Impact of Geoid Improvement on Ocean Mass and Heat Transport Estimates

One long-standing difficulty in estimating the large-scale ocean circulation is the inability to observe absolute current velocities. Both conventional hydrographic measurements and altimetric measurements provide observations of currents relative to an unknown velocity at a reference depth in the case of hydrographic data, and relative to mean currents calculated over some averaging period in the case of altimetric data. Space gravity missions together with altimetric observations have the potential to overcome this difficulty by providing absolute estimates of the velocity of surface oceanic currents. The absolute surface velocity estimates will in turn provide the reference level velocities that are necessary to compute absolute velocities at any depth level from hydrographic data. Several studies have been carried out to quantify the improvements expected from ongoing and future space gravity missions. The results of these studies in terms of volume flux estimates (transport of water masses) and heat flux estimates (transport of heat by the ocean) are reviewed in this paper. The studies are based on ocean inverse modeling techniques that derive impact estimates solely from the geoid error budgets of forthcoming space gravity missions. Despite some differences in the assumptions made, the inverse modeling calculations all point to significant improvements in estimates of oceanic fluxes. These improvements, measured in terms of reductions of uncertainties, are expected to be as large as a factor of 2. New developments in autonomous ocean observing systems will complement the developments expected from space gravity missions. The synergies of in situ and satellite observing systems are considered in the conclusion of this paper. This revised version was published online in August 2006 with corrections to the Cover Date.     

Resolution Needed for an Adequate Determination of the Mean Ocean Circulation from Altimetry and an Improved Geoid

The sea surface topography observed by satellite altimetry is a combination of the geoid and of the ocean dynamic topography. Satellite altimetry has thus the potential to supply quasi-global maps of mean sea surface heights from which the mean geostrophic surface ocean currents can be derived, provided that the geoid is known with a sufficient absolute accuracy. At present, however, given the limited accuracy of the best available geoid, altimetric mean sea surface topographies have been derived only up to degree 15 or so, i.e. for wavelengths of approximately 2000 km and larger. CHAMP, GRACE, and the future GOCE missions are dedicated to the improvement of the Earth's gravity field from space. Several studies have recently investigated the impact of these improvements for oceanography, concluding to reductions of uncertainties on the oceanic flux estimates as large as a factor of 2 in the regions of intense an narrow currents. The aim of this paper is to focus on what are the typical horizontal scales of the mean dynamic topography of the ocean, and to compare their characteristics to the error estimates expected from altimetry and these future geoids. It gives also an illustration of the oceanic features that will be resolved by the combination of altimetry and the GRACE and GOCE geoids. It further reassesses the very demanding requirements in term of accuracy and resolution agreed in the design of these new gravity missions for ocean science applications. The present study relies on recent very high-resolution numerical Ocean General Circulation Model simulations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Combined Use of Altimetry and In Situ Gravity Data for Coastal Dynamics Studies

Accurate local geoids derived from in situ gravity data will be valuable in the validation of GOCE results. In addition it will be a challenge to use GOCE data in an optimal way, in combination with in situ gravity, to produce better local geoid solutions. This paper discusses the derivation of a new geoid over the NW European shelf, and its comparison with both tide gauge and altimetric sea level data, and with data from ocean models. It is hoped that over the next few years local geoid methods such as these can be extended to cover larger areas and to incorporate both in situ and satellite measured gravity data. This revised version was published online in August 2006 with corrections to the Cover Date.     

