An iterative version of the adaptive Gaussian mixture filter

The adaptive Gaussian mixture filter (AGM) was introduced as a robust filter technique for large-scale applications and an alternative to the well-known ensemble Kalman filter (EnKF). It consists of two analysis steps, one linear update and one weighting/resampling step. The bias of AGM is determined by two parameters, one adaptive weight parameter (forcing the weights to be more uniform to avoid filter collapse) and one predetermined bandwidth parameter which decides the size of the linear update. It has been shown that if the adaptive parameter approaches one and the bandwidth parameter decreases, as an increasing function of the sample size, the filter can achieve asymptotic optimality. For large-scale applications with a limited sample size, the filter solution may be far from optimal as the adaptive parameter gets close to zero depending on how well the samples from the prior distribution match the data. The bandwidth parameter must often be selected significantly different from zero in order to make large enough linear updates to match the data, at the expense of bias in the estimates. In the iterative AGM we introduce here, we take advantage of the fact that the history matching problem is usually estimation of parameters and initial conditions. If the prior distribution of initial conditions and parameters is close to the posterior distribution, it is possible to match the historical data with a small bandwidth parameter and an adaptive weight parameter that gets close to one. Hence, the bias of the filter solution is small. In order to obtain this scenario, we iteratively run the AGM throughout the data history with a very small bandwidth to create a new prior distribution from the updated samples after each iteration. After a few iterations, nearly all samples from the previous iteration match the data, and the above scenario is achieved. A simple toy problem shows that it is possible to reconstruct the true posterior distribution using the iterative version of the AGM. Then a 2D synthetic reservoir is revisited to demonstrate the potential of the new method on large-scale problems.     

A Spectral Analysis Based Methodology to Detect Climatological Influences on Daily Urban Water Demand

Urban water demand (UWD) is highly dependent on interacting natural and socio-economic factors, and thus a wide range of data analysis and forecasting methods are required to fully understand the issue. This study applies, for the first time, the continuous wavelet transform to determine changes in the temporal pattern of UWD and its potential meteorological drivers for three major Canadian cities: Calgary, Montreal, and Ottawa. This analysis is complemented by Fourier and cross-spectral analysis to determine inter-relationships and the significance of the patterns detected. The results show that the annual (365 days) cycle provides the most consistent and significant relationship between UWD and meteorological drivers. Wavelet analysis shows that UWD is only sensitive to air temperature in the summer months when mean daily temperatures are greater than 10 to 12 °C. For the three cities studied, the UWD increases by between 10 ML (Montreal) and 50 ML (Calgary) per day with every 1 °C increase in air temperature. In an area with low precipitation (Calgary), there is an inverse relationship between UWD and precipitation during summer months. Wavelet transform and Fourier analysis also detected a 7-day cycle in UWD, particularly in the more industrialized city of Montreal, which is related to the working week. In general, applying the season dependent linear relationships between UWD and temperature is suggested as perhaps being more appropriate and potentially successful for forecasting, rather than continuous complex nonlinear algorithms that are designed to explain variability in the entire UWD record.     

Cu- and Mn-bearing tourmalines from Brazil and Mozambique: crystal structures, chemistry and correlations

Cu- and Mn-bearing tourmalines from Brazil and Mozambique were characterised chemically (EMPA and LA-ICP-MS) and by X-ray single-crystal structure refinement. All these samples are rich in Al, Li and F (fluor-elbaite) and contain significant amounts of CuO (up to ~1.8 wt%) and MnO (up to ~3.5 wt%). Structurally investigated samples show a pronounced positive correlation between the <Y-O> distances and the (Li + Mn²⁺ + Cu + Fe²⁺) content (apfu) at this site with R ² = 0.90. An excellent negative correlation exists between the <Y-O> distances and the Al₂O₃ content (R ² = 0.94). The samples at each locality generally show a strong negative correlation between the X-site vacancies and the (MnO + FeO) content. The Mn content in these tourmalines depends on the availability of Mn, on the formation temperature, as well as on stereochemical constraints. Because of a very weak correlation between MnO and CuO we believe that the Cu content in tourmaline is essentially dependent on the availability of Cu and on stereochemical constraints.     

