Some comparison theorems for weak nonnegative splittings of bounded operators

AbstractThe comparison of the asymptotic rates of convergence of two iteration matrices induced by two splittings of the same matrix has arisen in the works of many authors. In this paper we derive new comparison theorems for weak nonnegative splittings and weak splittings of bounded operators in a general Banach space and rather general cones, and in a Hilbert space, which extend some of the results obtained by Woźnicki (Japan J. Indust. Appl. Math. 11(1994) 289–342) and Marek and Szyld (Numer. Math. 44(1984) 23–35). Furthermore, we present new theorems also for bounded operator which extend some results by Csordas and Varga (Numer. Math. 44. (1984) 23–35) for weak nonnegative splittings of matrices

Rapid and sustained surface ocean acidification during the Paleocene-Eocene Thermal Maximum

The Paleocene-Eocene Thermal Maximum (PETM) has been associated with the release of several thousands of petagrams of carbon (Pg C) as methane and/or carbon dioxide into the ocean-atmosphere system within ~10 kyr, on the basis of the co-occurrence of a carbon isotope excursion (CIE), widespread dissolution of deep sea carbonates, and global warming. In theory, this rapid carbon release should have severely acidified the surface ocean, though no geochemical evidence has yet been presented. Using boron-based proxies for surface ocean carbonate chemistry, we present the first observational evidence for a drop in the pH of surface and thermocline seawater during the PETM. Planktic foraminifers from a drill site in the North Pacific (Ocean Drilling Program Site 1209) show a ~0.8‰ decrease in boron isotopic composition (δ11B) at the onset of the event, along with a 30–40% reduction in shell B/Ca. Similar trends in δ11B are present in two lower-resolution records from the South Atlantic and Equatorial Pacific. These observations are consistent with significant, global acidification of the surface ocean lasting at least 70 kyr and requiring sustained carbon release. The anomalies in the B records are consistent with an initial surface pH drop of ~0.3 units, at the upper range of model-based estimates of acidification

Anthropogenic carbon release rate unprecedented during the past 66 million years

Carbon release rates from anthropogenic sources reached a record high of ∼10 Pg C yr-1 in 2014. Geologic analogues from past transient climate changes could provide invaluable constraints on the response of the climate system to such perturbations, but only if the associated carbon release rates can be reliably reconstructed. The Palaeocene-Eocene Thermal Maximum (PETM) is known at present to have the highest carbon release rates of the past 66 million years, but robust estimates of the initial rate and onset duration are hindered by uncertainties in age models. Here we introduce a new method to extract rates of change from a sedimentary record based on the relative timing of climate and carbon cycle changes, without the need for an age model. We apply this method to stable carbon and oxygen isotope records from the New Jersey shelf using time-series analysis and carbon cycle-climate modelling. We calculate that the initial carbon release during the onset of the PETM occurred over at least 4,000 years. This constrains the maximum sustained PETM carbon release rate to less than 1.1 Pg C yr-1. We conclude that, given currently available records, the present anthropogenic carbon release rate is unprecedented during the past 66 million years. We suggest that such a 'no-analogue' state represents a fundamental challenge in constraining future climate projections. Also, future ecosystem disruptions are likely to exceed the relatively limited extinctions observed at the PETM

Astronomical calibration of the Ypresian timescale: implications for seafloor spreading rates and the chaotic behavior of the solar system?

