Uncertainties in extreme surge level estimates from observational records.

Ensemble simulations with a total length of 7540 years are generated with a climate model, and coupled to a simple surge model to transform the wind field over the North Sea to the skew surge level at Delfzijl, The Netherlands. The 65 constructed surge records, each with a record length of 116 years, are analysed with the generalized extreme value (GEV) and the generalized Pareto distribution (GPD) to study both the model and sample uncertainty in surge level estimates with a return period of 104 years, as derived from 116-year records. The optimal choice of the threshold, needed for an unbiased GPD estimate from peak over threshold (POT) values, cannot be determined objectively from a 100-year dataset. This fact, in combination with the sensitivity of the GPD estimate to the threshold, and its tendency towards too low estimates, leaves the application of the GEV distribution to storm-season maxima as the best approach. If the GPD analysis is applied, then the exceedance rate, lambda, chosen should not be larger than 4. The climate model hints at the existence of a second population of very intense storms. As the existence of such a second population can never be excluded from a 100-year record, the estimated 104-year wind-speed from such records has always to be interpreted as a lower limit.

A general setting for halo theory.

We describe a general framework for systematically treating halos that are due to refraction in preferentially oriented ice wedges, and we construct an atlas of such halos. Initially we are constrained neither by the interfacial angles nor the orientations of real ice crystals. Instead we consider "all possible" refraction halos. We therefore make no assumption regarding the wedge angle, and only a weak assumption regarding the allowable wedge orientations. The atlas is thus a very general collection of refraction halos that includes known halos as a small fraction. Each halo in the atlas is characterized by three parameters: the wedge angle, the zenith angle of the spin vector, and the spin vector expressed in the wedge frame. Together with the sun elevation, the three parameter values for a halo not only permit calculation of the halo shape, they also give much information about the halo without extensive calculation, so that often a crude estimate of the halo's appearance is possible merely from inspection of its parameters. As a result, the theory reveals order in what seems initially to be a staggering variety of halo shapes, and in particular it explains why halos look the way they do. Having constructed and studied the atlas, we then see where real or conceivable refraction halos, arising in specific crystal shapes and crystal orientations, fit into the atlas. Although our main goal is to understand halos arising in pyramidal crystals, the results also clarify and unify the classical halos arising in hexagonal prismatic crystals.

Identification of Odd-Radius Halo Arcs and of 44 degrees /46 degrees Parhelia by Their Inner-Edge Polarization.

Birefringence of ice causes the inner edges of refraction halos to be polarized. The direction of this polarization relates directly to the projection of the crystal main axis onto the sky. This implies that the inner-edge polarization can serve as an observational diagnostic for determining the actual nature of a halo arc if two competing explanations exist. The direction and the visibility of the inner-edge polarization of arcs and circular halos arising from usual ice crystals and from ice crystals with pyramidal ends are calculated. It is found that the observation of inner-edge polarization can be decisive for the identification of a spot that might be either a 44 degrees parhelion or a 46 degrees parhelion, of an arc that might be either a 22 degrees sunvex Parry arc or a 20 degrees Parroid arc arising from plate-oriented pyramidal crystals, and of an arc that might be either a 22 degrees suncave Parry arc or a 23 degrees Parroid arc from plate-oriented pyramidal crystals. (With a Parroid arc, a halo is that which arises from an ice wedge made up of two faces of a crystal that rotates about a vertically oriented spin axis, and the edge of the wedge is perpendicular to this spin axis.) Polarization properties of other rare arcs are discussed. Practical hints are given for observing visually the inner-edge polarization of halos.

Polarization Structures in Parhelic Circles and in 120 degrees Parhelia.

Parhelic circles due to plate-oriented crystals (hence, with main axes vertical) and 120 degrees parhelia change in position when viewed through a rotating polarizer. The parhelic circle moves vertically; its largest shift is found at an azimuthal distance between 90 degrees and 120 degrees from the Sun. The 120 degrees parhelia move both vertically and horizontally. The magnitudes of the shifts are between 0.1 degrees and 0.3 degrees , depending on solar elevation. The mechanism is polarization-sensitive internal reflection by prism faces of the ice crystals. We outline the theory and present three visual and one instrumental observation of the displacements of these halos in polarized light.

Halo polarization profiles and the interfacial angles of ice crystals.

Polarization and radiance of various types of refraction halo in ice-crystal swarms that extend to ground level were measured as a function of scattering angle. Simultaneously, samples of the crystals that produce these halos were collected and replicated. The halo polarization peaks are wider than the Fraunhofer theory of diffraction predicts for the observed size distribution of the replicated crystals. The explanation we put forward is that the angles between crystal prism faces are not always exact integer multiples of 60°, and the basal faces are not always exactly parallel, as is usually assumed. The collected crystals confirm this. The widths of the halo polarization peaks can be explained if the distributions of the interfacial angles around their means reach their half-maximum values at a deviation of 0.49° ± 0.05°. This corresponds to a deviation of 0.35° ± 0.03° of the face normals from their crystallographic positions. The presence of variation in interfacial angles in low-level halos seems to ari e from the fact that the crystals are growing. Some hitherto unexplained features in halo displays can be understood by considering variations in the interfacial angles.

Polarimetry of a 22 degrees halo.

The linear polarization and intensity of a 22 degrees halo has been measured simultaneously at seven wavelengths as a function of scattering angle. The polarization pattern is found to be dominated by a narrow peak centered at the halo angle. The amount of polarization in this peak is much higher than expected from Fresnel refraction alone. The observations are explained with a birefringence-diffraction halo polarization model. The effective diameter of the hexagonal face of the halo-generating crystals is found to be 41 and 54 microm for two separate scans. An independent single-wavelength parhelion observation indicates a stronger birefringence peak concentrated in an even smaller angular scattering range and a crystal diameter of 220 microm. Crystal sizes derived from the halo intensity distributions are found to be consistent with those obtained from polarization. The data demonstrate the power of halo polarimetry as a tool for detection and identification of birefringent crystals in terrestrial or extraterrestrial atmospheres.

Polarized rainbow.

The Airy theory of the rainbow is extended to polarized light. For both polarization directions a simple analytic expression is obtained for the intensity distribution as a function of the scattering angle in terms of the Airy function and its derivative. This approach is valid at least down to droplet diameters of 0.3 mm in visible light. The degree of polarization of the rainbow is less than expected from geometrical optics; it increases with droplet size. For a droplet diameter >1 mm the locations of the supernumerary rainbows are equal for both polarization directions, but for a diameter <1 mm the supernumerary rainbows of the weaker polarization component are located between those in the strong component.