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We give a geometric and elementary proof of the uniform $\\mathscr{C}^{p}$ -parametrization theorem of Yomdin and Gromov in arbitrary o-minimal structures.

We demonstrate that an extended eddy‐diffusivity mass‐flux (EDMF) scheme can be used as a unified parameterization of subgrid‐scale turbulence and convection across a range of dynamical regimes, from dry convective boundary layers, through shallow convection, to deep convection. Central to achieving this unified representation of subgrid‐scale motions are entrainment and detrainment closures. We model entrainment and detrainment rates as a combination of turbulent and dynamical processes. Turbulent entrainment/detrainment is represented as downgradient diffusion between plumes and their environment. Dynamical entrainment/detrainment is proportional to a ratio of a relative buoyancy of a plume and a vertical velocity scale, that is modulated by heuristic nondimensional functions which represent their relative magnitudes and the enhanced detrainment due to evaporation from clouds in drier environment. We first evaluate the closures off‐line against entrainment and detrainment rates diagnosed from large eddy simulations (LESs) in which tracers are used to identify plumes, their turbulent environment, and mass and tracer exchanges between them. The LES are of canonical test cases of a dry convective boundary layer, shallow convection, and deep convection, thus spanning a broad rangeof regimes. We then compare the LES with the full EDMF scheme, including the new closures, in a single‐column model (SCM). The results show good agreement between the SCM and LES in quantities that are key for climate models, including thermodynamic profiles, cloud liquid water profiles, and profiles of higher moments of turbulent statistics. The SCM also captures well the diurnal cycle of convection and the onset of precipitation. Plain Language Summary The dynamics of clouds and turbulence are too small in scale to be resolved in global models of the atmosphere, yet they play a crucial role in controlling weather and climate. These models rely on parameterizations for representing clouds and turbulence. Inadequacies in these parameterizations have hampered especially climate models for decades; they are the largest source of physical uncertainties in climate predictions. It has proven challenging to represent the wide rangeof cloud and turbulence regimes encountered in nature in a single parameterization. Here we present such a parameterization that does capture a wide range of cloud and turbulence regimes within a single, unified physical framework, with relatively few parameters that can be adjusted to fit data. The framework relies on a decomposition of turbulent flows into coherent updraft and downdraft (i.e., plumes) and random turbulence in their environment. A key contribution of this paper is to show how the exchange of mass and properties between the plumes and their turbulent environment—the so‐called entrainment and detrainment of air into and out of plumes—can be modeled. We show that the resulting parameterization represents well the most important features of dry convective boundary layers, shallow cumulus convection, and deep cumulonimbus convection. Key Points An extended eddy‐diffusivity mass‐flux (EDMF) scheme successfully captures diverse regimes of convective motions Unified closures are presented for entrainment and detrainment across the different convective regimes With the unified closures, the EDMF scheme can simulate dry convection, shallow cumulus, and deep cumulus

SPDroot is a specialized software package for modeling physics events in the SPD experiment [1]. The simulation of the SPD detector response is based on Geant4; however, its standard capabilities do not allow for reproducing effects related to detector construction details, specifically, readout electronics. This work presents an advancement in the modeling of the straw-based tracker in SPDroot, implemented through the introduction of a parameterized model of the straw response, dependent on the local track coordinate. This enables a more realistic description of the detector behavior. Also, the straw hit reconstruction procedure has been implemented. The hit reconstruction performance is presented for different types of the straw signal parametrization.

The representation of nonlinear subgrid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but only for short-term simulations of at most a few years because of computational limitations. Here we demonstrate that deep learning can be used to capture many advantages of cloud-resolving modeling at a fraction of the computational cost. We train a deep neural network to represent all atmospheric subgrid processes in a climate model by learning from a multiscale model in which convection is treated explicitly. The trained neural network then replaces the traditional subgrid parameterizations in a global general circulation model in which it freely interacts with the resolved dynamics and the surface-flux scheme. The prognostic multiyear simulations are stable and closely reproduce not only the mean climate of the cloud-resolving simulation but also key aspects of variability, including precipitation extremes and the equatorial wave spectrum. Furthermore, the neural network approximately conserves energy despite not being explicitly instructed to. Finally, we show that the neural network parameterization generalizes to new surface forcing patterns but struggles to cope with temperatures far outside its training manifold. Our results show the feasibility of using deep learning for climate model parameterization. In a broader context, we anticipate that data-driven Earth system model development could play a key role in reducing climate prediction uncertainty in the coming decade.

We initiate the study of external manipulations in Stable Marriage by considering  several manipulative actions as well as several manipulation goals. For instance, one goal  is to make sure that a given pair of agents is matched in a stable solution, and this may be  achieved by the manipulative action of reordering some agents' preference lists. We present  a comprehensive study of the computational complexity of all problems arising in this way.  We find several polynomial-time solvable cases as well as NP-hard ones. For the NP-hard  cases, focusing on the natural parameter \"budget\" (that is, the number of manipulative  actions one is allowed to perform), we also conduct a parameterized complexity analysis  and encounter mostly parameterized hardness results. 

