S<Subscript>2</Subscript> tide aliasing in GRACE time-variable gravity solutions

Errors in high-frequency ocean tide models alias to low frequencies in time-variable gravity solutions from the Gravity Recovery and Climate Experiment (GRACE). We conduct an observational study of apparent gravity changes at a period of 161 days, the alias period of errors in the S₂ semidiurnal solar tide. We examine this S₂ alias in the release 4 (RL04) reprocessed GRACE monthly gravity solutions for the period April 2002 to February 2008, and compare with that in release 1 (RL01) GRACE solutions. One of the major differences between RL04 and RL01 is the ocean tide model. In RL01, the alias is evident at high latitudes, near the Filchner-Ronne and Ross ice shelves in Antarctica, and regions surrounding Greenland and Hudson Bay. RL04 shows significantly lower alias amplitudes in many of these locations, reflecting improvements in the ocean tide model. However, RL04 shows continued alias contamination between the Ronne and Larson ice shelves, somewhat larger than in RL01, indicating a need for further tide model improvement in that region. For unknown reasons, the degree-2 zonal spherical harmonics (C₂₀) of the RL04 solutions show significantly larger S₂ aliasing errors than those from RL01.     

Reducing errors in the GRACE gravity solutions using regularization

The nature of the gravity field inverse problem amplifies the noise in the GRACE data, which creeps into the mid and high degree and order harmonic coefficients of the Earth’s monthly gravity fields provided by GRACE. Due to the use of imperfect background models and data noise, these errors are manifested as north-south striping in the monthly global maps of equivalent water heights. In order to reduce these errors, this study investigates the use of the L-curve method with Tikhonov regularization. L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems using Tikhonov regularization. However, the computational effort required to determine the L-curve is prohibitively high for a large-scale problem like GRACE. This study implements a parameter-choice method, using Lanczos bidiagonalization which is a computationally inexpensive approximation to L-curve. Lanczos bidiagonalization is implemented with orthogonal transformation in a parallel computing environment and projects a large estimation problem on a problem of the size of about 2 orders of magnitude smaller for computing the regularization parameter. Errors in the GRACE solution time series have certain characteristics that vary depending on the ground track coverage of the solutions. These errors increase with increasing degree and order. In addition, certain resonant and near-resonant harmonic coefficients have higher errors as compared with the other coefficients. Using the knowledge of these characteristics, this study designs a regularization matrix that provides a constraint on the geopotential coefficients as a function of its degree and order. This regularization matrix is then used to compute the appropriate regularization parameter for each monthly solution. A 7-year time-series of the candidate regularized solutions (Mar 2003–Feb 2010) show markedly reduced error stripes compared with the unconstrained GRACE release 4 solutions (RL04) from the Center for Space Research (CSR). Post-fit residual analysis shows that the regularized solutions fit the data to within the noise level of GRACE. A time series of filtered hydrological model is used to confirm that signal attenuation for basins in the Total Runoff Integrating Pathways (TRIP) database over 320 km radii is less than 1 cm equivalent water height RMS, which is within the noise level of GRACE.     

GRACE时变重力场的滤波理论及质量变化分析

正由于GRACE(gravity recovery and climate experiment)时变重力场模型直接解算质量变化时存在较大的误差,需要对其进行相应的滤波处理,提高质量变化的反演精度。本文总结了GRACE监测全球与区域质量变化的研究进展,分析了最新时变重力场模型的精度及其滤波方法;提出了基于重力位系数协方差阵的时变重力场滤波方法;分析了南极冰盖的质量变化、亚马孙流域陆地水质量和海平面变化。本文的研究成果及创新点主要包括以下几个方面:     

Geological mapping of Jharia Coalfield,India using GRACE EGM2008 gravity data: a vertical derivative approach

