# Publications by Tim Palmer

## Experimental Non-Violation of the Bell Inequality

ENTROPY **20** (2019) ARTN 356

## Stochastic weather and climate models

Nature Reviews Physics Springer Science and Business Media LLC **1** (2019) 463-471

## The ECMWF ensemble prediction system: Looking back (more than) 25 years and projecting forward 25 years

Quarterly Journal of the Royal Meteorological Society (2018)

© 2018 The Authors. Quarterly Journal of the Royal Meteorological Society published by John Wiley & Sons Ltd on behalf of the Royal Meteorological Society. This paper has been written to mark 25 years of operational medium-range ensemble forecasting. The origins of the ECMWF Ensemble Prediction System are outlined, including the development of the precursor real-time Met Office monthly ensemble forecast system. In particular, the reasons for the development of singular vectors and stochastic physics – particular features of the ECMWF Ensemble Prediction System - are discussed. The author speculates about the development and use of ensemble prediction in the next 25 years.

## How confident are predictability estimates of the winter North Atlantic Oscillation?

Quarterly Journal of the Royal Meteorological Society Wiley **145** (2018) 140-159

Atmospheric seasonal predictability in winter over the Euro-Atlantic region is studied with an emphasis on the signal-to-noise paradox of the North Atlantic Oscillation. Seasonal hindcasts of the ECMWF model for the recent period 1981-2009 show, in agreement with other studies, that correlation skill over Greenland and parts of the Arctic is higher than the signal-to-noise ratio implies. This leads to the paradoxical situation where the real world appears more predictable than the models suggest, with the forecast ensembles being overly dispersive (or underconfident). However, it is demonstrated that these conclusions are not supported by the diagnosed relationship between ensemble mean RMSE and ensemble spread which indicates a slight underdispersion (overconfidence). Furthermore, long atmospheric seasonal hindcasts suggest that over the 110-year period from 1900 to 2009 the ensemble system is well calibrated (neither over- nor underdispersive). The observed skill changed drastically in the middle of the 20th Century and paradoxical regions during more recent hindcast periods were strongly underdispersive during mid-Century decades. <br/><br/> Due to non-stationarities of the climate system in the form of decadal variability, relatively short hindcasts are not sufficiently representative for longer-term behaviour. In addition, small hindcast sample size can lead to skill estimates, in particular of correlation measures, that are not robust. It is shown that the relative uncertainty due to small hindcast sample size is often larger for correlation-based than for RMSE-based diagnostics. Correlation-based measures like the RPC are shown to be highly sensitive to the strength of the predictable signal, implying that disentangling of physical deficiencies in the models on the one hand, and the effects of sampling uncertainty on the other hand, is difficult. Given the current lack of a causal physical mechanism to unravel the puzzle, our hypotheses of non-stationarity and sampling uncertainty provide simple yet plausible explanations for the paradox.

## Scale-Selective Precision for Weather and Climate Forecasting

MONTHLY WEATHER REVIEW **147** (2019) 645-655

## Progress Towards a Probabilistic Earth System Model: Examining The Impact of Stochasticity in EC-Earth v3.2

Geoscientific Model Development European Geosciences Union **12** (2019) 3099-3118

We introduce and study the impact of three stochastic schemes in the EC-Earth climate model: two atmospheric schemes and one stochastic land scheme. These form the basis for a probabilistic Earth system model in atmosphere-only mode. Stochastic parametrization have become standard in several operational weather-forecasting models, in particular due to their beneficial impact on model spread. In recent years, stochastic schemes in the atmospheric component of a model have been shown to improve aspects important for the models long-term climate, such as El Niño–Southern Oscillation (ENSO), North Atlantic weather regimes, and the Indian monsoon. Stochasticity in the land component has been shown to improve the variability of soil processes and improve the representation of heatwaves over Europe. However, the raw impact of such schemes on the model mean is less well studied. It is shown that the inclusion of all three schemes notably changes the model mean state. While many of the impacts are beneficial, some are too large in amplitude, leading to significant changes in the model's energy budget and atmospheric circulation. This implies that in order to maintain the benefits of stochastic physics without shifting the mean state too far from observations, a full re-tuning of the model will typically be required.

