Low‐dimensional representation of error covariance

Ensemble and reduced‐rank approaches to prediction and assimilation rely on low‐dimensional approximations of the estimation error covariances. Here stability properties of the forecast/analysis cycle for linear, time‐independent systems are used to identify factors that cause the steady‐state analysis error covariance to admit a low‐dimensional representation. A useful measure of forecast/analysis cycle stability is the bound matrix , a function of the dynamics, observation operator and assimilation method. Upper and lower estimates for the steady‐state analysis error covariance matrix eigenvalues are derived from the bound matrix. The estimates generalize to time‐dependent systems. If much of the steady‐state analysis error variance is due to a few dominant modes, the leading eigenvectors of the bound matrix approximate those of the steady‐state analysis error covariance matrix. The analytical results are illustrated in two numerical examples where the Kalman filter is carried to steady state. The first example uses the dynamics of a generalized advection equation exhibiting non‐modal transient growth. Failure to observe growing modes leads to increased steady‐state analysis error variances. Leading eigenvectors of the steady‐state analysis error covariance matrix are well approximated by leading eigenvectors of the bound matrix. The second example uses the dynamics of a damped baroclinic wave model. The leading eigenvectors of a lowest‐order approximation of the bound matrix are shown to approximate well the leading eigenvectors of the steady‐state analysis error covariance matrix.     

Laurentide and Cordilleran fast ice flow: some sedimentological evidence from Wisconsinan subglacial till and its substrate

With the aid of three case studies we summarize sedimentological and structural evidence in Wisconsinan subglacial till and its substrate that can be used to infer the presence of former fast-moving ice. We compare sedimentological characteristics of till with its stone fabric, stone surface erosional features and orientations of fractures, faults and folds in till and substrate, in order to interpret the processes that formed the till. In the cases we studied, stones in tills that experienced ductile deformation (inferred to be associated with fast-moving ice) show variable alignment of latest surface striae. Moreover, striae are inconsistent with the orientations of lee ends and chattermarks on the same stones, and with the dip directions of shallow shear planes and (or) steeper tension fractures in the till matrix. These observations indicate that stones were rotating in a flowing till matrix prior to their final emplacement. Ductile shear of fine-textured, water-saturated till and Jeffrey-like rotation of stones are invoked where most of the following occur together: (i) delicate striae follow the curvature of stone surfaces; (ii) a-axis fabrics are multimodal to girdle-like; (iii) stone a axis eigenvectors, striae orientation and stone lee end alignments fall between the modes of stone fabrics; (iv) stone pavements are uneven with vertically oriented and inverted bullet-shaped stones; (v) soft sediment clasts and (or) fragile fossils are preserved.     

Integrating GIS and spatial data analysis: problems and possibilities

Abstract

This article is an agreed summary of a workshop held in Sheffield between 18-20 March 1991. The focus here is on three of the themes of the workshop: the mutual benefits of closer links between geographical information systems (GIS) and the methods of spatial data analysis (SDA); the specific areas of SDA that should be linked with GIS; how the linkage should be made in practice. Directions for future research are also reviewed. The emphasis throughout is on statistical SDA and principally from the perspective of human rather than physical geography.     

Magma Evolution and Open-System Processes at Shiveluch Volcano: Insights from Phenocryst Zoning

