and western North America, the sum of the responses to each forcing is actually opposite to that when all three are imposed simultaneously due to nonlinear interactions among the forcings. The source of the nonlinearity is diagnosed using the zonally anomalous steady-state thermodynamic balance, and it is shown that the background-state temperature field set up by each forcing dictates the stationary wave response to the other forcings. As all three forcings considered here strongly impact the temperature field and its zonal gradients, the nonlinearity and nonadditivity in our experiments can be explained, but only in a diagnostic sense. This nonadditivity extends up to the stratosphere, and also to surface temperature, where the sum of the responses to each forcing differs from the response if all forcings are included simultaneously. Only over western Eurasia is additivity a reasonable (though not perfect) assumption; in this sector land–sea contrast is most important over Europe, while topography is most important over western Asia. In other regions, where nonadditivity is pronounced, the question of which forcing is most important is ill-posed.

An essential step in implementing any new parameterization is calibration, where the parameterization is adjusted to work with an existing model and yield some desired improvement. In the context of gravity wave (GW) momentum transport, calibration is necessitated by the facts that: (i) Some GWs are always at least partially resolved by the model, and hence a parameterization should only account for the missing waves. Worse, the parameterization may need to correct for the misrepresentation of under-resolved GWs, i.e., coarse vertical resolution can bias GW breaking level, leading to erroneous momentum forcing. (ii) The parameterized waves depend on the resolved solution for both their sources and dissipation, making them susceptible to model biases. Even a "perfect" parameterization could then yield an undesirable result, e.g., an unrealistic Quasi-Biennial Oscillation (QBO). While model-specific calibration is required, one would like a general "recipe" suitable for most models. From a practical point of view, the adoption of a new parameterization will be hindered by a too-demanding calibration process. This issue is of particular concern in the context of data-driven methods, where the number of tunable degrees of freedom is large (possibly in the millions). Thus, more judicious ways for addressing the calibration step are required. To address the above issues, we develop a 1D QBO model, where the "true" gravity wave momentum deposition is determined from a source distribution and critical level breaking, akin to a traditional physics-based GW parameterization. The control parameters associated with the source consist of the total wave flux (related to the total precipitation for convectively generated waves) and the spectrum width (related to the depth of convection). These parameters can be varied to mimic the variability in GW sources between different models, i.e., biases in precipitation variability. In addition, the model’s explicit diffusivity and vertical advection can be varied to mimic biases in model numerics and circulation, respectively. The model thus allows us to assess the ability of a data-driven parameterization to (i) extrapolate, capturing the response of GW momentum transport to a change in the model parameters and (ii) be calibrated, adjusted to maintain the desired simulation of the QBO in response to a change in the model parameters. The first property is essential for a parameterization to be used for climate prediction, the second, for a parameterization to be used at all. We focus in particular on emulators of the GW momentum transport based on neural network and regression trees, contrasting their ability to satisfy both of these goals.

An intermediate complexity moist General Circulation Model is used to investigate the factor(s) controlling the magnitude of the surface impact from Southern Hemisphere springtime ozone depletion. ...

Accurate representation of stratospheric trace gas transport is important for ozone modeling and climate projection. Intermodel spread can arise from differences in the representation of transport by the diabatic (overturning) circulation vs. comparatively faster adiabatic mixing by breaking waves, or through numerical errors, primarily diffusion. This study investigates the impact of these processes on transport using an idealised tracer, the age-of-air. Transport is assessed in two state-of-the-art dynamical cores based on fundamentally different numerical formulations: finite volume and spectral element. Integrating the models in free-running and nudged tropical wind configurations reveals the crucial impact of tropical dynamics on stratospheric transport. Using age-budget theory, vertical and horizontal gradients of age allow comparison of the roles of the diabatic circulation, adiabatic mixing, and the numerical diffusive flux. Their respective contribution is quantified by connecting the full 3-d model to the tropical leaky pipe framework of Neu and Plumb (1999). Transport by the two cores varies significantly in the free-running integrations, with the age in the middle stratosphere differing by about 2 years primarily due to differences in adiabatic mixing. When winds in the tropics are constrained, the difference in age drops to about 0.5 years; in this configuration, more than half the difference is due to the representation of the diabatic circulation. Numerical diffusion is very sensitive to the resolution of the core, but does not play a significant role in differences between the cores when they are run at comparable resolution. It is concluded that fundamental differences rooted in dynamical core formulation can account for a substantial fraction of transport bias between climate models.

