Zero initial partial derivatives of satellite orbits with respect to force parameters violate the physics of motion of celestial bodies

Satellite orbits have been routinely used to produce models of the Earth’s gravity field. In connection with such productions, the partial derivatives of a satellite orbit with respect to the force parameters to be determined, namely, the unknown harmonic coefficients of the gravitational model, have been first computed by setting the initial values of partial derivatives to zero. In this note, we first design some simple mathematical examples to show that setting the initial values of partial derivatives to zero is generally erroneous mathematically. We then prove that it is prohibited physically. In other words, setting the initial values of partial derivatives to zero violates the physics of motion of celestial bodies. Supported by a Grant-in-Aid for Scientific Research (Grant No. B19340129)     

Assessment of GPS data for meteorological applications over Africa: Study of error sources and analysis of positioning accuracy

The aim of this study is to assess the availability and quality of data from the International GNSS Service (IGS) Global Positioning System (GPS) network in Africa, especially for retrieving zenith tropospheric delay (ZTD), from which precipitable water vapour (PWV) can be derived, in view of application to the African Monsoon Multidisciplinary Analysis (AMMA) project. Three major error sources for the GPS data analysis evaluating PWV in Africa are the accuracy of the satellite orbits, the correction for the radio delay induced by the ionosphere and the vertical site displacements due to ocean loading. The first part of this study examines these error sources and the validity of GPS data for meteorological applications in Africa in dedicated analyses spanning the year 2001. These analyses were performed using the IGS precise orbits. Weak degradation of baseline precision with increasing baseline lengths suggests that the average orbital error is not limiting the GPS analysis in Africa. The impact of the ionosphere has been evaluated during a maximum of solar activity in 2001. The loss of L₂ data has actually been observed. It amounts to 2% on average for 2001, with maxima of 8% during magnetic storm events. A slight decrease in formal accuracy of ZTD seems to be related to the loss of L₂ data at the end of the day. This indicates that scintillation effects are present in the GPS observations but however are not a major limitation. The impact of ocean loading is found to be significant on ZTD estimates (up to ±2 mm in equivalent PWV). The use of a proper ocean loading model eliminates this effect.The second aspect of this study concerns the IGS analysis quality for the African stations. The accuracy has been assessed through position dispersion between individual solutions and the most recent version of the IGS combined solution IGb00, and residuals from the transformation of the IGS combined solution into the International Terrestrial Reference Frame 2005. The positioning performance of the IGS analysis is consistent with an accuracy in ZTD of ±6 mm (±1 mm in PWV), as requested for meteorological applications such as planned in AMMA.     

Meta-heuristic maximum likelihood parameter estimation of the mixture normal distribution for hydro-meteorological variables

In the water resources field, there are emerging problems such as temporal changes of data and new additions of water sources. Non-mixture models are not efficient in analyzing these data because these models are developed under the assumption that data do not change and come from one source. Mixture models could successfully analyze these data because mixture models contain more than one modal. The expectation maximization (EM) algorithm has been widely used to estimate parameters of the mixture normal distribution for describing the statistical characteristics of hydro meteorological data. Unfortunately, the EM algorithm has some disadvantages, such as divergence, derivation of information matrices, local maximization, and poor accuracy. To overcome these disadvantages, this study proposes a new parameter estimation approach for the mixture normal distribution. The developed model estimates parameters of the mixture normal distribution by maximizing the log likelihood function using a meta-heuristic algorithm—genetic algorithm (GA). To verify the performance of the developed model, simulation experiments and practical applications are implemented. From the results of experiments and practical applications, the developed model presents some advantages, such as (1) the proposed model more accurately estimates the parameters even with small sample sizes compared to the EM algorithm; (2) not diverging in all application; and (3) showing smaller root mean squared error and larger log likelihood than those of the EM algorithm. We conclude that the proposed model is a good alternative in estimating the parameters of the mixture normal distribution for kutotic and bimodal hydrometeorological data.     

