Tongji-Grace02s and Tongji-Grace02k: high-precision static GRACE-only global Earth's gravity field models derived by refined data processing strategies

Abstract In order to derive high-precision static GRACE-only gravity field solutions, the following strategies were implemented in this study: (1) a refined accelerometer calibration model that treats monthly accelerometer scales as a 3-order polynomial and daily accelerometer biases as a 5-order polynomial was developed to calibrate accelerometer measurements; (2) the errors of the acceleration and attitude data were estimated together with the geopotential coefficients and accelerometer parameters on the basis of the weighted least-squares adjustments; (3) a nearly complete observation series of GRACE mission was used to decrease the condition number of normal equation; and (4) the GRACE data collected in lower orbit altitude were also included to decrease the condition number. Our results show that: (1) the refined accelerometer calibration model with much less parameters performs as well as previous methods (i.e. solving daily scales and hourly biases or estimating biases along with bias rates every two hours). However, it provides a system of more stable normal equation and less high-frequency noise in gravity field solutions; (2) high-frequency noise in the gravity field solution is reduced by modelling the errors of the acceleration and attitude data; (3) the geopotential coefficients at all degrees is greatly enhanced by using longer GRACE time series (especially the data by the end of 2010); and (4) due to lower orbit altitude, the GRACE data collected since 2014 lead to a significant improvement of the gravity field solution as the satellites are more sensitive to higher-frequency signal. Using the refined strategies, an unconstrained static solution (named Tongji-Grace02s) up to degree and order 180 was derived. For further suppressing the high-frequency noise, a regularization strategy based on the Kaula rule is applied to the degrees and orders beyond 80, leading to a regularized model Tongji-Grace02k. To validate the quality of the derived models, both Tongji-Grace02s and Tongji-Grace02k were compared to the latest GRACE-only models (i.e. GGM05S, ITU\_GRACE16, ITSG-Grace2014s and ITSG-Grace2014k) and validated using independent data (i.e. GNSS/Levelling data and DTU13 oceanic gravity data). Compared to other models, much less spatial noise in terms of global gravity anomalies with respect to the state-of-the-art model EIGEN6C4 and far higher accuracy at high degrees are achieved by Tongji-Grace02s. The same conclusions can be drawn for Tongji-Grace02k when the same analyses were applied to the regularized solutions ITSG-Grace2014k and Tongji-Grace02k. Validations with independent data confirm that Tongji-Grace02s has the least noise among the unconstrained GRACE-only models and Tongji-Grace02k is the one with the best accuracy among the regularized GRACE-only solutions. For the tests up to degree and order 180 using GNSS/Levelling data, the improvements of Tongji-Grace02s with respect to ITSG-Grace2014s reach 13\% over the Canada and 23\% in the Mexico. Even better, no less than 58\% of improvement is achieved by both Tongji-Grace02s relative to ITSG-Grace2014s and Tongji-Grace02k with respect to ITSG-Grace2014k in the validation based on DTU13 data.