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   

High-time resolution AMS C data sets for Lake Baikal and Lake Hovsgol sediment cores: Changes in radiocarbon age and sedimentation rates during the transition from the last glacial to the Holocene   总被引：1，自引：1，他引：0  

Takahiro Watanabe  Toshio Nakamura  Fumiko Watanabe Nara  Takeshi Kakegawa  Kazuho Horiuchi  Ryoko Senda  Takefumi Oda  Mitsugu Nishimura  Genki Inoue Matsumoto  Takayoshi Kawai 《Quaternary International》2009,205(1-2):12

High-time resolution ¹⁴C dating of Lake Baikal sediment cores indicates negative and positive anomalies of calculated linear sedimentation rate (LSR; 1.1 and 35.6 cm/ka, respectively) during the period of climate transition from the last glacial to Holocene. The timing of the Lake Baikal apparent LSR anomalies is consistent with that of the changes in the atmospheric radiocarbon concentration (Δ¹⁴C) during Younger Dryas rapid cooling event. ¹⁴C dating of lipids in the Lake Baikal surface sediments revealed that the sources of sedimentary lipids were different in each basin. In the Northern Basin of Lake Baikal, the ¹⁴C age of total lipids from the surface sediment (4.0 ¹⁴C ka) was found to be older than that of TOC (1.6 ¹⁴C ka). By contrast, the ¹⁴C age of total lipids in the Southern Basin was younger than that of the TOC by ca. 0.7–3.0 ka.In the Lake Hovsgol sediment cores, ages of the main lithologic boundaries during the last glacial–interglacial transition were estimated based on new ¹⁴C data sets. TOC concentration in the cores started to rapidly increase at 13.8 ± 0.3 ¹⁴C ka at the base of the basinwide finely laminated layer deposited during Bølling/Allerød. The base of the layer diatomaceous mud corresponds to the end of Younger Dryas event (10.6 ± 0.1 ¹⁴C ka).  相似文献   

Lower Triassic δC isotope curve from shallow-marine carbonates in Japan, Panthalassa realm: Confirmation of the Tethys δC curve     

Micha Horacek  Toshio Koike  Sylvain Richoz 《Journal of Asian Earth Sciences》2009,36(6):481

δ¹³C data from Tethyan sections provide evidence of profound changes in the carbon cycle during the Lower Triassic. Sections from the Panthalassa realm were investigated to establish whether these variations are also present there. In the Jurassic accretionary wedges in Japan, exotic blocks having a Panthalassan affinity, have been incorporated. The majority of the blocks are pelagic cherts but rare shallow-water carbonates are also present. We present a δ¹³C study on the Lower Triassic of a shallow-water carbonate succession deposited on a mid-oceanic seamount and accreted to the Chichibu Belt, Japan. Two sections have been measured at Kamura, central Kyushu Island. The carbon isotope curve shows depleted values across the Permian–Triassic boundary (PTB), subsequently followed by an increase to heavier values into the Dienerian, culminating in a maximum of almost +4‰ V-PDB, before a steep drop at a stratigraphic gap. Low values are recorded in the Smithian, but rise to enriched δ¹³C values > +3.5‰ near the Smithian–Spathian boundary. The observed trend of the stable carbon isotope curve from Japanese sediments mirrors the curves derived from sections in the Tethys (e.g. Italy, Iran, Turkey, Oman and the South China Nanpanjing Basin). Our results support the interpretation of this curve as representing a global trend across the PTB and in the Lower Triassic, although some distinct features are absent around the Dienerian/Smithian boundary. Profound variations of the carbon isotope curve in the Lower Triassic are presented for the first time from a marine section outside of the Tethys. They indicate severe, global changes in the Lower Triassic carbon cycle, and the causative processes must have significantly contributed to the delayed biotic recovery after the PTB. Large amounts of carbon were shifted between carbon reservoirs, most probably between shallow- and deep-ocean waters, and/or ocean and sediment. Anoxia followed by overturn of the ocean water masses may have been the mechanism which quickly altered ecological conditions in the ocean leading to variable availability of nutrients and oxygen, and changes in isotope composition of the available carbon in the surface waters that was incorporated in the precipitated carbonate.  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   

