Integration error over very long time spans

The main limit to the time span of a numerical integration of the planetary orbits is no longer set by the availability of computer resources, but rather by the accumulation of the integration error. By the latter we mean the difference between the computed orbit and the dynamical behaviour of the real physical system, whatever the causes. The analysis of these causes requires an interdisciplinary effort: there are physical model and parameters errors, algorithm and discretisation errors, rounding off errors and reliability problems in the computer hardware and system software, as well as instabilities in the dynamical system. We list all the sources of integration error we are aware of and discuss their relevance in determining the present limit to the time span of a meaningful integration of the orbit of the planets. At present this limit is of the order of 10⁸ years for the outer planets. We discuss in more detail the truncation error of multistep algorithms (when applied to eccentric orbits), the coefficient error, the method of Encke and the associated coordinate change error, the procedures used to test the numerical integration software and their limitations. Many problems remain open, including the one of a realistic statistical model of the rounding off error; at present, the latter can only be described by a semiempirical model based upon the simpleN ² formula (N=number of steps, =machine accuracy), with an unknown numerical coefficient which is determined only a posteriori.     

Holocene climate variability in Sicily from a discontinuous stalagmite record and the Mesolithic to Neolithic transition

Fabric and stable isotopic composition of a Holocene stalagmite (CR1) from a cave in northern Sicily record changes in paleorainfall in the early Holocene. High δ¹³C stable isotope values in the calcite deposited from ca. 8500 to ca. 7500 yr ago are interpreted as reflecting periods of high rainfall. The wet phase was interrupted by two periods of multi-century duration characterized by relatively cool and dry winters centered at ca. 8200 and ca. 7500 yr ago, highlighted by low δ¹³C and δ¹⁸O values. A high variability of δ¹³C values is recorded from ca. 7500 to ca. 6500 yr ago and indicates that the transition from a pluvial early Holocene to the present-day climate conditions was punctuated by decadal-scale periods of relatively dry winters. In northern Sicily, the traditional elements of the Neolithic appear at ca. 7700 yr ago. It is possible that changes in rainfall influenced the passage from hunter-gathering to farming and sheep-herding economies.     

Site Effects Study in the Serravalle Village (NE Italy) by Means of Spectral Ratios Analyses Relatively to Multiple Reference Sites

The area of Serravalle, sited in the northern part of the town of Vittorio Veneto (TV), NE Italy, has been the target of a seismic microzonation campaign. 10 seismic stations have been deployed for a 7 months period to record in continuous mode. Three stations were installed on bedrock outcrops and seven on sedimentary sites with variable cover thickness. Spectral analyses have been performed on the collected data-set using the Generalized Inversion Technique (GIT, e.g. Andrews, 1986). In particular, spectral ratios have been calculated for each station relatively to the average of the three reference, bedrock sites. The spectral ratios provide quantitative estimates of the seismic motion amplifications which occur in each of the monitored sites. Two sites show high values of amplification, 5 times larger than signal amplitude at the reference sites, in correspondence of well discernible peak frequencies of 5 Hz. Results for the other stations show smaller amounts of site amplification spreading over a broad range of frequencies. Sites where the highest amplifications were recorded all lie on the left bank of the Meschio River and in areas farther away from its outlet into the plain correlating with the presence of thick layers of Quaternary deposits.     

Validation of Landslide Susceptibility Maps; Examples and Applications from a Case Study in Northern Spain

A procedure for validating landslide susceptibility maps wasapplied in a study area in northern Spain and the results obtained compared. Validationwas used to carry out sensitivity analysis for individual variables and combinationsof variables. The validity of different map-making methods was tested, as well as theutility of different types of Favourability Functions. The results obtained show thatvalidation is essential to determine the predictive value of susceptibility maps. Italso helps to better select the most suitable function and significant variables, thus improving the efficiency of the mapping process. Validation based on a temporal strategy makes it possible to derive hazard maps from susceptibility maps.     