Abstract. To fully understand the global climate dynamics of the warm early Eocene with its reoccurring hyperthermal events, an accurate high-fidelity age model is required. The Ypresian stage (56–47.8 Ma) covers a key interval within the Eocene as it ranges from the warmest marine temperatures in the early Eocene to the long-term cooling trends in the middle Eocene. Despite the recent development of detailed marine isotope records spanning portions of the Ypresian stage, key records to establish a complete astronomically calibrated age model for the Ypresian are still missing. Here we present new high-resolution X-ray fluorescence (XRF) core scanning iron intensity, bulk stable isotope, calcareous nannofossil, and magnetostratigraphic data generated on core material from ODP Sites 1258 (Leg 207, Demerara Rise), 1262, 1263, 1265, and 1267 (Leg 208, Walvis Ridge) recovered in the equatorial and South Atlantic Ocean. By combining new data with published records, a 405 kyr eccentricity cyclostratigraphic framework was established, revealing a 300–400 kyr long condensed interval for magnetochron C22n in the Leg 208 succession. Because the amplitudes are dominated by eccentricity, the XRF data help to identify the most suitable orbital solution for astronomical tuning of the Ypresian. Our new records fit best with the La2010b numerical solution for eccentricity, which was used as a target curve for compiling the Ypresian astronomical timescale (YATS). The consistent positions of the very long eccentricity minima in the geological data and the La2010b solution suggest that the macroscopic feature displaying the chaotic diffusion of the planetary orbits, the transition from libration to circulation in the combination of angles in the precession motion of the orbits of Earth and Mars, occurred  ∼  52 Ma. This adds to the geological evidence for the chaotic behavior of the solar system. Additionally, the new astrochronology and revised magnetostratigraphy provide robust ages and durations for Chrons C21n to C24n (47–54 Ma), revealing a major change in spreading rates in the interval from 51.0 to 52.5 Ma. This major change in spreading rates is synchronous with a global reorganization of the plate–mantle system and the chaotic diffusion of the planetary orbits. The newly provided YATS also includes new absolute ages for biostratigraphic events, magnetic polarity reversals, and early Eocene hyperthermal events. Our new bio- and magnetostratigraphically calibrated stable isotope compilation may act as a reference for further paleoclimate studies of the Ypresian, which is of special interest because of the outgoing warming and increasingly cooling phase. Finally, our approach of integrating the complex comprehensive data sets unearths some challenges and uncertainties but also validates the high potential of chemostratigraphy, magnetostratigraphy, and biostratigraphy in unprecedented detail being most significant for an accurate chronostratigraphy

On the duration of magnetochrons C24r and C25n and the timing of early Eocene global warming events: Implications from the Ocean Drilling Program Leg 208 Walvis Ridge depth transect

Five sections drilled in multiple holes over a depth transect of more than 2200 m at the Walvis Ridge (SE Atlantic) during Ocean Drilling Program (ODP) Leg 208 resulted in the first complete early Paleogene deep-sea record. Here we present high-resolution stratigraphic records spanning a ~4.3 million yearlong interval of the late Paleocene to early Eocene. This interval includes the Paleocene-Eocene thermal maximum (PETM) as well as the Eocene thermal maximum (ETM) 2 event. A detailed chronology was developed with nondestructive X-ray fluorescence (XRF) core scanning records and shipboard color data. These records were used to refine the shipboard-derived spliced composite depth for each site and with a record from ODP Site 1051 were then used to establish a continuous time series over this interval. Extensive spectral analysis reveals that the early Paleogene sedimentary cyclicity is dominated by precession modulated by the short (100 kyr) and long (405 kyr) eccentricity cycles. Counting of precession-related cycles at multiple sites results in revised estimates for the duration of magnetochrons C24r and C25n. Direct comparison between the amplitude modulation of the precession component derived from XRF data and recent models of Earth’s orbital eccentricity suggests that the onset of the PETM and ETM2 are related to a 100-kyr eccentricity maximum. Both events are approximately a quarter of a period offset from a maximum in the 405-kyr eccentricity cycle, with the major difference that the PETM is lagging and ETM2 is leading a 405-kyr eccentricity maximum. Absolute age estimates for the PETM, ETM2, and the magnetochron boundaries that are consistent with recalibrated radiometric ages and recent models of Earth’s orbital eccentricity cannot be precisely determined at present because of too large uncertainties in these methods. Nevertheless, we provide two possible tuning options, which demonstrate the potential for the development of a cyclostratigraphic framework based on the stable 405-kyr eccentricity cycle for the entire Paleogene