The atmospheric circulation response to global warming is important for accurate prediction of climate change on regional scales. For the midlatitudes, shifts in the extratropical jet streams have important consequences for precipitation, blocking, and extreme events. It has proven to be a challenge, however, to predict. For example, the North Atlantic jet stream plays a vital role in the climate of eastern North America and Europe; in the last intercomparison of state‐of‐the‐art climate models, the models did not even agree on the sign of its wintertime response to global warming. Perhaps this should not come as a surprise, as we also lack a comprehensive theory for the impact of warming on the midlatitude circulation. In a recent study, Tan et al. (2019, https://doi.org/10.1029/2018MS001492) constructed models of simpler atmospheres to explore the response of the midlatitude jet to global warming. Their idealized atmospheres highlight the difficulty of developing a comprehensive theory for the midlatitude circulation but also provide pathways to improve models of Earth's atmosphere. Models of simpler atmospheres allow one to isolate the impact of specific atmospheric processes and connect theoretical understanding with comprehensive climate prediction systems. Such models can also be used to explore very different atmospheric regimes, from Earth's past to distant planets., Key Points The atmospheric circulation response to global warming is both a challenge to predict and to understandModels of idealized atmospheres allow a process‐oriented investigation of the circulation responseA growing number of models of simpler atmospheres are being developed and shared

The circulation of the stratosphere transports important trace gases, including ozone, and can be thought of as having a fast horizontal mixing component and a slow meridional overturning component...

Major disruptions to the stratospheric circulation have far-reaching effects, including increased likelihood of snowstorms, growth of the ozone hole, and interference in global telecommunications.

An intermediate complexity moist general circulation model is used to investigate the sensitivity of the quasi-biennial oscillation (QBO) to resolution, diffusion, tropical tropospheric waves, and parameterized gravity waves. Finer horizontal resolution is shown to lead to a shorter period, while finer vertical resolution is shown to lead to a longer period and to a larger amplitude in the lowermost stratosphere. More scale-selective diffusion leads to a faster and stronger QBO, while enhancing the sources of tropospheric stationary wave activity leads to a weaker QBO. In terms of parameterized gravity waves, broadening the spectral width of the source function leads to a longer period and a stronger amplitude although the amplitude effect saturates in the mid-stratosphere when the half-width exceeds

Nonlinear atmospheric dynamics produce rare events that are hard to predict and attribute due to many interacting degrees of freedom. A sudden stratospheric warming is a spectacular example in which the winter polar vortex in the stratosphere rapidly breaks down, inducing a shift in midlatitude tropospheric weather patterns that persist for up to 2-3 months. In principle, lengthy numerical simulations can be used to predict and understand these rare transitions. For complex models, however, the cost of the direct numerical simulation approach is often prohibitive. We describe an alternative approach which in principle only requires relatively short duration computer simulations of the system. Applying this methodology to a classical idealized stratospheric model with stochastic forcing, we compute optimal forecasts of sudden warming events and quantify the limits of predictability. Statistical analysis relates these optimal forecasts to a small number of easy-to-interpret physical variables.Remarkably, we are able to estimate these quantities using a data set of simulations much shorter than the return time of the warming event.

We present a novel, single-column gravity wave parameterization (GWP) that uses machine learning to emulate a physics-based GWP. An artificial neural network (ANN) is trained with output from an idealized atmospheric model and tested in an offline environment, illustrating that an ANN can learn the salient features of gravity wave momentum transport directly from resolved flow variables. We demonstrate that when trained on the westward phase of the Quasi-Biennial Oscillation, the ANN can skillfully generate the momentum fluxes associated with the eastward phase. We also show that the meridional and zonal wind components are the only flow variables necessary to predict horizontal momentum fluxes with a globally and temporally averaged R^2 value over 0.8. State-of-the-art GWPs are severely limited by computational constraints and a scarcity of observations for validation. This work constitutes a significant step towards obtaining observationally validated, computationally efficient GWPs in global climate models.

