Comparison of empirical noise models for GRACE Follow-On derived with the Celestial Mechanics Approach

2021 ◽  
Author(s):  
Martin Lasser ◽  
Ulrich Meyer ◽  
Daniel Arnold ◽  
Adrian Jäggi
Keyword(s):  
Gravity Field ◽  
Celestial Mechanics ◽  
Low Noise ◽  
Empirical Modelling ◽  
The Earth ◽  
Gravity Fields ◽  
Range Rate ◽  
University Of Bern ◽  
The Cost ◽  
Noise Models

<p>A key component of any model is the accurate specification of its quality. In gravity field modelling from satellite data, as it is done with the observation collected by GRACE Follow-On, usually least-squares adjustments are performed to obtain a monthly solution of the Earth’s gravity field. However,<br>the jointly estimated formal errors usually do not reflect the error level that could be expected but provides much lower error estimates. We take the Celestial Mechanics Approach (CMA), developed at the Astronomical Institute, University of Bern (AIUB), and extend it by an empirical modelling of the noise based on the post-fit residuals between the final GRACE Follow-On orbits, that are co-estimated together with the gravity field, and the   observations, expressed in position residuals to the kinematic positions and in K-band range-rate residuals. We compare and validate the solutions that employ empirical modelling with solutions that do not contain sophisticated noise modelling by examining the stochastic behaviour of the respective post-fit residuals, by investigating areas where a low noise is expected and by inspecting the mass trend estimates in certain areas of global interest. Finally, we investigate the influence of the empirically weighted solutions in a combination of monthly gravity fields based on other approaches as it is done in the COST-G framework.</p>

scholarly journals Benchmark data for verifying background model implementations in orbit and gravity field determination software

2020 ◽  
Author(s):  
Martin Lasser ◽  
Torsten Mayer-Gürr ◽  
Andreas Kvas ◽  
Igor Koch ◽  
Jean-Michel Lemoine ◽  
...  
Keyword(s):  
Gravity Field ◽  
Research Centre ◽  
Benchmark Data ◽  
University Of Technology ◽  
Gravity Fields ◽  
Gravity Field Determination ◽  
Order Of Magnitude ◽  
Correct Application ◽  
University Of Bern ◽  
The Cost

<div>In the framework of the COmbination Service of Time-variable Gravity fields (COST-G) gravity field solutions from different analysis centres are combined to provide a consolidated solution of improved quality to the user. As in many other satellite-related sciences, the correct application of background models plays a crucial role in gravity field determination. Therefore, we publish a set of data of various commonly used forces in orbit and gravity field modelling (gravity field, tides etc.) evaluated along a one day orbit arc of GRACE, together with some additional data to enable easy comparisons. The benchmark data is compiled with the GROOPS software by the Institute of Geodesy (IfG) at Graz University of Technology. It is intended to be used as a reference and provides the opportunity to test the implementation of these models at various analysis centres. In view of the COST-G GRACE (-FO) gravity field combinations, we show the outcome of such a background force field software validation for the GRACE-SIGMA software of the Leibniz University of Hannover (LUH), the GRGS GINS software, EPOS of the German Research Centre for Geosciences (GFZ) and the Bernese GNSS software from AIUB (Astronomical Institute, University of Bern). We consider differences in the force modelling for GRACE (-FO) of one order of magnitude less than the accelerometer noise to be negligible, and make an attempt to quantify and explain differences exceeding this threshold.</div>

scholarly journals Simulation of the time-variable gravity field by means of coupled geophysical models

2011 ◽  
Vol 4 (1) ◽  
pp. 27-70 ◽  
Author(s):  
Th. Gruber ◽  
J. L. Bamber ◽  
M. F. P. Bierkens ◽  
H. Dobslaw ◽  
M. Murböck ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Mass Distribution ◽  
Time Variable ◽  
Data Sets ◽  
Earth System ◽  
Time Variable Gravity ◽  
The Earth ◽  
Gravity Fields ◽  
Variable Gravity

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on "Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites". The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested via a Website.

