Non-stationary Approaches for Mapping Terrain and Assessing Prediction Uncertainty

It is well known that terrain may vary markedly over small areas and that statistics used to characterise spatial variation in terrain may be valid only over small areas. In geostatistical terminology, a non-stationary approach may be considered more appropriate than a stationary approach. In many applications, local variation is not accounted for sufficiently. This paper assesses potential benefits in using non-stationary geostatistical approaches for interpolation and for the assessment of uncertainty in predictions with implications for sampling design. Two main non-stationary approaches are employed in this paper dealing with (1) change in the mean and (2) change in the variogram across the region of interest. The relevant approaches are (1) kriging with a trend model (KT) using the variogram of residuals from local drift and (2) locally-adaptive variogram KT, both applied to a sampled photogrammetrically derived digital terrain model (DTM). The fractal dimension estimated locally from the double-log variogram is also mapped to illustrate how spatial variation changes across the data set. It is demonstrated that estimation of the variogram of residuals from local drift is worthwhile in this case for the characterisation of spatial variation. In addition, KT is shown to be useful for the assessment of uncertainty in predictions. This is shown to be true even when the sample grid is dense as is usually the case for remotely-sensed data. In addition, both ordinary kriging (OK) and KT are shown to provide more accurate predictions than inverse distance weighted (IDW) interpolation, used for comparative purposes.     

The regression of net radiation upon solar radiation

Theoretical and Applied Climatology - A number of studies have sought to relate net radiation over natural surfaces to incoming global radiation. Several deficiencies are noted in interpretation of...     

Carbonatite in the tuffs of the West Eifel,Germany

Newly-discovered carbonatitic fragments from the West Eifel are described in terms of their petrography and trace-element content.     

Acoustic-Gravity Wave Propagation in a Measured Atmosphere

Summary An atmosphere is modelled by averaging measurements taken at eight locations for 1968 September 9. The effectiveness of the modelling is evaluated by comparing the atmospheric dispersion properties determined from an experimentally recorded signal resulting from a nuclear explosion on that date and those computed from the model atmosphere. The effects of atmospheric winds are shown to change the dispersion properties.
A theoretical barogram is synthesized for a receiver located 7930 km from the source and is compared to the recorded signal for the event. Barograms are synthesized for two different source functions and the source functions are discussed.     

Sex expression and growth rates in natural populations of the desert soil crustal mossSyntrichia caninervis

The low elevation Mojave Desert cryptobiotic crust is dominated by the mossSyntrichia caninervis. In 16 populations of this moss, stem height and population were significantly associated with sex expression, with longer stems expressing sex more frequently and producing more perichaetia. The above-ground age of stems ranged up to 10 years, with a mean growth rate across populations of 0.36 mm year⁻¹. The overall stem sex ratio, as a proportion of the total number of stems, was 0.30♀: 0♂: 0.70 non-expressing. The probability of expressing sex in a given season was 0.09. The absence of sexual reproduction (no sporophytes) and likely absence of the male sex from the area indicate that the non-expressing plants are female individuals. The slow growth rates, low rates of sex expression, absence of male plants, and absence of sexual reproduction in this crustal species may help explain why re-establishment of mosses on desert soils can take decades.     

Mechanisms of orthopyroxene dissolution in silica-undersaturated melts at 1 atmosphere and implications for the origin of silica-rich glass in mantle xenoliths

