# Publications

## Revisiting the identification of wintertime atmospheric circulation regimes in the Euro‐Atlantic sector

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Atmospheric circulation is often clustered in so‐called circulation regimes, which are persistent and recurrent patterns. For the Euro‐Atlantic sector in winter, most studies identify four regimes: the Atlantic Ridge, Scandinavian Blocking and the two phases of the North Atlantic Oscillation. These results are obtained by applying k‐means clustering to the first several empirical orthogonal functions (EOFs) of geopotential height data. Studying the observed circulation in reanalysis data, it is found that when the full field data are used for the k‐means cluster analysis instead of the EOFs, the optimal number of clusters is no longer four but six. The two extra regimes that are found are the opposites of the Atlantic Ridge and Scandinavian Blocking, meaning they have a low‐pressure area roughly where the original regimes have a high‐pressure area. This introduces an appealing symmetry in the clustering result. Incorporating a weak persistence constraint in the clustering procedure is found to lead to a longer duration of regimes, extending beyond the synoptic time‐scale, without changing their occurrence rates. This is in contrast to the commonly used application of a time‐filter to the data before the clustering is executed, which, while increasing the persistence, changes the occurrence rates of the regimes. We conclude that applying a persistence constraint within the clustering procedure is a better way of stabilizing the clustering results than low‐pass filtering the data.

## Jet Latitude Regimes and the Predictability of the North Atlantic Oscillation

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In recent years, numerical weather prediction models have begun to show notable levels of skill at predicting the average winter North Atlantic Oscillation (NAO) when initialised one month ahead. At the same time, these model predictions exhibit unusually low signal-to-noise ratios, in what has been dubbed a `signal-to-noise paradox'. We analyse both the skill and signal-to-noise ratio of the Integrated Forecast System (IFS), the European Center for Medium-range Weather Forecasts (ECMWF) model, in an ensemble hindcast experiment. Specifically, we examine the contribution to both from the regime dynamics of the North Atlantic eddy-driven jet. This is done by constructing a statistical model which captures the predictability inherent to to the trimodal jet latitude system, and fitting its parameters to reanalysis and IFS data. Predictability in this regime system is driven by interannual variations in the persistence of the jet latitude regimes, which determine the preferred state of the jet. We show that the IFS has skill at predicting such variations in persistence: because the position of the jet strongly influences the NAO, this automatically generates skill at predicting the NAO. We show that all of the skill the IFS has at predicting the winter NAO over the period 1980-2010 can be attributed to its skill at predicting regime persistence in this way. Similarly, the tendency of the IFS to underestimate regime persistence can account for the low signal-to-noise ratio, giving a possible explanation for the signal-to-noise paradox. Finally, we examine how external forcing drives variability in jet persistence, as well as highlight the role played by transient baroclinic eddy feedbacks to modulate regime persistence.

## Constraining Projections using Decadal Predictions

Geophysical Research Letters American Geophysical Union (0)

## Does ENSO regularity increase in a warming climate?

Journal of Climate American Meteorological Society (0) JCLI-D-19-0545.1

<jats:p> The impact of a warming climate on El Nino-Southern Oscillation (ENSO) is investigated in large ensemble simulations of the Community Earth System Model (CESM1). These simulations are forced by historical emissions for the past and the RCP8.5-scenario emissions for future projections. The simulated variance of the Nino-3.4 ENSO index increases from 1.4<jats:sup>◦</jats:sup>C<jats:sup>2</jats:sup> in 1921-1980 to 1.9<jats:sup>◦</jats:sup>C<jats:sup>2</jats:sup> in 1981-2040 and 2.2<jats:sup>◦</jats:sup>C<jats:sup>2</jats:sup> in 2041-2100. The autocorrelation timescale of the index also increases, consistent with a narrowing of its spectral peak in the 3- to 7-yr ENSO band, raising the possibility of greater seasonal to interannual predictability in the future. Low-order linear inverse models (LIMs) fitted separately to the three 60-yr periods capture the CESM1 increase in ENSO variance and regularity. Remarkably, most of the increase can be attributed to the increase in the 23-month damping timescale of a single damped oscillatoryENSO eigenmode of these LIMs by 5 months in 1981-2040 and 6 months in 2041-2100. These apparently robust projected increases may however be compromised by CESM1 biases in ENSO amplitude and damping timescale. A LIM fitted to the 1921-1980 observations has an ENSO eigenmode with a much shorter 8-month damping timescale, similar to that of several other eigenmodes. When the mode’s damping timescale is increased by 5 and 6 months in this observational LIM, a much smaller increase of ENSO variance is obtained than in the CESM1 projections. This may be because ENSO is not as dominated by a single ENSO eigenmode in reality as it is in the CESM1. </jats:p>