V: SEA LEVEL: Benefits of GRACE and GOCE to sea level studies

The recently published Third Assessment Reports of the Intergovernmental Panel on Climate Change have underlined the scientific interest in, and practical importance of past and potential future sea level changes. Space gravity missions will provide major benefits to the understanding of the past, and, thereby, in the prediction of future, sea level changes in many ways. The proposal for the GOCE mission described well the improvements to be expected from improved gravity field and geoid models in oceanography (for example, in the measurement of the time-averaged, or ‘steady state’, ocean surface circulation and better estimation of ocean transports), in geophysics (in the improvement of geodynamic models for vertical land movements), in geodesy (in positioning of tide gauge data into the same reference frame as altimeter data, and in improvement of altimeter satellite orbits), and possibly in glaciology (in improved knowledge of bedrock topography and ice sheet mass fluxes). GRACE will make many important steps towards these ‘steady state’ aims. However, its main purpose is the provision of oceanographic (and hydrological and meteorological) temporally-varying gravity information, and should in effect function as a global ‘bottom pressure recorder’, providing further insight into the 3-D temporal variation of the ocean circulation, and of the global water budget in general. This paper summaries several of these issues, pointing the way towards improved accuracy of prediction of future sea level change. This revised version was published online in August 2006 with corrections to the Cover Date.     

Error Characteristics Estimated from Champ,GRACE and GOCE Derived Geoids and from Satellite Altimetry Derived Mean Dynamic Topography

This paper presents a review of geoid error characteristics of three satellite gravity missions in view of the general problem of separating scientifically interesting signals from various noise sources. The problem is reviewed from the point of view of two proposed applications of gravity missions, one is the observation of the mean oceanic circulation whereby an improved geoid model is used as a reference surface against the long term mean sea level observed by altimetry. In this case we consider the presence of mesoscale variability during assimilation of derived surface currents in inverse models. The other experiment deals with temporal changes in the gravity field observed by GRACE in which case a proposed experiment is to monitor changes in the geoid in order to detect geophysical interesting signals such as variations in the continental hydrology and non-steric ocean processes. For this experiment we will address the problem of geophysical signal contamination and the way it potentially affects monthly geoid solutions of GRACE. This revised version was published online in August 2006 with corrections to the Cover Date.     

Tidal Models in a New Era of Satellite Gravimetry

The high precision gravity measurements to be made by recently launched (and recently approved) satellites place new demands on models of Earth, atmospheric, and oceanic tides. The latter is the most problematic. The ocean tides induce variations in the Earth's geoid by amounts that far exceed the new satellite sensitivities, and tidal models must be used to correct for this. Two methods are used here to determine the standard errors in current ocean tide models. At long wavelengths these errors exceed the sensitivity of the GRACE mission. Tidal errors will not prevent the new satellite missions from improving our knowledge of the geopotential by orders of magnitude, but the errors may well contaminate GRACE estimates of temporal variations in gravity. Solar tides are especially problematic because of their long alias periods. The satellite data may be used to improve tidal models once a sufficiently long time series is obtained. Improvements in the long-wavelength components of lunar tides are especially promising. This revised version was published online in August 2006 with corrections to the Cover Date.     

How Operational Oceanography Can Benefit from Dynamic Topography Estimates as Derived from Altimetry and Improved Geoid

With a precise geoid, GOCE will allow an estimation of absolute dynamic topography from altimetry. The projected benefits to operational oceanography and its applications are analyzed herein. After a brief overview of operational oceanography, we explain how the new geoids will be used in the future to improve real time altimeter products and to better constrain modelling and data assimilation systems. A significant impact is expected both for mesoscale (e.g. better estimations and forecasts of currents for pollution monitoring, marine safety, offshore industry) and climate (better initialization of coupled ocean/atmosphere models) applications. This revised version was published online in August 2006 with corrections to the Cover Date.     

IV: GEODESY: Remarks on the Role of Height Datum in Altimetry-Gravimetry Boundary-Value Problems

The problem of global geoid determination is usually solved using satellite altimetry data on the oceans, together with an oceanographic model of sea surface topography, and gravity anomaly data on the continents. Such data, however, enable to obtain only potential differences with respect to a reference surface whose absolute potential is unknown. This situation suggests to modify the classical mixed boundary-value problem of physical geodesy by inserting into the boundary conditions an unknown additive constant, that must be determined by imposing a suitable additional constraint. Yet, such formulation of the boundary-value problem, from the point of view of its mathematical properties, is not unconditionally well-posed, and, furthermore, does not reflect faithfully the available physical model, as the present knowledge of ocean circulation does not allow to connect along coastlines the reference surfaces defined on the oceans and on the continents. The introduction of two different unknown additive constants, one for the oceans and one for the earth, to be determined by imposing two additional constraints, gives rise to a more faithful picture of the present physical knowledge, and, at the same time, to a new well-posed formulation of the boundary-value problem. This revised version was published online in August 2006 with corrections to the Cover Date.     