Rare events arising in nonlinear atmospheric dynamics remain hard to predict and attribute. We address the problem of forecasting rare events in a prototypical example, Sudden Stratospheric Warmings (SSWs). Approximately once every other winter, the boreal stratospheric polar vortex rapidly breaks down, shifting midlatitude surface weather patterns for months. We focus on two key quantities of interest: the probability of an SSW occurring, and the expected lead time if it does occur, as functions of initial condition. These \emph{optimal forecasts} concretely measure the event's progress. Direct numerical simulation can estimate them in principle, but is prohibitively expensive in practice: each rare event requires a long integration to observe, and the cost of each integration grows with model complexity. We describe an alternative approach using integrations that are \emph{short} compared to the timescale of the warming event. We compute the probability and lead time efficiently by solving equations involving the transition operator, which encodes all information about the dynamics. We relate these optimal forecasts to a small number of interpretable physical variables, suggesting optimal measurements for forecasting. We illustrate the methodology on a prototype SSW model developed by Holton and Mass (1976) and modified by stochastic forcing. While highly idealized, this model captures the essential nonlinear dynamics of SSWs and exhibits the key forecasting challenge: the dramatic separation in timescales between a single event and the return time between successive events. Our methodology is designed to fully exploit high-dimensional data from models and observations, and has the potential to identify detailed predictors of many complex rare events in meteorology., Comment: 26 pages, 7 figures, major revision after original. Accepted to Monthly Weather Review, American Meteorological Society

Accurate representation of tracer transport --- the movement of trace constituents by the atmospheric flow --- continues to be a challenge for climate models. Differences in the resolved circulation, biases due to physical parameterizations, and differences in the numerical representation of trace gases result in large variations in transport, even among state-of-the-art climate models. These differences result in disagreement among model projections of the evolution of stratospheric ozone throughout the 21st century particularly in the recovery of the Antarctic ozone hole. In addition to transport, the delicate momentum balance in the upper-troposphere and lower-stratosphere (UTLS) also presents a stiff challenge for model numerics, exposing the impacts of numerical dissipation, the resolution of waves, and the consequences of imperfect momentum conservation. Biases in this region impact the global circulation, e.g., influencing the extratropics jets and stratospheric polar vortices, and alter the transport and exchange of trace gases between and through the troposphere and stratosphere. In this study, we compare 2 modern dynamical cores (dycores) that employ very different numerics: the cubed sphere finite volume (CSFV) core from GFDL and the spectral element (SE) core from NCAR-CAM5. We force these dycores using identical Held-Suarez diabatic forcing in the troposphere and Polvani-Kushner diabatic forcing in the stratosphere, varying the horizontal and vertical resolution. We observe significant differences in circulation, between the two models at high vertical resolution in the lower and middle tropical stratosphere. While the finite volume core is relatively insensitive to any changes in vertical resolution, the PS and SE dycores resolve considerably different tropical stratospheric dynamics at high vertical resolution (80 levels). These models develop QBO-like westerly winds in the tropics and induce a secondary meridional circulation in the tropical stratosphere, which sets of transport between the models. Using the theoretical leaky pipe transport model we analyze and separate out the transport differences due to differences is diabatic circulation and isentropic mixing and infer that this secondary circulation strikingly modulates stratospheric tracer transport (age of air) by altering the tropical-extratropical mixing, and impacts the extratropical circulation through the subtropical jets. Implications for comprehensive atmospheric modeling are discussed.

Age of air is an idealized tracer often used as a measure of the stratospheric circulation. We will show how to quantitatively relate age to the diabatic circulation and the adiabatic mixing. As it is an idealized tracer, age cannot be measured itself and must be inferred from other tracers. Typically, the two primary trace gases used are sulfur hexafluoride and carbon dioxide. Other tracers have a compact relationship with age, however, and can also be used to calculate age. We will discuss a range of tracer measurements from both satellites and in situ, including sulfur hexafluoride, carbon dioxide, nitrous oxide, methane, and the ratio of argon to nitrogen. We will compare the age derived from these different species, including different calculation methods and caveats, and compare with modeled ideal age and trace gas concentrations. We conclude by showing the strength of the diabatic circulation and the adiabatic mixing calculated from these trace gas calculations.

