Inversion for tides in the Eastern North Pacific Ocean

A regional model of tides in the Eastern North Pacific Ocean is developed through the use of inversion with two-dimensional finite element codes. Since global tide models are least accurate in coastal environments, modeling tides on a regional scale allows tidal propagation and interaction along the coast to be more accurately represented. In this respect, a regional model can act as a liaison between open ocean dynamics and physical processes more pertinent to coastal systems. The region of interest in this study extends from the Aleutian Islands to Southern California and includes deep ocean, continental shelf, and shallow water features. Boundary conditions are determined from nonlinear inversion of harmonic data from both shallow water and deep ocean tide gauges. Spatial patterns of amplitudes and phases from the model are examined for major constituents. Results are also compared to global tide models at selected stations.     

中国大陆精密重力潮汐改正模型

利用理论和实验重力固体潮模型,充分考虑全球海潮和中国近海潮汐的负荷效应,建立了中国大陆的精密重力潮汐改正模型.结果表明,采用不同的固体潮模型会对重力潮汐结果产生相对变化幅度小于0.06％的差异;在沿海地区海潮负荷的影响约为整个潮汐的4％,而中部地区约为1％,其中中国近海潮汐模型的影响约占整个海潮负荷的10%,内插或外推潮波的负荷约占海潮负荷的3％.通过比较实测的重力数据表明,本文给出的重力潮汐改正模型的精度远远优于0.5×10-8 m·s-2,说明了本文构建的模型的实用性,可为中国大陆高精度重力测量提供有效参考和精密的改正模型.     

Ocean tides from satellite altimetry and GRACE

Satellite altimetry and GRACE observations carry both the signature of ocean tides and have in general complementary potential to resolve tidal constituents. It is therefore straightforward to perform a combined estimation of a global ocean tide model based on these two data sources. The present paper develops and applies a three step procedure for generating such a combined ocean tide model. First, the processing of multi-mission altimetry data is described along with the harmonic analysis applied to derive initially a pure empirical ocean tide model. Then the capability of GRACE to sense particular tidal constituents is elaborated and an approach to estimate tidal constituents from GRACE is outlined. In a third step a combination strategy with optimal stochastic data treatment is developed and applied to the altimetry-only tide model EOT08a and four years of GRACE observations, leading to the combined model EOT08ag. The differential contributions of GRACE to EOT08ag remain small and are mainly concentrated to the Arctic Ocean, an area with little or poor altimetry data. In comparison with other tide models, EOT08ag is validated by K-band range residuals, the impact on gravity field modelling and on precise orbit determination and by variance reduction of crossover differences. None of these comparison exhibits a significant improvement over the altimetry-only tide model except for a few areas above 60°N. Overall the improvements of the combination remain small and appear to stay below the current GRACE baseline accuracy.     

武汉台重力潮汐长期观测结果

采用武汉台超导重力仪(SG C032)14年多的长期连续观测资料,研究了固体地球对二阶和三阶引潮力的响应特征,精密测定了重力潮汐参数,系统研究了最新的固体潮模型和海潮模型在中国大陆的有效性.采用最新的8个全球海潮模型计算了海潮负荷效应,从武汉台SG C032的观测中成功分离出63个2阶潮汐波群和15个3阶潮汐波群信号,3阶潮波涵盖了周日、半日和1/3日三个频段.重力潮汐观测的精度非常高,标准偏差达到1.116 nm·s-2,系统反映了非流体静力平衡、非弹性地球对2阶和3阶引潮力的响应特征.结果表明,现有的武汉国际重力潮汐基准在半日频段非常精确,但在周日频段存在比较明显的偏差,需要进一步精化.对于中国大陆的大地测量观测,固体潮可以采用Dehant等考虑地球内部介质非弹性和非流体静力平衡建立的固体潮理论模型或Xu 等基于全球SG观测建立的重力潮汐全球实验模型作为参考和改正模型,海潮负荷效应应该采用Nao99作为改正模型.     

