Accurate computation of gravitational field of a tesseroid

We developed an accurate method to compute the gravitational field of a tesseroid. The method numerically integrates a surface integral representation of the gravitational potential of the tesseroid by conditionally splitting its line integration intervals and by using the double exponential quadrature rule. Then, it evaluates the gravitational acceleration vector and the gravity gradient tensor by numerically differentiating the numerically integrated potential. The numerical differentiation is conducted by appropriately switching the central and the single-sided second-order difference formulas with a suitable choice of the test argument displacement. If necessary, the new method is extended to the case of a general tesseroid with the variable density profile, the variable surface height functions, and/or the variable intervals in longitude or in latitude. The new method is capable of computing the gravitational field of the tesseroid independently on the location of the evaluation point, namely whether outside, near the surface of, on the surface of, or inside the tesseroid. The achievable precision is 14–15 digits for the potential, 9–11 digits for the acceleration vector, and 6–8 digits for the gradient tensor in the double precision environment. The correct digits are roughly doubled if employing the quadruple precision computation. The new method provides a reliable procedure to compute the topographic gravitational field, especially that near, on, and below the surface. Also, it could potentially serve as a sure reference to complement and elaborate the existing approaches using the Gauss–Legendre quadrature or other standard methods of numerical integration.     

藏北高原D110点土壤温度的极值分析

通过藏北高原Ｄ１１０点一年中不同深度的日最高值、日最低值及日温差的分析,表明从０ｃｍ￣４０ｃｍ,土壤温度的日最高值的变化剧烈,而日最低值的变化则相对平稳,冬半年土壤温度的日最低值、日最高值比较接近,日温差较小,而且它们随时间的变化比较平稳;但夏半年（５￣９月）波动较冬半年的大,且最高温的波动要比最低温的波动大得多;随深度的增加日温差减小,在８０ｃｍ深处已基本上看不到日温差的变化。     

Fast Procedure Solving Universal Kepler's Equation

We developed a procedure to solve a modification of the standard form of the universal Kepler’s equation, which is expressed as a nondimensional equation with respect to a nondimensional variable. After reducing the domain of the variable and the argument by using the symmetry and the periodicity of the equation, the method first separates the case where the solution is so small that it is given an inverted series. Second, it separates the cases where the elliptic, parabolic, or hyperbolic standard forms of Kepler’s equation are suitable. Here the separation is done by judging whether detouring these nonuniversal equations will cause a 1-bit loss of information to their nonuniversal solutions or not. Then the nonuniversal equations are solved by the author’s procedures to solve the elliptic Kepler’s equation (Fukushima, 1997a), Barker’s equation (Fukushima, 1998), and the hyperbolic Kepler’s equation (Fukushima, 1997b), respectively. And their nonuniversal solutions are transformed back to the solution of the universal equation. For the rest of the case, we obtain an approximate solution by solving roughly the approximated cubic equation as we did in solving Barker’s equation. Then the correction to the approximate solution is obtained by Halley’s method precisely. There the special function appeared in the universal equation is rewritten into a combination of similar special functions of small arguments, so that they are efficiently evaluated by their Taylor series. Numerical measurements showed that, in the case of Intel Pentium II processor, the new method is 10–25 times as fast as Shepperd’s method (Shepperd, 1985) and 7–13 times as fast as the standard Newton method. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Anomalous winter climate conditions in the Pacific rim during recent El Niño Modoki and El Niño events

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.     

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).