A multi-dimensional assessment of urban vulnerability to climate change in Sub-Saharan Africa

In this paper, we develop and apply a multi-dimensional vulnerability assessment framework for understanding the impacts of climate change-induced hazards in Sub-Saharan African cities. The research was carried out within the European/African FP7 project CLimate change and Urban Vulnerability in Africa, which investigated climate change-induced risks, assessed vulnerability and proposed policy initiatives in five African cities. Dar es Salaam (Tanzania) was used as a main case with a particular focus on urban flooding. The multi-dimensional assessment covered the physical, institutional, attitudinal and asset factors influencing urban vulnerability. Multiple methods were applied to cover the full range of vulnerabilities and to identify potential response strategies, including: model-based forecasts, spatial analyses, document studies, interviews and stakeholder workshops. We demonstrate the potential of the approach to assessing several dimensions of vulnerability and illustrate the complexity of urban vulnerability at different scales: households (e.g., lacking assets); communities (e.g., situated in low-lying areas, lacking urban services and green areas); and entire cities (e.g., facing encroachment on green and flood-prone land). Scenario modeling suggests that vulnerability will continue to increase strongly due to the expected loss of agricultural land at the urban fringes and loss of green space within the city. However, weak institutional commitment and capacity limit the potential for strategic coordination and action. To better adapt to urban flooding and thereby reduce vulnerability and build resilience, we suggest working across dimensions and scales, integrating climate change issues in city-level plans and strategies and enabling local actions to initiate a ‘learning-by-doing’ process of adaptation.     

Description of an aerodynamic levitation apparatus with applications in Earth sciences

Background  

In aerodynamic levitation, solids and liquids are floated in a vertical gas stream. In combination with CO₂-laser heating, containerless melting at high temperature of oxides and silicates is possible. We apply aerodynamic levitation to bulk rocks in preparation for microchemical analyses, and for evaporation and reduction experiments.     

Chondritic Mg isotope composition of the Earth

The processes of planetary accretion and differentiation have potentially been recorded as variations in the stable isotope ratios of the major elements between planetary objects. However, the magnitude of observed isotopic variations for several elements (Mg, Fe, Si) is at the limit of what current analytical precision and accuracy are able to resolve. Here, we present a comprehensive data set of Mg isotope ratios measured in ocean island and mid-ocean ridge basalts, peridotites and chondrites. The precision and accuracy were verified by isotopic standard addition for two samples, one carbonaceous chondrite (Murchison) and one continental flood basalt (BCR-1). In contrast with some previous studies, our data from terrestrial and chondritic materials have invariant Mg isotope ratios within the uncertainty of the method (0.1‰ for the ²⁶Mg/²⁴Mg ratio, 2SD). Although isotopic variations of less than about 0.1‰ could still be present, the data demonstrate that, at this level of uncertainty, the bulk silicate Earth and chondritic Mg reservoir have a homogeneous δ²⁶Mg = −0.23‰ (²⁶Mg/²⁴Mg ratio of the sample relative to the DSM3 standard set to zero by definition). This implies that neither planetary accretion processes nor partial mantle melting and subsequent shallow-level differentiation have fractionated Mg isotope ratios. These observations imply in particular that the formation of the Earth cannot stem from preferential sorting of chondrite constituents that would have been fractionated in their Mg isotope composition. It also implies that unlike oxygen isotopes, there was no zonation in Mg isotopes in the inner solar system.     

The Glarus thrust: excursion guide and report of a field trip of the Swiss Tectonic Studies Group (Swiss Geological Society, 14.–16. 09. 2006)

This excursion guide results form a field trip to the Glarus nappe complex organized by the Swiss Tectonic Studies Group in 2006. The aim of the excursion was to discuss old and recent concepts related to the evolution of the Glarus thrust. The major aspects were (i) the interplay between deformation, fluid flow and geochemical alteration, (ii) episodic versus continuous deformation and fluid flow, and (iii) the link between large-scale structures, microstructures, and geochemical aspects. Despite 150 years of research in the Glarus nappe complex and the new results discussed during the excursion, there exist controversies that still are unsolved.