Tropospheric features preceding sudden stratospheric warming events (SSWs) are identified using a large compendium of events obtained from a chemistry–climate model. In agreement with recent observational studies, it is found that approximately one-third of SSWs are preceded by extreme episodes of wave activity in the lower troposphere. The relationship becomes stronger in the lower stratosphere, where ~60% of SSWs are preceded by extreme wave activity at 100 hPa. Additional analysis characterizes events that do or do not appear to subsequently impact the troposphere, referred to as downward and non-downward propagating SSWs, respectively. On average, tropospheric wave activity is larger preceding downward-propagating SSWs compared to non-downward propagating events, and associated in particular with a doubly strengthened Siberian high. Of the SSWs that were preceded by extreme lower-tropospheric wave activity, ~2/3 propagated down to the troposphere, and hence the presence of extreme lower-tropospheric wave activity can only be used probabilistically to predict a slight increase or decrease at the onset, of the likelihood of tropospheric impacts to follow. However, a large number of downward and non-downward propagating SSWs must be considered (>35), before the difference becomes statistically significant. The precursors are also robust upon comparison with composites consisting of randomly selected tropospheric northern annular mode (NAM) events. The downward influence and precursors to split and displacement events are also examined. It is found that anomalous upward wave-1 fluxes precede both cases. Splits exhibit a near instantaneous, barotropic response in the stratosphere and troposphere, while displacements have a stronger long-term influence.

The annular modes characterize the dominant variability of the extratropical circulation in each hemisphere, quantifying vacillations in the position of the tropospheric jet streams and the strength of the stratospheric polar vortices. Their representation in all available reanalysis products is assessed. Reanalysis uncertainty associated with limitations in the ability to constrain the circulation with available observations, i.e., the inter-reanalysis spread, is contrasted with sampling uncertainty associated with the finite length of the reanalysis records. It is shown that the annular modes are extremely consistent across all modern reanalyses during the satellite era (ca. 1979 onward). Consequently, uncertainty in annular mode variability, e.g., the coupling between the stratosphere and troposphere and the variation in the amplitude and timescale of jet variations throughout the annual cycle, is dominated by sampling uncertainty. Comparison of reanalyses based on conventional (i.e., nonsatellite) or surface observations alone with those using all available observations indicates that there is limited ability to characterize the Southern Annular Mode (SAM) in the presatellite era. Notably, prior to 1979, surface-input reanalyses better capture the SAM at near-surface levels than full-input reanalyses. For the Northern Annular Mode, however, there is evidence that conventional observations are sufficient, at least from 1958 onward. The addition of 2 additional decades of records substantially reduces sampling uncertainty in several key measures of annular mode variability, demonstrating the value of more historic reanalyses. Implications for the assessment of atmospheric models and the strength of coupling between the surface and upper atmosphere are discussed.

Various criteria exist for determining the occurrence of a major sudden stratospheric warming (SSW), but the most common is based on the reversal of the climatological westerly zonal-mean zonal winds at 60° latitude and 10 hPa in the winter stratosphere. This definition was established at a time when observations of the stratosphere were sparse. Given greater access to data in the satellite era, a systematic analysis of the optimal parameters of latitude, altitude, and threshold for the wind reversal is now possible. Here, the frequency of SSWs, the strength of the wave forcing associated with the events, changes in stratospheric temperature and zonal winds, and surface impacts are examined as a function of the stratospheric wind reversal parameters. The results provide a methodical assessment of how to best define a standard metric for major SSWs. While the continuum nature of stratospheric variability makes it difficult to identify a decisively optimal threshold, there is a relatively narrow envelope of thresholds that work well—and the original focus at 60° latitude and 10 hPa lies within this window.

Isca is a framework for the idealized modelling of the global circulation of planetary atmospheres at varying levels of complexity and realism. The framework is an outgrowth of models from the Geophysical Fluid Dynamics Laboratory in Princeton, USA, designed for Earth's atmosphere, but it may readily be extended into other planetary regimes. Various forcing and radiation options are available, from dry, time invariant, Newtonian thermal relaxation to moist dynamics with radiative transfer. Options are available in the dry thermal relaxation scheme to account for the effects of obliquity and eccentricity (and so seasonality), different atmospheric optical depths and a surface mixed layer. An idealized grey radiation scheme, a two-band scheme, and a multiband scheme are also available, all with simple moist effects and astronomically based solar forcing. At the complex end of the spectrum the framework provides a direct connection to comprehensive atmospheric general circulation models. For Earth modelling, options include an aquaplanet and configurable continental outlines and topography. Continents may be defined by changing albedo, heat capacity, and evaporative parameters and/or by using a simple bucket hydrology model. Oceanic Q fluxes may be added to reproduce specified sea surface temperatures, with arbitrary continental distributions. Planetary atmospheres may be configured by changing planetary size and mass, solar forcing, atmospheric mass, radiation, and other parameters. Examples are given of various Earth configurations as well as a giant planet simulation, a slowly rotating terrestrial planet simulation, and tidally locked and other orbitally resonant exoplanet simulations. The underlying model is written in Fortran and may largely be configured with Python scripts. Python scripts are also used to run the model on different architectures, to archive the output, and for diagnostics, graphics, and post-processing. All of these features are publicly available in a Git-based repository.

