# Publications

## 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.

## The use of imprecise processing to improve accuracy in weather & climate prediction

Journal of Computational Physics **271** (2014) 2-18

The use of stochastic processing hardware and low precision arithmetic in atmospheric models is investigated. Stochastic processors allow hardware-induced faults in calculations, sacrificing bit-reproducibility and precision in exchange for improvements in performance and potentially accuracy of forecasts, due to a reduction in power consumption that could allow higher resolution. A similar trade-off is achieved using low precision arithmetic, with improvements in computation and communication speed and savings in storage and memory requirements. As high-performance computing becomes more massively parallel and power intensive, these two approaches may be important stepping stones in the pursuit of global cloud-resolving atmospheric modelling. The impact of both hardware induced faults and low precision arithmetic is tested using the Lorenz '96 model and the dynamical core of a global atmosphere model. In the Lorenz '96 model there is a natural scale separation; the spectral discretisation used in the dynamical core also allows large and small scale dynamics to be treated separately within the code. Such scale separation allows the impact of lower-accuracy arithmetic to be restricted to components close to the truncation scales and hence close to the necessarily inexact parametrised representations of unresolved processes. By contrast, the larger scales are calculated using high precision deterministic arithmetic. Hardware faults from stochastic processors are emulated using a bit-flip model with different fault rates. Our simulations show that both approaches to inexact calculations do not substantially affect the large scale behaviour, provided they are restricted to act only on smaller scales. By contrast, results from the Lorenz '96 simulations are superior when small scales are calculated on an emulated stochastic processor than when those small scales are parametrised. This suggests that inexact calculations at the small scale could reduce computation and power costs without adversely affecting the quality of the simulations. This would allow higher resolution models to be run at the same computational cost. © 2013 The Authors.

## 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

© 2013 Royal Meteorological Society. This article presents families of spatial discretizations of the nonlinear rotating shallow-water equations that conserve both energy and potential enstrophy. These are based on two-dimensional mixed finite-element methods and hence, unlike some finite-difference methods, do not require an orthogonal grid. Numerical verification of the aforementioned properties is also provided.

## Visualizing the uncertainty in the relationship between seasonal average climate and malaria risk.

Scientific reports **4** (2014) 7264-

Around $1.6 billion per year is spent financing anti-malaria initiatives, and though malaria morbidity is falling, the impact of annual epidemics remains significant. Whilst malaria risk may increase with climate change, projections are highly uncertain and to sidestep this intractable uncertainty, adaptation efforts should improve societal ability to anticipate and mitigate individual events. Anticipation of climate-related events is made possible by seasonal climate forecasting, from which warnings of anomalous seasonal average temperature and rainfall, months in advance are possible. Seasonal climate hindcasts have been used to drive climate-based models for malaria, showing significant skill for observed malaria incidence. However, the relationship between seasonal average climate and malaria risk remains unquantified. Here we explore this relationship, using a dynamic weather-driven malaria model. We also quantify key uncertainty in the malaria model, by introducing variability in one of the first order uncertainties in model formulation. Results are visualized as location-specific impact surfaces: easily integrated with ensemble seasonal climate forecasts, and intuitively communicating quantified uncertainty. Methods are demonstrated for two epidemic regions, and are not limited to malaria modeling; the visualization method could be applied to any climate impact.

## Stochastic modelling and energy-efficient computing for weather and climate prediction.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences **372** (2014) 20140118-

## On the use of inexact, pruned hardware in atmospheric modelling.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences **372** (2014) 20130276-

Inexact hardware design, which advocates trading the accuracy of computations in exchange for significant savings in area, power and/or performance of computing hardware, has received increasing prominence in several error-tolerant application domains, particularly those involving perceptual or statistical end-users. In this paper, we evaluate inexact hardware for its applicability in weather and climate modelling. We expand previous studies on inexact techniques, in particular probabilistic pruning, to floating point arithmetic units and derive several simulated set-ups of pruned hardware with reasonable levels of error for applications in atmospheric modelling. The set-up is tested on the Lorenz '96 model, a toy model for atmospheric dynamics, using software emulation for the proposed hardware. The results show that large parts of the computation tolerate the use of pruned hardware blocks without major changes in the quality of short- and long-time diagnostics, such as forecast errors and probability density functions. This could open the door to significant savings in computational cost and to higher resolution simulations with weather and climate models.

