国家高程基准与全球高程基准之间的垂直偏差

利用不同重力场模型（EIGEN-6C4、EGM2008）和海面高模型（DNSC08、DTU10、DTU13）确定了全球平均海面重力位均值62 636 856.550 7 m²s^-2,加入海面地形改正后得到全球大地水准面重力位均值62 636 858.179 0 m²s^-2。联合EGM2008模型与全国均匀分布的649个GPS/水准数据,根据异常位法、正常高反算法以及高程异常差法,分别计算了我国1985高程基准与全球高程基准之间的垂直偏差,并对3种垂直偏差结果通过加权方法进行了改善。最后,利用两种方法对垂直偏差结果的合理性与正确性进行验证。结果表明我国高程基准面高于全球平均海面0.298 0 m,高于全球大地水准面0.464 2 m。     

The CARIB97 high-resolution geoid height model for the Caribbean Sea

A 2×2 arc-minute resolution geoid model, CARIB97, has been computed covering the Caribbean Sea. The geoid undulations refer to the GRS-80 ellipsoid, centered at the ITRF94 (1996.0) origin. The geoid level is defined by adopting the gravity potential on the geoid as W ₀=62 636 856.88 m²/s² and a gravity-mass constant of GM=3.986 004 418×10¹⁴ m³/s². The geoid model was computed by applying high-frequency corrections to the Earth Gravity Model 1996 global geopotential model in a remove-compute-restore procedure. The permanent tide system of CARIB97 is non-tidal. Comparison of CARIB97 geoid heights to 31 GPS/tidal (ITRF94/local) benchmarks shows an average offset (h–H–N) of 51 cm, with an Root Mean Square (RMS) of 62 cm about the average. This represents an improvement over the use of a global geoid model for the region. However, because the measured orthometric heights (H) refer to many differing tidal datums, these comparisons are biased by localized permanent ocean dynamic topography (PODT). Therefore, we interpret the 51 cm as partially an estimate of the average PODT in the vicinity of the 31 island benchmarks. On an island-by-island basis, CARIB97 now offers the ability to analyze local datum problems which were previously unrecognized due to a lack of high-resolution geoid information in the area. Received: 2 January 1998 / Accepted: 18 August 1998     

The Gauss–Listing geopotential value W 0 and its rate from altimetric mean sea level and GRACE

In geopotential space, the fundamental geodetic parameter W ₀ defines the Gauss–Listing geoid which can be used to best represent the Earth’s mean sea level (MSL) and hence specifies a conventional zero height level to unify vertical datums employed by mapping agencies throughout the world. Further, W ₀ cannot be considered invariant as the parameter varies temporally as a direct response to sea level change and mass redistributions. This study determines W ₀ and its rate, dW ₀/dt, by utilizing altimetric MSL models and an independent mean dynamic topography (MDT) model to define points on the geoid. W ₀ and dW ₀/dt are estimated by two approaches: (i) by means of a global gravity field model (GGM) and (ii) within normal gravity field space as the geopotential value of the best fitting reference ellipsoid. The study shows that uncertainty in W ₀ is mainly influenced by MDT while the choice of methodology, GGM and MSL data coverage are not significant within reason. Our estimate W ₀ =?62636854.2 ± 0.2 m²?s^?2 at epoch 2005.0 differs by 1.8?m²s^?2 from the International Astronomical Union reference value. This study shows that, at a sub-decadal time scale, the time variation dW ₀/dt stems mainly from sea level change with negligible effect from gravity field variations. dW ₀/dt =?(?2.70 ± 0.03)?×?10^?2?m²?s^?2?year^?1, corresponding to a MSL rise of 2.9?mm?year^?1, is evaluated from sea level change based on 16?years of TOPEX and Jason-1 data.     

