Modelling the pole tide and its effect on the Earth's rotation

Summary. The pole tide is the response of the ocean to incremental centrifugal forces associated with the Chandler wobble. The tide has a potentially important effect on the period and damping of the wobble, but it is at present not well constrained by observations. Here, we construct both analytical and numerical models for the pole tide. The analytical models consider the tide first in a global ocean and then in an enclosed basin on a beta-plane. The results are found to approach equilibrium linearly with decreasing frequency and inversely with increasing basin depth. The numerical models solve Laplace's tidal equations over the world's oceans using realistic continental boundaries and bottom topography. The results indicate that the effects of the non-equilibrium portion of the deep ocean tide on the Chandler wobble period and damping are negligible.     

Self-consistent equilibrium ocean tides

Summary. We compute the static response of the world ocean to an external zonal gravitational potential. The computation includes the effects of the self-attraction of the ocean, and the yielding of the Earth caused both by the external potential and the change in ocean load. We compare the computed tide with measurements of the fortnightly and monthly ocean tides. The short-wavelength departures from equilibrium found by Wunsch are still present. An average of observations at Pacific islands shows that the fortnightly tide departs significantly from equilibrium but the monthly may not. We have also calculated the effects of our computed tide on measurements of tidal gravity and tidal fluctuations in the length of day. Existing tidal gravity data are too imprecise to enable us to determine whether or not the spatial average of the ocean tides departs from equilibrium. The length of day data suggest that the monthly tide is farther from equilibrium than the fortnightly. We have not been able to resolve the apparent discrepancy between the length of day and ocean tide data.     

Wind stress forcing of the North Sea 'pole tide'

We conduct numerical simulations of the wind forcing of sea level variations in the North Sea using a barotropic ocean model with realistic geography and bathymetry to examine the forcing of the 14 month 'pole tide', which is known to be anomalously large along the Denmark–Netherlands coast. The simulation input is the monthly mean surface wind stress field from the National Centers for Environmental Prediction (NCEP) reanalysis for the 40 year period 1958–1997. The ocean model output sea level response is then compared with 10 coastal tide gauge records from the Permanent Service for Mean Sea Level (PSMSL) over the same period of time. Besides the strong seasonal variations, several prominent quasi-periodicities exist near 7 years, 3 years, 14 months, 9 months and 6.5 months. Correlations and spectral analyses show remarkable agreement between the model output and the observations, particularly in the 14 month, or Chandler, period band. The latter indicates that the enhanced pole tide found in the North Sea along the Denmark–Netherlands coast is actually the coastal set-up response to wind stress forcing with a periodicity of around 14 months. We find no need to invoke a geophysical explanation involving resonance enhancement of the pole tide in the North Sea to explain the observations.     

The effect of polar wander on the tides of a hemispherical ocean

Summary. A numerical model is constructed of the tides in a hemispherical ocean driven by the forces corresponding to the Y₂^–2 equilibrium tide. The model is used to study how tidal dissipation is affected by changes in the position of the ocean relative to the Earth's rotational axis and to test a hypothesis concerning the Gerstenkorn event.
As the position of the Earth's axis is varied with respect to the ocean, the model shows changes in the dissipation rate due to the changing position and importance of individual resonances of the ocean. However, a cooperative effect is also observed which results, for an ocean of depth 4400 m, in broad frequency bands near 10 rad day⁻¹ and-6 rad day⁻¹ in which the dissipation rate remains high.
The cooperative effect is found to arise from the existence, in an unbounded ocean, of resonances at these frequencies which match the tidal forces. When ocean boundaries are introduced, the new resonances near these frequencies contain a large component of the underlying resonance and as a result are themselves a good match to the driving forces.
For the real ocean, these findings imply that changes in the position of the pole, and also possibly changes in the shape of the ocean, will on average have little effect on the energy dissipated by the tides. However in the past changes in the mean depth and area of the ocean or the increased rotation rate of the Earth may have resulted in a smaller dissipation rate.     

Extraction of the M2 ocean tide from SEASAT altimeter data

Summary. Three complementary methods for the extraction of the M2 ocean tide using SEASAT altimetry are presented and compared. The first method (that developed by Cartwright & Alcock), which provides 'point measurements'of the tide at the crossovers of the SEASAT repeat orbit ground track, has been applied to a study of the tide in tropical ocean areas. The other two methods involve spatial expansions of M2 in terms of either surface spherical harmonics (in the case of the method developed by Mazzega) or Platzman normal modes of the world ocean. The results obtained by each method from only one month of SEASAT data reproduce many features of the tide represented in recent tidal models, and promise well for satellite altimetry as a future source of tidal knowledge.     