Time-variable gravity field determination from GRACE-FO data using the Celestial Mechanics Approach

2020 ◽  
Author(s):  
Martin Lasser ◽  
Ulrich Meyer ◽  
Daniel Arnold ◽  
Adrian Jäggi
Keyword(s):  
Gravity Field ◽  
Celestial Mechanics ◽  
Noise Model ◽  
Stochastic Parameters ◽  
Gravity Field Determination ◽  
Phase Bias ◽  
Set Up ◽  
Noise Models ◽  
K Band

<p>We study gravity field determination from GRACE-FO satellite-to-satellite tracking using the inter-satellite K-band link and kinematic positions of the satellites as observations and pseudo-observations respectively. We employ 10-second kinematic positions from a precise point positioning where the undifferenced carrier phase ambiguities are fixed to integer values using observation-specific phase bias products from the CODE analysis centre.<br />We present an up-to-date GRACE-FO time series computed with the Celestial Mechanics Approach extended by empirical noise models derived from the post-fit residuals to better characterise the stochastic behaviour of both observation types. We investigate the interplay between the empirical noise model and the co-estimation of stochastic parameters set-up to absorb unmodelled signal (short term mass variations, accelerometer errors etc.).<br />We validate our results of GRACE-FO gravity field determination by analysing the residuals of combined orbits calculated using both kinematic positions and K-band data, and by analysing the quality of co-estimated gravity field solutions.</p>

scholarly journals Stochastic noise modelling of kinematic orbit positions in the Celestial Mechanics Approach

2020 ◽  
Vol 50 ◽  
pp. 101-113
Author(s):  
Martin Lasser ◽  
Ulrich Meyer ◽  
Daniel Arnold ◽  
Adrian Jäggi
Keyword(s):  
Stochastic Model ◽  
Gravity Field ◽  
Celestial Mechanics ◽  
Monthly Basis ◽  
Piecewise Constant ◽  
Kinematic Orbit ◽  
Noise Characteristics ◽  
Gravity Fields ◽  
Gravity Recovery ◽  
Gravity Field Models

Abstract. Gravity field models may be derived from kinematic orbit positions of Low Earth Orbiting satellites equipped with onboard GPS (Global Positioning System) receivers. An accurate description of the stochastic behaviour of the kinematic positions plays a key role to calculate high quality gravity field solutions. In the Celestial Mechanics Approach (CMA) kinematic positions are used as pseudo-observations to estimate orbit parameters and gravity field coefficients simultaneously. So far, a simplified stochastic model based on epoch-wise covariance information, which may be efficiently derived in the kinematic point positioning process, has been applied. We extend this model by using the fully populated covariance matrix, covering correlations over 50 min. As white noise is generally assumed for the original GPS carrier phase observations, this purely formal variance propagation cannot describe the full noise characteristics introduced by the original observations. Therefore, we sophisticate our model by deriving empirical covariances from the residuals of an orbit fit of the kinematic positions. We process GRACE (Gravity Recovery And Climate Experiment) GPS data of April 2007 to derive gravity field solutions up to degree and order 70. Two different orbit parametrisations, a purely dynamic orbit and a reduced-dynamic orbit with constrained piecewise constant accelerations, are adopted. The resulting gravity fields are solved on a monthly basis using daily orbital arcs. Extending the stochastic model from utilising epoch-wise covariance information to an empirical model, leads to a – expressed in terms of formal errors – more realistic gravity field solution.

scholarly journals Applicability of GRACE and GRACE-FO for monitoring water mass changes of the Aral Sea and the Caspian Sea

2020 ◽  
Vol 26 (2) ◽  
pp. 443-453
Author(s):  
Lorant Földváry ◽  
Victor Statov ◽  
Nizamatdin Mamutov
Keyword(s):  
Gravity Field ◽  
Caspian Sea ◽  
Large Scale ◽  
Aral Sea ◽  
Water Volume ◽  
Satellite Mission ◽  
The Caspian Sea ◽  
Gravity Fields ◽  
Range Rate ◽  
Sea Area

