Efficient evaluation of highly oscillatory acoustic scattering surface integrals

We consider the approximation of some highly oscillatory weakly singular surface integrals, arising from boundary integral methods with smooth global basis functions for solving problems of high frequency acoustic scattering by three-dimensional convex obstacles, described globally in spherical coordinates. As the frequency of the incident wave increases, the performance of standard quadrature schemes deteriorates. Naive application of asymptotic schemes also fails due to the weak singularity. We propose here a new scheme based on a combination of an asymptotic approach and exact treatment of singularities in an appropriate coordinate system. For the case of a spherical scatterer we demonstrate via error analysis and numerical results that, provided the observation point is sufficiently far from the shadow boundary, a high level of accuracy can be achieved with a minimal computational cost.

Modeled and observed atmospheric radiation balance during the West African dry season: role of mineral dust, biomass burning aerosol, and surface albedo

The global radiation balance of the atmosphere is still poorly observed, particularly at the surface. We investigate the observed radiation balance at (1) the surface using the ARM Mobile Facility in Niamey, Niger, and (2) the top of the atmosphere (TOA) over West Africa using data from the Geostationary Earth Radiation Budget (GERB) instrument on board Meteosat-8. Observed radiative fluxes are compared with predictions from the global numerical weather prediction (NWP) version of the Met Office Unified Model (MetUM). The evaluation points to major shortcomings in the NWP model's radiative fluxes during the dry season (December 2005 to April 2006) arising from (1) a lack of absorbing aerosol in the model (mineral dust and biomass burning aerosol) and (2) a poor specification of the surface albedo. A case study of the major Saharan dust outbreak of 6–12 March 2006 is used to evaluate a parameterization of mineral dust for use in the NWP models. The model shows good predictability of the large-scale flow out to 4–5 days with the dust parameterization providing reasonable dust uplift, spatial distribution, and temporal evolution for this strongly forced dust event. The direct radiative impact of the dust reduces net downward shortwave (SW) flux at the surface (TOA) by a maximum of 200 W m−2 (150 W m−2), with a SW heating of the atmospheric column. The impacts of dust on terrestrial radiation are smaller. Comparisons of TOA (surface) radiation balance with GERB (ARM) show the “dusty” forecasts reduce biases in the radiative fluxes and improve surface temperatures and vertical thermodynamic structure.

Calculating the ocean's mean dynamic topography from a mean sea surface and a geoid

In principle the global mean geostrophic surface circulation of the ocean can be diagnosed by subtracting a geoid from a mean sea surface (MSS). However, because the resulting mean dynamic topography (MDT) is approximately two orders of magnitude smaller than either of the constituent surfaces, and because the geoid is most naturally expressed as a spectral model while the MSS is a gridded product, in practice complications arise. Two algorithms for combining MSS and satellite-derived geoid data to determine the ocean’s mean dynamic topography (MDT) are considered in this paper: a pointwise approach, whereby the gridded geoid height field is subtracted from the gridded MSS; and a spectral approach, whereby the spherical harmonic coefficients of the geoid are subtracted from an equivalent set of coefficients representing the MSS, from which the gridded MDT is then obtained. The essential difference is that with the latter approach the MSS is truncated, a form of filtering, just as with the geoid. This ensures that errors of omission resulting from the truncation of the geoid, which are small in comparison to the geoid but large in comparison to the MDT, are matched, and therefore negated, by similar errors of omission in the MSS. The MDTs produced by both methods require additional filtering. However, the spectral MDT requires less filtering to remove noise, and therefore it retains more oceanographic information than its pointwise equivalent. The spectral method also results in a more realistic MDT at coastlines. 1. Introduction An important challenge in oceanography is the accurate determination of the ocean’s time-mean dynamic topography (MDT). If this can be achieved with sufficient accuracy for combination with the timedependent component of the dynamic topography, obtainable from altimetric data, then the resulting sum (i.e., the absolute dynamic topography) will give an accurate picture of surface geostrophic currents and ocean transports.