Abstract
The Bender-type constellation has become a feasible option of the next-generation gravimetric mission (NGGM) for improving the quality of temporal gravity field solutions. In the context of Bender-type NGGM, the payload requirement is limited to approximately 20 nm/Hz1/2 at the measurement bandwidth (MBW) of 0.01–1 Hz for laser ranging instrument (LRI), and 10–11 m/s2 at 0.001–0.1 Hz for accelerometer (ACC). Low-frequency noise is also, respectively, limited to 1/f and 1/f2 for LRI and ACCs due to unavoidable electronic noise. However, due to the complex payload manufacture procedures and volatile space observation environment, in reality, LRI or ACCs noise may not be rigorously consistent with the designed noise models in frequency domain. Frequency-dependent noise in in situ observations always results in different MBW boundaries or different low-frequency features. In this study, the potential impacts of this unaccounted frequency-dependent instrument noise are analyzed via various detailed simulations, and the conclusions are summarized as follows. (1) In the instrument noise only scenarios, a similar behavior is shown between the frequency spectrum of instrument’s frequency-dependent noise in terms of amplitude spectral density and the corresponding gravity solution in terms of geoid height error. (2) The ACC MBWs seriously affect the quality of gravity solution, while the impacts of low-frequency features (e.g., 1/f3/2 and 1/f2 behavior of LRI noise, 1/f5 and 1/f6 behavior of ACC noise) are quite minor. (3) Frequency-dependent instrument noise plays less role when the background force model errors are included, and significant improvement is observed when the atmospheric- and oceanic-induced aliasing error is excluded, indicating the necessity of accurate background force models as well as proper de-aliasing strategy. (4) In the full noise contaminated scenarios, to achieve the scientific goal of Bender-type NGGM, it is feasible to shift the low MBW boundary from 0.001 to 0.004 Hz for ACC, and from 0.01 to 0.1 Hz for LRI. The results are helpful to specify the requirement of manufacturing key payloads for the Bender-type NGGM.
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Data availability
The ESM AOHIS models used in this work are publicly available from the GFZ data services (https://doi.org/10.5880/GFZ.1.3.2014.001).
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Acknowledgements
This research was funded by the National Natural Science Foundation of China (Nos. 41931074, 42074018, 42061134007, 41704012), the National Key Research and Development Program of China (Nos. 2018YFC1503503, 2018YFC1503504) and the Fundamental Research Funds for the Central Universities (No. 2019kfyXJJ). The authors would like to thank Ms. Lu Tang for her suggestive advices and numerical simulation support during revising our manuscript. The authors would like to thank Dr. Natthachet Tangdamrongsub for the kind help to improve our manuscript. We thank the AE and reviewers for their constructive suggestions, which greatly helped to improve our manuscript.
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HZ, DT and HD proposed the idea of the manuscript. HZ designed the experiments, conducted the simulation study and wrote the paper. LT designed the experiments and conducted the simulation study during revision. DT and HD contributed to design the noise model of accelerometer and laser ranging interferometer. RP contributed the design of manuscript structure and extended the noise models of key payloads. ZL and ZZ contributed the theoretical foundation and technical understanding. LT, DT, HD, RP, ZL and ZZ reviewed the final manuscript.
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Appendix A. Reliability of simulation strategy
Appendix A. Reliability of simulation strategy
To assess the reliability of our simulation strategy, several tests are performed in this section. During the simulation, only the noise model ‘Case L1’ is considered, and the background model errors, accelerometer and orbit noise are not taken into account. Firstly, the gravity field solutions are estimated by setting different arc lengths and number of iterations. As shown in Fig.
Geoid height errors per degree of gravity field solutions determined with different arc lengths (1.5, 6 or 24 h) and different number of iterations (1 or 2 iterations). During the simulation, only the noise model ‘Case L1’ is considered, and the background model errors, accelerometer and orbit noise are not taken into account
21, although using different arc lengths, the results after 2 iterations present very similar performance in terms of geoid height per degree. It demonstrates the minor impact of setting different arc lengths with 2 iterations. Meanwhile, when the arc length is 6 h, the result of the second iteration is closest to that of the first iteration. Therefore, to improve the simulation efficiency, the arc length is set to 6 h and the number of iterations is set to 2 in our study.
During processing real GRACE data, the true initial state vectors are not known. To make our simulation as close as possible to the real observation environment, we also considered errors in initial state vector. During the simulation, the noise model ‘Nominal-B’ is considered, and APP-I is applied to simulate the non-tidal atmosphere and ocean aliasing error. As shown in Fig.
Geoid height errors per degree of gravity field solutions determined with or without initial state vector errors. During the simulation, the noise model ‘Nominal-B’ is considered, and APP-I is applied to simulate the non-tidal atmosphere and ocean aliasing error
22, there are very minor differences between the solutions determined with or without initial state vector errors.
Finally, we make a comparison with Flechtner et al. (2016), who implemented a comprehensive simulation by taking into account background force model errors and frequency-dependent instrument noise of laser ranging interferometer (LRI) and microwave instrument (MWI) in the context of GRACE-type mission. During the comparison, we set the simulation environment as close as possible to Flechtner et al. (2016). During the simulation, only the observations of polar pair satellites are considered, and the noise model ‘GRACE-B’ is applied. APP-I is applied to simulate the non-tidal atmosphere and ocean aliasing error. As shown in Fig.
Equivalent water height (EWH) errors per degree of gravity field solutions derived from MWI and LRI noise models in the context of GRACE-type mission. During the simulation, only the observations of polar pair satellites are considered, and the noise model ‘GRACE-B’ is applied. APP-I is applied to simulate the non-tidal atmosphere and ocean aliasing error
23, the result in terms of EWH errors per degree is similar to Fig. 4 of Flechtner et al. (2016). It demonstrates the comparable outcome of our simulation strategy with Flechtner et al. (2016).
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Zhou, H., Tang, L., Tan, D. et al. Impacts of frequency-dependent instrument noise for next-generation gravimetric mission on determining temporal gravity field model. J Geod 97, 23 (2023). https://doi.org/10.1007/s00190-023-01716-2
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DOI: https://doi.org/10.1007/s00190-023-01716-2