Perceived ambiguity about earthquake and house destruction risks     

Toshio Fujimi  Masahide Watanabe  Ryuji Kakimoto  Hirokazu Tatano 《Natural Hazards》2016,80(2):1243-1256

  相似文献   

Biogeochemical evidence of large diapycnal diffusivity associated with the subtropical mode water of the North Pacific     

Chiho Sukigara  Toshio Suga  Toshiro Saino  Katsuya Toyama  Daigo Yanagimoto  Kimio Hanawa  Nobuyuki Shikama 《Journal of Oceanography》2011,67(1):77-85

A profiling float equipped with a fluorimeter, a dissolved oxygen (DO) sensor, and temperature and salinity sensors was deployed in the subtropical mode water (STMW) formation region of the North Pacific. It acquired quasi-Lagrangian, 5-day-interval time-series records from March to July 2006. The time-series distribution of chlorophyll showed a sustained and sizable subsurface maximum at 50–100 m, just above the upper boundary of the STMW, throughout early summer (May–July). The DO concentration in this lower euphotic zone (50–100 m) was almost constant and supersaturated in the same period, becoming more supersaturated with time. On the other hand, the DO concentration at 100–150 m near the upper boundary of the STMW decreased much more slowly compared with the main layer of STMW below 150 m, even though oxygen consumption by organisms was expected to be larger in the former depth range. The small temporal variations of DO in the lower euphotic zone and near the upper boundary of the STMW were reasonably explained by downward oxygen transport because of large diapycnal diffusion near the top of the STMW. Assuming that the oxygen consumption rate at 100–150 m was the same as that in the main layer of STMW and compensated by the downward oxygen flux, the diapycnal diffusivity was estimated to be 1.7 × 10⁻⁴ m² s⁻¹. Nitrate transport into the euphotic zone by the same large diffusion was estimated to be 0.8 mmol N m⁻² day⁻¹. All of the transported nitrate could have been used for photosynthesis by the phytoplankton; net community production was estimated to be 5.3 mmol C m⁻² day⁻¹.  相似文献   

Origin of extreme summers in Europe: the Indo-Pacific connection     

Swadhin Behera  Jayanthi V. Ratnam  Yukio Masumoto  Toshio Yamagata 《Climate Dynamics》2013,41(3-4):663-676

Extreme summers of Europe are usually affected by blocking highs that shift between Western and Eastern Europe to cause regional variations in the surface temperature anomalies. Generally, the blocking high induces a regional temperature dipole with poles of warm and cold anomalies on two sides of Europe. The extreme summers of Western Europe, when the Eastern Europe is colder than normal, are usually associated with the teleconnections arising from positive Indian Ocean Dipole (IOD) events. In contrast, analogous warm events in Eastern Europe are usually associated with La Niña. The western Pacific conditions that prevail during the turnaround phase of El Niño to La Niña are found to be responsible for developing the extreme Eastern Europe events. The role of North Atlantic Oscillation (NAO) is not blatant for the Eastern Europe summers though it has a weaker influence on Western Europe summers for which IOD plays a dominant role: The seasonal July–August correlation for Western Europe temperature with IOD index is higher than that with the NAO index. The teleconnections for both types of extremes are associated with a Rossby wavetrain that travel around the globe to reach the Europe. This circumglobal teleconnection is largely determined by the location of the tropospheric heat source. For Western Europe warm events, major contributions come from the atmospheric convections/diabatic heating over northwest India and southern Pakistan. For the Eastern Europe events, the convections over northwest Pacific, south of Japan, are found to project the signals on to the mid-latitude wave-guide. These patterns of teleconnection are so robust that those can be seen on daily to seasonal time-scales of atmospheric anomalies. The wavetrains are found to set-in a couple of weeks prior to the development of blocking highs and extreme hot conditions over Europe.  相似文献   

