Mapping nonlinear shallow-water tides: a look at the past and future

Overtides and compound tides are generated by nonlinear mechanisms operative primarily in shallow waters. Their presence complicates tidal analysis owing to the multitude of new constituents and their possible frequency overlap with astronomical tides. The science of nonlinear tides was greatly advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost’s complementary work with satellite altimetry motivates our attempts to merge these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M tide over the northwest European Shelf. Future applications of altimetry to regions with fewer in situ measurements will require improved understanding of error covariance models because these control the tradeoffs between fitting hydrodynamics and data, a delicate issue in coastal regions. While M can now be robustly determined along the Topex/Poseidon satellite ground tracks, many other compound tides face serious aliasing problems. In memory of Christian Le Provost     

卫星测高混合边值问题的球谐级数解法

研究了球界面下卫星测高问题的解法,利用有限逼近方法得到了下列结论：若陆地部分是球冠,则卫星测高问题的解可以转换成关于球谐级数位系数的线性方程组,并且位系数的阶和次是以分离形式出现的,从而确保该解法具有实用意义. 利用重力场360阶模型进行模拟计算的结果表明：该解法得到的位系数的相对精度达到了10－１１. 同时证明了常用的Stokes问题、Dirichlet问题、Neumann问题可以看成卫星测高问题的特殊情况.     

利用多年卫星测高资料研究南海上层环流季节特征

利用10年高精度卫星测高海面高异常网格资料,联合EGM96稳态海面地形模型,构成南海海域合成海面地形的时间序列,并计算了各个时期的南海表层地转流场. 利用卫星跟踪漂流浮标观测结果与相应时期南海地转流场进行对比验证,结果显示本文结果可以很好地反映南海海域一些中小尺度的环流特征. 根据南海各季节多年平均表层环流场结构,对南海环流周年变化规律和季节特征进行了初步的探讨. 研究结果表明,南海表层环流始终处在不断演变过程之中,在时间和空间上都表现出明显的多尺度特征.     

联合卫星测高和模式资料研究海水热含量变化

本文在考虑洋底压力变化的情况下,利用2003~2008年融合多颗卫星的测高资料估计了全球和中国近海的海水热含量变化.顾及洋底压力(OBP)变化以及热膨胀系数随海水深度变化的影响,提出的改进方法提高了对中高纬度地区热含量变化的估算精度.在OBP变化较为明显的北太平洋区域I(30°N~50°N,170°E~190°E)、南印度洋区域II(40°S~60°S,100°E~120°E)和南太平洋区域III(40°S~60°S,100°W~120°W),改进方法的均方差较传统方法分别降低了16.3%、60.5%和48.4%.同时研究表明,卫星测高的精度以及盐度变化是影响中高纬度地区热含量估计精度的重要因素.在中国近海地区,东海和黄海的热含量主要表现为周年变化;南海区域的热含量除周年变化外,还存在半周年项和年际变化项,且南海的海水热含量近年有增加的趋势.     

联合多代卫星测高和多源重力数据的局部大地水准面精化方法

本文研究了基于泊松小波径向基函数融合多代卫星测高及多源重力数据精化大地水准面模型的方法.分别以沿轨垂线偏差和大地水准面高高差作为卫星测高观测量,研究了使用不同类型测高数据对于大地水准面建模精度的影响.针对全球潮汐模型在浅水区域及部分开阔海域精度较低的问题,引入局部潮汐模型研究了不同潮汐模型对于大地水准面的影响.数值分析表明:相比于使用沿轨垂线偏差作为测高观测量,基于沿轨大地水准面高高差解算得到的大地水准面模型的精度更高,特别是在海域区域,其精度提高了2.3 cm.由于使用沿轨大地水准面高高差作为测高观测量削弱了潮汐模型长波误差的影响,采用不同潮汐模型对大地水准面解算的影响较小.总体而言,船载重力及测高观测数据在海洋重力场的确定中呈现互补性关系,联合两类重力场观测量可以提高局部重力场的建模精度.     

