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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]

In this paper we demonstrate that reservoir computing can be used to learn the dynamics of the shallow-water equations. In particular, while most previous applications of reservoir computing have required training on a particular trajectory to further predict the evolution along that trajectory alone, we show the capability of reservoir computing to predict trajectories of the shallow-water equations with initial conditions not seen in the training process. However, in this setting, we find that the performance of the network deteriorates for initial conditions with ambient conditions (such as total water height and average velocity) that are different from those in the training dataset. To circumvent this deficiency, we introduce a transfer learning approach wherein a small additional training step with the relevant ambient conditions is used to improve the predictions. [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]

We demonstrate the use of a probabilistic machine-learning technique to develop stochastic parameterizations of atmospheric column physics. After suitable preprocessing of NASA's Modern-Era Retrospective analysis for Research and Applications, version 2 (MERRA2) data to minimize the effects of high-frequency, high-wavenumber component of MERRA2 estimate of vertical velocity, we use generative adversarial networks to learn the probability distribution of vertical profiles of diabatic sources conditioned on vertical profiles of temperature and humidity. This may be viewed as an improvement over previous similar but deterministic approaches that seek to alleviate both, shortcomings of human-designed physics parameterizations, and the computational demand of the "physics" step in climate models. [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]

Anomaly-diffusing energy balance models (AD-EBMs) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a deficiency in common multi-layer as well as continuous-diffusion AD-EBM variants: They are unable to, simultaneously, properly represent surface warming and the vertical distribution of heat uptake. We show that this inability is due to the diffusion approximation. On the other hand, it is well understood that transport of water from the surface mixed layer into the ocean interior is achieved, in large part, by the process of ventilation—a process associated with outcropping isopycnals. We, therefore, start from a configuration of outcropping isopycnals and demonstrate how an AD-EBM can be modified to include the effect of ventilation on ocean uptake of anomalous radiative forcing. The resulting EBM is able to successfully represent both surface warming and the vertical distribution of heat uptake, and indeed, a simple four-layer model suffices. The simplicity of the models notwithstanding, the analysis presented and the necessity of the modification highlight the role played by processes related to the down-welling branch of global ocean circulation in shaping the vertical distribution of ocean heat uptake. [ABSTRACT FROM AUTHOR]

The classic baroclinic, wind-driven, double gyre problem is considered over a range of deformation radii, wind stress amplitudes, and bottom friction coefficients with the aim of better understanding the transfer of energy across scales. In this β-plane basin setting, significant differences are found with respect to classic studies of geostrophic turbulence, which generally assume zonal periodicity and for which the β term does not play a direct role in the energy transfers. In a basin geometry, the β term can play a direct role in the transfers; for example, it can be the dominant term allowing for energy transfer between the basin scale and the baroclinic mesoscale. It is also found that barotropization of baroclinic energy forces the barotropic mode near scales at which bottom drag damps this mode. Associated with this, the barotropic, nonlinear, inverse energy cascade does not extend between mesoscale injection and large-scale dissipation wavenumbers, as is often assumed. Instead, it is part of a 'double cascade' of barotropic energy in which the nonlinear inverse cascade is nearly offset by a forward cascade associated with the β term. This is particularly evident in weak bottom drag simulations, for which a time eddy-mean decomposition of the flow reveals the double cascade to be associated with the eddy-only terms. [ABSTRACT FROM AUTHOR]

In the large eddy simulation (LES) framework for modeling a turbulent flow, when the large scale velocity field is defined by low-pass filtering the full velocity field, a Taylor series expansion of the full velocity field in terms of the large scale velocity field leads (at the leading order) to the nonlinear gradient model for the subfilter stresses. Motivated by the fact that while the nonlinear gradient model shows excellent a priori agreement in resolved simulations, the use of this model by itself is problematic, we consider two models that are related, but better behaved. The rational LES model that uses a sub-diagonal Pade approximation instead of a Taylor series expansion, and the Lagrangian averaged Navier-Stokes-α model that uses a regularization approach to modeling turbulence. In this article, we show that these two latter models are identical in two dimensions. [ABSTRACT FROM AUTHOR]