## Towards seasonal forecasting of malaria in India.

Malaria journal **13** (2014) 310-

Malaria presents public health challenge despite extensive intervention campaigns. A 30-year hindcast of the climatic suitability for malaria transmission in India is presented, using meteorological variables from a state of the art seasonal forecast model to drive a process-based, dynamic disease model.The spatial distribution and seasonal cycles of temperature and precipitation from the forecast model are compared to three observationally-based meteorological datasets. These time series are then used to drive the disease model, producing a simulated forecast of malaria and three synthetic malaria time series that are qualitatively compared to contemporary and pre-intervention malaria estimates. The area under the Relative Operator Characteristic (ROC) curve is calculated as a quantitative metric of forecast skill, comparing the forecast to the meteorologically-driven synthetic malaria time series.The forecast shows probabilistic skill in predicting the spatial distribution of Plasmodium falciparum incidence when compared to the simulated meteorologically-driven malaria time series, particularly where modelled incidence shows high seasonal and interannual variability such as in Orissa, West Bengal, and Jharkhand (North-east India), and Gujarat, Rajastan, Madhya Pradesh and Maharashtra (North-west India). Focusing on these two regions, the malaria forecast is able to distinguish between years of "high", "above average" and "low" malaria incidence in the peak malaria transmission seasons, with more than 70% sensitivity and a statistically significant area under the ROC curve. These results are encouraging given that the three month forecast lead time used is well in excess of the target for early warning systems adopted by the World Health Organization. This approach could form the basis of an operational system to identify the probability of regional malaria epidemics, allowing advanced and targeted allocation of resources for combatting malaria in India.

## Benchmark Tests for Numerical Weather Forecasts on Inexact Hardware

MONTHLY WEATHER REVIEW **142** (2014) 3809-3829

## 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.

## Atlantic meridional overturning circulation and the prediction of North Atlantic sea surface temperature

Earth and Planetary Science Letters **406** (2014) 1-6

© 2014 Elsevier B.V. The Atlantic Meridional Overturning Circulation (AMOC), a major current system in the Atlantic Ocean, is thought to be an important driver of climate variability, both regionally and globally and on a large range of time scales from decadal to centennial and even longer. Measurements to monitor the AMOC strength have only started in 2004, which is too short to investigate its link to long-term climate variability. Here the surface heat flux-driven part of the AMOC during 1900-2010 is reconstructed from the history of the North Atlantic Oscillation, the most energetic mode of internal atmospheric variability in the Atlantic sector. The decadal variations of the AMOC obtained in that way are shown to precede the observed decadal variations in basin-wide North Atlantic sea surface temperature (SST), known as the Atlantic Multidecadal Oscillation (AMO) which strongly impacts societally important quantities such as Atlantic hurricane activity and Sahel rainfall. The future evolution of the AMO is forecast using the AMOC reconstructed up to 2010. The present warm phase of the AMO is predicted to continue until the end of the next decade, but with a negative tendency.

## Addressing model error through atmospheric stochastic physical parametrizations: impact on the coupled ECMWF seasonal forecasting system.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences **372** (2014) 20130290-

