The Intriguing Structure of Stripes in GRACE Geopotential Models

Geopotential models derived from Gravity Recovery and Climate Experiment (GRACE) mission measurements are significantly obscured by the presence of a systematic artifact, known as longitudinal stripes. Based on our previous work (Peidou and Pagiatakis, 2020) we provide an in-depth analysis of the latitudinal sampling characteristics of GRACE and we reveal the intriguing sampling mechanism that creates sub-Nyquist artifacts (stripes). Because the sub-Nyquist artifacts are poorly understood, we provide a simple simulation example to elucidate the mechanism of the sub-Nyquist artifact generation. Subsequently, we randomly select June 2009 daily GPS precise science orbits for GRACE-A to produce ground tracks to sample the low frequency disturbing potential (geoid) along the parallel of ϕ=10° N. The sampled geoid is then deinterlaced in space to produce a monthly data sequence whose detailed analysis shows that the sub-Nyquist artifacts (stripes) are produced from a critical sampling rate of the low degree gravitational field that is related to the ratio m/n of two mutually prime integers, where m is the number of days it takes to have a nearly repeat orbit and n is the number of complete orbits in one day. We perform extensive analyses of GRACE Level-2 data over a period of eight years to show the variability in the orbital characteristics that are directly linked to the orbit resonances (via integers m and n). It turns out that during short repeat cycle resonances the stripes are amplified. Finally, to minimize the presence of stripes in Level-2 data products, it is recommended that orbits of future missions should be designed to avoid the critical m/n ratios while appropriately monitoring and adjusting them during the mission. For completed missions, or missions that are already active, force modelling the latitudinal low frequency disturbing potential may be a viable and most preferred approach to filtering.

GROUNDWATER MONITORING USING GRACE MISSION

Since last few decades, India has met to major crises related to groundwater. Major cities, for example, Delhi, Chennai, Bengaluru etc. are facing extreme risk of water crisis. In next few decades, this may lead to a major water crisis when this non-renewable resource is exhausted. Gravity Recovery and Climate Experiment (GRACE) mission, widely used for monitoring of groundwater storage change, could be utilized to get the information of exact amount of water above or below the surface of the earth that may be used to counter act over such situation of water crisis. GRACE mission consists of two earth orbiting satellite vehicles (SVs) separated by 220 km with the objective of computing change in gravity by increasing or decreasing distance between both the SVs caused by higher or lower gravity masses. The primary objective of the presented work is to obtain the liquid water equivalent height in a selected area using GRACE mission data with GLDAS soil moisture data. The advantage of using GRACE is that it provides better accuracy (fraction of 1cm) in comparison to traditional methods, therefore, larger extent could be covered. This paper extensively discusses about GRACE application (especially groundwater monitoring), challenges with GRACE missions and about effective methods for groundwater recharge.

Earth’s Time-Variable Gravity from GRACE Follow-On K-Band Range-Rates and Pseudo-Observed Orbits

During its science phase from 2002–2017, the low-low satellite-to-satellite tracking mission Gravity Field Recovery And Climate Experiment (GRACE) provided an insight into Earth’s time-variable gravity (TVG). The unprecedented quality of gravity field solutions from GRACE sensor data improved the understanding of mass changes in Earth’s system considerably. Monthly gravity field solutions as the main products of the GRACE mission, published by several analysis centers (ACs) from Europe, USA and China, became indispensable products for quantifying terrestrial water storage, ice sheet mass balance and sea level change. The successor mission GRACE Follow-On (GRACE-FO) was launched in May 2018 and proceeds observing Earth’s TVG. The Institute of Geodesy (IfE) at Leibniz University Hannover (LUH) is one of the most recent ACs. The purpose of this article is to give a detailed insight into the gravity field recovery processing strategy applied at LUH; to compare the obtained gravity field results to the gravity field solutions of other established ACs; and to compare the GRACE-FO performance to that of the preceding GRACE mission in terms of post-fit residuals. We use the in-house-developed MATLAB-based GRACE-SIGMA software to compute unconstrained solutions based on the generalized orbit determination of 3 h arcs. K-band range-rates (KBRR) and kinematic orbits are used as (pseudo)-observations. A comparison of the obtained solutions to the results of the GRACE-FO Science Data System (SDS) and Combination Service for Time-variable Gravity Fields (COST-G) ACs, reveals a competitive quality of our solutions. While the spectral and spatial noise levels slightly differ, the signal content of the solutions is similar among all ACs. The carried out comparison of GRACE and GRACE-FO KBRR post-fit residuals highlights an improvement of the GRACE-FO K-band ranging system performance. The overall amplitude of GRACE-FO post-fit residuals is about three times smaller, compared to GRACE. GRACE-FO post-fit residuals show less systematics, compared to GRACE. Nevertheless, the power spectral density of GRACE-FO and GRACE post-fit residuals is dominated by similar spikes located at multiples of the orbital and daily frequencies. To our knowledge, the detailed origin of these spikes and their influence on the gravity field recovery quality were not addressed in any study so far and therefore deserve further attention in the future. Presented results are based on 29 monthly gravity field solutions from June 2018 until December 2020. The regularly updated LUH-GRACE-FO-2020 time series of monthly gravity field solutions can be found on the website of the International Centre for Global Earth Models (ICGEM) and in LUH’s research data repository. These operationally published products complement the time series of the already established ACs and allow for a continuous and independent assessment of mass changes in Earth’s system.

