A Higher-Order Closure Model with an Explicit PBL Top

2010 ◽  
Vol 67 (3) ◽  
pp. 834-850 ◽  
Author(s):  
Cara-Lyn Lappen ◽  
David Randall ◽  
Takanobu Yamaguchi
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Higher Order ◽  
Entrainment Rate ◽  
Time Step ◽  
Vertical Coordinate ◽  
Second Moments ◽  
Scale Models ◽  
Vertical Grid ◽  
Flux Model

Abstract In 2001, the authors presented a higher-order mass-flux model called “assumed distributions with higher-order closure” (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higher-order closure models, are not suitable for use in large-scale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higher-order closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are “hidden” in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in large-scale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixed-layer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in large-scale models.

scholarly journals The Treatment of Shortwave Radiation and Open Water in Large-Scale Models of Sea-Ice Decay

1990 ◽  
Vol 14 ◽  
pp. 242-246
Author(s):  
Donald K. Perovich ◽  
Gary A. Maykut
Keyword(s):  
Sea Ice ◽  
Large Scale ◽  
Open Water ◽  
Shortwave Radiation ◽  
Areal Extent ◽  
Time Step ◽  
Climate Simulations ◽  
Scale Models ◽  
Ice Concentration ◽  
Ice Pack

Sea ice covering the polar oceans is only a thin veneer whose areal extent can undergo large and rapid variations in response to relatively small changes in thermal forcing. Positive feedback between variations in ice extent and global albedo has the potential to amplify small changes in climate. Particularly difficult to model is the summer decay and retreat of the ice pack which is strongly influenced by shortwave radiation entering the upper ocean through leads (Iw). Most models assume that all of this energy is expended in lateral melting at floe edges. In reality, only a portion of Iw contributes directly to lateral melting, with the remainder going to bottom ablation and warming of the water. This partitioning of Iw affects not only the magnitude, but also the character of the predicted ice decay, reducing the change in ice concentration and enhancing the thinning of the ice and the storage of heat in the water. In this paper we present an analytical model which includes many of these processes and is stable regardless of time step, making it suitable for use in climate simulations.

scholarly journals On the Need to Determine Accurately the Impact of Higher-Order Sensitivities on Model Sensitivity Analysis, Uncertainty Quantification and Best-Estimate Predictions

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6318
Author(s):  
Dan Gabriel Cacuci
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Confidence Intervals ◽  
Large Scale ◽  
Neutron Transport ◽  
Higher Order ◽  
High Order ◽  
Tolerance Limits ◽  
Scale Models ◽  
Accurate Quantification

This work aims at underscoring the need for the accurate quantification of the sensitivities (i.e., functional derivatives) of the results (a.k.a. “responses”) produced by large-scale computational models with respect to the models’ parameters, which are seldom known perfectly in practice. The large impact that can arise from sensitivities of order higher than first has been highlighted by the results of a third-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark, which will be briefly reviewed in this work to underscore that neglecting the higher-order sensitivities causes substantial errors in predicting the expectation and variance of model responses. The importance of accurately computing the higher-order sensitivities is further highlighted in this work by presenting a text-book analytical example from the field of neutron transport, which impresses the need for the accurate quantification of higher-order response sensitivities by demonstrating that their neglect would lead to substantial errors in predicting the moments (expectation, variance, skewness, kurtosis) of the model response’s distribution in the phase space of model parameters. The incorporation of response sensitivities in methodologies for uncertainty quantification, data adjustment and predictive modeling currently available for nuclear engineering systems is also reviewed. The fundamental conclusion highlighted by this work is that confidence intervals and tolerance limits on results predicted by models that only employ first-order sensitivities are likely to provide a false sense of confidence, unless such models also demonstrate quantitatively that the second- and higher-order sensitivities provide negligibly small contributions to the respective tolerance limits and confidence intervals. The high-order response sensitivities to parameters underlying large-scale models can be computed most accurately and most efficiently by employing the high-order comprehensive adjoint sensitivity analysis methodology, which overcomes the curse of dimensionality that hampers other methods when applied to large-scale models involving many parameters.

scholarly journals Bridging Hierarchies in Multi-Scale Models of Neural Systems: Look-Up Tables Enable Computationally Efficient Simulations of Non-linear Synaptic Dynamics

