Numerical Solution of an Extra-wide Angle Parabolic Equation through Diagonalization of a 1-D Indefinite Schr\"{o}dinger Operator with a Piecewise Constant Potential

We present a numerical method for computing the solution of a partial differential equation (PDE) for modeling acoustic pressure, known as an extra-wide angle parabolic equation, that features the square root of a differential operator. The differential operator is the negative of an indefinite Schr\"{o}dinger operator with a piecewise constant potential. This work primarily deals with the 3-piece case; however, a generalization is made the case of an arbitrary number of pieces. Through restriction to a judiciously chosen lower-dimensional subspace, approximate eigenfunctions are used to obtain estimates for the eigenvalues of the operator. Then, the estimated eigenvalues are used as initial guesses for the Secant Method to find the exact eigenvalues, up to roundoff error. An eigenfunction expansion of the solution is then constructed. The computational expense of obtaining each eigenpair is independent of the grid size. The accuracy, efficiency, and scalability of this method is shown through numerical experiments and comparisons with other methods.Comment: 27 pages, 13 figure

Lithium and carbon isotopic fractionations between the alteration assemblages of Nakhla and Lafayette

Nakhla and Lafayette delta 7Li values for samples and extracts (4.1-14.2�) are consistent with brine evaporation. Relatively 13C-poor siderite in Lafayette suggests more than one carbon source was sampled

A 30 Myr record of Late Triassic atmospheric pCO2 variation reflects a fundamental control of the carbon cycle by changes in continental weathering.

We generate a detailed ∼30 Myr record of pCO2 spanning most of the Late Triassic (Carnian-Norian-Rhaetian) to earliest Jurassic (Hettangian), based on stable carbon isotope ratios of soil carbonate and preserved organic matter from paleosols in the eastern North American Newark rift basin. Atmospheric pCO2 was near 4500 ppm in the late Carnian, decreasing to below ∼2000 ppm by the late Rhaetian just before the earliest Jurassic eruption of the Central Atlantic Magmatic Province, which triggered measurable pulses of CO2 outgassing. These data are consistent with published modeling results using the GEOCLIM model, which predict a decrease in pCO2 over the Late Triassic as a result of the progressive increase in continental area subject to the intense weathering regime of the tropical humid belt due to Pangea’s northward motion. The finer-scale pCO2 changes we observe may be dependent on the lithology introduced to the tropics, such as the dip to ∼2000 ppm around 212 Ma and its rebound to ∼4000 ppm at 209 Ma, which can be accomplished by introducing a more weatherable subaerial basaltic terrain. These observations indicate that the consumption of CO2 by continental silicate weathering can force long-term changes in pCO2 comparable to those driven by presumed changes in mantle degassing

Enhanced magnetization of the Marlboro Clay as a product of soil pyrogenesis at the Paleocene-Eocene boundary?

The kaolinite-rich Marlboro Clay was deposited on the inner shelf in the Salisbury Embayment of the U.S. Atlantic margin at the onset of the carbon isotope excursion marking the 56 Ma Paleocene– Eocene boundary and is characterized by an anomalously high concentration of magnetic nanoparticles of enigmatic origin that give rise to notably intense bulk magnetization. Recent studies point to a magnetic assemblage that is dominated by single-domain magnetite particles that tend to be isolated rather than arranged in chains, the most distinguishing feature of magnetotactic bacteria fossils. On the other hand, it is very unlikely that the nanoparticles can be condensates of an impact plume given the meter-scale thickness of the Marlboro Clay. We obtained new data from a landward proximal site at Wilson Lake on the New Jersey Coastal Plain and find that the abrupt increase in magnetite nanoparticles is virtually coincident stratigraphically with the recently reported impact spherule layer at the base of the Marlboro Clay in the same core. Yet the high field magnetic susceptibility, a measure of total iron concentration, and strontium isotope values on bulk sediment, an indicator of sediment weathering provenance, are not different in the Marlboro Clay from the immediately underlying Vincentown Formation. We suggest that the distinctive magnetic properties of the Marlboro Clay originated from pyromagnetic soil enhancement by widespread wildfires on the adjoining drainage area. The pyrogenetic products were soon washed from the denuded landscape and rapidly deposited as mud-waves across the shelf, becoming the Marlboro Clay. A few percent of incinerated biomass ends up as calcite known as wood ash stone and can inherit its light carbon isotope composition. Disseminated wood ash stone entrained in the Marlboro Clay could contribute to the landward increase in amplitude of the carbon isotope excursion in bulk carbonate data. A plausible trigger for the initial conflagration is a fireball from the impact of a sizable extraterrestrial object at moderate range

Impact ejecta at the Paleocene-Eocene boundary

Extraterrestrial impacts have left a substantial imprint on the climate and evolutionary history of Earth. A rapid carbon cycle perturbation and global warming event about 56 million years ago at the Paleocene-Eocene (P-E) boundary (the Paleocene-Eocene Thermal Maximum) was accompanied by rapid expansions of mammals and terrestrial plants and extinctions of deep-sea benthic organisms. Here, we report the discovery of silicate glass spherules in a discrete stratigraphic layer from three marine P-E boundary sections on the Atlantic margin. Distinct characteristics identify the spherules as microtektites and microkrystites, indicating that an extraterrestrial impact occurred during the carbon isotope excursion at the P-E boundary