Earth tides observed by gravity and GPS in southeastern Alaska

We analyzed gravity data obtained in Juneau and global positioning system (GPS) data obtained from three PBO sites in southeastern Alaska (SE-AK), which are part of a US research facility called ‘EarthScope’, and we compared the obtained tidal amplitudes and phases with those estimated from the predicted tides including both effects of the body tide and ocean tide. Global tide models predict the ocean tides in this region of complex coastline and bathymetry. To improve the accuracy of prediction, we developed a regional ocean tide model in SE-AK.Our comparison results suggest: (1) by taking into account the ocean tide effect, the amplitude differences between the observation and the predicted body tide is remarkably reduced for both the gravity and displacement (e.g. for the M₂ constituent, 8.5–0.3 μGal, and 2.4–0.1 cm at the AB50 GPS site in Juneau in terms of the vector sum of three components of the north–south, east–west and up–down), even though the ocean tide loading is large in SE-AK. (2) We have confirmed the precise point positioning (PPP) method, which was used to extract the tidal signals from the original GPS time series, works well to recover the tidal signals. Although the GPS analysis results still contain noise due to the atmosphere and multipath, we may conclude that the GPS observation surely detects the tidal signals with the sub-centimeter accuracy or better for some of the tidal constituents. (3) In order to increase the accuracy of the tidal prediction in SE-AK, it is indispensable to improve the regional ocean tide model developed in this study, especially for the phase.     

Earth tides observed by gravity and GPS in southeastern Alaska

We analyzed gravity data obtained in Juneau and global positioning system (GPS) data obtained from three PBO sites in southeastern Alaska (SE-AK), which are part of a US research facility called ‘EarthScope’, and we compared the obtained tidal amplitudes and phases with those estimated from the predicted tides including both effects of the body tide and ocean tide. Global tide models predict the ocean tides in this region of complex coastline and bathymetry. To improve the accuracy of prediction, we developed a regional ocean tide model in SE-AK.Our comparison results suggest: (1) by taking into account the ocean tide effect, the amplitude differences between the observation and the predicted body tide is remarkably reduced for both the gravity and displacement (e.g. for the M₂ constituent, 8.5–0.3 μGal, and 2.4–0.1 cm at the AB50 GPS site in Juneau in terms of the vector sum of three components of the north–south, east–west and up–down), even though the ocean tide loading is large in SE-AK. (2) We have confirmed the precise point positioning (PPP) method, which was used to extract the tidal signals from the original GPS time series, works well to recover the tidal signals. Although the GPS analysis results still contain noise due to the atmosphere and multipath, we may conclude that the GPS observation surely detects the tidal signals with the sub-centimeter accuracy or better for some of the tidal constituents. (3) In order to increase the accuracy of the tidal prediction in SE-AK, it is indispensable to improve the regional ocean tide model developed in this study, especially for the phase.     

西沙群岛西北深水海域的内潮特征分析

基于海南岛至西沙群岛之间深水海域一长达5年的锚定潜标测流资料,采用谱分析、调和分析和动力模态分解等方法主要分析了局部海域内潮的基本特征.结果表明:研究海域的正压和斜压潮均以全日振荡为主,500~900 m的海洋中层全日等密度线垂向振幅可达40 m;全日内潮主要沿垂直于陆坡方向传播,与天文潮锁相的全日内潮可占全日内潮总能量的41%;海洋上层,O1内潮垂向平均振幅与局地海面高度呈显著正相关关系,K1内潮则表现为夏、冬季增强的半年循环特征;超过70%的O1分潮能量集中于第一、二斜压模态上,K1分潮在第三斜压模态上亦有相当能量.     