High-resolution satellite gravity data of gravity recovery and climate experiment (GRACE) generated by Earth Gravity Model-2008 (EGM2008) have been utilised for geological mapping of the Jharia coalfield. The generated GRACE EGM2008 classical gravity data have been processed for estimation of gravity anomaly map. The gravity anomaly map has been enhanced using the first and second Vertical Derivatives techniques. Geological and structural maps of the study area have been overlapped over different derivative maps to analyse the correlation with the subsurface geological structures of the study area. Major distinct geological signatures, on different derivative maps, are correlated well with the existing geological map. Moreover, vertical derivative maps of the gravity data generated from GRACE EGM2008 model provide better agreement and understanding for geological setting of the Jharia coalfield.     

GRACE和GOCE卫星监测的青藏高原重力场特征

文章阐述了对青藏高原重力场进行研究的意义,并进一步利用重力卫星GRACE和GOCE的数据对该区域的重力场特征进行了描述.通过对该区域的重力异常、径向引力梯度的计算和分析,可以得出:在青藏高原的西部,有明显的3条重力异常区,这与当地的地形有关,也与断层的位置有关;引力梯度比重力异常具有更高的空间分辨率;重力变化剧烈的区域与梯度的异常区有一定的对应关系,同时也是地球动力活动变化剧烈的区域.     

基于SLR的GRACE卫星定轨中重力场模型对轨道精度的影响

以GRACE卫星为例,分析比较利用SLR观测资料进行卫星定轨时,采用不同重力场模型对GRACE卫星定轨精度的影响;以及重力场截断阶引起的积分轨道差异;同时,将定轨结果与采用GPS确定的定轨结果进行比较,分析与GPS定轨结果的差异.实验证明.重力场模型选择GGM02C的定轨结果优于选择JGM-3的定轨结果,基于SLR的定...     

Variations in the accuracy of gravity recovery due to ground track variability: GRACE,CHAMP, and GOCE

Following an earlier recognition of degraded monthly geopotential recovery from GRACE (Gravity Recovery And Climate Experiment) due to prolonged passage through a short repeat (low order resonant) orbit, we extend these insights also to CHAMP (CHAllenging Minisatellite Payload) and GOCE (Gravity field and steady state Ocean Circulation Explorer). We show wide track-density variations over time for these orbits in both latitude and longitude, and estimate that geopotential recovery will be as widely affected as well within all these regimes, with lesser track density leading to poorer recoveries. We then use recent models of atmospheric density to estimate the future orbit of GRACE and warn of degraded performance as other low order resonances are encountered in GRACE’s free fall. Finally implications for the GOCE orbit are discussed.     

基于ICESat-GLAS和GRACE卫星遥感资料的高亚洲冰川物质平衡变化研究

针对高亚洲冰川物质平衡和水资源的热点问题,首先利用2003—2009年ICESat-GLAS和2000年2月SRTM DEM V2.1资料,推算高亚洲地区冰川表面高程和冰量变化;其次,利用GRACE卫星的2002年8月至2012年12月时变重力场资料反演出研究区地表质量变化,继而在综合分析各流域内地表各种物质变化的基础上,恢复出流域冰川物质平衡;再次,根据高亚洲流域冰川的物质平衡状况,估算了外流河流域冰川物质亏损对海平面上升和内流河流域冰川物质亏损对内陆湖泊水量的贡献。     

Evaluation and validation of mascon recovery using GRACE KBRR data with independent mass flux estimates in the Mississippi Basin

