Estimation of the temporal autocorrelation structure by the collocation technique with an emphasis on soil moisture studies

Abstract

The collocation technique has become a popular tool in oceanography and hydrology for estimating the error variances of different data sources such as in situ sensors, models and remote sensing products. It is also possible to determine calibration constants, for example to account for an off-set between the data sources. So far, the temporal autocorrelation structure of the errors has not been studied, although it is known that it has detrimental effects on the results of the collocation technique, in particular when calibration constants are also determined. This paper shows how the (triple) collocation estimators can be adapted to retrieve the autocovariance functions; the statistical properties as well as the structural deficencies are described. The coupling between the autocorrelation of the error and the estimation of calibration constants is studied in detail, due to its importance for analysing temporal changes. In soil moisture applications, such time variations can be induced, for example, by seasonal changes in the vegetation cover, which affect both models and remote sensing products. The limitations of the proposed technique associated with these considerations are analysed using remote sensing and in situ soil moisture data. The variability of the inter-sensor calibration and the autocovariance are shown to be closely related to temporal patterns of the data.

Editor D. Koutsoyiannis

Citation Zwieback, S., Dorigo, W., and Wagner, W., 2013. Estimation of the temporal autocorrelation structure by the collocation technique with an emphasis on soil moisture studies. Hydrological Sciences Journal, 58 (8), 1729–1747.     

Mobile evaporite controls on the structural style and evolution of rift basins: Danish Central Graben,North Sea

The Southern Tail‐End Graben, Danish Central Graben, is characterized by a lateral variation in the thickness and mobility of pre‐rift Zechstein Supergroup evaporites, allowing investigation of how supra‐basement evaporite variability influences rift structural style and tectono‐stratigraphy. The study area is divided into two structural domains based on interpretations of the depositional thickness and mobility of the Zechstein Supergroup. Within each domain, we examine the overall basin morphology and the structural styles in the pre‐Zechstein and supra‐Zechstein (cover) units. Furthermore, integration of two‐way travel‐time (TWT)‐structure and ‐thickness maps allows fault activity and evaporite migration maps to be generated for pre‐ and syn‐rift stratal units within the two domains, permitting constraints to be placed on: (i) the timing of activity on pre‐Zechstein and cover faults and (ii) the onset, duration and migration direction of mobile evaporites. The northern domain is interpreted to be free from evaporite‐influence, and has developed in a manner typical of brittle‐only, basement‐involved rifts. Syn‐rift basins display classical half‐graben geometries bounded by thick‐skinned faults. In contrast, the southern domain is interpreted to be evaporite‐influenced, and cover structure reflects a southward increase in the thickness and mobility of the Zechstein Supergroup evaporites. Fault‐related and evaporite‐related folding is prominent in the southern domain, together with variable degrees of decoupling of sub‐Zechstein and cover fault and fold systems. The addition of mobile evaporites to the rift results in: (i) complex and spatially variable modes of tectono‐stratigraphic evolution; (ii) syn‐rift stratal geometries which are condensed above evaporite swells and over‐thickened in areas of withdrawal; (iii) compartmentalized syn‐rift depocentres; and (iv) masking of rift‐related megasequence boundaries. Through demonstrating these deviations from the characteristics of rifts free from evaporite influence, we highlight the first order control evaporites may exert upon rift structural style and the distribution and thicknesses of syn‐rift units.     

Mitigating the impact of ionospheric cycle slips in GNSS observations

Processing of data from global navigation satellite systems (GNSS), such as GPS, GLONASS and Galileo, can be considerably impeded by disturbances in the ionosphere. Cycle-slip detection and correction thus becomes a crucial component of robust software. Still, dealing with ionospheric cycle slips is not trivial due to scintillation effects in both the phase and the amplitude of the signals. In this contribution, a geometry-based approach with rigorous handling of the ionosphere is presented. A detailed analysis of the cycle-slip correction process is also tackled by examining its dependence on phase and code noise, non-dispersive effects and, of course, the ionosphere. The importance of stochastic modeling in validating the integer cycle-slip candidates is emphasized and illustrated through simulations. By examining the relationship between ionospheric bias and ionospheric constraint, it is shown that there is a limit in the magnitude of ionospheric delay variation that can be handled by the cycle-slip correction process. Those concepts are applied to GNSS data collected by stations in northern Canada, and show that enhanced cycle-slip detection can lead to decimeter-level improvements in the accuracy of kinematic PPP solutions with a 30-s sampling interval. Cycle-slip correction associated with ionospheric delay variations exceeding 50 cm is also demonstrated, although there are risks with such a procedure and these are pointed out.     

