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The equivalent depth of an atmospheric layer is of importance in determining the phase speed of gravity waves and characterizing wave phenomena. The value of the equivalent depth can be obtained from the eigenvalues of the vertical structure equation (the vertical part of the primitive equations) where the mean temperature profile is a coefficient. Both numerical solutions of the vertical structure equation and analytical considerations are employed to calculate the equivalent depth, hn, as a function of the atmospheric layer's thickness, Δz. Our solutions for layers of thickness 100 ≤Δz≤ 2000 m show that for baroclinic modes, hn can be over two orders of magnitudes smaller than Δz. Analytic expressions are derived for hn in layers of uniform temperature and numerical solutions are derived for layers in which the temperature changes linearly with height. A comparison between the two cases shows that a slight temperature gradient (of say 0.65 K across a 100 m layer) decreases hn by a factor of 3 (but can reach a factor of 10 for larger gradients) compared with its value in a layer of uniform temperature, while a change of 10 K in the layer's uniform temperature hardly changes hn. The n=0 baroclinic mode exists in all combinations of boundary conditions top and bottom while the barotropic mode only exists when the vertical velocity vanishes at both boundaries of the layer. [ABSTRACT FROM AUTHOR]

Roughly one‐third of sudden stratospheric warming (SSW) events lack a strong canonical surface response, and this can lead to a forecast bust if a strong response was predicted. Hence, it is desirable to predict before SSW onset if an event will propagate downward. The predictability of the downward response of SSWs is considered in seven subseasonal‐to‐seasonal forecast models for 16 major SSWs between 1998 and 2022, a larger sample size than considered by previous works. The models successfully predict before SSW onset which SSWs have a stronger downward response to 100 hPa, however they struggle to predict which have a stronger tropospheric response. The downward response is stronger if the magnitude of the deceleration of the 10 hPa winds is more accurately predicted. Downward response is stronger for split and absorbing SSWs. In contrast, there is little relationship between SSWs whose onset can be predicted at earlier leads and the downward response. Plain Language Summary: The wintertime stratosphere typically features circumpolar strong westerly winds, but on occasion these strong winds can reverse and temperatures over the pole can rise by tens of degrees in an event known as a sudden stratospheric warming (SSW). Such an event increases the likelihood of extreme cold over Northern Eurasia and wet conditions in Southern Europe, however roughly a third of events do not feature such downward propagation. Sixteen SSW events have occurred in the Northern Hemisphere over the period 1998 to 2022, and this study considers whether the models that have contributed to the subseasonal to seasonal (S2S) database are able to distinguish which are downward propagating and which are not. We also explore the factors that govern downward propagation of the SSW signal in these models. Key Points: Downward versus non‐downward response of SSWs to 100 hPa is predicted by subseasonal prediction models ∼20 days before SSW onsetIn contrast, models struggle to predict the presence/absence of a tropospheric response before SSW onsetDownward response and predictability of SSWs unrelated; split and absorbing SSWs show stronger downward response in models and reanalysis [ABSTRACT FROM AUTHOR]

Climate change has emerged across many regions. Some observed regional climate changes, such as amplified Arctic warming and land-sea warming contrasts have been predicted by climate models. However, many other observed regional changes, such as changes in tropical sea surface temperature and monsoon rainfall are not well simulated by climate model ensembles even when taking into account natural internal variability and structural uncertainties in the response of models to anthropogenic radiative forcing. This suggests climate model predictions may not fully reflect what our future will look like. The discrepancies between models and observations are not well understood due to several real and apparent puzzles and limitations such as the "signal-tonoise paradox" and real-world record-shattering extremes falling outside of the possible range predicted by models. Addressing these discrepancies, puzzles and limitations is essential, because understanding and reliably predicting regional climate change is necessary in order to communicate effectively about the underlying drivers of change, provide reliable information to stakeholders, enable societies to adapt, and increase resilience and reduce vulnerability. The challenges of achieving this are greater in the Global South, especially because of the lack of observational data over long time periods and a lack of scientific focus on Global South climate change. To address discrepancies between observations and models, it is important to prioritize resources for understanding regional climate predictions and analyzing where and why models and observations disagree via testing hypotheses of drivers of biases using observations and models. Gaps in understanding can be discovered and filled by exploiting new tools, such as artificial intelligence/machine learning, high-resolution models, new modeling experiments in the model hierarchy, better quantification of forcing, and new observations. Conscious efforts are needed toward creating opportunities that allow regional experts, particularly those from the Global South, to take the lead in regional climate research. This includes co-learning in technical aspects of analyzing simulations and in the physics and dynamics of regional climate change. Finally, improved methods of regional climate communication are needed, which account for the underlying uncertainties, in order to provide reliable and actionable information to stakeholders and the media. [ABSTRACT FROM AUTHOR]