The direct recovery of surface mass anomalies using GRACE KBRR data processed in regional solutions provides mass variation estimates with 10-day temporal resolution. The approach undertaken herein uses a tailored orbit estimation strategy based solely on the KBRR data and directly estimates mass anomalies from the GRACE data. We introduce a set of temporal and spatial correlation constraints to enable high resolution mass flux estimates. The Mississippi Basin, with its well understood surface hydrological modelling available from the Global Land Data Assimilation System (GLDAS), which uses advanced land surface modeling and data assimilation techniques, and a wealth of groundwater data, provides an opportunity to quantitatively compare GRACE estimates of the mass flux in the entire hydrological column with those available from independent and reliable sources. Evaluating GRACE’s performance is dependent on the accuracy ascribed to the hydrological information, which in and of itself is a complex challenge (Rodell in Hydrogeol J, doi:, 2007). Nevertheless, the Mississippi Basin is one of the few regions having a large hydrological signal that can support a meaningful GRACE comparison on the spatial scale resolved by GRACE. The isolation of the hydrological signal is dependent on the adequacy of the forward mass flux modeling for tides and atmospheric pressure variations. While these models have non-uniform global performance they are excellent in the Mississippi Basin. Through comparisons with the independent hydrology, we evaluate the effect on the solution of changing correlation times and distances in the constraints, altering the parameter recovery for areas external to the Mississippi Basin, and changing the relative strength of the constraints with respect to the KBRR data. The accuracy and stability of the mascon solutions are thereby assessed, especially with regard to the constraints used to stabilize the solution. We show that the mass anomalies, as represented by surface layer of water within regional cells have accuracy estimates of ±2–3 cm on par with the best hydrological estimates and consistent with our accuracy estimates for GRACE mass anomaly estimates. These solutions are shown to be very stable, especially for the recovery of semi-annual and longer period trends, where for example, the phase agreement for the dominant annual signal agrees at the 10-day level of resolution provided by GRACE. This validation confirms that mascons provide critical environmental data records for a wide range of applications including monitoring ground water mass changes.     

A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model

The Gravity and steady-state Ocean Circulation Explorer (GOCE) satellite mission measures Earth’s gravity field with an unprecedented accuracy at short spatial scales. In doing so, it promises to significantly advance our ability to determine the ocean’s general circulation. In this study, an initial gravity model from GOCE, based on just 2 months of data, is combined with the recent DTU10MSS mean sea surface to construct a global mean dynamic topography (MDT) model. The GOCE MDT clearly displays the gross features of the ocean’s steady-state circulation. More significantly, the improved gravity model provided by the GOCE mission has enhanced the resolution and sharpened the boundaries of those features compared with earlier satellite only solutions. Calculation of the geostrophic surface currents from the MDT reveals improvements for all of the ocean’s major current systems. In the North Atlantic, the Gulf Stream is stronger and more clearly defined, as are the Labrador and the Greenland currents. Furthermore, the finer scale features, such as eddies, meanders and branches of the Gulf Stream and North Atlantic Current system are visible. Similar improvements are seen also in the North Pacific Ocean, where the Kuroshio and its extension are well represented. In the Southern hemisphere, both the Agulhas and the Brazil-Malvinas Confluence current systems are well defined, and in the Southern ocean the Antarctic Circumpolar Current appears enhanced. The results of this preliminary analysis, using an initial GOCE gravity model, clearly demonstrate the potential of the GOCE mission. Already, at this early stage of the mission, the resolution of the MDT has been improved and the estimated surface current speeds have been increased compared with a GRACE satellite-only MDT. Future GOCE gravity models are expected to build further upon this early success.     

A methodology for least-squares local quasi-geoid modelling using a noisy satellite-only gravity field model

The paper is about a methodology to combine a noisy satellite-only global gravity field model (GGM) with other noisy datasets to estimate a local quasi-geoid model using weighted least-squares techniques. In this way, we attempt to improve the quality of the estimated quasi-geoid model and to complement it with a full noise covariance matrix for quality control and further data processing. The methodology goes beyond the classical remove–compute–restore approach, which does not account for the noise in the satellite-only GGM. We suggest and analyse three different approaches of data combination. Two of them are based on a local single-scale spherical radial basis function (SRBF) model of the disturbing potential, and one is based on a two-scale SRBF model. Using numerical experiments, we show that a single-scale SRBF model does not fully exploit the information in the satellite-only GGM. We explain this by a lack of flexibility of a single-scale SRBF model to deal with datasets of significantly different bandwidths. The two-scale SRBF model performs well in this respect, provided that the model coefficients representing the two scales are estimated separately. The corresponding methodology is developed in this paper. Using the statistics of the least-squares residuals and the statistics of the errors in the estimated two-scale quasi-geoid model, we demonstrate that the developed methodology provides a two-scale quasi-geoid model, which exploits the information in all datasets.     