National height datum,the Gauss–Listing geoid level value w0 and its time variation 0 (Baltic Sea Level Project: epochs 1990.8, 1993.8, 1997.4)

 A methodology for precise determination of the fundamental geodetic parameter w ₀, the potential value of the Gauss–Listing geoid, as well as its time derivative ₀, is presented. The method is based on: (1) ellipsoidal harmonic expansion of the external gravitational field of the Earth to degree/order 360/360 (130 321 coefficients; http://www.uni-stuttgard.de/gi/research/ index.html projects) with respect to the International Reference Ellipsoid WGD2000, at the GPS positioned stations; and (2) ellipsoidal free-air gravity reduction of degree/order 360/360, based on orthometric heights of the GPS-positioned stations. The method has been numerically tested for the data of three GPS campaigns of the Baltic Sea Level project (epochs 1990.8,1993.4 and 1997.4). New w ₀ and ₀ values (w ₀=62 636 855.75 ± 0.21 m²/s², ₀=−0.0099±0.00079 m²/s² per year, w ₀/&γmacr;=6 379 781.502 m,₀/&γmacr;=1.0 mm/year, and &γmacr;= −9.81802523 m²/s²) for the test region (Baltic Sea) were obtained. As by-products of the main study, the following were also determined: (1) the high-resolution sea surface topography map for the Baltic Sea; (2) the most accurate regional geoid amongst four different regional Gauss–Listing geoids currently proposed for the Baltic Sea; and (3) the difference between the national height datums of countries around the Baltic Sea. Received: 14 August 2000 / Accepted: 19 June 2001     

联合多种测高数据确定中国边缘海及全球海域的垂线偏差

On the basis of gravity field model （EIGEN_CG01C）, together with multi-altimeter data, the improved deflection of the vertical gridded in 2＇×2＇ in China marginal sea and gridded in 5＇×5＇ in the global sea was determined by using the weighted method of along-track least squares, and the accuracy is better than 1.2^# in China marginal sea. As for the quality of the deflection of the vertical, it meets the challenge for the gravity field of high resolution and accuracy, it shows that, compared with the shipboard gravimetry in the sea, the accuracy of the gravity anomalies computed with the marine deflection of the vertical by inverse Vening-Meinesz formula is 7.75 m.s ^-2.     

Making the connection between Geosat and TOPEX/Poseidon

We can presently construct two independent time series of sea level, each at a precision of a few centimeters, from Geosat (1985–1988) and TOPEX/Poseidon (1992–1995) collinear altimetry. Both are based on precise satellite orbits computed using a common geopotential model, JGM-2 (Nerem et al. 1994). We have attempted to connect these series using Geosat-T/P crossover differences in order to assess long-term ocean changes between these missions. Unfortunately, the observed result are large-scale sea level differences which appear to be due to a combination of geodetic and geopotential error sources. The most significant geodetic component seems to be a coordinate system bias for Geosat sea level (relative to T/P) of −7 to −9 cm in the y-axis (towards the Eastern Pacific). The Geosat-T/P sea height differences at crossovers (with JGM-2 orbits) probably also contain stationary geopotential-orbit error of about the same magnitude which also distort any oceanographic interpretation of the observed changes. We also found JGM-3 Geosat orbits have not resolved the datum errors evident from the JGM-2 Geosat -T/P results. We conclude that the direct altimetric approach to accurate determination of sea level change using Geosat and T/P data still depends on further improvement in the Geosat orbits, including definition of the geocenter. Received: 11 March 1996; Accepted: 19 September 1996     

联合GRACE/GOCE重力场模型和GPS/水准数据确定我国85高程基准重力位

GRACE、GOCE卫星重力计划的实施,对确定高精度重力场模型具有重要贡献。联合GRACE、GOCE卫星数据建立的重力场模型和我国均匀分布的649个GPS/水准数据可以确定我国高程基准重力位,但我国高程基准对应的参考面为似大地水准面,是非等位面,将似大地水准面转化为大地水准面后确定的大地水准面重力位为62 636 854.395 3m~2s~(-2),为提高高阶项对确定大地水准面的贡献,利用高分辨率重力场模型EGM2008扩展GRACE/GOCE模型至2190阶,同时将重力场模型和GPS/水准数据统一到同一参考框架和潮汐系统,最后利用扩展后的模型确定的我国大地水准面重力位为62 636 852.751 8m~2s~(-2)。其中组合模型TIM_R4+EGM2008确定的我国85高程基准重力位值62 636 852.704 5m~2s~(-2)精度最高。重力场模型截断误差对确定我国大地水准面的影响约16cm,潮汐系统影响约4~6cm。     

