Generalization of total least-squares on example of unweighted and weighted 2D similarity transformation

In this contribution it is shown that the so-called “total least-squares estimate” (TLS) within an errors-in-variables (EIV) model can be identified as a special case of the method of least-squares within the nonlinear Gauss–Helmert model. In contrast to the EIV-model, the nonlinear GH-model does not impose any restrictions on the form of functional relationship between the quantities involved in the model. Even more complex EIV-models, which require specific approaches like “generalized total least-squares” (GTLS) or “structured total least-squares” (STLS), can be treated as nonlinear GH-models without any serious problems. The example of a similarity transformation of planar coordinates shows that the “total least-squares solution” can be obtained easily from a rigorous evaluation of the Gauss–Helmert model. In contrast to weighted TLS, weights can then be introduced without further limitations. Using two numerical examples taken from the literature, these solutions are compared with those obtained from certain specialized TLS approaches.     

Petrography and geochemistry of manganiferous rocks in the Mankwadzi area in the southern Kibi‐Winneba metavolcanic belt,Ghana: Implications for genesis of Mn formations in the Birimian of West Africa

Manganiferous rocks in the Mankwadzi area in the southernmost portion of the Kibi‐Winneba metavolcanic belt, one of several Mn occurrences in the Paleoproterozoic Birimian of Ghana, are hosted in hornblende schist and amphibolite. These rocks are, in places, intruded by hornblende dyke. In outcrop, the manganiferous rocks appear to be conformable with the host schist and amphibolite, are macroscopically dark, fine‐grained and structurally massive to distinctly banded. Observed alternating light and dark occasionally macro‐folded bands suggest post‐depositional deformation of both light and dark bands. Microscopic observations revealed that the light bands are dominantly Si‐rich and the dark bands mainly of opaque minerals. Whole rock analyses of the manganiferous rocks show high contents of MnO (16.75–27.4 wt%) suggesting that the opaque minerals are likely rich in Mn. The analyzed rock samples show moderate to strong enrichments in light rare earth elements compared to heavy rare earth elements. Whereas the manganiferous rocks show perceptibly negative Eu anomaly, host hornblende schist and hornblende dyke do not. Eu anomaly in amphibolite samples is, however, uncertain as the three samples analyzed gave positive, negative and no Eu anomalies. Based on the field characteristics, microscopic and geochemical features, we suggest that the Mn occurrence in the Mankwadzi area originated via sedimentary deposition and was later modified by metamorphism, hydrothermal and/or supergene processes similar to manganiferous occurrences at Nsuta and Tambao in the Birimian of West Africa.     

Tidal response to sea level rise and bathymetric changes in the German Wadden Sea

Ocean Dynamics - Tidally dominated coasts are directly affected not only by projected rise in mean sea level, but also by changes in tidal dynamics due to sea level rise and bathymetric changes. By...     

Analysis of noble gases in water using a quadrupole mass spectrometer in static mode

A quadrupole-based mass spectrometer used in static mode has been employed to determine noble gas concentrations of water samples by isotope dilution. Water samples are degassed and spiked with minor isotopes of each noble gas. After separation of the various gas components, the isotopic ratios are measured in the mass spectrometer. Because a spike is added to each sample, the recovery of each gas component does not have to be quantitative. Equilibration temperatures are calculated from the gas concentrations, based on noble gas solubility data. An accuracy of ±1°C, from the air equilibration temperature, is attainable for air-saturated water samples prepared under controlled conditions in the laboratory. The method has been applied to groundwaters from the London Basin Chalk aquifer. The noble-gas-derived temperatures are consistent with climatic conditions prevailing at the periods of recharge.     

