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The dynamical core of the Department of Energy global climate model is used to understand the role of non‐hydrostatic dynamics in the simulation of dry and moist baroclinic waves. To reduce computational cost, the Diabatic Acceleration and REscaling approach is adopted. Scale analysis and numerical simulations suggest that the model solution is not distorted by the change of spherical metric terms due to the change of Earth radius, neither are the inter‐scale interactions strongly altered as indicated by the analysis of spectral flux. Compared with hydrostatic simulations, the onset of baroclinic instability is delayed under non‐hydrostatic dynamics as the associated weaker vertical motions tend to increase the critical wavelength and narrow the range of waves that can be baroclinically unstable. During the development of baroclinic waves, non‐hydrostatic dynamics tends to induce vertical motions in the upper troposphere, accelerating the eastward propagation of upper‐level ridges through their impact on local vorticity tendency. These processes reduce the westward tilt of the vertical ridge axes and suppress the conversion of mean flow available potential energy to eddy kinetic energy, leading to weaker baroclinic eddies than in hydrostatic simulations. The contrasts between hydrostatic and non‐hydrostatic settings hold in supplemental experiments that vary the background flow Rossby number, the amount of water vapor content and vertical resolution. We also find that mesoscale and smaller‐scale activities can be considerably under‐represented when the vertical resolution is limited to that typically used in global climate models. Plain Language Summary: Limited by computational resources, comprehensive climate simulations are usually conducted with a horizontal grid spacing of 50–100 km. At such coarse resolutions, vertical motions can be approximated using hydrostatic balance in which the gravity force is balanced by the vertical component of the pressure gradient force. In high‐resolution simulations that aim at improving the representation of the Earth′s climate, this approximation breaks down, and one has to solve the complete vertical momentum equation to address non‐hydrostatic effects. Here, we examine the role of non‐hydrostatic dynamics in the simulation of baroclinic instability that is responsible for much of the weather in the midlatitudes. Our results show that non‐hydrostatic dynamics tends to delay the onset of baroclinic instability and reduce the amplitude of simulated baroclinic waves. We also find that mesoscale and smaller‐scale activities can be considerably under‐represented when the vertical resolution is limited to that typically used in global climate models. Besides illustrating the underlying physical mechanisms associated with non‐hydrostatic effects, this study implies the importance of including non‐hydrostatic dynamics in modeling midlatitude weather and climate in global high‐resolution simulations that are becoming affordable in the foreseeable future. Key Points: Non‐hydrostatic dynamics tends to delay the onset of baroclinic instability and reduce the amplitude of the simulated baroclinic wavesMesoscale and smaller‐scale processes are under‐represented with limited vertical resolution as typically used in global climate models [ABSTRACT FROM AUTHOR]

Since model bias and associated initialization shock are serious shortcomings that reduce prediction skills in state‐of‐the‐art decadal climate prediction efforts, we pursue a complementary machine‐learning‐based approach to climate prediction. The example problem setting we consider consists of predicting natural variability of the North Atlantic sea surface temperature on the interannual timescale in the pre‐industrial control simulation of the Community Earth System Model. While previous works have considered the use of recurrent networks such as convolutional LSTMs and reservoir computing networks in this and other similar problem settings, we currently focus on the use of feedforward convolutional networks. In particular, we find that a feedforward convolutional network with a Densenet architecture is able to outperform a convolutional LSTM in terms of predictive skill. Next, we go on to consider a probabilistic formulation of the same network based on Stein variational gradient descent and find that in addition to providing useful measures of predictive uncertainty, the probabilistic (Bayesian) version improves on its deterministic counterpart in terms of predictive skill. Finally, we characterize the reliability of the ensemble of machine learning models obtained in the probabilistic setting by using analysis tools developed in the context of ensemble numerical weather prediction. Plain Language Summary: Businesses and government agencies rely heavily on numerical predictions of climate variables such as temperature and precipitation for a wide variety of purposes ranging from integrated assessment to developing mitigation strategies to developing resilience and adaptation strategies. Developing interannual to decadal predictions using comprehensive and complex climate and earth system models, however, are computationally intensive. As such, computationally efficient and accurate surrogates of comprehensive earth system models is highly desired. Data‐driven models using advanced deep learning algorithms are promising for this purpose. This paper first considers a recently proposed convolutional network architecture to develop such a surrogate and then integrates Bayesian inference to this architecture to further assess predictive uncertainty. We show that the resulting Bayesian deep learning model not only improves prediction accuracy but also quantifies the uncertainty arising from the data and model. Key Points: Model bias and associated initialization shock are serious shortcomings that reduce prediction skill in state‐of‐the‐art decadal climate prediction effortsA complementary machine‐learning‐based approach to climate prediction is considered. Both deterministic and probabilistic machine learning approaches are examinedIn addition to providing useful measures of predictive uncertainty, Bayesian versions of deep learning models outperform their deterministic counterparts in terms of predictive skill [ABSTRACT FROM AUTHOR]