A bias-free geodetic boundary value problem approach to height datum unification

A geodetic boundary value problem (GBVP) approach has been formulated which can be used for solving the problem of height datum unification. The developed technique is applied to a test area in Southwest Finland with approximate size of 1.5° × 3° and the bias of the corresponding local height datum (local geoid) with respect to the geoid is computed. For this purpose the bias-free potential difference and gravity difference observations of the test area are used and the offset (bias) of the height datum, i.e., Finnish Height Datum 2000 (N2000) fixed to Normaal Amsterdams Peil (NAP) as origin point, with respect to the geoid is computed. The results of this computation show that potential of the origin point of N2000, i.e., NAP, is (62636857.68 ± 0.5) (m²/s²) and as such is (0.191 ± 0.003) (m) under the geoid defined by W ₀ = 62636855.8 (m²/s²). As the validity test of our methodology, the test area is divided into two parts and the corresponding potential difference and gravity difference observations are introduced into our GBVP separately and the bias of height datums of the two parts are computed with respect to the geoid. Obtaining approximately the same bias values for the height datums of the two parts being part of one height datum with one origin point proves the validity of our approach. Besides, the latter test shows the capability of our methodology for patch-wise application.     

1985国家高程基准的系统差

基于异常位、高程异常差以及海面地形模型 3种方法 ,分别求出了 1985国家高程基准相对于全球大地水准面的垂直偏差 ,并取得了一致的结果     

The geopotential to (14, 14) from a combination of satellite and gravimetric data

A set of2261 5°×5° mean anomalies were used alone and with satellite determined harmonic coefficients of the Smithsonian' Institution to determine the geopotential expansion to various degrees. The basic adjustment was carried out by comparing a terrestrial anomaly to an anomaly determined from an assumed set of coefficients. The (14, 14) solution was found to agree within ±3 m of a detailed geoid in the United States computed using1°×1° anomalies for an inner area and satellite determined anomalies in an outer area. Additional comparisons were made to the input anomaly field to consider the accuracy of various harmonic coefficient solutions. A by-product of this investigation was a new γ_E=978.0463 gals in the Potsdam system or978.0326 gals in an absolute system if −13.7 mgals is taken as the Potsdam correction. Combining this value of γ_E withf=1/298.25, KM=3.9860122·10 ²² cm ³ /sec ² , the consistent equatorial radius was found to be6378143 m.     

The geopotential value <Emphasis Type="Italic">W</Emphasis><Subscript>0</Subscript> for specifying the relativistic atomic time scale and a global vertical reference system

The TOPEX/Poseidon (T/P) satellite alti- meter mission marked a new era in determining the geopotential constant W ₀. On the basis of T/P data during 1993–2003 (cycles 11–414), long-term variations in W ₀ have been investigated. The rounded value W ₀ = 62636856.0 ± 0.5) m ² s ⁻² has already been adopted by the International Astronomical Union for the definition of the constant L _G = W ₀/c ² = 6.969290134 × 10⁻¹⁰ (where c is the speed of light), which is required for the realization of the relativistic atomic time scale. The constant L _G , based on the above value of W ₀, is also included in the 2003 International Earth Rotation and Reference Frames Service conventions. It has also been suggested that W ₀ is used to specify a global vertical reference system (GVRS). W ₀ ensures the consistency with the International Terrestrial Reference System, i.e. after adopting W ₀, along with the geocentric gravitational constant (GM), the Earth’s rotational velocity (ω) and the second zonal geopotential coefficient (J ₂) as primary constants (parameters), then the ellipsoidal parameters (a,α) can be computed and adopted as derived parameters. The scale of the International Terrestrial Reference Frame 2000 (ITRF2000) has also been specified with the use of W ₀ to be consistent with the geocentric coordinate time. As an example of using W ₀ for a GVRS realization, the geopotential difference between the adopted W ₀ and the geopotential at the Rimouski tide-gauge point, specifying the North American Vertical Datum 1988 (NAVD88), has been estimated.     