The processes regulating the climatology and annual cycle of the tropical tropopause layer (TTL) and cold point are not fully understood. Three main drivers have been identified: planetary-scale equatorial waves excited by tropical convection, planetary-scale extratropical waves associated with the deep Brewer–Dobson circulation, and synoptic-scale waves associated with the midlatitude storm tracks. In both observations and comprehensive atmospheric models, all three coexist, making it difficult to separate their contributions. Here, a new intermediate-complexity atmospheric model is developed. Simple modification of the model’s lower boundary allows detailed study of the three processes key to the TTL, both in isolation and together. The model shows that tropical planetary waves are most critical for regulating the mean TTL, setting the depth and temperature of the cold point. The annual cycle of the TTL, which is coldest (warmest) in boreal winter (summer), however, depends critically on the strong annual variation in baroclinicity of the Northern Hemisphere relative to that of the Southern Hemisphere. Planetary-scale waves excited from either the tropics or extratropics then double the impact of baroclinicity on the TTL annual cycle. The remarkably generic response of TTL temperatures over a range of configurations suggests that the details of the wave forcing are unimportant, provided there is sufficient variation in the upward extent of westerly winds over the annual cycle. Westerly winds enable the propagation of stationary Rossby waves, and weakening of the subtropical jet in boreal summer inhibits their propagation into the lower stratosphere, warming the TTL.

The distribution of gases such as ozone and water vapour in the stratosphere - which affect surface climate - is influenced by the meridional overturning of mass in the stratosphere, the Brewer-Dobson circulation. However, observation-based estimates of its global strength are difficult to obtain. Here we present two calculations of the mean strength of the meridional overturning of the stratosphere. We analyze satellite data that document the global diabatic circulation between 2007- 2011, and compare these to three re-analysis data sets and to simulations with a state-of-the-art chemistry-climate model. Using measurements of sulfur hexafluoride (SF6) and nitrous oxide, we calculate the global mean diabatic overturning mass flux throughout the stratosphere. In the lower stratosphere, these two estimates agree, and at a potential temperature level of 460 K (about 20 km or 60 hPa in tropics), the global circulation strength is 6.3-7.6 × 109 kg/s. Higher in the atmosphere, only the SF6-based estimate is available, and it diverges from the re-analysis data and simulations. Interpretation of the SF6 data-based estimate is limited because of a mesospheric sink of SF6; however, the reanalyses also differ substantially from each other. We conclude that the uncertainty in the mean meridional overturning circulation strength at upper levels of the stratosphere amounts to at least 100 %.

A sudden stratospheric warming (SSW) is often defined as zonal-mean zonal wind reversal at 10 hPa and 60°N. This simple definition has been applied not only to the reanalysis data but also to climate model output. In the present study, it is shown that the application of this definition to models can be significantly influenced by model mean biases (i.e., more frequent SSWs appear to occur in models with a weaker climatological polar vortex). To overcome this deficiency, a tendency-based definition is proposed and applied to the multimodel datasets archived for phase 5 of the Coupled Model Intercomparison Project (CMIP5). In this definition, SSW-like events are defined by sufficiently strong vortex deceleration. This approach removes a linear relationship between SSW frequency and intensity of the climatological polar vortex in the CMIP5 models. The models’ SSW frequency instead becomes significantly correlated with the climatological upward wave flux at 100 hPa, a measure of interaction between the troposphere and stratosphere. Lower stratospheric wave activity and downward propagation of stratospheric anomalies to the troposphere are also reasonably well captured. However, in both definitions, the high-top models generally exhibit more frequent SSWs than the low-top models. Moreover, a hint of more frequent SSWs in a warm climate is found in both definitions.

Model hierarchies are fundamental to how we model Earth’s climate, allowing us to apply our theoretical understanding, connect simple ideas to the real atmosphere, and test new hypotheses.

