Secular tidal changes in lunar orbit and Earth rotation

Small tidal forces in the Earth–Moon system cause detectable changes in the orbit. Tidal energy dissipation causes secular rates in the lunar mean motion n, semimajor axis a, and eccentricity e. Terrestrial dissipation causes most of the tidal change in n and a, but lunar dissipation decreases eccentricity rate. Terrestrial tidal dissipation also slows the rotation of the Earth and increases obliquity. A tidal acceleration model is used for integration of the lunar orbit. Analysis of lunar laser ranging (LLR) data provides two or three terrestrial and two lunar dissipation parameters. Additional parameters come from geophysical knowledge of terrestrial tides. When those parameters are converted to secular rates for orbit elements, one obtains dn/dt = \(-25.97\pm 0.05 ''/\)cent\(^{2}\), da/dt = 38.30 ± 0.08 mm/year, and di/dt = ?0.5 ± 0.1 \(\upmu \)as/year. Solving for two terrestrial time delays and an extra de/dt from unspecified causes gives \(\sim \) \(3\times 10^{-12}\)/year for the latter; solving for three LLR tidal time delays without the extra de/dt gives a larger phase lag of the N2 tide so that total de/dt = \((1.50 \pm 0.10)\times 10^{-11}\)/year. For total dn/dt, there is \(\le \)1 % difference between geophysical models of average tidal dissipation in oceans and solid Earth and LLR results, and most of that difference comes from diurnal tides. The geophysical model predicts that tidal deceleration of Earth rotation is \(-1316 ''\)/cent\(^{2}\) or 87.5 s/cent\(^{2}\) for UT1-AT, a 2.395 ms/cent increase in the length of day, and an obliquity rate of 9 \(\upmu \)as/year. For evolution during past times of slow recession, the eccentricity rate can be negative.     

Line-of-Sight Anisotropies in the Cosmic Dawn and Epoch of Reionization 21-cm Power Spectrum

The line-of-sight direction in the redshifted 21-cm signal coming from the cosmic dawn and the epoch of reionization is quite unique in many ways compared to any other cosmological signal. Different unique effects, such as the evolution history of the signal, non-linear peculiar velocities of the matter etc. will imprint their signature along the line-of-sight axis of the observed signal. One of the major goals of the future SKA-LOW radio interferometer is to observe the cosmic dawn and the epoch of reionization through this 21-cm signal. It is thus important to understand how these various effects affect the signal for its actual detection and proper interpretation. For more than one and half decades, various groups in India have been actively trying to understand and quantify the different line-of-sight effects that are present in this signal through analytical models and simulations. In many ways the importance of this sub-field under 21-cm cosmology have been identified, highlighted and pushed forward by the Indian community. In this article, we briefly describe their contribution and implication of these effects in the context of the future surveys of the cosmic dawn and the epoch of reionization that will be conducted by the SKA-LOW.     

Splendid isolation: local uniqueness of the centered co-circular relative equilibria in the <Emphasis Type="Italic">N</Emphasis>-body problem

We study the neighborhood of the equal mass regular polygon relative equilibria in the N-body probem, and show that this relative equilibirum is isolated among the co-circular configurations (in which each point lies on a common circle) for which the center of mass is located at the center of the common circle. It is also isolated in the sense that a sufficiently small mass cannot be added to the common circle to form a \(N+1\)-body relative equilibrium. These results provide strong evidence for a conjecture that the equal mass regular polygon is the only co-circular relative equilibrium with its center of mass located at the center of the common circle.     