The finite resolution of general circulation models of the coupled atmosphere-ocean system and the effects of sub-grid-scale variability present a major source of uncertainty in model simulations on all time scales. The European Centre for Medium-Range Weather Forecasts has been at the forefront of developing new approaches to account for these uncertainties. In particular, the stochastically perturbed physical tendency scheme and the stochastically perturbed backscatter algorithm for the atmosphere are now used routinely for global numerical weather prediction. The European Centre also performs long-range predictions of the coupled atmosphere-ocean climate system in operational forecast mode, and the latest seasonal forecasting system--System 4--has the stochastically perturbed tendency and backscatter schemes implemented in a similar way to that for the medium-range weather forecasts. Here, we present results of the impact of these schemes in System 4 by contrasting the operational performance on seasonal time scales during the retrospective forecast period 1981-2010 with comparable simulations that do not account for the representation of model uncertainty. We find that the stochastic tendency perturbation schemes helped to reduce excessively strong convective activity especially over the Maritime Continent and the tropical Western Pacific, leading to reduced biases of the outgoing longwave radiation (OLR), cloud cover, precipitation and near-surface winds. Positive impact was also found for the statistics of the Madden-Julian oscillation (MJO), showing an increase in the frequencies and amplitudes of MJO events. Further, the errors of El Niño southern oscillation forecasts become smaller, whereas increases in ensemble spread lead to a better calibrated system if the stochastic tendency is activated. The backscatter scheme has overall neutral impact. Finally, evidence for noise-activated regime transitions has been found in a cluster analysis of mid-latitude circulation regimes over the Pacific-North America region.

## Lorenz, Godel and Penrose: new perspectives on determinism and causality in fundamental physics

CONTEMPORARY PHYSICS **55** (2014) 157-178

## Genesis of streamwise-localized solutions from globally periodic traveling waves in pipe flow.

Physical review letters **112** (2014) 164501-

The aim in the dynamical systems approach to transitional turbulence is to construct a scaffold in phase space for the dynamics using simple invariant sets (exact solutions) and their stable and unstable manifolds. In large (realistic) domains where turbulence can coexist with laminar flow, this requires identifying exact localized solutions. In wall-bounded shear flows, the first of these has recently been found in pipe flow, but questions remain as to how they are connected to the many known streamwise-periodic solutions. Here we demonstrate that the origin of the first localized solution is in a modulational symmetry-breaking Hopf bifurcation from a known global traveling wave that has twofold rotational symmetry about the pipe axis. Similar behavior is found for a global wave of threefold rotational symmetry, this time leading to two localized relative periodic orbits. The clear implication is that many global solutions should be expected to lead to more realistic localized counterparts through such bifurcations, which provides a constructive route for their generation.

## On the reliability of seasonal climate forecasts.

Journal of the Royal Society, Interface **11** (2014) 20131162-

Seasonal climate forecasts are being used increasingly across a range of application sectors. A recent UK governmental report asked: how good are seasonal forecasts on a scale of 1-5 (where 5 is very good), and how good can we expect them to be in 30 years time? Seasonal forecasts are made from ensembles of integrations of numerical models of climate. We argue that 'goodness' should be assessed first and foremost in terms of the probabilistic reliability of these ensemble-based forecasts; reliable inputs are essential for any forecast-based decision-making. We propose that a '5' should be reserved for systems that are not only reliable overall, but where, in particular, small ensemble spread is a reliable indicator of low ensemble forecast error. We study the reliability of regional temperature and precipitation forecasts of the current operational seasonal forecast system of the European Centre for Medium-Range Weather Forecasts, universally regarded as one of the world-leading operational institutes producing seasonal climate forecasts. A wide range of 'goodness' rankings, depending on region and variable (with summer forecasts of rainfall over Northern Europe performing exceptionally poorly) is found. Finally, we discuss the prospects of reaching '5' across all regions and variables in 30 years time.

## Rift valley fever outbreaks in Mauritania and related environmental conditions

International Journal of Environmental Research and Public Health **11** (2014) 903-918

Four large outbreaks of Rift Valley Fever (RVF) occurred in Mauritania in 1998, 2003, 2010 and 2012 which caused lots of animal and several human deaths. We investigated rainfall and vegetation conditions that might have impacted on RVF transmission over the affected regions. Our results corroborate that RVF transmission generally occurs during the months of September and October in Mauritania, similarly to Senegal. The four outbreaks were preceded by a rainless period lasting at least a week followed by heavy precipitation that took place during the second half of the rainy season. First human infections were generally reported three to five weeks later. By bridging the gap between meteorological forecasting centers and veterinary services, an early warning system might be developed in Senegal and Mauritania to warn decision makers and health services about the upcoming RVF risk. © 2014 by the authors; licensee MDPI, Basel, Switzerland.

## Atmospheric science. Record-breaking winters and global climate change.

Science (New York, N.Y.) **344** (2014) 803-804