Tropical cyclone contribution to extreme rainfall over southwest Pacific Island nations

Southwest Pacific nations are among some of the worst impacted and most vulnerable globally in terms of tropical cyclone (TC)-induced flooding and accompanying risks. This study objectively quantifies the fractional contribution of TCs to extreme rainfall (hereafter, TC contributions) in the context of climate variability and change. We show that TC contributions to extreme rainfall are substantially enhanced during active phases of the Madden–Julian Oscillation and by El Niño conditions (particularly over the eastern southwest Pacific region); this enhancement is primarily attributed to increased TC activity during these event periods. There are also indications of increasing intensities of TC-induced extreme rainfall events over the past few decades. A key part of this work involves development of sophisticated Bayesian regression models for individual island nations in order to better understand the synergistic relationships between TC-induced extreme rainfall and combinations of various climatic drivers that modulate the relationship. Such models are found to be very useful for not only assessing probabilities of TC- and non-TC induced extreme rainfall events but also evaluating probabilities of extreme rainfall for cases with different underlying climatic conditions. For example, TC-induced extreme rainfall probability over Samoa can vary from ~ 95 to ~ 75% during a La Niña period, if it coincides with an active or inactive phase of the MJO, and can be reduced to ~ 30% during a combination of El Niño period and inactive phase of the MJO. Several other such cases have been assessed for different island nations, providing information that have potentially important implications for planning and preparing for TC risks in vulnerable Pacific Island nations.

     

Micro‐PIXE Geochemical Fingerprinting of Nephrite Neolithic Artifacts from Southwest Bulgaria

Neolithic artifacts made of nephrite, □Ca₂(Fe,Mg)₅Si₈O₂₂(OH)_2, are found at prehistoric settlements in Bulgaria. This study investigates these objects based on particle induced X‐ray emission using a scanning nuclear microprobe (micro‐PIXE technique). Seven nephrite artifacts from the Neolithic sites of Kovachevo, Bulgarchevo and Galabnik in southwest Bulgaria were analyzed to quantify their composition and to establish if a correlation exists between the distribution of major and trace elements, color, impurities, and texture. The nephrite artifacts are tremolite in composition, with a proposed ultrabasic origin. Based on the geochemical data obtained by micro‐PIXE, we divide the artifacts into Group 1 objects from the Kovachevo site and Group 2 objects from the Galabnik and Bulgarchevo sites. The analytical data and microprobe analyses are compared with geochemical data of nephrite from across the globe. The results are in a good agreement with previous electron microprobe and electron paramagnetic resonance (EPR) spectroscopy data. Our study provides a better understanding of the mineralogy and geochemistry of nephrite artifacts and helps to address questions regarding origin and the distribution of such materials in Bulgaria and other Balkan countries.     

Proximate environmental drivers of coral communities at Palmyra Atoll: establishing baselines prior to removing a WWII military causeway

A management proposal aims to partly remove a WWII military causeway at Palmyra Atoll to improve lagoon water circulation and alleviate sedimentation stress on the southeast backreef, an area of high coral cover and diversity. This action could result in a shift in sedimentation across reef sites. To provide management advice, we quantified the proximate environmental factors driving scleractinian coral cover and community patterns at Palmyra. The proportion of fine sedimentation was the optimal predictor of coral cover and changes in community structure, explaining 23.7% and 24.7% of the variation between sites, respectively. Scleractinian coral cover was negatively correlated with increases in fine sedimentation. Removing the causeway could negatively affect the Montipora corals that dominate the western reef terrace, as this genus was negatively correlated with levels of fine sedimentation. The tolerance limits of corals, and sediment re-distribution patterns, should be determined prior to complete removal of the causeway.     

The chemical composition including the Rare Earth Elements of the three major glass types of Europe and the Orient used in late antiquity and the Middle Ages

Sets of 20 soda ash glasses, 16 soda lime glasses and 23 wood ash glasses mainly from excavations in Europe (additional soda ash glasses from Egypt) were analysed on 61 chemical elements. Average SiO₂ is about 62% in soda glasses and 50% in wood ash glasses. The three groups of glasses contain on average 13% Na₂O, 18% Na₂O and 13% K₂O as fluxes to lower the melting temperature of quartz at their production. The starting materials beside quartz were halophytic plant ash for soda ash glass, trona (Na₃H(CO₃)₂·2H₂O) and lime (clamshells) for soda lime glass and beech ash for wood ash glass. Each of the three major glass types contains specific Rare Earth Element (REE) concentrations mainly contained in quartz and its intergrown minerals. 50 Paleozoic and Mesozoic sandstones from Central Europe represent the quartz composition. The REE pattern of these glasses apparently indicates major compositional stages of the Continental Earth's Crust. The boron to lithium and sodium to potassium ratios as in seawater suggest reactions of materials for soda glass with seawater. Negative Ce anomalies in the three glasses are caused by reactions of quartz with seawater.     

