Fast computation of complete elliptic integrals and Jacobian elliptic functions     

Toshio Fukushima 《Celestial Mechanics and Dynamical Astronomy》2009,105(4):305-328

As a preparation step to compute Jacobian elliptic functions efficiently, we created a fast method to calculate the complete elliptic integral of the first and second kinds, K(m) and E(m), for the standard domain of the elliptic parameter, 0 < m < 1. For the case 0 < m < 0.9, the method utilizes 10 pairs of approximate polynomials of the order of 9–19 obtained by truncating Taylor series expansions of the integrals. Otherwise, the associate integrals, K(1 − m) and E(1 − m), are first computed by a pair of the approximate polynomials and then transformed to K(m) and E(m) by means of Jacobi’s nome, q, and Legendre’s identity relation. In average, the new method runs more-than-twice faster than the existing methods including Cody’s Chebyshev polynomial approximation of Hastings type and Innes’ formulation based on q-series expansions. Next, we invented a fast procedure to compute simultaneously three Jacobian elliptic functions, sn(u|m), cn(u|m), and dn(u|m), by repeated usage of the double argument formulae starting from the Maclaurin series expansions with respect to the elliptic argument, u, after its domain is reduced to the standard range, 0 ≤ u < K(m)/4, with the help of the new method to compute K(m). The new procedure is 25–70% faster than the methods based on the Gauss transformation such as Bulirsch’s algorithm, sncndn, quoted in the Numerical Recipes even if the acceleration of computation of K(m) is not taken into account.  相似文献   

The Indian Ocean subtropical dipole mode simulated in the CMIP3 models     

Takahito Kataoka  Tomoki Tozuka  Yukio Masumoto  Toshio Yamagata 《Climate Dynamics》2012,39(6):1385-1399

Using observation data and outputs from the “twentieth-century climate in coupled models” (20c3m) control runs of coupled general circulation models submitted to the Coupled Model Intercomparison Project, phase 3 (CMIP3), the ability of CMIP3 models to simulate the Indian Ocean subtropical dipole (IOSD) and its influence on the rainfall anomaly over the southern African region is investigated. Many models simulate the IOSD, but the location and shape of the sea surface temperature anomaly vary among models. This model bias is closely linked to the bias in simulating the anomalous strengthening and southward shift of the subtropical high. Almost all models fail to simulate the rainfall anomaly associated with the IOSD owing to the inaccurate simulation of the location of sea surface temperature and sea level pressure anomalies.  相似文献   

Q-bursts from various distances on the Earth     

Toshio Ogawa  Masayuki Komatsu   《Atmospheric Research》2009,91(2-4):538-545

The mechanism of the Q-burst is investigated in the time and frequency domains. Electric fields in the ELF (extremely low frequency) to VLF (very low frequency) range have been observed with a ball antenna since 2003 in Kochi City, Japan (latitude 33.3°north, longitude 133.4°east). Source-to-observer distances (SODs) of Q-bursts are estimated by analyzing the waveforms. It is found as a result that the Q-burst is produced by combination of direct and antipodal pulses from a source lightning stroke occurring all over the world.  相似文献   

Anomalous winter climate conditions in the Pacific rim during recent El Niño Modoki and El Niño events   总被引：2，自引：1，他引：1  

Hengyi Weng  Swadhin K. Behera  Toshio Yamagata 《Climate Dynamics》2009,32(5):663-674

