How Bayesian data assimilation can be used to estimate the mathematical structure of a model

In previous work, we presented a method for estimation and correction of non-linear mathematical model structures, within a Bayesian framework, by merging uncertain knowledge about process physics with uncertain and incomplete observations of dynamical input-state-output behavior. The resulting uncertainty in the model input-state-output mapping is expressed as a weighted combination of an uncertain conceptual model prior and a data-derived probability density function, with weights depending on the conditional data density. Our algorithm is based on the use of iterative data assimilation to update a conceptual model prior using observed system data, and thereby construct a posterior estimate of the model structure (the mathematical form of the equation itself, not just its parameters) that is consistent with both physically based prior knowledge and with the information in the data. An important aspect of the approach is that it facilitates a clear differentiation between the influences of different types of uncertainties (initial condition, input, and mapping structure) on the model prediction. Further, if some prior assumptions regarding the structural (mathematical) forms of the model equations exist, the procedure can help reveal errors in those forms and how they should be corrected. This paper examines the properties of the approach by investigating two case studies in considerable detail. The results show how, and to what degree, the structure of a dynamical hydrological model can be estimated without little or no prior knowledge (or under conditions of incorrect prior information) regarding the functional forms of the storage–streamflow and storage–evapotranspiration relationships. The importance and implications of careful specification of the model prior are illustrated and discussed.     

Carbon-bearing phases in shock-induced melt zones of the Elga meteorite

The mineralogy and texture of shock-induced melt veinlets and melt pockets in silicate inclusions in the Elga IIE iron meteorite have been studied by reflected-light optical microscopy, EMPA, SEM, Raman spectroscopy and TEM. The results suggest that Elga experienced two discrete impact events. The earlier event involved the collision of a metallic projectile with a silicate target and resulted in partial melting and recrystallization of the silicate material, forming schreibersite and oxide rims between the metal and silicate. The later impact event resulted in melt pockets in the silicate inclusions and was associated with fragmentation, melting, and brecciation of the rims and displacement of some fragments into the melt pockets. These fragments are shown to contain carbon-bearing phases: siderite and amorphous sp ² carbon, which form carbon–oxide, siderite–oxide, and siderite–schreibersite associations. The fact that the carbon-bearing fragments are spatially constrained to shock breccia and melt zones indicates that these fragments are genetically related to the impact process and that their carbon-bearing phases are of cosmic origin.     

The Kaidun meteorite: Composition and origin of inclusions in the metal of an enstatite chondrite clast

Abstract— Metal nodules are one of the major textural components of Kaidun sample #01.3.06 EH3-4. In terms of structure, the nodules are of three types: (1) globular, (2) zoned with a massive core and globular mantle, and (3) nodules with no internal structure. The size and composition of the globules in the nodules and grains of metal of the matrix are almost identical: no greater than 20 μm and Ni, 5.95; Si, 3.33 wt%. The nodules contain small (usually <5 μm) inclusions of SiO₂; albitic glass; enstatite; roedderite; and a mixture of SiO₂ and Na₂S₂. This is the first reported occurrence of a simple sulfide of an alkaline metal in nature. The formation of the inclusions appears to be related to condensation of material onto the surfaces of metal grains. The nodules appear to have formed by aggregation of separate grains (globules) of metal, with conservation of condensates on the grain surfaces as inclusions. The inclusions probably condensed over a significant temperature range from 1400 to 600 K. The aggregation of metal grains and formation of the nodules probably occurred simultaneously with condensation.     

Cation distribution and exsolution in the Luna-20 pyroxenes as the chronological indicator of their thermal history

