to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

The Ensemble Kalman Filter: Theoretical formulation and practical implementation

The monsoon circulation of the Indian Ocean

The potential for sea ice-albedo feedback to give rise to nonlinear climate change in the Arctic Ocean – defined as a nonlinear relationship between polar and global temperature change or, equivalently, a time-varying polar amplification – is explored in IPCC AR4 climate models. Five models supplying SRES A1B ensembles for the 21 st century are examined and very linear relationships are found between polar and global temperatures (indicating linear Arctic Ocean climate change), and between polar temperature and albedo (the potential source of nonlinearity). Two of the climate models have Arctic Ocean simulations that become annually sea ice-free under the stronger CO 2 increase to quadrupling forcing. Both of these runs show increases in polar amplification at polar temperatures above-5 o C and one exhibits heat budget changes that are consistent with the small ice cap instability of simple energy balance models. Both models show linear warming up to a polar temperature of-5 o C, well above the disappearance of their September ice covers at about-9 o C. Below-5 o C, surface albedo decreases smoothly as reductions move, progressively, to earlier parts of the sunlit period. Atmospheric heat transport exerts a strong cooling effect during the transition to annually ice-free conditions. Specialized experiments with atmosphere and coupled models show that the main damping mechanism for sea ice region surface temperature is reduced upward heat flux through the adjacent ice-free oceans resulting in reduced atmospheric heat transport into the region.

Geophysical fluid dynamics.

Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

The dynamics of the flow of dense water through Barrow Canyon is investigated using data from a hydrographic survey in summer 2002. The focus is on the winter-transformed Bering water—the highest volumetric mode of winter water in the Chukchi Sea—which drains northward through the canyon in spring and summer. The transport of this water mass during the time of the survey was 0.2–0.3 Sv. As the layer flowed from the head of the canyon to the mouth, it sank, decelerated, and stretched. Strong cyclonic relative vorticity was generated on the seaward side of the jet, which compensated for the stretching. This adjustment was incomplete, however, in that it did not extend across the entire current, possibly because of internal mixing due to shear instabilities. The resulting vorticity structure of the flow at the canyon mouth was conducive for baroclinic instability and eddy formation. Multiple eddies of winter-transformed Bering water were observed along the Chukchi–Beaufort shelfbreak. Those to the west of Barrow Canyon were in the process of being spawned by the eastward-flowing shelfbreak current emanating from Herald Canyon, while the single eddy observed to the east originated from the Barrow Canyon outflow. It is argued that such an eddy formation is a major source of the ubiquitous cold-core anti-cyclones observed historically throughout the Canada Basin. Implications for the ventilation of the upper halocline of the Western Arctic are discussed.

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Flow of winter-transformed Pacific water into the Western Arctic

Suppose one were given the task of mapping the general circulation in an unfamiliar ocean. The ocean, like our own, is subdivided into basins and marginal seas interconnected by sea straits. Assuming a limited budget for this undertaking, one would do well to choose the straits as observational starting points. To begin with, the currents flowing from one basin to the next, over possibly wide and time-varying paths, are confined to narrow and stable routes within the straits. Mass, heat and chemical budgets for individual basins can be formulated in terms of the fluxes measured across the straits using a relatively small number of instruments. The confinement of the flow by a strait can also give rise to profound dynamical conse quences including choking or hydraulic control, a process similar to that by which a dam regulates the flow from a reservoir. The funneling geometry can lead to enhanced tidal modulation and increased velocities, giving rise to local instabilities, mixing, internal bores, jumps, and other striking hydraulic and fine scale phenomena. In short, sea straits repre sent choke points which are observationally and dynamically strategic and which contain a full range of fascinating physical processes."

The physical oceanography of sea straits

The flow of summer and winter Pacific water masses through Herald Canyon is investigated using data from a high-resolution hydrographic/velocity survey conducted in summer 2004. The survey was part of the Russian-American Long Term Census of the Arctic (RUSALCA) program, and consisted of four cross-canyon transects occupied over a 2-day period. At the time of the survey dense winter water was entering the western side of the canyon from the Chukchi Sea, flowing alongside a poleward jet of summer water on the canyon’s eastern flank. As the dense water progressed northward it switched sides of the canyon and underwent a sudden increase in layer thickness. This coincided with vertical mixing near the interface of the winter and summer water, producing a new water mass mode exiting the canyon. All of these features are consistent with the notion of hydraulic activity occurring in the canyon. A three-layer hydraulic theory is applied to the flow, which suggests that it is supercritical and that hydraulic control is likely. A lock-exchange formulation accurately predicts the northward transport of the winter water. The origin of the winter water and the manner in which it drains into the canyon is investigated using satellite ice-concentration data, atmospheric re-analysis fields, historical in-situ data, and a simple circulation model. Finally, the fate of the Pacific water exiting the canyon, and its connection to the Chukchi shelfbreak current, is discussed.

