Summary statistics in geochemistry: A study of the performance of robust estimates

Numerical data summaries in many geochemical papers rely on arithmetic means, with or without standard deviations. Yet the mean is the worst average (estimate of location) for those extremely common geochemical data sets which are non-normally distributed or include outliers. The widely used geometric mean, although allowing for skewed distributions, is equally susceptible to outliers. The superior performance of 19 robust estimates of location (simple median, plus various combined, adaptive, trimmed, and skipped,L, M, andW estimates) is illustrated using real geochemical data sets varying in sources of error (pure analytical error to multicomponent geological variability), modality (unimodal to polymodal), size (20 to >2000 data values), and continuity (continuous to truncated in either or both tails). The arithmetic mean tends to overestimate location of many geochemical data sets because of positive skew and large outliers; robust estimates yield consistent smaller averages, although some (e.g., Hampel's and Andrew's) do perform better than others (e.g., Shorth mean, dominant cluster mode). Recommended values for international standard rocks, and for such important geochemical concepts as average chondrite, can be reproduced far more simply via robust estimation on complete interlaboratory data sets than via the rather complicated and subjective methods (e.g., laboratory ratings) so far used in the literature. Robust estimates also seem generally less affected by truncation than the mean; for example, if values below machine detection limits are alternatively treated as missing values or as real values of zero, similar averages are obtained. The standard (and mean) deviations yield consistently larger values of scale for many geochemical data sets than the hinge width (interquartile range) or median absolute deviation from the median. Therefore, summaries of geochemical data should always include at least the simple median and hinge width, to complement the often misleading mean and standard deviation.     

Hydrologic history of the Mississippi and Lower Missouri Rivers based upon a refined specific‐gauge approach

A refined specific‐gauge approach was developed to quantify changes over time in hydrological response on 3260 km of the Mississippi River system using long‐term data observed at 67 hydrologic measurement stations. Of these stations, 49 were unrated (stage‐only) stations, for which over 2 000 000 ‘synthetic discharges’ were generated based on measured discharge values at nearby rated stations. The addition of these synthetic discharges nearly tripled the number of stations in the study area for which specific‐gauge analysis could be performed. In order to maintain spatial homogeneity across such a broad study area, discharges were normalized to multiples of mean daily flow (MDF). Specific‐gauge analysis calculates stage changes over time for invariant discharge conditions. Two discharges were analysed: low‐flow and flood conditions at each station. In order to avoid the large errors associated with extrapolation of annual rating curves, a new ‘enhanced interpolation’ technique was developed that calculates continuous specific‐stage time series, even for rare discharges. Thus enhanced, specific‐gauge analysis is a useful reconnaissance tool for detecting geomorphic and hydrologic trends over time. Results show that on the Middle Mississippi River and Lower Missouri River, flood stages increased at all stations in spite of widespread incision of the river bed. On the Lower Mississippi River, both low‐flow and flood stages decreased, mainly the result of artificial meander cutoffs in the late 1920s and 1930s, except downstream of Natchez, MS, where net aggradation was observed. On the Upper Mississippi River, the specific‐gauge trends were dominated by emplacement of navigational dams and impoundment of slackwater pools. On all four river reaches, these results document hydrologic responses to the different engineering toolkits used on the different portions of the Mississippi River system during the past 75–150 years. Copyright © 2008 John Wiley & Sons, Ltd.     

Late Holocene sea-surface temperature and precipitation variability in northern Patagonia, Chile (Jacaf Fjord, 44°S)

A high-resolution multi-proxy study including the elemental and isotopic composition of bulk organic matter, land plant-derived biomarkers, and alkenone-based sea-surface temperature (SST) from a marine sedimentary record obtained from the Jacaf Fjord in northern Chilean Patagonia (44°20′S) provided a detailed reconstruction of continental runoff, precipitation, and summer SST spanning the last 1750 yr. We observed two different regimes of climate variability in our record: a relatively dry/warm period before 900 cal yr BP (lower runoff and average SST 1°C warmer than present day) and a wet/cold period after 750 cal yr BP (higher runoff and average SST 1°C colder than present day). Relatively colder SSTs were found during 750–600 and 450–250 cal yr BP, where the latter period roughly corresponds to the interval defined for the Little Ice Age (LIA). Similar climatic swings have been observed previously in continental and marine archives of the last two millennia from central and southern Chile, suggesting a strong latitudinal sensitivity to changes in the Southern Westerly Winds, the main source of precipitation in southern Chile, and validating the regional nature of the LIA. Our results reveal the importance of the Chilean fjord system for recording climate changes of regional and global significance.     