Global occurrence of tellurium-rich ferromanganese crusts and a model for the enrichment of tellurium

Hydrogenetic ferromanganese oxyhydroxide crusts (Fe-Mn crusts) precipitate out of cold ambient ocean water onto hard-rock surfaces (seamounts, plateaus, ridges) at water depths of about 400 to 4000 m throughout the ocean basins. The slow-growing (mm/Ma) Fe-Mn crusts concentrate most elements above their mean concentration in the Earth’s crust. Tellurium is enriched more than any other element (up to about 50,000 times) relative to its Earth’s crustal mean of about 1 ppb, compared with 250 times for the next most enriched element.We analyzed the Te contents for a suite of 105 bulk hydrogenetic crusts and 140 individual crust layers from the global ocean. For comparison, we analyzed 10 hydrothermal stratabound Mn-oxide samples collected from a variety of tectonic environments in the Pacific. In the Fe-Mn crust samples, Te varies from 3 to 205 ppm, with mean contents for Pacific and Atlantic samples of about 50 ppm and a mean of 39 ppm for Indian crust samples. Hydrothermal Mn samples have Te contents that range from 0.06 to 1 ppm. Continental margin Fe-Mn crusts have lower Te contents than open-ocean crusts, which is the result of dilution by detrital phases and differences in growth rates of the hydrogenetic phases.Correlation coefficient matrices show that for hydrothermal deposits, Te has positive correlations with elements characteristic of detrital minerals. In contrast, Te in open-ocean Fe-Mn crusts usually correlates with elements characteristic of the MnO₂, carbonate fluorapatite, and residual biogenic phases. In continental margin crusts, Te also correlates with FeOOH associated elements. In addition, Te is negatively correlated with water depth of occurrence and positively correlated with crust thickness. Q-mode factor analyses support these relationships. However, sequential leaching results show that most of the Te is associated with FeOOH in Fe-Mn crusts and ≤10% is leached with the MnO₂.Thermodynamic calculations indicate that Te occurs predominantly as H₅TeO₆⁻ in ocean water. The speciation of Te in ocean water and charge balance considerations indicate that Te should be scavenged by FeOOH, which is in agreement with our leaching results. The thermodynamically more stable Te(IV) is less abundant by factors of 2 to 3.5 than Te(VI) in ocean water. This can be explained by preferential (not exclusive) scavenging of Te(IV) by FeOOH at the Fe-Mn crust surface and by Fe-Mn colloids in the water column. We propose a model in which the extreme enrichment of Te in Fe-Mn crusts is likely the result of an oxidation reaction on the surface of FeOOH. A similar oxidation process has been confirmed for Co, Ce, and Tl at the surface of MnO₂ in crusts, but has not been suggested previously to occur in association with FeOOH in Fe-Mn crusts. Mass-balance considerations indicate that ocean floor Fe-Mn deposits are the major sink for Te in the oceans. The concentration and redox chemistry of Te in the global ocean are likely controlled by scavenging on Fe-Mn colloids in the water column and Fe-Mn deposits on the ocean floor, as is also the case for Ce.     

International greenhouse gas inventory systems: A comparison between CORINAIR and IPCC methodologies in the EU

There are several different approaches currently taken by the 15 EU countries in compiling their IPCC inventories for the FCCC. Six countries (France, Ireland, Italy, Luxembourg, Portugal, Spain) use the CORINAIR system and then aggregate and reformat the data into the required IPCC format. Of the remaining countries, two strictly follow the IPCC methodology (Finland and Greece), five (Denmark, Germany, Netherlands, Sweden, United Kingdom) estimate emissions using a combination of national and IPCC methodologies, while the final two (Austria and Belgium) use a combination of national and CORINAIR methodologies (transformed to IPCC). Comparison of the national inventories in both the IPCC and CORINAIR formats shos some revealing discrepancies between the two systems at both sector and gas level that by chance cancel out when aggregated at the EU level.     