## Introducing the Probabilistic Earth-System Model: Examining The Impact of Stochasticity in EC-Earth v3.2

Geoscientific Model Development European Geosciences Union (0)

<jats:p>&lt;p&gt;&lt;strong&gt;Abstract.&lt;/strong&gt; 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 parametrisations 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 ENSO, North Atlantic weather regimes and the Indian monsoon. Stochasticity in the land-component has been shown to improve 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 all three schemes notably change the model mean state. While many of the impacts are beneficial, some are too large in amplitude, leading to large changes in the model's energy budget. This implies that in order to keep 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.&lt;/p&gt; </jats:p>

## On the Magnetic Flux Linkage of an Electrically-Conducting Fluid: A Treatment of the Relativistic Case Using the Exterior Calculus Formalism

Geophysical & Astrophysical Fluid Dynamics **12** (1979) 177-180

Hide's (1979) theorem on the rnagnetic flux linkage of an electrically-conducting fluid is extended to the fully general relativistic case by rederiving the theorem in the elegant and succinct formalism of Cartan's exterior calculus. © Gordon and Breach Science Publishers Ltd., 1979

## MOMENTUM-TRANSFER IN GRAVITATION THEORY

GENERAL RELATIVITY AND GRAVITATION **10** (1979) 623-629

## DERRICKS THEOREM IN CURVED SPACE

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL **12** (1979) L17-L19

## COVARIANT CONSERVATION EQUATIONS AND THEIR RELATION TO THE ENERGY-MOMENTUM CONCEPT IN GENERAL RELATIVITY

PHYSICAL REVIEW D **18** (1978) 4399-4407

## COVARIANT CONSERVATION EQUATIONS AND THEIR RELATION TO THE ENERGY-MOMENTUM CONCEPT IN GENERAL RELATIVITY

PHYSICAL REVIEW C (1978) 4399-4407

## CONSERVATION EQUATIONS AND GRAVITATIONAL SYMPLECTIC FORM

JOURNAL OF MATHEMATICAL PHYSICS **19** (1978) 2324-2331

## Recovering valuations on Demushkin fields

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Let $K$ be a field with $G_K(2) \simeq G_{\mathbb{Q}_2}(2)$, where $G_F(2)$ denotes the maximal pro-2 quotient of the absolute Galois group of a field $F$. We prove that then $K$ admits a (non-trivial) valuation $v$ which is 2-henselian and has residue field $\mathbb{F}_2$. Furthermore, $v(2)$ is a minimal positive element in the value group $\Gamma_v$ and $[\Gamma_v:2\Gamma_v]=2$. This forms the first positive result on a more general conjecture about the structure of pro-$p$ Galois groups. As an application, we prove a strong version of the birational section conjecture for smooth, complete curves $X$ over $\mathbb{Q}_2$, as well as an analogue for varieties.

## Continuous Structural Parameterization: A method for representing different model parameterizations within one structure demonstrated for atmospheric convection

Wiley (0)

## Canonical Valuations and the Birational Section Conjecture

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We develop a notion of a `canonical $\mathcal{C}$-henselian valuation' for a class $\mathcal{C}$ of field extensions, generalizing the construction of the canonical henselian valuation of a field. We use this to show that the $p$-adic valuation on a finite extension $F$ of $\mathbb{Q}_p$ can be recovered entirely (or up to some indeterminacy of the residue field) from various small quotients of $G_F$, the absolute Galois group of $F$. In particular, it can be recovered fully from the maximal solvable quotient. We use this to prove several versions of the birational section conjecture for varieties over $p$-adic fields.

