Improving strategies with constraints regarding non-Gaussian statistics in a three-dimensional variational assimilation method

We assess validity of a Gaussian error assumption, the basic assumption in data assimilation theory, and propose two kinds of constraints regarding non-Gaussian statistics. In the mixed water region (MWR) off the east coast of Japan exhibiting complicated frontal structures, a probability density function (PDF) of subsurface temperature shows double peaks corresponding to the Kuroshio and Oyashio waters. The complicated frontal structures characterized by the temperature PDF sometimes cause large innovations, bringing about a non-Gaussianity of errors. It is also revealed that assimilated results with a standard three-dimensional variational (3DVAR) scheme have some issues in MWR, arising from the non-Gaussianity of errors. The Oyashio water sometimes becomes unrealistically cold. The double peaks seen in the observed temperature PDF are too smoothed. To improve the assimilated field in MWR, we introduce two kinds of constraints, J _c1 and J _c2, which model the observed temperature PDF. The constraint J _c1 prevents the unrealistically cold Oyashio water, and J _c2 intends to reproduce the double peaks. The assimilated fields are significantly improved by using these constraints. The constraint J _c1 effectively reduces the unrealistically cold Oyashio water. The double peaks in the observed temperature PDF are successfully reproduced by J _c2. In addition, not only subsurface temperature but also whole level temperature and salinity (T–S) fields are improved by adopting J _c1 and J _c2 to a multivariate 3DVAR scheme with vertical coupled T–S empirical orthogonal function modes.     

Effects of mass source/sink at the western boundary on the wind-driven gyres: Implications for the ventilation of the north pacific intermediate layer through convection in the Okhotsk Sea and tidal mixing at the Kuril Straits

A steady quasi-geostrophic 2.5-layer model, forced by both Ekman pumping and a mass source/sink situated at the western boundary has been constructed to investigate the effect of diapycnal transport due to convection in the Okhotsk Sea and tidal mixing at the Kuril Straits on the intermediate layer in the North Pacific. The model illustrates a combined effect of the wind-driven and mass-driven circulations. First, net mass input induces a “barotropic” mode inter-gyre flow along the western boundary through the dynamical influence of Kelvin waves. This flow creates characteristic curves (geostrophic contours) that facilitate inter-gyre communication through the western boundary layer from the location of the mass source to the subtropical gyre. Due to the effect of wind-driven circulation, the offshore part turns eastward into the interior, encircles the outer rim of the region (which would otherwise be the pool region in the absence of mass input), and then encounters the western boundary. Eventually, the water fed into the lower layer flows mostly along this path and later flows away to the equatorial region. Conversely, in the upper layer, water is fed from the equator to the subtropics, and to the subpolar interior region through the western boundary current. The water then circulates along the outer rim and is absorbed into the mass sink. The model is controlled mainly by three nondimensional parameters: (1) the ratio of net mass input rate to the maximum Sverdrup transport (Q/T _Sv ^max ), which affects the inter-gyre communication by altering the paths of geostrophic contours, (2) the ratio of a mass input rate into the lower layer to that in total (Q ₂/Q), which controls the vertical structure of the inter-gyre flow, and (3) the measure of the wind forcing effect relative to the β effect, which determines the horizontal extent of the area influenced by the mass input. The other parameter regimes with respect to Q/T _Sv ^max and Q ₂/Q are also presented.     

小型激光天文动力学空间计划概念

小型激光天文动力学空间计划是 :使用在太阳轨道上无拖曳航天器和地面站以激光干涉和脉冲测距的方法 ,精确地探讨天文动力学 ,检测相对论与时空基本定律 ,改进探测引力波的灵敏度以及更准确地测定太阳、行星和小行星的参数。 1 969年开始的月球激光 (反射 )测距 ,对地球物理、参考坐标的选定、相对论的检验均有重要的贡献。 3 0年来 ,激光技术的长足进步 ,使现在正是适合于开始进行研究空间有源 (主动 )测距和光波空间通讯的时候。激光天文动力学的兴起是必然的趋势 ,其精确度将比现在提高 3到 6个数量级 ,将是天文动力学革命性的发展。小型激光天文动力学空间计划可以起到带头作用。它的关键技术有三 ,即 :弱光锁相、极精确无拖曳航天和高衰减日冕仪。弱光锁相已有长足的进步。对高衰减日冕仪的研究 ,也有了初步的方案。LISA空间计划将于 2 0 0 6年 8月发射SMART -2 ,研究测试极精确无拖曳航天。小型激光天文动力学空间计划的关键技术已日趋成熟。在第一届国际激光天文动力学研讨会 ( 2 0 0 1 ,9.1 3 -2 3 )中介绍了各相关学科背景及前沿研究 ,讨论了激光天文动力学空间计划科学目标及相关技术 ,并召开了两次小型激光天文动力学空间计划预研究筹备会 ,建立了和欧洲的合作关系。会后着手进行此项对基础     