Reduction of gravity by isostatic methods and by model earth methods contrasted

Conclusions The Model Earth reduction is less laborious than the current isostatic reductions and can lead to more accurate results. It has general application also as well as for the Stokes problem and the Earth's External Potential.     

GIS 优化 SRM 储流函数模型变量与参数方法研究

水文模型的结构确定后,模型参数的选择对水文模型整体性能和水文预报结果的好坏有着至关重要的影响。为使得模型的输出值能够尽可能地接近实际值,文中结合数字高程模型(DEM)和流域地质资料,使用GIS方法分别从优化数据源和加入地质因素影响分析优化模型参数两方面入手,对SRM储流函数模型进行优化,并以北海道沙流川流域为例对上述方法进行检验,结果说明了方法的可行性。     

Combination of temporal gravity variations resulting from superconducting gravimeter (SG) recordings, GRACE satellite observations and global hydrology models

Gravity recovery and climate experiment (GRACE)-derived temporal gravity variations can be resolved within the μgal (10^?8 m/s ²) range, if we restrict the spatial resolution to a half-wavelength of about 1,500 km and the temporal resolution to 1 month. For independent validations, a comparison with ground gravity measurements is of fundamental interest. For this purpose, data from selected superconducting gravimeter (SG) stations forming the Global Geodynamics Project (GGP) network are used. For comparison, GRACE and SG data sets are reduced for the same known gravity effects due to Earth and ocean tides, pole tide and atmosphere. In contrast to GRACE, the SG also measures gravity changes due to load-induced height variations, whereas the satellite-derived models do not contain this effect. For a solid spherical harmonic decomposition of the gravity field, this load effect can be modelled using degree-dependent load Love numbers, and this effect is added to the satellite-derived models. After reduction of the known gravity effects from both data sets, the remaining part can mainly be assumed to represent mass changes in terrestrial water storage. Therefore, gravity variations derived from global hydrological models are applied to verify the SG and GRACE results. Conversely, the hydrology models can be checked by gravity variations determined from GRACE and SG observations. Such a comparison shows quite a good agreement between gravity variation derived from SG, GRACE and hydrology models, which lie within their estimated error limits for most of the studied SG locations. It is shown that the SG gravity variations (point measurements) are representative for a large area within the accuracy, if local gravity effects are removed. The individual discrepancies between SG, GRACE and hydrology models may give hints for further investigations of each data series.     

Modeling pedestrian shopping behavior using principles of bounded rationality: model comparison and validation

Models of geographical choice behavior have been dominantly based on rational choice models, which assume that decision makers are utility-maximizers. Rational choice models may be less appropriate as behavioral models when modeling decisions in complex environments in which decision makers may simplify the decision problem using heuristics. Pedestrian behavior in shopping streets is an example. We therefore propose a modeling framework for pedestrian shopping behavior incorporating principles of bounded rationality. We extend three classical heuristic rules (conjunctive, disjunctive and lexicographic rule) by introducing threshold heterogeneity. The proposed models are implemented using data on pedestrian behavior in Wang Fujing Street, the city center of Beijing, China. The models are estimated and compared with multinomial logit models and mixed logit models. Results show that the heuristic models are the best for all the decisions that are modeled. Validation tests are carried out through multi-agent simulation by comparing simulated spatio-temporal agent behavior with the observed pedestrian behavior. The predictions of heuristic models are slightly better than those of the multinomial logit models.