Phenocryst zoning patterns are used to identify open-systemmagmatic processes in the products of the 2001 eruption of ShiveluchVolcano, Kamchatka. The lavas and pumices studied are hornblende–plagioclaseandesites with average pre-eruptive temperatures of 840°Cand fO₂ of 1·5–2·1 log units above nickel–nickeloxide (NNO). Plagioclase zoning includes oscillatory and patchyzonation and sieve textures. Hornblendes are commonly unzoned,but some show simple, multiple or patchy zoning. Apatite microphenocrystsdisplay normal and reverse zoning of sulphur. The textural similarityof patchy hornblende and plagioclase, together with Ba–Srsystematics in patchy plagioclase, indicate that the cores ofthese crystals were derived from cumulate material. Plagioclase–liquidequilibria suggest that the patchy texture develops by resorptionduring H₂O-undersaturated decompression. When H₂O-saturatedcrystallization recommences at lower pressure, reduced pH₂Oresults in lower X_An in plagioclase, causing more Al-rich hornblendeto crystallize. Plagioclase cores with diffuse oscillatory zoning,and unzoned hornblende crystals, probably represent a populationof crystals resident in the magma chamber for long periods oftime. In contrast, oscillatory zoning in the rims of plagioclasephenocrysts may reflect eruption dynamics during decompressioncrystallization. Increasing Fe/Al in oscillatory zoned rimssuggests oxidation as a result of degassing of H₂O during decompression.A general lack of textural overlap between phenocryst typessuggests that different phenocryst populations were spatiallyor temporally isolated during crystallization. We present evidencethat the host andesite has mixed with both more felsic and moremafic magmas. Olivine and orthopyroxene xenocrysts with reactionor overgrowth rims and strong normal zoning indicate mixingwith basalt. Sieve-textured plagioclase resulted from mixingof a more felsic magma with the host andesite. The mineralogyand mineral compositions of a mafic andesite enclave are identicalto those of the host magma, which implies efficient thermalquenching, and thus small volumes of intruding magma. Mixingof this magma with the host andesite results in phenocryst zoningbecause of differences in dissolved volatile contents. We suggestthat small magma pulses differentiated at depth and ascendedintermittently into the growing magma chamber, producing incrementalvariations in whole-rock compositions. KEY WORDS: patchy zoning; magma mixing; Shiveluch     

Æolian dust deposition rates, particle-sizes and contributions to soils along a transect in semi-arid New South Wales, Australia

The entrainment, transport and deposition of æolian dust are important processes affecting soil development at the margins of deserts. To assess accurately the impact of deposited æolian dust on soil development, it is important not only to measure total dust deposition rates, but to distinguish additions of remotely and regionally sourced dust from locally derived material as well (which should not be viewed as new soil material as it is derived from æolian re‐mobilization of an existing soil). Because of the well‐established relationship between dust particle‐size and distance travelled from source, the particle‐size distribution of deposited dusts can be used to identify the distance to probable source regions, in addition to identifying matching topsoil particle populations. Three dust traps were located along a transect of semi‐arid south‐eastern Australia, to measure æolian dust deposition rates between late 2000 and late 2001. The particle‐size distributions of selected dust deposits were measured and, with the aid of meteorological data, probable dust source regions determined. Particle‐size distributions of the topsoils at each dust trap location were also measured to determine if any dust and soil particle populations matched. Although the sampling period was relatively short, and there was relatively little dust storm activity in this part of Australia during this time, a clear pattern of diminishing total dust deposition was measured downwind along the south‐east dust path. Dust deposition rates were also moderate to low by global standards. Source regions of deposited dust were interpreted as being: (i) a combination of south‐western and local sources; (ii) a combination of north‐western and local sources; and (iii) a mixed source where dust was rained‐out. The relative importance of these sources was correlated strongly with seasonal weather conditions, although the proportion of local dust in each deposit was greater at the arid (western) end of the transect. The effects of deposited dust on soil profile development are greatest at the western and central transect locations. At the western location, a fine‐grained particle population distinctive of the south‐western and north‐western regional dusts and a coarse silt‐sized particle population characteristic of local dusts, are also present in the topsoil, altering the texture of this Arenosol derived from dune sand. At the central location, where a Calcisol has formed in lacustrine lunette sediment, local dust of the same size as the dominant silt population of the topsoil continues to be deposited, while minor topsoil populations of very fine‐grained silt match regional and long‐distance dusts deposited at the site. Deposited dust appears to have been a less important soil development factor at the more humid eastern site because of the much smaller rates of dust deposition there. Nevertheless, a minor population of very fine silt particles in the Vertisol topsoil matches long‐distance dusts deposited at the site, suggesting a small input of dust to this alluvial soil. The particle‐size methodology used here has applications in other studies of dust contributions to peri‐desert soils. In particular, particle‐size distribution ‘smoothness’ may provide an indication of whether soils have simple or complex origins.