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Evolution and dynamics of the flow through Herald Canyon in the western Chukchi Sea

The overturning circulation in the Red Sea exhibits a distinct seasonally reversing pattern and is studied using high-resolution MIT general circulation model simulations. In the first part of this study, the vertical and horizontal structure of the summer overturning circulation and its dynamical mechanisms are presented from the model results. The seasonal water exchange in the Strait of Bab el Mandeb is successfully simulated, and the structures of the intruding subsurface Gulf of Aden intermediate water are in good agreement with summer observations in 2011. The model results suggest that the summer overturning circulation is driven by the combined effect of the shoaling of the thermocline in the Gulf of Aden resulting from remote winds in the Arabian Sea and an upward surface slope from the Red Sea to the Gulf of Aden set up by local surface winds in the Red Sea. In addition, during late summer two processes associated, respectively, with latitudinally differential heating and increased salinity in the southern Red Sea act together to cause the reversal of the contrast of the vertical density structure and the cessation of the summer overturning circulation. Dynamically, the subsurface northward pressure gradient force is mainly balanced by vertical viscosity resulting from the vertical shear and boundary friction in the Strait of Bab el Mandeb. Unlike some previous studies, the three-layer summer exchange flows in the Strait of Bab el Mandeb do not appear to be hydraulically controlled.

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Seasonal overturning circulation in the Red Sea: 1. Model validation and summer circulation

The circulation in an ocean basin containing an island is studied under nearly geostrophic, beta plane dynamics. The model is a fluid of uniform density driven by wind forcing or sources and sinks of mass at the upper boundary of the flow. The circulation is studied analytically, numerically, as well as in the laboratory through the device of the “sliced cylinder” model for the ocean circulation. Of particular interest is the estimate of the transport between the island and the oceanic basin’s boundary. The model is conceived as relevant to both the wind-driven circulation as well as the circulation of abyssal waters around deep topographic features such as mid-ocean ridge segments. Godfrey’s Island Rule for the transport is rederived in general form and the validity of the original approximation of Godfrey (1989) is examined in a variety of circumstances. In particular, the role of dissipative boundary layers and inertial effects such as vortex shedding are scrutinized to determine their role in determining the net transport around the island. Linear theory in many cases predicts a recirculation on the eastern side of the island, provided the meridional extent of the island is large enough. The existence of the recirculation, containing trapped fluid, is confirmed in both laboratory and numerical experiments and the evolution of the structure of the recirculation is examined as a function of the boundary layer Reynolds number. In both the laboratory and numerical studies, the recirculation predicted by linear theory is joined and then superseded by an inertial recirculation springing from boundary layer separation as the Reynolds number increases past a critical value. Even in the linear limit it is shown that the recirculation region, which is closed in quasigeostrophic theory, is subject to a small leak due to planetary geostrophic effects, which prediction is confirmed in the laboratory. The original island rule of Godfrey yields an estimate of the transport which is surprisingly robust and generally within 75% of the values measured in our numerical experiments. Agreement is moderately good when island western boundary layer transport is used as a basis for comparison. Several cases are discussed, however, in which the assumptions made by Godfrey are violated. One occurs when the frictional boundary layers of the island and the basin boundary overlap. We derive a threshold width for the gap for the case where the island is close to a northern or southern boundary of the basin and show how the transport is increasingly blocked as the gap is reduced. A second case occurs when the island is thin and zonally elongated so that the dissipative effects on the northern and southern boundaries of the island become important. Here the vorticity balance assumed in the simple Island Rule is fundamentally altered, and we extend the Island Rule to account for the new dissipation.

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Lawrence J. Pratt

Papers

Flow of winter-transformed Pacific water into the Western Arctic

The physical oceanography of sea straits

Evolution and dynamics of the flow through Herald Canyon in the western Chukchi Sea

Seasonal overturning circulation in the Red Sea: 1. Model validation and summer circulation

Circulation around islands and ridges