The usability of the undifferenced positioning techniques in establishing regional geodetic control networks: a case study in Poland

Recently undifferenced Precise Point Positioning (PPP) technique has become a subject of interest not only among researchers, but also satellite positioning practitioners like surveyors and engineers. Along with the development of precise clocks and orbits products, and the improvement of models mitigating interfering phenomena like atmospheric refraction, PPP has become an alternative to relative positioning in many field applications. This study concerns the usability of Undifferenced Positioning techniques in establishing geodetic control networks. Satellite observations from 13 stations equipped with high-end receivers and survey grade commercial receivers were processed using the NAvigation Package for Earth Observation Satellites -NAPEOS v. 3.3.1. In the study the standard PPP (float) and Undifferenced Network solution with clocks/orbits fixed strategies of post-processing were carried out using various observing intervals (30 min., 1 h, 2 h, 4 h, daily). The high accuracy results obtained with PPP and UD Network solution predisposes these strategies for the use in surveying tasks requiring even centimeter positioning accuracy.     

Improvement of ERS-1 orbits using along-track accelerations from DORIS data on SPOT2

In long-arc precise orbit determinations of altimetric satellites such as ERS-1, large errors may occur from mismodelling of aerodynamic drag and solar radiation pressure. Such surface forces for non-spherical satellites require accurate modelling of the effective area and particle-surface interactions, but the dominant source of error is neutral air density as derived from thermospheric models for aerodynamic drag. Several techniques can be employed to alleviate air-drag mismodelling but all require the solution of additional parameters from the tracking data. However, for ERS-1 the sparsity of laser range data limits the application of such empirical techniques. To overcome this, use can be made of the dense DORIS Doppler tracking for SPOT2 which is in a similar orbit to ERS-1. A recent investigation by CNES examined the use of drag scale factors from SPOT2 to constrain the ERS-1 orbit. An improvement to that methodology is to consider along-track mismodelling as observed by timing errors in the Doppler data for each pass of SPOT2. The along-track correction to the acceleration as derived from SPOT2 can then be applied to ERS-1 orbits, solving for a scale factor to absorb systematic errors - particularly that arising from the 50 km altitude difference. Results are presented of the associated improvement in ERS-1 orbits as derived from concurrent SPOT2 arcs. It will be seen that the procedure not only improves the laser range fit, but more importantly, leads to more precise radial positioning as evident in the altimeter and crossover residuals.     

Simulation of the transport of particles in coastal waters using forward and reverse time diffusion

Particle models are often used to simulate the spreading of a pollutant in coastal waters in case of a calamity at sea. Here many different particle tracks starting at the point of release are generated to determine the particle concentration at some critical locations. This Monte Carlo method, however, consumes a large CPU time. Recently, Milstein, et al. [Milstein, GN, Schoenmakers JGM, Spokoiny, V. Transition density estimation for stochastic differential equations via forward–reverse representations. Bernoulli 2004:10(2);281–312] introduced the concept of reverse-time diffusion and derived a reverse particle model from the original forward simulation model. While the original forward model provides results on where the pollutant will go to, the reverse system gives information about where the pollutant came from. The Monte Carlo estimator for the particle concentration can also be based on realizations of this reverse system. In this paper we apply this concept to estimate particle concentrations in coastal waters. The results of the experiments show that the CPU time compared with the classical Monte Carlo method is reduced at least order of magnitude.     

利用动力学方法解算GRACE时变重力场研究

本文利用动力学方法建立GRACE(Gravity Recovery And Climate Experiment)K波段距离变率(KBRR)观测、轨道观测与重力场系数的观测方程,通过GRACE Level 1B观测数据,成功解算出全球月时变重力场模型——IGG时变重力场模型,并将2008—2009年的解算结果与GRACE三大数据处理机构美国德克萨斯大学空间中心CSR(Center for Space Research)、美国宇航局喷气推进实验室JPL(Jet Propulsion Laboratory)和德国地学研究中心GFZ(GeoForschungs Zentrum)发布的最新全球时变重力场模型进行详细对比分析.结果表明:IGG结果在全球质量异常、中国及周边地区质量异常的趋势变化、全球质量异常均方差、2~60每阶位系数差值以及亚马逊流域和撒哈拉沙漠等典型区域平均质量异常等方面与CSR、JPL和GFZ解算的RL05结果较为一致.其中,IGG解算结果在2~20阶与CSR、GFZ和JPL最新解算结果基本一致,20~40阶IGG解算结果与GFZ、JPL单位最新解算结果较为接近,大于40阶IGG结果介于CSR与GFZ、JPL之间;亚马逊流域平均质量异常周年振幅IGG、CSR、GFZ和JPL获取到的结果分别为17.6±1.1cm、18.9±1.2cm、17.8±0.9cm和18.9±1.0cm等效水柱高.利用撒哈拉沙漠地区的平均质量异常做反演精度评定,IGG、CSR、GFZ和JPL的时变重力场获取到的平均质量异常均方差分别为1.1cm、0.9cm、0.8cm和1.2cm,表明IGG解算结果与CSR、GFZ和JPL最新发布的RL05结果在同一精度水平.     