The importance of distribution types on finite element analyses of foundation settlement

We investigate the effects of using different types of statistical distributions (lognormal, gamma, and beta) to characterize the variability of Young’s modulus of soils in random finite element analyses of shallow foundation settlement. We use a two-dimensional linear elastic, plane-strain, finite element model with a rigid footing founded on elastic soil. Poisson’s ratio of the soil is considered constant, and Young’s modulus is characterized using random fields with extreme values of the scale of fluctuation. We perform an extensive sensitivity analysis to compare the distributions of computed settlements when different types of statistical distributions of Young’s modulus, different coefficients of variation of Young’s modulus, and different scales of fluctuation of the random field of Young’s modulus are considered. A large number of realizations are employed in the Monte Carlo simulations to investigate the influence of the tails of the statistical distributions under study. Results indicate the type of distribution considered for characterization of the random field of Young’s modulus can have a significant impact on computed settlement results. In particular, considering different types of distributions of Young’s modulus can lead to more than 600% differences on computed mean settlements for cases with high coefficient of variation and large scale of fluctuation of Young’s modulus. The effect of considering different types of distributions is reduced, but not completely eliminated, for smaller coefficients of variation of Young’s modulus (because the differences between distributions decrease) and for small values of the scale of fluctuation of Young’s modulus (because of an identified “averaging effect”).     

Spectral analysis and design approach for high force‐to‐volume extrusion damper‐based structural energy dissipation

High force‐to‐volume extrusion damping devices can offer significant energy dissipation directly in structural connections and significantly reduce seismic response. Realistic force levels up to 400 kN have been obtained experimentally validating this overall concept. This paper develops spectral‐based design equations for their application. Response spectra analysis for multiple, probabilistically scaled earthquake suites are used to delineate the response reductions due to added extrusion damping. Representative statistics and damping reduction factors are utilized to characterize the modified response in a form suitable for current performance‐based design methods. Multiple equation regression analysis is used to characterize reduction factors in the constant acceleration, constant velocity, and constant displacement regions of the response spectra. With peak device forces of 10% of structural weight, peak damping reduction factors in the constant displacement region of the spectra are approximately 6.5 ×, 4.0 ×, and 2.8 × for the low, medium, and high suites, respectively. At T = 1 s, these values are approximately 3.6 ×, 1.8 ×, and 1.4 ×, respectively. The maximum systematic bias introduced by using empirical equations to approximate damping reduction factors in design analyses is within the range of +10 to ?20%. The seismic demand spectrum approach is shown to be conservative across a majority of the spectrum, except for large added damping between T = 0.8 and 3.5 s, where it slightly underestimates the demand up to a maximum of approximately 10%. Overall, the analysis shows that these devices have significant potential to reduce seismic response and damage at validated prototype device force levels. Copyright © 2007 John Wiley & Sons, Ltd.     

Holocene climate and glacier variability at Hallet and Greyling Lakes,Chugach Mountains,south-central Alaska

Evidence from lake sediments and glacier forefields from two hydrologically isolated lake basins is used to reconstruct Holocene glacier and climate history at Hallet and Greyling Lakes in the central Chugach Mountains of south-central Alaska. Glacial landform mapping, lichenometry, and equilibrium-line altitude reconstructions, along with changes in sedimentary biogenic-silica content, bulk density, and grain-size distribution indicate a dynamic history of Holocene climate variability. The evidence suggests a warm early Holocene from 10 to 6 ka, followed by the onset of Neoglaciation in the two drainage basins, beginning between 4.5 and 4.0 ka. During the past 2 ka, the glacial landforms and lacustrine sediments from the two valleys record a remarkably similar history of glaciation, with two primary advances, one during the first millennium AD, from ~500 to 800 AD, and the second during the Little Ice Age (LIA) from ~1400 to 1900 AD. During the LIA, the reconstructed equilibrium-line altitude in the region was no more than 83 ± 44 m (n = 21) lower than the modern, which is based on the extent of glaciers during 1978. Differences between the summer temperature inferred from the biogenic-silica content and the evidence for glacial advances and retreats suggest a period of increased winter precipitation from 1300 to 1500 AD, and reduced winter precipitation from 1800 to 1900 AD, likely associated with variability in the strength of the Aleutian Low.