On azimuthal eigenwavenumbers associated with Laplace's tidal equations

Laplace's tidal equations for the case of an ocean of constant depth bounded by meridians were considered by two authors at a specific frequency as an eigenvalue problem in the azimuthal wavenumber. A finite spectrum of eigenwavenumbers was found. That eigenvalue problem is re-examined by means of asymptotic techniques and numerical integration of the governing equation of the problem. At low frequencies a formula connecting the frequency and the number of eigensolutions is established. It is shown that at a given frequency the spectrum of eigenwavenumbers is wider than that reported, but (for this type of solution) the meridional boundary conditions are satisfied approximately only for the case of very low frequencies.     

Tidal gravity and ocean tide loading in Europe

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The results are presented from tidal gravity measurements at five sites in Europe using LaCoste and Romberg ET gravimeters. Improvements that we have made to the accuracies of these gravimeters are discussed. It is shown that the 'standard' calibration of the International Center for Earth Tides, used for worldwide tidal gravity profiles, is 1.2 per cent too high. The M₂ and O₁ observations are compared with model calculations of the Earth's body tide and ocean tide loading and it is shown that there is a very significant improvement in the agreement between observations and models compared to that obtained with previous tidal gravity measurements. For O₁, where the ocean tide loading and attraction in central Europe is only 0.4 per cent of the body tide, our measurements verify that the Dehant-Wahr anelastic body tide model gravimetric factor is accurate to 0.2 per cent. It is also shown that the effects of lateral heterogeneities in Earth structure on tidal gravity are too small to explain the large anomalies in previously published tidal gravity amplitudes. The observations clearly show the importance of conserving tidal mass in the Schwiderski ocean tide model. For sites in central Europe, the M₂ and O₁ observations and the models are in agreement at the 0.1 μgal (10⁻⁹ m s⁻²) level and tidal corrections to this accuracy can now be made to absolute gravity measurements.     

New aspects of the equilibrium pole tide

Summary. We have developed a new spherical harmonic algorithm for the calculation of the loading and self-gravitating equilibrium pole tide. Based on a suggestion of Dahlen, this approach minimizes the distortions in tide height caused by an incomplete representation of the ocean function. With slight modification our approach easily could be used to compute self-gravitating and loading luni-solar tides as well.
Using our algorithm we have compared the static pole tide with tide observations at a variety of locations around the world. We find statistically significant evidence for pole tide enhancements in mid-ocean as well as the shallow seas.
We have also re-investigated the effect of the static tide on the Chandler wobble period. The difference between the wobble period of an oceanless, elastic earth with a fluid core (Smith & Dahlen) and the period of an earth minus static oceans yields a 7.4-day discrepancy. We conclude from tide observations that much of the discrepancy can probably be accounted for by non-equilibrium pole tide behaviour in the deep oceans.     

The tidal signals extraction from GPS data on the Amery Ice Shelf, Antarctica

Tidal motion is the source of short-term vertical motion that an ice shelf experiences, and hence has a significant impact on ice shelves. During the 2003/2004 Austral summer season, five days of GPS measurements were carried out on the front of the Amery Ice Shelf （AIS）, East Antarctica, by the 20th Chinese National Antarctica Research Expedition （CHINARE）. The GPS data was processed using GAMIT/GLOBK software with 2-hour static data segment and the vertical precision is less than 0.18 m. To verify our results for the vertical component, we compare the ice shelf GPS tidal signal with a tidal result derived from tide gauge measurements at China＇s Zhongshan Station on Antarctica. Comparison of the GPS results with the tide gauge were in good agreement in amplitude at the few cm level, which indicates that the tide under the front of Amery Ice Shelf is irregular semidiurnal tide, the maximal tidal differences is approximately 2 m. GPS data can be used to validate the ocean tide model around the Antarctic area and such studies are important to improve our knowledge of the Antarctic ice shelf mass balance and dynamical models of ice sheet/ocean interaction.     

Tidal gravity in Britain: tidal loading and the spatial distribution of the marine tide

Summary. Tidal gravity measurements have been made at six sites in Britain with two nulled LaCoste and Romberg Earth tide gravitymeters. The M ₂ observations from these and two further sites are compared with calculations of the tidal loading from the seas around the British Isles and the major oceans. Models of the M ₂ marine tides are convolved with Green's functions for appropriate radially stratified Earth models. The differences between the M ₂ observations and the theoretical calculations are less than 0.6 μ gals and it is shown that these differences contain further information concerning the errors in the marine tide models. The M ₂ marine tides on the north-west European continental shelf are reasonably well known and this allows a useful test of the feasibility of using tidal gravity measurements for the inverse ocean tide problem in areas where the ocean tides are less well known. The differential gravity loading signal between pairs of gravity stations is shown to be important for considerations of the uniqueness and accuracy of the inverse problem. M ₂ tidal gravity loading maps for the British Isles and Europe have been produced which are of use in making corrections to various geodetic measurements.     

