LSTM-Based Forecasting Model for GRACE Accelerometer Data

The Gravity Recovery and Climate Experiment (GRACE) satellite mission, spanning from 2002 to 2017, has provided a valuable dataset for monitoring variations in Earth's gravity field, enabling diverse applications in geophysics and hydrology. The mission was followed by GRACE Follow-On in 2018, continuing data collection efforts. The monthly Earth gravity field, derived from the integration different instruments onboard satellites, has shown inconsistencies due to various factors, including gaps in observations for certain instruments since the beginning of the GRACE mission. With over two decades of GRACE and GRACE Follow-On data now available, this paper proposes an approach to fill the data gaps and forecast GRACE accelerometer data. Specifically, we focus on accelerometer data and employ Long Short-Term Memory (LSTM) networks to train a model capable of predicting accelerometer data for all three axes. In this study, we describe the methodology used to preprocess the accelerometer data, prepare it for LSTM training, and evaluate the model's performance. Through experimentation and validation, we assess the model's accuracy and its ability to predict accelerometer data for the three axes. Our results demonstrate the effectiveness of the LSTM forecasting model in filling gaps and forecasting GRACE accelerometer data

Tuning a gravimetric quasigeoid to GPS-levelling by non-stationary least-squares collocation

This paper addresses implementation issues in order to apply non-stationary least-squares collocation (LSC) to a practical geodetic problem: fitting a gravimetric quasigeoid to discrete geometric quasigeoid heights at a local scale. This yields a surface that is useful for direct GPS heighting. Non-stationary covariance functions and a nonstationary model of the mean were applied to residual gravimetric quasigeoid determination by planar LSC in the Perth region ofWestern Australia. The non-stationarymodel of the mean did not change the LSC results significantly. However, elliptical kernels in non-stationary covariance functions were used successfully to create an iterative optimisation loop to decrease the difference between the gravimetric quasigeoid and geometric quasigeoid at 99 GPS-levelling points to a user-prescribed tolerance

A review of non-stationary spatial methods for geodetic least-squares collocation

This paper reviews a field that is herein termed spatial ?non-stationarity?, which is specifically concerned with non-stationarity in the geodetic theory of least-squares collocation (LSC). In practice, many geodesists rely on stationary assumptions in LSC, i.e., using a constant mean and isotropic and spatially invariant covariance for estimation and prediction of geodetic quantities. However, new theories in spatial statistics and geostatistics allow for better statistical methodologies to be used in geodesy. The aim of this paper is to introduce these methodologies and adapt them for dealing with non-stationarity in LSC

Progress Towards the New Australian Geoid-type Model as a Replacement for AUSGeoid98

We are nearing the final stages of producing a new geoid-type model for Australia that will replace AUSGeoid98. The terminology geoid-type reflects that the gravimetric quasigeoid model will be fitted to Australia-wide GPS-levelling data, probably using least-squares collocation. This will provide a user-friendly product for the more direct transformation of GPS-derived ellipsoidal heights to normal-orthometric heights on the Australian Height Datum (AHD). This has become necessary because Australian government geodetic authorities have decided to retain the AHD for the 'foreseeable future', whereas it is well known that the AHD contains about 1-2m distortions mainly due to fixing the AHD height to zero at 32 tide gauges. Another driver is that there is an increasing trend towards establishing vertical control using carrier-phase GPS via the single-point precise point positioning (PPP) technique or over very long baselines using the AUSPOS on-line service. When the quasigeoid model was used with differential GPS over short baselines, common/correlated errors cancelled in this relative mode, whereas they do not in the absolute or long-baseline modes. As such, AUSPOS and PPP users of AUSGeoid98 can sometimes find up to 2m discrepancies with existing AHD benchmarks. In addition, we will use improved quasigeoid modelling techniques and the most recent datasets available, such as GRACE (Gravity Recovery and Climate Experiment) global gravity field models, satellite-altimeter-derived gravity anomalies in marine areas that have been re-tracked to improve them in the coastal zone, the latest cleaned release of the Australian land gravity database, the version 2 Australian digital elevation model, which now allows the computation of nine arc-second resolution topographical effects. Some emphasis will be placed on the use of modified kernels as high-pass filters to manage long-wavelength errors in the Australian terrestrial gravity and terrain data, so that they do not contaminate the high-quality GRACE data

Instrument data simulations for GRACE Follow-on: Observation and noise models

The Gravity Recovery and Climate Experiment (GRACE) mission has yielded data on the Earth's gravity field to monitor temporal changes for more than 15 years. The GRACE twin satellites use microwave ranging with micrometre precision to measure the distance variations between two satellites caused by the Earth's global gravitational field. GRACE Follow-on (GRACE-FO) will be the first satellite mission to use inter-satellite laser interferometry in space. The laser ranging instrument (LRI) will provide two additional measurements compared to the GRACE mission: Interferometric inter-satellite ranging with nanometre precision and inter-satellite pointing information. We have designed a set of simulated GRACE-FO data, which include LRI measurements, apart from all other GRACE instrument data needed for the Earth's gravity field recovery. The simulated data files are publicly available via https://doi.org/10.22027/AMDC2 and can be used to derive gravity field solutions like from GRACE data. This paper describes the scientific basis and technical approaches used to simulate the GRACE-FO instrument data.data. This paper describes the scientific basis and technical approaches used to simulate the GRACE-FO instrument data

