Modelling detrital cooling-age populations: insights from two Himalayan catchments

The distribution of detrital mineral cooling ages in river sediment provides a proxy record for the erosional history of mountain ranges. We have developed a numerical model that predicts detrital mineral age distributions for individual catchments in which particle paths move vertically toward the surface. Despite a restrictive set of assumptions, the model permits theoretical exploration of the effects of thermal structure, erosion rate, and topography on cooling ages. Hypsometry of the source‐area catchment is shown to exert a fundamental control on the frequency distribution of bedrock and detrital ages. We illustrate this approach by generating synthetic ⁴⁰Ar/³⁹Ar muscovite age distributions for two catchments with contrasting erosion rates in central Nepal and then by comparing actual measured cooling‐age distributions with the synthetic ones. Monte Carlo sampling is used to assess the mismatch between observed and synthetic age distributions and to explore the dependence of that mismatch on the complexity of the synthetic age signal and on the number of grains analysed. Observed detrital cooling ages are well matched by predicted ages for a more slowly eroding Himalayan catchment. A poorer match for a rapidly eroding catchment may result from some combination of large analytical uncertainties in the detrital ages and inhomogeneous erosion rates within the basin. Such mismatches emphasize the need for more accurate thermal and kinematic models and for sampling strategies that are adapted to catchment‐specific geologic and geomorphic conditions.     

An iterative method for simultaneously computing the synthesis of light and heavy elements

We propose an iterative algorithm for computing the synthesis of heavy elements through the rapid capture of neutrons (r-process) and, at sufficiently high temperatures, protons by simultaneously using two distinct computer codes. One of the codes describes the kinetics of nuclear reactions between light and intermediate chemical elements, which are the source of free neutrons and protons used by the second code to synthesize heavy elements from seed nuclides (isotopes near the iron peak of the cosmic abundance curve). The two codes interact through the neutron and proton reaction channels. We demonstrate the efficiency of our method with an example of the nucleosynthesis in a supernova’s helium shell triggered by the evaporation of neutrons and protons from α particles exposed to the neutrino flux from a collapsing stellar core. In this case, three or four iterations are enough to obtain an almost exact self-consistent solution.     

Convex optimization under inequality constraints in rank-deficient systems

Many geodetic applications require the minimization of a convex objective function subject to some linear equality and/or inequality constraints. If a system is singular (e.g., a geodetic network without a defined datum) this results in a manifold of solutions. Most state-of-the-art algorithms for inequality constrained optimization (e.g., the Active-Set-Method or primal-dual Interior-Point-Methods) are either not able to deal with a rank-deficient objective function or yield only one of an infinite number of particular solutions. In this contribution, we develop a framework for the rigorous computation of a general solution of a rank-deficient problem with inequality constraints. We aim for the computation of a unique particular solution which fulfills predefined optimality criteria as well as for an adequate representation of the homogeneous solution including the constraints. Our theoretical findings are applied in a case study to determine optimal repetition numbers for a geodetic network to demonstrate the potential of the proposed framework.     

Predictions of Energy and Helicity in Four Major Eruptive Solar Flares

In order to better understand the solar genesis of interplanetary magnetic clouds (MCs), we model the magnetic and topological properties of four large eruptive solar flares and relate them to observations. We use the three-dimensional Minimum Current Corona model (Longcope, 1996, Solar Phys. 169, 91) and observations of pre-flare photospheric magnetic field and flare ribbons to derive values of reconnected magnetic flux, flare energy, flux rope helicity, and orientation of the flux-rope poloidal field. We compare model predictions of those quantities to flare and MC observations, and within the estimated uncertainties of the methods used find the following: The predicted model reconnection fluxes are equal to or lower than the reconnection fluxes inferred from the observed ribbon motions. Both observed and model reconnection fluxes match the MC poloidal fluxes. The predicted flux-rope helicities match the MC helicities. The predicted free energies lie between the observed energies and the estimated total flare luminosities. The direction of the leading edge of the MC’s poloidal field is aligned with the poloidal field of the flux rope in the AR rather than the global dipole field. These findings compel us to believe that magnetic clouds associated with these four solar flares are formed by low-corona magnetic reconnection during the eruption, rather than eruption of pre-existing structures in the corona or formation in the upper corona with participation of the global magnetic field. We also note that since all four flares occurred in active regions without significant pre-flare flux emergence and cancelation, the energy and helicity that we find are stored by shearing and rotating motions, which are sufficient to account for the observed radiative flare energy and MC helicity.     