Antarctic Ice Mass Change Products from GRACE/GRACE-FO Using Tailored Sensitivity Kernels

We derived gravimetric mass change products, i.e., gridded and basin-averaged mass changes, for the Antarctic Ice Sheet (AIS) from time-variable gravity-field solutions acquired by the Gravity Recovery and Climate Experiment (GRACE) mission and its successor GRACE-FO, covering more than 18 years. For this purpose, tailored sensitivity kernels (TSKs) were generated for the application in a regional integration approach. The TSKs were inferred in a formal optimization approach minimizing the sum of both propagated mission errors and leakage errors. We accounted for mission errors by means of an empirical error covariance model, while assumptions on signal variances of potential sources of leakage were used to minimize leakage errors. To identify the optimal parameters to be used in the TSK generation, we assessed a set of TSKs by quantifying signal leakage from the processing of synthetic data and by inferring the noise level of the derived basin products. The finally selected TSKs were used to calculate mass change products from GRACE/GRACE-FO Level-2 spherical harmonic solutions covering 2002-04 to 2020-07. These products were compared to external data sets from satellite altimetry and the input–output method. For the period under investigation, the mass balance of the AIS was quantified to be −90.9±43.5 Gt a−1, corresponding to a mean sea-level rise of 0.25±0.12 mm a−1.

Evaluation of Pendulum NGGM Scenarios by Full Closed-Loop Simulation

<p>The GRACE mission (2002-2017) delivered temporal gravity field solutions of the Earth for 15 years. It's successor, GRACE follow-on (GRACE-FO) is continuing it's legacy since May 2018. The time series of monthly gravity fields revealed global mass redistribution in in the near surface layer of the Earth with unprecedented accuracy. This assessed a completely new observable in geoscience disciplines and has become a crucial data product for climate research.<br>Despite the groundbreaking success and relevance of the GRACE mission(s) for Earth observation and climate science, no further successor gravity mission is planned, yet. Summarized by the name Next Generation Gravity Mission (NGGM) concepts for future gravimetry missions have been proposed and analyzed for a while. As an outcome of these studies the so called Bender-configuration (two GRACE-like satellite pairs, one in a polar orbit and a second in an inclined orbit around 60° to 70°) is the concept currently favored by the scientific community for a candidate of the next gravity mission to be realized.</p><p><br>However, an other concept still remains interesting due to specific advantages that might contribute to future improvements of gravity missions. In order to emphasize this, we present results of a full closed loop-simulation for a different ll-SST approach, the so called pendulum. It offers a quite similar overall performance with just two satellites. For this configuration the satellites are following each other in orbits with slightly different longitudes of the ascending nodes, thus the inter-satellite measurement direction is varying between along-track and cross-track. This configuration makes an interferometric laser ranging (LRI) quite challenging on the technical level. Nevertheless, the LRI accuracy is not necessarily needed. The relevance of the pendulum configuration has also been shifted into the focus of the French MARVEL mission proposal.</p><p><br>In this contribution we analyze in detail the performance of the pendulum formation with the main parameters being the angle between along-track and cross-track component of the ranging direction at the equator, and the mean distance between the satellites. We conduct the angle variation for different mean ranges and assumed ranging accuracies. As reference, the GRACE and Bender concepts are simulated, as well. The orbit simulations are performed using a derivative of the ZARM/DLR XHPS mission simulator including high precision implementations of non-gravitational accelerations.<br>The different concepts and configurations include complete GRACE-FO like attitude control and realistic environment models. State-of-the-art instrument noise models based on GRACE/-FO are used to generate observation data for accelerometer (ACC), range dependent inter satellite ranging (KBR/LRI), kinematic orbit solution (KOS) and star camera (SCA). For the gravity recovery process we use the classical variational equation approach. As for real GRACE processing, ACC calibration parameter are estimated and KOS and KBR range-rate observations are weighted by VCE.</p>