## Through a Jet Speed Darkly: The Emergence of Robust Euro-Atlantic Regimes in the Absence of Jet Speed Variability

ArXiv (0)

Euro-Atlantic regimes are typically identified using either the latitude of the eddy-driven jet, or clustering algorithms in the phase space of 500hPa geopotential height (Z500). However, while robust trimodality is visibly apparent in jet latitude indices, Z500 clusters require highly sensitive significance tests to distinguish them from autocorrelated noise. As a result, even small shifts in the time-period considered can notably alter the diagnosed regimes. Fixing the optimal regime number is also hard to justify. We argue that the jet speed, a near-Gaussian distribution projecting strongly onto the Z500 field, is the source of this lack of robustness. Once its influence is removed, the Z500 phase space becomes visibly non-Gaussian, and clustering algorithms easily recover three extremely stable regimes, corresponding to the jet latitude regimes. Further analysis supports the existence of two additional regimes, corresponding to a tilted and split jet. This framework therefore naturally unifies the two regime perspectives.

## Using reduced-precision arithmetic in the adjoint model of MITgcm

ArXiv (0)

In recent years, it has been convincingly shown that weather forecasting models can be run in single-precision arithmetic. Several models or components thereof have been tested with even lower precision than this. This previous work has largely focused on the main nonlinear `forward' model. A nonlinear model (in weather forecasting or otherwise) can have corresponding tangent linear and adjoint models, which are used in 4D variational data assimilation. The linearised models are plausibly far more sensitive to reductions in numerical precision since unbounded error growth can occur with no possibility of nonlinear saturation. In this paper, we present a geophysical experiment that makes use of an adjoint model to calculate sensitivities and perform optimisation. Using software emulation, we investigate the effect of degrading the numerical precision of the adjoint model. We find that reasonable results are obtained with as few as 10 significand bits, equal to the significand precision in the IEEE half-precision standard.

## Calibrating large-ensemble European climate projections using observational data

Earth System Dynamics European Geosciences Union (0)

## On the shallow atmosphere approximation in finite element dynamical cores

ArXiv (0)

We provide an approach to implementing the shallow atmosphere approximation in three dimensional finite element discretisations for dynamical cores. The approach makes use of the fact that the shallow atmosphere approximation metric can be obtained by writing equations on a three-dimensional manifold embedded in $\mathbb{R}^4$ with a restriction of the Euclidean metric. We show that finite element discretisations constructed this way are equivalent to the use of a modified three dimensional mesh for the construction of metric terms. We demonstrate our approach via a convergence test for a prototypical elliptic problem.

## Compatible finite element methods for numerical weather prediction

ArXiv (0)

This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often referred to as compatible finite elements, mimetic finite elements, discrete differential forms or finite element exterior calculus. We provide an elementary introduction in the case of the one-dimensional wave equation, before summarising recent results in applications to the rotating shallow water equations on the sphere, before taking an outlook towards applications in three-dimensional compressible dynamical cores.

## Identification of storm surge events over the German Bight from atmospheric reanalysis and climate model data

Natural Hazards and Earth System Sciences Copernicus GmbH **15** (0) 1437-1447

<jats:p>Abstract. A new procedure for the identification of storm surge situations for the German Bight is developed and applied to reanalysis and global climate model data. This method is based on the empirical approach for estimating storm surge heights using information about wind speed and wind direction. Here, we hypothesize that storm surge events are caused by high wind speeds from north-westerly direction in combination with a large-scale wind storm event affecting the North Sea region. The method is calibrated for ERA-40 data, using the data from the storm surge atlas for Cuxhaven. It is shown that using information of both wind speed and direction as well as large-scale wind storm events improves the identification of storm surge events. To estimate possible future changes of potential storm surge events, we apply the new identification approach to an ensemble of three transient climate change simulations performed with the ECHAM5/MPIOM model under A1B greenhouse gas scenario forcing. We find an increase in the total number of potential storm surge events of about 12 % [(2001–2100)–(1901–2000)], mainly based on changes of moderate events. Yearly numbers of storm surge relevant events show high interannual and decadal variability and only one of three simulations shows a statistical significant increase in the yearly number of potential storm surge events between 1900 and 2100. However, no changes in the maximum intensity and duration of all potential events is determined. Extreme value statistic analysis confirms no frequency change of the most severe events. </jats:p>