海潮误差对GRACE时变重力场解算的影响研究

海潮误差是 GRACE 时变重力场反演中重要的误差源,目前发布的海潮模型中主要包含振幅较大的主潮波分量模型,在时变重力场反演中次潮波的影响也是不可忽略的,因此,GRACE 时变重力场反演中的海潮误差主要包括受限于海潮模型误差和次潮波影响.本文利用轨道模拟方法检测了短周期潮波的混频周期以及次潮波对ΔC20, ΔC30的时序特征,并进一步通过轨道模拟结果分析了海潮误差对时变重力场反演的影响,然后通过实测数据解算分析了海潮误差对当前 GRACE 时变重力场解算的影响,研究发现:(1) 利用轨道模拟能够有效地检测短周期潮波的混频周期;(2)时变重力场解算过程中,次潮波的影响大于海潮模型误差的影响;(3)海潮模型误差以及次潮波影响是当前 GRACE 没有达到基准精度的重要因素之一.     

A simple approach to adjust tidal forcing in fjord models

To model currents in a fjord accurate tidal forcing is of extreme importance. Due to complex topography with narrow and shallow straits, the tides in the innermost parts of a fjord are both shifted in phase and altered in amplitude compared to the tides in the open water outside the fjord. Commonly, coastal tide information extracted from global or regional models is used on the boundary of the fjord model. Since tides vary over short distances in shallower waters close to the coast, the global and regional tidal forcings are usually too coarse to achieve sufficiently accurate tides in fjords. We present a straightforward method to remedy this problem by simply adjusting the tides to fit the observed tides at the entrance of the fjord. To evaluate the method, we present results from the Oslofjord, Norway. A model for the fjord is first run using raw tidal forcing on its open boundary. By comparing modelled and observed time series of water level at a tidal gauge station close to the open boundary of the model, a factor for the amplitude and a shift in phase are computed. The amplitude factor and the phase shift are then applied to produce adjusted tidal forcing at the open boundary. Next, we rerun the fjord model using the adjusted tidal forcing. The results from the two runs are then compared to independent observations inside the fjord in terms of amplitude and phases of the various tidal components, the total tidal water level, and the depth integrated tidal currents. The results show improvements in the modelled tides in both the outer, and more importantly, the inner parts of the fjord.     

Coastal tides in West Greenland derived from tide gauge records

Based on pressure tide-gauge observations, sea-level records are derived for ten sites along the coast of West Greenland. The ocean tidal signal is extracted by a harmonic tidal analysis. The accuracy of the determined tidal constants is discussed in detail. The tides account for 85% of the observed sea-level standard deviation. The tide gauge records reveal significant shallow-water tidal effects, in particular compound and overtide amplitudes reaching 5 cm. The propagation of the tidal waves into the fjords depends strongly on local conditions and is in some cases accompanied by an amplification of the tidal amplitudes. The observed tidal signals are compared to the predictions of the global ocean tide model FES2004. At the outer coast, a good agreement is found. Inside the fjords, however, the model performs worse and tide gauge observations may still be indispensable when accurate tidal signals are required.     

Tsunami–tide interactions: A Cook Inlet case study

First, we investigated some aspects of tsunami–tide interactions based on idealized numerical experiments. Theoretically, by changing total ocean depth, tidal elevations influence the speed and magnitude of tsunami waves in shallow regions with dominating tidal signals. We tested this assumption by employing a simple 1-D model that describes propagation of tidal waves in a channel with gradually increasing depth and the interaction of the tidal waves with tsunamis generated at the channel's open boundary. Important conclusions from these studies are that computed elevations by simulating the tsunami and the tide together differ significantly from linear superposing of the sea surface heights obtained when simulating the tide and the tsunami separately, and that maximum tsunami–tide interaction depends on tidal amplitude and phase. The major cause of this tsunami–tide interaction is tidally induced ocean depth that changes the conditions of tsunami propagation, amplification, and dissipation. Interactions occur by means of momentum advection, bottom friction, and variable water flux due to changing total depth and velocity. We found the major cause of tsunami–tide interactions to be changing depth. Secondly, we investigate tsunami–tide interactions in Cook Inlet, Alaska, employing a high-resolution 2-D numerical model. Cook Inlet has high tides and a history of strong tsunamis and is a potential candidate for tsunami impacts in the future. In agreement with previous findings, we find that the impacts of tsunamis depend on basin bathymetries and coastline configurations, and they can, in particular, depend on tsunami–tide interactions. In regions with strong tides and tsunamis, these interactions can result in either intensification or damping of cumulative tsunami and tide impacts, depending on mean basin depth, which is regulated by tides. Thus, it is not possible to predict the effect of tsunami–tide interaction in regions with strong tides without making preliminary investigations of the area. One approach to reduce uncertainties in tsunami impact in regions with high tides is to simulate tsunamis together with tidal forcing.     

