Използване на системата MATLAB в техническите университети

Mihail Konstantinov, Vladimir Todorov, Galina Pelova, Juliana Boneva - We consider some aspect of the mathematical education in technical universities using MATLAB. Special attention is paid to the subjects Analytical Geometry and Differential Equations.

Loss of Accuracy in Numerical Computations

Михаил М. Константинов, Петко Х. Петков - Разгледани са възможните катастрофални ефекти от неправилното използване на крайна машинна аритметика с плаваща точка. За съжаление, тази тема не винаги се разбира достатъчно добре от студентите по приложна и изчислителна математика, като положението в инженерните и икономическите специалности в никакъв случай не е по-добро. За преодоляване на този образователен пропуск тук сме разгледали главните виновници за загубата на точност при числените компютърни пресмятания. Надяваме се, че представените резултати ще помогнат на студентите и лекторите за по-добро разбиране и съответно за избягване на основните фактори, които могат да разрушат точността при компютърните числени пресмятания. Последното не е маловажно – числените катастрофи понякога стават истински, с големи щети и човешки жертви.

Numerical Issues in Using MATLAB

Михаил Константинов, Весела Пашева, Петко Петков - Разгледани са някои числени проблеми при използването на компютърната система MATLAB в учебната дейност: пресмятане на тригонометрични функции, повдигане на матрица на степен, спектрален анализ на целочислени матрици от нисък ред и пресмятане на корените на алгебрични уравнения. Причините за възникналите числени трудности могат да се обяснят с особеностите на използваната двоичната аритметика с плаваща точка.

Compilation of downward flux observations from sediment trap deployments in the Atlantic Ocean - Contribution to EURO-BASIN's Data integration

We provide a compilation of downward fluxes (total mass, POC, PON, BSiO2, CaCO3, PIC and lithogenic/terrigenous fluxes) from over 6000 sediment trap measurements distributed in the Atlantic Ocean, from 30 degree North to 49 degree South, and covering the period 1982-2011. Data from the Mediterranean Sea are also included. Data were compiled from different sources: data repositories (BCO-DMO, PANGAEA), time series sites (BATS, CARIACO), published scientific papers and/or personal communications from PI's. All sources are specifed in the data set. Data from the World Ocean Atlas 2009 were extracted to provide each flux observation with contextual environmental data, such as temperature, salinity, oxygen (concentration, AOU and percentage saturation), nitrate, phosphate and silicate.

Global compilation of benthic data sets I

Approaches to quantify the organic carbon accumulation on a global scale generally do not consider the small-scale variability of sedimentary and oceanographic boundary conditions along continental margins. In this study, we present a new approach to regionalize the total organic carbon (TOC) content in surface sediments (<5 cm sediment depth). It is based on a compilation of more than 5500 single measurements from various sources. Global TOC distribution was determined by the application of a combined qualitative and quantitative-geostatistical method. Overall, 33 benthic TOC-based provinces were defined and used to process the global distribution pattern of the TOC content in surface sediments in a 1°x1° grid resolution. Regional dependencies of data points within each single province are expressed by modeled semi-variograms. Measured and estimated TOC values show good correlation, emphasizing the reasonable applicability of the method. The accumulation of organic carbon in marine surface sediments is a key parameter in the control of mineralization processes and the material exchange between the sediment and the ocean water. Our approach will help to improve global budgets of nutrient and carbon cycles.

A high-resolution sedimentology and age determination of core PS2185 from the central Arctic Ocean

A high-resolution multiparameter stratigraphy allows the identification of late Quaternary glacial and interglacial cycles in a central Arctic Ocean sediment core. Distinct sandy layers in the upper part of the otherwise fine-grained sediment core from the Lomonosov Ridge (lat 87.5°N) correlate to four major glacials since ca. 0.7 Ma. The composition of these ice-rafted terrigenous sediments points to a glaciated northern Siberia as the main source. In contrast, lithic carbonates derived from North America are also present in older sediments and indicate a northern North American glaciation since at least 2.8 Ma. We conclude that large-scale northern Siberian glaciation began much later than other Northern Hemisphere ice sheets.