Reduced‐complexity flow routing models for sinuous single‐thread channels: intercomparison with a physically‐based shallow‐water equation model

Reduced‐complexity models of fluvial processes use simple rules that neglect much of the underlying governing physics. This approach is justified by the potential to use these models to investigate long‐term and/or fundamental river behaviour. However, little attention has been given to the validity or realism of reduced‐complexity process parameterizations, despite the fact that the assumptions inherent in these approaches may limit the potential for elucidating the behaviour of natural rivers. This study presents two new reduced‐complexity flow routing schemes developed specifically for application in single‐thread rivers. Output from both schemes is compared with that from a more sophisticated model that solves the depth‐averaged shallow water equations. This comparison provides the first demonstration of the potential for deriving realistic predictions of in‐channel flow depth, unit discharge, energy slope and unit stream power using simple flow routing schemes. It also highlights the inadequacy of modelling unit stream power, shear stress or sediment transport capacity as a function of local bed slope, as has been common practice in a number of previous reduced‐complexity models. Copyright © 2009 John Wiley & Sons, Ltd.     

Chemical and isotopic compositions of thermal springs,fumaroles and bubbling gases at Tacaná Volcano (Mexico–Guatemala): implications for volcanic surveillance

This study presents baseline data for future geochemical monitoring of the active Tacaná volcano–hydrothermal system (Mexico–Guatemala). Seven groups of thermal springs, related to a NW/SE-oriented fault scarp cutting the summit area (4,100m a.s.l.), discharge at the northwest foot of the volcano (1,500–2,000m a.s.l.); another one on the southern ends of Tacaná (La Calera). The near-neutral (pH from 5.8 to 6.9) thermal (T from 25.7°C to 63.0°C) HCO₃–SO₄ waters are thought to have formed by the absorption of a H₂S/SO₂–CO₂-enriched steam into a Cl-rich geothermal aquifer, afterwards mixed by Na/HCO₃-enriched meteoric waters originating from the higher elevations of the volcano as stated by the isotopic composition (δD and δ¹⁸O) of meteoric and spring waters. Boiling temperature fumaroles (89°C at ~3,600m a.s.l. NW of the summit), formed after the May 1986 phreatic explosion, emit isotopically light vapour (δD and δ¹⁸O as low as −128 and −19.9‰, respectively) resulting from steam separation from the summit aquifer. Fumarolic as well as bubbling gases at five springs are CO₂-dominated. The δ¹³C_CO2 for all gases show typical magmatic values of −3.6 ± 1.3‰ vs V-PDB. The large range in ³He/⁴He ratios for bubbling, dissolved and fumarolic gases [from 1.3 to 6.9 atmospheric ³He/⁴He ratio (R _A)] is ascribed to a different degree of near-surface boiling processes inside a heterogeneous aquifer at the contact between the volcanic edifice and the crystalline basement (⁴He source). Tacaná volcano offers a unique opportunity to give insight into shallow hydrothermal and deep magmatic processes affecting the CO₂/³He ratio of gases: bubbling springs with lower gas/water ratios show higher ³He/⁴He ratios and consequently lower CO₂/³He ratios (e.g. Zarco spring). Typical Central American CO₂/³He and ³He/⁴He ratios are found for the fumarolic Agua Caliente and Zarco gases (3.1 ± 1.6 × 10¹⁰ and 6.0 ± 0.9 R _A, respectively). The L/S (5.9 ± 0.5) and (L + S)/M ratios (9.2 ± 0.7) for the same gases are almost identical to the ones calculated for gases in El Salvador, suggesting an enhanced slab contribution as far as the northern extreme of the Central American Volcanic Arc, Tacaná.