Isotopic and noble gas study of Chalk groundwater in the London Basin, England

The chemical and isotopic composition of groundwater from 52 sites in the London (U.K.) area was determined as part of a project aimed at assessing the spatial variation in the age of Chalk groundwater, and in determining the relationship between fracture and matrix groundwater in this dual porosity system.Systematic changes in groundwater chemistry take place in the downgradient direction in response to several chemical processes. These processes include early concentration by evaporation and congruent dissolution of calcite followed by widespread incongruent dissolution and ion exchange in addition to local oxidation-reduction reactions, gypsum dissolution and saline intrusion. As a result of the above processes, Chalk groundwater follows an evolutionary path from Ca bicarbonate type to Na bicarbonate type.The age of Chalk groundwater was modelled using¹⁴C, δ¹³C,³H, δ²H and δ¹⁸0. There is a general increase in the groundwater age in a downgradient direction with the oldest water found in N central areas of the basin. Groundwater in the unconfined zones and in areas S of the Greenwich fault is almost entirely of unevolved, modem composition. Carbon-14 modelling suggests that Chalk groundwater in the S basin is generally less than 10000 a old while that in the north is generally between 10000 and 25000 a old. The presence of³H in concentrations of up to 7 TU in groundwater which yields ages of several 1000 a, however, indicates that mechanisms exist for the rapid introduction of recent groundwater to the confined aquifer. Results of palaeorecharge temperature determinations using δ²H, δ¹⁸0 and noble gas analytical results suggest that significant Devensian recharge did indeed occur in the aquifer.A model of the development of the Chalk recognizes that it is a classic dual porosity aquifer in which groundwater flow occurs predominantly in the fracture system. The upper 50 m of the aquifer was flushed with fresh water during the 2–3 × 10⁶ a of the Quaternary and therefore meteoric water largely replaced the Tertiary and Cretaceous marine water that previously saturated the system. Most processes which control the chemistry of the groundwater occur in the matrix where the surface area is exceptionally high. Although fracture flow dominates the flow regime, diffusion from the matrix into the fracture porosity controls the chemistry of Chalk groundwater.     

Composition and sediment dispersal pattern of the Upper Triassic flysch in the eastern Himalayas,China: significance to provenance and basin analysis

International Journal of Earth Sciences - The paleogeography and basin type of Upper Triassic flysch (Langjiexue Group) in the eastern Himalayan Orogen are disputed. In order to shed new light on...     

Efficacy of Coagulants and Ballast Compounds in Removal of Cyanobacteria (<Emphasis Type="Italic">Microcystis</Emphasis>) from Water of the Tropical Lagoon Jacarepaguá (Rio de Janeiro,Brazil)

Eutrophication is considered the most important water quality problem in freshwaters and coastal waters worldwide promoting frequent occurrence of blooms of potentially toxic cyanobacteria. Removal of cyanobacteria from the water column using a combination of coagulant and ballast is a promising technique for mitigation and an alternative to the use of algaecides. In laboratory, we tested experimentally the efficiency of two coagulants, polyaluminium chloride (PAC) and chitosan (made of shrimp shells), alone and combined with two ballasts: red soil (RS) and the own lagoon sediment, to remove natural populations of cyanobacteria, from an urban brackish coastal lagoon. PAC was a very effective coagulant when applied at low doses (≤8 mg Al L^?1) and settled the cyanobacteria, while at high doses (≥16 mg Al L^?1) large flocks aggregated in the top of test tubes. In contrast, chitosan was not able to form flocks, even in high doses (>16 mg L^?1) and did not efficiently settle down cyanobacteria when combined with ballast. The RS itself removed 33–47 % of the cyanobacteria. This removal was strongly enhanced when combined with PAC in a dose-dependent matter; 8 mg Al L^?1 was considered the best dose to be applied. The lagoon sediment alone did not promote any settling of cyanobacteria but removal was high when combined with PAC. Combined coagulant and ballast seems a very efficient, cheap, fast and safe curative measure to lessen the harmful cyanobacteria bloom nuisance in periods when particularly needed, such as around the 2016 Olympics in Jacarepaguá Lagoon.     