Neodymium and Strontium chemistry of Arctic Ocean sediments

The early oceanographic history of the Arctic Ocean is important in regulating, and responding to, climatic changes. However, constraints on its oceanographic history preceding the Quaternary (the past 1.8 Myr) have become available only recently, because of the difficulties associated with obtaining continuous sediment records in such a hostile setting. Here, we use the neodymium isotope compositions of two sediment cores recovered near the North Pole to reconstruct over the past ~5 Myr the sources contributing to Arctic Intermediate Water, a water mass found today at depths of 200 to 1,500 m. We interpret high neodymium ratios for the period between 15 and 2 Myr ago, and for the glacial periods thereafter, as indicative of weathering input from the Siberian Putoranan basalts into the Arctic Ocean. Arctic Intermediate Water was then derived from brine formation in the Eurasian shelf regions, with only a limited contribution of intermediate water from the North Atlantic. In contrast, the modern circulation pattern, with relatively high contributions of North Atlantic Intermediate Water and negligible input from brine formation, exhibits low neodymium isotope ratios and is typical for the interglacial periods of the past 2 Myr. We suggest that changes in climatic conditions and the tectonic setting were responsible for switches between these two modes.

Physical oceanography, nutrients, and d18O measured on water bottle samples during POLARSTERN cruise ARK-XXII/2

Extremely low summer sea-ice coverage in the Arctic Ocean in 2007 allowed extensive sampling and a wide quasi-synoptic hydrographic and d18O dataset could be collected in the Eurasian Basin and the Makarov Basin up to the Alpha Ridge and the East Siberian continental margin. With the aim of determining the origin of freshwater in the halocline, fractions of river water and sea-ice meltwater in the upper 150 m were quantified by a combination of salinity and d18O in the Eurasian Basin. Two methods, applying the preformed phosphate concentration (PO*) and the nitrate-to-phosphate ratio (N/P), were compared to further differentiate the marine fraction into Atlantic and Pacific-derived contributions. While PO*-based assessments systematically underestimate the contribution of Pacific-derived waters, N/P-based calculations overestimate Pacific-derived waters within the Transpolar Drift due to denitrification in bottom sediments at the Laptev Sea continental margin. Within the Eurasian Basin a west to east oriented front between net melting and production of sea-ice is observed. Outside the Atlantic regime dominated by net sea-ice melting, a pronounced layer influenced by brines released during sea-ice formation is present at about 30 to 50 m water depth with a maximum over the Lomonosov Ridge. The geographically distinct definition of this maximum demonstrates the rapid release and transport of signals from the shelf regions in discrete pulses within the Transpolar Drift. The ratio of sea-ice derived brine influence and river water is roughly constant within each layer of the Arctic Ocean halocline. The correlation between brine influence and river water reveals two clusters that can be assigned to the two main mechanisms of sea-ice formation within the Arctic Ocean. Over the open ocean or in polynyas at the continental slope where relatively small amounts of river water are found, sea-ice formation results in a linear correlation between brine influence and river water at salinities of about 32 to 34. In coastal polynyas in the shallow regions of the Laptev Sea and southern Kara Sea, sea-ice formation transports river water into the shelf's bottom layer due to the close proximity to the river mouths. This process therefore results in waters that form a second linear correlation between brine influence and river water at salinities of about 30 to 32. Our study indicates which layers of the Arctic Ocean halocline are primarily influenced by sea-ice formation in coastal polynyas and which layers are primarily influenced by sea-ice formation over the open ocean. Accordingly we use the ratio of sea-ice derived brine influence and river water to link the maximum in brine influence within the Transpolar Drift with a pulse of shelf waters from the Laptev Sea that was likely released in summer 2005.

