Decorrelated GRACE time-variable gravity solutions by GFZ,and their validation using a hydrological model

We have analyzed recent gravity recovery and climate experiment (GRACE) RL04 monthly gravity solutions, using a new decorrelating post-processing approach. We find very good agreement with mass anomalies derived from a global hydrological model. The post-processed GRACE solutions exhibit only little amplitude damping and an almost negligible phase shift and period distortion for relevant hydrological basins. Furthermore, these post-processed GRACE solutions have been inspected in terms of data fit with respect to the original inter-satellite ranging and to SLR and GPS observations. This kind of comparison is new. We find variations of the data fit due to solution post-processing only within very narrow limits. This confirms our suspicion that GRACE data do not firmly ‘pinpoint’ the standard unconstrained solutions. Regarding the original Kusche (J Geod 81:733–749, 2007) decorrelation and smoothing method, a simplified (order-convolution) approach has been developed. This simplified approach allows to realize a higher resolution—as necessary, e.g., for generating computed GRACE observations—and needs far less coefficients to be stored.     

Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACE monthly solutions using an improved mascon approach

We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35–69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24–47%.     

Annual variations in water storage and precipitation in the Amazon Basin

We combine satellite gravity data from the gravity recovery and climate experiment (GRACE) and precipitation measurements from the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center’s (CPC) Merged Analysis of Precipitation (CMAP) and the Tropical Rainfall Measuring Mission (TRMM), over the period from mid-2002 to mid-2006, to investigate the relative importance of sink (runoff and evaporation) and source (precipitation) terms in the hydrological balance of the Amazon Basin. When linear and quadratic terms are removed, the time-series of land water storage variations estimated from GRACE exhibits a dominant annual signal of 250 mm peak-to-peak, which is equivalent to a water volume change of ~1,800 km³. A comparison of this trend with accumulated (i.e., integrated) precipitation shows excellent agreement and no evidence of basin saturation. The agreement indicates that the net runoff and evaporation contributes significantly less than precipitation to the annual hydrological mass balance. Indeed, raw residuals between the de-trended water storage and precipitation anomalies range from ±40 mm. This range is consistent with stream-flow measurements from the region, although the latter are characterized by a stronger annual signal than our residuals, suggesting that runoff and evaporation may act to partially cancel each other.     

High-frequency signal and noise estimates of CSR GRACE RL04

A sliding window technique is used to create daily-sampled Gravity Recovery and Climate Experiment (GRACE) solutions with the same background processing as the official CSR RL04 monthly series. By estimating over shorter time spans, more frequent solutions are made using uncorrelated data, allowing for higher frequency resolution in addition to daily sampling. Using these data sets, high-frequency GRACE errors are computed using two different techniques: assuming the GRACE high-frequency signal in a quiet area of the ocean is the true error, and computing the variance of differences between multiple high-frequency GRACE series from different centers. While the signal-to-noise ratios prove to be sufficiently high for confidence at annual and lower frequencies, at frequencies above 3 cycles/year the signal-to-noise ratios in the large hydrological basins looked at here are near 1.0. Comparisons with the GLDAS hydrological model and high frequency GRACE series developed at other centers confirm CSR GRACE RL04’s poor ability to accurately and reliably measure hydrological signal above 3–9 cycles/year, due to the low power of the large-scale hydrological signal typical at those frequencies compared to the GRACE errors.     

Mumbai 2005, Bihar 2008 Flood Reflected in Mass Changes Seen by GRACE Satellites

Gravity Recovery And Climate Experiment (GRACE) satellites were launched on March 17 2002 to derive with unprecedented accuracy, estimates of the global high resolution model of the earth’s gravity field. Local gravity changes with change in mass or mass redistribution. The mass changes can be due to hydrological events, seismic events or postglacial rebound, majorly. GRACE is sensitive to changes at large spatial scale since the resolution of GRACE is 400 km. Hydrological activities over basins provide sufficient mass changes to be detected by GRACE. In this research paper the discussion would be about two major flooding events in India, one being the 2005 monsoon flooding in Mumbai and nearby states and other being flood experienced by Bihar in 2008. The GRACE data is in the form of matrix consisting spherical harmonic coefficients. These coefficients are processed to obtain mass changes in terms of equivalent water height at a spatial scale of 400 km. The strategy of analysis is also discussed which need to be followed depending upon limitations of GRACE observation and requirement of application, here in this case application is flood induced mass change detection. Time-series and residual plots are generated and they show the flooding events for the concerned area as outliers. Better visualisation is obtained by residual plot, if there is a trend or systematic behaviour in time-series. This work points towards the qualitative capability of GRACE to detect flooding events at large spatial scale. Quantitative analysis requires in-situ data over the period of GRACE which is not possible for the cases discussed here.     

