Expansions of elliptic motion based on elliptic function theory

New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k ²)^1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia     

Ocean anoxic events in the mid-Cretaceous simulated by a 3-D biogeochemical general circulation model

The mid-Cretaceous is well known for its ocean anoxic events. The causal mechanisms are controversial: stagnant deepwater, high biological productivity in the surface waters, and other possibilities have been suggested. Our study simulated the mid-Cretaceous ocean, using general circulation models combined with a marine biogeochemical cycle model to explore the relationship between thermohaline circulation and biogeochemical cycles and investigate the causes of ocean anoxic events. The simulated thermohaline circulation shows an unsteady inactive state. Oxygen concentrations in the deepwater decrease under the inactive state, but a horizontal gradient develops, with higher oxygen concentrations in the Tethys and lower concentrations in eastern Panthalassa. This is not due to the different ages of the deepwater but rather to the differences in biological productivity in the surface water, meaning that the relationship between thermohaline circulation and biogeochemical cycles under the inactive state is different from that in the present ocean. In the standard simulation, assuming the present level of the total amount of phosphate in the ocean, 29% of the bottom water is anoxic. The experiments increasing the amount of phosphate show its high sensitivity for extending the anoxic region with global-scale anoxia simulated under the doubled amount of phosphate. The high amount of phosphate would be reasonable because the inactive state would induce an imbalance of phosphate between riverine input and sediment output. Therefore, both the inactive thermohaline circulation and the increase in the total amount of phosphate in the ocean induce the global-scale anoxic condition in the deepwater.     

Effects of the introduction of rice on evapotranspiration in seasonal wetlands

Land use changes in wetland areas can alter evapotranspiration, a major component of the water balance, which eventually affects the water cycle and ecosystem. This study assessed the effect of introduced rice‐cropping on evapotranspiration in seasonal wetlands of northern Namibia. By using the Bowen ratio–energy balance method, measurements of evapotranspiration were performed over a period of 2.5 years at two wetland sites—a rice field (RF) and a natural vegetation field (NVF)—and at one upland field (UF) devoid of surface water. The mean evapotranspiration rates of RF (1.9 mm daytime^?1) and NVF (1.8 mm daytime^?1) were greater than that in UF (1.0 mm daytime^?1). RF and NVF showed a slight difference in seasonal variations in evapotranspiration rates. During the dry season, RF evapotranspiration was less than the NVF evapotranspiration. The net radiation in RF was less in this period because of the higher albedo of the non‐vegetated surface after rice harvesting. In the early growth period of rice during the wet season, evapotranspiration in RF was higher than that in NVF, which was attributed to a difference in the evaporation efficiency and the transfer coefficient for latent heat that were both affected by leaf area index (LAI). Evapotranspiration sharply negatively responded to an increase in LAI when surface water is present according to sensitivity analysis, probably because a higher LAI over a surface suppresses evaporation. The control of LAI is therefore a key for reducing evaporation and conserving water. Copyright © 2013 John Wiley & Sons, Ltd.     

Characterizing the flush of stream chemical runoff from forested watersheds

A flush can be defined as stream chemical exhibiting higher concentrations during the prophase of a storm event at an event scale, or exhibiting progressively lower concentrations during several successive storms at a seasonal scale. Investigating the flush characteristics of chemical runoff from forested watersheds is important and helpful to understand the chemical dynamics as well as to design a sampling schedule strategy during storm events. Here, three parameters describing the flush characteristic are quantified and the flush characteristics of chemicals from four Japanese forested watersheds (Mie, Kochi, Nagano and Tokyo) were investigated at both event and seasonal levels. We found that the characteristics of the flush were complicated, and depended on the constituents of the hydrochemistry, climate and runoff quality. Generally, the flush occurs more readily for particulate components than for those in solution; the flush on nitrate‐nitrogen is weaker in regions of nitrogen saturation, such as Nagano and Tokyo, than in Mie and Kochi. Rainfall feature was the main factor controlling the flush of particulate components. However, the source available in a watershed plays a main role on the flushes of dissolve chemicals. Copyright © 2010 John Wiley & Sons, Ltd.     

