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.

Forecast impact of targeted observations: sensitivity to observation error and proximity to steep orography

For a targeted observations case, the dependence of the size of the forecast impact on the targeted dropsonde observation error in the data assimilation is assessed. The targeted observations were made in the lee of Greenland; the dependence of the impact on the proximity of the observations to the Greenland coast is also investigated. Experiments were conducted using the Met Office Unified Model (MetUM), over a limited-area domain at 24-km grid spacing, with a four-dimensional variational data assimilation (4D-Var) scheme. Reducing the operational dropsonde observation errors by one-half increases the maximum forecast improvement from 5% to 7%–10%, measured in terms of total energy. However, the largest impact is seen by replacing two dropsondes on the Greenland coast with two farther from the steep orography; this increases the maximum forecast improvement from 5% to 18% for an 18-h forecast (using operational observation errors). Forecast degradation caused by two dropsonde observations on the Greenland coast is shown to arise from spreading of data by the background errors up the steep slope of Greenland. Removing boundary layer data from these dropsondes reduces the forecast degradation, but it is only a partial solution to this problem. Although only from one case study, these results suggest that observations positioned within a correlation length scale of steep orography may degrade the forecast through the anomalous upslope spreading of analysis increments along terrain-following model levels.

Death on the beach: the recycled utopia of Midnight

The chapter conducts close analysis of the film Midnight (O primeiro dia) in the light of Brazilian history and Brazilian film history

Comments on some recent measurements of anomalously steep N2O and O3tracer spectra in the stratospheric surf zone

Recent aircraft measurements, primarily in the extratropics, of the horizontal variance of nitrous oxide (N2O) and ozone (O3) in the middle stratosphere indicate that horizontal spectra of the tracer variance scale nearly as k−2, where k is the spatial wavenumber along the aircraft flight track [Strahan and Mahlman, 1994; Bacmeister et al., 1996]. This spectral scaling has been regarded as inconsistent with the accepted picture of stratospheric tracer motion; large-scale quasi-two-dimensional tracer advection typically yields a k−1 scaling (i.e., the classical Batchelor spectrum). In this paper it is argued that the nearly k−2 scaling seen in the measurements is a natural outcome of quasi-two-dimensional filamentation of the polar vortex edge. The accepted picture of stratospheric tracer motion can thus be retained: no additional physical processes are needed to account for deviations from the Batchelor spectrum. Our argument is based on the finite lifetime of tracer filaments and on the “singularity spectrum” associated with a one-dimensional field composed of randomly spaced jumps in concentration.