The wadic project: A comprehensive field evaluation of directional wave instrumentation

The results of a comprehensive field trial of nearly all commercially available directional wave measurement systems at the Edda field in the North Sea during winter 1985-86 are presented. The results summarize the accuracy of the principal engineering wave parameters from each system and the dependence on sea state. Limiting factors on system performance and operational problems are also included in the assessment. Overall experience has been good with systems utilizing widely different measurement principles returning consistent results.     

Heat flow near obstacles in the solar convection zone

Disturbances in the heat flow in the solar convection zone are calculated with a turbulent thermal diffusion coefficient based on a mixing length approximation. As a consequence of the radiative boundary condition at the surface and the strong increase of the diffusion coefficient with depth, the convection zone resembles a thermally superconducting shell enclosed between a thin surface layer and an interior core of low thermal conductivity. Thermal disturbances originating in the convection zone do not penetrate into the interior, and penetrate only weakly through the solar surface. A thermally isolating obstacle buried entirely in the convection zone casts a shadow of reduced temperature at the solar surface; the brightening surrounding this shadow is undetectable. The shadow is weak unless the object is located close to the surface (less than 2000 km). Assuming a sunspot to be an area of reduced thermal conductivity which extends a finite depth into the convection zone, the heat flow around this obstacle is calculated. The heat flux blocked below the spot (missing flux) spreads over a very extended area surrounding the spot. The brightening corresponding to this missing flux is undetectable if the reduction of the thermal conductivity extends to a depth greater than 1000 km. It is concluded that no effect other than a decrease of the convective efficiency is needed to explain the temperature change observed at the solar surface in and around a sunspot. The energy balance is calculated between magnetic flux tubes, oriented vertically in the solar surface, (magnetic elements in active regions and the quiet network) and their surroundings. Near the visible surface radiation enters the tube laterally from the surrounding convection zone. The heating effect of this influx is important for small tubes (less than a few arcseconds). Due to this influx tubes less than about 1 in diameter can appear as bright structures irrespective of the amount of heat conveyed along the tube itself. Through the lateral influx, small tubes such as are found in the quiet network act as little leaks in the solar surface through which an excess heat flux escapes from the convection zone.     

Diffusion-deposition patterns in Martian streaks

The spreading angle of a number of light and dark Martian streaks is determined from selected Mariner 9 images. The resulting frequency distributions of spreading half-angles have maxima at ～5° for light, and ～7° for dark streaks; however the dark streaks have a secondary maximum spreading angle at ～14°. The smaller values, which include most streaks, are interpreted as crater-wake spreading phenomena. The larger value, found in only a few dark streaks or “tails,” may result from atmospheric diffusion and subsequent deposition of material from isolated sources such as vents or blowouts. An atmospheric diffusion-deposition analysis is presented, assuming this streak origin, from which it is possible to deduce the eddy diffusivity, K, in Mars' boudary layer. Calculated K values are found to agree with various theoretical estimates. They lie in the range 10⁷ and 10⁹ cm² sec^?1 and exhibit the proper scale dependence. Thus it appears that, in addition to streak-derived wind direction patterns and speed information, it is possible in a few cases to derive information on Mars' boundary-layer turbulence from streak-spreading measurements.     

Velocity-space maps and transforms of tracking observations for orbital trajectory state analysis

The orbital state of a satellite in a central force field can be uniquely described by its velocity hodograph, a circle, rather than the Keplerian conic. Also, its coordinate-frame rotation about the attracting center is definable, without singularity, by the four-parameter set of Euler parameters. A unified state model of orbital trajectory and attitude dynamics has previously been developed by use of state variables of the orbital velocity hodograph and Euler parameters. The dynamical constraint equations of this orbital state model are especially effective in advanced techniques of state estimation, used for orbit determination and prediction. External observations of orbital vehicles, such as provided by optical and radar sensors of tracking systems, are transformable into corresponding velocity state maps, as presented in this paper. These transformations and the consequent state maps are essential for development of the orbit observation matrix used with the unified state matrix, in recursive estimators such as the Kalman filters. Line-of-sight rays and range spheres (or hemispheres) of observations map conformally into orthogonal spherical surfaces in velocity space, as the result of the point-contact transformations. In bispherical coordinates, the field of observation maps for a ground-based tracking system site is shown to be a reduced (or degenerate) form of the general field of observation maps for a satellite-based tracking site. These orbital state maps and transforms are directly useful in development of observation matrices for candidate observation sets, such as range only, angle only, or range plus range-rate tracking schemes. Also, surface coverage patterns can be generated for proposed new tracking systems, in mission analysis and system synthesis studies.     

Inferring erosional resistance of bedrock units in the east Tennessee mountains from digital elevation data

Measures of local relief, regional relief, and slope were calculated from digital elevation models (DEMs) for 50 bedrock units in the Ridge and Valley and Blue Ridge provinces of Tennessee. Each of these measures was normalized and the three were then averaged to produce the erosional resistance index (ERI). Bedrock units with higher ERI values include coarse clastics, intermediate clastics, and metaplutonics. Units with lower values include shales, limestones, limestones plus dolostones, and carbonates plus fine clastics. Dolostones tend to have intermediate values. The calculated ERI values were compared with subjective ratings by a geologist with decades of field experience in east Tennessee. Generally, the agreement between the two ratings was good, the most glaring exception being several shales with improbably high ERI values. These turned out to be thin units cropping out beneath very hard sandstones, allowing them to stand higher and steeper than would otherwise be possible. A systematic method for detecting such erroneously high ERI values is suggested. Inspection of a drainage map superimposed on the geology map shows that in a given area, streams tend to flow on rock units with the lowest ERI values. In addition, statistical analysis shows that bedrock units with the lowest ERI values are, on average, almost three times closer to the nearest stream and six times as likely to have streams flowing on them than are units with highest values. Further, the effect of ERI on stream location is strongest for streams with drainage areas between 1 and 30 km². Thus, small streams appear to be subject to greater lithologic control than are larger streams.     

A canonical theory for short GPS baselines. Part II: the ambiguity precision and correlation

The present contribution is the second of four parts. It considers the precision and correlation of the least-squares estimators of the carrier phase ambiguities. It is shown how the precision and correlation of the double-differenced ambiguities as well as of the widelane ambiguities are effected by the observation weights, by the number of satellites tracked, by the number of observation epochs used, and by the change over time of the relative receiver-satellite geometry. Also the ability of the widelane transformation to decorrelate and to improve the precision is investigated. Received: 16 July 1996 / Accepted: 14 November 1996