武汉超导重力仪观测最新结果和海潮模型研究

利用武汉台站GWR_C032超导重力仪观测资料,在对原始数据进行有效预处理的基础上作调和分析,获得反映地球内部介质特征的重力潮汐参数.基于卫星测高技术和有限元方法同时考虑验潮站数据作约束条件获得的多个全球海潮模型,利用负荷理论和数值褶积积分技术计算了重力负荷,对周日和半日频段内的重力潮汐参数实施负荷改正,提出了“负荷改正有效性”概念,研究了全球海潮模型适应性.数值结果说明,海潮改正的有效性高达91%（O1,NAO99）和92%（M2,ORI96）.基于11个海潮模型对主波（O1,K1,M2和S2）的负荷改正说明平均有效性为（86%,70%,73%和84%）,振幅因子与理论模型间的差异分别从（212%,155%,116%和080%）降到（031%,039%,034%和008%）,同时还说明利用NAO99和ORI96全球海潮模型能获得比其他模型更佳的负荷改正效果.文章还利用国际地球动力学计划网络其他7个台站的超导重力仪观测研究了全球海潮模型的适定性问题,结果说明不同模型中不同潮波具有明显的区域特点,早期构制的SCW80全球海潮模型仍可作为大地测量研究中的重要参考模型.     

The predictability of near-coastal currents using a baroclinic unstructured grid model

A limited domain, coastal ocean forecast system consisting of an unstructured grid model, a meteorological model, a regional ocean model, and a global tidal database is designed to be globally relocatable. For such a system to be viable, the predictability of coastal currents must be well understood with error sources clearly identified. To this end, the coastal forecast system is applied at the mouth of Chesapeake Bay in response to a Navy exercise. Two-day forecasts are produced for a 10-day period from 4 to 14 June 2010 and compared to real-time observations. Interplay between the temporal frequency of the regional model boundary forcing and the application of external tides to the coastal model impacts the tidal characteristics of the coastal current, even contributing a small phase error. Frequencies of at least 3 h are needed to resolve the tidal signal within the regional model; otherwise, externally applied tides from a database are needed to capture the tidal variability. Spatial resolution of the regional model (3 vs 1 km) does not impact skill of the current prediction. Tidal response of the system indicates excellent representation of the dominant M ₂ tide for water level and currents. Diurnal tides, especially K ₁, are amplified unrealistically with the application of coarse 27-km winds. Higher-resolution winds reduce current forecast error with the exception of wind originating from the SSW, SSE, and E. These winds run shore parallel and are subject to strong interaction with the shoreline that is poorly represented even by the 3-km wind fields. The vertical distribution of currents is also well predicted by the coastal model. Spatial and temporal resolution of the wind forcing including areas close to the shoreline is the most critical component for accurate current forecasts. Additionally, it is demonstrated that wind resolution plays a large role in establishing realistic thermal and density structures in upwelling prone regions.     

