Until recently, long-range forecast systems showed only modest levels of skill in predicting surface winter climate around the Atlantic Basin and associated fluctuations in the North Atlantic Oscillation at seasonal lead times. Here we use a new forecast system to assess seasonal predictability of winter North Atlantic climate. We demonstrate that key aspects of European and North American winter climate and the surface North Atlantic Oscillation are highly predictable months ahead. We demonstrate high levels of prediction skill in retrospective forecasts of the surface North Atlantic Oscillation, winter storminess, near-surface temperature, and wind speed, all of which have high value for planning and adaptation to extreme winter conditions. Analysis of forecast ensembles suggests that while useful levels of seasonal forecast skill have now been achieved, key sources of predictability are still only partially represented and there is further untapped predictability.

This article describes the implementation of an incremental first guess at an appropriate time three‐dimensional variational (3DVAR) data assimilation scheme, NEMOVAR, in the Met Office's operational 1/4 degree global ocean model. NEMOVAR assimilates observations of sea‐surface temperature (SST), sea‐surface height (SSH), in situ temperature and salinity profiles and sea ice concentration. The Met Office is the first centre to implement NEMOVAR at 1/4 degree and the required developments are discussed, with particular focus on the specification of the background‐error covariances. Background‐error correlations in NEMOVAR are modelled using a diffusion operator. The horizontal background‐error correlations for temperature, salinity and sea ice concentration are parametrized using the Rossby radius, which produces relatively short correlation length‐scales at mid to high latitudes, while a flow‐dependent mixed‐layer depth parametrization is used to define the vertical length‐scales for the 3D variables. Results from a one‐year reanalysis with NEMOVAR are presented and compared with the preceding operational data assimilation scheme at the Met Office. NEMOVAR is shown to provide significant improvements to SST, SSH and sea ice concentration fields, with the largest improvements seen in regions of high variability such as eddy shedding and frontal regions and the marginal ice zone. This improvement is associated with shorter correlation length‐scales in the extratropics and an improved fit to observations in NEMOVAR. Some degradation to subsurface temperature and salinity fields where data are sparse is identified and this will be the focus of future improvements to the system.

Abstract. The Forecast Ocean Assimilation Model (FOAM) is an operational ocean analysis and forecast system run daily at the Met Office. FOAM provides modelling capability in both deep ocean and coastal shelf sea regimes using the NEMO (Nucleus for European Modelling of the Ocean) ocean model as its dynamical core. The FOAM Deep Ocean suite produces analyses and 7-day forecasts of ocean tracers, currents and sea ice for the global ocean at 1/4° resolution. Satellite and in situ observations of temperature, salinity, sea level anomaly and sea ice concentration are assimilated by FOAM each day over a 48 h observation window. The FOAM Deep Ocean configurations have recently undergone a major upgrade which has involved the implementation of a new variational, first guess at appropriate time (FGAT) 3D-Var, assimilation scheme (NEMOVAR); coupling to a different, multi-thickness-category, sea ice model (CICE); the use of coordinated ocean-ice reference experiment (CORE) bulk formulae to specify the surface boundary condition; and an increased vertical resolution for the global model. In this paper the new FOAM Deep Ocean system is introduced and details of the recent changes are provided. Results are presented from 2-year reanalysis integrations of the Global FOAM configuration including an assessment of short-range ocean forecast accuracy. Comparisons are made with both the previous FOAM system and a non-assimilative FOAM system. Assessments reveal considerable improvements in the new system to the near-surface ocean and sea ice fields. However there is some degradation to sub-surface tracer fields and in equatorial regions which highlights specific areas upon which to focus future improvements.

This paper addresses some fundamental methodological issues concerning the sensitivity analysis of chaotic geophysical systems. We show, using the Lorenz system as an example, that a naïve approach to variational (“adjoint”) sensitivity analysis is of limited utility. Applied to trajectories which are long relative to the predictability time scales of the system, cumulative error growth means that adjoint results diverge exponentially from the “macroscopic climate sensitivity”(that is, the sensitivity of time‐averaged properties of the system to finite‐amplitude perturbations). This problem occurs even for time‐averaged quantities and given infinite computing resources. Alternatively, applied to very short trajectories, the adjoint provides an incorrect estimate of the sensitivity, even if averaged over large numbers of initial conditions, because a finite time scale is required for the model climate to respond fully to certain perturbations. In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble of adjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climate sensitivity. While this ensemble‐adjoint approach is unlikely to be reliable for more complex systems, it may provide useful guidance in identifying important parameter‐combinations to be explored further through direct finite‐amplitude perturbations.

A traditional subject in statistical physics is the linear response of a molecular dynamical system to changes in an external forcing agency, e.g. the Ohmic response of an electrical conductor to an applied electric field. For molecular systems the linear response matrices, such as the electrical conductivity, can be represented by Green-Kubo formulae as improper time-integrals of 2-time correlation functions in the system. Recently, Ruelle has extended the Green-Kubo formalism to describe the statistical, steady-state response of a 'sufficiently chaotic' nonlinear dynamical system to changes in its parameters. This formalism potentially has a number of important applications. For instance, in studies of global warming one wants to calculate the response of climate-mean temperature to a change in the atmospheric concentration of greenhouse gases. In general, a climate sensitivity is defined as the linear response of a long-time average to changes in external forces. We show that Ruelle's linear response formula can be computed by an ensemble adjoint technique and that this algorithm is equivalent to a more standard ensemble adjoint method proposed by Lea, Allen and Haine to calculate climate sensitivities. In a numerical implementation for the 3-variable, chaotic Lorenz model it is shown that the two methods perform very similarly. However, because of a power-law tail in the histogram of adjoint gradients their sum over ensemble members becomes a Lévy flight, and the central limit theorem breaks down. The law of large numbers still holds and the ensemble-average converges to the desired sensitivity, but only very slowly, as the number of samples is

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This paper addresses some fundamental methodological issues concerning the sensitivity analysis of chaotic geophysical systems. We show, using the Lorenz system as an example, that a naïve approach to variational (''adjoint'') sensitivity analysis is of limited utility. Applied to trajectories which are long relative to the predictability time scales of the system, cumulative error growth means that adjoint results diverge exponentially from the ''macroscopic climate sensitivity'' (that is, the sensitivity of time-averaged properties of the system to finite-amplitude perturbations). This problem occurs even for time-averaged quantities and given infinite computing resources. Alternatively, applied to very short trajectories, the adjoint provides an incorrect estimate of the sensitivity, even if averaged over large numbers of initial conditions, because a finite time scale is required for the model climate to respond fully to certain perturbations. In the Lorenz (1963) system, an intermediate time scale is found on which an ensemble of adjoint gradients can give a reasonably accurate (O(10%)) estimate of the macroscopic climate sensitivity. While this ensemble-adjoint approach is unlikely to be reliable for more complex systems, it may provide useful guidance in identifying important parameter-combinations to be explored further through direct finite-amplitude perturbations.

[1] The Atlantic meridional overturning circulation (AMOC) has been observed at 26.