COST-G: towards a new GRACE and GRACE-FO combination

The combination service for time-variable gravity fields (COST-G) provides the full time-series of monthly GRACE gravity fields: COST-G GRACE RL01, combined in reprocessing mode, and a steadily growing time-series of monthly GRACE-FO gravity fields: COST-G GRACE-FO RL01 OP, combined on an operational basis. Both time-series are currently considered for re-combination. In case of GRACE, new high-quality time-series from Chinese analysis centers are available for combination. In case of GRACE-FO, a revision of the weighting scheme, developed in the frame of the Horizon2020 project Global Gravity-based Groundwater Product (G3P), and the availability of reprocessed GRACE-FO time-series from AIUB, CSR, GFZ, and JPL, lead to a significant improvement of the combined gravity fields. We present the preliminary re-combined GRACE and GRACE-FO time-series and quantify the differences with respect to the COST-G RL01 series in terms of signal and noise content

Modification of the least-squares collocation method for non-stationary gravity field modelling

Geodesy deals with the accurate analysis of spatial and temporal variations in the geometry and physics of the Earth at local and global scales. In geodesy, least-squares collocation (LSC) is a bridge between the physical and statistical understanding of different functionals of the gravitational field of the Earth. This thesis specifically focuses on the [incorrect] implicit LSC assumptions of isotropy and homogeneity that create limitations on the application of LSC in non-stationary gravity field modeling. In particular, the work seeks to derive expressions for local and global analytical covariance functions that account for the anisotropy and heterogeneity of the Earth's gravity field.Standard LSC assumes 2D stationarity and 3D isotropy, and relies on a covariance function to account for spatial dependence in the observed data. However, the assumption that the spatial dependence is constant throughout the region of interest may sometimes be violated. Assuming a stationary covariance structure can result in over-smoothing, e.g., of the gravity field in mountains and under-smoothing in great plains. The kernel convolution method from spatial statistics is introduced for non-stationary covariance structures, and its advantage in dealing with non-stationarity in geodetic data is demonstrated.Tests of the new non-stationary solutions were performed over the Darling Fault, Western Australia, where the anomalous gravity field is anisotropic and non-stationary. Stationary and non-stationary covariance functions are compared in 2D LSC to the empirical example of gravity anomaly interpolation. The results with non-stationary covariance functions are better than standard LSC in terms of formal errors and cross-validation. Both non-stationarity of mean and covariance are considered in planar geoid determination by LSC to test how differently non-stationarity of mean and covariance affects the LSC result compared with GPS-levelling points in this area. Non-stationarity of the mean was not very considerable in this case, but non-stationary covariances were very effective when optimising the gravimetric quasigeoid to agree with the geometric quasigeoid.In addition, the importance of the choice of the parameters of the non-stationary covariance functions within a Bayesian framework and the improvement of the new method for different functionals on the globe are pointed out

The ANU GRACE visualisation web portal

The launch of the Gravity Recovery and Climate Experiment (GRACE) space gravity mission opened new horizons to the scientific community for environmental monitoring. Through the provision of estimates of temporal changes in the Earth's gravity field, th

GRACETOOLS—GRACE Gravity Field Recovery Tools

This paper introduces GRACETOOLS, the first open source gravity field recovery tool using GRACE type satellite observations. Our aim is to initiate an open source GRACE data analysis platform, where the existing algorithms and codes for working with GRACE data are shared and improved. We describe the first release of GRACETOOLS that includes solving variational equations for gravity field recovery using GRACE range rate observations. All mathematical models are presented in a matrix format, with emphasis on state transition matrix, followed by details of the batch least squares algorithm. At the end, we demonstrate how GRACETOOLS works with simulated GRACE type observations. The first release of GRACETOOLS consist of all MATLAB M-files and is publicly available at Supplementary Materials

Assessing Terrestrial Water Storage Variations in Southern Spain Using Rainfall Estimates and GRACE Data

This paper investigates the relationship between rainfall, groundwater and Gravity Recovery and Climate Experiment (GRACE) data to generate regional-scale estimates of terrestrial water storage variations in the Andalucía region of southern Spain. These estimates can provide information on groundwater depletion (caused by periods of low rainfall or droughts) and groundwater recovery. The spatial distribution of groundwater bodies in southern Spain is complex and current in situ groundwater monitoring methods are deficient, particularly in terms of obtaining representative samples and in implementing and maintaining groundwater monitoring networks. The alternative approach proposed here is to investigate the relationship between precipitation time series and changes in the terrestrial water storage estimated from GRACE observations. The results were validated against the estimated fluctuation in regional groundwater. The maximum correlation between the mean groundwater level and the GRACE observations is 0.69 and this occurs at a lag of one month because the variation in gravity is immediate, but rainfall water requires around one month to travel across the vadose zone before it reaches the groundwater table. Using graphical methods of accumulated deviations from the mean, we show that, in general, groundwater storage follows the smooth, multi-year trends of terrestrial water storage but with less short-term trends; the same is true of rainfall, for which the local trends are more pronounced. There is hysteresis-like behaviour in the variations in terrestrial water storage and in the variations of groundwater. In practical terms, this study shows that, despite the abnormal dryness of the Iberian Peninsula during the 2004–2010 drought, the depleted groundwater storage in Andalucía recovered almost to its pre-drought level by 2016. In addition, groundwater storage and terrestrial water storage show very similar trends but with a delay in the groundwater trend