During the process of continuous post-crystallization cooling, the degree of phase transformation in pyroxenes (ordering and decomposition of solid solutions) is determined by the total cooling time and by cooling rates at individual stages; this degree can also be applied to the estimation of the sub-solidus cooling time of pyroxenes and of rocks, genetically associated with them (geochronometer). The degree of Fe²⁺-Mg order in distribution between theM ₁ andM ₂ sites observed in orthopyroxenes can be used as the criterion for the sub-solidus cooling rates of orthopyroxenes. A technique for approximate estimation of cooling time (rates) of orthopyroxenes in the 1000–500°C interval is suggested on the basis of an ion exchange reaction kinetic model, with the adoption of a few assumptions. X-ray structural analysis study revealed the character of the Fe²⁺-Mg intersite distribution in the M-511 and M-533 orthopyroxenes from the Luna-20 regolith; the obtainedK _D values make 0.072(T _e ^o ~ 460°C) and 0.06 (T _e ^o ~ 480°C), respectively. The corresponding evaluation of the linear cooling rate in the 1000-500°C range, as inferred by the obtained data, gave the value of 0.2–0.25° h^–1. Two features of the exosolution relate to the sub-solidus cooling rate of clinopyroxenes: the degree of phase separation by composition W_o and the exsolution scale . The monocrystal X-ray diffraction study, the transmission electron microscopy and the X-ray microprobe analysis produced the exsolution parameters for clinopyroxenes 2001-3, 2001-6 and 559 from the Luna-20 regolith: W_o 26%, 28% and 45% respectively; 300 Å, 1000 Å and 60 , respectively. The solvus temperatures (T _e) of the clinopyroxenes 2001-3 and 2001-6 make, respectively, 1100 ± 25°C and 1095 ± 45°C; the spinodal temperatures (T _s) areT _s =T _e – 50°C and represent quenching temperatures of the given pyroxenes in relation to the exsolution process. The cooling time fromT _cryst. toT _s was estimated and the value of the formal linear cooling rate was found to be ~ 90° h^–1 (2001-3) and ~ 8° h^–1 (2001-6). The average value of the pyroxene 559 sub-soldius cooling rate in the 1150–1000°C range was four orders less. The obtained data were discussed in view of the possible genesis of the studied Luna-20 pyroxenes.     

Possible variation in methane flux caused by gas hydrate formation on the northeastern continental slope off Sakhalin Island, Russia

The Sakhalin Slope Gas Hydrate Project (SSGH) is an international collaborative effort by scientists from Japan, Korea, and Russia to investigate natural gas hydrates (GHs) that have accumulated on the continental slope off Sakhalin Island, Okhotsk Sea. From 2009 to 2011, field operations of the SSGH-09, -10, and -11 projects were conducted. GH-bearing and -free sediment cores were retrieved using steel hydro- and gravity corers. The concentrations of sulfate ions in sediment pore waters were measured to investigate sulfate concentration–depth profiles. Seventeen cores showed linear depth profiles of sulfate concentrations. In contrast, eight cores and two cores showed concave-up and -down profiles plausibly explained by sudden increase and decrease in methane flux from below, respectively, presumably caused by the formation of gas hydrate adjacent to the core sampling sites.     

Insights into the structure of the Wyville Thomson Ridge overflow current from a fine-scale numerical model

One of the major pathways in the northern part of the Meridional Overturning Circulation (MOC) is that of the deep water in the Nordic Seas that runs through the Faroe-Shetland Channel (FSC) and Faroe Bank Channel (FBC), as well as crossing the Wyville Thomson Ridge (WTR), on its way into the Atlantic Ocean. The WTR overflow cascades down the southern side of the ridge via the narrow Ellett Gully to the Cirolana Deep (CD) which, at 1700 m, is the deepest hole in the extreme north of the Rockall Trough. The overflow accounts for nearly 1/10th of the total Faroe-Shetland Channel Bottom Water (FSCBW) discharged through the Faroese channels and is an important intermediate water mass in the Rockall Trough. Over a period of only seven days in April 2003 bottom water temperatures cooled dramatically, from 4.46 to 3.03 °C in the CD and from 3.93 to 2.54 °C in the Ymir Trough (YT). A numerical general circulation model (MITgcm) has been applied in order to reproduce the details of this dense water overflow event. Model results were consistent with the observed cooling and total water transport. It was found that the descending gravity current forms a pair of mesoscale eddies with cyclonic and anticyclonic vorticity at the exit to the CD. Analysis of mixing processes were obtained when a passive tracer was included in the model. It was found that downstream flow is characterized by an explosive detrainment regime in the CD. The model sensitivity runs revealed that the final depth to which the overflow descends depends on the initial upstream velocity of the overflow, as well as the buoyancy difference. It is argued that models of overflows need to have realistic representations of the density structure of the overflow, and sufficiently fine vertical resolution, for the subsequent fate of the overflow to be accurately represented.     