高程基准历元及其统一状态归化

平均海面存在趋势性变化，对于四维大地测量定位而言，必须赋予高程基准以时间特征，本文认为最好是确定高程基准历元。文章提出了高程基准历元的定义，给出了计算公式，求得中国１９８５国家高程基准历元为１９６６．０。文章还讨论了平均海面趋势性变化的数学问题，及提出了高程基准归化至统一状态的概念，研究了由于海水密度不同引起的平均海面高度变化，计算得中国１９８５国家高程基准对于通常海水状态的修正值为－０．０１２ｍ     

The effect of topography on the determination of the geoid using analytical downward continuation

The method of analytical downward continuation has been used for solving Molodensky’s problem. This method can also be used to reduce the surface free air anomaly to the ellipsoid for the determination of the coefficients of the spherical harmonic expansion of the geopotential. In the reduction of airborne or satellite gradiometry data, if the sea level is chosen as reference surface, we will encounter the problem of the analytical downward continuation of the disturbing potential into the earth, too. The goal of this paper is to find out the topographic effect of solving Stoke’sboundary value problem (determination of the geoid) by using the method of analytical downward continuation. It is shown that the disturbing potential obtained by using the analytical downward continuation is different from the true disturbing potential on the sea level mostly by a −2πGρh 2/p. This correction is important and it is very easy to compute and add to the final results. A terrain effect (effect of the topography from the Bouguer plate) is found to be much smaller than the correction of the Bouguer plate and can be neglected in most cases. It is also shown that the geoid determined by using the Helmert’s second condensation (including the indirect effect) and using the analytical downward continuation procedure (including the topographic effect) are identical. They are different procedures and may be used in different environments, e.g., the analytical downward continuation procedure is also more convenient for processing the aerial gravity gradient data. A numerical test was completed in a rough mountain area, 35°<ϕ<38°, 240°<λ<243°. A digital height model in 30″×30″ point value was used. The test indicated that the terrain effect in the test area has theRMS value ±0.2−0.3 cm for geoid. The topographic effect on the deflections of the vertical is around1 arc second.     

Determination of geoidal heights and deflections of the vertical for the hellenic area using heterogeneous data

Mean gravity anomalies, deflections of the vertical, and a geopotential model complete to degree and order180 are combined in order to determine geoidal heights in the area bounded by [34°≦ϕ≤42°, 18°≦λ≦28°]. Moreover, employing point gravity anomalies simultaneously with the above data, an attempt is made to predict deflections of the vertical in the same area. The method used in the computations is least squares collocation. Using empirical covariance functions for the data, the suitable errors for the different sources of observations, and the optimum cap radius around each point of evaluation, an accuracy better than±0.60m for geoidal heights and±1″.5 for deflections of the vertical is obtained taking into account existing systematic effects. This accuracy refers to the comparison between observed and predicted values.     

The GEOID96 high-resolution geoid height model for the United States

The 2 arc-minute × 2 arc-minute geoid model (GEOID96) for the United States supports the conversion between North American Datum 1983 (NAD 83) ellipsoid heights and North American Vertical Datum 1988 (NAVD 88) Helmert heights. GEOID96 includes information from global positioning system (GPS) height measurements at optically leveled benchmarks. A separate geocentric gravimetric geoid, G96SSS, was first calculated, then datum transformations and least-squares collocation were used to convert from G96SSS to GEOID96. Fits of 2951 GPS/level (ITRF94/NAVD 88) benchmarks to G96SSS show a 15.1-cm root mean square (RMS) around a tilted plane (0.06 ppm, 178^∘ azimuth), with a mean value of −31.4 cm (15.6-cm RMS without plane). This mean represents a bias in NAVD 88 from global mean sea level, remaining nearly constant when computed from subsets of benchmarks. Fits of 2951 GPS/level (NAD 83/NAVD 88) benchmarks to GEOID96 show a 5.5-cm RMS (no tilts, zero average), due primarily to GPS error. The correlated error was 2.5 cm, decorrelating at 40 km, and is due to gravity, geoid and GPS errors. Differences between GEOID96 and GEOID93 range from −122 to +374 cm due primarily to the non-geocentricity of NAD 83. Received: 28 July 1997 / Accepted: 2 September 1998     

Unification of vertical datums by GPS and gravimetric geoid models with application to Fennoscandia