A wetting and drying algorithm with a combined pressure/free-surface formulation for non-hydrostatic models

A wetting and drying method for free-surface problems for the three-dimensional, non-hydrostatic Navier–Stokes equations is proposed. The key idea is to use a horizontally fixed mesh and to apply different boundary conditions on the free-surface in wet and dry zones. In wet areas a combined pressure/free-surface kinematic boundary condition is applied, while in dry areas a positive water level and a no-normal flow boundary condition are enforced. In addition, vertical mesh movement is performed to accurately represent the free-surface motion. Non-physical flow in the remaining thin layer in dry areas is naturally prevented if a Manning–Strickler bottom drag is used. The treatment of the wetting and drying processes applied through the boundary condition yields great flexibility to the discretisation used. Specifically, a fully unstructured mesh with any finite element choice and implicit time discretisation method can be applied. The resulting method is mass conservative, stable and accurate. It is implemented within Fluidity-ICOM [1] and verified against several idealized test cases and a laboratory experiment of the Okushiri tsunami.     

The origin of high δ<Superscript>18</Superscript>O zircons: marbles,megacrysts, and metamorphism

The oxygen isotope ratios (δ¹⁸O) of most igneous zircons range from 5 to 8‰, with 99% of published values from 1345 rocks below 10‰. Metamorphic zircons from quartzite, metapelite, metabasite, and eclogite record δ¹⁸O values from 5 to 17‰, with 99% below 15‰. However, zircons with anomalously high δ¹⁸O, up to 23‰, have been reported in detrital suites; source rocks for these unusual zircons have not been identified. We report data for zircons from Sri Lanka and Myanmar that constrain a metamorphic petrogenesis for anomalously high δ¹⁸O in zircon. A suite of 28 large detrital zircon megacrysts from Mogok (Myanmar) analyzed by laser fluorination yields δ¹⁸O from 9.4 to 25.5‰. The U–Pb standard, CZ3, a large detrital zircon megacryst from Sri Lanka, yields δ¹⁸O = 15.4 ± 0.1‰ (2 SE) by ion microprobe. A euhedral unzoned zircon in a thin section of Sri Lanka granulite facies calcite marble yields δ¹⁸O = 19.4‰ by ion microprobe and confirms a metamorphic petrogenesis of zircon in marble. Small oxygen isotope fractionations between zircon and most minerals require a high δ¹⁸O source for the high δ¹⁸O zircons. Predicted equilibrium values of Δ¹⁸O(calcite-zircon) = 2–3‰ from 800 to 600°C show that metamorphic zircon crystallizing in a high δ¹⁸O marble will have high δ¹⁸O. The high δ¹⁸O zircons (>15‰) from both Sri Lanka and Mogok overlap the values of primary marine carbonates, and marbles are known detrital gemstone sources in both localities. The high δ¹⁸O zircons are thus metamorphic; the 15–25‰ zircon values are consistent with a marble origin in a rock-dominated system (i.e., low fluid_(external)/rock); the lower δ¹⁸O zircon values (9–15‰) are consistent with an origin in an external fluid-dominated system, such as skarn derived from marble, although many non-metasomatized marbles also fall in this range of δ¹⁸O. High δ¹⁸O (>15‰) and the absence of zoning can thus be used as a tracer to identify a marble source for high δ¹⁸O detrital zircons; this recognition can aid provenance studies in complex metamorphic terranes where age determinations alone may not allow discrimination of coeval source rocks. Metamorphic zircon megacrysts have not been reported previously and appear to be associated with high-grade marble. Identification of high δ¹⁸O zircons can also aid geochronology studies that seek to date high-grade metamorphic events due to the ability to distinguish metamorphic from detrital zircons in marble.     

Gold solubility in oxidized and reduced, water-saturated mafic melt

We have performed experiments to evaluate Au solubility in natural, water-saturated basaltic melts as a function of oxygen fugacity. Experiments were carried out at 1000 °C and 200 MPa, and oxygen fugacity was controlled at the fayalite-magnetite-quartz (FMQ) oxygen fugacity buffer and FMQ + 4. All experiments were saturated with a metal-chloride aqueous solution loaded initially as a 10 wt% NaCl eq. fluid. The stable phase assemblage at FMQ consists of basalt melt, olivine, clinopyroxene, a single-phase aqueous fluid, and metallic Au. The stable phase assemblage at FMQ + 4 consists of basalt melt, clinopyroxene, magnetite-spinel solid solution, a single-phase aqueous fluid, and metallic Au. Silicate glasses (i.e., quenched melt) and their contained crystalline material were analyzed by using both electron probe microanalysis (EPMA) and laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS). Measured Au concentrations in the quenched melt range from 4.8 μg g⁻¹ to 0.64 μg g⁻¹ at FMQ + 4, and 0.54 μg g⁻¹ to 0.1 μg g⁻¹ at FMQ. The measured solubility of Au in olivine and clinopyroxene was consistently below the LA-ICP-MS limit of detection (i.e., 0.1 μg g⁻¹). These melt solubility data place important limitations on the dissolved Au content of water-saturated, Cl- and S-bearing basaltic liquids at geologically relevant fO₂ values. The new data are compared to published, experimentally-determined values for Au solubility in dry and hydrous silicate liquids spanning the compositional range from basalt to rhyolite, and the effects of melt composition, oxygen fugacity, pressure and temperature are discussed.