An approach to estimation problems containing uncertain parameters

We consider how to treat a finite-dimensional linear inverse problem when the form of the forward problem is known exactly, but is dependent upon some parameters whose exact value is uncertain and which enter the forward problem multiplicatively. We show one way to proceed when the uncertainty is treatable in a statistical manner. Predicting the secular variation ∂_tB(t) produced by a particular fluid flow V at the core-mantle boundary (when magnetic diffusion is ignored) is one such example, because the results depend on the main magnetic field B(t) originating in the core which is improperly known because of contamination by the crustal magnetic field. This infinite-dimensional inverse problem is often solved by projection on to a finite-dimensional basis, and the resulting parameters found by a maximum likelihood technique. If the main field is contaminated with errors from a Gaussian distribution, this paper describes how the maximum likelihood solution can take this into account, and we show the probability density function that must be maximised in this case. We give an example of the effects for a simple model system, and suggest possible areas of application.     

GEOEssential – mainstreaming workflows from data sources to environment policy indicators with essential variables

ABSTRACT

When defining indicators on the environment, the use of existing initiatives should be a priority rather than redefining indicators each time. From an Information, Communication and Technology perspective, data interoperability and standardization are critical to improve data access and exchange as promoted by the Group on Earth Observations. GEOEssential is following an end-user driven approach by defining Essential Variables (EVs), as an intermediate value between environmental policy indicators and their appropriate data sources. From international to local scales, environmental policies and indicators are increasingly percolating down from the global to the local agendas. The scientific business processes for the generation of EVs and related indicators can be formalized in workflows specifying the necessary logical steps. To this aim, GEOEssential is developing a Virtual Laboratory the main objective of which is to instantiate conceptual workflows, which are stored in a dedicated knowledge base, generating executable workflows. To interpret and present the relevant outputs/results carried out by the different thematic workflows considered in GEOEssential (i.e. biodiversity, ecosystems, extractives, night light, and food-water-energy nexus), a Dashboard is built as a visual front-end. This is a valuable instrument to track progresses towards environmental policies.     

Reaction of montmorillonite with acid aqueous solutions: solute activity control by a secondary phase

Al, Ca, Mg and Na montmorillonites were reacted with acid aqueous solutions in order to test the assumption of equilibrium underlying solubility determinations of thermodynamic properties of montmorillonite. The value calculated for the equilibrium constant varied with pH over the pH range 1.5–4.2. Hence montmorillonite was not in a unique state of equilibrium with all solutions over this range. Therefore the derivation of thermodynamic properties of montmorillonite by the application of a single step dissolution equation to results of solubility studies in mildly acidic solutions is invalid. Indications of solute activity control by a secondary solid phase were given by: (1) the dependence of the solution concentrations of some, but not all, montmorillonite constituent elements upon each other; and (2) a lack of congruency in the dissolution of montmorillonite. These indications were confirmed by a principal components statistical analysis, which showed that the solution activities of Si, Al and H after long-term treatments of the mineral from undersaturation were always related by the same expression. This particular expression is equivalent to an equilibrium constant for the reversible dissolution of a secondary solid phase that is enriched in silicon by comparison with montmorillonite. An aluminous solid phase was also shown to be formed.     

Effects of aging on silica solubility: A laboratory study

In three separate experiments, one using a bicarbonate buffered aqueous NaCl solution and two using natural seawater. the solubility of chemically pure X-ray amorphous precipitated silica decreased by approximately 20‰ after aging in contact with solution for several months. The specific surface area of the silica decreased by approximately half during the same experimental time periods. The solubility decrease in buffered NaCl solution occurred at both 2 and 22°C and over the pressure range from 1.01 × 10⁵ to 7.45 × 10⁷ Pa (1–740 atm). The aging process which causes the solubility and surface area decreases may be caused by the formation of a smooth surface silica layer that is more dense than the original surface. No change in the bulk chemistry of the silica could be defined after aging. This short term aging process contributes to the scatter in published solubilities for amorphous silica in seawater.     

Crustal structure measurements near FRAM II in the pole abyssal plain

An extensive refraction profiling program was carried out during the FRAM II experiment (March–May, 1980) in the eastern Arctic Ocean. Two structural areas were covered: north of the ice camp (86°N, 24°W) into the basin of the Pole Abyssal Plain and south onto the flanks of the Morris Jesup Rise. Digital multichannel data on an 800 by 800 m, 24 channel hydrophone array and a single 2-component ocean bottom seismometer (OBS) were recorded for offsets from 2.5 to 100 km. Arrival times, amplitudes and phase velocities of the seismic signals recieved on the hydrophone array were determined using high resolution array processing. From these measurements and the OBS data, preliminary velocity structural models of the crust have been derived. For the purposes of this paper, 2 refraction lines have been analyzed, a 40 km line on a flat region of the Pole Abyssal Plain and an 86 km line on a slightly dipping region taken as the drifting ice camp shoaled on the Morris Jesup Rise. These preliminary analyses yield a sedimentary layer with a gradually increasing velocity 1.5–2 km thick. This cover overlays a crust with a thin layer 2 (< 1 km) and yields a total ocean bottom to mantle thickness of 4–7 km.     

Late-glacial vegetation associated with caribou and mastodon in central Indiana

The Christensen Mastodon Site, located in central Indiana, contains a rich assemblage of vertebrates (including mastodon, caribou, and giant beaver), invertebrates, and plant macrofossils in situ in lake and bog sediments of late-glacial age. Studies of pollen and plant macrofossils suggest the existence of open, white spruce-dominated boreal forests from >; 14,000 yr B.P. to ca. 13,000 yr B.P. The regional decline of spruce, local occurrence of black spruce, white spruce, and larch, immigration of many hardwood taxa (e.g., ash, oak, elm), and the initiation of bog development are recorded beginning about 13,000 yr B.P. Recent reconstructions of late-glacial and early postglacial vegetational changes provide a context for understanding the disappearance of mastodons. The dramatic and rapid restriction of boreal forests along the retreating ice margin from 11,000 to 9000 yr B.P. may have caused a substantial reduction of mastodon populations. A diminished population would be more susceptible to small-scale, stochastic events such as short-term extremes of weather, outbreaks of disease, or predation pressure from paleoindian hunters.