A geopause satellite system concept

The forthcoming 10 cm range tracking accuracy capability holds much promise in connection with a number of Earth and ocean dynamics investigations. These include a set of earthquake-related studies of fault motions and the Earth's tidal, polar and rotational motions, as well as studies of the gravity field and the sea surface topography which should furnish basic information about mass and heat flow in the oceans. The state of the orbit analysis art is presently at about the 10 m level, or about two orders of magnitude away from the 10 cm range accuracy capability expected in the next couple of years or so. The realization of a 10 cm orbit analysis capability awaits the solution of four kinds of problems, namely, those involving orbit determination and the lack of sufficient knowledge of tracking system biases, the gravity field, and tracking station locations. The Geopause satellite system concept offers promising approaches in connection with all of these areas. A typical Geopause satellite orbit has a 14 hour period, a mean height of about 4.6 Earth radii, and is nearly circular, polar, and normal to the ecliptic. At this height only a relatively few gravity terms have uncertainties corresponding to orbital perturbations above the decimeter level. The orbit s, in this sense, at the geopotential boundary, i.e., the geopause. The few remaining environmental quantities which may be significant can be determined by means of orbit analyses and accelerometers. The Geopause satellite system also provides the tracking geometery and coverage needed for determining the orbit, the tracking system biases and the station locations. Studies indicate that the Geopause satellite, tracked with a 2 cm ranging system from nine NASA affiliated sites, can yield decimeter station location accuracies. Five or more fundamental stations well distributed in longitude can view Geopause over the North Pole. This means not only that redundant data are available for determining tracking system biases, but also that both components of the polar motion can be observed frequently. When tracking Geopause, the NASA sites become a two-hemisphere configuration which is ideal for a number of Earth physics applications such as the observation of the polar motion with a time resolution of a fraction of a day. Geopause also provides the basic capability for satellite-to-satellite tracking of drag-free satellites for mapping the gravity field and altimeter satellites for surveying the sea surface topography. Geopause tracking a coplanar, drag-free satellite for two months to 0.03 mm per second accuracy can yield the geoid over the entire Earth to decimeter accuracy with 2.5° spatial resolution. Two Geopause satellites tracking a coplanar altimeter satellite can then yield ocean surface heights above the geoid with 7° spatial resolution every two weeks. These data will furnish basic boundary condition information about mass and heat flows in the oceans which are important in shaping weather and climate.     

Spatial Gauss-Markov Models of Ocean Currents

Ocean currents are an important error source in marine inertial navigation systems (INS). Satellite radar altimeter data are used to construct self- consistent Gauss- Markov models of ocean currents. These models are useful for INS error analysis and optimal (Kalman) filtering of INS outputs.     

A Hybrid Navigation Concept Using a Spinning Satellite?Borne Interferometer and Self?Contained Equipment

This paper analyzes a hybrid navigation concept that uses signals from a radio interferometer mounted on a spinning geostationary satellite, preliminary position estimates from self-contained equipment, and stored a priori information on the past performance of this equipment. The craft-borne processor, optimum in the maximum a posteriori (MAP) sense, is designed to estimate position coordinates using only the incoming radio signals, although improved estimates result if the other two items are available. An error analysis starts with the derivation of an estimation error covariance matrix, whose elements depend on additive receiver noise and the physical parameters of the system. A minimum 1? estimation error in position is obtained by trading off these parameters. The effects of other major error sources, such as tropospheric phase fluctuations, multipath, and craft altitude uncertainty, are added to the estimation error to give a total 1? position error on the order of 3.7 to 5.6 km.     