Placing our current 'hyperthermal' in the context of rapid climate change in our geological past

‘ ... there are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don’t know. But there are also unknown unknowns. There are things we don’t know we don’t know.’ Donald Rumsfeld 12th February 2002. This article is part of a discussion meeting issue ‘Hyperthermals: rapid and extreme global warming in our geological past’

Coupled evolution of temperature and carbonate chemistry during the Paleocene–Eocene; new trace element records from the low latitude Indian Ocean

This is the final version. Available on open access from Elsevier via the DOI in this recordThe early Paleogene represents the most recent interval in Earth’s history characterized by global greenhouse warmth on multi-million year timescales, yet our understanding of long-term climate and carbon cycle evolution in the low latitudes, and in particular the Indian Ocean, remains very poorly constrained. Here we present the first long-term sub-eccentricity-resolution stable isotope (δ13 30 C and δ 18 O) and trace element (Mg/Ca and B/Ca) records spanning the late Paleocene–early Eocene (~58– 53 Ma) across a surface–deep hydrographic reconstruction of the northern Indian Ocean, resolving late Paleocene 405-kyr paced cyclicity and a portion of the PETM recovery. Our new records reveal a long-term warming of ~4–5°C at all depths in the water column, with absolute surface ocean temperatures and magnitudes of warming comparable to the low latitude Pacific. As a result of warming, we observe a long-term increase in δ 18 Osw of the mixed layer, implying an increase in net evaporation. We also observe a collapse in the temperature gradient between mixed layer- and thermocline-dwelling species from ~57–54 Ma, potentially due to either the development of a more homogeneous water column with a thicker mixed layer, or depth migration of the Morozovella in response to warming. Synchronous warming at both low and high latitudes, along with decreasing B/Ca ratios in planktic foraminifera indicating a decrease in ocean pH and/or increasing dissolved inorganic carbon, suggest that global climate was forced by rising atmospheric CO2 concentrations during this time.European Consortium for Ocean Research Drilling (ECORD)International Association of Sedimentologists (IAS)NSFNatural Environment Research Council (NERC

Exploring how to use scenarios to discover requirements

This paper investigates the effectiveness of different uses of scenarios on requirements discovery using results from requirements processes in two projects. The first specified requirements on a new aircraft management system at a regional UK airport to reduce its environmental impact. The second specified new work-based learning tools to be adopted by a consortium of organizations. In both projects scenarios were walked through both in facilitated workshops and in the stakeholders’ workplaces using different forms of a scenario tool. In the second project, scenarios were also walked through with a software prototype and creativity prompts. Results revealed both qualitative and quantitative differences in discovered requirements that have potential implications for models of scenario-based requirements discovery and the design of scenario tools

The impact of fire on habitat use by the short-snouted elephant shrew ('Elephantulus brachyrhynchus') in North West Province, South Africa

Several studies have investigated the response of small mammal populations to fire, but few have investigated behavioural responses to habitat modification. In this study we investigated the impact of fire on home range, habitat use and activity patterns of the short-snouted elephant shrew (Elephantulus brachyrhynchus) by radio-tracking individuals before and after a fire event. All animals survived the passage of fire in termite mound refugia. Before the fire, grassland was used more than thickets, but habitat utilization shifted to thickets after fire had removed the grass cover. Thickets were an important refuge both pre- and post-fire, but the proportion of thicket within the home range was greater post-fire. We conclude that fire-induced habitat modification resulted in a restriction of E. brachyrhynchus movements to patches of unburned vegetation. This may be a behavioural response to an increase in predation pressure associated with a reduction in cover, rather than a lack of food. This study highlights the importance of considering the landscape mosaic in fire management and allowing sufficient island patches to remain post-fire ensures the persistence of the small mammal fauna