Evaluation of ADEOS-II GLI ocean color atmospheric correction using SIMBADA handheld radiometer data

The performance of the “version 2” Global Imager (GLI) standard atmospheric correction algorithm, which includes empirical absorptive aerosol correction and sun glint correction, was evaluated using data collected with handheld above-water SIMBADA radiometers during 23 cruises of opportunity (research vessels, merchant ships), mostly in the North Atlantic and European seas. A number of 100 match-up data sets of GLI-derived and SIMBADA-measured normalized water-leaving radiance (nL _W ) and aerosol optical thickness (AOT) were sorted out, using objective selection criteria, and analyzed. The Root-Mean-Square (RMS) difference between GLI and SIMBADA nL _W was about 0.32 μW/cm²/nm/sr for the 412 nm band, showing improvement by 30% in RMS difference with respect to the conventional “version 1” GLI atmospheric correction algorithm, and the mean difference (or bias) was reduced significantly. For AOT, the RMS difference was 0.1 between GLI estimates and SIMBADA measurements and the bias was small (a few 0.01), but the ?ngstr?m exponent was systematically underestimated, by 0.4 on average, suggesting a potential GLI calibration offset in the near infrared. The nL _W differences were not correlated to AOT, although performance was best in very clear conditions (AOT less than 0.05 in the 865 nm band). Despite the relatively large scatter between estimated and measured nL _W , the derived chlorophyll-a concentration estimates, applying the same ratio algorithm (GLI OC4V4) to GLI and SIMBADA, were consistent and highly correlated in the range of 0.05–2 μg/l. The large variability in chlorophyll-a concentration estimate for clear clean water areas (e.g. with the concentration range lower than about 0.05 μg/l) turns out to be due to the nature of the “band ratio” based in-water algorithm.     

Radiatively heated, protoplanetary discs with dead zones – I. Dust settling and thermal structure of discs around M stars

The irradiation of protoplanetary discs by central stars is the main heating mechanism for discs, resulting in their flared geometric structure. In a series of papers, we investigate the deep links between two-dimensional self-consistent disc structure and planetary migration in irradiated discs, focusing particularly on those around M stars. In this first paper, we analyse the thermal structure of discs that are irradiated by an M star by solving the radiative transfer equation by means of a Monte Carlo code. Our simulations of irradiated hydrostatic discs are realistic and self-consistent in that they include dust settling with multiple grain sizes  ( N = 15)  , the gravitational force of an embedded planet on the disc and the presence of a dead zone (a region with very low levels of turbulence) within it. We show that dust settling drives the temperature of the mid-plane from an   r ^−3/5  distribution (well mixed dust models) towards an   r ^−3/4  . The dead zone, meanwhile, leaves a dusty wall at its outer edge because dust settling in this region is enhanced compared to the active turbulent disc at larger disc radii. The disc heating produced by this irradiated wall provides a positive gradient region of the temperature in the dead zone in front of the wall. This is crucially important for slowing planetary migration because Lindblad torques are inversely proportional to the disc temperature. Furthermore, we show that low turbulence of the dead zone is self-consistently induced by dust settling, resulting in the Kelvin–Helmholtz instability (KHI). We show that the strength of turbulence arising from the KHI in the dead zone is  α= 10⁻⁵  .     

Cell contact-dependent lethal effect of the dinoflagellate Heterocapsa circularisquama on phytoplankton–phytoplankton interactions

We used bi-algal culture experiments to investigate and verify the roles of growth interaction between Heterocapsa circularisquama and Prorocentrum dentatum in monospecific bloom formation. Growth of H. circularisquama was slightly inhibited when inoculated at 10² cells mL^–1 along with P. dentatum at 10⁴ cells mL^–1. In other combinations of inoculation densities, P. dentatum density rapidly decreased to extremely low levels in the presence of H. circularisquama. We used a mathematical model to simulate growth and interactions of H. circularisquama and P. dentatum in bi-algal cultures. The model indicates that one species will always inhibit the growth of the other and that the relative initial cell densities of the species are critical in determining the outcome. When cultured together under conditions without cell contact, growth of H. circularisquama and P. dentatum was not inhibited. As with P. dentatum, the growth of Heterosigma akashiwo and Skeletonema costatum was inhibited in intact cell suspensions with H. circularisquama, but a nontoxic species, Heterocapsa triquetra, did not affect the growth of P. dentatum or the other species. Similarly, cell suspensions of H. circularisquama showed hemolytic activity toward rabbit erythrocytes, but those of H. triquetra did not. In addition, the cell-free supernatant of H. circularisquama cultures showed no significant hemolytic activity. These results suggest that H. circularisquama causes lethality in P. dentatum by direct cell contact in which live-cell-mediated hemolytic activity might be a contributing factor.     