The Elusive Stationary Geoid

We discuss the various problems occurring when trying to fix a geoid or geopotential model using sea level observations sampled during a limited time span from a bounded geographical domain. Such problems are on the one hand aliasing and spectral leakage, and on the other, the non-conservation of matter over only part of the world ocean. In the light of these issues we discuss whether it is sensible to include in a definition of the global geoid the radially symmetric part of either the mean sea level field itself, or its linear or nonlinear time dependence, arriving at a negative conclusion. This revised version was published online in August 2006 with corrections to the Cover Date.     

Detection of small objects in clutter using a GA-RBF neural network

Detection of small objects in a radar or satellite image is an important problem with many applications. Due to a recent discovery that sea clutter, the electromagnetic wave backscatter from a sea surface, is chaotic rather than purely random, computational intelligence techniques such as neural networks have been applied to reconstruct the chaotic dynamic of sea clutter. The reconstructed sea clutter dynamical system which usually takes the form of a nonlinear predictor does not only provide a model of the sea scattering phenomenon, but it can also be used to detect the existence of small targets such as fishing boats and small fragments of icebergs by observing abrupt changes in the prediction error. We applied a genetic algorithm (GA) to obtain an optimal reconstruction of sea clutter dynamic based on a radial basis function (RBF) neural network. This GA-RBF uses a hybrid approach that employes a GA to search for the optimum values of the following RBF parameters: centers, variance, and number of hidden nodes, and uses the least square method to determine the weights. It is shown here that if the functional form of an unknown nonlinear dynamical system can be represented exactly using an RBF net (i.e., no approximation error), this GA-RBF approach can reconstruct the exact dynamic from its time series measurements. In addition to the improved accuracy in modeling sea clutter dynamic, the GA-RBF is also shown to enhance the detectability of small objects embedded in the sea. Using real-life radar data that are collected in the east coast of Canada by two different radar systems: a ground-based radar and a satellite equipped with synthetic aperture radar (SAR), we show that the GA-RBF network is a reliable detector for small surface targets in various sea conditions and is practical for real-life search and rescue, navigation, and surveillance applications     

Aerosol-Cloud Interactions Control of Earth Radiation and Latent Heat Release Budgets

Aircraft observations and model simulations show that cloud development is strongly modulated by the impact of cloud-aerosol interactions on precipitation forming processes. New insights into the mechanisms by which aerosols dominate the cloud cover of marine shallow clouds suggest that feedbacks between the cloud microstructure and cloud dynamics through precipitation processes play a major role in determining when a solid cloud cover will break up into a field of trade wind cumulus. Cloud-aerosol interactions dominate not only the dynamics of marine shallow clouds, but also the lifetime and the vertical disposition of latent heat of deep convective clouds over ocean and even more strongly over land. Recent coincident satellite measurements of aerosols and cloud properties quantify the aerosol effects on cloud cover and radiative forcing on regional and global scales. The shapes of the satellite retrieved relations between aerosols and cloud properties are consistent with the suggested ways by which aerosols affect clouds via precipitation processes, particularly by affecting the intensity of the cloud vertical air motions and its vertical development.     

Measuring the Distribution of Ocean Mass Using GRACE

The Gravity Recovery and Climate Experiment (GRACE), which was successfully launched March 17, 2002, has the potential to create a new paradigm in satellite oceanography with an impact perhaps as large as was observed with the arrival of precision satellite altimetry via TOPEX/Poseidon (T/P) in 1992. The simulations presented here suggest that GRACE will be able to monitor non-secular changes in ocean mass on a global basis with a spatial resolution of ≈500 km and an accuracy of ≈3 mm water equivalent. It should be possible to recover global mean ocean mass variations to an accuracy of ≈1 mm, possibly much better if the atmospheric pressure modeling errors can be reduced. We have not considered the possibly significant errors that may arise due to temporal aliasing and secular gravity variations. Secular signals from glacial isostatic adjustment and the melting of polar ice mass are expected to be quite large, and will complicate the recovery of secular ocean mass variations. Nevertheless, GRACE will provide unprecedented insight into the mass components of sea level change, especially when combined with coincident satellite altimeter measurements. Progress on these issues would provide new insight into the response of sea level to climate change. This revised version was published online in August 2006 with corrections to the Cover Date.     