A method that enables a mass-flux cumulus parameterization scheme (CPS) to work seamlessly in various model grids across CPS gray-zone resolutions is proposed. The convective cloud-base mass flux, convective inhibition, and convective detrainment in the simplified Arakawa–Schubert (SAS) scheme are modified to be functions of the convective updraft fraction. The combination of two updraft fractions is used to modulate the cloud-base mass flux; the first one depends on the horizontal grid space and the other is a function of the grid-scale and convective vertical velocity. The convective inhibition and detrainment of hydrometeors are also modified to be a function of the grid-size-dependent convective updraft fraction. A set of sensitivity experiments with the Weather Research and Forecasting (WRF) Model is conducted for a heavy rainfall case over South Korea. The results show that the revised SAS CPS outperforms the original SAS. At 3 and 1 km, the precipitation core over South Korea is well reproduced by the experiments with the revised SAS scheme. On the contrary, the simulated precipitation is widespread in the case of the original SAS experiment and there are multiple spurious cores when the CPS is removed at those resolutions. The modified mass flux at the cloud base is found to play a major role in organizing the grid-scale precipitation at the convective core. A 1-month simulation at 3 km confirms that the revised scheme produces slightly better summer monsoonal precipitation results as compared to the typical model setup without CPS.

To explore the driving mechanisms of elevation-dependent warming (EDW) over the Tibetan Plateau (TP), the output from a suite of numerical experiments with different cumulus parameterization schemes (CPs) under the Coordinated Regional Climate Downscaling Experiments-East Asia (CORDEX-EA-II) project is examined. Results show that all experiments can broadly capture the observed temperature distributions over the TP with consistent cold biases, and the spread in temperature simulations commonly increases with elevation with the maximum located around 4000–5000 m. Such disagreements among the temperature simulations could to a large extent be explained by their spreads in the surface albedo feedback (SAF). All the experiments reproduce the observed EDW below 5000 m in winter but fail to capture the observed EDW above 4500 m in spring. Further analysis suggests that the simulated EDW during winter is mainly caused by the SAF, and the clear-sky downward longwave radiation (LWclr) plays a secondary role in shaping EDW. The models’ inability in simulating EDW during spring is closely related to the SAF and the surface cloud radiative forcing (CRFs). Furthermore, the magnitude and structure of the simulated EDW are sensitive to the choice of CPs. Different CPs generate diverse snow cover fractions, which can modulate the simulated SAF and its effect on EDW. Also, the CPs show great influence on the LWclr via altering the low-level air temperature. Additionally, the mechanism for different temperature changes among the experiments varies with altitudes during summer and autumn, as the diverse temperature changes appear to be caused by the LWclr for the low altitudes while by the SAF for the middle-high altitudes.

We study the problem of training deep fully connected neural networks with Rectified Linear Unit (ReLU) activation function and cross entropy loss function for binary classification using gradient descent. We show that with proper random weight initialization, gradient descent can find the global minima of the training loss for an over-parameterized deep ReLU network, under certain assumption on the training data. The key idea of our proof is that Gaussian random initialization followed by gradient descent produces a sequence of iterates that stay inside a small perturbation region centered at the initial weights, in which the training loss function of the deep ReLU networks enjoys nice local curvature properties that ensure the global convergence of gradient descent. At the core of our proof technique is (1) a milder assumption on the training data; (2) a sharp analysis of the trajectory length for gradient descent; and (3) a finer characterization of the size of the perturbation region. Compared with the concurrent work (Allen-Zhu et al. in A convergence theory for deep learning via over-parameterization, 2018a; Du et al. in Gradient descent finds global minima of deep neural networks, 2018a) along this line, our result relies on milder over-parameterization condition on the neural network width, and enjoys faster global convergence rate of gradient descent for training deep neural networks.

Global cloud-resolving models (GCRMs) are a new category of atmospheric global models designed to solve different flavors of the nonhydrostatic equations through the use of kilometer-scale global meshes. GCRMs make it possible to explicitly simulate deep convection, thereby avoiding the need for cumulus parameterization and allowing for clouds to be “resolved” by microphysical models responding to grid-scale forcing. GCRMs require high-resolution discretization over the globe, for which a variety of mesh structures have been proposed and employed. The first GCRM was constructed 15 years ago, and in recent years, other groups have also begun adopting this approach, enabling the first intercomparison studies of such models. Because conventional general circulation models (GCMs) suffer from large biases associated with cumulus parameterization, GCRMs are attractive tools for researchers studying global weather and climate. In this review, GCRMs are described, with some emphasis on their historical development and the associated literature documenting their use. The advantages of GCRMs are presented, and currently existing GCRMs are listed and described. Future prospects for GCRMs are also presented in the final section.

Several methods for studying the nature of a resonance are applied to resonances recently discovered in the bottonomium and charmonium sectors. We employ the effective-range expansion, the saturation of the width and compositeness of a resonance, as well as direct fits to data. The latter stem from generic S -matrix parameterization that account for relevant dynamical features associated to channels that couple strongly in an energy region around the resonance masses, in which their thresholds also lie. We report on results obtained with these methods for the resonances Z b (10610), Z b (10650), Z cs (3985), Z c (3900), X (4020), X (6900), X (6825), and P cs (4459).