Changes in stream flow regime in headwater catchments of the Yellow River basin since the 1950s

The headwater catchments of the Yellow River basin generate over 35% of the basin's total stream flow and play a vital role in meeting downstream water resources requirements. In recent years the Yellow River has experienced significant changes in its hydrological regime, including an increased number of zero‐flow days. These changes have serious implications for water security and basin management. We investigated changes in stream flow regime of four headwater catchments since the 1950s. The rank‐based non‐parametric Mann–Kendall test was used to detect trends in annual stream flow. The results showed no significant trend for the period 1956 to 2000. However, change‐point analysis showed that a significant change in annual stream flow occurred around 1990, and hence the stream‐flow data can be divided into two periods: 1956–1990 and 1991–2000. There was a considerable difference in average annual stream flow between the two periods, with a maximum reduction of 51%. Wet‐season rainfall appears to be the main factor responsible for the decreasing trend in annual stream flow. Reductions in annual stream flow were associated with decreased interannual variability in stream flow. Seasonal stream flow distribution changed from bimodal to unimodal between the two periods, with winter stream flow showing a greater reduction than other seasons. Daily stream flow regime represented by flow duration curves showed that all percentile flows were decreased in the second period. The high flow index (Q₅/Q₅₀) reduced by up to 28%, whereas the reduction in the low flow index (Q₉₅/Q₅₀) is more dramatic, with up to 100% reduction. Copyright © 2006 John Wiley & Sons, Ltd.     

Reference systems

A reference system is a relation connecting observables and their mathematical represententions. The principle of general relativity assures that any sort of coordinate system can be used to describe physical phenomena. Thus, any reference system is only a convention, There is no absolutely true reference system. Instead, people seek for a best reference system, whose meaning may differ thus need to clarify, Taking an example from Earth rotation, we discuss how to find such a best reference system. The definition of the best system will change as scientific understandings deepen and computational environments develop. Therefore, we can not stop improving reference systems. However, when replacing an existing widely-spread system, one must take great care to minimize the inconvenience caused by its transition, especially the inconvenience which users might endure. The Standards Of Fundamental Astronomy (SOFA) project being conducted by the IAU WG on Astronomical Standards has the opportunity to ease this troublesome task. The World Wide Web (WWW) will be a main device to realize the project, namely to provide working standards including reference systems to the world.     

Non-destructive elemental analysis of lunar meteorites using a negative muon beam

We report the result of a non-destructive elemental analysis of lunar meteorites using a negative muon beam at J-PARC. An experimental system of six Ge semiconductor detectors and a newly designed He analysis chamber (to enable quantitative analysis of Al) was used to provide a high signal-to-noise ratio for the detection of major elements from lunar rocks (Mg, Si, Fe, O, Ca, and Al). We performed a Monte Carlo simulation to determine the chemical compositions at two sides and the center of a sample (at depths of 0.33 and 0.96 mm below the sample surface, respectively) of the lunar meteorite DEW 12007. These results indicate that the three interior regions of DEW 12007 are likely to be 55.8:44.2, 51.4:48.6, and 54.4:45.6 wt% mixtures of anorthositic and basaltic clasts, respectively. This study is the first quantitative analysis of a heterogeneous meteorite interior using a negative muon beam. As elemental analysis using a muon beam is non-destructive and highly sensitive to light elements, including C, N, and O, the protocols established in this study are applicable to initial characterization of returned samples from the South Pole of the Moon.