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Related Concept Videos

Maxwell-Boltzmann Distribution: Problem Solving01:20

Maxwell-Boltzmann Distribution: Problem Solving

Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
This distribution function f(v) is defined by saying that the expected number N (v1,v2) of particles with speeds between v1 and v2 is given by
State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
Magnetostatic Boundary Conditions01:28

Magnetostatic Boundary Conditions

An electric field suffers a discontinuity at a surface charge. Similarly, a magnetic field is discontinuous at a surface current. The perpendicular component of a magnetic field is continuous across the interface of two magnetic mediums. In contrast, its parallel component, perpendicular to the current, is discontinuous by the amount equal to the product of the vacuum permeability and the surface current. Like the scalar potential in electrostatics, the vector potential is also continuous...

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Related Experiment Videos

Efficient stochastic superparameterization for geophysical turbulence.

Ian Grooms1, Andrew J Majda

  • 1Department of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA. grooms@cims.nyu.edu

Proceedings of the National Academy of Sciences of the United States of America
|March 15, 2013
PubMed
Summary
This summary is machine-generated.

New stochastic superparameterization algorithms efficiently model geophysical turbulence in the atmosphere and ocean. These methods significantly speed up simulations, improving uncertainty quantification for climate predictions and reanalyses.

Related Experiment Videos

Area of Science:

  • Geophysics
  • Computational Fluid Dynamics
  • Atmospheric and Oceanic Sciences

Background:

  • Geophysical turbulence, prevalent in Earth's atmosphere and oceans, presents significant computational challenges due to complex dynamics like waves, jets, and vortices.
  • Accurate modeling is crucial for quantifying uncertainties in climate predictions and reanalyses through data assimilation and filtering.

Purpose of the Study:

  • Introduce a novel class of efficient stochastic superparameterization algorithms.
  • Address limitations of conventional superparameterization and heterogeneous multiscale methods in representing geophysical turbulence.

Main Methods:

  • Developed stochastic superparameterization algorithms that avoid simulating nonlinear eddy dynamics on embedded domains.
  • Represented small-scale turbulence using a one-dimensional stochastic model of random-direction plane waves.
  • Avoided requirements for strong scale separation or conditional equilibration of local statistics.

Main Results:

  • The simplest implemented algorithm demonstrated a significant improvement in efficiency, achieving speedups of several orders of magnitude over direct simulations.
  • The method effectively represents a wider range of unresolved scales and improves the depiction of small-scale instabilities.
  • Showcased excellent performance on prototype problems for geophysical turbulence, including waves, jets, and vortices.

Conclusions:

  • Stochastic superparameterization offers a computationally efficient approach for modeling geophysical turbulence.
  • These algorithms enhance the representation of complex turbulent phenomena, paving the way for larger ensemble simulations.
  • The developed methods provide a powerful tool for improving climate modeling and data assimilation techniques.