# Publications

## The response of the Pacific storm track and atmospheric circulation to Kuroshio Extension variability

Quarterly Journal of the Royal Meteorological Society Wiley **141** (2015) 52-66

## Decomposition of a New Proper Score for Verification of Ensemble Forecasts

MONTHLY WEATHER REVIEW **143** (2015) 1517-1532

## Stochastic and Perturbed Parameter Representations of Model Uncertainty in Convection Parameterization*

JOURNAL OF THE ATMOSPHERIC SCIENCES **72** (2015) 2525-2544

## Evaluation of ensemble forecast uncertainty using a new proper score: Application to medium-range and seasonal forecasts

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY **141** (2015) 538-549

## Invariant set theory: Violating measurement independence without fine tuning, conspiracy, constraints on free will or retrocausality

Electronic Proceedings in Theoretical Computer Science, EPTCS **195** (2015) 285-294

© 2015 T. N. Palmer. Invariant Set (IS) theory is a locally causal ontic theory of physics based on the Cosmological Invariant Set postulate that the universe U can be considered a deterministic dynamical system evolving precisely on a (suitably constructed) fractal dynamically invariant set in U's state space. IS theory violates the Bell inequalities by violating Measurement Independence. Despite this, IS theory is not fine tuned, is not conspiratorial, does not constrain experimenter free will and does not invoke retrocausality. The reasons behind these claims are discussed in this paper. These arise fromproperties not found in conventional ontic models: the invariant set has zero measure in its Euclidean embedding space, has Cantor Set structure homeomorphic to the p-adic integers (p⋙0) and is non-computable. In particular, it is shown that the p-adic metric encapulates the physics of the Cosmological Invariant Set postulate, and provides the technical means to demonstrate no fine tuning or conspiracy. Quantum theory can be viewed as the singular limit of IS theory when when p is set equal to infinity. Since it is based around a top-down constraint from cosmology, IS theory suggests that gravitational and quantum physics will be unified by a gravitational theory of the quantum, rather than a quantum theory of gravity. Some implications arising from such a perspective are discussed.

## Demonstration of successful malaria forecasts for Botswana using an operational seasonal climate model

ENVIRONMENTAL RESEARCH LETTERS **10** (2015) ARTN 044005

## On the use of programmable hardware and reduced numerical precision in earth-system modeling.

Journal of advances in modeling earth systems **7** (2015) 1393-1408

Programmable hardware, in particular Field Programmable Gate Arrays (FPGAs), promises a significant increase in computational performance for simulations in geophysical fluid dynamics compared with CPUs of similar power consumption. FPGAs allow adjusting the representation of floating-point numbers to specific application needs. We analyze the performance-precision trade-off on FPGA hardware for the two-scale Lorenz '95 model. We scale the size of this toy model to that of a high-performance computing application in order to make meaningful performance tests. We identify the minimal level of precision at which changes in model results are not significant compared with a maximal precision version of the model and find that this level is very similar for cases where the model is integrated for very short or long intervals. It is therefore a useful approach to investigate model errors due to rounding errors for very short simulations (e.g., 50 time steps) to obtain a range for the level of precision that can be used in expensive long-term simulations. We also show that an approach to reduce precision with increasing forecast time, when model errors are already accumulated, is very promising. We show that a speed-up of 1.9 times is possible in comparison to FPGA simulations in single precision if precision is reduced with no strong change in model error. The single-precision FPGA setup shows a speed-up of 2.8 times in comparison to our model implementation on two 6-core CPUs for large model setups.

## Bell's conspiracy, Schrödinger's black cat and global invariant sets.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences **373** (2015)

A locally causal hidden-variable theory of quantum physics need not be constrained by the Bell inequalities if this theory also partially violates the measurement independence condition. However, such violation can appear unphysical, implying implausible conspiratorial correlations between the hidden variables of particles being measured and earlier determinants of instrumental settings. A novel physically plausible explanation for such correlations is proposed, based on the hypothesis that states of physical reality lie precisely on a non-computational measure-zero dynamically invariant set in the state space of the universe: the Cosmological Invariant Set Postulate. To illustrate the relevance of the concept of a global invariant set, a simple analogy is considered where a massive object is propelled into a black hole depending on the decay of a radioactive atom. It is claimed that a locally causal hidden-variable theory constrained by the Cosmological Invariant Set Postulate can violate the Clauser-Horne-Shimony-Holt inequality without being conspiratorial, superdeterministic, fine-tuned or retrocausal, and the theory readily accommodates the classical compatibilist notion of (experimenter) free will.

## Impact of hindcast length on estimates of seasonal climate predictability

Geophysical Research Letters **42** (2015) 1554-1559

© 2015. The Authors. It has recently been argued that single-model seasonal forecast ensembles are overdispersive, implying that the real world is more predictable than indicated by estimates of so-called perfect model predictability, particularly over the North Atlantic. However, such estimates are based on relatively short forecast data sets comprising just 20 years of seasonal predictions. Here we study longer 40 year seasonal forecast data sets from multimodel seasonal forecast ensemble projects and show that sampling uncertainty due to the length of the hindcast periods is large. The skill of forecasting the North Atlantic Oscillation during winter varies within the 40 year data sets with high levels of skill found for some subperiods. It is demonstrated that while 20 year estimates of seasonal reliability can show evidence of overdispersive behavior, the 40 year estimates are more stable and show no evidence of overdispersion. Instead, the predominant feature on these longer time scales is underdispersion, particularly in the tropics.

