North Atlantic subtropical mode waters and ocean memory in HadCM3

A study of the formation and propagation of volume anomalies in North Atlantic Mode Waters is presented, based on 100 yr of monthly mean fields taken from the control run of the Third Hadley Centre Coupled Ocean-Atmosphere GCM (HadCM3). Analysis of the temporal and. spatial variability in the thickness between pairs of isothermal surfaces bounding the central temperature of the three main North Atlantic subtropical mode waters shows that large-scale variability in formation occurs over time scales ranging from 5 to 20 yr. The largest formation anomalies are associated with a southward shift in the mixed layer isothermal distribution, possibly due to changes in the gyre dynamics and/or changes in the overlying wind field and air-sea heat fluxes. The persistence of these anomalies is shown to result from their subduction beneath the winter mixed layer base where they recirculate around the subtropical gyre in the background geostrophic flow. Anomalies in the warmest mode (18 degrees C) formed on the western side of the basin persist for up to 5 yr. They are removed by mixing transformation to warmer classes and are returned to the seasonal mixed layer near the Gulf Stream where the stored heat may be released to the atmosphere. Anomalies in the cooler modes (16 degrees and 14 degrees C) formed on the eastern side of the basin persist for up to 10 yr. There is no clear evidence of significant transformation of these cooler mode anomalies to adjacent classes. It has been proposed that the eastern anomalies are removed through a tropical-subtropical water mass exchange mechanism beneath the trade wind belt (south of 20 degrees N). The analysis shows that anomalous mode water formation plays a key role in the long-term storage of heat in the model, and that the release of heat associated with these anomalies suggests a predictable climate feedback mechanism.

Very large inverse problems in atmosphere and ocean modelling

For the very large nonlinear dynamical systems that arise in a wide range of physical, biological and environmental problems, the data needed to initialize a numerical forecasting model are seldom available. To generate accurate estimates of the expected states of the system, both current and future, the technique of ‘data assimilation’ is used to combine the numerical model predictions with observations of the system measured over time. Assimilation of data is an inverse problem that for very large-scale systems is generally ill-posed. In four-dimensional variational assimilation schemes, the dynamical model equations provide constraints that act to spread information into data sparse regions, enabling the state of the system to be reconstructed accurately. The mechanism for this is not well understood. Singular value decomposition techniques are applied here to the observability matrix of the system in order to analyse the critical features in this process. Simplified models are used to demonstrate how information is propagated from observed regions into unobserved areas. The impact of the size of the observational noise and the temporal position of the observations is examined. The best signal-to-noise ratio needed to extract the most information from the observations is estimated using Tikhonov regularization theory. Copyright © 2005 John Wiley & Sons, Ltd.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.