On the long-term stability of terrestrial reference frame solutions based on Kalman filtering     

Benedikt Soja  Richard S. Gross  Claudio Abbondanza  Toshio M. Chin  Michael B. Heflin  Jay W. Parker  Xiaoping Wu  Tobias Nilsson  Susanne Glaser  Kyriakos Balidakis  Robert Heinkelmann  Harald Schuh 《Journal of Geodesy》2018,92(9):1063-1077

The Global Geodetic Observing System requirement for the long-term stability of the International Terrestrial Reference Frame is 0.1 mm/year, motivated by rigorous sea level studies. Furthermore, high-quality station velocities are of great importance for the prediction of future station coordinates, which are fundamental for several geodetic applications. In this study, we investigate the performance of predictions from very long baseline interferometry (VLBI) terrestrial reference frames (TRFs) based on Kalman filtering. The predictions are computed by extrapolating the deterministic part of the coordinate model. As observational data, we used over 4000 VLBI sessions between 1980 and the middle of 2016. In order to study the predictions, we computed VLBI TRF solutions only from the data until the end of 2013. The period of 2014 until 2016.5 was used to validate the predictions of the TRF solutions against the measured VLBI station coordinates. To assess the quality, we computed average WRMS values from the coordinate differences as well as from estimated Helmert transformation parameters, in particular, the scale. We found that the results significantly depend on the level of process noise used in the filter. While larger values of process noise allow the TRF station coordinates to more closely follow the input data (decrease in WRMS of about 45%), the TRF predictions exhibit larger deviations from the VLBI station coordinates after 2014 (WRMS increase of about 15%). On the other hand, lower levels of process noise improve the predictions, making them more similar to those of solutions without process noise. Furthermore, our investigations show that additionally estimating annual signals in the coordinates does not significantly impact the results. Finally, we computed TRF solutions mimicking a potential real-time TRF and found significant improvements over the other investigated solutions, all of which rely on extrapolating the coordinate model for their predictions, with WRMS reductions of almost 50%.  相似文献   

The assessment of surface water resources for the semi‐arid Yongding River Basin from 1956 to 2000 and the impact of land use change     

Lei Wang  Zhongjing Wang  Toshio Koike  Hang Yin  Dawen Yang  Shan He 《水文研究》2010,24(9):1123-1132

The assessment of surface water resources (SWRs) in the semi‐arid Yongding River Basin is vital as the basin has been in a continuous state of serious water shortage over the last 20 years. In this study, the first version of the geomorphology‐based hydrological model (GBHM) has been applied to the basin over a long period of time (1956–2000) as part of an SWR assessment. This was done by simulating the natural hydrological processes in the basin. The model was first evaluated at 18 stream gauges during the period from 1990 to 1992 to evaluate both the daily streamflows and the annual SWRs using the land use data for 1990. The model was further validated in 2000 with the annual SWRs at seven major stream gauges. Second, the verified model was used in a 45‐year simulation to estimate the annual SWRs for the basin from 1956 to 2000 using the 1990 land use data. An empirical correlation between the annual precipitation and the annual SWRs was developed for the basin. Spatial distribution of the long‐term mean runoff coefficients for all 177 sub‐basins was also achieved. Third, an additional 10‐year (1991–2000) simulation was performed with the 2000 land use data to investigate the impact of land use changes from 1990 to 2000 on the long‐term annual SWRs. The results suggest that the 10‐year land use changes have led to a decrease of 8·3 × 10⁷ m³ (7·9% of total) for the 10‐year mean annual SWRs in the simulation. To our knowledge, this work is the first attempt to assess the long‐term SWRs and the impact of land use change in the semi‐arid Yongding River Basin using a semi‐distributed hillslope hydrological model. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献