2021 ◽  
Vol 15 ◽  
Author(s):  
Duy-Tan J. Pham ◽  
Gene J. Yu ◽  
Jean-Marie C. Bouteiller ◽  
Theodore W. Berger
Keyword(s):  
Large Scale ◽  
Computational Models ◽  
Computational Cost ◽  
Synaptic Activity ◽  
Emergent Properties ◽  
Linear Dynamics ◽  
Multi Scale ◽  
Scale Models ◽  
Non Linear ◽  
Synaptic Dynamics

Synapses are critical actors of neuronal transmission as they form the basis of chemical communication between neurons. Accurate computational models of synaptic dynamics may prove important in elucidating emergent properties across hierarchical scales. Yet, in large-scale neuronal network simulations, synapses are often modeled as highly simplified linear exponential functions due to their small computational footprint. However, these models cannot capture the complex non-linear dynamics that biological synapses exhibit and thus, are insufficient in representing synaptic behavior accurately. Existing detailed mechanistic synapse models can replicate these non-linear dynamics by modeling the underlying kinetics of biological synapses, but their high complexity prevents them from being a suitable option in large-scale models due to long simulation times. This motivates the development of more parsimonious models that can capture the complex non-linear dynamics of synapses accurately while maintaining a minimal computational cost. We propose a look-up table approach that stores precomputed values thereby circumventing most computations at runtime and enabling extremely fast simulations for glutamatergic receptors AMPAr and NMDAr. Our results demonstrate that this methodology is capable of replicating the dynamics of biological synapses as accurately as the mechanistic synapse models while offering up to a 56-fold increase in speed. This powerful approach allows for multi-scale neuronal networks to be simulated at large scales, enabling the investigation of how low-level synaptic activity may lead to changes in high-level phenomena, such as memory and learning.

scholarly journals On the Progressive Attenuation of Finescale Orography Contributions to the Vertical Coordinate Surfaces within a Terrain-Following Coordinate System

2020 ◽  
Vol 148 (10) ◽  
pp. 4143-4158
Author(s):  
Syed Zahid Husain ◽  
Claude Girard ◽  
Leo Separovic ◽  
André Plante ◽  
Shawn Corvec
Keyword(s):  
Complex Terrain ◽  
Large Scale ◽  
Computational Cost ◽  
Vertical Motion ◽  
Atmospheric Model ◽  
Vertical Coordinate ◽  
Global Environmental ◽  
Terrain Following ◽  
Prediction Systems ◽  
Global Environmental Multiscale

AbstractA modified hybrid terrain-following vertical coordinate has recently been implemented within the Global Environmental Multiscale atmospheric model that introduces separately controlled height-dependent progressive decaying of the small- and large-scale orography contributions on the vertical coordinate surfaces. The new vertical coordinate allows for a faster decay of the finescale orography imprints on the coordinate surfaces with increasing height while relaxing the compression of the lowest model levels over complex terrain. A number of tests carried out—including experiments involving Environment and Climate Change Canada’s operational regional and global deterministic prediction systems—demonstrate that the new vertical coordinate effectively eliminates terrain-induced spurious generation and amplification of upper-air vertical motion and kinetic energy without increasing the computational cost. Results also show potential improvements in precipitation over complex terrain.

scholarly journals HatchEnsemble: an efficient and practical uncertainty quantification method for deep neural networks

2021 ◽  
Author(s):  
Yufeng Xia ◽  
Jun Zhang ◽  
Tingsong Jiang ◽  
Zhiqiang Gong ◽  
Wen Yao ◽  
...  
Keyword(s):  
Neural Networks ◽  
Uncertainty Quantification ◽  
Bayesian Methods ◽  
Large Scale ◽  
Deep Neural Networks ◽  
Computational Cost ◽  
Main Idea ◽  
Quantification Theory ◽  
Complete Uncertainty ◽  
Scale Models

AbstractQuantifying predictive uncertainty in deep neural networks is a challenging and yet unsolved problem. Existing quantification approaches can be categorized into two lines. Bayesian methods provide a complete uncertainty quantification theory but are often not scalable to large-scale models. Along another line, non-Bayesian methods have good scalability and can quantify uncertainty with high quality. The most remarkable idea in this line is Deep Ensemble, but it is limited in practice due to its expensive computational cost. Thus, we propose HatchEnsemble to improve the efficiency and practicality of Deep Ensemble. The main idea is to use function-preserving transformations, ensuring HatchNets to inherit the knowledge learned by a single model called SeedNet. This process is called hatching, and HatchNet can be obtained by continuously widening the SeedNet. Based on our method, two different hatches are proposed, respectively, for ensembling the same and different architecture networks. To ensure the diversity of models, we also add random noises to parameters during hatching. Experiments on both clean and corrupted datasets show that HatchEnsemble can give a competitive prediction performance and better-calibrated uncertainty quantification in a shorter time compared with baselines.