日地L2点航天器编队的分布式自主相对导航

为了实现航天器编队在日地L2点轨道的高精度相对导航,设计了一种分布式的自主导航方法。首先通过信息交互形成局部的测量构型,每颗卫星只基于邻居间的测量进行状态估计,降低了状态维数和计算量;然后根据相互估计的结果进行信息融合,提升估计的精度。在此基础上,对仿真结果进行了定量分析,给出了影响最终估计误差的主要因素测距精度、测量点间的基线与导航精度间的经验公式。在数值仿真中,所提方法达到了厘米量级定位精度和毫米每秒的测速精度。仿真结果表明：该方法有效,且对工程应用具有一定的参考价值。     

Present-Day Sea Level Change: Observations and Causes

We investigate climate-related processes causing variations of the global mean sea level on interannual to decadal time scale. We focus on thermal expansion of the oceans and continental water mass balance. We show that during the 1990s where global mean sea level change has been measured by Topex/Poseidon satellite altimetry, thermal expansion is the dominant contribution to the observed 2.5 mm/yr sea level rise. For the past decades, exchange of water between continental reservoirs and oceans had a small, but not totally negligible contribution (about 0.2 mm/yr) to sea level rise. For the last four decades, thermal contribution is estimated to about 0.5 mm/yr, with a possible accelerated rate of thermosteric rise during the 1990s. Topex/Poseidon shows an increase in mean sea level of 2.5 mm/yr over the last decade, a value about two times larger than reported by historical tide gauges. This would suggest that there has been significant acceleration of sea level rise in the recent past, possibly related to ocean warming. This revised version was published online in August 2006 with corrections to the Cover Date.     

星载GPS测量数据预处理方法研究

针对低地球轨道(LEO)卫星星载全球定位系统(GPS)接收机应用的特点,对星载GPS测量数据误差及其对周跳探测的影响进行了分析,提出TurboEdit数据预处理方法中周跳探测算法的改进算法。在原周跳判断算法的基础上,通过引入与测量数据观测高度角相关的加权系数,将周跳探测与测量误差紧密联系起来。根据观测高度角的变化对测量数据误差进行估计,并根据估计情况对加权系数取值,从而实现对周跳探测算法进行调节,达到降低周跳探测失误率的目的。增加参与定轨计算的观测数据量,提高了低轨卫星连续定轨的能力。通过GRACE编队卫星实测数据对改进算法进行了仿真验证。     

磁暴下的LEO卫星精密轨道确定

对低轨卫星（LEO）,大气阻尼摄动是主要的定轨误差源.尤其在发生磁暴时,求解一个大气阻尼因子的定轨方法已不能充分吸收大气密度计算不准所造成的定轨误差,因而在标校统一S波段（USB）的测量系统差和随机差时往往计算失真.本文提出了一种求解折线型Cd因子的新方法,克服了动力学模型不准所带来的定轨误差,通过与独立的GPS数据比较,定轨精度有明显提高,同时给出的测量系统差和随机差更加真实可信.     

空间信号完好性监测技术研究

星基增强导航系统(SBAS)通过向用户提供用户差分距离误差(UDRE:User Differential RangeError),来保证广播星历和星钟改正数的精度。本文设计了UDRE的一种改进算法,建立卫星导航系统星钟和星历误差的状态方程和量测方程,进行卡尔曼滤波计算星历与星钟误差改正数与改正精度,通过滤波误差估计精度矩阵计算UDRE,并做了相应的仿真分析和比较,结果表明:改进算法能够对UDRE做出更好的估计来满足星历及钟差改正误差相对应的伪距误差的置信限值。