## The scientific challenge of understanding and estimating climate change.

Proceedings of the National Academy of Sciences of the United States of America **116** (2019) 24390-24395

Given the slow unfolding of what may become catastrophic changes to Earth's climate, many are understandably distraught by failures of public policy to rise to the magnitude of the challenge. Few in the science community would think to question the scientific response to the unfolding changes. However, is the science community continuing to do its part to the best of its ability? In the domains where we can have the greatest influence, is the scientific community articulating a vision commensurate with the challenges posed by climate change? We think not.

## Signal and noise in regime systems: A hypothesis on the predictability of the North Atlantic Oscillation

Quarterly Journal of the Royal Meteorological Society (2019)

© 2018 Royal Meteorological Society Studies conducted by the UK Met Office reported significant skill in predicting the winter North Atlantic Oscillation (NAO) index with their seasonal prediction system. At the same time, a very low signal-to-noise ratio was observed, as measured using the “ratio of predictable components” (RPC) metric. We analyse both the skill and signal-to-noise ratio using a new statistical toy model, which assumes NAO predictability is driven by regime dynamics. It is shown that if the system is approximately bimodal in nature, with the model consistently underestimating the level of regime persistence each season, then both the high skill and high RPC value of the Met Office hindcasts can easily be reproduced. Underestimation of regime persistence could be attributable to any number of sources of model error, including imperfect regime structure or errors in the propagation of teleconnections. In particular, a high RPC value for a seasonal mean prediction may be expected even if the model's internal level of noise is realistic.

## The Impact of a Stochastic Parameterization Scheme on Climate Sensitivity in EC-Earth

JOURNAL OF GEOPHYSICAL RESEARCH-ATMOSPHERES (2019)

## Estimates of flow-dependent predictability of wintertime Euro-Atlantic weather regimes in medium-range forecasts

QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY **144** (2018) 1012-1027

## Choosing the optimal numerical precision for data assimilation in the presence of model error

Journal of Advances in Modeling Earth Systems American Geophysical Union **10** (2018) 2177-2191

The use of reduced numerical precision within an atmospheric data assimilation system is investigated. An atmospheric model with a spectral dynamical core is used to generate synthetic observations, which are then assimilated back into the same model using an ensemble Kalman filter. The effect on the analysis error of reducing precision from 64 bits to only 22 bits is measured and found to depend strongly on the degree of model uncertainty within the system. When the model used to generate the observations is identical to the model used to assimilate observations, the reduced‐precision results suffer substantially. However, when model error is introduced by changing the diffusion scheme in the assimilation model or by using a higher‐resolution model to generate observations, the difference in analysis quality between the two levels of precision is almost eliminated. Lower‐precision arithmetic has a lower computational cost, so lowering precision could free up computational resources in operational data assimilation and allow an increase in ensemble size or grid resolution.

## Reliable low precision simulations in land surface models

CLIMATE DYNAMICS **51** (2017) 2657-2666

## A power law for reduced precision at small spatial scales: Experiments with an SQG model

Quarterly Journal of the Royal Meteorological Society Wiley **144** (2018) 1179-1188

Representing all variables in double‐precision in weather and climate models may be a waste of computer resources, especially when simulating the smallest spatial scales, which are more difficult to accurately observe and model than are larger scales. Recent experiments have shown that reducing to single‐precision would allow real‐world models to run considerably faster without incurring significant errors. Here, the effects of reducing precision to even lower levels are investigated in the Surface Quasi‐Geostrophic system, an idealised system that exhibits a similar power‐law spectrum to that of energy in the real atmosphere, by emulating reduced precision on conventional hardware. It is found that precision can be reduced much further for the smallest scales than the largest scales without inducing significant macroscopic error, according to a ‐4/3 power law, motivating the construction of a ‘scale‐selective’ reduced‐precision model that performs as well as a double‐precision control in short‐ and long‐range forecasts but for a much lower estimated computational cost. A similar scale‐selective approach in real‐world models could save resources that could be re‐invested to allow these models to be run at greater resolution, complexity or ensemble size, potentially leading to more efficient, more accurate forecasts.