The GRACE gravity satellite mission has provided monthly gravity field solutions for about 15 years enabling a unique opportunity to monitor large scale mass variation processes. By the end of the GRACE, the GRACE-FO mission was launched in order to continue the time series of monthly gravity fields. The two missions are similar in most aspects apart from the improved intersatellite range rate measurements, which is performed with lasers in addition to microwaves. An obvious demand for the geoscientific applications of the monthly gravity field models is to understand the consistency of the models provided by the two missions. This study provides a case-study related consistency investigation of GRACE and GRACE-FO monthly solutions for the Aral Sea region. As the closeness of the Caspian Sea may influence the monthly mass variations of the Aral Sea, it has also been involved in the investigations. According to the results, GRACE-FO models seem to continue the mass variations of the GRACE period properly, therefore their use jointly with GRACE is suggested. Based on the justified characteristics of the gravity anomaly by water volume variations in the case of the Aral Sea, GRACE models for the period March–June 2017 are suggested to be neglected. Though the correlation between water volume and monthly gravity field variations is convincing in the case of the Aral Sea, no such a correlation for the Caspian Sea could have been detected, which suggests to be the consequence of other mass varying processes, may be related to the seismicity of the Caspian Sea area.

scholarly journals Simulation of the time-variable gravity field by means of coupled geophysical models

2011 ◽  
Vol 3 (1) ◽  
pp. 19-35 ◽  
Author(s):  
Th. Gruber ◽  
J. L. Bamber ◽  
M. F. P. Bierkens ◽  
H. Dobslaw ◽  
M. Murböck ◽  
...  
Keyword(s):  
Time Series ◽  
Gravity Field ◽  
Mass Distribution ◽  
Time Variable ◽  
Data Sets ◽  
Earth System ◽  
Time Variable Gravity ◽  
The Earth ◽  
Gravity Fields ◽  
Variable Gravity

Abstract. Time variable gravity fields, reflecting variations of mass distribution in the system Earth is one of the key parameters to understand the changing Earth. Mass variations are caused either by redistribution of mass in, on or above the Earth's surface or by geophysical processes in the Earth's interior. The first set of observations of monthly variations of the Earth gravity field was provided by the US/German GRACE satellite mission beginning in 2002. This mission is still providing valuable information to the science community. However, as GRACE has outlived its expected lifetime, the geoscience community is currently seeking successor missions in order to maintain the long time series of climate change that was begun by GRACE. Several studies on science requirements and technical feasibility have been conducted in the recent years. These studies required a realistic model of the time variable gravity field in order to perform simulation studies on sensitivity of satellites and their instrumentation. This was the primary reason for the European Space Agency (ESA) to initiate a study on ''Monitoring and Modelling individual Sources of Mass Distribution and Transport in the Earth System by Means of Satellites''. The goal of this interdisciplinary study was to create as realistic as possible simulated time variable gravity fields based on coupled geophysical models, which could be used in the simulation processes in a controlled environment. For this purpose global atmosphere, ocean, continental hydrology and ice models were used. The coupling was performed by using consistent forcing throughout the models and by including water flow between the different domains of the Earth system. In addition gravity field changes due to solid Earth processes like continuous glacial isostatic adjustment (GIA) and a sudden earthquake with co-seismic and post-seismic signals were modelled. All individual model results were combined and converted to gravity field spherical harmonic series, which is the quantity commonly used to describe the Earth's global gravity field. The result of this study is a twelve-year time-series of 6-hourly time variable gravity field spherical harmonics up to degree and order 180 corresponding to a global spatial resolution of 1 degree in latitude and longitude. In this paper, we outline the input data sets and the process of combining these data sets into a coherent model of temporal gravity field changes. The resulting time series was used in some follow-on studies and is available to anybody interested.

scholarly journals Benchmark data for verifying background model implementations in orbit and gravity field determination software

