# Publications

## AUTOMATED GENERATION AND SYMBOLIC MANIPULATION OF TENSOR PRODUCT FINITE ELEMENTS

SIAM JOURNAL ON SCIENTIFIC COMPUTING **38** (2016) S25-S47

## The role of human influence on climate in recent UK winter floods and their impacts.

Nature Climate Change Nature Publishing Group (2016)

A succession of storms reaching southern England in the winter of 2013/2014 caused severe floods and £451 million insured losses. In a large ensemble of climate model simulations, we find that, as well as increasing the amount of moisture the atmosphere can hold, anthropogenic warming caused a small but significant increase in the number of January days with westerly flow, both of which increased extreme precipitation. Hydrological modelling indicates this increased extreme 30-day-average Thames river flows, and slightly increased daily peak flows, consistent with the understanding of the catchment’s sensitivity to longer-duration precipitation and changes in the role of snowmelt. Consequently, flood risk mapping shows a small increase in properties in the Thames catchment potentially at risk of riverine flooding, with a substantial range of uncertainty, demonstrating the importance of explicit modelling of impacts and relatively subtle changes in weather-related risks when quantifying present-day effects of human influence on climate.

## The role of the tropical West Pacific in the extreme northern hemisphere winter of 2013/14

Journal of Geophysical Research: Atmospheres American Geophysical Union (2016)

In the 2013/14 winter, the eastern USA was exceptionally cold, the Bering Strait region was exceptionally warm, California was in the midst of drought and the UK suffered severe flooding. It has been suggested that elevated SSTs in the tropical West Pacific (TWPAC) were partly to blame due to their producing a Rossby wavetrain that propagated into the extratropics. We find that seasonal forecasts with the tropical atmosphere relaxed towards a reanalysis give 2013/14 winter-mean anomalies with strong similarities to those observed in the Northern Hemisphere, indicating that low-latitude anomalies had a role in the development of the extremes. Relaxing just the TWPAC produces a strong wavetrain over the North Pacific and North America in January, but not in the winter-mean. This suggests that anomalies in this region alone had a large influence, but cannot explain the extremes through the whole winter. We also examine the response to applying the observed TWPAC SST anomalies in two atmospheric general circulation models. We find that this does produce winter-mean anomalies in the North Pacific and North America resembling those observed, but that the tropical forcing of Rossby waves due to the applied SST anomalies appears stronger than that in reanalysis, except in January. Therefore both experiments indicate that the TWPAC influence was important, but the true strength of the TWPAC influence is uncertain. None of the experiments indicate a strong systematic impact of the TWPAC anomalies on Europe.

## Benchmarking Northern Hemisphere midlatitude atmospheric synoptic variability in centennial reanalysis and numerical simulations

Geophysical Research Letters American Geophysical Union **43** (2016) 5442-5449

The representation of midlatitude winter atmospheric synoptic variability in centennial reanalysis products, which assimilate surface observations only, and atmospheric model simulations constrained by observation-based data sets is assessed. Midlatitude waves activity in twentieth century reanalyses (20CR, ERA-20C) and atmospheric model simulations are compared with those estimated from observationally complete reanalysis products. All reanalyses are in good agreement regarding the representation of the synoptic variability during the last decades of the twentieth century. This suggests that the assimilation of surface observations can generate high-quality extratropical upper air fields. In the first decades of the twentieth century a suppression of high-frequency variability is apparent in the centennial reanalysis products. This behavior does not have a counterpart in the atmospheric model integrations. Since the latter differ from one of the reanalysis products considered here (ERA-20C) only in the assimilation of surface observations, it seems reasonable to attribute the high-frequency variability suppression to the poor coverage of the observations assimilated.

## Simulating weather regimes: impact of stochastic and perturbed parameter schemes in a simple atmospheric model

CLIMATE DYNAMICS **44** (2015) 2195-2214

## 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 American Geophysical Union **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.

## New geometric concepts in the foundations of physics.

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

## 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

## 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.

## Simulating weather regimes: impact of model resolution and stochastic parameterization

CLIMATE DYNAMICS **44** (2015) 2177-2193

## 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.