Footprint Radius Research Articles

Backscattering enhancement on spheroid‐shaped hydrometeors: Considerations in water and ice particles of uniform size and Marshall‐Palmer distributed rains

A second‐order scattering theory is derived for uniformly oriented spheroidal hydrometeors with a general drop size distribution in a single layer. Effects of backscattering enhancement are evaluated for a nadir pointing radar with a finite beam width at millimeter wave frequencies. Spheroids of uniform size are first studied to characterize the deviations from the spherical theories. For water spheroids, the difference between the cross term (backscattering enhancement term) and the ladder term (conventional multiscattering term) becomes larger as the spheroids deviate from the spherical shape. On the contrary, for ice spheroids, this difference is negligible. Marshall‐Palmer distributed rains with Pruppacher‐Pitter‐form drops are studied using the spheroidal approximation. The results confirm the validity of the spherical approximation used in the preceding works within the accuracy limit of measurement. In the Marshall‐Palmer distributed rains, the second‐order scattering effect becomes serious as the footprint radius increases. Hence the second‐order scattering is to be taken into account for accurate measurement of hydrometeor reflectivity for a spaceborne radar because of its large footprint radius.

Second‐order multiple‐scattering theory associated with backscattering enhancement for a millimeter wavelength weather radar with a finite beam width

Effects of multiple scattering on reflectivity are studied for millimeter wavelength weather radars. A time‐independent vector theory, including up to second‐order scattering, is derived for a single layer of hydrometeors of a uniform density and a uniform diameter. In this theory, spherical waves with a Gaussian antenna pattern are used to calculate ladder and cross terms in the analytical scattering theory. The former terms represent the conventional multiple scattering, while the latter terms cause backscattering enhancement in both the copolarized and cross‐polarized components. As the optical thickness of the hydrometeor layer increases, the differences from the conventional plane wave theory become more significant, and essentially, the reflectivity of multiple scattering depends on the ratio of mean free path to radar footprint radius. These results must be taken into account when analyzing radar reflectivity for use in remote sensing.

Noncontact atomic force microscopy studies of ultrathin films of amorphous solid water deposited on Au(111)

Noncontact atomic force microscopy was used to study the morphological changes of an ultrathin amorphous solid water (ASW) film as a function of deposition temperature, annealing temperature, and annealing time. ASW deposited at 80 or 108 K on Au(111) formed truncated hemispherical clusters of increasing size during annealing at 134 K; these clusters were inferred to be crystalline. The number of nuclei present at the outer surface of the film after deposition was greater for higher deposition temperature. For lower cluster densities, depletion of the ASW film around the clusters was observed when the clusters became larger and dendritic growth was observed when the apparent cluster footprint radius exceeded 100 nm.

Prediction of weld toe magnification factors for semi-elliptical cracks in T–butt joints

This paper reports the background development of a set of equations for estimating weld toe magnification factors (Mk) for semi-elliptical cracks in T–butt joints. This set of equations has been included in the new British Standard BS 7910. The extensive finite element parametric study from which the database of Mk factors was generated is first reported. The parameters studied — crack depth and aspect ratios, attachment footprint, weld angle and weld toe radius — and the ranges covered are those likely to be found in real structures. The procedures for numerical modelling, analysis and stress intensity factor evaluation are described, and the effects of the various influencing parameters on the Mk factors are discussed. Estimation equations that were developed from multiple regression analyses of the database of Mk factors are detailed. The equations are shown, through statistical analyses, to be a very good fit to the database from which they were derived.