The equations of relative motion in the orbital reference frame

The analysis of relative motion of two spacecraft in Earth-bound orbits is usually carried out on the basis of simplifying assumptions. In particular, the reference spacecraft is assumed to follow a circular orbit, in which case the equations of relative motion are governed by the well-known Hill–Clohessy–Wiltshire equations. Circular motion is not, however, a solution when the Earth’s flattening is accounted for, except for equatorial orbits, where in any case the acceleration term is not Newtonian. Several attempts have been made to account for the \(J_2\) effects, either by ingeniously taking advantage of their differential effects, or by cleverly introducing ad-hoc terms in the equations of motion on the basis of geometrical analysis of the \(J_2\) perturbing effects. Analysis of relative motion about an unperturbed elliptical orbit is the next step in complexity. Relative motion about a \(J_2\)-perturbed elliptic reference trajectory is clearly a challenging problem, which has received little attention. All these problems are based on either the Hill–Clohessy–Wiltshire equations for circular reference motion, or the de Vries/Tschauner–Hempel equations for elliptical reference motion, which are both approximate versions of the exact equations of relative motion. The main difference between the exact and approximate forms of these equations consists in the expression for the angular velocity and the angular acceleration of the rotating reference frame with respect to an inertial reference frame. The rotating reference frame is invariably taken as the local orbital frame, i.e., the RTN frame generated by the radial, the transverse, and the normal directions along the primary spacecraft orbit. Some authors have tried to account for the non-constant nature of the angular velocity vector, but have limited their correction to a mean motion value consistent with the \(J_2\) perturbation terms. However, the angular velocity vector is also affected in direction, which causes precession of the node and the argument of perigee, i.e., of the entire orbital plane. Here we provide a derivation of the exact equations of relative motion by expressing the angular velocity of the RTN frame in terms of the state vector of the reference spacecraft. As such, these equations are completely general, in the sense that the orbit of the reference spacecraft need only be known through its ephemeris, and therefore subject to any force field whatever. It is also shown that these equations reduce to either the Hill–Clohessy–Wiltshire, or the Tschauner–Hempel equations, depending on the level of approximation. The explicit form of the equations of relative motion with respect to a \(J_2\)-perturbed reference orbit is also introduced.     

Uncertainty propagation in orbital mechanics via tensor decomposition

Uncertainty forecasting in orbital mechanics is an essential but difficult task, primarily because the underlying Fokker–Planck equation (FPE) is defined on a relatively high dimensional (6-D) state–space and is driven by the nonlinear perturbed Keplerian dynamics. In addition, an enormously large solution domain is required for numerical solution of this FPE (e.g. encompassing the entire orbit in the \(x-y-z\) subspace), of which the state probability density function (pdf) occupies a tiny fraction at any given time. This coupling of large size, high dimensionality and nonlinearity makes for a formidable computational task, and has caused the FPE for orbital uncertainty propagation to remain an unsolved problem. To the best of the authors’ knowledge, this paper presents the first successful direct solution of the FPE for perturbed Keplerian mechanics. To tackle the dimensionality issue, the time-varying state pdf is approximated in the CANDECOMP/PARAFAC decomposition tensor form where all the six spatial dimensions as well as the time dimension are separated from one other. The pdf approximation for all times is obtained simultaneously via the alternating least squares algorithm. Chebyshev spectral differentiation is employed for discretization on account of its spectral (“super-fast”) convergence rate. To facilitate the tensor decomposition and control the solution domain size, system dynamics is expressed using spherical coordinates in a noninertial reference frame. Numerical results obtained on a regular personal computer are compared with Monte Carlo simulations.     

Study of the Cosmic-Ray Modulation During the Passage of ICMEs and CIRs

We compare the cosmic-ray response to interplanetary coronal mass ejections (ICMEs) and corotating interaction regions (CIRs) during their passage in near-Earth space. We study the relative importance of various structures/features identified during the passage of the ICMEs and CIRs observed during Cycle 23 (1995?–?2009). The identified ICME structures are the shock front, the sheath, and the CME ejecta. We isolate the shock arrival time, the passage of the sheath region, the arrival of ejecta, and the end time of their passage. Similarly, we isolate the CIR arrival, the associated forward shock, the stream interface, and the reverse shock during the passage of a CIR. For the cosmic-ray intensity, we utilize the data from high counting rate neutron monitors. In addition to neutron monitor data, we utilize near-simultaneous and same time-resolution data of interplanetary plasma and field, namely the solar-wind velocity, the interplanetary magnetic field (IMF) vector, and its variance. Further, we also utilize some derived interplanetary parameters. We apply the method of the superposed-epoch analysis. As the plasma and field properties are different during the passage of different structures, both in ICMEs and CIRs, we systematically vary the epoch time in our superposed-epoch analysis one by one. In this way, we study the role and effects of each of the identified individual structures/features during the passage of the ICMEs and CIRs. Relating the properties of various structures and the corresponding variations in plasma and field parameters with changes of the cosmic-ray intensity, we identify the relative importance of the plasma/field parameters in influencing the amplitude and time profiles of the cosmic-ray intensity variations during the passage of the ICMEs and CIRs.     