Experiments dissolving orthopyroxene (En₉₃) in a variety of Si-undersaturated alkaline melts at 1 atmosphere and variable f _O2 demonstrate that orthopyroxene dissolves to form olivine, Si-rich melt and clinopyroxene. These phases form a texturally and chemically distinct boundary layer around the partly dissolved orthopyroxene crystals. The occurrence of clinopyroxene in the boundary layer is due to inward diffusion of Ca from the solvent melt to the boundary layer causing clinopyroxene saturation. Compositional profiles through the solvent and the boundary layer for a number of experiments demonstrate rapid diffusion of cations across the boundary layer – solvent interface. SiO₂ diffuses outward from the boundary layer whereas CaO and Al₂O₃ diffuse toward the Si-enriched boundary layer melt. The rate of Al diffusion is slower under reducing conditions compared to the rates in experiments performed in air. Concentrations of FeO and MgO in the boundary layer and solvent are approximately equal indicating rapid diffusion and attainment of equilibrium despite ongoing crystallisation of clinopyroxene within the boundary layer. The behaviour of Na₂O and K₂O is strongly affected by f _O2. Under reducing conditions Na₂O and K₂O concentrations are approximately equal in the boundary layer and solvent indicating normal diffusion down the concentration gradient and attainment of equilibrium. Under oxidising conditions, K₂O and to a lesser extent Na₂O, have compositional profiles indicative of uphill diffusion likely due to their preference for more polymerised Si- and Al-rich melts. Under reduced conditions Al-enrichment in the boundary layer melt is not as extreme and uphill diffusion did not occur. The composition of the solvent melt after the experiments indicates that it was contaminated by the boundary layer by convective mixing due to the onset of hydrodynamic instabilities brought on by density and viscosity contrasts between the two melts. Despite using a wide variety of solvent melt compositions we find that the boundary layer melts converge toward a common composition at high SiO₂ contents. The composition of glass generated by orthopyroxene dissolution at 1 atmosphere is similar in many respects to Si-rich glass found in many orthopyroxene-rich mantle xenoliths that have been attributed to high pressure in situ processes including mantle metasomatism. The results of this study suggest that at least some Si-rich melts are likely to have formed by dissolution of xenolith orthopyroxene at low pressure possibly by their Si-undersaturated host magmas. Received: 30 August 1996 / Accepted: 15 April 1998     

Sea level,climate change and coastal evolution in Morar,northwest Scotland

Analyses of geomorphologically contrasting sites in Morar, NW Scotland, describe the forcing mechanisms of coastal change. Isolation basins (i.e. basins behind rock sills and now isolated from the sea following isostatic uplift) accumulated continuous marine and freshwater sediments from c.12 to 2 ka BP. Raised dune, marsh and wetland sites register breaching, migration and stability of dunes from c. 9 to 2 ka BP. High-resolution methods designed to address issues of macroscale and microscale sea-level changes and patterns of storminess include 1-mm sampling for pollen, dinocyst and diatom analyses, infra-red photography, X-ray photography and thin-section analysis. The data enhance the record of relative sea-level change for the area. Major phases of landward migration of the coast occurred during the period of low sea-level rise in the mid-Holocene as the rate of rise decreased from c. 3 to < 1 mm/year. Relative sea-level change controls the broad pattern of coastal evolution at each site; local site-specific factors contribute to short-term process change. There is no record of extreme events such as tsunami. Within a system of dynamic metastable equilibrium, the Holocene records show that site-specific factors determine the exact timing of system breakdown, e.g. dune breaching, superimposed on regional sea-level rise. The global average sea-level rise of 3 to 6 mm/yr by AD 2050 predicted by IPCC would only partly be offset in the Morar area by isostatic uplift of about 1 mm/yr. A change from relative sea-level fall to sea-level rise, in areas where the regional rate of uplift no longer offsets global processes, is a critical factor in the management of coastal resources.     

On the mechanical interaction between a growing porphyroblast and its surrounding matrix

Whether or not a growing porphyroblast can displace its surrounding matrix is an important but contentious issue affecting the interpretation of metamorphic textures. As an alternative to treating the problem in terms of force of crystallization, this paper examines the mechanics of porphyroblast-matrix interaction using a different and much simpler conceptual framework. New microstructural evidence for matrix displacement is then presented and analysed in detail. This evidence, from a hornfelsed metagreywacke, consists of dome-shaped accumulations of muscovite and graphite, each dome being attached to (and concave towards) a rhombdodecahedral face of a garnet porphyroblast. Muscovite within the domes shows a dimensional preferred orientation subparallel to the dome outlines while, in the matrix away from the domes, there is no preferred orientation.Our model for the origin of the mica domes envisages muscovite and graphite being swept ahead of, and mechanically accumulated onto, the growing garnet faces as they advance through the matrix. Rigorous testing of this model provides strong evidential support for matrix displacement by growing porphyroblasts. A new analysis is provided of the conditions under which matrix grains are included or displaced by porphyroblasts. It is concluded that matrix grain displacement may be very common, although the special combination of circumstances necessary to produce a diagnostic microstructural pattern probably occurs very rarely.