Stochastic weather and climate models

Palmer, Tim

doi:10.1038/s42254-019-0062-2

Cited by 121 publications

(104 citation statements)

References 84 publications

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“…The corresponding total Hamiltonian (22) for the fluid in M is then obtained by integrating the energies over the infinitesimal sub-volumes ∆V α and summing over all indices α. Since this Hamiltonian describes a system consisting of N sub-parcels, it is a function…”

Section: Description Of Resultsmentioning

confidence: 99%

“…The density dependence of the viscosity, as manifested by the ρ-factor in (3), is a consequence of the form of the Hamiltonian (22). The compressible Navier-Stokes equations are often expressed with respect to a density-independent viscosity, but it is not clear how this independence can be realized in the HIPS framework.…”

Section: Description Of Resultsmentioning

confidence: 99%

“…Reviews regarding NWP systems and climate models are contained in [20][21][22]. These also address the need for stochastic parameterizations of unknown subgrid processes.…”

Section: Numerical Weather Prediction (Nwp) and Climate Modelingmentioning

confidence: 99%

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A Hamiltonian Interacting Particle System for Compressible Flow

Hochgerner¹

2020

Water

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The decomposition of the energy of a compressible fluid parcel into slow (deterministic) and fast (stochastic) components is interpreted as a stochastic Hamiltonian interacting particle system (HIPS). It is shown that the McKean–Vlasov equation associated to the mean field limit yields the barotropic Navier–Stokes equation with density-dependent viscosity. Capillary forces can also be treated by this approach. Due to the Hamiltonian structure, the mean field system satisfies a Kelvin circulation theorem along stochastic Lagrangian paths.

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Section: Description Of Resultsmentioning

confidence: 99%

Section: Description Of Resultsmentioning

confidence: 99%

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A Hamiltonian Interacting Particle System for Compressible Flow

Hochgerner¹

2020

Water

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“…This facilitates upscale energy transfer. It also avoids imposing a hard truncation scale, which is inconsistent with the scaling symmetries of the Navier-Stokes equations (Palmer, 2019). Evaluating missing upscale energy transfer is not possible within this SCM framework, so it is possible that larger correlation scales than those measured could be warranted.…”

Section: Discussionmentioning

confidence: 99%

Constraining stochastic parametrisation schemes using high‐resolution simulations

Christensen

2020

Quart J Royal Meteoro Soc

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Stochastic parametrisations can be used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared with a deterministic model, a stochastic model represents “model uncertainty”, that is, sources of error in the forecast due to the limitations of the forecast model. A technique is presented for systematically deriving new stochastic parametrisations or constraining existing stochastic approaches. A high‐resolution model simulation is coarse‐grained to the desired forecast model resolution. This provides the initial conditions and forcing data needed to drive a single‐column model (SCM). Comparing the SCM parametrised tendencies with the evolution of the high‐resolution model provides an estimate of the error in the SCM tendencies that a stochastic parametrisation seeks to represent. This approach is used to assess the physical basis of the widely used stochastically perturbed parametrisation tendencies (SPPT) scheme. Justification is found for the multiplicative nature of SPPT, along with some evidence for the use of spatio‐temporally correlated stochastic perturbations. Evidence that the stochastic perturbation should be positively skewed is found, indicating that occasional large‐magnitude positive perturbations are physically realistic. However, other key assumptions of SPPT are less well justified, including coherency of the stochastic perturbations with height, coherency of the perturbations for different physical parametrisation schemes, and coherency for different prognostic variables. Relaxing these SPPT assumptions allows for an error model that explains a larger fractional variance than traditional SPPT. In particular, it is suggested that independently perturbing the tendencies associated with different parametrisation schemes is justifiable and would improve the realism of the SPPT approach.

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“…In this way, some computations will be susceptible to noise. In weather and climate model simulations, noise is certainly advantageous [ 18 ]. The energy cost of generating stochasticity through hardware would be negative, compared with the positive cost today of using pseudo-random number generators.…”

Section: Lessons For Supercomputers?mentioning

confidence: 99%

Human Creativity and Consciousness: Unintended Consequences of the Brain’s Extraordinary Energy Efficiency?

Palmer

2020

Entropy

Self Cite

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It is proposed that both human creativity and human consciousness are (unintended) consequences of the human brain's extraordinary energy efficiency. The topics of creativity and consciousness are treated separately, though have a common sub-structure. It is argued that creativity arises from a synergy between two cognitive modes of the human brain (which broadly coincide with Kahneman's Systems 1 and 2). In the first, available energy is spread across a relatively large network of neurons. As such, the amount of energy per active neuron is so small that the operation of such neurons is susceptible to thermal (ultimately quantum decoherent) noise. In the second, available energy is focussed on a small enough subset of neurons to guarantee a deterministic operation. An illustration of how this synergy can lead to creativity with implications for computing in silicon are discussed. Starting with a discussion of the concept of free will, the notion of consciousness is defined in terms of an awareness of what are perceived to be nearby counterfactual worlds in state space. It is argued that such awareness arises from an interplay between our memories on the one hand, and quantum physical mechanisms (where, unlike in classical physics, nearby counterfactual worlds play an indispensable dynamical role) in the ion channels of neural networks. As with the brain's susceptibility to noise, it is argued that in situations where quantum physics plays a role in the brain, it does so for reasons of energy efficiency. As an illustration of this definition of consciousness, a novel proposal is outlined as to why quantum entanglement appears so counter-intuitive.

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Stochastic weather and climate models

Cited by 121 publications

References 84 publications

A Hamiltonian Interacting Particle System for Compressible Flow

A Hamiltonian Interacting Particle System for Compressible Flow

Constraining stochastic parametrisation schemes using high‐resolution simulations

Human Creativity and Consciousness: Unintended Consequences of the Brain’s Extraordinary Energy Efficiency?

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