Mass evolution of Mediterranean,Black, Red,and Caspian Seas from GRACE and altimetry: accuracy assessment and solution calibration

We present new measurements of mass evolution for the Mediterranean, Black, Red, and Caspian Seas as determined by the NASA Goddard Space Flight Center (GSFC) GRACE time-variable global gravity mascon solutions. These new solutions are compared to sea surface altimetry measurements of sea level anomalies with steric corrections applied. To assess their accuracy, the GRACE- and altimetry-derived solutions are applied to the set of forward models used by GSFC for processing the GRACE Level-1B datasets, with the resulting inter-satellite range-acceleration residuals providing a useful metric for analyzing solution quality. We also present a differential correction strategy to calibrate the time series of mass change for each of the seas by establishing the strong linear relationship between differences in the forward modeled mass and the corresponding range-acceleration residuals between the two solutions. These calibrated time series of mass change are directly determined from the range-acceleration residuals, effectively providing regionally-tuned GRACE solutions without the need to form and invert normal equations. Finally, the calibrated GRACE time series are discussed and combined with the steric-corrected sea level anomalies to provide new measurements of the unmodeled steric variability for each of the seas over the span of the GRACE observation record. We apply ensemble empirical mode decomposition (EEMD) to adaptively sort the mass and steric components of sea level anomalies into seasonal, non-seasonal, and long-term temporal scales.     

Simulation study of a follow-on gravity mission to GRACE

The gravity recovery and climate experiment (GRACE) has been providing monthly estimates of the Earth’s time-variable gravity field since its launch in March 2002. The GRACE gravity estimates are used to study temporal mass variations on global and regional scales, which are largely caused by a redistribution of water mass in the Earth system. The accuracy of the GRACE gravity fields are primarily limited by the satellite-to-satellite range-rate measurement noise, accelerometer errors, attitude errors, orbit errors, and temporal aliasing caused by un-modeled high-frequency variations in the gravity signal. Recent work by Ball Aerospace & Technologies Corp., Boulder, CO has resulted in the successful development of an interferometric laser ranging system to specifically address the limitations of the K-band microwave ranging system that provides the satellite-to-satellite measurements for the GRACE mission. Full numerical simulations are performed for several possible configurations of a GRACE Follow-On (GFO) mission to determine if a future satellite gravity recovery mission equipped with a laser ranging system will provide better estimates of time-variable gravity, thus benefiting many areas of Earth systems research. The laser ranging system improves the range-rate measurement precision to ~0.6 nm/s as compared to ~0.2 μm/s for the GRACE K-band microwave ranging instrument. Four different mission scenarios are simulated to investigate the effect of the better instrument at two different altitudes. The first pair of simulated missions is flown at GRACE altitude (~480 km) assuming on-board accelerometers with the same noise characteristics as those currently used for GRACE. The second pair of missions is flown at an altitude of ~250 km which requires a drag-free system to prevent satellite re-entry. In addition to allowing a lower satellite altitude, the drag-free system also reduces the errors associated with the accelerometer. All simulated mission scenarios assume a two satellite co-orbiting pair similar to GRACE in a near-polar, near-circular orbit. A method for local time variable gravity recovery through mass concentration blocks (mascons) is used to form simulated gravity estimates for Greenland and the Amazon region for three GFO configurations and GRACE. Simulation results show that the increased precision of the laser does not improve gravity estimation when flown with on-board accelerometers at the same altitude and spacecraft separation as GRACE, even when time-varying background models are not included. This study also shows that only modest improvement is realized for the best-case scenario (laser, low-altitude, drag-free) as compared to GRACE due to temporal aliasing errors. These errors are caused by high-frequency variations in the hydrology signal and imperfections in the atmospheric, oceanographic, and tidal models which are used to remove unwanted signal. This work concludes that applying the updated technologies alone will not immediately advance the accuracy of the gravity estimates. If the scientific objectives of a GFO mission require more accurate gravity estimates, then future work should focus on improvements in the geophysical models, and ways in which the mission design or data processing could reduce the effects of temporal aliasing.     