Chemical and isotopic equilibrium between CO2 and CH4 in fumarolic gas discharges: Generation of CH4 in arc magmatic-hydrothermal systems

The chemical and isotopic composition of fumarolic gases emitted from Nisyros Volcano, Greece, and of a single gas sample from Vesuvio, Italy, was investigated in order to determine the origin of methane (CH₄) within two subduction-related magmatic-hydrothermal environments.Apparent temperatures derived from carbon isotope partitioning between CH₄ and CO₂ of around 340°C for Nisyros and 470°C for Vesuvio correlate well with aquifer temperatures as measured directly and/or inferred from compositional data using the H₂O-H₂-CO₂-CO-CH₄ geothermometer. Thermodynamic modeling reveals chemical equilibrium between CH₄, CO₂ and H₂O implying that carbon isotope partitioning between CO₂ and CH₄ in both systems is controlled by aquifer temperature.N₂/³He and CH₄/³He ratios of Nisyros fumarolic gases are unusually low for subduction zone gases and correspond to those of midoceanic ridge environments. Accordingly, CH₄ may have been primarily generated through the reduction of CO₂ by H₂ in the absence of any organic matter following a Fischer-Tropsch-type reaction. However, primary occurrence of minor amounts of thermogenic CH₄ and subsequent re-equilibration with co-existing CO₂ cannot be ruled out entirely. CO₂/³He ratios and δ¹³C_CO2 values imply that the evolved CO₂ either derives from a metasomatized mantle or is a mixture between two components, one outgassing from an unaltered mantle and the other released by thermal breakdown of marine carbonates. The latter may contain traces of organic matter possibly decomposing to CH₄ during thermometamorphism.     

Eocene-Pliocene time scale and stratigraphy of the Upper Rhine Graben (URG) and the Swiss Molasse Basin (SMB)

We present a general stratigraphic synthesis for the Upper Rhine Graben (URG) and the Swiss Molasse Basin (SMB) from Eocene to Pliocene times. The stratigraphic data were compiled both from literature and from research carried out by the authors during the past 6 years ; an index of the stratigraphically most important localitites is provided. We distinguish 14 geographical areas from the Helvetic domain in the South to the Hanau Basin in the North. For each geographical area, we give a synthesis of the biostratigraphy, lithofacies, and chronostratigraphic ranges. The relationships between this stratigraphic record and the global sea-level changes are generally disturbed by the geodynamic (e.g., subsidence) evolution of the basins. However, global sea-level changes probably affected the dynamic of transgression–regression in the URG (e.g., Middle Pechelbronn Beds and Serie Grise corresponding with sea-level rise between Ru1/Ru2 and Ru2/Ru3 sequences, respectively) as well as in the Molasse basin (regression of the UMM corresponding with the sea-level drop at the Ch1 sequence). The URGENT-project (Upper Rhine Graben evolution and neotectonics) provided an unique opportunity to carry out and present this synthesis. Discussions with scientists addressing sedimentology, tectonics, geophysics and geochemistry permitted the comparison of the sedimentary history and stratigraphy of the basin with processes controlling its geodynamic evolution. Data presented here back up the palaeogeographic reconstructions presented in a companion paper by the same authors (see Berger et al. in Int J Earth Sci 2005).     

Is robustness really robust? How different definitions of robustness impact decision-making under climate change

Robust decision-making is being increasingly used to support environmental resources decisions and policy analysis under changing climate and society. In this context, a robust decision is a decision that is as much as possible insensitive to a large degree of uncertainty and ensures certain performance across multiple plausible futures. Yet, the concept of robustness is neither unique nor static. Multiple robustness metrics, such as maximin, optimism-pessimism, max regret, have been proposed in the literature, reflecting diverse optimistic/pessimistic attitudes by the decision maker. Further, these attitudes can evolve in time as a response to sequences of favorable (or adverse) events, inducing possible dynamic changes in the robustness metrics. In this paper, we explore the impact of alternative definitions of robustness and their evolution in time for a case of water resources system management under changing climate. We study the decisions of the Lake Como operator, who is called to regulate the lake by balancing irrigation supply and flood control, under an ensemble of climate change scenarios. Results show a considerable variability in the system performance across multiple robustness metrics. In fact, the mis-definition of the actual decision maker’s attitude biases the simulation of its future decisions and produces a general underestimation of the system performance. The analysis of the dynamic evolution of the decision maker’s preferences further confirms the potentially strong impact of changing robustness definition on the decision-making outcomes. Climate change impact assessment studies should therefore include the definition of robustness among the uncertain parameters of the problem in order to analyze future human decisions under uncertainty.