Thermal diffusivity of lunar rocks under atmospheric and vacuum conditions

Thermal diffusivity, k, of three lunar rocks (10049 and 10069; Type A, Apollo 11 and 14311; Apollo 14) and a terrestrial basalt (alkaline olivine basalt, Oki-do?go, Japan) was measured under one atmosphere and in vacuum conditions (10^?3 ～ 10^?5 mmHg) in the temperature range from 85 to 850°K. The semi-empirical curve of k =A + B/T +CT³ is fitted to the data in each condition. The porosity of rocks strongly affects the thermal diffusivity at low temperature ( T ? 500°K) in vacuum condition. At 150°K, thermal diffusivity of lunar rocks with porosity of 5.5% (10049) and 11% (10069) at one atmosphere is about 1.7 and 3.2 times of that in vacuum, respectively. The difference between the values at one atmosphere and those in vacuum decreases as the temperature increases. Measurements of k should be made at gas pressures at least lower than 10^?3 mmHg to estimate the value under lunar surface conditions.     

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure. This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress (Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small.     

Sulfate reduction using methane in sediments beneath a bathyal “cold seep” giant clam community off Hatsushima Island, Sagami Bay, Japan

Two sandy sediment cores (Cores D227-120 and D380) were collected from inside a deep-sea giant clam (Calyptogena soyoae) community off Hatsushima Island, western Sagami Bay, central Japan (35°59.9′N, 139°13.6′E; 1160 m deep) and a muddy sediment core (Core D227-202) was obtained from outside the community by the submersibleShinkai 2000. The chloride concentration of the pore waters is constant vertically and sulfate reduction using sedimentary organic matter occurs in Core D227-202 (21 cm long). The chloride concentrations are lower by 7% at the 7.5–9 cm depth in Core D227-120 (9 cm long) and by 3% at the 11–12 cm depth in Core D380 (16 cm long) than those of the overlying bottom waters in the cores from inside of the community. Sulfate concentration decreases remarkably and dissolved inorganic carbon, alkalinity, ammonium-N, and hydrogen sulfide concentrations increase significantly with increasing depth in Core D380.δ³⁴S values of sulfate ions increase from +20.5 to +35.3‰ andδ¹³C values of dissolved inorganic carbon decrease drastically from −7.0 to −45‰ with increasing depth from the top to the bottom of the core, although theδ¹³C values of the organic carbon of the sediments are−23.7 ± 0.9‰ in Core D380. These results indicate that sulfate reduction using methane is active within the sediments just beneath the living clams and that the hydrogen sulfide produced can be used by endosymbiotic sulfur oxidizing bacteria living in the gills ofC. soyoae in the community.     

Instabilities in the consumption and production for cobalt

Cobalt is obtained mainly as a byproduct of the mining and metallurgical processing of copper and nickel. The amount of minable cobalt has a characteristic supply limit, which is dependent upon demand for copper and nickel. It is considered that cobalt consumption will be affected by the amount mined in the near future, because world demand has been gradually increasing, while the production from copper sulfide ores in Zaire and Zambia, major producing countries, has decreased for political, economical and technological reasons. The world demand for cobalt has surpassed the world mine production, and cobalt sales from the National Defense Stockpile of the United States and exports from Russia and cobalt recovered from stockpiled intermediates contributed to the supply in 1994. It is concluded, from a statistical point of view, that this trend of shortage and high prices for cobalt will continue in the near future.     