Attenuation effect on seasonal basin-scale water storage changes from GRACE time-variable gravity

In order to effectively recover surface mass or geoid height changes from the gravity recovery and climate experiment (GRACE) time-variable gravity models, spatial smoothing is required to minimize errors from noise. Spatial smoothing, such as Gaussian smoothing, not only reduces the noise but also attenuates the real signals. Here we investigate possible amplitude attenuations and phase changes of seasonal water storage variations in four drainage basins (Amazon, Mississippi, Ganges and Zambezi) using an advanced global land data assimilation system. It appears that Gaussian smoothing significantly affects GRACE-estimated basin-scale seasonal water storage changes, e.g., in the case of 800 km smoothing, annual amplitudes are reduced by about 25–40%, while annual phases are shifted by up to 10°. With these effects restored, GRACE-estimated water storage changes are consistently larger than model estimates, indicating that the land surface model appears to underestimate terrestrial water storage change. Our analysis based on simulation suggests that normalized attenuation effects (from Gaussian smoothing) on seasonal water storage change are relatively insensitive to the magnitude of the true signal. This study provides a numerical approach that can be used to restore seasonal water storage change in the basins from spatially smoothed GRACE data.     

不同模型的地表质量异常一阶项、二阶项估计

为了合理补充重力场恢复与气候试验卫星（Gravity Recovery and Climate Experiment,GRACE）时变重力场的一阶斯托克斯系数（C₁₀、C₁₁、S₁₁）和替换二阶斯托克斯系数（C₂₀）,介绍了相关GRACE-OBP算法及其改进的算法,比较了相应的Chamber Model和4个Sun Model的一阶系数及其计算的地表质量异常,同时比较了基于卫星激光测距观测的Cheng Model与4个Sun Model的C₂₀及其地表质量异常。结果表明,GRACE-OBP算法的一阶系数、卫星激光测距观测的C₂₀及其地表质量异常与改进的GRACE-OBP算法在趋势项上有很大差异,但周年项差异相对较小。利用不同截断阶数和不同机构的GRACE时变重力场模型,对其趋势项和周年项都有一定影响,且对趋势项影响更大。因此,在计算陆地水储量变化时,建议使用改进的GRACE-OBP算法的估计结果,使用较理想的、截断阶数较高的GRACE时变重力模型。     

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.     

Simulated estimation of hydrological loads from GRACE

Four different basin functions are developed to estimate water storage variations within individual river basins from time variations in the Stokes coefficients now available from the GRACE mission. The four basin functions are evaluated using simulated data. Basin functions differ in how they minimize effects of three major error sources: measurement error; leakage of signal from one region to another; and errors in the atmospheric pressure field removed during GRACE data processing. Three of the basin functions are constant in time, while the fourth changes monthly using information about the signal (hydrologic and oceanic load variations). To test basin functions performance, Stokes coefficient variations from land and ocean models are synthesized, and error levels 50 and 100 times greater than pre-launch GRACE error estimate are used to corrupt them. Errors at 50 times pre-launch estimates approximately simulate current GRACE data. GRACE recovery of water storage variations is attempted for five different river basins (Amazon, Mississippi, Lena, Huang He and Oranje), representing a variety of sizes, locations, and signal variance. In the large basins (Amazon, Mississippi and Lena), water storage variations are recovered successfully at both error levels. As the error level increases from 50 to 100 times, basin functions change their shape, yielding less atmospheric pressure error and more leakage error. Amplitude spectra of measurement and atmospheric pressure errors have different shapes, but the best results are obtained when both are used in basin function design. When high-quality information about the signal is available, for example from climate and ocean models, changing the basin function each month can reduce leakage error and improve estimates of time variable water storage within basins.     

Black sea annual and inter-annual water mass variations from space

This study evaluates the performance of two widely used GRACE solutions (CNES/GRGS RL02 and CSR RL04) in deriving annual and inter-annual water mass variations in the Black Sea for the period 2003–2007. It is demonstrated that the GRACE derived water mass variations in the Black Sea are heavily influenced by the leakage of hydrological signals from the surrounding land. After applying the corresponding correction, we found a good agreement with water mass variations derived from steric-corrected satellite altimetry observations. Both GRACE and altimetry show significant annual water mass variations of roughly 7 cm amplitude peaking in May and a semi-annual signal of roughly 3 cm peaking in June and in December. The amplitude of the annual water mass signal varies significantly from year to year and is significantly larger during 2004–2006 than in 2003 and 2007. This is also in agreement with the steric corrected altimetry.     

