Precise computation of acceleration due to uniform ring or disk

We describe a precise numerical method to evaluate the acceleration vector of an inverse-square force law caused by a uniform ring or disk. The method consists of two parts. One is rewriting of the analytic expressions of the vector to reduce the loss of information in its computation. The other is a procedure to compute a special linear combination of the complete elliptic integrals of the first and the second kind appeared in the rewritten expressions.     

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

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.     

Q-bursts from various distances on the Earth

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.     

Fast computation of complete elliptic integrals and Jacobian elliptic functions

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.     

The Indian Ocean subtropical dipole mode simulated in the CMIP3 models

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.     

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

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).     

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

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.     

Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers

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.     

Auto-detection and integration of tectonically significant lineaments from SRTM DEM and remotely-sensed geophysical data

A set of techniques was developed for automatically detecting tectonic lineaments from multi-source remotely-sensed data at various scales. The techniques include adaptive shading of grid data to enhance linear features, a segment-tracing algorithm to extract line segments from the shaded grid data, grouping of the segments by concatenating short segments, and connecting them by proximity and co-linearity criteria to form a lineament that represents significant tectonic structure. B-spline smoothing was adopted for lineament representation. Finally, a technique for assessing the orientations and styles of faulting (normal, reverse, and strike-slip types) was developed for use in characterizing the extrapolated fracture planes. The applicability of the developed techniques was examined using 30 arc-second topography/bathymetry grids, 1-min gravity anomaly grids, and 2-min total field magnetic intensity grids covering Egypt and its surroundings. Lineaments derived from data types so diverse in composition and from various depths corresponded well with the referenced tectonic features over much of the region. Prominent trends and faulting styles of lineaments provided important clues as to the timing of their development as well as strong support for a structural inheritance model. Results demonstrated the effectiveness of the developed techniques combined with integration of remotely-sensed data in detecting regional fracture systems accurately and in characterizing geodynamics over a long timeframe.