Orbital climate forcing of δ^13 excursions in the late Paleocene-early Eocene (chrons C24n-C25n)

High-resolution stable carbon isotope records for upper Paleocene-lower Eocene sections at Ocean Drilling Program Sites 1051 and 690 and Deep Sea Drilling Project Sites 550 and 577 show numerous rapid (40-60 kyr duration) negative excursions of up to 1‰. We demonstrate that these transient decreases are the expected result of nonlinear insolation forcing of the carbon cycle in the context of a long carbon residence time. The transients occur at maxima in Earth's orbital eccentricity, which result in high-amplitude variations in insolation due to forcing by climatic precession. The construction of accurate orbital chronologies for geologic sections older than ~35 Ma relies on identifying a high-fidelity recorder of variations in Earth's orbital eccentricity. We use the carbon isotope records as such a recorder, establishing a robust orbitally tuned chronology for latest Paleocene-earliest Eocene events. Moreover, the transient decreases provide a means of precise correlation among the four sites that is independent of magnetostratigraphic and biostratigraphic data at the <10^5-year scale. While the eccentricity-controlled transient decreases bear some resemblance to the much larger-amplitude carbon isotope excursion (CIE) that marks the Paleocene/Eocene boundary, the latter event is found to occur near a minimum in the ~400-kyr eccentricity cycle. Thus the CIE occurred during a time of minimal variability in insolation, the dominant mechanism for forcing climate change on 10^4-year scales. We argue that this is inconsistent with mechanisms that rely on a threshold climate event to trigger the Paleocene/Eocene thermal maximum since any threshold would more likely be crossed during a period of high-amplitude climate variations

Miocene stable isotopic stratigraphy and magnetostratigraphy of Buff Bay, Jamaica

Previously reported biostratigraphic relationships from middle-upper Miocene sections exposed near Buff Bay, Jamaica (18°N, tropical bioprovince), differ from the subtropical North Atlantic (Sites 563 and 558). Time scales for this interval rely on correlations established at these subtropical sites, and the differences with the tropical section have implications to global correlations. Planktonic foraminiferal Zones N13 and N15 are thick at Buff Bay but are virtually absent at Sites 563 and 558; nannofossil Zone NN9 is associated with Zone N15 and uppermost Zone N14 at Buff Bay but is associated with Zone N16 at the other sites. Magnetostratigraphic data presented here further complicate the interpretation: Zone NN9 is associated with a thick normal magnetozone at Sites 563 and 558; at Buff Bay, it is associated with a thick reversed magnetozone. Although a secondary magnetization at Buff Bay makes it difficult to identify confidently Miocene normal magnetozones, the thick reversed magnetozone most likely represents the paleomagnetic field and correlates with Chron C5r. The magnetobiostratigraphic relationships require either diachrony of taxa or two mutually exclusive hiatuses in Jamaica and the North Atlantic. We address this problem by analyzing benthic foraminiferal δ^18O and δ^13C from the Buff Bay section. These isotopic data allow us to evaluate three hypotheses that reconcile the magneto-, bio-, and isotopic stratigraphic data and conclude that the first and last occurrences of five taxa were diachronous by ~0.3-0.5 m.y. between tropical and subtropical locations. This requires revised age estimates for late middle to early late Miocene biostratigraphic datum levels. We suggest that the ranges of several taxa are useful for endemic tropical or subtropical zonations, but correlations between the low and midlatitudes were affected by an increase in latitudinal thermal gradients during the late middle Miocene. However, we admit that further studies are needed before this issue is resolved

Conduction in rectangular plates with boundary temperatures specified

Steady-state components of heat conduction solutions may have very slowly convergent series for temperatures and non-convergent heat fluxes for temperature boundary conditions. Previous papers have proposed methods to remove these convergence problems. However, even more effective procedures based on insights of Morse and Feshbach are given herein. In some cases it is possible to replace poorly-convergent or non-convergent series by closed-form algebraic solutions. Examples are given

Climate-driven changes in the predictability of seasonal precipitation

Climate-driven changes in precipitation amounts and their seasonal variability are expected in many continental-scale regions during the remainder of the 21st century. However, much less is known about future changes in the predictability of seasonal precipitation, an important earth system property relevant for climate adaptation. Here, on the basis of CMIP6 models that capture the present-day teleconnections between seasonal precipitation and previous-season sea surface temperature (SST), we show that climate change is expected to alter the SST-precipitation relationships and thus our ability to predict seasonal precipitation by 2100. Specifically, in the tropics, seasonal precipitation predictability from SSTs is projected to increase throughout the year, except the northern Amazonia during boreal winter. Concurrently, in the extra-tropics predictability is likely to increase in central Asia during boreal spring and winter. The altered predictability, together with enhanced interannual variability of seasonal precipitation, poses new opportunities and challenges for regional water management