As the planet warms, climate models predict that rain will become heavier but less frequent and that the circulation will weaken. Here, two heuristic models relating moisture, vertical velocity, and rainfall distributions are developed—one in which the distribution of vertical velocity is prescribed and another in which it is predicted. These models are used to explore the response to warming and moistening as well as changes in circulation, atmospheric energy budget, and stability. Some key assumptions of the models include that relative humidity is fixed within and between climate states and that stability is constant within each climate state. The first model shows that an increase in skewness of the vertical velocity distribution is crucial for capturing salient characteristics of the changing distribution of rain, including the muted rate of mean precipitation increase relative to extremes and the decrease in the total number or area of rain events. The second model suggests that this increase in the skewness of the vertical velocity arises from the asymmetric impact of latent heating on vertical motion.

The enhancement of the stratospheric aerosol layer by volcanic eruptions induces a complex set of responses causing global and regional climate effects on a broad range of timescales. Uncertainties exist regarding the climatic response to strong volcanic forcing identified in coupled climate simulations that contributed to the fifth phase of the Coupled Model Intercomparison Project (CMIP5). In order to better understand the sources of these model diversities, the Model Intercomparison Project on the climatic response to Volcanic forcing (VolMIP) has defined a coordinated set of idealized volcanic perturbation experiments to be carried out in alignment with the CMIP6 protocol. VolMIP provides a common stratospheric aerosol data set for each experiment to minimize differences in the applied volcanic forcing. It defines a set of initial conditions to assess how internal climate variability contributes to determining the response. VolMIP will assess to what extent volcanically forced responses of the coupled ocean–atmosphere system are robustly simulated by state-of-the-art coupled climate models and identify the causes that limit robust simulated behavior, especially differences in the treatment of physical processes. This paper illustrates the design of the idealized volcanic perturbation experiments in the VolMIP protocol and describes the common aerosol forcing input data sets to be used.

The first multimodel study to estimate the predictability of a boreal sudden stratospheric warming (SSW) is performed using five NWP systems. During the 2012/13 boreal winter, anomalous upward propagating planetary wave activity was observed toward the end of December, which was followed by a rapid deceleration of the westerly circulation around 2 January 2013, and on 7 January 2013 the zonal-mean zonal wind at 60°N and 10 hPa reversed to easterly. This stratospheric dynamical activity was followed by an equatorward shift of the tropospheric jet stream and by a high pressure anomaly over the North Atlantic, which resulted in severe cold conditions in the United Kingdom and northern Europe. In most of the five models, the SSW event was predicted 10 days in advance. However, only some ensemble members in most of the models predicted weakening of westerly wind when the models were initialized 15 days in advance of the SSW. Further dynamical analysis of the SSW shows that this event was characterized by the anomalous planetary wavenumber-1 amplification followed by the anomalous wavenumber-2 amplification in the stratosphere, which resulted in a split vortex occurring between 6 and 8 January 2013. The models have some success in reproducing wavenumber-1 activity when initialized 15 days in advance, but they generally failed to produce the wavenumber-2 activity during the final days of the event. Detailed analysis shows that models have reasonably good skill in forecasting tropospheric blocking features that stimulate wavenumber-2 amplification in the troposphere, but they have limited skill in reproducing wavenumber-2 amplification in the stratosphere.

Proxy data and observations suggest that large tropical volcanic eruptions induce a poleward shift of the North Atlantic jet stream in boreal winter. However, there is far from universal agreement in models on this effect and its mechanism, and the possibilities of a corresponding jet shift in the Southern Hemisphere or the summer season have received little attention. Using a hierarchy of simplified atmospheric models, this study examines the impact of stratospheric aerosol on the extratropical circulation over the annual cycle. In particular, the models allow the separation of the dominant shortwave (surface cooling) and longwave (stratospheric warming) impacts of volcanic aerosol. It is found that stratospheric warming shifts the jet poleward in both the summer and winter hemispheres. The experiments cannot definitively rule out the role of surface cooling, but they provide no evidence that it shifts the jet poleward. Further study with simplified models demonstrates that the response to stratospheric warming is remarkably generic and does not depend critically on the boundary conditions (e.g., the planetary wave forcing) or the atmospheric physics (e.g., the treatment of radiative transfer and moist processes). It does, however, fundamentally involve both zonal-mean and eddy circulation feedbacks. The time scales, seasonality, and structure of the response provide further insight into the mechanism, as well as its connection to modes of intrinsic natural variability. These findings have implications for the interpretation of comprehensive model studies and for postvolcanic prediction.

