A detailed study of the duality relation for the least squares adjustment in euclidean spaces

The Euclidean spaces with their inner products are used to describe methods of least squares adjustment as orthogonal projections on finite-dimensional subspaces. A unified Euclidean space approach to the least squares adjustment methods “observation equations” and “condition equations” is suggested. Hence not only the two adjustment solutions are treated from the view-point of Euclidean space theory in a unified frame but also the existing duality relation between the methods of “observation equations” and “condition equations” is discussed in full detail. Another purpose of this paper is to contribute to the development of some familiarity with Euclidean and Hilbert space concepts. We are convinced that Euclidean and Hilbert space techniques in least squares adjustment are elegant and powerful geodetic methods.     

Olivine phenocrysts of Hawaiian olivine tholeiite and oceanite

Olivine phenocrysts of Hawaiian tholeiites display a variety of textures and a variation in composition which is due to supercooled crystallization. The highest forsterite content measured is 91%, and the highest magnesia content estimated for a tholeiitic liquid is 17%, using the olivine geothermometer. The liquid of this composition may be either a primary magma or a primitive magma. It is not yet possible to specify any particular composition range for the primary Hawaiian tholeiites.     

Hypersthene-ilmenite(/magnetite) symplectites in coronitic olivine-gabbronorites

Symplectitic intergrowths of hypersthene (host) with ilmenite and minor magnetite (vermicules) in a gabbroic sill from the Precambrian of southwest Sweden occur as replacement products of olivine, and are thought to have formed simulataneously with the replacement of nearby crystals of ilmenite and Timagnetite by biotite and hornblende (and spinel). These interrelated replacement processes may have taken place during, or immediately after, the final stages of the magmatic crystallization, at temperatures of about 660–680°C, as part of the inherent metamorphism of the gabbroic rock. Another expression of this metamorphic imprint is the occurrence of two-tiered corona shells of hypersthene/hornblende (+spinel) at the interface of olivine and plagioclase crystals.     

The non-independence of rainfall erosivity and soil erodibility

Three high erosivity conditions (50 mm hr^?1, 100 mm hr^?1, and 200 mm hr^?1) were generated in a laboratory using a rainfall simulator and coherent soil block samples from fourteen different soil erodibility conditions. The data acquired supports the theoretical contention that soil loss should not increase as a simple linear function of storm intensity. Rather, a variable relationship is caused by the rupturing of surface seals and the changing relative significance of splash, wash and rainwash processes. Slope angle appears to influence soil loss at the higher erosivity conditions of 100 mm hr^?1 and 200 mm hr^?1 on slopes that were either very steep (> 20°) or very shallow (< 3°), but on moderate slopes the relationship is unclear. Examination of the variation of soil loss with erosivity when soil loss for a specific high erosivity condition is known revealed that conversion and power factors are of doubtful value and little generality. A satisfactory predictive equation, a power curve, is seen to be of value only when comparing rainwash soil loss between the higher erosivity conditions. The relationship is most safely considered as soil and site specific. Where the influence of slope and soil erodibility are disregarded, a strong association between soil loss and rainfall intensity is found. That soil loss, and hence, soil erodibility varies non-uniformly with erosivity is clear. The findings indicate caution is required when comparing conclusions drawn from studies based upon different erosivity conditions.     

Tracer experiments with turbulently dispersed air ions

Unipolar air ions released into the wind constitute a tracer which can be measured with high resolution. An ion source produces a cloud with homogeneous charge density, insensitive to source strength, dependent on time since formation only. It is well suited for tracing concentration changes due to turbulence, less suited for cloud size tracing. A tight array of 8 sensors has been used to examine turbulently dispersed ions. High-resolution records are presented and discussed. The highest concentrations measured could be undiluted source material. The frequency distribution within a plume did not differ from that in a multitude of puffs. The distribution seems to be log-normal with a geometric standard deviation of about 2.45. The time resolution used corresponds to volume resolutions of 40, 225, and 650 cm³. Sample size had no apparent effect.     

Low frequency waves in plasmas with spatially varying electron temperature

Low frequency electrostatic waves are studied in magnetized plasmas with an electron temperature which varies with position in a direction perpendicular to the magnetic field. For wave frequencies below the ion cyclotron frequency, the waves need not follow any definite dispersion relation. Instead a band of phase velocities is allowed, with a range of variation depending on the maximum and minimum values of the electron temperature. Simple model equations are obtained for the general case which can be solved to give the spatial variation of a harmonically time varying potential. A simple analytical model for the phenomenon is presented and the results are supported by numerical simulations carried out in a 2.5-dimensional particle-in-cell numerical simulation. We find that when the electron temperature is striated along B₀ and low frequency waves (_ci) are excited in this environment, then the intensity of these low frequency waves will be striated in a manner following the electron temperature striations. High frequency ion acoustic waves (_ci) will on the other hand have a spatially more uniform intensity distribution.     

Downscaling a twentieth century global climate simulation to the North Sea

The regional ocean model system (ROMS) is used to downscale a 26-year period of the twentieth century 20C3M experiment from the global coupled Bergen climate model (BCM) for the North Sea. Compared to an observational-based climatology, BCM have good results on the mean temperature, except for too low winter temperature. This is connected to a too weak inflow of Atlantic water. The downscaling gives added value to the BCM results by providing regional details, doubling the Atlantic inflow, and improving the mean winter temperature. For mean salinity, BCM has values very close to the climatology, whereas the downscaling becomes too fresh. The downscaling, however, improves the sea surface salinity, the vertical structure, and the Norwegian Coastal Current. It is concluded that the downscaling procedure as presented here is a suitable tool for assessing the future Atlantic inflow and sea temperature in the North Sea based on a global climate projection.