Contribution of satellite altimetry data in the geophysical investigation of the Red Sea Region, Egypt

Successful development of geodetic satellite missions has aroused new interest in determining global and regional gravity field based on satellite data. Satellite altimetry data enable direct determination of the geoid over sea regions. In Egypt, where land and marine geophysical data are inadequate because of rough topography and economic reasons, the use of satellite altimetry data is of special importance. The northern Red Sea region has been selected as a site for case study of the current research, after applying spectral analysis to reveal near-surface structure, the residual geoid of the studied region shows a good correlation with the known geologic features. Moreover, satellite-based gravity data enhance small-scale features and agrees well with land and marine gravity data. Thus, geoid undulation and satellite gravity data can be a complementary source of data to determine near-surface and deep structures.     

The 18.6 yr nodal modulation in the tides of Southern European coasts

The nodal modulation of the diurnal (K₁ and O₁) and semi-diurnal (M₂ and K₂) tidal constituents at the coasts of the Mediterranean Sea and the eastern Atlantic is estimated and its spatial variability mapped. Fourteen hourly tide gauge records each spanning more than 18 years are considered in this analysis. Ten tide gauges are located in the Mediterranean Sea and four in the Bay of Biscay. The nodal modulation of the most energetic tidal constituent (M₂) reaches up to 5 cm at the eastern Atlantic coasts, while within the Mediterranean Sea its modulation is in general less than 1.1 cm. The largest K₂ nodal modulation found is 3.7 cm in the eastern Atlantic coasts. In the Mediterranean Sea, smaller modulation amplitudes, ranging between 0.4 and 1.4 cm are found. The K₁ tide constituent has the largest amplitude nodal modulation within the Mediterranean Sea of 1.9 cm in the north Adriatic Sea, which is also larger than the modulation of this constituent at the eastern Atlantic coasts. The O₁ tide constituent has the highest amplitude nodal modulation (1.4 cm) at the eastern Atlantic coasts. In the Mediterranean Sea the maximum value is 1 cm in the north Adriatic Sea.     

利用GRACE数据反演东海沉积物变化

GRACE卫星的成功发射为海底沉积物的监测提供了新的方法.利用2003-2014年间的GRACE RL05数据,采用同期的测高数据对海面高变化进行改正,使用水文模式数据和基于均一假设的尺度因子估计方法处理泄漏误差,反演了东海地区的沉积物变化情况,并对GIA效应进行了改正.结果表明：东海入海口处沉积物的平均变化速率为5.44±0.88 mm·a^-1,最大值出现在浙江沿海地区,变化速率为6~7 mm·a^-1;在空间分布上,呈现河口处沉积速率大,远离河口的大洋地区沉积速率小的特征.在时空分布上均与实测数据很好的吻合.沉积物变化时间序列的周年项振为6.8 cm,周年变化主要与东海泥沙扩散路径相关的海洋环流模式有关;半周年项和两周年项振幅分别为0.6 cm和0.7 cm,这两项变化主要与长江流域降水引起的土壤侵蚀变化有关.最后,分析讨论了本文沉积物监测方法推广到其他地区的适用性和局限性.

     

Using satellite altimetry data to augment flow estimation techniques on the Mekong River

Satellite altimetry is routinely used to provide levels for oceans or large inland water bodies from space. By utilizing retracking schemes specially designed for inland waters, meaningful river stages can also be recovered when standard techniques fail. Utilizing retracked waveforms from ERS‐2 and ENVISAT along the Mekong, comparisons against observed stage measurements show that the altimetric measurements have a root mean square error (RMSE) of 0·44–0·65 m for ENVISAT and 0·46–0·76 m for ERS‐2. For many applications, however, stage is insufficient because discharge is the primary requirement. Investigations were therefore undertaken to estimate discharges at a downstream site (Nakhon Phanom (NP)) assuming that in situ data are available at a site 400 km upstream (Vientiane). Two hypothetical, but realistic scenarios were considered. Firstly, that NP was the site of a de‐commissioned gauge and secondly, that the site has never been gauged. Using both scenarios, predictions were made for the daily discharge using methods with and without altimetric stage data. In the first scenario using a linear regression approach the altimetry data improved the Nash‐Sutcliffe r² value from 0·884 to 0·935. The second scenario used known river cross‐sections while lateral inflows were inferred from a hydrological model: this scenario gave an increase in the r² value from 0·823 to 0·893. The use of altimetric stage data is shown to improve estimated discharges and further applications are discussed. Copyright © 2010 John Wiley & Sons, Ltd.     