Phase relation of CaSO<Subscript>4</Subscript> at high pressure and temperature up to 90 GPa and 2300 K

Calcium sulfate (CaSO₄), one of the major sulfate minerals in the Earth’s crust, is expected to play a major role in sulfur recycling into the deep mantle. Here, we investigated the crystal structure and phase relation of CaSO₄ up to ~90 GPa and 2300 K through a series of high-pressure experiments combined with in situ X-ray diffraction. CaSO₄ forms three thermodynamically stable polymorphs: anhydrite (stable below 3 GPa), monazite-type phase (stable between 3 and ~13 GPa) and barite-type phase (stable up to at least 93 GPa). Anhydrite to monazite-type phase transition is induced by pressure even at room temperature, while monazite- to barite-type transition requires heating at least to 1500 K at ~20 GPa. The barite-type phase cannot always be quenched from high temperature and is distorted to metastable AgMnO₄-type structure or another modified barite structure depending on pressure. We obtained the pressure–volume data and density of anhydrite, monazite- and barite-type phases and found that their densities are lower than those calculated from the PREM model in the studied P–T conditions. This suggests that CaSO₄ is gravitationally unstable in the mantle and fluid/melt phase into which sulfur dissolves and/or sulfate–sulfide speciation may play a major role in the sulfur recycling into the deep Earth.     

Effects of a kappa distribution function of electrons on incoherent scatter spectra

In usual incoherent scatter data analysis, the plasma distribution function is assumed to be Maxwellian. In space plasmas, however, distribution functions with a high energy tail which can be well modeled by a generalized Lorentzian distribution function with spectral index kappa (kappa distribution) have been observed. We have theoretically calculated incoherent scatter spectra for a plasma that consists of electrons with kappa distribution function and ions with Maxwellian neglecting the effects of the magnetic field and collisions. The ion line spectra have a double-humped shape similar to those from a Maxwellian plasma. The electron temperatures are underestimated, however, by up to 40% when interpreted assuming Maxwellian distribution. Ion temperatures and electron densities are affected little. Accordingly, actual electron temperatures might be underestimated when an energy input maintaining a high energy tail exists. We have also calculated plasma lines with the kappa distribution function. They are enhanced in total strength, and the peak frequencies appear to be slightly shifted to the transmitter frequency compared to the peak frequencies for a Maxwellian distribution. The damping rate depends on the electron temperature. For lower electron temperatures, plasma lines for electrons with a distribution function are more strongly damped than for a Maxwellian distribution. For higher electron temperatures, however, they have a relatively sharp peak.     

Examination of a Rock Failure Criterion Based on Circumferential Tensile Strain

—Uniaxial compression, triaxial compression and Brazialian tests were conducted on several kinds of rock, with particular attention directed to the principal tensile strain. In this paper we aim to clarify the effects of the experimental environment—such as confining pressure, loading rate, water content and anisotropy—on the critical tensile strain, i.e., the measured principal tensile strain at peak load.¶It was determined that the chain-type extensometer is a most suitable method for measuring the critical tensile strain in uniaxial compression tests. It is also shown that the paper-based strain gage, whose effective length is less than or equal to a tenth of the specimen’s diameter and glued on with a rubber-type adhesive, can be effectively used in the Brazilian tests.¶The effect of confining pressure P _C on the critical tensile strain ? _TC in the brittle failure region was between ?0.02 × 10^?10 Pa^?1 and 0.77 × 10^?10 Pa^?1. This pressure sensitivity is small compared to the critical tensile strain values of around ?0.5 × 10^?2. The strain rate sensitivities ?? _TC /?{log(d|?|/dt)} were observed in the same way as the strength constants in other failure criteria. They were found to be from ?0.10 × 10^?3 to ?0.52 × 10^?3 per order of magnitude in strain rate in the triaxial tests. The average magnitude of the critical tensile strain ? _TC increased due to the presence of water by 4% to 20% for some rocks, and decreased by 22% for sandstone. It can at least be said that the critical tensile strain is less sensitive to water content than the uniaxial compressive strength under the experimental conditions reported here. An obvious anisotropy was observed in the P-wave velocity and in the uniaxial compressive strength of Pombetsu sandstone. It was not observed, however, in the critical tensile strain, although the data do show some variation.¶A "tensile strain criterion" was proposed, based on the above experimental results. This criterion signifies that stress begins to drop when the principal tensile strain reaches the critical tensile strain. The criterion is limited to use within the brittle failure region. The critical tensile strain contains an inelastic strain component as well as an elastic one. It is affected by the strain rate, however, it is relatively insensitive to the confining pressure, the presence of water and anisotropy.