南极绕极流研究进展综述

南极绕极流是自西向东横贯太平洋、大西洋和印度洋的全球性环流,也是世界上唯一一支和地球上所有其他洋流都有关联的洋流。尽管对南极绕极流的观测和研究历史相对较短,但是对其特征、变化和机制的研究已取得了许多重要进展,对其在全球变化中的作用的研究也日益深入。南极绕极流成为海洋和大气科学领域的前沿研究内容。以绕极流锋面分布、流速特征、纬向输运、经向输运及其响应的动力机制为重点,总结了过去数十年里对绕极流观测和理论的研究结果,明确了研究中仍然薄弱的环节,并提出了相应的工作建议,以促进我国关于南极绕极流及相关海洋和大气过程的研究。     

COMPARISONS BETWEEN ZONAL AND MERIDIONAL EDDY SENSIBLE HEAT TRANSPORT IN THE NORTHERN HEMISPHERE WINTER

The size and geographical distribution of the zonal eddy sensible heat flux and its divergence in the Northern Hemisphere winter are examined. Special attention is paid to the zonal eddy contribution to the total heat transport and the relationship between the zonal and meridional heat transport. The heat fluxes are calculated using 700mb air temperatures and geostrophic winds spanning the period 1947–1987. The zonal fluxes are much larger than the meridional fluxes, particularly in the regions of strongest flux. The sign and strength of the zonal flux are largely controlled by the direction and strength of the meridional transport. Zonal eddy transfer appears to be as important a source of energy as the meridional eddy transfer, particularly over North America and Siberia. Changes in atmospheric circulation strengths may be interpreted in terms of energy flux divergence to establish links with temperature changes. [Key words: sensible heat flux, zonal heat flux, meridional heat flux, energy flux divergence].     

新疆地区25 a地面风场特征分析

 地面风除了受大范围环流影响外,还受地形影响较大。新疆既有大的盆地,又有高山垭口,造就了特殊的新疆地面风场。利用新疆54个气象站1980—2004年,每日4个时次的地面风资料,分析了该地区地面风场的长期特征,并进行经验正交函数分解。研究表明,新疆长期地面风场北疆、东疆和南疆有显著差别,主要表现在风向的转变,即北疆总体表现为西北风,南疆表现为偏东风,东疆表现为由西北风向偏东风转换的反气旋性弯曲气流;新疆经向风的长期变化表现为南风距平加强,而纬向风则表现为东风距平加强;经向风在整个时间序列上有3~5 a的短期变化,而纬向风在整个时间序列上有3~6 a的短期变化,且都表现为随时间延续周期变长;经向风南风距平增大趋势的最大值发生在七角井,而北风距平增大趋势的最大值则在阿拉山口。纬向风西风距平增大趋势的最大值在七角井,东风距平增大趋势的最大值位于安德河;EOF分析表明,第一特征向量的贡献达到87.5％,而第一特征向量对应的时间系数的距平值以1987年和1999年为界,表现为“正负正”的趋势。     

Solar Prediction of Climatic Change

In their broad synoptic features the basic hemispheric patterns of climate, on which the patterns of climatic change depend, fall into two distinctive categories, the zonal and meridional. Distinctive synoptic features of the primary zonal patterns are first described. Then statistically significant relationships are examined between the temporal changes in these patterns and the long secular cycles of sunspot and related variable solar activity. It is these relationships that lend them selves to the statistical prediction of long-term climatic trends. Possible physical linkage between disturbing solar impulses and atmospheric response is suggested. A significant relationship between zonal climatic patterns and shorter term (22 years) double sunspot cycles is noted. Distinctive syn optic features of the primary meridional patterns of climate and climatic change are then described. They are of short duration and relate significantly only to double sunspot (DSS) and shorter cycles, notably at higher latitudes and during the winter season. They are apparently responsive to solar corpuscular (solar wind) impulses in contrast to the apparent response of the zonal long-term trend patterns of change to solar electromagnetic (radiational) changes. The research approach best suited to investigate the physical mechanism of solar-climatic linkage is discussed as a necessary basis for the development of effective models for the solar prediction of climatic change.     