Toward a global ocean data assimilation system based on ensemble optimum interpolation: altimetry data assimilation experiment

A global ocean data assimilation system based on the ensemble optimum interpolation (EnOI) has been under development as the Chinese contribution to the Global Ocean Data Assimilation Experiment. The system uses a global ocean general circulation model, which is eddy permitting, developed by the Institute of Atmospheric Physics of the Chinese Academy of Sciences. In this paper, the implementation of the system is described in detail. We describe the sampling strategy to generate the stationary ensembles for EnOI. In addition, technical methods are introduced to deal with the requirement of massive memory space to hold the stationary ensembles of the global ocean. The system can assimilate observations such as satellite altimetry, sea surface temperature (SST), in situ temperature and salinity from Argo, XBT, Tropical Atmosphere Ocean (TAO), and other sources in a straightforward way. As a first step, an assimilation experiment from 1997 to 2001 is carried out by assimilating the sea level anomaly (SLA) data from TOPEX/Poseidon. We evaluate the performance of the system by comparing the results with various types of observations. We find that SLA assimilation shows very positive impact on the modeled fields. The SST and sea surface height fields are clearly improved in terms of both the standard deviation and the root mean square difference. In addition, the assimilation produces some improvements in regions where mesoscale processes cannot be resolved with the horizontal resolution of this model. Comparisons with TAO profiles in the Pacific show that the temperature and salinity fields have been improved to varying degrees in the upper ocean. The biases with respect to the independent TAO profiles are reduced with a maximum magnitude of about 0.25°C and 0.1 psu for the time-averaged temperature and salinity. The improvements on temperature and salinity also lead to positive impact on the subsurface currents. The equatorial under current is enhanced in the Pacific although it is still underestimated after the assimilation.     

体应变潮汐观测资料信息提取与映震效果

根据体应变观测资料的特点, 研究了体应变观测资料的处理方法, 提出了在时间域分析的数学模型。在数学模型中, 将潮汐因子、气压系数、非潮汐应变速率和加速度一并考虑, 在资料处理结果中, 这些参数可同时取得。分别用时间域分析方法和频率域分析方法对观测数据进行了处理, 发现潮汐因子、气压系数、应变速率和加速度等参数在大同地震前均有大小不同、持续时间不等的异常, 这些参数可作为物理意义明确的地震中短期预测的指标。     

Effects of self-attraction and loading at a regional scale: a test case for the Northwest European Shelf

The impact of the self-attraction and loading effect (SAL) in a regional 2D barotropic tidal model has been assessed, a term with acknowledged and well-understood importance for global models but omitted for boundary-forced, regional models, for which the implementation of SAL is non-trivial due to its non-local nature. In order to understand the impact of the lack of SAL effects in a regional scale, we have forced a regional model of the Northwest European Continental Shelf and the North Sea (continental shelf model (CSM)) with the SAL potential field derived from a global model (GTSM), in the form of a pressure field. Impacts have been studied in an uncalibrated setup and with only tidal forcing activated, in order to isolate effects. Additionally, the usually adopted simple SAL parameterization, in which the SAL contribution to the total tide is parameterized as a percentage of the barotropic pressure gradient (typically chosen 10%), is also implemented and compared to the results obtained with a full SAL computation. A significant impact on M2 representation is observed in the English Channel, Irish Sea and the west (UK East coast) and south (Belgian and Dutch Coast) of the North Sea, with an impact of up to 20 cm in vector difference terms. The impact of SAL translates into a consistent M2 amplitude and propagation speeds reduction throughout the domain. Results using the beta approximation, with an optimal domain-wide constant value of 1.5%, show a somewhat comparable impact in phase but opposite direction of the impact in amplitude, increasing amplitudes everywhere. In relative terms, both implementations lead to a reduction of the tidal representation error in comparison with the reference run without SAL, with the full SAL approach showing further impacted, improved results. Although the overprediction of tidal amplitudes and propagation speeds in the reference run might have additional sources like the lack of additional dissipative processes and non-considered bottom friction settings, results show an overall significant impact, most remarkable in tidal phases. After showing evidence of the SAL impact in regional models, the question of how to include this physical process in them in an efficient way arises, since SAL is a non-local effect and depends on the instantaneous water levels over the whole ocean, which is non-trivial to implement.     