Present work compares impacts of El Niño Modoki and El Niño on anomalous climate in the Pacific rim during boreal winters of 1979–2005. El Niño Modoki (El Niño) is associated with tripole (dipole) patterns in anomalies of sea-surface temperature, precipitation, and upper-level divergent wind in the tropical Pacific, which are related to multiple “boomerangs” of ocean-atmosphere conditions in the Pacific. Zonal and meridional extents of those “boomerangs” reflect their independent influences, which are seen from lower latitudes in the west to higher latitudes in the east. In the central Pacific, more moisture is transported from the tropics to higher latitudes during El Niño Modoki owing to displacement of the wet “boomerang” arms more poleward toward east. Discontinuities at outer “boomerang” arms manifest intense interactions between tropical and subtropical/extratropical systems. The Pacific/North American pattern and related climate anomalies in North America found in earlier studies are modified in very different ways by the two phenomena. The seesaw with the dry north and the wet south in the western USA is more likely to occur during El Niño Modoki, while much of the western USA is wet during El Niño. The moisture to the southwestern USA is transported from the northward shifted ITCZ during El Niño Modoki, while it is carried by the storms traveling along the southerly shifted polar front jet during El Niño. The East Asian winter monsoon related anticyclone is over the South China Sea during El Niño Modoki as compared to its position over the Philippine Sea during El Niño, causing opposite precipitation anomalies in the southern East Asia between the two phenomena.  相似文献   

Effect of the variation in the lower tropospheric temperature on the wind onset of the Indian summer monsoon     

Kenji Taniguchi  Devraj Rajan  Toshio Koike 《Meteorology and Atmospheric Physics》2010,106(1-2):75-94

There is a large thermal contrast between the Arabian Peninsula and India (Δθ _AI) at the mature stage of the Indian summer monsoon (ISM). The forming process of Δθ _AI is investigated analyzing various datasets. It forms earlier in the lower troposphere than in the middle and upper layers. The potential temperature in the lower troposphere over the west coast of India (θ _IW) abruptly decreases in advance of the rapid enhancement of the westerly wind over the Arabian Sea corresponding to the ISM onset. Such a process was observed for all the target years and the rapid decrease in θ _IW could trigger the ISM onset. The decrease in θ _IW had two patterns. In one case, cooler air is brought by the strong winds around a cyclone over the Arabian Sea. In another case, θ _IW decreases gradually by a synergy of a southwesterly wind over the Arabian Sea and the enlargement of Δθ _AI.  相似文献   

Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers   总被引：4，自引：3，他引：1  

Toshio Fukushima 《Journal of Geodesy》2012,86(4):271-285

By extending the exponent of floating point numbers with an additional integer as the power index of a large radix, we compute fully normalized associated Legendre functions (ALF) by recursion without underflow problem. The new method enables us to evaluate ALFs of extremely high degree as 2³² =  4,294,967,296, which corresponds to around 1 cm resolution on the Earth’s surface. By limiting the application of exponent extension to a few working variables in the recursion, choosing a suitable large power of 2 as the radix, and embedding the contents of the basic arithmetic procedure of floating point numbers with the exponent extension directly in the program computing the recurrence formulas, we achieve the evaluation of ALFs in the double-precision environment at the cost of around 10% increase in computational time per single ALF. This formulation realizes meaningful execution of the spherical harmonic synthesis and/or analysis of arbitrary degree and order.  相似文献   

Hydrogen, Oxygen and Sulfur Isotope Studies of Seafloor Hydrothermal System at the Desmos Caldera, Manus Back-arc Basin, Papua New Guinea: An Analogue of Terrestrial Acid Hot Crater-lake   总被引：2，自引：0，他引：2  

Kaul R. Gena    Hitoshi Chiba    Toshio Mizuta  Osamu Matsubaya 《Resource Geology》2006,56(2):183-190

Abstract. The Onsen site is an active submarine hydrothermal system hosted by the Desmos caldera in the Eastern Manus Basin, Papua New Guinea. The hydrothermal fluid is very acidic (pH=1.5) and abundant native sulfur is deposited around the vent. The δ³⁴S values of native sulfur range from -6.5 to -9.3 %o. δ³⁴S values of H₂S and SO₄ in the hydrothermal fluid are -4.3 to -9.9 %o and +18.6 to +20.0 %o, respectively. These δ³⁴S values are significantly lower than those of the other hydrothermal systems so far reported. These low δ³⁴S values and the acidic nature of the vent fluids suggest that volcanic SO₂ gas plays an important role on the sulfur isotope systematic of the Onsen hydrothermal system. Relationship among the δ³⁴S values of S-bearing species can be successively explained by the model based on the disproportionation reaction starting from the volcanic SO₂ gas. The predicted δ³⁴S values of SO₂ agree with the measured whole rock δ³⁴S values. δD and δ¹⁸O values of clay minerals separated from the altered rock samples also suggest the contribution of the magmatic fluid to the hydrothermal system. Present stable isotopic study strongly suggests that the Onsen hydrothermal site in the Desmos caldera is a magmatic submarine hydrothermal system.  相似文献   