## Improving weather forecast skill through reduced precision data assimilation

Monthly Weather Review American Meteorological Society **146** (2017) 49–62-

A new approach for improving the accuracy of data assimilation, by trading numerical precision for ensemble size, is introduced. Data assimilation is inherently uncertain due to the use of noisy observations and imperfect models. Thus, the larger rounding errors incurred from reducing precision may be within the tolerance of the system. Lower precision arithmetic is cheaper, and so by reducing precision in ensemble data assimilation, computational resources can be redistributed towards, for example, a larger ensemble size. Because larger ensembles provide a better estimate of the underlying distribution and are less reliant on covariance inflation and localization, lowering precision could actually permit an improvement in the accuracy of weather forecasts. Here, this idea is tested on an ensemble data assimilation system comprising the Lorenz ’96 toy atmospheric model and the ensemble square root filter. The system is run at double, single and half precision (the latter using an emulation tool), and the performance of each precision is measured through mean error statistics and rank histograms. The sensitivity of these results to the observation error and the length of the observation window are addressed. Then, by reinvesting the saved computational resources from reducing precision into the ensemble size, assimilation error can be reduced for (hypothetically) no extra cost. This results in increased forecasting skill, with respect to double precision assimilation.

## Seasonal to annual ocean forecasting skill and the role of model and observational uncertainty

Quarterly Journal of the Royal Meteorological Society Wiley **144** (2018) 1947-1964

Accurate forecasts of the ocean state and the estimation of forecast uncertainties are crucial when it comes to providing skilful seasonal predictions. In this study we analyse the predictive skill and reliability of the ocean component in a seasonal forecasting system. Furthermore, we assess the effects of accounting for model and observational uncertainties. Ensemble forcasts are carried out with an updated version of the ECMWF seasonal forecasting model System 4, with a forecast length of ten months, initialized every May between 1981 and 2010. We find that, for essential quantities such as sea surface temperature and upper ocean 300 m heat content, the ocean forecasts are generally underdispersive and skilful beyond the first month mainly in the Tropics and parts of the North Atlantic. The reference reanalysis used for the forecast evaluation considerably affects diagnostics of forecast skill and reliability, throughout the entire ten‐month forecasts but mostly during the first three months. Accounting for parametrization uncertainty by implementing stochastic parametrization perturbations has a positive impact on both reliability (from month 3 onwards) as well as forecast skill (from month 8 onwards). Skill improvements extend also to atmospheric variables such as 2 m temperature, mostly in the extratropical Pacific but also over the midlatitudes of the Americas. Hence, while model uncertainty impacts the skill of seasonal forecasts, observational uncertainty impacts our assessment of that skill. Future ocean model development should therefore aim not only to reduce model errors but to simultaneously assess and estimate uncertainties.

## A simple pedagogical model linking initial-value reliability with trustworthiness in the forced climate response

Bulletin of the American Meteorological Society American Meteorological Society **March 2018** (2017) 605-614

<p>Using a simple pedagogical model, it is shown how information about the statistical reliability of initial-value ensemble forecasts can be relevant in assessing the trustworthiness of the climate system’s response to forcing.</p><p> Although the development of seamless prediction systems is becoming increasingly common, there is still confusion regarding the relevance of information from initial-value forecasts for assessing the trustworthiness of the climate system’s response to forcing. A simple system which mimics the real climate system through its regime structure is used to illustrate this potential relevance. The more complex version of this model defines “REALITY” and a simplified version of the system represents the “MODEL”. The MODEL’s response to forcing is profoundly incorrect. However, the untrustworthiness of the MODEL’s response to forcing can be deduced from the MODEL’s initial-value unreliability. The nonlinearity of the system is crucial in accounting for this result.</p>