A climatology of nonmigrating semidiurnal tides from TIMED Doppler Interferometer (TIDI) wind data

With the launch of the TIMED satellite in December 2001, continuous temperature and wind data sets amenable to MLT tidal analyses became available. The wind measuring instrument, the TIMED Doppler Interferometer (TIDI), is operating since early 2002. Its day- and nighttime capability allows to derive tidal winds over a range of MLT altitudes. This paper presents climatologies (June 2002–June 2005) of monthly mean amplitudes and phases for six nonmigrating semidiurnal tidal components between 85 and 105 km altitude and between 45°S and 45°N latitude (westward propagating wave numbers 4, 3, 1; the standing oscillation s0; and eastward propagating wave numbers 1, 2) in the zonal and meridional wind directions.Amplitude errors are 15–20% (accuracy) and 0.8 m/s (precision). The phase error is 2 h. The TIDI analysis agrees well with 1991–1994 UARS results at 95 km. During boreal winter, amplitudes of a single component can reach 10 m/s at latitudes equatorward of 45°. Aggregate effects of nonmigrating tides can easily reach or exceed the amplitude of the migrating tide. Comparisons with the global scale wave model (GSWM) and the thermosphere–ionosphere–mesosphere–electrodynamics general circulation model (TIME-GCM) are partly inconclusive but they suggest that wave–wave interaction and latent heat release in the tropical troposphere both play an important role in forcing the semidiurnal westward 1, westward 3, and standing components. Latent heat release is the leading source of the eastward propagating components.     

Recovery of marine gravity anomalies from ERS1, ERS2 and ENVISAT satellite altimetry data for geoid computations over Norway

Free-Air Anomalies (FAA) for the Norwegian marine area including some parts of the North Sea, the Norwegian Sea and the Barents Sea are computed from satellite altimetry data. A total of 84 cycles of ERS2 along-track data, 25 cycles of ENVISAT along-track data and high density ERS1 data during its geodetic mission are used. The new geopotential model from the Gravity Recovery and Climate Experiment (GRACE) mission, GGM02S (Tapely et al., 2005) is used to compute the long wavelength contributions of the geoid and the FAA. To correct data for mean dynamic topography, the available Levitus climatology model (Levitus and Boyer, 1994) is used. Corrected data are then used to compute along-track gradients in each cycle-pass to suppress the orbital and the atmospheric errors below the noise level of the altimeter. Resulted gradients are then stacked and the east-west and the north-south components of the deflection of verticals are computed where ascending and descending tracks meet each other. Finally, the inverse Vening-Meinesz formula is implemented on the gridded deflections to compute FAA. Results are then compared with available marine and airborne data. Standard deviations of ± 4.301 and ± 6.159 mGal in comparison with airborne and marine FAA were achieved. Thereafter, the derived anomalies are combined with marine and airborne FAA together with the land FAA to compute a fine resolution geoid for Norway and the surrounding marine areas. This geoid is evaluated over sea and land with the synthetic geoid (the geoid derived from the mean sea surface by subtracting the mean dynamic topography) and Global Positioning System (GPS)-levelling and the standard deviations of the differences are ± 20.9 and ± 12.8 cm respectively. ali.soltanpour@ntnu.no, hossein.nahavandchi@ntnu.no, kourosh.ghazavi@ntnu.no     

CryoSat-2测高数据与Landsat 8光学数据融合提取南极Amery冰架接地线

本文利用CryoSat-2测高数据与Landsat 8光学数据,针对南极Amery冰架区域开展接地线提取研究.首先通过Landsat 8光学影像三次Hermite多项式插值处理,在坡度分析的基础上利用表面曲率改进方法获取接地线特征点;同时对CryoSat-2测高数据进行坡度分析和表面曲率计算,通过沿轨梯度分析方法提取接地点;最后将Landsat 8与CryoSat-2数据获取的接地点进行最小二乘融合得到融合接地线.实验结果表明,融合结果利用高空间分辨率光学数据不仅能保证接地线提取精度,同时测高数据还能够弥补光学数据受云遮挡导致的数据空缺,保持接地线的完整性.与MOA产品比较可以看出,融合数据点与MOA接地线平均距离为367 m,标准差为601 m,所有数据点中距离小于1 km的点占总数的93.19%,与MOA产品具有较好一致.本文提出的融合算法可以实现空间连续的接地线提取结果,对后续研究南极物质平衡、冰流速计算等具有重要的意义.     