Assessing Risks of Shallow Riparian Groundwater Quality Near an Oil Sands Tailings Pond

The potential discharge of groundwater contaminated by oil sands process‐affected water (OSPW) is a concern for aquatic ecosystems near tailings ponds. Groundwater in the area, but unaffected by OSPW, may contain similar compounds, complicating the assessment of potential ecological impacts. In this study, 177 shallow groundwater samples were collected from riparian areas along the Athabasca River and tributaries proximate to oil sands developments. For “pond‐site” samples (71; adjacent to study tailings pond), Canadian aquatic life guidelines were exceeded for 11 of 20 assessed compounds. However, “non‐pond” samples (54; not near any tailings pond) provided similar exceedances. Statistical analyses indicate that pond‐site and non‐pond samples were indistinguishable for all but seven parameters assessed, including salts, many trace metals, and fluorescence profiles of aromatic naphthenic acids (ANA). This suggests that, regarding the tested parameters, groundwater adjacent to the study tailings pond generally poses no greater ecological risk than other nearby groundwaters at this time. Multivariate analyses applied to the groundwater data set separated into 11 smaller zones support this conclusion, but show some variation between zones. Geological and potential OSPW influences could not be distinguished based on major ions and metals concentrations. However, similarities in indicator parameters, namely ANA, F, Mo, Se, and Na‐Cl ratio, were noted between a small subset of samples from two pond‐site zones and two OSPW samples and two shallow groundwater samples documented as likely OSPW affected. This indicator‐based screening suggests that OSPW‐affected groundwater may be reaching Athabasca River sediments at a few locations.     

A Hierarchical Bayesian Model Averaging Framework for Groundwater Prediction under Uncertainty

Groundwater prediction models are subjected to various sources of uncertainty. This study introduces a hierarchical Bayesian model averaging (HBMA) method to segregate and prioritize sources of uncertainty in a hierarchical structure and conduct BMA for concentration prediction. A BMA tree of models is developed to understand the impact of individual sources of uncertainty and uncertainty propagation to model predictions. HBMA evaluates the relative importance of different modeling propositions at each level in the BMA tree of model weights. The HBMA method is applied to chloride concentration prediction for the “1,500‐foot” sand of the Baton Rouge area, Louisiana from 2005 to 2029. The groundwater head data from 1990 to 2004 is used for model calibration. Four sources of uncertainty are considered and resulted in 180 flow and transport models for concentration prediction. The results show that prediction variances of concentration from uncertain model elements are much higher than the prediction variance from uncertain model parameters. The HBMA method is able to quantify the contributions of individual sources of uncertainty to the total uncertainty.     

Can GPS-Derived Surface Loading Bridge a GRACE Mission Gap?

We investigated two ‘gap-filler’ methods based on GPS-derived low-degree surface loading variations (GPS-I and GPS-C) and a more simple method (REF-S) which extends a seasonal harmonic variation into the expected Gravity Recovery and Climate Experiment (GRACE) mission gap. We simulated two mission gaps in a reference solution (REF), which is derived from a joint inversion of GRACE (RL05) data, GPS-derived surface loading and simulated ocean bottom pressure. The GPS-I and GPS-C methods both have a new type of constraint applied to mitigate the lack of GPS station network coverage over the ocean. To obtain the GPS-C solution, the GPS-I method is adjusted such that it fits the reference solution better in a 1.5 year overlapping period outside of the gap. As can be expected, the GPS-I and GPS-C solutions contain larger errors compared to the reference solution, which is heavily constrained by GRACE. Within the simulated gaps, the GPS-C solution generally fits the reference solution better compared to the GPS-I method, both in terms of spherical harmonic loading coefficients and in terms of selected basin-averaged hydrological mass variations. Depending on the basin, the RMS-error of the water storage variations (scaled for leakage effects) ranges between 1.6 cm (Yukon) and 15.3 cm (Orinoco). In terms of noise level, the seasonal gap-filler method (REF-S) even outperforms the GPS-I and GPS-C methods, which are still affected by spatial aliasing problems. However, it must be noted that the REF-S method cannot be used beyond the study of simple harmonic seasonal variations.