Hydrothermal Alteration of Oman Ophiolite Extrusives in Ghuzayn Area     

Durair A'Shaikh    Hiroharu Matsueda  Toshio Mizuta  Sumio Miyashita 《Resource Geology》2006,56(2):167-182

Abstract. The hydrothermal alteration in Ghuzayn Volcanics was associated with mineralization and accumulation of three massive sulfide deposits. The Ghuzayn Volcanics were discriminated into basaltic and andesitic lavas. The crossplots of Zr versus Nb, Y, Hf, La and Lu show that they fall in the same linear fractionation trends with more evolved affinities in the andesitic lavas compared to the less evolved affinities in the basaltic lavas. The immobile trace element contents of the Ghuzayn Volcanics show that they are of oceanic to continental tholeiitic affinity which fall in the fields of back‐arc basin basalt, N‐MORB and island arc tholeiite all meet and match with the field of the Lau‐Tonga back‐arc basin lavas. The ore‐body No. 2 is underlain by a zone of intense argillization and silicification which are so‐called alteration pipe as in some of the Cyprus‐type massive sulfide deposits. The alteration in the proximity of the ore‐body No. 2 is characterized by a zone of epidotization and slight silicification and sulfide disseminations, and surrounded by another zone of slight silicification and sulfide dissemination in the outermost rim around the ore‐body No. 2. The alteration zones in the proximity of the ore‐body No. 2 were divided into Zones I and II based on the abundance of the secondary minerals in the altered basaltic lavas. The Zone I is located in the most northern upper part of the ore‐body No. 2 and characterized by corrensite, saponite and prehnite. However, the Zone II is located in the southern part of the ore‐body No. 2 and characterized by chlorite and epidote. Both alteration zones were formed by different alteration stages. Stage 1 was formed by non to partly reacted fluids, to crystallize Mg‐chlorite and albite at temperatures ranging from 150 to 250d?C. Further, these fluids evolved with time and became Mg‐depleted, Si‐ and metal‐enriched to crystallize Fe²⁺‐chlorite, epidote, quartz and sulfides at temperatures ranging from 250 to 350d?C in stage 2. Later, these fluids were evolved again to be Mg‐ and Ca‐enriched in stage 3 to crystallize prehnite, laumontite, corrensite and saponite at temperatures ranging from 150 to 220d?C. Late zeolite and calcite have overgrown the previously crystallized phases and crosscutting veins along the altered basaltic lavas in stage 4. Finally, the lavas were cracked and refractured to facilitate penetration of seawater into deeper parts to heat up again and re‐leach the silica and metals in a new mineralizing event.  相似文献   

In memoriam     

Toshio Matsumoto 《Astrophysics and Space Science》1992,197(2):iv-177

  相似文献   

Numerical computation of incomplete elliptic integrals of a general form     

Toshio Fukushima  Hideharu Ishizaki 《Celestial Mechanics and Dynamical Astronomy》1994,59(3):237-251

We present an algorithm to compute the incomplete elliptic integral of a general form. The algorithm efficiently evaluates some linear combinations of incomplete elliptic integrals of all kinds to a high precision. Some numerical examples are given as illustrations. This enables us to numerically calculate the values and the partial derivatives of incomplete elliptic integrals of all kinds, which are essential when dealing with many problems in celestial mechanics, including the analytic solution of the torque-free rotational motion of a rigid body around its barycenter.  相似文献