Ocean tidal effects on Earth rotation

Tidal forces due to the tide-raising potential deform the solid and fluid regions of the Earth, causing the Earth's inertia tensor to change, and hence causing the Earth's rate of rotation and length-of-day to change. Because both the tide-raising potential and the solid Earth's elastic response to the tidal forces caused by this potential are well-known, accurate models for the effects of the elastic solid body tides on the Earth's rotation are available. However, models for the effect of the ocean tides on the Earth's rotation are more problematic because of the need to model the dynamic response of the oceans to the tidal forces. Hydrodynamic ocean tide models that have recently become available are evaluated here for their ability to account for long-period ocean tidal signals in length-of-day observations. Of the models tested here, the older altimetric data-constrained model of Kantha et al. (1998) is shown to still do the best job of accounting for ocean tidal effects in length-of-day, particularly at the fortnightly tidal frequency. The model currently recommended by the IERS is shown to do the worst job.     

基于近岸海岛GPS数据反演海洋分潮负荷影响

本文探索了海潮负荷特征值的反演方法.基于中国近岸海岛GPS站（平潭与闸坡）观测数据,采用FFT方法提取了海潮负荷特征值,分析了反演特征值与全球海潮模型FES2004、NAO.99b和GOT4.7计算出的相关特征值之间的差异,评估了反演海潮分潮频率项的精度,并利用平潭站得到的海潮负荷特征值对附近的三沙站进行海潮改正以评价反演效果.结果表明：（1）频谱分析可精确提取4个半日分潮和4个全日分潮负荷的频率信息;与已知频率相比,P1分潮的反演频率误差为1.4%,其他7种分潮负荷反演频率误差均小于1%.（2）两个海岛分属不同的潮波入侵通道,反演分潮振幅和初相存在差异,但反演分潮频率几乎一致,间接证实它们属于同一潮波系统,也表明其潮差有别.（3）反演振幅与三种全球模型具有较好的一致性;其中S2、O1、P1、Q1四个分潮在水平方向互差为1~2 mm,高程方向上的互差均小于3 mm;K2、K1、M2、N2在水平方向振幅互差多数小于2 mm,个别差异高达4 mm,高程方向互差多为5~6 mm,个别超过10 mm.（4）反演得到海潮负荷改正模型相对于3种全球模型在三沙站的改正效果略佳,间接表明反演结果有效、可靠.（5）动态PPP结果中虽然存在多种误差,其时间序列仍可分离并提取海潮负荷的影响.

     

LAGEOS Sensitivity to Ocean Tides

Satellite Laser Ranging (SLR) to LAGEOS has a remarkable contribution to high-precise geodesy and geodynamics through deriving and validating various global geophysical models. This paper validates ocean tide models based on the analysis of satellite altimetry data, coastal tide gauges, and hydrodynamic data, i.e., CSR3.0, TOPEX4.0, CSR4.0A, FES2004, GOT00.2, and the CSRC Schwiderski model. LAGEOS orbits and SLR observation residuals from solutions based on different ocean tide models are compared and examined. It is found that LAGEOS orbits are sensitive to tidal waves larger than 5 mm. The analysis of the aliasing periods of LAGEOS orbits and tidal waves reveals that, in particular, the tidal constituent S₂ is not well established in the recent ocean tide models. Some of the models introduce spurious peaks to empirical orbit parameters, which can be associated with S₂, S_a, and K₂ tidal constituents, and, as a consequence, can be propagated to fundamental parameters derived from LAGEOS observations.     