电磁卫星地震应用进展及未来发展思考

法国DEMETER(Detection of Electro-Magnetic Emissions Transmitted from Earthquake Regions)卫星是世界上第一颗专门针对地震电离层扰动监测的电磁卫星, 于2004年发射, 2010年底结束运行, 共在轨飞行6.5年, 获得3万多条整轨数据, 为地震监测及电离层物理研究提供了坚实的数据基础。 全球科学家利用这颗卫星的数据开展了大量的地震应用研究, 发表文章上百篇, 将电磁卫星的地震应用研究推向了新的阶段。 中国第一颗电磁监测试验卫星CSES(China Seismo-Electromagnetic Satellite)于2018年2月2日成功发射, 目前已完成在轨测试并交付使用, 科学数据也已正式对外发布。 如何充分发挥CSES卫星的应用效能, 将空间电磁监测向业务化运行转化, 总结和思考DEMETER卫星的技术进步、 研究成果及曾经出现过的问题, 十分重要。 因此, 本文着重介绍DEMETER卫星在地震监测应用领域的代表性研究进展, 并结合CSES卫星的设计和运转实践, 对未来空间地震电磁探测及科学研究的发展方向进行一些初步讨论。     

基于多源卫星数据的小型水体蓝藻水华联合监测——以天津于桥水库为例

近年来水体富营养化呈扩张趋势,蓝藻水华不仅在太湖等大型湖泊频发,水面面积较小的天津于桥水库等也形势严峻,亟需加强卫星遥感监测.但是,以往在太湖等业务化使用非常成功的MODIS等卫星数据(约500 m),由于空间分辨率较低,难以满足小型水体的监测要求;而Landsat-8等空间分辨率较高的卫星数据(30 m),通常重返周期较长,无法满足水华高频监测需求.本文以天津市于桥水库(面积约80 km2)为研究区,针对常用的卫星数据,从空间、时间、光谱范围和数据可获取性共4个方面,评价不同卫星数据蓝藻水华监测能力和算法,同时对不同卫星监测结果一致性进行评估.结果表明:(1)筛选出国产HJ-1A\B CCD、GF-1 WFV和美国Landsat-8 OLI这3种卫星波段合适,空间分辨率较高,适用于桥水库蓝藻水华监测,但考虑到其重返周期较长,建议多星联合观测;(2)各个卫星监测结果与卫星影像目视解译结果基本一致,均方根误差和相对误差均分别控制在0.78 km2和4.9%以内;(3)不同卫星监测结果一致性良好,一致性精度达到99.5%;(4)根据历史影像结果,发现于桥水库2016年水质开始呈富营养化,藻华现象在夏、秋两季最为严重.研究表明,针对小型水面水体蓝藻水华监测,利用较高分辨率数据联合监测,是一种有效的替代策略,今后可在更多小型水域推广.     

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.     