Meteorological excitation of the annual polar motion

Summary. Numerous studies have indicated that the annual term in the polar motion cannot be explained in any detail by meteorological/hydrological excitation and no reasonable alternative excitations have been put forward. Part of the problem has been that the hydrostatic adjustment of the oceans to the atmospheric pressure changes has traditionally been computed using the inverse barometer approach. This approach does not properly model the gravitational interaction between the atmosphere and oceans, and the inverse barometer theory is modified in this paper to account for this properly. The information necessary to compute the ocean tide and polar excitation caused by any change in the atmospheric pressure pattern is presented. The results of the application of this theory to two global atmospheric pressure data sets are examined and compared to results of other workers.
It is concluded that the atmosphere is observed well enough to answer the question of the annual excitation of polar motion and it is argued that the ground water excitation is the component with the largest error and remains the chief obstacle to the successful solution of this problem.     

Temporal variations of tides on the west coast of Great Britain

Summary. Temporal variations of tides are investigated by analysing tidal observations from five ports on the west coast of Great Britain. Variations considered here are those occurring in the semi-diurnal species daily, in the tidal constituents resolved from analyses of 29 day sets over a period of two years, 1980–81, and in the tidal constituents resolved from 1 yr sets over a period of 19 yr. The time variations of tidal constituents are mainly due to inseparable terms grouping with the principal term due to the short length of data and the insufficiency of the procedures to account for them. Surges and surge-tide interaction are affecting the resolution of tides. Time variations of constituents of the diurnal species induced by non-tidal forces are spatially consistent. The use of equilibrium relationships to account for modulations of principal constituents by waves separable in an 18.61 yr nodal cycle improves the analysis. However, the modulation is smaller in the real tide than in the equilibrium tide. When the application of this principle is extended to a wider frequency band to cover constituents which cannot be resolved from one month of observations, it may produce the opposite effect. These problems start compounding with decreasing length of data, i.e. increasing band width of resolution.
Functional approximations of interaction coefficients (bi-admittance) of non-linear tides, similar to the response (admittance) of linear tides are computed for semi-diurnal, fourth-diurnal and sixth-diurnal bands. These functional estimates may be used to interpolate unseparable constituents to improve the quality of analyses. The results are consistent with the fact that the response of the sea does not change in a narrow frequency band covering a nodal cycle of the Moon. The change in the equilibrium relationship between the principal term and its nodal term can be interpreted in terms of the damping effect of bottom friction.     

近50年东北地区生态地理界线的代际变化

以吉良(Kira)的热量指数(温暖指数WI和寒冷指数CI)和徐文铎的湿度指数HI为指标,以10 a为尺度定量研究1961~2007年东北地区4条主要生态地理界线变化。在此基础上分析东北地区生态地理界线变化对气候变化的响应。结果表明:东北地区1961 ~ 2007年整体上纬向生态地理界线向高纬(垂直带向上)移动,经向生态地理界线向东移动,但阶段性上表现出波动性移动。东北地区生态地理区域界线从整体上位置、移动速度的变化和阶段性位置、移动速度的变化都很好响应气候变化。它们对水热等生态气候基本要素十分敏感。     

地-气耦合气候动力系统的解析研究

ENSO事件是影响全球气候表象大尺度的海洋-大气耦合系统,其规律和预防的研究,为当前国际学术界关注的对象。非线性摄动理论和方法在国际学术界研究中是十分热门的。许多学者做了一类常微分方程非线性奇摄动边值问题, 反应扩散问题, 椭圆型边值问题,双曲型初始边值问题,非线性方程奇摄动问题的冲击层解等。文章讨论一类大气物理中海-气现象的ENSO模型,在一定条件下,利用摄动理论和方法较简捷得到相应非线性问题解组的任意次近似的渐近展开式。     

Tidal deformation of a viscoelastic body

Summary. The tidal deformation of a homogeneous viscoelastic sphere due to the gravitational attraction of an external body is calculated. The sphere is modelled as an incompressible Kelvin-Voigt solid. An equation for the displacement field is obtained assuming that strains are small and inertia is negligible. This equation has a series solution in terms of Legendre polynomials. The resulting expression for the displacement field reduces to that for an elastic solid and a viscous fluid in the appropriate limits of the material constants. The first term in the viscoelastic solution is used to calculate the moments induced by tidal deformation assuming a circular orbit. In the absence of obliquity and precession, these moments reduced to a torque about the spin axis. This torque is compared to that predicted by a phase lag analysis. These two approaches are formally equivalent if the tidal dissipation function Q ⁻¹ depends in a specific way on the difference of the spin and orbital angular velocities.