The GeoForschungsZentrum Potsdam/Groupe de Recherche de Gèodésie Spatiale satellite-only and combined gravity field models: EIGEN-GL04S1 and EIGEN-GL04C

The recent improvements in the Gravity Recovery And Climate Experiment (GRACE) tracking data processing at GeoForschungsZentrum Potsdam (GFZ) and Groupe de Recherche de Géodésie Spatiale (GRGS) Toulouse, the availability of newer surface gravity data sets in the Arctic, Antarctica and North-America, and the availability of a new mean sea surface height model from altimetry processing at GFZ gave rise to the generation of two new global gravity field models. The first, EIGEN-GL04S1, a satellite-only model complete to degree and order 150 in terms of spherical harmonics, was derived by combination of the latest GFZ Potsdam GRACE-only (EIGEN-GRACE04S) and GRGS Toulouse GRACE/LAGEOS (EIGEN-GL04S) mean field solutions. The second, EIGEN-GL04S1 was combined with surface gravity data from altimetry over the oceans and gravimetry over the continents to derive a new high-resolution global gravity field model called EIGEN-GL04C. This model is complete to degree and order 360 and thus resolves geoid and gravity anomalies at half- wavelengths of 55 km at the equator. A degree-dependent combination method has been applied in order to preserve the high accuracy from the GRACE satellite data in the lower frequency band of the geopotential and to form a smooth transition to the high-frequency information coming from the surface data. Compared to pre-CHAMP global high-resolution models, the accuracy was improved at a spatial resolution of 200 km (half-wavelength) by one order of magnitude to 3 cm in terms of geoid heights. The accuracy of this model (i.e. the commission error) at its full spatial resolution is estimated to be 15 cm. The model shows a reduced artificial meridional striping and an increased correlation of EIGEN-GL04C-derived geostrophic meridional currents with World Ocean Atlas 2001 (WOA01) data. These improvements have led to select EIGEN-GL04C for JASON-1 satellite altimeter data reprocessing. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

利用局部高空间分辨率大气数据计算GRACE大气去混频模型

在计算GRACE重力场反演中的大气去混频模型时,针对ECMWFop或ERA-Interim大气数据空间水平分辨率不足的问题,提出了一种局部区域高空间水平分辨率大气数据与全球大气数据合理拼接融合的方法。利用欧洲局部区域的大气数据与ERA-Interim大气数据融合计算了一组改进的大气去混频模型,从谱域、空域及星间距离变率残差角度分析了改进大气去混频模型的质量。结果表明改进大气去混频模型相对于常规大气去混频模型的质量提高最大比例为1.87%,与AOD1BRL05相对于RL04的提高比例2.27%相当,验证了高空间水平分辨率大气数据确实有助于提高大气去混频模型质量的结论,为改进GRACE提取局部区域特定质量变化信号提供了一种方法。     

Bias in GRACE estimates of ice mass change due to accompanying sea-level change

Observations of spatio-temporal variations in the geopotential using the GRACE satellites have been used to estimate recent mass fluxes from polar ice sheets and glaciers. However, these estimates have not considered the potential bias associated with the migration of water that accompanies the ice melt. This migration is driven by the diminished gravitational attraction of the melting ice reservoir, and this migration, as well as the crustal loading it induces, will contribute to the observed geopotential anomaly. The extent to which this contribution contaminates the ice mass flux estimates depends on how far the smoothing filters applied to the GRACE data extend beyond the ice margins into the ocean. Using the Antarctic Peninsula as a case study, we estimate the magnitude of this bias for a range of melt areas and Gaussian smoothing filter radii. We conclude that GRACE estimates of ice mass loss over the Antarctic Peninsula are systematically overestimating the loss by up to 10  $\%$ for filter radii of less than 500 km.     

Accuracy assessment of the monthly GRACE geoids based upon a simulation

The purpose of this paper is to demonstrate the effect of geophysical background model errors that affects temporal gravity solutions provided by the Gravity Recovery And Climate Experiment (GRACE). Initial performance estimates by Dickey et al. (1997) suggested a formal geoid RMS error better than 0.1 mm up to spherical harmonic degree 5. Now that the GRACE gravity models and data are available, it is evident that these original expectations were too optimistic. Our hypothesis is that this is partially explained by errors in geophysical background models that need to be applied in the GRACE data reduction, and that this effect was not considered by Dickey et al. (1997). We discuss the results of a closed-loop simulation, where satellite trajectory prediction software is used for the generation of GRACE range-rate data and GRACE orbit solutions with the help of the Global Positioning System (GPS). During the recovery step in our closed-loop simulation, we show that simulated nuisance signals (based on tide and air pressure model differences) map to a 0.7 mm geoid effect for periods longer than 3 months and to less than 0.4 mm for periods shorter than 3 months. The long-period geoid hydrology signal is at a level of 4.5 mm, while the short-period hydrology is at 0.25 mm. The long-period ocean bottom pressure (OBP) signal maps at 0.8 mm and for short periods it is 0.4 mm. We conclude that short-period effects are difficult to observe by GRACE and that long-period effects, like hydrology, are easier to recover than OBP variations.     