A new ellipsoidal gravimetric, satellite altimetry and astronomic boundary value problem, a case study: The geoid of Iran

A new gravimetric, satellite altimetry, astronomical ellipsoidal boundary value problem for geoid computations has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential, (ii) gravity intensity (i.e. modulus of gravity acceleration), (iii) astronomical longitude, (iv) astronomical latitude and (v) satellite altimetry observations. The ellipsoidal coordinates of the observation points have been considered as known quantities in the set-up of the problem in the light of availability of GPS coordinates. The developed boundary value problem is ellipsoidal by nature and as such takes advantage of high precision GPS observations in the set-up. The algorithmic steps of the solution of the boundary value problem are as follows:

- Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and of the ellipsoidal centrifugal field for the removal of the effect of global gravity and the isostasy field from the gravity intensity and the astronomical observations at the surface of the Earth.

- Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the gravity intensity and the astronomical observations at the surface of the Earth the effect of the residual masses at the radius of up to 55 km from the computational point.

- Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and ellipsoidal centrifugal field for the removal from the geoidal undulations derived from satellite altimetry the effect of the global gravity and isostasy on the geoidal undulations.

- Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the geoidal undulations derived from satellite altimetry the effect of the water masses outside the reference ellipsoid within a radius of 55 km around the computational point.

- Least squares solution of the observation equations of the incremental quantities derived from aforementioned steps in order to obtain the incremental gravity potential at the surface of the reference ellipsoid.

- The removed effects at the application points are restored on the surface of reference ellipsoid.

- Application of the ellipsoidal Bruns’ formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights with respect to the reference ellipsoid.

- Computation of the geoid of Iran has successfully tested this new methodology.

CryoSat-2测高数据与Landsat 8光学数据融合提取南极Amery冰架接地线

本文利用CryoSat-2测高数据与Landsat 8光学数据,针对南极Amery冰架区域开展接地线提取研究.首先通过Landsat 8光学影像三次Hermite多项式插值处理,在坡度分析的基础上利用表面曲率改进方法获取接地线特征点;同时对CryoSat-2测高数据进行坡度分析和表面曲率计算,通过沿轨梯度分析方法提取接地点;最后将Landsat 8与CryoSat-2数据获取的接地点进行最小二乘融合得到融合接地线.实验结果表明,融合结果利用高空间分辨率光学数据不仅能保证接地线提取精度,同时测高数据还能够弥补光学数据受云遮挡导致的数据空缺,保持接地线的完整性.与MOA产品比较可以看出,融合数据点与MOA接地线平均距离为367 m,标准差为601 m,所有数据点中距离小于1 km的点占总数的93.19%,与MOA产品具有较好一致.本文提出的融合算法可以实现空间连续的接地线提取结果,对后续研究南极物质平衡、冰流速计算等具有重要的意义.

     

Investigating the uncertainty of satellite altimetry products for hydrodynamic modelling

Satellite altimetry products are increasingly used in many hydraulic applications, and recent studies demonstrate their suitability for the calibration of hydraulic models. The study investigates the effect of satellite‐data uncertainty on the calibration of a quasi‐two‐dimensional (quasi‐2D) model of the middle‐lower portion of the Po river (~140 km). We refer to extended (~16 years of observations) ERS and ENVISAT altimetry products (i.e. River and Lake Hydrology data, RLH) to investigate the effect of (i) record length (i.e. number of satellite measurements at a given satellite track) and (ii) data uncertainty (i.e. altimetry measurements errors) on the calibration of the quasi‐2D model. We first present an assessment of ERS and ENVISAT altimetry errors and then perform the investigations in a Monte Carlo framework by generating datasets of synthetic altimetry products. The results of our analysis further emphasize the suitability of satellite data for the calibration of hydraulic models, providing also a quantitative assessment of the effect of the uncertainty of altimetry products. The analysis highlights the higher accuracy of ENVISAT data, which ensures a stable calibration with ~1.5 years of data (Mean Absolute Error, MAE, lower than 0.4 m, ~0.2 m of which results directly from the uncertainty of ENVISAT data). ERS‐based calibrations become stable with longer series (~3.5–5 years of data), and the negative effect of uncertainty in ERS data is higher (i.e. MAE of 0.6–0.9 m, of which 0.4–0.6 m results from the uncertainty of ERS measurements). Copyright © 2015 John Wiley & Sons, Ltd.