中高纬度大气低频模态研究进展

大气低频模态是导致中高纬地区季节及气候变化的主要因素,加强低频模态动力机制的认识对于提高短期气候预测水平具有十分重要的科研意义和应用价值。由于中高纬大气低频环流本身的复杂性,关于其动力机制的研究仍然是大气动力学中重点难点问题。本文简单回顾了激发维持低频模态的前两种机制,即:外源强迫、气流的纬向非均匀性对大气低频模态的影响。从观测事实和模式结果出发,着重介绍了瞬变波与基本气流相互作用激发维持低频模态的第三种机制,且详细阐述了线性假设条件下,瞬变波与基本气流相互作用的动力机制。本文最后针对瞬变波与基本气流相互作用研究中一些尚未解决的问题进行了讨论。     

华东地区月平均气温统计降尺度方法比较

用中国地面气象观测站的逐日气温观测资料和NCEP/NCAR再分析资料,分别使用基于多元线性回归(MLR)和3种主成分分析(PCA)的统计降尺度方法,对1959-2008年的华东地区的月平均气温分两个时段进行统计降尺度分析并加以检验,比较了不同降尺度方法的结果。结果表明:对于华东地区气温的统计降尺度预报,基于MLR的统计降尺度方法相对于3种PCA方法而言,对单站年际变化模拟方面有一定优势。PCA方法应用于统计降尺度时,预报因子的区域选择是影响统计降尺度结果的重要因素之一。对于温度进行统计降尺度分析时,预报因子中包含温度因子是非常必要的;所试验的4种降尺度方法,对各站点多年平均情况的模拟要好于对区域平均的年际变化的模拟。     

太阳活动变化对东亚冬季气候的非对称影响及可能机制

基于1959～2013年的观测和再分析资料以及10.7 cm(2800 MHz)太阳射电通量资料, 本文分析了太阳活动变化与东亚冬季气候的相关关系, 分析结果表明:太阳活动变化与东亚冬季大气环流有较好的相关性, 且在太阳活动的强、弱时期该相关关系存在很大差异, 在强太阳活动时期太阳活动变化与东亚冬季气候的联系更为显著, 而在弱太阳活动时期二者之间的直接联系微弱, 这表明太阳活动变化对东亚冬季气候的影响具有非对称性特征。在太阳活动较强的时期, 随着太阳活动的增强, 东亚中高纬对流层中层的大气环流倾向纬向型, 东亚大槽减弱, 850 hPa出现异常偏南风, 地面上西伯利亚高压以及冬季风减弱, 东亚大部分地区气温显著偏高;而在太阳活动较弱的时期, 太阳活动的年际差异与东亚冬季大气环流之间几乎不存在显著联系。分析太阳活动较强和较弱时期纬向平均纬向风的差异发现, 其间平流层行星波活动、热带西北太平洋海表温度的差异可能是造成这种非对称影响的重要原因。在强太阳活动时期, 平流层行星波在太阳活动的异常增强年有异常的从极地向赤道的水平传播, 高纬地区E-P通量(Eliassen-Palm flux)异常辐散, 导致中高纬西风及北极涛动(AO)增强, 同时热带西北太平洋海温异常偏冷, 海陆热力差异缩小, 大气环流经向度减弱, 东亚冬季风偏弱。     

The Project Siberian High in CMIP5 Models

The Siberian high(SH)experienced a decline from the 1970s to 1990s and a recovery in recent years.The evolution of the SH under global warming is unclear.In this study,41 Coupled Model Intercomparison Project Phase 5(CMIP5)climate models are evaluated in terms of their ability to simulate the temporal evolution of the SH in the 19th and 20th centuries and the spatial pattern of the SH during 1981–2005.The results show that 12models can capture the temporal evolution of the SH center intensity(SHCI)for 1872–2005.The linear correlation coefficient between the SHCI from the Twentieth Century Reanalysis and the simulated SHCI from the multi-model ensemble(MME)of the 12 models is 0.3 on annual and inter-annual scales(above the 99%confidence level).On decadal and multi-decadal time scales,the MME also captures the pronounced reduction(between 1981–2000and 1881–1900 period)and the recovery(during1991–2005)of the SH intensity.Finally,the future evolution of the SH is investigated using the MME of the 12models under the+4.5 and+8.5 W m-2 Representative Concentration Pathway(RCP)scenarios(RCP4.5 and RCP8.5).It is shown that the SHCI,similar to the SHCI in the 20th century,has no significant long-term trend in the 21st century under global warming(RCP8.5 scenario).At the end of 21st century(2081–2100),the SH shows stronger interannual variability than the SH at the end of20th century(1981–2000).The increased interannual variability likely favors the increased interannual variability in winter air temperature over midlatitude Eurasia at the end of 21st century.