利用卫星观测数据评估GLDAS与WGHM水文模型的适用性

利用2002—2012年的GLDAS和WGHM模型模拟水文产品,以及重力恢复与气候试验卫星（Gravity Recovery and Climate Experiment,GRACE）观测数据,计算了全球范围内30个主要流域的水储量变化时间序列,从模拟数据与观测数据的年周期振幅、长期趋势项及时空分布一致性等几个方面,对GLDAS和WGHM进行了评估。结果表明,GLDAS的4个子模型都表现出了明显的季节性变化,CLM年周期振幅输出最小,MOSAIC和VIC最大,NOAH居中,且最接近4个子模型的平均值。与GRACE结果相比,约80%流域的GLDAS与WGHM模型年周期振幅输出呈明显低估现象,且GLDAS的低估程度大于WGHM,但靠近北极高纬度地区的流域有相反的情况出现。在长期趋势项方面,三者结果差异较大,尤其是对于面积较小且人类活动影响较大的流域,GLDAS与WGHM模型不能充分反映人类活动的影响,模型输出表现较差,GRACE结果更接近实际情况。此外,还研究了流域水储量长期变化趋势与灌溉率的关系,发现呈现明显下降趋势的流域主要集中在高灌溉率（>10%）地区,而灌溉率是影响流域水储量变化的重要因素之一。     

Detection of small hydrological variations in gravity by repeated observations with relative gravimeters

Recently, a new application of time-dependent gravity observations is emerging: the study of natural hydrological mass changes and their underlying processes. Complementary to GRACE data and continuous recordings with superconducting gravimeters, repeated observations with relative instruments on a local network may contribute to gain additional information on spatial changes in hydrology. The questions that need to be addressed are whether the results of these repeated measurements will be of sufficiently high resolution and accuracy, as well as how unique the information obtained will be. To examine this, a local gravity network with maximum point distances of 65 m was established in a hilly area around the Geodynamic Observatory Moxa, Germany. Using three to five LaCoste & Romberg relative gravimeters repeated measurements were carried out in a seasonal rhythm as well as at particular events like snowmelt or dryness in 17 campaigns between November 2004 and April 2007. The standard deviations obtained by least squares adjustment range from ±9 to ±14 nm/s² for a gravity difference of one campaign, thus for gravity changes between two campaigns from ±13 to ±20 nm/s². Between the points of the network, spatial gravity changes of up to 171 nm/s² (139 nm/s² between two successive campaigns) could be proven significantly. They correlate with changes in the local hydrological situation. Particularly, a steep slope next to the observatory is identified as a gravimetrically significant hydrological compartment. The results obtained contribute to an improved reduction of the local hydrological signal in continuous gravity recordings and provide constraints to hydrological models.     

利用ICA方法提取奥卡万戈三角洲水储量变化信号

利用重力恢复与气候实验(gravity recovery and climate experiment, GRACE)时变地球重力场模型计算得到非洲奥卡万戈三角洲地区2003-01—2014-12的陆地水储量变化信息,分别采用主成分分析(principal component analysis, PCA)和独立成分分析(independent component analysis, ICA)提取质量变化信号,并与全球陆地数据同化系统(global land data assimilation system, GLDAS)的水文模型进行对比。结果显示,在奥卡万戈河流域东北部,水储量表现出很强的周期性变化,两种数据空间特征分布的信号出现在相同位置的成分GRACE-IC1和GLDAS-IC1对应的时间序列的相关系数达到0.85。奥卡万戈三角洲地区水储量从2003-01—2011-10呈现上升趋势,两种数据空间特征分布的信号出现在相同位置的成分GRACE-IC2和GLDAS-IC3对应的时间序列的相关系数达到0.81,说明GRACE反演结果与GLDAS水文模型反演结果在研究区域内具有很强的一致性。引入全球降水气候中心降水数据和Water GAP全球水文模型数据对研究区域陆地水储量变化的原因进行分析。实验结果表明,相对于传统的多项式拟合方法,ICA可以在较大区域内直接对特定位置质量变化信号的时空特征进行提取;对比GRACE数据两种方法分解结果的第3成分可以看出,在空间尺度和时间尺度上,ICA方法对信号的分解能力要优于主成分分析方法。