(Table 1) Elemental mean values of the upper Paleocene and lower Eocene in IODP Hole 302-M0004A

We reconstruct the latest Paleocene and early Eocene (~57-50 Ma) environmental trends in the Arctic Ocean and focus on the Paleocene-Eocene thermal maximum (PETM) (~55 Ma), using strata recovered from the Lomonosov Ridge by the Integrated Ocean Drilling Program Expedition 302. The Lomonosov Ridge was still partially subaerial during the latest Paleocene and earliest Eocene and gradually subsided during the early Eocene. Organic dinoflagellate cyst (dinocyst) assemblages point to brackish and productive surface waters throughout the latest Paleocene and early Eocene. Dinocyst assemblages are cosmopolitan during this time interval, suggesting warm conditions, which is corroborated by TEX86'-reconstructed temperatures of 15°-18°C. Inorganic geochemistry generally reflects reducing conditions within the sediment and euxinic conditions during the upper lower Eocene. Spectral analysis reveals that the cyclicity, recorded in X-ray fluorescence scanning Fe data from close to Eocene thermal maximum 2 (~53 Ma, presence confirmed by dinocyst stratigraphy), is related to precession. Within the lower part of the PETM, proxy records indicate enhanced weathering, runoff, anoxia, and productivity along with sea level rise. On the basis of total organic carbon content and variations in sediment accumulation rates, excess organic carbon burial in the Arctic Ocean appears to have contributed significantly to the sequestration of injected carbon during the PETM.

(Table 1) The 10Be and 9Be isotope record of IODP EXP202 composite Site

The upper 200 m of the sediments recovered during IODP Leg 302, the Arctic Coring Expedition (ACEX), to the Lomonosov Ridge in the central Arctic Ocean consist almost exclusively of detrital material. The scarcity of biostratigraphic markers severely complicates the establishment of a reliable chronostratigraphic framework for these sediments, which contain the first continuous record of the Neogene environmental and climatic evolution of the Arctic region. Here we present profiles of cosmogenic 10Be together with the seawater-derived fraction of stable 9Be obtained from the ACEX cores. The down-core decrease of 10Be/9Be provides an average sedimentation rate of 14.5 ± 1 m/Ma for the uppermost 151 m of the ACEX record and allows the establishment of a chronostratigraphy for the past 12.3 Ma. The age corrected 10Be concentrations and 10Be/9Be ratios suggest the existence of an essentially continuous sea ice cover over the past 12.3 Ma.

Radiogenic isotope record of Arctic Ocean circulation and weathering inputs of the past 15 million years

Lead (Pb), neodymium (Nd), and strontium (Sr) isotopic analyses were carried out on sediment leachates (reflecting the isotope composition of past seawater) and digests of the bulk residues (reflecting detrital continental inputs) of Integrated Ocean Drilling Program (IODP) Leg 302 and core PS2185 from the Lomonosov Ridge (Arctic Ocean). Our records are interpreted to reflect changes in continental erosion and oceanic circulation, driven predominantly by tectonic forcing on million-year timescales in the older (pre-2 Ma) part of the record and by climatic forcing of weathering and erosion of the Eurasian continental margin on thousand-year timescales in the younger (post-2 Ma) part. These data, covering the past ~15 Ma, show that continental inputs to the central Arctic Ocean have been more closely linked to glacial and hydrological processes occurring on the Eurasian margin than on continental North America and Greenland. The constancy of the detrital input signatures supports the early existence of an Arctic sea ice cover, whereas the major initiation of Northern Hemisphere glaciation at 2.7 Ma appears to have had little impact on the weathering regime of the Eurasian continental margin.

Stable isotope ratios on planktonic foraminifer N. pachyderma of surface sediments from the Arctic Ocean (Table 1)