## Impact of Initial Conditions versus External Forcing in Decadal Climate Predictions: A Sensitivity Experiment*

JOURNAL OF CLIMATE **28** (2015) 4454-4470

## Does the ECMWF IFS Convection Parameterization with Stochastic Physics Correctly Reproduce Relationships between Convection and the Large-Scale State?

JOURNAL OF THE ATMOSPHERIC SCIENCES **72** (2015) 236-242

## Architectures and precision analysis for modelling atmospheric variables with chaotic behaviour

2015 IEEE 23RD ANNUAL INTERNATIONAL SYMPOSIUM ON FIELD-PROGRAMMABLE CUSTOM COMPUTING MACHINES (FCCM) (2015) 171-178

## Impact of hindcast length on estimates of seasonal climate predictability.

Geophysical research letters **42** (2015) 1554-1559

It has recently been argued that single-model seasonal forecast ensembles are overdispersive, implying that the real world is more predictable than indicated by estimates of so-called perfect model predictability, particularly over the North Atlantic. However, such estimates are based on relatively short forecast data sets comprising just 20 years of seasonal predictions. Here we study longer 40 year seasonal forecast data sets from multimodel seasonal forecast ensemble projects and show that sampling uncertainty due to the length of the hindcast periods is large. The skill of forecasting the North Atlantic Oscillation during winter varies within the 40 year data sets with high levels of skill found for some subperiods. It is demonstrated that while 20 year estimates of seasonal reliability can show evidence of overdispersive behavior, the 40 year estimates are more stable and show no evidence of overdispersion. Instead, the predominant feature on these longer time scales is underdispersion, particularly in the tropics.Predictions can appear overdispersive due to hindcast length sampling errorLonger hindcasts are more robust and underdispersive, especially in the tropicsTwenty hindcasts are an inadequate sample size to assess seasonal forecast skill.

## Localization in a spanwise-extended model of plane Couette flow.

Physical review. E, Statistical, nonlinear, and soft matter physics **91** (2015) 043005-

We consider a nine-partial-differential-equation (1-space and 1-time) model of plane Couette flow in which the degrees of freedom are severely restricted in the streamwise and cross-stream directions to study spanwise localization in detail. Of the many steady Eckhaus (spanwise modulational) instabilities identified of global steady states, none lead to a localized state. Spatially localized, time-periodic solutions were found instead, which arise in saddle node bifurcations in the Reynolds number. These solutions appear global (domain filling) in narrow (small spanwise) domains yet can be smoothly continued out to fully spanwise-localized states in very wide domains. This smooth localization behavior, which has also been seen in fully resolved duct flow (S. Okino, Ph.D. thesis, Kyoto University, Kyoto, 2011), indicates that an apparently global flow structure does not have to suffer a modulational instability to localize in wide domains.

## Opportunities for Energy Efficient Computing: A Study of Inexact General Purpose Processors for High-Performance and Big-data Applications

2015 DESIGN, AUTOMATION & TEST IN EUROPE CONFERENCE & EXHIBITION (DATE) (2015) 764-769

## Solving difficult problems creatively: a role for energy optimised deterministic/stochastic hybrid computing.

Frontiers in Computational Neuroscience **9** (2015) 124-

How is the brain configured for creativity? What is the computational substrate for 'eureka' moments of insight? Here we argue that creative thinking arises ultimately from a synergy between low-energy stochastic and energy-intensive deterministic processing, and is a by-product of a nervous system whose signal-processing capability per unit of available energy has become highly energy optimised. We suggest that the stochastic component has its origin in thermal (ultimately quantum decoherent) noise affecting the activity of neurons. Without this component, deterministic computational models of the brain are incomplete.

## Energy- and enstrophy-conserving schemes for the shallow-water equations, based on mimetic finite elements

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY **140** (2014) 2223-2234

## More reliable forecasts with less precise computations: a fast-track route to cloud-resolved weather and climate simulators?

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences **372** (2014) 20130391-

This paper sets out a new methodological approach to solving the equations for simulating and predicting weather and climate. In this approach, the conventionally hard boundary between the dynamical core and the sub-grid parametrizations is blurred. This approach is motivated by the relatively shallow power-law spectrum for atmospheric energy on scales of hundreds of kilometres and less. It is first argued that, because of this, the closure schemes for weather and climate simulators should be based on stochastic-dynamic systems rather than deterministic formulae. Second, as high-wavenumber elements of the dynamical core will necessarily inherit this stochasticity during time integration, it is argued that the dynamical core will be significantly over-engineered if all computations, regardless of scale, are performed completely deterministically and if all variables are represented with maximum numerical precision (in practice using double-precision floating-point numbers). As the era of exascale computing is approached, an energy- and computationally efficient approach to cloud-resolved weather and climate simulation is described where determinism and numerical precision are focused on the largest scales only.