Reduced‐order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate models. In this context, the linear inverse modeling (LIM) approach, by capturing a few essential interactions between dynamical components of the full system, has proven valuable in providing insights into predictability of the full system. We demonstrate that reservoir computing (RC), a form of learning suitable for systems with chaotic dynamics, provides an alternative nonlinear approach that improves on the predictive skill of the LIM approach. We do this in the example setting of predicting sea surface temperature in the North Atlantic in the preindustrial control simulation of a popular earth system model, the Community Earth System Model so that we can compare the performance of the new RC‐based approach with the traditional LIM approach both when learning data are plentiful and when such data are more limited. The improved predictive skill of the RC approach over a wide range of conditions—larger number of retained EOF coefficients, extending well into the limited data regime, etc.—suggests that this machine‐learning technique may have a use in climate predictability studies. While the possibility of developing a climate emulator—the ability to continue the evolution of the system on the attractor long after failing to be able to track the reference trajectory—is demonstrated in the Lorenz‐63 system, it is suggested that further development of the RC approach may permit such uses of the new approach in more realistic predictability studies. Plain Language Summary: Because of the chaotic nature of the dynamics underlying many complex systems such as weather and climate, evolution of ensembles of trajectories have to be considered in order to produce future predictions of such systems. An analysis of the dynamics of such ensembles provides insights into mechanisms that make the system predictable. Because comprehensive models of such complex systems are very costly to run, reduced‐order dynamical models of them are a useful tool in conducting such ensemble‐based predictability studies. We develop such a computationally inexpensive reduced‐order model using machine learning and show that its predictive skill is comparable to those of linear inverse model (state‐of‐the‐art) when training data are plentiful, but much better when such data are more limited. Consequently, we think that this new method has wide applicability. Furthermore, given the nonlinear nature of the new method, it has the potential to provide new insights into predictability of complex systems. Key Points: A machine‐learning (ML)‐based reduced‐order modeling method is developed to study predictability of regional SST of a popular climate modelThe method extends the state‐of‐the‐art, particularly, when data are limited and when a large number of EOF coefficients are retainedThe new method has wide applicability, could act as a climate emulator with further developments, and can give new insights [ABSTRACT FROM AUTHOR]

Since near‐term predictions of present‐day climate are controlled by both initial condition predictability and boundary condition predictability, initialized prediction experiments aim to augment the external‐forcing‐related predictability realized in uninitialized projections with initial‐condition‐related predictability by appropriate observation‐based initialization. However, and notwithstanding the considerable effort expended in finding such "good" initial states, a striking feature of current, state‐of‐the‐art, initialized decadal hindcasts is their tendency to quickly drift away from the initialized state, with attendant loss of skill. We derive a dynamical model for such drift, and after validating it we show that including a recalibrated version of the model in a postprocessing framework is able to significantly augment the skill of initialized predictions beyond that achieved by a use of current techniques of postprocessing alone. We also show that the new methodology provides further crucial insights into issues related to initialized predictions. Key Points: A model for the behavior of initialized decadal predictions is presented and then used to develop a technique for postprocessing predictionsThe technique is shown to improve hindcast skill in scenarios with widely different bias and interannual variability characteristicsThe technique throws light on issues such as expected versus realized time scale for loss of memory of IC and regional quirks in initialization [ABSTRACT FROM AUTHOR]