The dominant pattern of Northern Hemisphere extratropical climate variability is the Northern Annular Mode (NAM), which in wintertime represents the coupling of the stratospheric and tropospheric circulations. The internal variability associated with the NAM has been shown to give rise to substantial uncertainty in climate projections of regional surface air temperatures (SATs), but it's unclear how much of this variability arises from stratosphere‐troposphere coupling processes. Here, using three large‐ensemble coupled climate model simulations from 1850 to 2100 with varying fidelity of stratosphere‐troposphere coupling processes, we demonstrate that regional SAT variability across timescales is amplified when the tropospheric NAM is coupled to the stratospheric NAM. Moreover, models that lack adequate simulation of stratosphere‐troposphere coupling processes may not capture the magnitude of uncertainty in near‐term SAT projections associated with this coupling. Plain Language Summary: Large‐scale atmospheric circulation variability drives substantial variation in regional surface air temperatures (SATs), so that even on 30–40 year timescales local cooling trends are possible even as global‐mean temperatures increase. We provide evidence that when the stratospheric mean flow is coupled to the tropospheric mean flow, the decadal variability of SATs is amplified in some regions. Some models do not represent well the observed coupling of the stratosphere to the troposphere, and these models may underestimate decadal variability associated with this coupling. Key Points: The Northern Annular Mode (NAM) exhibits decadal variability that can accelerate or slow the rate of anthropogenic regional surface warmingAmplified decadal variability of extratropical surface temperatures occurs when the NAM is coupled from the stratosphere to the troposphereModels that fail to adequately capture vertical coupling may underestimate the magnitude of decadal variations in surface air temperatures [ABSTRACT FROM AUTHOR]

We extend the Matsuno–Gill model, originally developed on the equatorial $\beta$ -plane, to the surface of the sphere. While on the $\beta$ -plane the non-dimensional model contains a single parameter, the damping rate $\gamma$ , on a sphere the model contains a second parameter, the rotation rate $\epsilon ^{1/2}$ (Lamb number). By considering the different combinations of damping and rotation, we are able to characterize the solutions over the $(\gamma, \epsilon ^{1/2})$ plane. We find that the $\beta$ -plane approximation is accurate only for fast rotation rates, where gravity waves traverse a fraction of the sphere's diameter in one rotation period. The particular solutions studied by Matsuno and Gill are accurate only for fast rotation and moderate damping rates, where the relaxation time is comparable to the time on which gravity waves traverse the sphere's diameter. Other regions of the parameter space can be described by different approximations, including radiative relaxation, geostrophic, weak temperature gradient and non-rotating approximations. The effect of the additional parameter introduced by the sphere is to alter the eigenmodes of the free system. Thus, unlike the solutions obtained by Matsuno and Gill, where the long-term response to a symmetric forcing consists solely of Kelvin and Rossby waves, the response on the sphere includes other waves as well, depending on the combination of $\gamma$ and $\epsilon ^{1/2}$. The particular solutions studied by Matsuno and Gill apply to Earth's oceans, while the more general $\beta$ -plane solutions are only somewhat relevant to Earth's troposphere. In Earth's stratosphere, Venus and Titan, only the spherical solutions apply. [ABSTRACT FROM AUTHOR]