A Method Solving Kepler’s Equation for Hyperbolic Case

We developed a method to solve Keplers equation for the hyperboliccase. The solution interval is separated into three regions; F 1, F 1, F 1. For the region F is large, we transformed the variablefrom F to exp F and applied the Newton method to the transformed equation.For the region F is small, we expanded the equation with respect to F andapplied the Newton method to the approximated equations. For the middleregion, we adopted a discretization of the Newton method and used the Taylorseries expansion for the evaluation of transcendental functions (Fukushima,1997). Numerical measurements showed that, in the case of Intel Pentiumprocessor, the new method is more than 3.7 times as fast as the combinationof a fourth order correction formula (Fukushima, 1997) and Roysstarting procedure (Roy, 1988) and others.     

Expansions of elliptic motion based on elliptic function theory

New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k ²)^1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia     

Groundwater age rejuvenation caused by excessive urban pumping in Jakarta area,Indonesia

Rapid urbanization in the Jakarta area has become a severe subsurface environmental issue as it entails groundwater level decline and land subsidence caused by excessive groundwater pumping. In this study, apparent groundwater age rejuvenation in the deep aquifer under DKI Jakarta was found by comparing ¹⁴C activities between 1985 and 2008. We discussed the use of a numerical groundwater flow model to evaluate the rejuvenation process in this urbanized area. When considering the deep aquifer in the DKI Jakarta area, we can assume six direction fluxes toward the aquifer: two vertical fluxes (downward and upward flux) and four horizontal fluxes (northern, southern, western, and eastern flux). Results of model calculations show that the greatest groundwater flux among six flux directions became ‘vertical downward flux’, which means that shallower groundwater intrudes into the deep one because of excessive groundwater pumping from the mid‐1980s. This flux grows about 50% during the 2000s. This result is consistent with the detection of CFC‐12 and SF₆, which functions as an indicator of young groundwater even in the deep groundwater. The rejuvenation ratio ‘R’ was determined using ¹⁴C activity in the groundwater; R increases with the CFC‐12 concentration and both show good correlation. Furthermore, we estimated the ‘vertical downward flux’ at each well's screen depth using model estimation. Results show that this flux is greater in the urban groundwater depression area and especially at shallower parts of the deep aquifer, and that it affects the magnitude of the shallow groundwater intrusion. Copyright © 2012 John Wiley & Sons, Ltd.     

Large-scale landslides in Toyama Prefecture,central Japan,and their probable relationship with earthquakes

Large-scale landslides along the Kubusu and Besso rivers in Toyama Prefecture are developed in the Miocene Iwaine Formation, which is composed of andesitic lava, tuff, and tuff breccia. In the middle member of this formation, the tuff is easily altered to montmorillonite-bearing rock, and subsequently plays an important role in the development of landslides events, which tend to be large-scale events, as the massive lava of the upper member forms a cap rock over the tuff. The Kiritani and Koinami basins, which are flat intermontane basins located along the Kubusu and Besso rivers, respectively, are interpreted as landslide-dammed lakes, later filled with sediment. Accelerator mass spectrometry ¹⁴C ages show that the landslides forming each dam occurred simultaneously, at approximately 2500 BP. These ages were measured from wood fragments embedded in the landslide material of Kiritani, and from an in situ stump drowned during the impoundment of Koinami. If the trigger of these landslides was an earthquake, it is most likely to have been the penultimate event along the Atotsugawa fault zone.     

Determination of regional net radiation and soil heat flux over a heterogeneous landscape of the Tibetan Plateau

This paper explores the potential for documenting regional fields of surface energy fluxes over the Tibetan plateau using published algorithms and previously calibrated empirical formulae with data from NOAA‐14 AVHRR and atmospheric data collected during the GAME‐Tibet field experiment. Comparison with observations at three field sites suggests errors in the resulting estimates are less than 10% in the clear sky conditions necessary for application of this approach. Because of the need for clear skies, it was only possible to calculate the desired regional fields for one satellite scene during the 5 month study period. Maps of surface energy fluxes, and frequency analyses of these maps, are presented for this scene. The need for an alternative, more consistently applicable, satellite‐based method to map surface energy fields is highlighted. Copyright © 2002 John Wiley & Sons, Ltd.     