We study the modulational instability of geophysical Rossby and plasma drift waves within the Charney-Hasegawa-Mima (CHM) model both theoretically, using truncated (four-mode and three-mode) models, and numerically, using direct simulations of CHM equation in the Fourier space. We review the linear theory of Gill (Geophys. Fluid Dyn., vol. 6, 1974, p. 29) and extend it to show that for strong primary waves the most unstable modes are perpendicular to the primary wave, which correspond to generation of a zonal flow if the primary wave is purely meridional. For weak waves, the maximum growth occurs for off-zonal inclined modulations that are close to being in three-wave resonance with the primary wave. Our numerical simulations confirm the theoretical predictions of the linear theory as well as the nonlinear jet pinching predicted by Manin & Nazarenko (Phys. Fluids, vol. 6, 1994, p. 1158). We find that, for strong primary waves, these narrow zonal jets further roll up into Kármáan-like vortex streets, and at this moment the truncated models fail. For weak primary waves, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominate primary wave, so that the truncated description holds for longer. The two-dimensional vortex streets appear to be more stable than purely one-dimensional zonal jets, and their zonal-averaged speed can reach amplitudes much stronger than is allowed by the Rayleigh-Kuo instability criterion for the one-dimensional case. In the long term, the system transitions to turbulence helped by the vortex-pairing instability (for strong waves) and the resonant wave-wave interactions (for weak waves). [ABSTRACT FROM AUTHOR]

This paper presents analytical and numerical results for a class of turbulence closure models called “alpha models,” in which Lagrangian averaging and turbulence closure assumptions modify the Eulerian nonlinearity. The alpha models are investigated in the setting of the barotropic, double-gyre circulation in an ocean basin. Two variants of the alpha models for the barotropic vorticity (BV) equation are found to produce the correct four-gyre configuration for the mean barotropic circulation in numerical simulations performed at a resolution 4 times as coarse as that required in a resolved BV model. These are the BV-α model and the BV-Leray-α model. However, at a resolution 8 times as coarse, only the BV-α model produces the proper four-gyre configuration. Thus, the combination of modified nonlinearity and viscous dissipation (the viscosity is the same in all of the runs) in the BV-α model is found to provide a promising approach to modeling the mean effects of unresolved mesoscale (subgrid scale) activity in this problem. [ABSTRACT FROM AUTHOR]

Examines the dynamics of an idealized double-gyre circulation model in an ocean basin. Focus on the variability of ocean circulations; Importance of considering global bifurcations of the circulation; Identification of a complicated global bifurcation phenomenon known as the Shilkinov phenomenon.

Recently a new class of coarse-grained equations, known as α models, have been proposed for the mean motion of an ideal incompressible fluid. The use of one such model to represent the time-mean component of a turbulent β-plane circulation characterized by potential vorticity mixing is considered. In particular, the focus is on the wind-driven circulation in a shallow ocean basin, a problem well studied as a prototype of more realistic ocean dynamics. The authors demonstrate the ability of an α model to reproduce qualitatively the structure of a four-gyre circulation that forms (in the time mean) when the barotropic vorticity equation is driven by a symmetric, double-gyre wind forcing, and when the dissipation is weak. This is offered as a first step in assessing the utility of the α-model approach to simulating more complex geophysical flows. [ABSTRACT FROM AUTHOR]

The recently derived Lagrangian-averaged Navier-Stokes equations model the large-scale flow of the Navier-Stokes fluid at spatial scales larger than some a priori fixed α>0, while coarse-graining the behavior of the small scales. In this communication, we numerically study the behavior of the two-dimensional (2D) isotropic version of this model, also known as the α model. The inviscid dynamics of this model exactly coincide with the vortex blob algorithm for a certain choice of smoothing kernel, as well as the equations of an inviscid second-grade non-Newtonian fluid. While previous studies of this system in 3D have noted the suppression of nonlinear interaction between modes smaller than α, we show that the modification of the nonlinear advection term also acts to enhance the inverse-cascade of energy in 2D turbulence and thereby affects scales of motion larger than α as well. This, we note, (a) may preclude a straightforward use of the model as a subgrid model in coarsely resolved 2D computations, (b) is reminiscent of the drag-reduction that occurs in a turbulent flow when a dilute polymer is added, and (c) can be qualitatively understood in terms of known dimensional arguments. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]