Magnetometer data from the GRACE satellite duo

This paper describes and discusses the preprocessing and calibration of the magnetic data taken by the navigational magnetometers onboard the two GRACE satellites, with focus on the almost 10 years period from January 2008 to the end of the GRACE mission in October 2017 for which 1-Hz magnetic data are available. A calibration of the magnetic data is performed by comparing the raw magnetometer sensor readings with model magnetic vector values as provided by the CHAOS-7 geomagnetic field model for the time and position of the GRACE data. The presented approach also accounts for magnetic disturbances produced by the satellite’s magnetorquer and for temperature effects, which are parametrized by the Sun incident angle. The root-mean-squared error of the difference between the calibrated data and CHAOS-7 model values is about 10 nT, which makes the GRACE magnetometer data relevant for geophysical investigations.

Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry

Since its launch in March 2002, the Gravity Recovery And Climate Experiment (GRACE) mission has been mapping the time variations of the Earth’s gravity field with a precision of 2–3 cm in terms of geoid height at the surface resolution of 300–400 km. The unprecedented precision of this twin satellite system enables to detect tiny changes of gravity that are due to the water mass variations inside the fluid envelops of our planet. Once they are corrected from known gravitational contributions of the atmosphere and the oceans, the monthly and (bi)weekly GRACE solutions reveal the continental water storage redistributions, and mainly the dominant seasonal cycle in the largest drainage river basins such as Amazon, Congo, Mississippi. The potential differences measured between the twin GRACE satellites represent the sum of integrated surface waters (lakes and rivers), soil moisture, snow, ice and groundwater. Once they are inverted for estimating surface water mass densities, GRACE solutions are also used to establish the long-term mass balance of the ice sheets impacted by global warming, for quantifying the interannual variations of the major aquifers, as well as for surveying the hydrological signatures of intense meteorological events lasting a few days such as tropical hurricanes. This chapter describes GRACE gravity products and the different data processings used for mapping continental water storage variations, it also presents the most remarkable results concerning global continental hydrology and climate changes.

The Role of Non-tidal Atmospheric Loading in the Task of Gravity Field Estimation by Inter-Satellite Measurements

The paper reviews models of tidal and non-tidal variations of the Earth's gravitational field. Proposing an algorithm for the estimation of the Stokes coefficients based on inter-satellite measurements of low-orbit spacecrafts. By processing measurements of the GRACE mission, we obtained experimental estimates of gravity field monthly variations. The analysis of these values was carried out by calculating the change in the equivalent water height for a given area.

State-of-the-art potential of the GRACE satellite mission for solving modern hydrological problems

The paper presents main results of GRACE mission using in such fields of study as estimations of components of basins water storage and water balance, hydrological modeling. It is shown that error of GRACE data is of the order 11 mm for watersheds with area about 100 000 km2 and decreasing with increasing of basin area. This accuracy made it possible to identify long-term and seasonal water storage. It is shown, that decreasing of total water storage in the Don basin for 2002–2019 is approximately equally caused by both soil moisture and groundwater changes. At the same time, minimum of groundwater was already reached in 2010, and soil moisture in 2015. Since 2016, Don basin groundwater changes a little during the winter period that is due, probably, with increase number of thaws and thinning of the freezing layer during this period. By the data of meteorological stations for the precipitation of cold period for the European Russia the value of their systematic error was estimated, it is about 20-25%. The comparison of the values of total water storage for the river basins of the north part of European part of Russia, according GRACE data and ECOMAG runoff modeling results has shown their good coincidence (NSE =0.78 0.89). In comparison with GRACE, ECOMAG shows a smaller increase in water storage during the winter and a faster decline during spring flood period. Currently, progress in the use of GRACE in hydrology is limited by low spatial-temporal resolution of data, which, within the framework of the GRACE mission itself, will not be improved in the coming years. At the same time, the principle of GRACE operation can be applied in future to various satellite constellations.