Accuracy of the earth's gravity field models

Accuracy tests on the most recent GEM (Goddard Earth Model) gravity models for the representation of the Earth's gravity field, using specially devised statistical techniques of comparative evaluation, show that there is steady improvement in these models with time. On this comparative basis, the accuracy of determination for the spherical harmonic coefficients of the Earth's gravity field is ～ 100% for n = 2–6, 90–99% for n = 7–10, 55–80% for n = 11–14 and ? 50% for n ? 15, deteriorating rapidly with increasing n. The higher degree coefficients corresponding to n ≥ 15 do not seem to be determined accurately enough to be useful from a geophysical standpoint, though their cumulative contribution is undoubtedly useful for specific orbital computations. The estimated errors are 0.3 mGal for n = 2–6, 1.5 mgal for the frequency range n = 2–10, 3 mGal for n = 2–14 and 5–6 mGal for n = 2–22. These error estimates, especially the ones for the higher frequency range, may have been affected by possible errors in the comparison standards used for this evaluation. Consequently, some of the higher degree coefficients of recent GEM models may be more accurate than predicted by these tests.Due to the inherent deficiency of the comparison standards, the errors given in this paper should be treated as error estimates. The steady and progressive improvement, shown by the various GEM gravity models when tested against comparison standards 10E and WGS 72, i.e. the more recent a gravity model, the better it tests against the comparison standards in contrast to its predecessors, is remarkable, as the comparison standards themselves are several years older than the gravity models tested here. This clearly validates our choice of comparison standards, as well as the premises and predictions of our evaluation techniques. It also demonstrates the power and potential of these techniques, which only seem to be limited by the level of accuracy of the available standard of comparison.     

On the sampling errors from raingauges and microwave attenuation measurements

The sampling error formalism by North and Nakamoto (1989) has been widely referenced in research papers on sampling using space-borne sensors or ground-borne sensors. However, their formalism is found to not only underestimate the sampling error, especially for the raingauge network case, but also not be applicable for the cases of using a line of raingauges or microwave attenuation measurements. In this paper, the sampling error formalism has been revised and applied to the same sampling design and the same rainrate model as in North and Nakamoto (1989) for the comparison. The sampling error estimated using the revised formula was found to be more than 50% higher than that by North and Nakamoto (1989). For the case of using a line of raingauges we found that the sampling error converges to a certain value, not zero as in North and Nakamoto formalism, as the number of gauges increases. The microwave attenuation measurements case, which is the same as the case of using a line of infinite raingauges, also gives non-zero sampling errors. Finally, the combined sampling using both satellite and ground-borne sensors (e.g., raingauge network, a line of raingauges, or microwave attenuation measurements) was reviewed to check their design orthogonality and estimated the sampling errors for the combination of satellite and raingauge network case to see its behavior depending on various settings of these two different measurements.     

A Trade-Off Solution between Model Resolution and Covariance in Surface-Wave Inversion

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data.     

Comparing 1D and combined 1D/2D hydraulic simulations using high-resolution topographic data: a case study of the Koiliaris basin,Greece

The development of high spatial resolution digital elevation models takes place via the use of GeoEye-1 stereo-pair imagery, providing highly accurate geometrical representations of complex riverine systems. The combination of geographic information systems with hydraulic models facilitates the exploitation of satellite topographic information throughout the cross-section extraction process. One-dimensional HEC-RAS and combined 1D/2D HEC-RAS models are adjusted by making use of the resulting high-resolution input. Several hydraulic simulations are effectuated in order to test how significantly DEM resolution affects hydraulic modelling results, with regard also to the model dimensionality. The ability of the combined 1D/2D model, based mainly on the high-accuracy input data, provides an accurate estimate of the flood hazard area. Flood-prone areas could take advantage of high-accuracy results and facilitate the effective management of extreme events and sufficient decision making.     

基于CHAMP卫星与地面矢量数据联合建立中国地磁模型

首先对地面台站以及CHAMP卫星的矢量磁测数据进行预处理,结合12个子午工程台站最新的磁测数据,并利用第十二代国际地磁参考场模型(IGRF12)对不同数据归算至统一时间点,再结合第四代地磁场综合模型(CM4)计算并移除主磁场、磁层磁场、电离层磁场、感应磁场及较为微弱的环形场,最后通过球冠谐(SCH)模型联合建立了中国地区岩石圈磁场(地磁要素X、Y、Z和总强度F)的球冠谐模型(SCH2000),结合IGRF12得到了中国地磁模型(CGRF2000).建模同时考虑了测点数据海拔高度的影响,并讨论了截断阶数的选取以及边界效应的控制问题.通过比较均方偏差(RMS),认为8阶SCH2000模型可较好地反映中国地区岩石圈磁场,其分布与SCH1936、CM4以及Taylor多项式模型具有一定的相似性.从位置和强度来看,SCH2000模型所反映的岩石圈磁场更为准确,而与CM4存在一定差异,除了测点不同,截断阶数也是原因之一.通过验证,SCH2000模型各要素随高度的变化与CM4模型较为一致,所建立的CGRF2000与IGRF12模型的分布也较为相似.     