2020 ◽  
Vol 55 ◽  
pp. 1-11
Author(s):  
Martin Lasser ◽  
Ulrich Meyer ◽  
Adrian Jäggi ◽  
Torsten Mayer-Gürr ◽  
Andreas Kvas ◽  
...  
Keyword(s):  
Gravity Field ◽  
Research Centre ◽  
Data Set ◽  
Benchmark Data ◽  
University Of Technology ◽  
Gravity Field Determination ◽  
Order Of Magnitude ◽  
Correct Application ◽  
University Of Bern ◽  
The Cost

Abstract. In the framework of the COmbination Service for Time-variable Gravity fields (COST-G) gravity field solutions from different analysis centres are combined to provide a consolidated solution of improved quality and robustness to the user. As in many other satellite-related sciences, the correct application of background models plays a crucial role in gravity field determination. Therefore, we publish a set of data of various commonly used forces in orbit and gravity field modelling (Earth's gravity field, tides etc.) evaluated along a one day orbit arc of GRACE, together with auxiliary data to enable easy comparisons. The benchmark data is compiled with the GROOPS software by the Institute of Geodesy (IfG) at Graz University of Technology. It is intended to be used as a reference data set and provides the opportunity to test the implementation of these models at various institutions involved in orbit and gravity field determination from satellite tracking data. In view of the COST-G GRACE and GRACE Follow-On gravity field combinations, we document the outcome of the comparison of the background force models for the Bernese GNSS software from AIUB (Astronomical Institute, University of Bern), the EPOS software of the German Research Centre for Geosciences (GFZ), the GINS software, developed and maintained by the Groupe de Recherche de Géodésie Spatiale (GRGS), the GRACE-SIGMA software of the Leibniz University of Hannover (LUH) and the GRASP software also developed at LUH. We consider differences in the force modelling for GRACE (-FO) which are one order of magnitude smaller than the accelerometer noise of about 10−10 m s−2 to be negligible and formulate this as a benchmark for new analysis centres, which are interested to contribute to the COST-G initiative.

scholarly journals Noise and Breakdown Characterization of SPAD Detectors with Time-Gated Photon-Counting Operation

Sensors ◽  
2021 ◽  
Vol 21 (16) ◽  
pp. 5287
Author(s):  
Hiwa Mahmoudi ◽  
Michael Hofbauer ◽  
Bernhard Goll ◽  
Horst Zimmermann
Keyword(s):  
Breakdown Voltage ◽  
Single Photon ◽  
Photon Counting ◽  
Low Noise ◽  
Dark Count ◽  
Fully Integrated ◽  
Trade Offs ◽  
And Performance ◽  
Noise Models

Being ready-to-detect over a certain portion of time makes the time-gated single-photon avalanche diode (SPAD) an attractive candidate for low-noise photon-counting applications. A careful SPAD noise and performance characterization, however, is critical to avoid time-consuming experimental optimization and redesign iterations for such applications. Here, we present an extensive empirical study of the breakdown voltage, as well as the dark-count and afterpulsing noise mechanisms for a fully integrated time-gated SPAD detector in 0.35-μm CMOS based on experimental data acquired in a dark condition. An “effective” SPAD breakdown voltage is introduced to enable efficient characterization and modeling of the dark-count and afterpulsing probabilities with respect to the excess bias voltage and the gating duration time. The presented breakdown and noise models will allow for accurate modeling and optimization of SPAD-based detector designs, where the SPAD noise can impose severe trade-offs with speed and sensitivity as is shown via an example.

scholarly journals GRACETOOLS—GRACE Gravity Field Recovery Tools

Geosciences ◽  
2018 ◽  
Vol 8 (9) ◽  
pp. 350 ◽  
Author(s):  
Neda Darbeheshti ◽  
Florian Wöske ◽  
Matthias Weigelt ◽  
Christopher Mccullough ◽  
Hu Wu
Keyword(s):  
Open Source ◽  
Gravity Field ◽  
Transition Matrix ◽  
State Transition ◽  
Satellite Observations ◽  
Gravity Field Recovery ◽  
Grace Data ◽  
Range Rate ◽  
Analysis Platform ◽  
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.

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