The second Baltic Sea Level (BSL) GPS campaign was run for one week in June 1993. Data from 35 tide gauge sites and five fiducial stations were analysed, for three fiducial stations (Onsala, Mets?hovi and Wettzell) fixed at the ITRF93 system. On a time-scale of 5 days, precision was several parts in 10⁹ for the horizontal and vertical components. Accuracies were about 1 cm in comparison with the International GPS Geodynamical Service (IGS) coordinates in three directions. To connect the Swedish and the Finnish height systems, our numerical application utilises three approaches: a rigorous approach, a bias fit and a three-parameter fit. The results between the Swedish RH70 and the Finnish N 60 systems are estimated to −19.3 ± 6.5, −17 ± 6 and −15 ± 6 cm, respectively, by the three approaches. The results of the three indirect methods are in an agreement with those of a direct approach from levelling and gravity measurements. Received: 3 April 1996 / Accepted: 4 August 1997     

Determination of Geoid over South China Sea and Philippine Sea from Multi-satellite Altimetry Data

A new computational procedure for derivation of marine geoid on a 2.5′×2.5′grid in a non-tidal system over the South China Sea and the Philippine Sea from multi-satellite altimeter sea surface heights is discussed. Single-and dual-satellite crossovers were performed, and components of deflections of the vertical were determined at the crossover positions using Sand-well's computational theory, and gridded onto a 2.5′×2.5′resolution grid by employing the Shepard's interpolation procedure. 2.5′×2.5′grid of EGM96-derived components of deflections of the vertical and geoid heights were then used as reference global geopotential model quantities in a remove-restore procedure to implement the Molodensky-like formula via 1D-FFT technique to predict the geoid heights over the South China Sea and the Philippine Sea from the gridded altimeter-derived components of deflec-tions of the vertical. Statistical comparisons between the altimeter-and the EGM96- derived geoid heights showed that there was a root-mean-square agreement of ±0.35 m between them in a region of less tectonically active geological structures. However, over areas of tectonically active structures such as the Philippine trench, differences of about -19.9 m were obtained.     

区域性高程基准的统一

全球或区域性高程基准面的统一始终是大地测量学研究的主要内容之一 ,对于构建“数字区域”和“数字地球”及研究全球或区域性环境变化具有重要的科学意义和现实意义。本文利用全球重力场模型EGM 96和WDM94及GPS水准数据 ,确定了香港主要高程基准面与我国 195 6黄海高程基准面的重力位差。计算结果表明 ,这两个基准面的重力位差为 (8 36 6± 0 76 5 )m2 s-2 ,表明香港主要高程基准面平均低于我国 195 6黄海高程基准面 (0 85 5± 0 0 78)m2 s-2 。本文的计算结果有助于本地区高程基准面的统一     

Examining the impacts of urbanization on surface radiation using Landsat imagery

Metropolitan Beijing is facing many environmental problems such as haze and urban heat island due to the rapid urbanization. Surface shortwave, longwave, and net radiations are key components of the surface-atmosphere radiation budget. Since megacities are affected by the thermal radiation of complex landscape structures and atmospheric environments, quantitative and spatially explicit retrieval from remotely sensed data remains a challenge. We collected the surface radiation fluxes from seven fixed sites representing different land-use types to calibrate the local parameters for remotely sensed retrieval of net radiation. We proposed a remote sensing–based surface radiation retrieval method by embedding the underlying land covers and integrating the observational data. The improved method is feasible to accurately retrieve surface radiation and delineate spatial characteristics in metropolitan areas. The accuracy evaluation indicated that the difference between remotely sensed and in situ observed net radiation ranged within 0~± 40 W· m^?2. The root mean squared error of the estimated net surface radiation was 32.71 W· m^?2. The strongly spatial heterogeneity of surface radiation components in metropolitan Beijing was closely related to land-cover patterns from urban area to outskirts. We also found that the surface net radiation had a decreasing trend from 1984 to 2014, and the net radiation in the urban area was lower than that in the outskirts. According to the surface radiation budgets, urbanization resulted in the cooling effect in net radiation flux in the daytime, which was stemmed from low atmospheric transmittances from massive aerosol concentration and high surface albedo from light building materials.     

The absolute value of the geopotential

It is suggested that it would be worthwhile to determine the absolute value of the geopotential on the geopotential surface which corresponds to mean sea level. This number would replace the earth’s semi-major axis as the parameter which fixes the earth’s size; but slight variations in the parameter might be employed to study the dynamics of the sea. Fixing this number involves knowing the geopotential for a point on the orbit of a satellite whose true gravitational potential is also known.