An analysis of changes in the urban landscape composition and configuration in the Sancaktepe District of Istanbul Metropolitan City,Turkey using landscape metrics and satellite data

Changes in landscape composition and configuration patterns of Sancaktepe Municipal District in the Asian side of Istanbul Metropolitan City of Turkey were analysed using landscape metrics. Class-level and landscape-level metrics were calculated from the land cover/land use data using Patch Analyst, an extension in the Arc View GIS. The land cover/land use data were derived from classified satellite images of Landsat Thematic Mapper of 2002 and 2009 for Sancaktepe District. There was evidence of increase in agglomeration process of built-up patches as indicated by the increases in mean patch size, decrease in total edge and number of patches between 2002 and 2009. The urban expansion pattern experienced overall was not fragmented but concentrated due to infilling around existing patches. Changes in Area-Weighted Mean Shape Index and Area-Weighted Patch Fractal Dimension Index indicated that the physical shapes within built-up, forest and bareland areas were relatively complex and irregular. A conclusion is made in this study that spatial metrics are useful tools to describe the urban landscape composition and configuration in its various aspects and certain decisions whether to approve a specific development in urban planning could, for example, be based on some measures of urban growth form or pattern in terms of uniformity and irregularity, attributable to the dynamic processes of agglomeration and fragmentation of land cover/land use patches caused by urban expansion.     

On the evaluation of the gravity effects of polyhedral bodies and a consistent treatment of related singularities

We show that the singularities which can affect the computation of the gravity effects (potential, gravity and tensor gradient fields) can be systematically addressed by invoking distribution theory and suitable formulas of differential calculus. Thus, differently from previous contributions on the subject, the use of a-posteriori corrections of the formulas derived in absence of singularities can be ruled out. The general approach presented in the paper is further specialized to the case of polyhedral bodies and detailed for a rectangular prism having a constant mass density. With reference to this last case, we derive novel expressions for the related gravitational field, as well as for its first and second derivative, at an observation point coincident with a prism vertex and show that they turn out to be more compact than the ones reported in the specialized literature.     

Understanding the Spatial Variability of Chlorophyll a and Total Suspended Matter Distribution Along the Southwest Bay of Bengal Using In-Situ and OCM-2 & MODIS-Aqua Measurements

Spatial and temporal distribution of chlorophyll a (chl a) and Total Suspended Matter (TSM) and inter comparison of Ocean Color Monitor-2 (OCM-2) and Moderate Resolution Imaging Spectro-radiometer (MODIS-Aqua) derived chlorophyll a and TSM was made along the southwest Bay of Bengal (BoB). The in-situ chl a and TSM concentration measured during different seasons were ranged from 0.09 to 10.63 μgl^?1 and 11.04–43.75 mgl^?1 respectively. OCM-2 and MODIS derived chl a showed the maximum (6–8 μgl^?1) at nearshore waters and the minimum (0–1 μgl^?1) along the offshore waters. OCM-2 derived TSM imageries showed the maximum (50–60 mgl^?1) along the nearshore waters of Palk Strait and the moderate concentration (2–5 mgl^?1) was observed in the offshore waters. MODIS derived minimum TSM concentration (13.244 mgl^?1) was recorded along the offshore waters, while the maximum concentration of 15.78 mgl^?1 was found along the Kodiakarai region. The inter-comparison of OCM-2 and MODIS chl a data (R ² ?=?0.549, n?=?49, p?<?0.001, SEE?=?±0.117) indicate that MODIS data overestimates chl a concentration in the nearshore waters of the southern BoB compared to the OCM-2. The correlation between OCM-2 and MODIS-Aqua TSM data (R ² ?=?0.508, N?=?53, P?<?0.001 and SEE?=?±0.024) confirms that variation in the range of values measured by OCM-2 (2–60 mgl^?1) and the MODIS (13–16 mgl^?1) derived TSM values. Despite problems in range of measurements, persistent cloud cover etc., the launch of satellites like OCM-2 with relatively high spatial resolutions makes job easier and possible to monitor chl a distribution and sediment discharges on day to day basis in the southwest BoB.