Fine grid tidal modeling of the Yellow and East China Seas

A fine grid tidal modeling experiment is carried out in order to investigate the tidal regimes for major five tidal constituents, the nonlinear tidal phenomena in terms of M₄ and MS₄ generation, and the independent tide by the tide generating force in the Yellow and East China Seas (YECS). In this study a two-dimensional numerical model based upon a subgrid-scale (SGS) stress modeling technique is used with the tide generating force included. The model was validated with recently observed tide and current data. The calculated tidal charts for tidal elevation show a generally good agreement with existing ones, with more accurate feature of the M₂ cotidal chart in comparison with both the observed data and the existing tidal charts. A careful comparison of the computed diurnal amplitude with observations suggests that the diurnal constituents seem to be overdamped especially in the Kyunggi Bay region, for the case when quadratic bottom friction law is used.Propagation features of the M₄(MS₄) tides are discussed in the YECS, based upon the analyses of the observed and calculated results. The amphidromic system of the M₄ is quite complicated and one noticeable characteristic is that the propagation direction of the M₄ tidal wave along the west coast of Korean peninsula is opposite to that of the M₂ tidal wave. This result coincides with observations. The propagation feature of the MS₄ is almost similar to that of the M₄, but with lesser amplitude. The responses of the M₄ tidal features to momentum diffusion term and depth-dependent form of the friction coefficient are also discussed.It is also shown that when the independent tide (Defant, 1960) arising from tide generating force (TGF) coexists with tidal waves (co-oscillating tide) arising from external boundary forcing, the TGF tidal waves are dissipated and their amphidromes tend to move westward. This may be interpreted as a process whereby the incident and reflected TGF tidal waves are damped by co-oscillating tide arising from external force at open boundaries. The TGF amplitude is found to be up to 10 cm and 4 cm in the Kyunggi Bay for the M₂ and S₂ constituents while those for all diurnal constituents are less than 1 cm over the entire model domain.     

北京地区最新重力潮汐结果及其在检测液核共振效应中的应用

利用中国计量科学研究院北京昌平基地iGrav-012超导重力仪最新观测资料,对其作仔细地预处理,根据调和分析方法精密测定了重力潮汐参数,基于负荷理论与卷积积分技术获得了包含HAM11a,DTU10,EOT11a在内的14个全球海潮模型的重力海潮负荷效应,利用近周日频段内潮波振幅因子的共振效应求解了自由核章动（FCN）的本征参数.调和分析结果表明,重力潮汐的观测精度非常高,标准差达到1.184 nm·s^-2.基于加汉宁窗的快速傅里叶变换方法获得地震频段的地震噪声等级（SNM）为0.206,说明该台站是低背景噪声的.周日主波O₁和K₁经海潮模型作负荷效应改正的平均有效性分别为83%和85%;使用13个高精度海潮模型进行迭积计算获得的FCN本征周期为430.0（427.8,432.3）恒星日,品质因子Q值为-5137.

     

27.3-day and 13.6-day atmospheric tide

An analysis of time variations in the earth's length of day (LOD) for 25 years (1973-1998) versus at- mospheric circulation changes and lunar phase is presented. It is found that, on the average, there is a 27.3-day and 13.6-day period oscillation in global zonal wind speed, atmospheric geopotential height, and LOD following alternating changes in lunar phase. Every 5-9 days (6.8 days on average), the fields of global atmospheric zonal wind and geopotential height and LOD undergo a sudden change in rela- tion to a change in lunar declination. The observed atmospheric oscillation with this time period may be viewed as a type of atmospheric tide. Ten atmospheric tidal cases have been analyzed by comparing changes in LOD, global zonal wind speed and atmospheric geopotential height versus change in lunar declination. Taken together these cases reveal prominent 27.3-day and 13.6-day tides. The lunar forcing on the earth's atmosphere is great and obvious changes occur in global fields of zonal wind speed and atmospheric geopotential height over the equatorial and low latitude areas. The driving force for the 27.3-day and 13.6-day atmospheric tides is the periodic change in lunar forcing during the moon's revolution around the earth. When the moon is located on the celestial equator the lunar declination equals zero and the lunar tidal forcing on the atmosphere reaches its maximum, at this time the global zonal wind speed increases and the earth's rotation rate decreases and LOD increases. Conversely, when the moon reaches its most northern or southern positions the lunar declination is maximized, lunar tidal forcing decreases, global zonal wind speed decreases, earth's rotation rate increases and LOD decreases. 27.3-day and 13.6-day period atmospheric tides deserve deeper study. Lunar tidal forcing should be considered in models of atmospheric circulation and in short and medium range weather forecasting.