## Flow dependent ensemble spread in seasonal forecasts of the boreal winter extratropics

Atmospheric Science Letters Royal Meteorological Society **19** (2018) e815

Flow-dependent spread (FDS) is a desirable characteristic of probabilistic forecasts; ensemble spread should represent the expected forecast error. However this is difficult to estimate for seasonal hindcasts as they tend to have a relatively small sample size. Here we use a long (110 year) seasonal hindcast dataset to evaluate FDS in forecasts of boreal winter North Atlantic Oscillation (NAO) and Pacific North American pattern (PNA). A good FDS relationship is found for interannual variations in both the NAO and PNA , with mild underdispersion for negative NAO and PNA events and slight overdispersion for positive NAO. Decadal-scale variability is seen in forecast errors but not in ensemble spread, which shows little variation on this timescale. Links between forecast errors and tropical heating anomalies are also investigated, though no strong links are found. However a weak link between strong El Niño warming in the East Pacific and reduced PNA error is suggested.

## Exploiting the chaotic behaviour of atmospheric models with reconfigurable architectures

COMPUTER PHYSICS COMMUNICATIONS **221** (2017) 160-173

## Bitwise efficiency in chaotic models

Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences Royal Society **473** (2017) 20170144

Motivated by the increasing energy consumption of supercomputing for weather and climate simulations, we introduce a framework for investigating the bit-level information efficiency of chaotic models. In comparison with previous explorations of inexactness in climate modelling, the proposed and tested information metric has three specific advantages: (i) it requires only a single high-precision time series; (ii) information does not grow indefinitely for decreasing time step; and (iii) information is more sensitive to the dynamics and uncertainties of the model rather than to the implementation details. We demonstrate the notion of bit-level information efficiency in two of Edward Lorenz’s prototypical chaotic models: Lorenz 1963 (L63) and Lorenz 1996 (L96). Although L63 is typically integrated in 64-bit ‘double’ floating point precision, we show that only 16 bits have significant information content, given an initial condition uncertainty of approximately 1% of the size of the attractor. This result is sensitive to the size of the uncertainty but not to the time step of the model. We then apply the metric to the L96 model and find that a 16-bit scaled integer model would suffice given the uncertainty of the unresolved sub-grid-scale dynamics. We then show that, by dedicating computational resources to spatial resolution rather than numeric precision in a field programmable gate array (FPGA), we see up to 28.6% improvement in forecast accuracy, an approximately fivefold reduction in the number of logical computing elements required and an approximately 10-fold reduction in energy consumed by the FPGA, for the L96 model.

## Stochastic subgrid-scale ocean mixing: Impacts on low-frequency variability

Journal of Climate American Meteorological Society **30** (2017) 4997-5019

In global ocean models, the representation of small-scale, high-frequency processes considerably influences the large-scale oceanic circulation and its low-frequency variability. This study investigates the impact of stochastic perturbation schemes based on three different subgrid-scale parameterizations in multidecadal ocean-only simulations with the ocean model NEMO at 1° resolution. The three parameterizations are an enhanced vertical diffusion scheme for unstable stratification, the Gent-McWilliams (GM) scheme, and a turbulent kinetic energy mixing scheme, all commonly used in state-of-the-art ocean models. The focus here is on changes in interannual variability caused by the comparatively high-frequency stochastic perturbations with subseasonal decorrelation time scales. These perturbations lead to significant improvements in the representation of low-frequency variability in the ocean, with the stochastic GM scheme showing the strongest impact. Interannual variability of the Southern Ocean eddy and Eulerian streamfunctions is increased by an order of magnitude and by 20%, respectively. Interannual sea surface height variability is increased by about 20%-25% as well, especially in the Southern Ocean and in the Kuroshio region, consistent with a strong underestimation of interannual variability in the model when compared to reanalysis and altimetry observations. These results suggest that enhancing subgrid-scale variability in ocean models can improve model variability and potentially its response to forcing on much longer time scales, while also providing an estimate of model uncertainty.