Extrinsic and intrinsic mode of hydrogen occurrence in natural olivines: FTIR and TEM investigation

Olivine crystals from two mantle nodules in kimberlites (pipe Udachnaya and pipe Obnazennaya, Yakutiya, Siberia) were investigated using EMP, TEM, AEM and FTIR techniques to determine the mode of hydrogen occurrence in olivine. Olivine contains three types of nanometer-sized inclusions: “large” inclusions of hexagonal-like shape up to several hundred nm in size (1), lamellar defects (2) and small inclusions of hexagon-like shape up to several 10?nm in size (3). Lamellar defects and small inclusions are considered to be a “hydrous” olivine. All three types of inclusions contain OH^? or water, but they are different with respect to their phase composition. In “large” inclusions (1) hydrous magnesium silicates, such as serpentine?+?talc (“kerolite”?) and 10-Å phase?+?talc were identified. Lamellar defects (2) and small inclusions (3) are depleted in Mg and Fe compared to the olivine matrix, while the silica content is the same as that of olivine. Modulations in the periodicity of the olivine structure are observed in SAED patterns and HREM images of (2) and (3). The superperiodicity can be referred to OH^?-bearing point defect ordering in the olivine structure. If this is the case, the material of both lamellar defects and small inclusions can be assumed to be a “hydrous olivine” Mg_{2– x} v _x SiO₄H_{2 x} with a cation-deficient olivine crystal structure. Thus, both an extrinsic mode of hydrogen occurrence in olivine, such as nanometer-sized inclusions of OH^?-bearing magnesium silicates, and an intrinsic mode of hydrogen incorporation into the olivine structure, such as “hydrous olivine” in itself, were found. The data obtained here show that the OH absorption bands observed in olivine spectra at 3704(3717) and 3683(3688) cm^?1 can be unambiguously identified with serpentine; the band at 3677(3676) cm^?1 can be associated with talc. The absorption bands observed at 3591 and 3660?cm^?1 in olivine match those of the 10-Å phase at 3594, 3662 and 3666?cm^?1.     

Integrated Onshore‐Offshore Investigation of a Mediterranean Layered Coastal Aquifer

Most of the Mediterranean coastal porous aquifers are intensively exploited. Because of climatic and anthropogenic effects, understanding the physical and geological controls on groundwater distribution and flow dynamics in such aquifers is crucial. This study presents the results of a structural investigation of a system located along the coastline of the Gulf of Lions (NW Mediterranean). A key aspect of this study relies on an onshore‐offshore integrated approach combining outcrops, seismic profiles, and borehole data analysis. This multidisciplinary approach provides constraints on pore‐fluid salinity distribution and stratigraphic organization, which are crucial in assessing the modes of groundwater/seawater exchanges. Onshore, Lower Pliocene deposits dip gently seaward. They are unconformably overlain by Holocene clays in the lagoons. Offshore the Pliocene deposits either outcrop at the seabed or are buried below nonconsolidated sands infilling paleo‐valleys. Beneath the lido, the groundwater salinity distribution consists of salty pore water, overlying fresher pore water. Active circulation of groundwater masses is inferred from the geophysical results. In particular, offshore outcrops and paleo‐valleys may play an important role in salt water intrusion.     

The behavior of protons during wet olivine deformation under the conditions of the kimberlite process

This paper reports the results of optical and electron microscopic investigations of mantle olivine samples with H₂O contents of tens-hundreds ppm weight. Samples were obtained from the xenoliths and xenocrysts of the Udachnaya pipe. At the scale of optical microscope magnification, a peculiar banded microstructure was observed in thin sections prepared parallel to the olivine (010) plane. It is formed by cross-hatched bands parallel to four crystallographic directions of the olivine structure: [100], [001], [101], and [−101]. At the scale of electron optical magnifications, the banded microstructure is observed as nanometer-sized heterogeneities of various types which are related to olivine deformation: (a) planar defects parallel to (100) and (001) corresponding to the (100)[010] and (001)[100] dislocation glide systems, respectively; they are occasionally transformed into lamellae or decorated by nanoinclusions; and (b) nanometer-sized heterogeneities formed by nanoinclusion arrays not related to planar defects and oriented along the same directions of the olivine structure as the optically visible bands. The deformation structures are decorated by coupled point OH-bearing defects, which were initially present in the olivine. The crystallographically oriented arrays of nanoinclusions of high-pressure hydrous silicates are considered as a result of olivine deprotonization (elimination of OH-bearing defects from the olivine structure) in the zones of previous deformation compression in the crystal. Light refraction effects on the nanoinclusions make these zones optically visible and produce the banded microstructure, which is a consequence of previous deformation.