Reference systems

A reference system is a relation connecting observables and their mathematical represententions. The principle of general relativity assures that any sort of coordinate system can be used to describe physical phenomena. Thus, any reference system is only a convention, There is no absolutely true reference system. Instead, people seek for a best reference system, whose meaning may differ thus need to clarify, Taking an example from Earth rotation, we discuss how to find such a best reference system. The definition of the best system will change as scientific understandings deepen and computational environments develop. Therefore, we can not stop improving reference systems. However, when replacing an existing widely-spread system, one must take great care to minimize the inconvenience caused by its transition, especially the inconvenience which users might endure. The Standards Of Fundamental Astronomy (SOFA) project being conducted by the IAU WG on Astronomical Standards has the opportunity to ease this troublesome task. The World Wide Web (WWW) will be a main device to realize the project, namely to provide working standards including reference systems to the world.     

Origin of near-surface high-salinity water observed in the Kuroshio Extension region

Hydrographic data in the Kuroshio Extension (KE) region from 2008 to 2010 show large year-to-year variability in near-surface salinity, including a very large anomalous event in February 2010. During this event, the deep winter mixed layer in the southern KE region had higher salinity than had existed during the previous summer in September 2009. Our analysis shows that advection from the Philippine Sea along the western branch of the North Pacific subtropical gyre, taking approximately 9 months, resulted in this large salinity anomaly in February 2010 and contributes to the interannual salinity variability in the southern KE region.     

The self-organizing map,a new approach to apprehend the Madden–Julian Oscillation influence on the intraseasonal variability of rainfall in the southern African region

The Madden–Julian Oscillation (MJO) is the major mode of intraseasonal variability (30–60 days) in the tropics, having large rainfall impacts globally, and possibly on southern Africa. However, the latter impact is not well understood and needs to be further explored. The life cycle of the MJO, known to be asymmetric, has been nevertheless analyzed usually through methods constrained by both linearity and orthogonality, such as empirical orthogonal function analysis. Here we explore a non-linear classification method, the self-organizing map (SOM), a type of artificial neural network used to produce a low-dimensional representation of high-dimensional datasets, to capture more accurately the life cycle of the MJO and its global impacts. The classification is applied on intraseasonal anomalies of outgoing longwave radiation within the tropical region over the 1980–2009 period. Using the SOM to describe the MJO is a new approach, complimentary to the usual real-time multivariate MJO index. It efficiently captures this propagative phenomenon and its seasonality, and is shown to provide additional temporal and spatial information on MJO activity. For each node, the subtropical convection is analyzed, with a particular focus on the southern Africa region. Results show that the convection activity over the central tropical Indian Ocean is a key factor influencing the intraseasonal convective activity over the southern African region. Enhanced (suppressed) convection over the central Indian Ocean tends to suppress (enhance) convection over the southern African region with a 10-day lag by modulating the moisture transport.     

Successive formation of planetary lenses in an intermediate layer

Abstract

We study the formation of lenses of the ocean's intermediate water using a 2.5-layerβ-plane primitive equation model with localized injection of water mass. For the injecting rate of 1.0 Sv, we have observed that strong vortices are shed regularly. These vortices propagate westward much faster than the second baroclinic long Rossby wave. They are totally isolated from each other and show strong baroclinicity as well. Moreover, they remain stable over a sufficiently long period of time. Regular formation of such strong vortices in the intermediate layer has not been reported previously. The translation speed is explained using the Euler's momentum integral theorem for the nonlinear baroclinic vortex on the β-plane. We have demonstrated that coupling between the primary motion in the intermediate layer and the secondary motion in the upper layer with a meridional shift is crucial to the fast westward translation of the intense vortices. A simple dispersion formula relating the zonal translation speed with the vortex radius is also derived under the assumption of quasi-geostrophy. It has turned out that the analytical relation explains the numerical results surprisingly well despite the limitation of its derivation.