In this review, we highlight the complementary relationship between simple and comprehensive models in addressing key scientific questions to describe Earth's atmospheric circulation. The systematic representation of models in steps, or hierarchies, connects our understanding from idealized systems to comprehensive models and ultimately the observed atmosphere. We define three interconnected principles that can be used to characterize the model hierarchies of the atmosphere. We explore the rich diversity within the governing equations in the dynamical hierarchy, the ability to isolate and understand atmospheric processes in the process hierarchy, and the importance of the physical domain and resolution in the hierarchy of scale. We center our discussion on the large-scale circulation of the atmosphere and its interaction with clouds and convection, focusing on areas where simple models have had a significant impact. Our confidence in climate model projections of the future is based on our efforts to ground the climate predictions in fundamental physical understanding. This understanding is, in part, possible due to the hierarchies of idealized models that afford the simplicity required for understanding complex systems.

The meridional circulation of the stratosphere, or Brewer-Dobson circulation (BDC), is projected to accelerate with increasing greenhouse gas (GHG) concentrations. The acceleration is typically quantified by changes in the tropical upward mass flux (Ftrop) across a given pressure surface. Simultaneously, models project a lifting of the entire atmospheric circulation in response to GHGs; notably, the tropopause rises about a kilometer over this century. In this study, it is shown that most of the BDC trend is associated with the rise in the circulation. Using a chemistry-climate model (CCM), Ftrop trends across 100 hPa are contrasted with those across the tropopause: while Ftrop at 100 hPa increases 1–2 %/decade, the mass flux entering the atmosphere above the tropopause actually decreases. Similar results are found for other CCMs, suggesting that changes in the BDC may better be described as an upward shift of the circulation, as opposed to an increase, with implications for the mechanism and stratosphere-troposphere exchange.

Recent studies link climate change around Antarctica to the sea surface temperature of tropical oceans, with teleconnections from the Pacific, Atlantic, and Indian Oceans making different contributions to Antarctic climate. In this study, the impacts of each ocean basin on the wintertime Southern Hemisphere circulation are identified by comparing simulation results using a comprehensive atmospheric model, an idealized dynamical core model, and a theoretical Rossby wave model. The results herein show that tropical Atlantic Ocean warming, Indian Ocean warming, and eastern Pacific cooling are all able to deepen the Amundsen Sea low located adjacent to West Antarctica, while western Pacific warming increases the pressure to the west of the international date line, encompassing the Ross Sea and regions south of the Tasman Sea. In austral winter, these tropical ocean basins work together linearly to modulate the atmospheric circulation around West Antarctica. Further analyses indicate that these teleconnections critically depend on stationary Rossby wave dynamics and are thus sensitive to the background flow, particularly the subtropical/midlatitude jet. Near these jets, wind shear is amplified, which strengthens the generation of Rossby waves. On the other hand, near the edges of the jets the meridional gradient of the absolute vorticity is also enhanced. As a consequence of the Rossby wave dispersion relationship, the jet edge may reflect stationary Rossby wave trains, serving as a waveguide. The simulation results not only identify the relative roles of each of the tropical ocean basins in the tropical–Antarctica teleconnection, but also suggest that a deeper understanding of teleconnections requires a better estimation of the atmospheric jet structures.

The seasonal variability of the polar stratospheric vortex is studied in a simplified AGCM driven by specified equilibrium temperature distributions. Seasonal variations in equilibrium temperature are imposed in the stratosphere only, enabling the study of stratosphere–troposphere coupling on seasonal time scales, without the complication of an internal tropospheric seasonal cycle. The model is forced with different shapes and amplitudes of simple bottom topography, resulting in a range of stratospheric climates. The effect of these different kinds of topography on the seasonal variability of the strength of the polar vortex, the average timing and variability in timing of the final breakup of the vortex (final warming events), the conditions of occurrence and frequency of midwinter warming events, and the impact of the stratospheric seasonal cycle on the troposphere are explored. The inclusion of wavenumber-1 and wavenumber-2 topographies results in very different stratospheric seasonal variability. Hemispheric differences in stratospheric seasonal variability are recovered in the model with appropriate choices of wave-2 topography. In the model experiment with a realistic Northern Hemisphere–like frequency of midwinter warming events, the distribution of the intervals between these events suggests that the model has no year-to-year memory. When forced with wave-1 topography, the gross features of seasonal variability are similar to those forced with wave-2 topography, but the dependence on forcing magnitude is weaker. Further, the frequency of major warming events has a nonmonotonic dependence on forcing magnitude and never reaches the frequency observed in the Northern Hemisphere.