Simple formulas for the dynamic stiffness of pile groups

Simple formulas are derived for the dynamic stiffness of pile group foundations subjected to horizontal and rocking dynamic loads. The formulations are based on the construction of a general model of impedance matrices as the condensation of matrices of mass, damping, and stiffness, and on the identification of the values of these matrices on an extensive database of numerical experiments computed using coupled finite element–boundary element models. The formulations obtained can be readily used for the design of both floating piles on homogeneous half‐space and end‐bearing piles and are applicable for a wide range of mechanical and geometrical parameters of the soil and piles, in particular for large pile groups. For the seismic design of a building, the use of the simple formulas rather than a full computational model is shown to induce little error on the evaluation of the response spectra and time histories. Copyright © 2009 John Wiley & Sons, Ltd.     

Detecting surface geostrophic currents using wavelet filter from satellite geodesy

According to the features of spatial spectrum of the dynamic ocean topography (DOT),wavelet filter is proposed to reduce short-wavelength and noise signals in DOT. The surface geostrophic currents calculated from the DOT models filtered by wavelet filter in global and Kuroshio regions show more detailed information than those from the DOT models filtered by Gaussian filter. Based on a satellite gravity field model (CG01C) and a gravity field model (EGM96),combining an altimetry-derived mean sea surface height model (KMSS04),two mean DOT models are estimated. The short-wavelength and noise signals of these two DOT models are removed by using wavelet filter,and the DOT models asso-ciated global mean surface geostrophic current fields are calculated separately. Comparison of the surface geostrophic currents from CG01C and EGM96 model in global,Kuroshio and equatorial Pacific regions with that from oceanography,and comparison of influences of the two gravity models errors on the precision of the surface geostrophic currents velocity show that the accuracy of CG01C model has been greatly improved over pre-existing models at long wavelengths. At large and middle scale,the surface geostrophic current from satellite gravity and satellite altimetry agrees well with that from oceanography,which indicates that ocean currents detected by satellite measurement have reached relatively high precision.     

Tide model comparison over the Southwestern Atlantic Shelf

Sea surface height (SSH) as measured by satellites has become a powerful tool for oceanographic and climate related studies. Whereas in the open ocean good accuracy has been achieved, more energetic dynamics and a number of calibration problems have limited applications over continental shelves and near the coast. Tidal ranges in the Southwestern Atlantic (SWA) continental shelf are among the highest in the world ocean, reaching up to 12 m at specific locations. This fact highlights the relevance of the accuracy of the tidal correction that must be applied to the satellite data to be useful in the region. In this work, amplitudes and phases of tidal constituents are extracted from five global tide models and three regional models and compared to the corresponding harmonics estimated from coastal tide gauges (TGs) and satellite altimetry data. The Root Sum Square (RSS) of the misfit of the common set of the five tidal constituents solved by the models (M₂, N₂, S₂, K₁ and O₁) is higher than 18 cm close to the coast for two of the regional models and higher than 24.5 cm for the rest of the models considered. Both values are too high to provide an accurate estimation of geostrophic non-tidal currents from satellite altimetry in the coastal region. On the other hand, the global model with the highest spatial resolution has a RSS lower than 4.5 cm over the continental shelf even when the non-linear M₄ overtide is considered. Comparison with in-situ current measurements suggests that this model can be used to de-tide altimetry data to compute large-scale patterns of SSH and associated geostrophic velocities. It is suggested that a local tide model with very high resolution that assimilates in-situ and satellite data should meet the precision needed to estimate geostrophic velocities at a higher resolution both close to the coast and over the Patagonian shelf.