Treatment of Noise in GRACE Gravity Field Recovery: A Comparison between Empirical Parameterization and Stochastic Modelling

Continuous efforts have been made by different GRACE data analysis centers to improve the quality of monthly gravity field solutions, where one of the key issues concerns the treatment of noise in the parameter estimation process. In the broader context, the noise is not limited to the imperfection of sensor measurements only but also includes unmodelled and/or mismodelled parts of the satellite dynamics. In this contribution, we revisit four widely used strategies to reduce the influence of noise in GRACE gravity field recovery, which are: the estimation of high-frequency (constrained) empirical accelerations (ACC for short); the estimation of K-band range-rate empirical parameters (KBR); the utilization of fully populated covariance matrix for data weighting (COV), and the time series model-based filtering technique (FILT). In their ways to deal with the noise, the ACC and KBR strategies can be grouped into the method of empirical parameterization, while the COV and FILT strategies belong to the treatment of stochastic modelling. From a theoretical aspect, we regard the ACC and COV strategies as special cases of the least-squares collocation (LSC); the ACC and KBR strategies can be directly linked by the linear perturbation theory, while the COV and FILT strategies resemble different spectral estimation methods. Furthermore, we use numerical simulations to evaluate the performances of the four strategies, which show that the ACC, COV and FILT are more effective in mitigating noise than the KBR strategy. In the spectral domain, the stochastic modelling-based strategies (COV and FILT) have the full-spectrum capability to treat noise, while empirical parameters adopted in the ACC and KBR strategies work as high-pass filters. Consequently, stochastic modelling can lead to more consistent formal error estimates than empirical parameterization, especially for high-degree spherical harmonic coefficients.