Space–time adaptive numerical methods for geophysical applications

2009 ◽  
Vol 367 (1907) ◽  
pp. 4613-4631 ◽  
Author(s):  
C. E. Castro ◽  
M. Käser ◽  
E. F. Toro
Keyword(s):  
Wave Propagation ◽  
Large Scale ◽  
Computational Cost ◽  
Taylor Series Expansion ◽  
Space Time ◽  
High Order ◽  
Optimal Time ◽  
Mathematical Framework ◽  
Time Step ◽  
Tsunami Waves

In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space–time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost.

scholarly journals The Treatment of Shortwave Radiation and Open Water in Large-Scale Models of Sea-Ice Decay

1990 ◽  
Vol 14 ◽  
pp. 242-246 ◽  
Author(s):  
Donald K. Perovich ◽  
Gary A. Maykut
Keyword(s):  
Sea Ice ◽  
Large Scale ◽  
Open Water ◽  
Shortwave Radiation ◽  
Areal Extent ◽  
Time Step ◽  
Climate Simulations ◽  
Scale Models ◽  
Ice Concentration ◽  
Ice Pack

Sea ice covering the polar oceans is only a thin veneer whose areal extent can undergo large and rapid variations in response to relatively small changes in thermal forcing. Positive feedback between variations in ice extent and global albedo has the potential to amplify small changes in climate. Particularly difficult to model is the summer decay and retreat of the ice pack which is strongly influenced by shortwave radiation entering the upper ocean through leads (I w). Most models assume that all of this energy is expended in lateral melting at floe edges. In reality, only a portion of I w contributes directly to lateral melting, with the remainder going to bottom ablation and warming of the water. This partitioning of I w affects not only the magnitude, but also the character of the predicted ice decay, reducing the change in ice concentration and enhancing the thinning of the ice and the storage of heat in the water. In this paper we present an analytical model which includes many of these processes and is stable regardless of time step, making it suitable for use in climate simulations.

scholarly journals Higher order Hamiltonian Monte Carlo sampling for cosmological large-scale structure analysis

2021 ◽  
Vol 502 (3) ◽  
pp. 3976-3992
Author(s):  
Mónica Hernández-Sánchez ◽  
Francisco-Shu Kitaura ◽  
Metin Ata ◽  
Claudio Dalla Vecchia
Keyword(s):  
Fourth Order ◽  
Large Scale ◽  
Equations Of Motion ◽  
Large Scale Structure ◽  
Real Space ◽  
Higher Order ◽  
Second Order ◽  
Scale Structure ◽  
Integration Schemes ◽  
Reconstruction Methods

ABSTRACT We investigate higher order symplectic integration strategies within Bayesian cosmic density field reconstruction methods. In particular, we study the fourth-order discretization of Hamiltonian equations of motion (EoM). This is achieved by recursively applying the basic second-order leap-frog scheme (considering the single evaluation of the EoM) in a combination of even numbers of forward time integration steps with a single intermediate backward step. This largely reduces the number of evaluations and random gradient computations, as required in the usual second-order case for high-dimensional cases. We restrict this study to the lognormal-Poisson model, applied to a full volume halo catalogue in real space on a cubical mesh of 1250 h−1 Mpc side and 2563 cells. Hence, we neglect selection effects, redshift space distortions, and displacements. We note that those observational and cosmic evolution effects can be accounted for in subsequent Gibbs-sampling steps within the COSMIC BIRTH algorithm. We find that going from the usual second to fourth order in the leap-frog scheme shortens the burn-in phase by a factor of at least ∼30. This implies that 75–90 independent samples are obtained while the fastest second-order method converges. After convergence, the correlation lengths indicate an improvement factor of about 3.0 fewer gradient computations for meshes of 2563 cells. In the considered cosmological scenario, the traditional leap-frog scheme turns out to outperform higher order integration schemes only when considering lower dimensional problems, e.g. meshes with 643 cells. This gain in computational efficiency can help to go towards a full Bayesian analysis of the cosmological large-scale structure for upcoming galaxy surveys.

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