Planktic foraminifers Neogloboquadrina pachyderma (sin.) from 87 eastern and central Arctic Ocean surface sediment samples were analyzed for stable oxygen and carbon isotope composition. Additional results from 52 stations were taken from the literature. The lateral distribution of delta18O (18O/16O) values in the Arctic Ocean reveals a pattern of roughly parallel, W-E stretching zones in the Eurasian Basin, each ~0.5 per mil wide on the delta18O scale. The low horizontal and vertical temperature variability in the Arctic halocline waters (0-100 m) suggests only little influence of temperature on the oxygen isotope distribution of N. pachyderma (sin.). The zone of maximum delta18O values of up to 3.8 per mil is situated in the southern Nansen Basin and relates to the tongue of saline (> 33%.) Atlantic waters entering the Arctic Ocean through the Fram Strait. delta18O values decrease both to the Barents Shelf and to the North Pole, in accordance with the decreasing salinities of the halocline waters. In the Nansen Basin, a strong N-S delta18O gradient is in contrast with a relatively low salinity change and suggests contributions from different freshwater sources, i.e. salinity reduction from sea ice meltwater in the south and from light isotope waters (meteoric precipitation and river-runoff) in the northern part of the basin. North of the Gakkel Ridge, delta18O and salinity gradients are in good accordance and suggest less influence of sea ice melting processes. The delta13C (13C/12C) values of N. pachyderma (sin.) from Arctic Ocean surface sediment samples are generally high (0.75-0.95 per mil). Lower values in the southern Eurasian Basin appear to be related to the intrusion of Atlantic waters. The high delta13C values are evidence for well ventilated surface waters. Because the perennial Arctic sea ice cover largely prevents atmosphere-ocean gas exchange, ventilation on the seasonally open shelves must be of major importance. Lack of delta13C gradients along the main routes of the ice drift from the Siberian shelves to the Fram Strait suggests that primary production (i.e. CO2 consumption) does probably not change the CO2 budget of the Arctic Ocean significantly.

(Table 1) Relarive abundance of foraminiferal species in the surface layer of bottom sediments from the Atlantic Ocean

Quantitative ratios of tests of planktonic foraminiferal species in thanatocoenoses within the surface layer of bottom sediments from Iceland to the Equator are described. Subarctic, boreal, subtropical and tropical types of thanatocoenoses and their subtypes are distinguished. Each subtype corresponds to a 2-3°C interval of mean annual temperature of the upper layer of ocean water. Comparison of fossil thanatocoenoses from Quaternary sediment cores with recent thanatocoenoses offers new potentials for paleotemperature analysis.

Epibenthic foraminiferal d13C in the Recent deep Arctic Ocean

Low planktic and benthic d18O and d13C values in sediments from the Nordic seas of cold stadials of the last glaciation have been attributed to brines, formed similar to modern ones in the Arctic Ocean. To expand on the carbon isotopes of this hypothesis I investigated benthic d13C from the modern Arctic Ocean. I show that mean d13C values of live epibenthic foraminifera from the deep Arctic basins are higher than mean d13C values of upper slope epibenthic foraminifera. This agrees with mean high d13C values of dissolved inorganic carbon (DIC) in Arctic Bottom Water (ABW), which are higher than mean d13CDIC values from shallower water masses of mainly Atlantic origin. However, adjustments for oceanic 13C-Suess depletion raise subsurface and intermediate water d13CDIC values over ABW d13CDIC ones. Accordingly, during preindustrial Holocene times, the d13CDIC of ABW was as high or higher than today, but lower than the d13CDIC of younger subsurface and intermediate water. If brine-enriched water significantly ventilated ABW, brines should have had high d13CDIC values. Analogously, high-d13CDIC brines may have been formed in the Nordic seas during warm interstadials. During cold stadials, when most of the Arctic Ocean was perennially sea-ice covered, a cessation of high-d13CDIC brine rejection may have lowered d13CDIC values of ABW, and ultimately the d13CDIC in Nordic seas intermediate and deep water. So, in contrast to the idea of enhanced brine formation during cold stadials, the results of this investigation imply that a cessation of brine rejection would be more likely.

(Table 2) Chemical composition of Fe-Mn nodules and volcanic glass in sediments of the Atlantic Ocean

Distribution pattern of titanium in Quaternary sediments of the Atlantic Ocean are examined on the base of 750 Ti and Fe determinations, and several dozen of complete chemical analyses. Analyses of surface sediment samples and sediment cores up to 6 m long were made. Stratigraphic levels from Middle Pleistocene to Holocene were identified from planktonic foraminifera. Distributions of Ti in recent and Pleistocene deposits were mapped. High titanium contents were found in sediments containing products of basalt vulcanism and in iron-manganese nodules. To determine origin of titanium concentrations in sediments, Ti/Fe ratios were calculated. Maximal values of this ratio were found in areas of basaltic volcanism and of intensive terrigenous sedimentation.